William B. Wright

QSS Group, Inc., Cleveland, Ohio

User Manual for the NASA Glenn

Ice Accretion Code LEWICE

Version 2.2.2

NASA/CR—2002-211793

August 2002
The NASA STI Program Office . . . in Profile

Since its founding, NASA has been dedicated to

the advancement of aeronautics and space

science. The NASA Scientific and Technical

Information (STI) Program Office plays a key part

in helping NASA maintain this important role.

The NASA STI Program Office is operated by

Langley Research Center, the Lead Center for

NASA’s scientific and technical information. The

NASA STI Program Office provides access to the

NASA STI Database, the largest collection of

aeronautical and space science STI in the world.

The Program Office is also NASA’s institutional

mechanism for disseminating the results of its

research and development activities. These results

are published by NASA in the NASA STI Report

Series, which includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major significant

phase of research that present the results of

NASA programs and include extensive data

or theoretical analysis. Includes compilations

of significant scientific and technical data and

information deemed to be of continuing

reference value. NASA’s counterpart of peerreviewed formal professional papers but

has less stringent limitations on manuscript

length and extent of graphic presentations.

• TECHNICAL MEMORANDUM. Scientific

and technical findings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies

that contain minimal annotation. Does not

contain extensive analysis.

• CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scientific and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by

NASA.

• SPECIAL PUBLICATION. Scientific,

technical, or historical information from

NASA programs, projects, and missions,

often concerned with subjects having

substantial public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scientific

and technical material pertinent to NASA’s

mission.

Specialized services that complement the STI

Program Office’s diverse offerings include

creating custom thesauri, building customized

data bases, organizing and publishing research

results . . . even providing videos.

For more information about the NASA STI

Program Office, see the following:

• Access the NASA STI Program Home Page

at http://www.sti.nasa.gov

• E-mail your question via the Internet to

help@sti.nasa.gov

• Fax your question to the NASA Access

Help Desk at 301–621–0134

• Telephone the NASA Access Help Desk at

301–621–0390

• Write to:

 NASA Access Help Desk

 NASA Center for AeroSpace Information

 7121 Standard Drive

 Hanover, MD 21076
William B. Wright

QSS Group, Inc., Cleveland, Ohio

User Manual for the NASA Glenn

Ice Accretion Code LEWICE

Version 2.2.2

NASA/CR—2002-211793

August 2002

National Aeronautics and

Space Administration

Glenn Research Center

Prepared under Grant NAG3–00145
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.

Available electronically at http://gltrs.grc.nasa.gov
 Summary

The baseline module of LEWICE is an ice accretion prediction code that applies a time stepping procedure to calculate the shape of an ice accretion. The potential flow field can be calculated in LEWICE using the Douglas Hess-Smith 2-D panel code (S24Y)5. In the current version,

the potential flow module can be bypassed by setting a flag in the user input file. In this mode, the

user has the option to call a grid generator and grid-based flow solver (Euler or Naviér-Stokes) or

to read in the solution file from this flow solver. For any of the methods chosen, the flow solution

is then used to calculate the trajectories of particles and the impingement points on the body6.

These calculations are performed to determine the distribution of liquid water impinging on the

body, which then serves as input to the icing thermodynamic model. The icing model, which was

first developed by Messinger7, is used to calculate the ice growth rate at each point on the surface

of the geometry. By specifying an icing time increment, the ice growth rate can be interpreted as

an ice thickness which is added to the body, resulting in the generation of new coordinates. This

procedure is repeated, beginning with the flow calculations, until the desired icing time is reached.

The thermal module used for the de-icing and anti-icing analysis is an extension of two previously separate programs. LEWICE/Thermal8 analyzed the performance of electrothermal deicers

where the user controlled heater power and cycle times. Its output included temperatures in the

deicer and the ice as well as ice shedding times and residual ice growth. ANTICE9 analyzed the

performance of a hot air anti-icing system where the user controlled mass flow rate and bleed air

temperature. Its output included temperatures and residual ice thickness distributions. Both of

these programs have been included in this release integrated into the LEWICE 2.2 structure with

expanded capabilities.

The operation of LEWICE is illustrated through the use of several examples. These examples

are representative of the types of applications expected for LEWICE. A more extensive set of

example cases are provided in a validation report on this version of LEWICE10. LEWICE has

been used to calculate a variety of ice shapes, and is considered a validated production code.

However, development continues toward improvement of the physical models. Any modifications

identified as a result of this research, or of additional experimental results, will be incorporated

into the model.

User Manual for the NASA Glenn Ice Accretion Code LEWICE

Version 2.2.2

William B. Wright

QSS Group, Inc.

Cleveland, Ohio 44135

NASA/CR—2002-211793 iii
 Table of Contents

Summary iii

Table of Contents iv

List of Tables x

List of Figures xii

Chapter 1: Introduction 1

Chapter 2: Installation Procedure 4

Chapter 3: Running LEWICE on a PC 5

3.1 LEWICE Quick Start Guide 5

3.2 PC Requirements 6

Chapter 4: Running LEWICE on Other Systems 7

4.1 Source Code Modification 7

Chapter 5: Changes From Version 2.0 8

Chapter 6: Recommended Practices 9

6.1 Panel Criteria 9

6.2 Time Step 10

6.3 DSMN (Point Spacing) 11

6.4 Number of Trajectories 12

6.5 One-Dimensional Anti-Icing 12

6.6 Droplet Distribution 13

6.7 Collection Efficiencies and Droplet Trajectories 14

6.8 Static Pressure/Altitude 15

6.9 Temperature 15

6.10 Relative Humidity 15

6.11 Printer Flags 15

6.12 Geometry Input 16

6.13 De-icer Input 17

Chapter 7: Interactive Input 23

7.1 Enter Input File Name 23

7.2 Enter File Name for Body 1 24

7.3 Confirmation of Warnings 25

7.4 Enter De-icer File Name for Body 1 26

Chapter 8: Main Input File 27

8.1 Listing Variables in a Namelist 27

8.1.1 Variable not in namelist error 27

8.1.2 Namelists Listed Out of Order or Missing Namelist 28

8.2 Line 1 29

8.3 LEW20 Namelist 29

8.3.1 ITIMFL 29

8.3.2 TSTOP 31

8.3.3 IBOD 32

8.3.4 IFLO 33

8.3.5 DSMN 35

8.3.6 NPL 37

NASA/CR—2002-211793 iv
8.3.7 RHOP 37

8.3.8 IGRID 38

8.3.9 IDEICE 39

8.3.10 ICP 41

8.3.11 IBETA 42

8.3.12 IHTC 43

8.3.13 IQEX 44

8.4 DIST Namelist 46

8.4.1 FLWC 46

8.4.2 DPD 47

8.5 ICE1 Namelist 50

8.5.1 CHORD 50

8.5.2 AOA 51

8.5.3 VINF 51

8.5.4 LWC 52

8.5.5 TINF 53

8.5.6 PINF 54

8.5.7 RH 55

8.6 LPRNT Namelist 56

8.6.1 FPRT 56

8.6.2 HPRT 57

8.6.3 BPRT 57

8.6.4 EPRT 58

8.6.5 MPRT 58

8.6.6 TPRT 58

8.6.7 IDBF 59

8.7 RDATA Namelist 60

8.7.1 ISCOLC, JSCOLC, KSCOLC, SSLOPC, SZEROC 60

8.7.2 ISCOLB, JSCOLB, KSCOLB, SSLOPB, SZEROB 62

8.7.3 ISCOLH, JSCOLH, KSCOLH, SSLOPH, SZEROH 65

8.7.4 ISCOLX, JSCOLX, KSCOLX, SSLOPX, SZEROX 67

8.8 Complete Example Case Input File 70

8.9 Extent of Data in Validation Database 72

Chapter 9: Body Geometry Input 73

9.1 Number of Points 78

9.2 Blank Lines 78

9.3 Too Few Points 78

9.4 Too Many Points 79

9.5 Body Not Closed 79

9.6 Small Point Spacing 79

9.7 Body Input Backwards 80

9.8 Large Angles Between Neighboring Segments 80

9.9 Intersecting Bodies 82

9.10 Concentric Bodies 82

9.11 Bodies Out of Order 82

Chapter 10: Optional Input Files 84

NASA/CR—2002-211793 v
10.1 De-icer Input File 84

10.1.1 De-icer Section 1 84

10.1.2 De-icer Section 2 95

10.1.3 De-icer Section 3 103

10.1.4 De-icer Section 4 107

10.1.5 De-icer Section 5 130

10.1.6 Complete example for de-icer input file 138

10.2 Hot Air Heat Transfer Coefficient Input File (HI.INP) 144

10.3 Hot Air Heat Flux Input File (QAIN.INP) 146

10.4 3D Streamline Input file (STREAM.INP) 147

10.5 Grid Input Files (XY.PLT and Q.PLT) 148

10.5.1 Grid read statements (XY.PLT) 148

10.5.2 Flow solution read statements (Q.PLT) 148

10.6 Pressure Coefficient Input File (RFLOW.INP) 149

10.7 Collection Efficiency Input File (RBETA.INP) 150

10.8 External Heat Transfer Coefficient Input File (RHTC.INP) 151

10.9 External Heat Flux Input File (QEXTIN.INP) 151

Chapter 11: Output Files 153

11.1 BETA.DAT 153

11.2 DENS.DAT 154

11.3 DYICE.DAT 154

11.4 FINAL1.DAT 154

11.5 FINAL2.DAT, FINAL3.DAT, FINAL4.DAT, FINAL5.DAT 155

11.6 FIXED.DAT 155

11.7 FLOW.DAT 155

11.8 FRACT.DAT 156

11.9 HTC.DAT 156

11.10 ICE1.DAT 156

11.11 ICE2.DAT, ICE3.DAT, ICE4.DAT, ICE5.DAT 157

11.12 IMP.DAT 157

11.13 JUNK.DAT 158

11.14 LIMIT.DAT 158

11.15 MASS.DAT 158

11.16 MISC.DAT 159

11.17 PRES.DAT 159

11.18 QENER.DAT 159

11.19 TEMP.DAT 160

11.20 THICK.DAT 160

11.21 TRAJ1.DAT 160

11.22 TRAJ2.DAT, TRAJ3.DAT, TRAJ4.DAT, TRAJ5.DAT 161

11.23 XKINIT.DAT 161

11.24 XKINIT2.DAT 161

Chapter 12: Additional Output Files 162

12.1 NOICE.DAT 162

12.2 CTEMP.DAT 162

12.3 GEOMETRY.DAT 163

NASA/CR—2002-211793 vi
12.4 FORCE.DAT 163

12.5 FORCE2.DAT 163

12.6 QOPT.DAT 163

12.7 DUMMY.INP 164

12.8 TEMPS1.DAT, TEMPS2.DAT, TEMPS3.DAT, TEMPS4.DAT, 

TEMPS5.DAT, TEMPS6.DAT, TEMPS7.DAT 164

12.9 FORT.54 166

12.10 FORT.80, FORT.81, etc. 166

Chapter 13: Utility Programs 167

13.1 Program THICK 167

13.1.1 Interactive Input for Program THICK 167

13.1.2 File Format for Clean Geometry and Iced Geometry 169

13.1.3 THICK output files 170

13.1.4 THICK Judgment Errors 174

13.2 Program EXPAND 177

13.2.1 Interactive Input for Program EXPAND 178

13.2.2 File Format for Input and Output Geometries 179

13.3 Program CONVERT 179

13.3.1 Interactive Input for Program CONVERT 180

13.3.2 Format for the LEWICE 1.6 Input File 180

13.3.3 Warning Message for CONVERT 181

13.4 Program TOBINARY 181

13.5 Program TOASCII 182

13.6 Program ANTICON 183

13.7 Program ANTICON2 183

13.8 Program REDUCE 183

Chapter 14: Runtime Errors 184

14.1 Flow Solver Errors 184

14.2 Errors when Using Grid Solutions 186

14.3 Trajectory Errors 187

14.4 Energy Balance Errors 189

14.5 Ice Growth Errors 190

14.6 De-icer Routine Errors 193

14.6.1 Other de-icer routine messages 196

Chapter 15: Example Cases 198

15.1 Case 1: Run 072501 from Validation Report 198

15.2 Case 2: Run 072504 from Validation Report 202

15.3 Case 3: Cylinder Benchmark Case 206

15.4 Case 4: Langmuir ‘D’ distribution 211

15.5 Case 5: Exceedence condition 215

15.6 Case 6: Exceedence condition w/Langmuir ‘D’ distribution 220

15.7 Case 7: Run 072504 without automated time step and fewer time steps 225

15.8 Case 8: Run 072504 with Larger Point Spacing 229

15.9 Case 9: First benchmark conditions with an evaporative hot air anti-icer. 233

15.10 Case 10: First benchmark condition with a running wet electrothermal anti-icer. 240

15.11 Case 11: Three body example 247

NASA/CR—2002-211793 vii
15.12 Case 12: Grid input 254

15.12.1 Grid Input Problems 258

15.12.2 LEWICE Errors Associated with Grid Input Problems 260

15.13 Case 13: Example Using Detailed Thermal Module 260

15.14 Case 14: Laminar Example Using Detailed Thermal Module 275

15.15 Case 15: Running Wet Example Using Detailed Thermal Module 287

15.16 Case 16: Evaporative Example Using Detailed Thermal Module 300

15.17 Case 17: Hot Air Evaporative Example Using Detailed Thermal Module 313

15.18 Case 18: Hot Air Example Interfaced with LEWICE3D 316

15.18.1 Procedure for 2.5D Anti-Icing and De-Icing Analysis 328

Chapter 16: User Tips and Notes 332

16.1 Old Input Files 332

16.2 Input File Errors 332

16.3 Porting ASCII Files 333

16.4 PC Application 333

16.5 Listing Variables in a Namelist 334

16.6 Multiple Bodies / Multi-Element Airfoils 334

16.7 Grid-Based Flow Solutions 335

16.8 Chord Length 335

16.9 Multiple Stagnation Points 335

16.10 Flow Module Limitation 336

16.11 Ice Density 336

16.12 Icing Limit 336

Chapter 17: Procedure for Acquiring LEWICE or other NASA Icing Software 337

17.1 Current Address for Icing Software Requests 337

Chapter 18: Sample Software Request Letter 338

Chapter 19: Technical Support 339

References 340

Appendix A Functional Requirements for LEWICE version 2.2 342

Section 1 Geometry Smoothing 343

Section 2 Point Generation 344

Section 3 Ice Addition 345

Section 4 Trajectory Integration 346

Section 5 Droplet Breakup * 349

Section 6 Droplet Splashing * 350

Section 7 Impingement Limits 351

Section 8 Collection Efficiency 352

Section 9 Other Droplet Trajectory Requirements 353

Section 10 Potential Flow 355

Section 11 Grid-based Flow 357

Section 12 Compressibility Correction 358

Section 13 Stagnation Point 361

Section 14 Roughness Height 362

Section 15 Heat Transfer Coefficient 363

Section 16 Energy Balance Equation 367

Section 17 Mass Balance Equation 372

NASA/CR—2002-211793 viii
Section 18 One Dimensional Anti-Icing 375

Section 19 Effective Heat Transfer Coefficient 378

Section 20 Two Dimensional De-icing/Anti-Icing 380

Section 21 Error Checking 384

References for Appendix A 392

NASA/CR—2002-211793 ix
 List of Tables

Table 1: Example LEW20 Namelist 46

Table 2: Example of bad input for FLWC 47

Table 3: Example of correct input for FLWC 47

Table 4: Example DIST Namelist 50

Table 5: Example ICE1 Namelist 56

Table 6: Example LPRNT Namelist 59

Table 7: Example input for RDATA namelist 69

Table 8: Example Test Input File 70

Table 9: Example Body Geometry (NACA 23014) 73

Table 10: First section of data file with comments 85

Table 11: Sample data for each layer 88

Table 12: Sample data for each layer with comments 88

Table 13: Sample data for each section with comments 92

Table 14: Example data for first section of de-icer input. 94

Table 15: Example data line 97

Table 16: Complete input data for de-icer section 2 101

Table 17: Complete input data for de-icer section 2 using temperature controlled heaters 102

Table 18: Example input for boundary condition data 106

Table 19: Sample input line for hot air anti-icer 108

Table 20: Sample input for anti-icing flags 111

Table 21: Example input for the third line of the fourth de-icer input section. 118

Table 22: Example input for 1D anti-icing approximation (IDEICE = 1) 120

Table 23: Example input for rotating body information. 121

Table 24: Example input for time step data input line 124

Table 25: Example data for spray time data input line 125

Table 26: Example input for hot air data file characteristics 128

Table 27: Example input for wall heat flux data file characteristics 128

Table 28: Example input for 3D streamline data file characteristics 129

Table 29: Complete input example for fourth data section 129

Table 30: Example input for PLOT3D style output 132

Table 31: Example input for temperature output flags 136

Table 32: Example of complete de-icer input file 138

Table 33: Example of Data Format in Output Files 153

Table 34: Excerpt of Script Commands 172

Table 35: Main Input File for Example Case 1 199

Table 36: Main Input File for Example Case 2 203

Table 37: Main Input File for Example Case 3 207

Table 38: Main Input File for Example Case 4 212

Table 39: Main Input File for Example Case 5 216

Table 40: Main Input File for Example Case 6 221

Table 41: Main Input File for Example Case 7 226

Table 42: Main Input File for Example Case 8 230

Table 43: Main Input File for Example Case 9 234

Table 44: De-ice input file for Example Case 9 235

NASA/CR—2002-211793 x
Table 45: Main Input File for Example Case 10 241

Table 46: De-ice Input File for Example Case 10 242

Table 47: Main Input File for Example Case 11 248

Table 48: Main Input File for Example Case 12 255

Table 49: Main Input File for Example Case 13 262

Table 50: De-ice Input File for Example Case 13 263

Table 51: Main Input File for Example Case 14 276

Table 52: De-ice Input File for Example Case 14 277

Table 53: Main Input File for Example Case 15 288

Table 54: De-ice Input File for Example Case 15 289

Table 55: Main Input File for Example Case 16 301

Table 56: De-ice Input File for Example Case 16 302

Table 57: Main Input File for Example Case 18-1 317

Table 58: De-ice Input File for Example Case 18-1 318

NASA/CR—2002-211793 xi
 List of Figures

Figure 1: Test Conditions in Database Used for Software Validation 49

Figure 2: Example of a 45 degree panel angle 81

Figure 3: Example of a 135 degree panel angle 81

Figure 4: Grid block in the computational domain (left) and the physical domain (right) 85

Figure 5: Additional thickness case 91

Figure 6: Example of heater cycle types 98

Figure 7: Temperature location for temperature controlled heaters 99

Figure 8: Boundaries on Sample Geometry 103

Figure 9: Boundaries on Computational Geometry 103

Figure 10: First hot air model 107

Figure 11: Potential IOTYPE = 1 (thermocouple) locations in a grid block 134

Figure 12: Representation of 3D streamline data 147

Figure 13: Diagram of temperature output for IOTYPE = 4 and IOTYPE = 5 output 166

Figure 14: Horn Angle Definition for THICK 171

Figure 15: Ice Shape Misalignment 174

Figure 16: Shifted Ice Shape Plot 175

Figure 17: Expanded View of Airfoil Misalignment 176

Figure 18: THICK Horn Angle Problem 177

Figure 19: Ice Shape for Example Case 1 200

Figure 20: Ice Thickness for Example Case 1 200

Figure 21: Heat Transfer Coefficient for Example Case 1 201

Figure 22: Pressure Coefficient for Example Case 1 201

Figure 23: Collection Efficiency for Example Case 1 202

Figure 24: Ice Shape for Example Case 2 204

Figure 25: Ice Thickness for Example Case 2 204

Figure 26: Heat Transfer Coefficient for Example Case 2 205

Figure 27: Pressure Coefficient for Example Case 2 205

Figure 28: Collection Efficiency for Example Case 2 206

Figure 29: Ice Shape for Example Case 3 208

Figure 30: Ice Thickness for Example Case 3 209

Figure 31: Heat Transfer Coefficient for Example Case 3 209

Figure 32: Pressure Coefficient for Example Case 3 210

Figure 33: Collection Efficiency for Example Case 3 210

Figure 34: Collection Efficiency as a Function of Wrap Distance for Example Case 3 211

Figure 35: Ice Shape for Example Case 4 213

Figure 36: Ice Thickness for Example Case 4 213

Figure 37: Heat Transfer Coefficient for Example Case 4 214

Figure 38: Pressure Coefficient for Example Case 4 214

Figure 39: Collection Efficiency for Example Case 4 215

Figure 40: Ice Shape for Example Case 5 217

Figure 41: Ice Thickness for Example Case 5 218

Figure 42: Heat Transfer Coefficient for Example Case 5 218

Figure 43: Flow Solution for Example Case 5 219

Figure 44: Collection Efficiency for Example Case 5 219

NASA/CR—2002-211793 xii
Figure 45: Ice Shape for Example Case 6 222

Figure 46: Ice Thickness for Example Case 6 222

Figure 47: Comparison of Ice Shapes for Monodispersed and Langmuir ‘D’ Cases 223

Figure 48: Comparison of Ice Thicknesses for Monodispersed and Langmuir ‘D’ Cases 223

Figure 49: Heat Transfer Coefficient for Example Case 6 224

Figure 50: Pressure Coefficient for Example Case 6 224

Figure 51: Collection Efficiency for Example Case 6 225

Figure 52: Ice Shape for Example Case 7 227

Figure 53: Ice Thickness for Example Case 7 227

Figure 54: Heat Transfer Coefficient for Example Case 7 228

Figure 55: Pressure Coefficient for Example Case 7 228

Figure 56: Collection Efficiency for Example Case 7 229

Figure 57: Ice Shape for Example Case 8 231

Figure 58: Ice Thickness for Example Case 8 231

Figure 59: Heat Transfer Coefficient for Example Case 8 232

Figure 60: Pressure Coefficient for Example Case 8 232

Figure 61: Collection Efficiency for Example Case 8 233

Figure 62: Heat Requirement for the Evaporative Hot Air System in Example Case 9 238

Figure 63: Surface Temperature for the Evaporative Hot Air System in Example Case 9 239

Figure 64: Hot Air Temperature for the Evaporative Hot Air System in Example Case 9 239

Figure 65: Effective Heat Transfer in Example Case 9 240

Figure 66: Heat Requirement for the Running Wet Thermal De-icer in Example Case 10 245

Figure 67: Heater Temperature for the Running Wet Thermal De-icer in Example Case 10 246

Figure 68: Effective Heat Transfer Coefficient in Example Case 10 246

Figure 69: Ice Shape on Slat and Main Elements for Example Case 11 249

Figure 70: Ice Shape on Flap for Example Case 11 249

Figure 71: Ice Thickness on Slat for Example Case 11 250

Figure 72: Ice Thickness on Main Element for Example Case 11 250

Figure 73: Ice Thickness on Flap for Example Case 11 251

Figure 74: Slat Heat Transfer Coefficient for Example Case 11 251

Figure 75: Main Heat Transfer Coefficient for Example Case 11 252

Figure 76: Flap Heat Transfer Coefficient for Example Case 11 252

Figure 77: Pressure Coefficient for Example Case 11 253

Figure 78: Collection Efficiency for Example Case 11 253

Figure 79: Ice Shape for Example Case 12 256

Figure 80: Ice Thickness for Example Case 12 256

Figure 81: Heat Transfer Coefficient for Example Case 12 257

Figure 82: Pressure Coefficient for Example Case 12 257

Figure 83: Collection Efficiency for Example Case 12 258

Figure 84: Schematic of Heaters for Example Case13 269

Figure 85: Heater Power for Example Case 13 269

Figure 86: Heat Transfer Coefficient for Example Case 13 270

Figure 87: Pressure Coefficient for Example Case 13 270

Figure 88: Collection Efficiency for Example Case 13 271

Figure 89: Heater A Temperature for Example Case 13 271

Figure 90: Heater B Temperature for Example Case 13 272

NASA/CR—2002-211793 xiii
Figure 91: Heater C Temperature for Example Case 13 272

Figure 92: Heater D Temperature for Example Case 13 273

Figure 93: Heater E Temperature for Example Case 13 273

Figure 94: Heater F Temperature for Example Case 13 274

Figure 95: Heater G Temperature for Example Case 13 274

Figure 96: Heat Transfer Coefficient for Example Case 14 282

Figure 97: Pressure Coefficient for Example Case 14 283

Figure 98: Collection Efficiency for Example Case 14 283

Figure 99: Heater A Temperature for Example Case 14 284

Figure 100: Heater B Temperature for Example Case 14 284

Figure 101: Heater C Temperature for Example Case 14 285

Figure 102: Heater D Temperature for Example Case 14 285

Figure 103: Heater E Temperature for Example Case 14 286

Figure 104: Heater F Temperature for Example Case 14 286

Figure 105: Heater G Temperature for Example Case 14 287

Figure 106: Heat Transfer Coefficient for Example Case 15 295

Figure 107: Pressure Coefficient for Example Case 15 295

Figure 108: Collection Efficiency for Example Case 15 296

Figure 109: Heater A Temperature for Example Case 15 296

Figure 110: Heater B Temperature for Example Case 15 297

Figure 111: Heater C Temperature for Example Case 15 297

Figure 112: Heater D Temperature for Example Case 15 298

Figure 113: Heater E Temperature for Example Case 15 298

Figure 114: Heater F Temperature for Example Case 15 299

Figure 115: Heater G Temperature for Example Case 15 299

Figure 116: Comparison of One-Dimensional Assumption to 2D Result 300

Figure 117: Heat Transfer Coefficient for Example Case 16 308

Figure 118: Pressure Coefficient for Example Case 16 308

Figure 119: Collection Efficiency for Example Case 16 309

Figure 120: Heater A Temperature for Example Case 16 309

Figure 121: Heater B Temperature for Example Case 16 310

Figure 122: Heater C Temperature for Example Case 16 310

Figure 123: Heater D Temperature for Example Case 16 311

Figure 124: Heater E Temperature for Example Case 16 311

Figure 125: Heater F Temperature for Example Case 16 312

Figure 126: Heater G Temperature for Example Case 16 312

Figure 127: Comparison of 2D Anti-Icing Results to 1D Anti-Icing Results 313

Figure 128: Jet Locations on Bleed Air Model 314

Figure 129: Internal Heat Transfer Coefficients for Bleed Air Case 315

Figure 130: Surface Temperature Distribution for Bleed Air Case 315

Figure 131: Engine Inlet Cross-Section for Example Case 18-1 323

Figure 132: Internal Heat Transfer Coefficient for Example Case 18-1 324

Figure 133: Surface Temperature Distribution for Example Case 18-1 324

Figure 134: Ice Shape for Example Case 18-1 325

Figure 135: Ice Thickness for Example Case 18-1 325

Figure 136: Heat Transfer Coefficient for Example Case 18-1 326

NASA/CR—2002-211793 xiv
Figure 137: Pressure Coefficients for Example Case 18-1 326

Figure 138: Collection Efficiency for Example Case 18-1 327

Figure 139: 3D Engine Inlet (Half-model) Surface Grid (Ice is Shaded) 328

NASA/CR—2002-211793 xv
Chapter 1: Introduction

The evaluation of both commercial and military aircraft systems in icing conditions continues

to be important during both design and certification. These systems can be evaluated in flight in

natural icing, in a simulated cloud produced by a lead aircraft, and in ground test facilities

equipped with a droplet spray system. Icing testing is relatively expensive, and each test technique, i.e., flight or ground testing, has operational considerations which limit the range of icing

conditions that can be evaluated. As a result, it benefits the aircraft or flight system manufacturer

to be able to analytically predict the performance of the system for a range of icing conditions.

The first step in the prediction of the performance characteristics is the determination of the

location, size, and shape of the ice that will form on the surface of interest. Analytical modeling of

the ice accretion process allows the evaluation of a wide range of proposed test conditions in

order to identify those that will be most critical to the flight system. This can substantially reduce

the amount of test time required to adequately evaluate a system and increase the quality and confidence level of the final evaluation. The analytically predicted ice accretion could also serve as

the input to an advanced aerodynamic or ice protection software to allow more complete evaluation in the design phases of the aircraft. 

The computer software LEWICE contains an analytical ice accretion model that evaluates the

thermodynamics of the freezing process that occurs when supercooled droplets impinge on a

body. The atmospheric parameters of temperature, pressure, and velocity, and the meteorological

parameters of liquid water content (LWC), droplet diameter, and relative humidity are specified

and used to determine the shape of the ice accretion. The software consists of four major modules.

They are 1) the flow field calculation, 2) the particle trajectory and impingement calculation, 3)

the thermodynamic and ice growth calculation, and 4) the modification of the current geometry by

adding the ice growth to it.

LEWICE applies a time-stepping procedure to “grow” the ice accretion. Initially, the flow

field and droplet impingement characteristics are determined for the clean geometry. The ice

growth rate on each segment defining the surface is then determined by applying the thermodynamic model. When a time increment is specified, this growth rate can be interpreted as an ice

NASA/CR—2002-211793 1
thickness and the body coordinates are adjusted to account for the accreted ice. This procedure is

repeated, beginning with the calculation of the flow field about the iced geometry, and continued

until the desired icing time has been reached.

Ice accretion shapes for cylinders and several single-element and multi-element airfoils have

been calculated using this software. The calculated results have been compared to experimental

ice accretion shapes obtained both in flight and in the Icing Research Tunnel at NASA Glenn

Research Center. The results of this comparison with the experimental database is described in a

recent contractor report3.

The thermal module of LEWICE 2.2 can model any number of heaters, any heater chordwise

length, and any heater gap desired. The heaters may be fired in unison, or they may be cycled with

periods independent of each other. The heater intensity may also be varied. In addition, the user

may specify any number of layers and thicknesses depthwise into the airfoil. Thus, the new addition has maximum flexibility in modeling virtually any electrothermal de-icer installed into any

airfoil. It can also model a bleed air anti-icing system where the user can specify the heat flux (or

heat transfer coefficient) from the bleed air or the user can set an “optimal” operating temperature

and have the program iteratively solve for the required heat flux

The new module has several enhancements over previous de-icing and anti-icing models.

These features include heaters (or bleed air supply) which are temperature-controlled, heaters

with a variable (temperature-dependant) resistance, improved stability as well as improved ice

shedding and runback freezing. 

As mentioned in the previous paragraph, the model simulates both shedding and runback.

With the runback capability, it can simulate the anti-icing mode of heater performance, as well as

detect icing downstream of the heaters due to runback over unprotected portions of the geometry.

The shedding model allows for the ice to be shed as a whole, by control volume or by heater section.

This version of LEWICE can be run in two modes. In the first mode, all heat transfer is considered to be caused by conduction, but no heaters are firing. This is equivalent to the LEWICE

NASA/CR—2002-211793 2
2.0 model. In the second mode, conduction heat transfer where the heaters are engaged is modeled, with subsequent ice shedding. When run in the first mode, there is virtually identical agreement with LEWICE 2.0 in the prediction of accreted ice shapes. Output from the software has

been expanded to include support for PLOT3D, TECPLOT and selected temperature distributions

either depthwise at a specific chord location or chordwise at a specific depth. 

The purpose of the current research has been to modularize the program so that the user could

utilize a wide variety of options for modeling the complete icing problem. For example, LEWICE

2.0 has an option where the user can bypass the potential flow module and read in results from a

Naviér-Stokes program. The user simply selects the grid option in the current input file and a

grid-based flow solver of the users choice can be used with any of the other modules of LEWICE.

For the first time, a Naviér-Stokes program can be used with the thermal de-icing module or with

the hot air anti-icing module. For both of these modules, features such as multiple bodies (such as

multi-element airfoils) and multi-time step flow solutions can also be utilized. This streamlined

approach also means that separate routines no longer need to be maintained for common features

such as ice shedding, water runback and freezing (including rivulet formation) which can accelerate future module development. 

NASA/CR—2002-211793 3
Chapter 2: Installation Procedure

The PC executable for LEWICE is distributed on a CD-ROM compatible with PC, Macintosh

and Unix systems. The PC executable will run only on the PC systems or under PC emulation

with the other operating systems. Simply copy the executable and input files to a suitable directory onto a hard disk to install LEWICE. LEWICE cannot be run from the CD. Users who wish to

run LEWICE on other systems should consult Chapter 4. 

NASA/CR—2002-211793 4
Chapter 3: Running LEWICE on a PC

The PC executable provided on the disk can be run by double-clicking the icon in Windows

3.1 or higher. It can also be run by typing “lewice” at a DOS prompt if the user is in the directory

where LEWICE resides or if the proper path has been set in the AUTOEXEC.BAT file. However,

it must be run from the user’s hard disk and not from the CD-ROM. When run from Windows, a

console shell opens for interactive input and output. This console shell disappears when the run is

finished. For this reason, it is highly recommended that the user run the PC executable from a

DOS Shell instead of from the console shell.

3.1 LEWICE Quick Start Guide

This section is intended for users unfamiliar with LEWICE and/or DOS Shell commands. 

The commands below (indented bold lines) should be typed at the C:\ prompt in a DOS Shell

window on a Windows machine. Alternatively, the user can use the Windows interface for any of

the commands shown.

1) Create a directory on the hard drive to store output

md lewice

2) Insert the LEWICE CD-ROM and copy all files from this disk to the lewice directory as

described in the Installation Procedure.

3) Inside the lewice directory, make additional directories for each run 

md case1

4) Run LEWICE

lewice <return>

- program will prompt for input file name. Enter the following:

case1.inp <return>

- after printing a copyright notice, the program will prompt for a geometry file name. Enter the

following:

NASA/CR—2002-211793 5
case1.xyd <return>

- if any warning messages appear, type 

Y <return> 

to continue the simulation.

5) copy output data files to the proper directory

copy *.dat case1

6) repeat steps 3-5 for each case to be run

3.2 PC Requirements

This program was run successfully on a Compaq Presario® with a 133MHz Pentium® CPU

and 24MB of RAM running Windows95®. This machine took 9 minutes to run the first example

case provided. Lower end systems were not available for testing. It is believed that the program

should run on at least a 486 and Windows 3.1, although this has not been verified. LEWICE 2.2

was developed on a Silicon Graphics Indigo2 running IRIX 6.2. Various changes were made in

this software to make conversion to personal computers much easier. The validation report1

shows comparisons of ice shape predictions on a personal computer and a Silicon Graphics workstation. The ice shape predictions on various PCs using the executable provided on the distribution disk were identical to the results shown in the validation report. 

Most of the output data is provided in columns of text, with a text header identifying the variable. This file format can be easily imported into any spreadsheet package for plotting. The program takes about 650 KB of hard disk space for the executable, and several megabytes for output

files. The second example case shows the program’s potential to produce large output files. The

output files for this case take only 3.3 MB of disk space. However, several of the larger output

files were not printed in this example and output was further reduced using the print flags in the

main input file. If this same case were to be run with all of the outputs activated, the output for

this case would occupy over 45 MB of disk space.

NASA/CR—2002-211793 6
Chapter 4: Running LEWICE on Other Systems

Source code is not included in the general release of LEWICE. The software has been successfully compiled and tested on Sun and SGI workstations. The executables for those systems

are included on the distribution CD-ROM. The SGI executable was created on the SGI under

IRIX 6.2. Test cases were run on a SGI Indigo2 and a SGI Power Challenge. The Sun executable

was created under Solaris 2.6. Test cases were run on a Sun Enterprise 3500 system. Users who

are interested in running LEWICE on these systems or other platforms should contact the Icing

Branch office for the source code and the documents describing the benchmark procedure for different platforms. Due to a small variability in output for different compilers and platforms, it is

important for users to revalidate LEWICE using the benchmark tests if the code is recompiled.

The complete set of benchmark tests is included on the distribution CD-ROM. The run procedure

described in Chapter 3 can also be used on unix machines, with the exception that DOS commands should be replaced with unix commands.

4.1 Source Code Modification

Developers who wish to obtain source code for LEWICE 2.2 for modification should also

contact the Icing Branch office for access to source code. If the code is modified in any way and

not simply recompiled, the developer will need to repeat the complete set of validation tests1 in

order to establish the validity of the modified code. Several different combinations of compiler

flags were used during testing to establish software sensitivity to those flags. It was discovered

that the variation was very minimal to non-existent, depending upon the flag set. For the PC executable, the default flags were used in Digital’s Visual Fortran 5.0.A with the configuration set to

“Win32 release”. For the Sun and SGI executables, the only flag used was the optimization flag

O2. The precise procedure used to compile the codes and test the executable will be supplied with

any source code distribution.

NASA/CR—2002-211793 7
Chapter 5: Changes From Version 2.0

LEWICE 2.2 differs from LEWICE 2.0 in the procedure for analyzing hot air or electrothermal ice removal (de-icing) or prevention (anti-icing) systems. Other aspects of the software have

seen minor changes and the ice shapes generated using LEWICE 2.2 should be very similar if not

the same as those generated using LEWICE 2.0. However, enough discrepancies exist such that a

complete revalidation is warranted to consider this version validated. As an interim release, that

validation has not yet been performed. Section 7.4 will describe the additional interactive input

needed for the de-icing/anti-icing option. Section 8.3.1 will describe a change made to the automatic time step criteria. Section 8.3.9 will describe an additional setting for the input flag IDEICE. Sections 8.3.10 through 8.3.13 describe additional input flags added since the last release.

Section 8.7 will describe the addition of a new namelist which can be read. Section 10.1 will

cover the inputs for the revised de-icing function. Sections 10.5 through 10.11 describe additional

input files which can be read. Chapter 12 will cover the additional output files for this option. Section 14.6 will summarize the runtime errors for the de-icer input. Sections 15.13 to 15.18 will

describe de-icing and anti-icing example cases. Chapter 16 will summarize the user tips for running de-icing and anti-icing cases.

Note: At a minimum, the user must add the following two lines to the end of the main input

file for existing LEWICE 2.0 input files for them to work with LEWICE 2.2:

&RDATA

&END

See Section 8.7 for details of the new namelist.

NASA/CR—2002-211793 8
Chapter 6: Recommended Practices

This section will list a set of recommended practices for running LEWICE 2.2. These recommendations are provided at various locations in this manual. They are summarized here for convenient reference by the user. Each paragraph may contain a recommended practice which is not

directly related to other notes in that section. This section differs from Chapter 16 which list user

notes in that this section contains those notes considered most important for accurate use of the

software.

6.1 Panel Criteria

The key to obtaining good ice shape prediction for glaze ice is to run multiple time step cases

where each time step produces a flow solution which is acceptable. Poor flow solutions in potential flow are characterized by ‘noise’ in the CP vs. S curve which is caused by the rough surface.

Spikes in this solution will result in irregular ice shape formations. In LEWICE 2.2, this is highly

automated by the software, but the user has some control to attempt to obtain better flow solutions. 

The number of panels and control volumes used are virtually independent of the number of

points contained in the geometry input file.

The input parameter DSMN will control the number of control volumes and panels used. For

single body simulations, very few problems have been encountered. The effect of DSMN on ice

shape has been documented in the validation report1. However, multiple bodies sometimes have

problems when running multiple time step simulations. Common problems are for the user to

specify a value for DSMN which is too small or too large. Values in the range 2*10-4 ≤ DSMN ≤

8*10-4 are recommended. The lower limit reflects the current limits of the array sizes in the program and is not a reflection of the accuracy for low DSMN values. For DSMN values of 8*10-4 or

higher, quantitative differences occur due the coarse spacing provided. An exception was found

for cylinders which have a very large surface area compared to similarly sized airfoils. Larger

DSMN values are necessary for this geometry due the limitations on array sizes. Please check the

geometry output file(s) to determine how many panels the program is using for each body.

NASA/CR—2002-211793 9
It is recommended that the user supply approximately 100 or more points for each body input.

The modification of the initial input points can sometimes have the adverse side effect of

slightly changing the airfoil shape, especially for a sparse initial geometry. The initial geometry

written to the geometry output file(s) should be examined very carefully for anomalies regarding

this side effect.

6.2 Time Step

As stated before, one of the keys to good ice shape prediction in glaze ice is the use of multiple time steps. The original LEWICE manual stated that the maximum amount of ice accreted in

any time step should be no greater than 1% of the chord. This is still a reasonable value. The computation used is 

(1)

where N is the number of time steps, LWC is the liquid water content, V is the velocity (airspeed), and ρice is the ice density. The user should insure that they are using consistent units for

this calculation.

This will give the user a rough idea of the time step size needed for an accurate simulation.

Even for long runs (for example 45 min. hold conditions) small time steps can be used. 

The variability of LEWICE results for various time steps and point spacings is discussed in

the section on Numerical Variability in the report on the validation tests. Due to this variability,

LEWICE 2.2 selects automatic time stepping to be on as its default setting. 

For very small (< 6 inch) chord geometries such as cylinders, the number of time steps recommended by the software may be considered prohibitive by the user. It may be possible (and even

necessary) to decrease the number of time steps for these cases. It should be noted though that the

smallest chord airfoil in the validation database is a 14 inch chord NACA0015 for which 8 ice

shapes have been digitized.

N ( ) LWC ( ) V ( ) Time

( ) chord ρice ( )( ) 0.01 = --------------------------------------------------

NASA/CR—2002-211793 10
Time steps smaller than 30 seconds are discouraged as they can cause undesirable numerical

effects. The software should not choose a time step this small unless the chord length is very

small as well.

The procedure for the validation report set the number of time steps equal to the number of

minutes of icing or 15, whichever was lower. This procedure is highly recommended to maintain

consistency with the validation report results. The automated time step procedure will use this

methodology by default.

6.3 DSMN (Point Spacing)

The number of panels and control volumes used are virtually independent of the number of

points contained in the geometry input file.

In version 2.2 the number of control volumes will be much greater than the number of panels.

The ratio of control volumes to panels is approximately 50 to 1. The default value for DSMN is

4*10-4.

There is one value of DSMN for each body. If only one body exists, only the first value input

is used by the software. For multi-body simulations, it is to the user’s advantage to use smaller

DSMN values on the smaller bodies and larger values on the larger bodies which are input.

Unless otherwise indicated, the user should not select excessively large values for DSMN. Values

smaller than 2*10-4 have been used for small airfoil elements such as slats and flaps.

DSMN values larger than 8*10-4 are sometimes needed when the ice shape is extremely large

in comparison to the airfoil. An example of this condition occurs for cylinders below six inches in

diameter, especially when a lengthy accretion time is used (20 minutes or more). The time step for

this case may have to be increased from the recommended values in order to run this case as well. 

The total wrap distance around a typical airfoil is slightly greater than 2 (dimensionless

value). For a DSMN value of 4*10-4, the number of control volumes produced will exceed 5000.

Since the array size limit is 10000 points, the total wrap distance around the iced geometry needs

to be more than four times greater than the chord length for the array bounds to be exceeded. For

a DSMN value of 8*10-4, the total wrap distance around the iced geometry needs to be more than

NASA/CR—2002-211793 11
eight times greater than the chord length. The ratio of wrap distance to chord length for a cylinder

is by definition pi (3.1415926536...). This ratio will increase as the ice grows on the cylinder. This

example shows why larger DSMN values are likely needed for a cylinder.

6.4 Number of Trajectories

The number of trajectories used in the impingement region is an input to the software. A good

approximation would be to first estimate how many panels are expected to be in the impingement

region. The number of trajectories should not be less than one trajectory for every three panels

and should not be greater than one for each panel. An excessive number of trajectories should be

avoided as this will slow down the solution. The actual number which the software uses for the

collection efficiency calculation may be different than the value input. The software is limited to

one trajectory strike per panel. If more than one trajectory hits a given panel, only the first hit will

be saved.

6.5 One-Dimensional Anti-Icing

This program will calculate the heat requirements using a hot air or an electrothermal antiicer. It will then compute the ice shape as if the surface were unheated. Layers are input with the

inner surface first, and the outer surface last. The information in the de-icer input file will be used

for each body in a multi-element calculation. The desired surface temperature input in the de-icer

input file must be above freezing (in Kelvin) for this option to work properly. NASA Glenn also

had programs which performed more detailed analysis of de-icer and anti-icer performance. The

LEWICE/Thermal program8 performed a 2D transient de-icer simulation and the ANTICE

program9 performed a 2D steady-state anti-icing simulation. These two programs have been integrated into this version of LEWICE. If the user needs a more detailed analysis than provided with

the one-dimensional anti-icing function, they are encouraged to try IDEICE = 2 or IDEICE = 3

options in the main input file. 

This routine does not affect the ice accretion routine. The software will output an ice shape as

if no heat had been applied. This routine generates a separate file containing the temperatures and

heat fluxes needed to maintain a desired surface temperature which is input by the user.

NASA/CR—2002-211793 12
This routine treats the current geometry as the airfoil and does not distinguish an iced airfoil

from an un-iced airfoil. Therefore, only the results obtained in the first time step are applicable to

an anti-icing problem.

The text accompanying the input fields in the examples listed is provided for informational

purposes. Only the numerical value is read by LEWICE.

Typical running wet anti-icing systems operate in the region 5-10  ̊C while an evaporative

system may operate at 50  ̊C or even higher.

The internal heat transfer coefficient for regions outside those specified by the user will be

zero.

The results for a desired surface temperature at (or below) freezing will be inaccurate since

the anti-icing module does not have provisions to freeze surface water as does the LEWICE icing

module.

6.6 Droplet Distribution

Most cases run with LEWICE 2.2 in the validation database use a single drop size, the Median

Volume Diameter (MVD) for the flight condition. Although multiple drop size distributions can

be run with LEWICE 2.2, execution times will be increased. The difference in ice shape and icing

limits are documented in the validation report1. This report shows that the effect is very slight for

single body simulations. The procedure used by LEWICE for multiple drop size distributions is to

calculate a collection efficiency for each drop size, and then to superimpose the solutions. For a

five drop size distribution, this feature essentially makes the software five times slower to obtain

what is often a marginal effect. The main practical use for this feature would be to determine

more accurate impingement limits on the clean airfoil. Preliminary results have shown that multiple drop size distributions can have a large impact on the collection efficiencies and ice accretion

of multi-element airfoils.

The FLWC values input in the main input file are Fraction Liquid Water Content. These values must add to one (1). The program will adjust the FLWC values proportionately so they add to

1.

NASA/CR—2002-211793 13
The program will determine the number of drop sizes in the distribution by looking for the

first occurrence where FLWC = 0. Therefore, the user should not place zeros in the FLWC field

until the end of the distribution is reached.

MVD is not an input variable to LEWICE. The MVD is calculated from the individual drop

sizes input in this section. 

Important: The validation database contains MVD drop sizes in the range 15≤ MVD ≤ 270.

Although some experimental data has been collected in the 50 < MVD ≤ 270 micron range and

has been used for software validation, there is not enough data available to consider the software

validated for these drop sizes. Caution should be exercised when running cases above 50 micron

MVD. Due to the recent popularity of drop size inputs in these exceedence conditions, it is worth

emphasizing the above statement. This statement does not imply that LEWICE cannot run the

drop size distribution input by the user. It most likely can. The warning statement does not imply

that the results will be inaccurate. LEWICE results for exceedence conditions are quite encouraging in this respect. The statement simply points out that insufficient experimental data is available

at these drop sizes. Since the results cannot be experimentally validated, the true accuracy of the

results cannot be verified.

6.7 Collection Efficiencies and Droplet Trajectories

The wrap distance from the leading edge output in the collection efficiency data file

(BETA.DAT) and the impingement limit data file (IMP.DAT) may lose physical meaning past

the first time step. This occurs since the calculated “leading edge” of a glaze ice shape will likely

be at the tip of the upper ice horn and nowhere near the leading edge of the clean geometry.

The impingement limit listed in the output file “IMP.DAT” may not match the wrap distance

location where the collection efficiency (beta) goes to zero in the output file “BETA.DAT”. The

difference is due to the resolution of surface points in the impingement limit region. The value

quoted in the file “IMP.DAT” is the computed impingement limit. The location where the collection efficiency goes to zero is the surface point closest to this value.

NASA/CR—2002-211793 14
Droplet trajectory output is sequential. The first set of coordinates contain the coordinates of

the first trajectory calculated. Subsequent output contains coordinates for each successive trajectory calculated. No indicator is present in the output file to offset trajectory output from one time

step to another. Hence, this output is only recommended for the first time step. 

6.8 Static Pressure/Altitude

Ambient pressure is not recorded as part of the tunnel data, so the exact value during the tests

is unknown. However, since ambient pressure is at best a secondary effect on the ice accretion

process, a representative value near atmospheric pressure was used for the comparison.

To a good approximation, for a ‘standard atmosphere’, the following equation can be used:

 where

P = pressure in N/m2 and 

H = height (altitude) in meters

6.9 Temperature

The input variable for temperature in LEWICE is the ambient static temperature in degrees

Kelvin. The data supplied to researchers is often the total temperature, not the static temperature.

Make certain the value input is correct!

6.10 Relative Humidity

Relative humidity is not recorded as part of the tunnel data, so the exact value during the tests

is unknown. However, since it is at best a secondary effect on the ice accretion process, a representative value of 100% humidity can be used.

6.11 Printer Flags

Output files from LEWICE can be very large. If all of this information is not needed, the user

can save a great deal of disk space by not generating individual files or by reducing the amount of

information which is sent to those files. Example Case 2 illustrates this effect. As listed in this

example, the case produces 3.3 MB of output. If all of the printer flags are activated, the output

P 100920 11.35 – 0.00039456 H H2

+=

NASA/CR—2002-211793 15
will exceed 45 MB. Finally, it should be noted that the definition for the print flag TPRT has

changed from version 1.6. The current definition of TPRT has the opposite meaning for input values of TPRT = 1 and TPRT = 2 than the definition used in version 1.6.

6.12 Geometry Input

It should be noted that all of the validation data uses airfoils. Although LEWICE can simulate

any enclosed body (or bodies), the validation performed to date has been limited to the available

data.

A separate input file must be provided for each body being simulated. If only one body

exists, only one geometry file will be read. Each line of the geometry input file contains an x,y

coordinate pair for the body geometry. The x-coordinate is listed first. The format of the data is

free format for the x,y coordinates. It is quite common for problems to arise when inputting a new

geometry for the first time. The following discussion will describe some of the common errors

made by users in generating an input file.

If the body geometry is too coarse, the panel model created may not replicate the body geometry input. The initial set of coordinates output to file “ICE1.DAT” contain the initial panel model

of the first body geometry. The user should check that this airfoil matches their geometry input

file whenever a new geometry is input or if the point spacing (DSMN) has increased. Standard

geometry input files used for testing purposes range from 50 to 150 points.

The panel solution used in this software assumes that the body(s) being simulated are closed

bodies. Several tests have been run using airfoils with open trailing edges and some of the results

appear acceptable. If the flow solution calculated with an open trailing edge is acceptable to the

user, then there may be no need to alter the trailing edge simply to enclose the body.

LEWICE requires that the body geometry points should be input in a clockwise fashion. This

means that the points are input starting at the trailing edge and proceed sequentially toward the

leading edge along the lower surface up to the leading edge, then traverse back to the trailing edge

along the upper surface.

NASA/CR—2002-211793 16
Several errors can occur when points are typed in. These errors may cause the geometry to be

different from the one intended by the user. Some common errors include: points input in reverse

order; missing or misplaced decimal points; or mistyped numbers. LEWICE cannot check for all

possible errors. The user should always check the first panel geometry printed to “ICE1.DAT” to

ensure that the body being used by LEWICE closely resembles the intended geometry. Specifically, the user should ensure that there are sufficient input points in regions of high curvature. The

point distribution methodology used in LEWICE will tend to “round off” corners if an insufficient

number of points are used.

Additional input problems may arise when the user attempts to input more than one body. One

such problem can occur when the bodies intersect. This can easily occur with multi-element airfoils if the user does not properly rotate the flap or use the proper gap settings.

LEWICE cannot run multiple bodies where one body is completely inside another body. This

can occur if the coordinates for the bodies are supplied relative to different points of origin rather

than relative to the same point of origin.

The logic used by the trajectory module dictates that multiple bodies need to be input in

sequential order in the x-direction. This means that the first body a particle could encounter must

be listed first, the second body it could encounter must be listed second and so on. This criteria is

based upon the leading edge of each body, not on the trailing edge as particles are most likely to

impinge on the leading edge of each body. 

6.13 De-icer Input

The program will only ask for the de-icer input file name for cases where IDEICE is not equal

to zero.

Both the IDEICE = 2 and IDEICE = 3 options will perform a detailed thermal analysis within

the airfoil, ice and water. The IDEICE = 2 option is recommended for failed thermal cases with

significant ice accretion. The laminar flag, IDEICE = 3, provides consistently better predictions

for cases with a clean leading edge. However, it is the less conservative option and has a tendency

to overpredict temperatures for some cases.

NASA/CR—2002-211793 17
The output file “NOICE.DAT” contains output from the simplified 1D thermal analysis. This

analysis is provided for all cases where IDEICE > 0. When IDEICE = 1, it is the only thermal

analysis performed. It is also performed for IDEICE = 2 and IDEICE = 3 cases as the 1D option

does not take significant computation time. Also see Section 10.1.4.4 for additional capabilities

when IDEICE = 2 or 3.

The de-icer geometry is specified by the user in the (rectangular) computational domain, not

in the physical domain.

Unlike thermal conductivity and density, the specific heat of materials is often difficult to find

in references. Manufacturers often do not measure (or list) this quantity in spec sheets. However,

this parameter is only important for transient (time-dependant) cases.

Data is read free-form. The numbers do not have to reside in any particular column and do not

have to line up with the comments. The numbers must be input in the correct order however.

The input units for LEWICE 2.2 are metric. Due to the relative scale of certain values, the

input units can be watts or kilowatts.

W/in2 * 1.55 = kW/m2

Heat flux values are input (and output) in units of kW/m2 while thermal conductivity and heat

transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively.

The first layer input is the innermost layer and the last layer will be the top surface.

While performing de-icing or anti-icing simulations, make certain that the top layer contains

the thermal properties of ice. If the ice melts, the software will change the properties accordingly.

For any icing, de-icing or anti-icing simulation, the thickness given to the ice layer in this section will only be used to determine the grid spacing within the ice. The actual ice thickness at each

grid point is part of the output from this module.

NASA/CR—2002-211793 18
The total number of points in the normal direction is currently limited to 310 points. The total

number of points is the sum of the points in each individual layer minus the number of layers, plus

2.

Only the lines with data are used by the software. The comments included in this example are

extraneous and are ignored by LEWICE 2.2. 

The section data is entered from the left side of the computational domain toward the right

side. In the physical domain, data is entered starting from the lower surface trailing edge clockwise toward the leading edge an ending back at the trailing edge.

The length of the end segments will be changed so that the total segment length equals the

total wrap distance calculated by LEWICE 2.2. An identical amount will be added (or subtracted)

from each end segment. Segments may be eliminated, if needed, to match the airfoil wrap distance.

The center of the middle section is not aligned with the body leading edge by default. This

can be changed in the next set of input data using variable OFFSET.It is not necessary for the

input data to align on a given column. This was done in the example cases to improve readability.

Comment lines have been added to improve readability. The software will ignore the comments and only read the data lines.

If there was an error reading data in the first section, the software will continue to read the rest

of the input file. However, an error in an earlier section can cause incorrect error messages to

appear for subsequent sections. It is highly recommended that the user fix the first errors encountered and resubmit the case.

Normal operation of this software uses one parameter study per run (IPAR = 1). While a multiple parameter study option has been included, it is possible that output from a multiple parameter study run may be different from the output that would have been achieved if the case were run

separately. This option has seen limited testing. Section 13.1 describes a potentially better way to

perform a parameter study by using external scripts.

NASA/CR—2002-211793 19
Temperature controlled heaters as modeled in this software do not necessarily determine the

“optimum” heat flux. Initially, it uses the wattages input until the temperature exceeds the ON

temperature. It then turns off all heat until the temperature drops below the OFF temperature.

Heat is then turned on, but at a lower wattage. This process continues until the simulation time

(TSTOP) is reached. If the simulation time is sufficiently long and the wattage has not changed

for a long time, then the wattage reported in “QOPT.DAT” may be close to the optimum heat

flux. Results to date have been inconsistent for this option.

To model a section which does not have a heater, simply input QDE = 0.

To model an electrothermal anti-icing system or parting strip, set TOFF = 0.

The heat transfer coefficient input at the top surface may be overwritten using the IBOUND

flag in the next input section.

The inside heat transfer coefficient, H1, can be used to model a hot air anti-icer. Section

10.1.4 provides a better way to model of this type of system.

The wall heat flux, QW1, can be used to model a hot air anti-icer. Section 10.1.4 provides a

better way to model of this type of system.

The IQW flag does not necessarily determine the “optimum” heat flux. Initially, it uses the

wattages input until the temperature exceeds the ON temperature. It then turns off all heat until

the temperature drops below the OFF temperature. Heat is then turned on, but at a lower wattage.

This process continues until the simulation time (TSTOP) is reached. If the simulation time is sufficiently long and the wattage has not changed for a long time, then the wattage reported in

“QOPT.DAT” may be close to the optimum heat flux. Also see the description of temperature

controlled heaters in Section 10.1.2.2. Results to date have been inconsistent for this option.

IBLEED and IQAIN flags are most often used when the input data is known. Examples of this

condition occur when experimental test data is available or when values are calculated by another

program or via correlation. IQW is most often used when this data is not available.

NASA/CR—2002-211793 20
IBOUND values are ignored by the software unless IBC2 = 2 boundary condition is used.

Most of the cases performed to date (especially those which have experimental data) use INIT

= 2 and ICOND = 1. Other combinations have seen limited testing.

If a node of ice melts, the software will automatically change the thermal properties of that

node to water.

If phase change is considered (IGDE = 1), the length (ELDE) given to the top layer in Section

10.1.1.2 will only be used to define the normal direction grid spacing in the ice layer. In this case,

the ice thickness at time = 0 will be zero. 

Some combinations of flags in Table 22 may generate warning messages but the flag values

will not be changed

To model a fixed-body problem, simply set RPM = 0.

The software uses the rotor data input for three calculations: 1) the rotational speed is used to

calculate an increase in the aerodynamic heating term in the energy balance; 2) the rotational

force is used to shed ice; and, 3) the rotational force is used to find the resultant force of the shed

ice particle, which is used to track the particle after it sheds.

The rotating body information is not used by the potential flow solver in LEWICE 2.2 nor is

the rotating body information used by the trajectory equation.

If STA = 0 or RPM = 0, then there is no difference between IROT = 0 and IROT = 1 (rotational force is zero).

De-icer time steps less than 10-4 seconds are not allowed as the software will run very slowly

at such de-icer time steps. De-icer time steps greater than 1 second cannot accurately capture temperature distributions even for cases where only the steady-state output (an anti-icing case) is simulated. This occurs because convergence cannot be maintained for larger de-icer time steps.

NASA/CR—2002-211793 21
DTAUI values other than 0.1 seconds have been used in test cases which have a large initial

transient in the temperature distribution. Smaller initial time steps were chosen in these cases to

accurately model the temperature distribution. Larger initial time steps were chosen for steadystate anti-icing cases. Note that since the phase of each node in the ice layer must be iterated upon,

a larger time step does not always provide a faster solution. 

Times for temperature output selected by the user do not have to be in equal time increments.

Equal increments were used in the example cases for convenience.

Previous versions of the LEWICE/Thermal software used time step instead of time.

The last two output types (IOTYPE = 4 or 5) are intended for debugging purposes and should

not normally be needed by the user.

The shed trajectory computation assumes that shed ice particles are spheres. 

The shed force data files can be extremely large and should be deleted if they are not needed.

NASA/CR—2002-211793 22
Chapter 7: Interactive Input

This section will describe the interactive input required by LEWICE. Error messages are also

described along with suggested corrective measures. The error messages are generated by the

operating system and are unique to the platform being used. Since LEWICE can be compiled and

run on a wide variety of operating systems and hardware platforms, it is not possible to identify

the error messages for every platform. Two operating systems were chosen to provide representative examples of the operating system errors. The systems chosen were those generated by

Windows95/DOS for PCs and those generated by IRIX 6.2 for SGI workstations. The latter

example should be representative of error messages provided by other unix operating systems.

The error generated by the system will be listed in italics, while the explanation of the error is

listed in plain text. The errors listed in this document are those which result from running the executable provided on the LEWICE distribution disks. Users who recompile the program for their

system may generate different errors.

7.1 Enter Input File Name

The first interactive input directs the user to input the name of the main input file. The name

can be up to 80 characters long. This filename length is necessary as the user must also input the

directory path of this file if it is different from the directory containing the program. Please read

the error messages in this section concerning the proper form of the input using a directory path.

If the file cannot be accessed, the following system error will be generated:

IRIX 6.2 Message

open(name): No such file or directory

apparent state: unit 35 named

last format:

Unit 35 is a sequential formatted external file

*** Execution terminated (2) ***

Windows DOS Shell Message

forrtl: The system cannot find the file specified.

forrtl: severe (29): file not found, unit 35, file C:\Lewice\test.inp

NASA/CR—2002-211793 23
This error indicates that the file name input does not exist, or does not exist in this directory.

Common problems: 

1) The file name was not typed correctly (in the example case, remember to include the extension - i.e. use “case1.inp” not simply “case1”); 

2) The input file is in a different directory than the program. The input file can be in a different directory than the program, but in order for LEWICE to recognize the input file the path must

be specified. For example, use “inputs\naca0012\case1.inp” instead of simply “case1.inp” to read

the input file “case1.inp” in the directory “inputs” and subdirectory “naca0012”. Note: The above

example used the DOS directory convention of backward slashes “\” to list subdirectories. IRIX

and many other unix systems use forward slashes “/” instead.

PC Note: To get to the root directory, first type a backward slash “\”, then the path and file

name. For example, the command “\lewice\inputs\naca0012\case1.inp” can also be used to read

the file “case1.inp” in the directory “C:\lewice\inputs\naca0012”.

Unix Note: It is common practice in unix to place all programs in a predefined directory such

as /usr/bin so that everyone using that system can run the program. The path for specifying the

input file in this case is to provide the path from the directory the user is in. For example, if the

user is in their home directory and the input file is in the home directory, no path should be provided. If the user is in their home directory and the input files are in directory ../inputs/naca0012,

then the proper path to input is “inputs/naca0012/case1.inp”. If the user is in directory ../inputs/

naca0012 and the input file is in this directory, then no path needs to be provided in this case

either. P.S.: This sequence is correct based on the IRIX 6.2 operating system. Behavior for other

unix operating systems are expected to be the same, but potentially could be different.

7.2 Enter File Name for Body 1

This interactive input directs the user to input the name of the file containing the body geometry points for the first body being used. If only one body is being run, the program will not ask for

additional geometry files. If more than one body is being simulated, the software will prompt the

user for additional file names for each body. If the file cannot be accessed, the error message

NASA/CR—2002-211793 24
listed previously for the main input file name will also be generated. In this case however, the unit

number referenced in the error message will be unit 44 for the first body, unit 45 for the second

body, unit 46 for the third body, unit 47 for the fourth body and 48 for the fifth body. The corrective measures concerning file name and directory path listed earlier for this error will also apply to

errors involving the body geometry.

7.3 Confirmation of Warnings

The file name inputs for the main input file name and geometry input file name(s) are the only

interactive inputs to LEWICE unless the program has a problem reading the input files or if a deicer input file is being used. LEWICE may issue a warning message or an error message in accordance with the nature of the problem. These warning messages and error messages are listed in

the following chapters which describe the input files for LEWICE. After any warning messages

are issued, the user will have to confirm the settings to continue the run from the following interactive input:

There is a problem with your input. (value) warnings have been issued. Do you wish to continue? Answer Y or N

This question will be asked after all of the input fields have been processed within the software. The listing (value) in the above statement will be replaced by the actual number of warning

messages issued. The program will only continue running if the response to this question is Y or

y. Other responses (including no response) will be interpreted as a negative response and the program will exit. This message will not appear if there are no warnings issued. If the user wishes to

correct the input file based on a warning message, simply respond negatively to the prompt and

edit the file after the program quits.

For every error message, the following line will be printed:

The program will stop because of the above error.

This message indicates that the statement above this error message has caused the program to

exit. The program will then continue processing the input file. Once all of the input fields have

been processed, the following line will be printed:

NASA/CR—2002-211793 25
(value) problems have occurred with the input which cannot be corrected by the program.

Please correct the input and resubmit the case.

Once again, the (value) field in the above statement will be replaced with the actual number of

errors detected. After this statement prints out, the user must correct the errors listed. Refer to the

sections on that variable for assistance with correcting the error. 

7.4 Enter De-icer File Name for Body 1

This interactive input directs the user to input the name of the file containing the internal

geometry of the body, physical properties, heater wattages and various flags. If only one body is

being run, the program will not ask for additional de-icer input files. If more than one body is

being simulated, the program will prompt the user for additional file names for each body. The

same file can be used for different bodies if the user desires. If the file cannot be accessed, the

error message listed previously for the main input file name will also be generated. In this case

however, the unit number referenced in the error message will be unit 10 for the first body, unit 11

for the second body, unit 12 for the third body, unit 13 for the fourth body and 14 for the fifth

body. The corrective measures concerning file name and directory path listed earlier for this error

will also apply to errors involving the de-icer input. The de-icer input file will be checked for any

errors or warning messages. If any problems occur with this input file, the warning and error messages described in the previous section will be issued.

Note: The program will only ask for the de-icer input file name for cases where IDEICE is not

equal to zero.

NASA/CR—2002-211793 26
Chapter 8: Main Input File

This section will define the variables in the main input file to LEWICE. Several notes are also

added to aid the user in properly setting up an input file for this software. Any warning messages

or error messages based on improper inputs will also be described in this section. 

In the examples provided in this section, the input file was named “test.inp” and was located

in a directory called “Lewice”. In every instance where a screen message is referenced, the message is also written to the debug file, “JUNK.DAT”.

8.1 Listing Variables in a Namelist

The main input file for LEWICE is formatted as a series of namelists. Variables in namelist

format are input on separate lines. Each line contains a unique variable which is listed in that

namelist. The line should contain the variable name followed by an equal sign (=) followed by the

value to be assigned to that variable. The value can be in integer, real or exponential format

regardless of the definition used within the program. For example, an integer variable does not

have to be input as an integer. The value will be truncated for use in the program. In addition, the

user is not required to list every variable in the namelist. If a variable is not listed in the input file,

the program will use the default value. Default values are listed in this section for each variable.

Examples of valid inputs are provided for each namelist section. 

8.1.1 Variable not in namelist error

If the user lists a variable which is not in one of the namelists, the following system error is

generated:

IRIX 6.2 Message

namelist read: variable not in namelist

apparent state: unit 35 named test.inp

last format: namelist io

Unit 35 is a sequential unformatted external file

*** Execution Terminated (119) ***

NASA/CR—2002-211793 27
Windows DOS Shell Message

forrtl: severe (19): invalid reference to variable in NAMELIST input, unit 35,

file C:\Lewice\test.inp

Common causes for this error occur when the user mistypes the variable name or when the

user enters a variable from a previous LEWICE version which is no longer input into that namelist. IRIX 6.2 has an additional constraint that the first character of each namelist and each namelist variable resides in column 2. This constraint was not noticed on the PC. Also note that the

LEWICE input files are ASCII text. PCs, Macs and Unix workstations all have different formats

for treating line breaks with ASCII files which may cause problems when transferring input files

to different platforms. Specifically, when PC ASCII files are moved to an SGI with IRIX 6.2,

there is an extraneous character (^M) at the end of each line. This character must be removed

from each line to use the file on the SGI.

8.1.2 Namelists Listed Out of Order or Missing Namelist

The namelists used for LEWICE 2.2 are LEW20, DIST, ICE1, and LPRNT in that order. If a

namelist appears out of order or is missing, the following system error is generated:

IRIX 6.2 Message

namelist read: cannot position within current file

apparent state: unit 35 named test.inp

last format: namelist io

Unit 35 is a sequential unformatted external file

*** Execution Terminated (170) ***

Windows DOS Shell Message

forrtl: severe (24): end-of-file during read, unit 35, file C:\Lewice\test.inp

Each section of the main input file will now be explained. Statements which are output to the

screen are in italics. Statements which contain the phrase (value) indicate that a numerical value

will be output where the phrase (value) is located.

NASA/CR—2002-211793 28
8.2 Line 1

Line 1 is the title assigned to the run by the user. The title can be up to 80 characters in length

and will be written to the output files “MISC.DAT” and “JUNK.DAT”. If no title exists, the following system error will be generated:

IRIX 6.2 Message

namelist read: cannot position within current file

apparent state: unit 35 named test.inp

last format: namelist io

Unit 35 is a sequential unformatted external file

*** Execution Terminated (170) ***

Windows DOS Shell Message

forrtl: severe (24): end-of-file during read, unit 35, file C:\Lewice\test.inp

8.3 LEW20 Namelist

The LEW20 namelist contains a collection of inputs from a number of separate namelists

from version 1.66. The inputs have been rearranged for clarity. Input for the LEW20 namelist is

identified by the line:

&LEW20

This line should immediately follow the title line. Refer to the list of namelist errors at the

beginning of this section if there are problems with this input.

LEW20 Namelist Variables

8.3.1 ITIMFL

Default Value: ITIMFL = 1

ITIMFL is a flag indicating whether LEWICE will use automatic time stepping or will use a

user-defined number of time steps. If ITIMFL = 0 then the number of time steps will remain as

input by the user in the IFLO variable. If ITIMFL = 1 then the time step will be calculated based

NASA/CR—2002-211793 29
on the accumulation parameter. In either case, the time steps are of equal length throughout the

run. When ITIMFL = 1, the minimum number of time steps is calculated internally in the program

by the following procedure. First, a preliminary number is calculated based upon the accumulation parameter as given below.

(2)

where 

LWC = liquid water content (g/m3)

V = velocity (m/s)

Time = accretion time (s)

chord = airfoil chord (m)

ρice = ice density = 9.17*105 g/m3

A second time step number is calculated by

(3)

IFLO is then calculated by the following expression

(4)

The values of IFLO calculated in this fashion will correspond to the values used in the

LEWICE validation report. When ITIMFL = 1 and the number of time steps input by the user is

less than the number calculated, the number of time steps will be increased and a warning message will be generated. If the number of time steps input by the user is greater than the value calculated, no adjustment is made and no warning message will be generated. The variability of

LEWICE results for various time steps and point spacings is discussed in the section on Numerical Variability in the validation report1. Due to this variability, LEWICE 2.2 selects automatic

N ( ) LWC ( ) V ( ) Time

( ) chord ρice ( )( ) 0.01 = --------------------------------------------------

N2 Time

60 ------------=

IFLO Max Min N = [ ] ( ) , 30 , Min N( ) 2 15 ,

NASA/CR—2002-211793 30
time stepping to be on as its default setting. The warning message listed below will be printed

whenever the user sets automatic time stepping to the off value:

You are not using automated time stepping procedure. The accuracy of the program in this

situation is unknown.

In addition, if the number of time steps selected (see IFLO input) is less than the recommended value, the following additional warning message will print out:

You are running fewer time steps than recommended. Number of time steps recommended =

(value). Number of time steps selected = (value). Ice shapes produced may be different from those

used to validate this program.

The valid inputs for ITIMFL are 0 and 1. If any other value is input, the following warning

occurs:

Valid inputs of ITIMFL are 0 and 1. Your input value of (value) is out of range. Setting

ITIMFL to 1.

If ITIMFL is not specified in the namelist, its default value will be set to 1 (automatic time

stepping is on).

8.3.2 TSTOP

Default Value: TSTOP = 60

TSTOP is the total time of the icing simulation in seconds. This value must be > 0. An input

value < 0 will generate the following error:

Severe input error: Time cannot be negative! TSTOP = (value) is an invalid input.

After checking the other inputs, the program will exit due to this error.

NASA/CR—2002-211793 31
An input of zero for TSTOP will cause a “divide by zero” problem because the calculated

time step will also be zero. The following error message will be generated:

Calculated time step is <= zero! dtime = (value)

After checking the other inputs, the program will exit due to this error. 

An extensive validation effort has been performed to define the regimes where LEWICE produces acceptable results. The existing experimental data base does not contain any data points for

icing times greater than 45 minutes (2700 seconds). If a TSTOP value greater than 2700 seconds

is input, the following warning message will be generated:

The maximum icing time used for evaluation of this software was 45 min. Your time of tstop =

(value) exceeds this value. The accuracy of the program in this situation is unknown.

The default time used by LEWICE is 60 seconds if the user does not specify a value.

8.3.3 IBOD

Default Value: IBOD = 1

IBOD is the number of bodies to be simulated. For example, a three body simulation can consist of a slat, main element and flap. However, multi-body simulations are not limited to this

example.Valid input values for IBOD are 1 ≤ IBOD ≤ 5. If the input value for IBOD is ≤ 0, the

following error message will be generated:

Severe input error: You must run at least 1 body! IBOD = (value)

After checking the other inputs, the program will exit due to this error.

If the input value for IBOD is > 5, the following error message will be generated:

NASA/CR—2002-211793 32
Array size limits the number of bodies to 5. Your input value of (value) is out of range.

Decrease the number of bodies input or increase the array size to fix this problem. The latter suggestion requires changes to the source code.

After checking the other inputs, the program will exit due to this error. The last statement is

intended for code developers. The size of the array can be easily increased to run more than five

bodies. This change would require that the code be recompiled.

As stated earlier, LEWICE 2.2 can run multiple body simulations including multi-element airfoils. A report of its capabilities in this region shows very encouraging results7. However, much

of the development effort for version 2.2 has centered on validating the existing features of the

program. Even though the results to date have been encouraging, there is not enough data available to consider LEWICE 2.2 validated for multi-body flows. Therefore, if the input value for

IBOD is in the region 2 ≤ IBOD ≤ 5, the following warning message will be generated:

NASA does not have enough data to thoroughly validate LEWICE for multi-body conditions.The built-in flow solver is for incompressible and inviscid (potential) flow. This is usually

inadequate for the flow around multi-element wings. It is often necessary to alter the angle of

attack and flap angle to analyze these cases. Number of bodies input = (value)

The default number of bodies is equal to 1 if the user does not specify a value.

8.3.4 IFLO

Default Value: IFLO = 1

IFLO is the number of time steps to be used in the simulation. A value greater than 0 is

required for this input. If the input value is ≤ 0, the following warning message will be generated:

Number of flow solutions input is <= zero! Resetting number of flow solutions (IFLO) = 1.

IFLO input = (value)

NASA/CR—2002-211793 33
As stated in this message, the program will continue with a single time step. This value may

be changed again if the auto-time step flag is on (ITIMFL = 1).

If the automatic time step option is used (ITIMFL = 1), then the number of time steps may be

overwritten with the calculated number of time steps. The program will use the value of IFLO

input if it is ≥ the calculated value and no warning will be issued. If the number of time steps is

less than the recommended value and ITIMFL = 1, the following warning message is generated:

The input number of time steps (5) has been changed to the calculated value of (19). Unless

otherwise noted, this occurred because the auto-time stamp ITIMFL is set = 1.

In the above example, the calculated number of time steps was 19 and the input value was 5.

The actual values printed out will depend on the conditions input by the user.

If the automatic time step option is not used (ITIMFL = 0) and the number of time steps input

less than the recommended value, the following warning message is generated:

You are running fewer time steps than recommended. Number of time steps recommended =

(value). Number of time steps selected = (value). Ice shapes produced may be different from those

used to validate this program.

If no time step value is specified by the user, the default number of time steps is set equal to 1

if auto-time stepping is off and will be calculated if auto-time stepping is set on.

Note: For very small (< 6”) chord geometries such as cylinders, the number of time steps recommended by the program may be considered prohibitive by the user. It may be possible (and

even necessary) to decrease the number of time steps for these cases. It should be noted though

that the smallest chord airfoil in the validation database is a 14” NACA0015 for which 8 ice

shapes have been digitized. Therefore, results for chord lengths smaller than this have not been

validated.

NASA/CR—2002-211793 34
Note: Time steps smaller than 30 seconds are discouraged as they can cause undesirable

numerical effects. The software should not choose a time step this small unless the chord length is

very small as well.

Note: The procedure for the validation report set the number of time steps equal to the number

of minutes of icing or 15, whichever was lower. This procedure is highly recommended to maintain consistency with the validation report results.

8.3.5 DSMN

Default Value: DSMN = 4*10-4

DSMN is the minimum size of the control volumes (non-dimensionalized). It is also tied indirectly to the number of panels produced for the flow solution. The exact number of panels and

control volumes used will depend on the surface area and complexity of the input geometry.

Larger values of DSMN create fewer control volumes and fewer panels while smaller values of

DSMN create more control volumes and more panels. 

Part of the validation effort for LEWICE 2.2 centered on defining practical ranges for the values of DSMN. The results of these tests are provided in the validation report1. For all of the airfoils studied, the range of DSMN values was 2*10-4 ≤ DSMN ≤ 8*10-4. The lower limit reflects

the current limits of the array sizes in the program and is not a reflection of the accuracy for low

DSMN values. For DSMN values of 8*10-4 or higher, quantitative differences occur due to the

coarse spacing provided. An exception was found for cylinders which have a very large surface

area compared to similarly sized airfoils. However, results on cylinders have not been validated

against experimental data. Larger DSMN values are necessary for cylinders due to the limitations

on array sizes. The value of DSMN input must be greater than zero however. If a value of DSMN

≤ 0 is input, the following error message is generated:

Severe input error: DSMN must be greater than zero! DSMN = (value)

After checking the other inputs, the program will exit due to this error.

NASA/CR—2002-211793 35
If a value of DSMN greater than 8*10-4 is input, the following warning message is generated:

The point spacing input is larger than those tested. DSMN(i) = (value). Ice shapes produced

may be different from those used to validate this program.

There is no warning message generated for DSMN values below 2*10-4. However, the user

should expect that for values of 2*10-4 or below, the program may generate an error message that

the array size has been exceeded. See the section in this manual on runtime errors for a listing of

errors produced when the array sizes have been exceeded. All of the validation tests were run with

a DSMN value of 4*10-4.

The following notes also contain useful information regarding the use of DSMN.

Note: In version 2.2 the number of control volumes will be much greater than the number of

panels. The ratio of control volumes to panels based on the validation tests is approximately 50 to

1. The default value for DSMN is 4*10-4. As the total wrap distance around a typical airfoil is

slightly greater than 2 (dimensionless), the default DSMN value will produce over 5000 control

volumes. The number of panels produced in this case will be approximately 100.

Note: There is one value of DSMN for each body. If only one body exists, only the first value

input is used by the program. For multi-body simulations, it is to the user’s advantage to use

smaller DSMN values on the smaller bodies and larger values on the larger bodies. Unless otherwise indicated, the user should select values within the appropriate range.

Note: The number of panels and control volumes used are virtually independent of the number of points contained in the geometry input file.

Note: DSMN values larger than 8*10-4 are sometimes needed when the ice shape is extremely

large in comparison to the airfoil. An example of this condition occurs for cylinders below six

inches in diameter, especially when a lengthy accretion time is used (20 minutes or more). The

time step for this case may have to be increased from the recommended values in order to run this

case as well. 

NASA/CR—2002-211793 36
8.3.6 NPL 

Default Value: NPL = 24

NPL is the number of particle trajectories (including the impingement limit trajectories)

which define the collection efficiency distribution. LEWICE needs at least 10 trajectories in order

to calculate an accurate collection efficiency curve. If the input value for NPL is less than 10, the

following warning message will be generated:

Number of trajectories input (5) is insufficient for this program. Increasing to default value

(24).

In this example, the value input for NPL was 5. In addition, LEWICE will issue a warning if

the user attempts to run an excessive number of trajectories. This warning message reads:

The number of trajectories input (500) is quite large. Although not a real problem, you can

likely reduce NPL without loss of accuracy. Default NPL = 24

In this example, a value of 500 for NPL was input. The warning message will occur for any

value of NPL over 50. It should be noted that in this case the value input by the user is not overwritten (the extra trajectories will be performed). All of the validation tests were run with a value

of 24 for NPL, which is the default value if none is specified by the user.

Note: The actual number which the software uses for the collection efficiency calculation

may be different than the value input. The program is limited to one trajectory strike per panel. If

more than one trajectory hits a given panel, only the first hit will be saved. Thus the use of large

NPL values may result in unnecessary computations which do not enhance the accuracy of the

final result.

8.3.7 RHOP

Default Value: RHOP = 1000

NASA/CR—2002-211793 37
RHOP is the density of the water particle in kg/m3. This has been placed in the input file to

broaden the utility of this software to industry. Except for very large particle sizes, the physics of

water droplet trajectories is the same as for sand particle trajectories. The only required change to

model sand particle trajectories is the density of the particle, as sand has different properties than

water. If sand density is substituted, the software can be used to predict deposition of sand (sand

collection efficiency). In this mode, the ice accretion results should be ignored and the program

can be run using a single time step. 

This input value must be greater than zero. If a value of RHOP ≤ 0 is input, the following error

message will be generated:

Severe input error: Density must be greater than zero! RHOP = (value)

After checking the other inputs, the program will exit due to this error.

In addition, LEWICE will warn the user when this input is not equal to the density of water

(1000 kg/m3).

The value input for particle density (value) is different than for water (1000). Most likely, this

was done in order to simulate sand particle trajectories. The output for this run should not be

used for ice accretion studies. Ice shapes produced may be different from those used to validate

this software.

8.3.8 IGRID

Default Value: IGRID = 0

IGRID is a flag which allows a grid solution to be used in place of the potential flow solver.

If IGRID = 0, off-body air velocities are determined directly from the potential flow solution. If

IGRID = 1, the panel solution will not be used. Instead, a grid solution will be read in from files

XY.PLT and Q.PLT which are supplied by the user. These files are the grid and flow solution

files in PLOT3D format. The user is referred to Section 10.5 for details on the format for these

files. LEWICE will then interpolate from these points to find the air velocity at the drop location

NASA/CR—2002-211793 38
when calculating trajectories. Valid inputs for this variable are 0 and 1. Other input values will

produce the following warning message:

Valid inputs of IGRID are 0 and 1. Your input value of (value) is out of range. Setting to

IGRID = 0.

Some cases have been made using a grid solution as input to verify that the routines function

as designed. However, this module has not been thoroughly tested and could contain errors. In

addition, since only one time step can be used with this option, it has limited use for ice accretion

results. Therefore if the user selects IGRID = 1, the following warning message is issued:

You are bypassing the potential flow solution to use a grid solution. This option has been

tested on exactly two grids: one single body and one multi-body grid. This procedure may still

contain errors and is not recommended unless you are willing to customize the software for your

use. This option can only be used with a single time step. Setting IFLO = 1

Since the grid read in can only be applicable for the clean airfoil, the number of time steps will

be set to 1 if the user has not already done so. The default value for IGRID is 0 if not specified.

8.3.9 IDEICE

Default Value: IDEICE = 0

IDEICE is a flag that controls which de-icer model will be invoked. If IDEICE = 0 (default),

this routine will not be run. If IDEICE = 1, then a 1D steady state anti-icer will be run to generate

an estimate of the heat required to keep the surface ice free. This solution can then be used as a

starting point for using the de-icing or anti-icing models. If IDEICE = 2 or IDEICE = 3, the software will access a module to analyze 2D transient icing with heater inputs. For IDEICE = 2, the

software will perform the analysis using the standard heat transfer coefficients predicted assuming an ice roughened surface. This option is often preferable for de-icing simulations where ice

will form. For IDEICE = 3, the software will use the laminar heat transfer coefficient, which

assumes a clean surface. This option is recommended for anti-icing simulations or cases which

generate a very small ice shape. A value of IDEICE > 0 also requires an additional input file

NASA/CR—2002-211793 39
which contains information needed for the additional module. The software will prompt the user

for the name of the de-icer input file. The software will ask for an input file for each body in a

multi-element calculation. However, the user can input the same file if the information is the same

for each body. Valid input values are 0, 1, 2, and 3. Other input values will produce the following

warning message:

Valid inputs of IDEICE are 0 to 3. Your input value of (value) is out of range. Setting IDEICE

= 0.

In order to distinguish the attributes of the various options, the following warning message is

generated when IDEICE = 1 is selected:

The anti-icing analysis performed with this option provides only an approximate solution.

Surface temperature and heat flux predictions are reasonable. Heater temperature and hot air

temperature predictions are much higher than actual. IDEICE = 2 or IDEICE = 3 should be used

for more accurate predictions. 

Note: Setting IDEICE = 1 does not affect the ice accretion routine. The software will output

an ice shape as if no heat had been applied. This routine generates a separate file containing the

temperatures and heat fluxes needed to maintain a desired surface temperature which is input by

the user.

Note: This routine treats the current geometry as the airfoil and does not distinguish an iced

airfoil from an un-iced airfoil. Therefore, for IDEICE = 1, only the results obtained in the first

time step are applicable to an anti-icing problem.

When IDEICE = 2 or 3, the following warning message will be displayed:

This option accesses a module which will run MUCH more slowly than a standard (IDEICE =

0) LEWICE run.

When IDEICE = 3, the following additional warning message will be displayed:

NASA/CR—2002-211793 40
This option will use laminar heat transfer coefficients.Some users believe this option will

produce more accurate results for anti-icing cases. However, it is less conservative than the

IDEICE = 2 option.

Note: Both the IDEICE = 2 and IDEICE = 3 options will perform a detailed thermal analysis

within the airfoil, ice and water. The IDEICE = 2 option is recommended for failed thermal cases

with significant ice accretion. The laminar flag, IDEICE = 3, provides consistently better predictions for cases with a clean leading edge. However, it is a less conservative option and has a tendency to overpredict temperatures for some cases.

Note: The output file “NOICE.DAT” contains output from the simplified 1D thermal analysis. This analysis is provided for all cases where IDEICE > 0. When IDEICE = 1, it is the only

thermal analysis performed. It is also performed for IDEICE = 2 and IDEICE = 3 cases as the 1D

option does not take significant computation time. Also see Section 10.1.4.4 for additional capabilities when IDEICE = 2 or 3.

8.3.10 ICP

Default Value: ICP = 0

ICP is a flag which allows surface pressure coefficients from another program to be used in

place of the potential flow module. If ICP = 0, surface pressure coefficients (and hence air velocities) are determined directly from the potential flow solution. If ICP = 1, the panel solution will

not be used. Instead, a file will be read in from file “RFLOW.INP” which is supplied by the user.

This file contains surface pressure coefficients referenced to specified wrap distance values. The

wrap distance is the distance along the surface of the body geometry as measured from some initial reference location. All of the input files for LEWICE 2.2 use the trailing edge on the lower

surface as the reference location. Output files will normally use the stagnation point as the reference location. The format for the input file is covered in Section 10.6 and additional information

is given in Section 8.7. LEWICE 2.2 will then bypass the potential flow module and use these values. Valid inputs for this variable are 0 and 1. Other input values will produce the following warning message:

NASA/CR—2002-211793 41
Valid inputs of ICP are 0 and 1. Your input value of (value) is out of range. Setting to 0.

In addition, since pressure coefficients alone are insufficient to calculate collection efficiencies, this option can only be used in conjunction with the IBETA flag or the IGRID flag. If ICP =

1 and IBETA = 0 and IGRID = 0, the following warning message is issued:

The program cannot calculate trajectories using only surface pressure coefficients. Either

read in collection efficiencies (IBETA = 1) or read in a grid-based flow solution (IGRID = 1).

Setting ICP = 0

Some cases have been made using surface pressure coefficients as input to verify that the routines function as designed. In addition, since the pressure coefficients read in can only be applicable for the initial geometry, only one time step can be used with this option thus it has limited use

for ice accretion results. Therefore if the user selects ICP =1, the following warning message is

issued:

You are bypassing the potential flow solution to use individual pressure coefficients. This

option has seen limited testing. This option can only be used with a single time step. Setting IFLO

= 1

The number of time steps will be set to 1 if the user has not already done so. The default value

for ICP is 0 if not specified.

8.3.11 IBETA

Default Value: IBETA = 0

IBETA is a flag which allows collection efficiencies from another program to be used in place

of the particle trajectory module. If IBETA = 0, collection efficiencies are determined directly

from the particle trajectory module. If IBETA = 1, the trajectory module will not be used. Instead,

a file will be read in from file “RBETA.INP” which is supplied by the user. This file contains collection efficiencies referenced to specified wrap distance values. The format for this file is covered in Section 10.7 and additional information is given in Section 8.7. LEWICE 2.2 will then

NASA/CR—2002-211793 42
bypass the particle trajectory module and use these values. Valid inputs for this variable are 0 and

1. Other input values will produce the following warning message:

Valid inputs of IBETA are 0 and 1. Your input value of (value) is out of range. Setting to 0.

Some cases have been made using collection efficiencies as input to verify that the routines

function as designed. In addition, since only one time step can be used with this option, it has limited use for ice accretion results. Therefore if the user selects IBETA =1, the following warning

message is issued:

You are bypassing the trajectory module to use individual collection efficiencies. This option

has seen limited testing. This option can only be used with a single time step. Setting IFLO = 1

Since the collection efficiencies read in can only be applicable for the initial geometry, the

number of time steps will be set to 1 if the user has not already done so. The default value for

IBETA is 0 if not specified.

8.3.12 IHTC

Default Value: IHTC = 0

IHTC is a flag which allows convective heat transfer coefficients from another program to be

used in place of the integral boundary layer in LEWICE 2.2. If IHTC = 0, convective heat transfer

coefficients are determined directly from the integral boundary layer. If IHTC = 1, the integral

boundary layer will not be used. Instead, a file will be read in from file “RHTC.INP” which is

supplied by the user. This file contains convective heat transfer coefficients referenced to specified wrap distance values. The format for this file is covered in Section 10.8 and additional information is given in Section 8.7. LEWICE 2.2 will then bypass the integral boundary layer routines

and use these values. Valid inputs for this variable are 0 and 1. Other input values will produce the

following warning message:

Valid inputs of IHTC are 0 and 1. Your input value of (value) is out of range. Setting to IHTC

= 0.

NASA/CR—2002-211793 43
The IHTC flag and the IQEX flag from Section 8.3.13 are mutually exclusive. If both are set

equal to one, the following warning message will appear:

This program can use either a convective heat transfer coefficient on the outer surface or a

heat flux, but not both. Setting both IHTC = 0 and IQEX = 0

Some cases have been run using convective heat transfer coefficients as input to verify that

the routines function as designed. In addition, since only one time step can be used with this

option, it has limited use for ice accretion results. Therefore if the user selects IHTC = 1, the following warning message is issued:

You are bypassing the integral boundary layer to use individual convective heat transfer coefficients. This option has seen limited testing. This option can only be used with a single time step.

Setting IFLO = 1

Since the convective heat transfer coefficients read in can only be applicable for the initial

geometry, the number of time steps will be set to 1 if the user has not already done so. The default

value for IHTC is 0 if not specified.

8.3.13 IQEX

Default Value: IQEX = 0

IQEX is a flag which allows external heat fluxes from another program to be used in place of

the integral boundary layer in LEWICE 2.2. If IQEX = 0, convective heat transfer coefficients are

determined directly from the integral boundary layer. If IQEX = 1, the integral boundary layer

will not be used. Instead, a file will be read in from file “QEXTIN.INP” which is supplied by the

user. This file contains external heat fluxes referenced to specified wrap distance values. The format for this file is covered in Section 10.9 and additional information is given in Section 8.7.

LEWICE 2.2 will then bypass the integral boundary layer routines and calculate convective heat

transfer coefficients from the equation

NASA/CR—2002-211793 44
(5)

where q is the heat flux read in, Ts is the surface temperature at a given wrap distance location

and T∞ is the ambient temperature. Some users may find external heat flux input more convenient

than the convective heat transfer coefficient.

Valid inputs for this variable are 0 and 1. Other input values will produce the following warning message:

Valid inputs of IQEX are 0 and 1. Your input value of (value) is out of range. Setting to 0.

The IHTC flag from Section 8.3.12 and the IQEX flag from Section 8.3.13 are mutually

exclusive. If both are set equal to one, the following warning message will appear:

This program can use either a convective heat transfer coefficient on the outer surface or a

heat flux, but not both. Setting both IHTC = 0 and IQEX = 0

Some cases have been run using external heat fluxes as input to verify that the routines function as designed. In addition, since only one time step can be used with this option, it has limited

use for ice accretion results. Therefore if the user selects IQEX = 1, the following warning message is issued:

You are bypassing the integral boundary layer to use individual heat flux values. This option

has seen limited testing. This option can only be used with a single time step. Setting IFLO = 1

Since the external heat fluxes read in can only be applicable for the initial geometry, the number of time steps will be set to 1 if the user has not already done so. The default value for IQEX is

0 if not specified.

&END

This line concludes the section for the LEW20 namelist. The following table lists an example

input for this namelist.

h q

Ts T ∞ ( ) – = -----------------------

NASA/CR—2002-211793 45
Table 59: Example LEW20 Namelist

 &LEW20

 ITIMFL = 1

 TSTOP = 300.

 IBOD = 1

 IFLO = 5

 DSMN = 4.D-4

 NPL = 24

 RHOP = 1000.

 IGRID = 0

 IDEICE = 0

 ICP = 0

 IBETA = 0

 IHTC = 0

 IQEX = 0

 &END 

8.4 DIST Namelist

The DIST namelist defines the particle size and distribution. For each variable, there are 10

possible values, as the software can handle up to a 10 drop size distribution.

&DIST

This line identifies the start of this namelist section. Refer to the list of namelist errors at the

beginning of this section if there are problems with this input.

8.4.1 FLWC

Default Value: FLWC = 1.

FLWC is the volume fraction of the total liquid water content contained in each drop size. The

associated drop sizes are discussed in the next section. The sum of the FLWC values must equal

one. If the sum of the FLWC values is not one, the following warning message is generated:

NASA/CR—2002-211793 46
The FLWC values are the Fractional Liquid Water Content attributed to each droplet size.

These values must add to one (1). Your input of (value) does not add up to 1. The program will

adjust your FLWC values proportionately so they add to 1.

If the sum of the FLWC values is greater than zero, the individual values input will be

increased/decreased so that their sum equals one. If this sum is ≤ 0, then the water mass will be

equally distributed for each of the drop sizes input (FLWC = 1/[number of drop sizes input]). 

The program will determine the number of drop sizes in the distribution by looking for the

first occurrence where FLWC = 0. Therefore, the user should not place zeros until the end of the

distribution is reached.

Table 60: Example of bad input for FLWC

&DIST

 FLWC = 0.05, 0.1, 0.2, 0.3, 0.0, 0.0, 0.0, 0.2, 0.1, 0.05

 DPD = 6.2, 10.4, 14.2, 20.0, 0.0, 0.0, 0.0, 27.4, 34.8, 44.4

 &END

Table 61: Example of correct input for FLWC

 &DIST

 FLWC = 0.05, 0.1, 0.2, 0.3, 0.2, 0.1, 0.05, 0.0, 0.0, 0.0

 DPD = 6.2, 10.4, 14.2, 20.0, 27.4, 34.8, 44.4, 0.0, 0.0, 0.0

 &END

8.4.2 DPD

Default Value: DPD = 20

DPD is the size, in microns, of the water drops. If only one size is input, it is the MVD

(median volume droplet). MVD is not an input variable to LEWICE. The MVD is calculated from

the individual drop sizes input in this section. The individual drop sizes and the calculated MVD

must both be greater than zero. An input drop size less than zero will generate the following error

message:

Severe input error: Drop size must be > 0! DPD = (value) for bin number (value).

NASA/CR—2002-211793 47
After checking the other inputs, the program will exit due to this error.

A calculated MVD less than zero will generate the following additional error message:

Severe input error: MVD drop size <= 0! MVD = (value)

In addition, LEWICE will generate warning messages if the drop size input is outside of the

range in the validation database. If the MVD drop size is below 15 microns, the following warning message is generated:

Your MVD value of (value) is below 15 microns. No validation data is available. The accuracy of the software in this situation is unknown.

If the MVD drop size is greater than 270 microns, the following warning message is generated:

The MVD of your drop size distribution exceeds 270 microns. No validation data is available

for your drop size of (value) microns. The accuracy of the software in this situation is unknown.

Due to the recent popularity of drop size inputs outside the FAA certification envelope, it is

worth emphasizing the above warning message. This statement does not imply that LEWICE cannot run the drop size distribution input. It most likely can. The warning statement does not imply

that the results will be inaccurate. LEWICE results for exceedence conditions are quite encouraging in this respect. The statement simply points out that limited experimental data is yet available

at these drop sizes. Since the results cannot be experimentally validated, the true accuracy of the

results cannot be verified. The following plot shows the range of drop sizes in the validation database versus liquid water content.

NASA/CR—2002-211793 48
Figure 1: Test Conditions in Database Used for Software Validation

If the MVD drop size is greater than 50 microns, the following warning message is generated:

Your MVD of (value) exceeds the FAA intermittent maximum drop size of 50 microns.

Although some data has been collected in this regime and used for software validation, there is

not enough data available to consider the software validated for this drop size. The accuracy of

the software in this situation is unknown.

Once again, consult the earlier statement concerning the implications of running exceedence

conditions. An analysis of the capabilities of LEWICE in this regime can also be found in the proceedings of an FAA conference in 199610.

&END

This line concludes the section for the DIST namelist. The following table lists an example

input for this namelist.

0

0.5

1

1.5

2

2.5

3

0 50 100 150 200 250 300

Range of Experimental Data

LWC

MVD

FAR Part 25 App. C Continuous Maximum

FAR Part 25 App. C Intermittent Maximum

Exceedence Conditions

NASA/CR—2002-211793 49
Table 62: Example DIST Namelist

 &DIST

 FLWC = 0.05, 0.1, 0.2, 0.3, 0.2, 0.1, 0.05, 0.0, 0.0, 0.0

 DPD = 6.2, 10.4, 14.2, 20.0, 27.4, 34.8, 44.4, 0.0, 0.0, 0.0

 &END

Note: The example provided is a Langmuir ‘D’ drop size distribution, with an MVD of 20

μm.

Note: If the user does not specify input values, the default value for this namelist is a monodispersed drop size of 20 μm.

8.5 ICE1 Namelist

The ICE1 namelist provides the meteorological and flight conditions of the icing simulation.

&ICE1

This line identifies the start of this namelist section. Refer to the list of namelist errors at the

beginning of this section if there are problems with this input.

8.5.1 CHORD

Default Value: CHORD = 0.9144

CHORD is the distance from the leading edge to the trailing edge in meters. For a cylinder,

this represents the cylinder diameter. For airfoils, it is the standard chord length. For a multi-body

simulation, CHORD represents the reference length used to nondimensionalize the coordinates

input. A typical value used for multi-element airfoils is the length of the airfoil in the stowed configuration. The input must be greater than zero. For input values of CHORD ≤ 0, the following

error message is generated:

Severe input error: Chord must be greater than zero! CHORD = (value)

After checking the other inputs, the program will exit due to this error.

NASA/CR—2002-211793 50
If no value is input for chord, its default value is 0.9144 m (36”). The range of chord lengths

in the experimental database is 13.9” to 78”.

8.5.2 AOA

Default Value: AOA = 0.

This is the angle of the body(s) as input with respect to the flow in degrees. There are no error

messages associated with this input. If the angle of attack is greater than 6° (or less than -6°), the

following warning message will be generated:

Angle of attack value of (value) may incur separation once ice forms. This may not be modeled well by the software. The accuracy of the software in this situation is unknown.

Potential flow cannot model stall or post-stall behavior. The user should also note that in the

validation test procedure, the angle of attack input into the software was sometimes different from

the actual angle of attack value. This difference was made to compensate for the difference in predicted lift using a potential flow software and the actual lift of the clean airfoil.

If no value of AOA is supplied by the user, the value will be set to 0 degrees. The range of

angle of attack values in the validation database is -4 to +7 degrees.

8.5.3 VINF

Default Value: VINF = 90

VINF is the ambient velocity (the flight speed) in m/s. 

Note: Knots * 0.51481 = m/s; MPH * 0.447 = m/s

The input value for VINF must be greater than zero. If a value of VINF ≤ 0 is input, the following error message will be generated:

Severe input error: Velocity must be greater than zero! VINF = (value)

NASA/CR—2002-211793 51
After checking the other inputs, the program will exit due to this error.

An upper limit on Mach number exists within the software. If the ambient Mach number is ≥

1, the following error message is generated:

Mach number is => 1! Cannot calculate supersonic flow with this software! Mach No. =

(value)

After checking the other inputs, the program will exit due to this error.

In addition, high subsonic Mach numbers have not been validated against experimental data.

Problems may exist due to the limitations of potential flow. The following warning message is

generated if the ambient Mach number exceeds 0.45 (the highest value in the validation database).

High mach number of (value) may not be modeled well by the software.The accuracy of the

software in this situation is unknown.

If no value of VINF is supplied by the user, its default value is 90 m/s. The range of velocity

values in the validation database was 56 m/s to 146 m/s. In terms of Reynolds number, the range

of data was 2.26*106 to 1.3*107. In terms of Mach number, the range of data was 0.17 to 0.45.

8.5.4 LWC

Default Value: LWC = 0.54

LWC is the liquid water content of the air in g/m3. This value must be ≥ 0. If a negative value

is input, the following error message will be generated:

Severe input error: LWC cannot be negative! LWC = (value)

After checking the other inputs, the program will exit due to this error.

In addition, if the LWC value input is greater than 2 g/m3, the following warning message will

be generated:

NASA/CR—2002-211793 52
There is no data available to validate the software for LWC values this high. LWC = (value).

The accuracy of the software in this situation is unknown.

The user should also consult the statement concerning the use of exceedence conditions listed

in the description of the drop size input.

If no value of LWC is input by the user, its default value is 0.54 g/m3. The range of values for

Liquid Water Content in the validation database was 0.31 to 1.8 g/m3. See Figure 1 for a plot of

LWC versus MVD for the validation database test points.

8.5.5 TINF

Default Value: TINF = 268.15

TINF is the ambient static temperature in degrees Kelvin. This input value must be greater

than zero. A value of TINF ≤ 0 will generate the following error message:

Temperature input is <= zero! Make sure temperature is in degrees Kelvin. TINF = (value)

After checking the other inputs, the program will exit due to this error.

In addition, warning messages are generated when the static temperature is outside the normal

icing regime. If the input value of TINF is less than 240 K, the following warning message is generated:

It is unlikely that supercooled droplets exist below 240 Kelvin. TINF = (value) Make sure

your input value is in degrees Kelvin. The accuracy of the software in this situation is unknown.

If the input value of TINF is greater than 273.15 K, the following warning message is generated:

No ice will form at above freezing temperatures! Is this what you want? TINF = (value)

NASA/CR—2002-211793 53
An example of a case where the use of above freezing temperatures is warranted would be to

match experimental data on droplet collection efficiency which is taken at above freezing temperatures.

Note: The data supplied to researchers is often the total temperature, not the static temperature. Make certain the value input is correct!

 (6)

where 

Ts = static temperature, K

To = total temperature, K

V∞ = velocity, m/s

cp = specific heat of air, J/kg/K

If no value of TINF is input by the user, its default value is 268.15 K. The range of values in

the validation database was 241.3 K to 270.2 K.

8.5.6 PINF

Default Value: PINF = 100000.

PINF is the ambient static pressure in Pascals (N/m2). The input value for PINF must be

greater than zero. An input value of PINF ≤ 0 will generate the following error message:

Severe input error: Pressure input is <= zero! PINF = (value)

After checking the other inputs, the program will exit due to this error.

Ts To

V ∞

2

2c p

---------–=

NASA/CR—2002-211793 54
No other warning messages or error messages are generated for this input variable. However,

it should be noted that all of the validation tests used an input of 105 N/m2. 

Note: Ambient pressure is not recorded as part of the tunnel data, so the exact value during

the tests is unknown. However, since ambient pressure is at best a secondary effect on the ice

accretion process and since the NASA Glenn Research Center Icing Research Tunnel (IRT) is not

a pressurized tunnel, a representative value near atmospheric pressure was used for the comparison.

Note: To a good approximation, for a ‘standard atmosphere’, the following equation can be

used:

 where

P = pressure in N/m2 and 

H = height (altitude) in meters

Note: lbf/in2 * 6894.7 = N/m2; atmospheres * 101330 = N/m2; in. Hg * 3386.4 = N/m2

If no value of PINF is input by the user, its default value is 105 N/m2.

8.5.7 RH

Default Value: RH = 100.

RH is the relative humidity and is input in percent relative humidity. This input value is normally assumed to be 100%, unless the actual value is known. Relative humidity is not recorded as

part of the tunnel data, so the exact value during the tests is unknown. However, since relative

humidity is at best a secondary effect on the ice accretion process, a value of 100% can be

assumed. The value of relative humidity must be in the range 0% ≤ RH ≤ 100%. Input values outside this range will produce the following error message:

Relative humidity must be between 0% and 100%. Your input of (value) is outside this range.

P 100920 11.35 – 0.00039456 H H2

+=

NASA/CR—2002-211793 55
After checking the other inputs, the program will exit due to this error.

If no value of relative humidity is input by the user, its default value is 100%.

&END

This line concludes the section for the ICE1 namelist. The following table lists an example

input for this namelist.

Table 63: Example ICE1 Namelist

 &ICE1

 CHORD = 0.9144

 AOA = 0.0 

 VINF = 89.5

 LWC = 0.34

 TINF = 269.

 PINF = 100000.0

 RH = 100.0

 &END

8.6 LPRNT Namelist

The LPRNT namelist controls output file print options for LEWICE 2.2. Users can limit the

amount of information sent to each printout file which saves disk space and computation time.

&LPRNT

This line identifies the start of this namelist section. Refer to the list of namelist errors at the

beginning of this section if there are problems with this input.

8.6.1 FPRT

 Default Value: FPRT = 1

If FPRT = 0, the flow solution output (FLOW.DAT and PRES.DAT) will not be written. If

FPRT = 1, every 10th control volume will be written to reduce the size of the output. If FPRT = 2,

NASA/CR—2002-211793 56
every control volume will be output. Valid inputs for FPRT are 0, 1 and 2. Other input values will

produce the following warning message:

Valid inputs of FPRT are 0, 1, and 2. Your input value of (value) is out of range. Setting to 1.

If no value of FPRT is input by the user, its value will default to 1.

8.6.2 HPRT

Default Value: HPRT = 1

If HPRT = 0, the heat transfer coefficients (HTC.DAT) will not be written. If HPRT = 1,

every 10th control volume will be written to reduce the size of the output. If HPRT = 2, every

control volume will be output. Valid inputs for HPRT are 0, 1 and 2. Other input values will produce the following warning message:

Valid inputs of HPRT are 0, 1, and 2. Your input value of (value) is out of range. Setting to 1.

If no value of HPRT is input by the user, its value will default to 1.

8.6.3 BPRT

 Default Value: BPRT = 1

If BPRT = 0, the collection efficiencies will not be written. If BPRT = 1, they will be written.

Collection efficiencies are only written for the panel geometry, not for the control volume geometry. There is no need for a reduced input flag. Valid inputs for BPRT are 0 and 1. Other input values will produce the following warning message:

Valid inputs of BPRT are 0 and 1. Your input value of (value) is out of range. Setting to 1.

If no value of BPRT is input by the user, its value will default to 1.

NASA/CR—2002-211793 57
8.6.4 EPRT

 Default Value: EPRT = 0

If EPRT = 0, the energy balance output (,TEMP.DAT QENER.DAT, XKINIT2.DAT) will

not be written. If EPRT = 1, every 10th control volume will be written to reduce the size of the

output. If EPRT = 2, every control volume will be output. Valid inputs for EPRT are 0, 1 and 2.

Other input values will produce the following warning message:

Valid inputs of EPRT are 0, 1, and 2. Your input value of (value) is out of range. Setting to 0.

If no value of EPRT is input by the user, its value will default to 0. Note that the default state

results in no printout to these files.

8.6.5 MPRT

 Default Value: MPRT = 0

If MPRT = 0, the mass balance output (MASS.DAT, FRACT.DAT, DYICE.DAT,

DENS.DAT) will not be written. If MPRT = 1, every 10th control volume will be written to

reduce the size of the output. If MPRT = 2, every control volume will be output. Valid inputs for

MPRT are 0, 1 and 2. Other input values will produce the following warning message:

Valid inputs of MPRT are 0, 1, and 2. Your input value of (value) is out of range. Setting to 0.

If no value of EPRT is input by the user, its value will default to 0. Note that the default state

results in no data written to these files.

8.6.6 TPRT

Default Value: TPRT = 0

If TPRT = 0, the x,y coordinates of individual droplet trajectories will not be written

(TRAJ1.DAT, TRAJ2.DAT, TRAJ3.DAT, TRAJ4.DAT, TRAJ5.DAT). If TPRT = 1, only trajecNASA/CR—2002-211793 58
tories used for the collection efficiency calculation will be written. If TPRT = 2, all trajectories

will be written. Valid inputs for TPRT are 0, 1 and 2. Other input values will produce the following warning message:

Valid inputs of TPRT are 0, 1, and 2. Your input value of (value) is out of range. Setting to 0.

If no value of TPRT is input by the user, its value will default to 0. Note that the default state

results in no data written to these files.

Note: The trajectories calculated for a given body are all written sequentially to the file. If

only one body exists, only TRAJ1.DAT will be created.

Note: The definition of this flag has been reversed from version 1.6!

8.6.7 IDBF

 Default Value: IDBF = 0

If IDBF = 0, debug information will not be written. If IDBF = 1, debug info will be written to

the screen and to the file “JUNK.DAT”.Valid inputs for IDBF are 0 and 1. Other input values will

produce the following warning message:

Valid inputs of IDBF are 0 and 1. Your input value of (value) is out of range. Setting to 0.

If no value of IDBF is input by the user, its value will default to 0. Note that the default state

results in only limited data written to this file.

&END

This line concludes the section for the LPRNT namelist. The following table lists an example

input for this namelist.

Table 64: Example LPRNT Namelist

 &LPRNT 

 FPRT = 1

NASA/CR—2002-211793 59
 HPRT = 1

 BPRT = 1

 EPRT = 0

 MPRT = 0

 TPRT = 0

 IDBF = 0

 &END

8.7 RDATA Namelist

The RDATA namelist controls additional input file options for LEWICE 2.2. Users can

bypass various calculations within LEWICE 2.2 by reading in data from external files. This

approach is useful for reading in results from other programs such as a 2D Naviér-Stokes flow

program or 2D streamlines extracted from a 3D CFD package. The input flags were presented in

the LEW20 Namelist in Section 8.3.

&RDATA

This line identifies the start of this namelist section. Refer to the list of namelist errors at the

beginning of this section if there are problems with this input.

8.7.1 ISCOLC, JSCOLC, KSCOLC, SSLOPC, SZEROC

The first five lines of this data input section contains variables used when reading pressure

coefficient data (i.e. when ICP = 1). This input option can be useful to transfer data from a

Naviér-Stokes program such as WIND for a 2D anti-icing analysis with LEWICE 2.2. These variables can be read regardless of the value of ICP however. The data line contains five variables

which define the format of the pressure coefficient data. The first three variables (ISCOLC,

JSCOLC and KSCOLC) define the column numbers in the pressure coefficient input data file

which contain the requested values. ISCOLC defines which column contains the wrap distance.

JSCOLC defines the column which contains the pressure coefficients, and KSCOLC defines the

total number of columns in the file. A file which contained only the necessary data would therefore have ISCOLC = 1, JSCOLC = 2, and KSCOLC = 2. (ISCOLC = 2, JSCOLC = 1 and

KSCOLC = 2 would also be valid.) This type of data input format was used since the data probaNASA/CR—2002-211793 60
bly came from a separate program and this format style reduces the amount of reformatting

needed for LEWICE 2.2. ISCOLC must be at least 1 and no greater than KSCOLC. If a value is

read which is outside this range, the following warning message will be generated:

Columns for 1st variable must be at least one (1)

and no greater than the number of columns.

Your value of (value) is out of range. Setting ISCOLC = 1

Similarly, JSCOLC must be at least 1 and no greater than KSCOLC. It also cannot be the

same as ISCOLC. If a value is read which is outside this range, the following warning message

will be generated:

Columns for 2nd variable must be at least one (1) 

and no greater than the number of columns.

Your value of (value) is out of range. Setting JSCOLC = 1

If the values for ISCOLC and JSCOLC are the same, the following warning message will be

generated:

Columns for 1st and 2nd variable cannot be the same.

Setting ISCOLC = 1 and JSCOLC = KSCOLC

The total number of columns, KSCOLC must be at least 2, but can be higher. If a value is read

which is outside this range, the following warning message will be generated:

Number of columns must be at least two (2) 

 Your value of (value) is out of range. Setting KSCOLC = 2

NASA/CR—2002-211793 61
The fourth variable, SSLOPC, defines the conversion factor which will be applied to the wrap

distance values input. LEWICE 2.2 uses wrap distances in dimensionless values (value divided by

chord). The wrap distance values input can be in any set of units if the user supplies the correct

conversion to SSLOPC. The slope can be positive or negative, but not zero. If a value of zero is

read for this data input, the following warning message will be generated:

Slope cannot be zero.

Setting slope = 1.

The fifth value in this data input section, SZEROC, defines the offset of the input wrap distances from those needed for LEWICE 2.2. If SZEROC = 0., the software will assume that a wrap

distance value of 0 in the input data corresponds to the lower surface of the trailing edge. If this is

not the case, the user should supply a value (in dimensionless distance) which supplies the correct

offset. The value for SZEROC should not be greater than the wrap distance from the leading edge

to the trailing edge. If the value read is greater than 1.2 (1.2 chord lengths), the following warning

message will be generated:

Offset may be past the trailing edge. Setting SZEROC = 1.

The following equation is used within LEWICE to convert wrap distance values using

SSLOPC and SZEROC:

(7)

where sLEWICE is the wrap distance used by LEWICE and sinput is the wrap distance in the

input file.

The format of the input data file “RFLOW.INP” and corresponding error messages will be

described in Section 10.6.

8.7.2 ISCOLB, JSCOLB, KSCOLB, SSLOPB, SZEROB

sLEWICE sinputsslopc szeroc +=

NASA/CR—2002-211793 62
The next five lines of this data input section contains variables used when reading collection

efficiency data (i.e. when IBETA = 1). This input option can be useful to transfer data from a 3D

trajectory program such as LEWI3DGR for a 2D anti-icing analysis with LEWICE 2.2. These

variables can be read regardless of the value of IBETA however. The data line contains five variables which define the format of the collection efficiency data. The first three variables (ISCOLB,

JSCOLB and KSCOLB) define the column numbers in the collection efficiency input data file

which contain the requested values. ISCOLB defines which column contains the wrap distance.

JSCOLB defines the column which contains the collection efficiencies, and KSCOLB defines the

total number of columns in the file. A file which contained only the necessary data would therefore have ISCOLB = 1, JSCOLB = 2, and KSCOLB = 2. (ISCOLB = 2, JSCOLB = 1 and

KSCOLB = 2 would also be valid.) This type of data input format was used since the data probably came from a separate program and this format style reduces the amount of reformatting

needed for LEWICE 2.2. ISCOLB must be at least 1 and no greater than KSCOLB. If a value is

read which is outside this range, the following warning message will be generated:

Columns for 1st variable must be at least one (1)

and no greater than the number of columns.

Your value of (value) is out of range. Setting ISCOLB = 1

Similarly, JSCOLB must be at least 1 and no greater than KSCOLB. It also cannot be the

same as ISCOLB. If a value is read which is outside this range, the following warning message

will be generated:

Columns for 2nd variable must be at least one (1) 

and no greater than the number of columns.

Your value of (value) is out of range. Setting JSCOLB = 1

If the values for ISCOLB and JSCOLB are the same, the following warning message will be

generated:

NASA/CR—2002-211793 63
Columns for 1st and 2nd variable cannot be the same.

Setting ISCOLB = 1 and JSCOLB = KSCOLB

The total number of columns, KSCOLB must be at least 2, but can be higher. If a value is read

which is outside this range, the following warning message will be generated:

Number of columns must be at least two (2) 

 Your value of (value) is out of range. Setting KSCOLB = 2

The fourth variable, SSLOPB, defines the conversion factor which will be applied to the wrap

distance values input. LEWICE 2.2 uses wrap distances in dimensionless values (value divided by

chord). The wrap distance values input can be in any set of units if the user supplies the correct

conversion to SSLOPB. The slope can be positive or negative, but not zero. If a value of zero is

read for this data input, the following warning message will be generated:

Slope cannot be zero.

Setting slope = 1.

The last value in this data input subsection, SZEROB, defines the offset of the input wrap distances from those needed for LEWICE 2.2. If SZEROB = 0., the software will assume that a wrap

distance value of 0 in the input data corresponds to the lower surface trailing edge. If this is not

the case, the user should supply a value (in dimensionless distance) which supplies the correct

offset. The value for SZEROB should not be greater than the wrap distance from the leading edge

to the trailing edge. If the value read is greater than 1.2 (1.2 chord lengths), the following warning

message will be generated:

Offset may be past the trailing edge. Setting SZEROB = 1.

The following equation is used within LEWICE to convert wrap distance values using

SSLOPB and SZEROB:

NASA/CR—2002-211793 64
(8)

where sLEWICE is the wrap distance used by LEWICE and sinput is the wrap distance in the

input file. The format of the input data file “RBETA.INP” and corresponding error messages will

be described in Section 10.7.

8.7.3 ISCOLH, JSCOLH, KSCOLH, SSLOPH, SZEROH

The next five lines of this data input section contains variables used when reading external

heat transfer coefficient data (i.e. when IHTC = 1). This input option can be useful to transfer data

from a 2D Naviér-Stokes program or a 3D trajectory program such as LEWI3DGR for a 2D icing

or anti-icing analysis with LEWICE 2.2. These variables can be read regardless of the value of

IHTC however. The data line contains five variables which define the format of the external heat

transfer coefficient data. The first three variables (ISCOLH, JSCOLH and KSCOLH) define the

column numbers in the external heat transfer coefficient input data file which contain the

requested values. ISCOLH defines which column contains the wrap distance. JSCOLH defines

the column which contains the external heat transfer coefficients, and KSCOLH defines the total

number of columns in the file. A file which contained only the necessary data would therefore

have ISCOLH = 1, JSCOLH = 2, and KSCOLH = 2. (ISCOLH = 2, JSCOLH = 1 and KSCOLH =

2 would also be valid.) This type of data input format was used since the data probably came from

a separate program and this format style reduces the amount of reformatting needed for LEWICE

2.2. ISCOLH must be at least 1 and no greater than KSCOLH. If a value is read which is outside

this range, the following warning message will be generated:

Columns for 1st variable must be at least one (1)

and no greater than the number of columns.

Your value of (value) is out of range. Setting ISCOLH = 1

Similarly, JSCOLH must be at least 1 and no greater than KSCOLH. It also cannot be the

same as ISCOLH. If a value is read which is outside this range, the following warning message

will be generated:

sLEWICE sinputsslopb szerob +=

NASA/CR—2002-211793 65
Columns for 2nd variable must be at least one (1) 

and no greater than the number of columns.

Your value of (value) is out of range. Setting JSCOLH = 1

If the values for ISCOLH and JSCOLH are the same, the following warning message will be

generated:

Columns for 1st and 2nd variable cannot be the same.

Setting ISCOLH = 1 and JSCOLH = KSCOLH

The total number of columns, KSCOLH must be at least 2, but can be higher. If a value is read

which is outside this range, the following warning message will be generated:

Number of columns must be at least two (2) 

 Your value of (value) is out of range. Setting KSCOLH = 2

The fourth variable, SSLOPH, defines the conversion factor which will be applied to the wrap

distance values input. LEWICE 2.2 uses wrap distances in dimensionless values (value divided by

chord). The wrap distance values input can be in any set of units if the user supplies the correct

conversion to SSLOPH. The slope can be positive or negative, but not zero. If a value of zero is

read for this data input, the following warning message will be generated:

Slope cannot be zero.

Setting slope = 1.

The last value in this data input subsection, SZEROH, defines the offset of the input wrap distances from those needed for LEWICE 2.2. If SZEROH = 0., the software will assume that a wrap

distance value of 0 in the input data corresponds to the lower surface trailing edge. If this is not

the case, the user should supply a value (in dimensionless distance) which supplies the correct

offset. The value for SZEROH should not be greater than the wrap distance from the leading edge

NASA/CR—2002-211793 66
to the trailing edge. If the value read is greater than 1.2 (1.2 chord lengths), the following warning

message will be generated:

Offset may be past the trailing edge. Setting SZEROH = 1.

The following equation is used within LEWICE to convert wrap distance values using

SSLOPH and SZEROH:

(9)

where sLEWICE is the wrap distance used by LEWICE and sinput is the wrap distance in the

input file. The format of the input data file “RHTC.INP” and corresponding error messages will

be described in Section 10.8.

8.7.4 ISCOLX, JSCOLX, KSCOLX, SSLOPX, SZEROX

The final five lines of this data input section contains variables used when reading external

heat flux data (i.e. when IQEX = 1). This input option can be useful to transfer data from a

Naviér-Stokes program such as WIND for a 2D anti-icing analysis with LEWICE 2.2. This option

was provided since the convective heat flux may be easier for the user to obtain from the NaviérStokes flow solver. These variables can be read regardless of the value of IQEX however. The

data line contains five variables which define the format of the external heat flux data. The first

three variables (ISCOLX, JSCOLX and KSCOLX) define the column numbers in the external

heat flux input data file which contain the requested values. ISCOLX defines which column contains the wrap distance. JSCOLX defines the column which contains the external heat fluxes, and

KSCOLX defines the total number of columns in the file. A file which contained only the necessary data would therefore have ISCOLX = 1, JSCOLX = 2, and KSCOLX = 2. (ISCOLX = 2,

JSCOLX = 1 and KSCOLX = 2 would also be valid.) This type of data input format was used

since the data probably came from a separate program and this format style reduces the amount of

reformatting needed for LEWICE 2.2. ISCOLX must be at least 1 and no greater than KSCOLX.

If a value is read which is outside this range, the following warning message will be generated:

Columns for 1st variable must be at least one (1)

sLEWICE sinputssloph szeroh +=

NASA/CR—2002-211793 67
and no greater than the number of columns.

Your value of (value) is out of range. Setting ISCOLX = 1

Similarly, JSCOLX must be at least 1 and no greater than KSCOLX. It also cannot be the

same as ISCOLX. If a value is read which is outside this range, the following warning message

will be generated:

Columns for 2nd variable must be at least one (1) 

and no greater than the number of columns.

Your value of (value) is out of range. Setting JSCOLX = 1

If the values for ISCOLX and JSCOLX are the same, the following warning message will be

generated:

Columns for 1st and 2nd variable cannot be the same.

Setting ISCOLX = 1 and JSCOLX = KSCOLX

The total number of columns, KSCOLX must be at least 2, but can be higher. If a value is read

which is outside this range, the following warning message will be generated:

Number of columns must be at least two (2) 

 Your value of (value) is out of range. Setting KSCOLX = 2

The fourth variable, SSLOPX, defines the conversion factor which will be applied to the wrap

distance values input. LEWICE 2.2 uses wrap distances in dimensionless values (value divided by

chord). The wrap distance values input can be in any set of units if the user supplies the correct

conversion to SSLOPX. The slope can be positive or negative, but not zero. If a value of zero is

read for this data input, the following warning message will be generated:

Slope cannot be zero.

NASA/CR—2002-211793 68
Setting slope = 1.

The last value in this data input section, SZEROX, defines the offset of the input wrap distances from those needed for LEWICE 2.2. If SZEROX = 0., the software will assume that a wrap

distance value of 0 in the input data corresponds to the lower surface of the trailing edge. If this is

not the case, the user should supply a value (in dimensionless distance) which supplies the correct

offset. The value for SZEROX should not be greater than the wrap distance from the leading edge

to the trailing edge. If the value read is greater than 1.2 (1.2 chord lengths), the following warning

message will be generated:

Offset may be past the trailing edge. Setting SZEROX = 1.

The following equation is used within LEWICE to convert wrap distance values using

SSLOPX and SZEROX:

(10)

where sLEWICE is the wrap distance used by LEWICE and sinput is the wrap distance in the

input file. The format of the input data file “QEXTIN.INP” and corresponding error messages

will be described in Section 10.9. Table 7 shows an example of the input data for this section.

Table 65: Example input for RDATA namelist 

 &RDATA

 ISCOLC = 4

 JSCOLC = 6

 KSCOLC = 6

 SSLOPC = 3.937d0

 SZEROC = 0.d0

 ISCOLB = 1

 JSCOLB = 2

 KSCOLB = 2

 SSLOPB = 3.937d0

 SZEROB = 0.d0

 ISCOLH = 1

 JSCOLH = 2

sLEWICE sinputsslopx szerox +=

NASA/CR—2002-211793 69
 KSCOLH = 2

 SSLOPH = 3.937d0

 SZEROH = 0.d0

 ISCOLX = 1

 JSCOLX = 2

 KSCOLX = 2

 SSLOPX = 3.937d0

 SZEROX = 0.d0

 $END

8.8 Complete Example Case Input File

This concludes the section describing the variables in the main input file. The following table

lists an example input for this file.

Table 66: Example Test Input File

 Example 1

 &LEW20

 ITIMFL = 1

 TSTOP = 300.

 IBOD = 1

 IFLO = 5

 DSMN = 4.D-4

 NPL = 24

 RHOP = 1000.

 IGRID = 0

 IDEICE = 0

 ICP = 1

 IBETA = 1

 IHTC = 1

 I3D = 1

 IQEX = 1

 &END 

 &DIST

 FLWC = 0.05, 0.1, 0.2, 0.3, 0.2, 0.1, 0.05, 0.0, 0.0, 0.0

 DPD = 6.2, 10.4, 14.2, 20.0, 27.4, 34.8, 44.4, 0.0, 0.0, 0.0

NASA/CR—2002-211793 70
 &END

 &ICE1

 CHORD = 0.9144

 AOA = 0.0 

 VINF = 89.5

 LWC = 0.34

 TINF = 269.

 PINF = 100000.0

 RH = 100.0

 &END

 &LPRNT 

 FPRT =1

 HPRT =1

 BPRT =1

 EPRT =0

 MPRT =0

 TPRT =0

 IDBF =0

 &END

 &RDATA

 ISCOLB = 1

 JSCOLB = 2

 KSCOLB = 2

 SSLOPB = 3.937d0

 SZEROB = 0.d0

 ISCOLH = 1

 JSCOLH = 2

 KSCOLH = 2

 SSLOPH = 3.937d0

 SZEROH = 0.d0

 ISCOLC = 4

 JSCOLC = 6

 KSCOLC = 6

 SSLOPC = 3.937d0

 SZEROC = 0.d0

 ISCOLX = 1

NASA/CR—2002-211793 71
 JSCOLX = 2

 KSCOLX = 2

 SSLOPX = 3.937d0

 SZEROX = 0.d0

 $END

8.9 Extent of Data in Validation Database

This section will summarize the range of experimental data used to validate LEWICE 2.2.

LEWICE will most likely produce results outside of these ranges. However, since no experimental data is available for validation, the true accuracy of the results cannot be verified. This statement does not imply that LEWICE cannot run the data input. It most likely can. The warning

statement(s) generated do not imply that the results will be inaccurate. The statement simply

points out that no experimental data is yet available.

Table 67: Range of Experimental Data for Validation

Variable Range

Time: 2 min. to 45 min.

Chord: 13.9 inches to 78 inches

AOA: -4° to 7°

Velocity: 56 m/s to 146 m/s

Reynolds Number: 2.26*106 to 1.3*107

Mach Number: 0.17 to 0.45

LWC: 0.31 g/m3 to 1.8 g/m3

MVD: 15 μm to 270 μm

Temperature (static): -25.3°F to 26.7°F

Temperature (total): -15°F to 33°F

NASA/CR—2002-211793 72
Chapter 9: Body Geometry Input

This section will describe the proper format for the input to the geometry file(s). It will also

describe warning messages and error messages which could result from an improperly formatted

file. It should be noted that all of the validation data uses airfoils. Although LEWICE can simulate

any enclosed body (or bodies), the validation performed to date has been limited to the available

data1.

 In the interactive input to the program, LEWICE 2.2 will prompt the user for the file name(s)

of the geometry input file(s). A separate input file must be provided for each body being simulated. If only one body is simulated, only one geometry file will be read in. Each line of the geometry input file contains an x,y coordinate pair for the body geometry. The x-coordinate is listed

first. The format of the data is free-format for the x,y coordinates. A sample body input geometry

is listed in Table 10 below.

Table 68: Example Body Geometry (NACA 23014)

1.0006 -0.0025295

0.98460 -0.0049304

0.96895 -0.0072317

0.95325 -0.0094792

0.93745 -0.011684

0.92169 -0.013835

0.90590 -0.015936

0.89007 -0.017990

0.87424 -0.019997

0.85838 -0.021958

0.84252 -0.023873

0.82664 -0.025742

0.81073 -0.027568

0.79485 -0.029346

0.77894 -0.031082

0.76300 -0.032776

0.74707 -0.034426

0.73111 -0.036035

0.71518 -0.037598

NASA/CR—2002-211793 73
0.69924 -0.039116

0.68326 -0.040598

0.66732 -0.042033

0.65137 -0.043424

0.63540 -0.044773

0.61946 -0.046076

0.60351 -0.047332

0.58753 -0.048547

0.57164 -0.049710

0.55575 -0.050817

0.53965 -0.051897

0.52374 -0.052927

0.50808 -0.053878

0.49217 -0.054777

0.47619 -0.055636

0.46031 -0.056440

0.44448 -0.057185

0.42891 -0.057849

0.41336 -0.058424

0.39764 -0.058929

0.38194 -0.059367

0.36661 -0.059710

0.35146 -0.059932

0.33633 -0.060041

0.32141 -0.060016

0.30661 -0.059853

0.29100 -0.059549

0.27610 -0.059218

0.26159 -0.058688

0.24626 -0.058063

0.23351 -0.057365

0.21934 -0.056303

0.20485 -0.055197

0.19167 -0.053961

0.17837 -0.052466

0.16365 -0.050700

NASA/CR—2002-211793 74
0.15032 -0.049074

0.13639 -0.047096

0.12273 -0.045124

0.10983 -0.043093

0.10580 -0.042443

0.10062 -0.041576

0.094406 -0.040509

0.088393 -0.039431

0.081019 -0.038064

0.072426 -0.036360

0.065461 -0.034918

0.057876 -0.033223

0.048544 -0.030964

0.041900 -0.029167

0.035180 -0.027125

0.028754 -0.024882

0.022044 -0.022105

0.016585 -0.019234

0.013220 -0.017132

0.010646 -0.015314

0.0083173 -0.013440

0.0059869 -0.011249

0.0037424 -0.0085095

0.0025648 -0.0066507

0.0014672 -0.0044964

0.00058515 -0.0022445

0.00022853 -0.0010844

3.0568e-05 -0.00027511

-0.00015575 0.00062445

-0.00039301 0.0021397

-0.00053857 0.0042402

-0.00046579 0.0061892

-0.00021252 0.0082460

0.00014993 0.0099811

0.00083843 0.012354

0.0018108 0.014868

NASA/CR—2002-211793 75
0.0029083 0.017135

0.0048311 0.020258

0.0067977 0.022936

0.0087496 0.025330

0.012939 0.029991

0.015252 0.032287

0.017814 0.034591

0.020953 0.037204

0.023386 0.039080

0.026571 0.041418

0.030689 0.044188

0.033220 0.045771

0.036504 0.047745

0.038999 0.049176

0.041659 0.050643

0.044448 0.052116

0.047613 0.053697

0.050539 0.055095

0.053291 0.056346

0.056412 0.057696

0.058997 0.058773

0.061712 0.059879

0.064857 0.061087

0.066489 0.061718

0.073202 0.063984

0.080154 0.066505

0.088125 0.068774

0.099735 0.071726

0.11462 0.074895

0.12940 0.077445

0.14454 0.079325

0.15802 0.080718

0.18655 0.083164

0.20491 0.084047

0.22594 0.084694

0.24642 0.085044

NASA/CR—2002-211793 76
0.26546 0.085239

0.28616 0.085354

0.30437 0.084924

0.32198 0.084534

0.34505 0.083789

0.36169 0.083010

0.37983 0.082035

0.40332 0.080534

0.42432 0.079198

0.45166 0.076774

0.48189 0.074390

0.51205 0.071520

0.53792 0.068763

0.56294 0.065910

0.58539 0.062993

0.63827 0.056776

0.67977 0.051450

0.70802 0.047307

0.72582 0.044603

0.74476 0.041645

0.76651 0.038213

0.78926 0.034527

0.80617 0.031748

0.82429 0.028683

0.84640 0.024814

0.86233 0.022217

0.87581 0.020070

0.88985 0.017608

0.90557 0.014849

0.92131 0.012070

0.93709 0.0092346

0.95298 0.0063447

0.96881 0.0034328

0.98460 0.00048670

1.0006 -0.0025295

NASA/CR—2002-211793 77
It is quite common for problems to arise when inputting a new geometry for the first time. The

following discussion will describe some of the common errors made by users in generating an

input file. Error messages and warning messages printed to the screen will also be covered. As

mentioned in the previous section, all warning and error messages are also written to the debug

file “JUNK.DAT”.

9.1 Number of Points

An empty (blank) file will produce the following error:

Severe input error: Number of points must be greater than zero! 

The software will stop because of the above error.

After checking the other inputs, the program will exit due to this error. A file which does not

exist at run time (missing file) should generate a system error. That error is listed in Chapter 5:

Interactive Input.

9.2 Blank Lines

Blank lines in the geometry file should be avoided. On an SGI workstation running IRIX 6.2,

blank lines are ignored by the software. Other systems may read blank lines as an additional data

point of x = 0, y = 0. The software is set to check for this occurrence at the end of the file. If blank

lines exist at the end of the file, the following warning message may print out:

Removing blank line from geometry input file.

9.3 Too Few Points

If the body geometry is too coarse, the panel model created may not replicate the body geometry input. The initial set of coordinates output to file “ICE1.DAT” contain the initial panel model

of the body geometry. The user should check that this shape matches their input file for any new

geometry or if the user increases the point spacing (DSMN). If the number of points input is less

than 30, the following warning message will be generated:

NASA/CR—2002-211793 78
The number of geometry points input (5) is less than 30. A coarse geometry such as this may

not run well.

In the example above, a input data file consisting of five points was used.

9.4 Too Many Points

The only true upper limit to the number of points which the user can input is 10000, which is

the internal array size. Standard geometry input files used for testing purposes range from 50 to

150 points. The program will print the following warning if more than 1000 points are input:

The number of geometry points input (2000) is very high. You probably do not need this many

points.

In this example, the number of points input was 2000.

9.5 Body Not Closed

The panel solution used in this software assumes that the body(s) being simulated are closed

bodies. Several tests have been run using airfoils with open trailing edges and most of the results

appear acceptable. The following warning message is generated when the program detects an

unclosed body:

Warning! The trailing edge is not closed. Check the flow solution carefully.

If the flow solution calculated with an open trailing edge is acceptable to the user, then there

may be no need to alter the trailing edge simply to enclose the body.

9.6 Small Point Spacing

LEWICE may have problems with input points which are very close together or exactly the

same (duplicate point). This can easily occur when points are typed into the computer or when

two airfoil segments are joined together. LEWICE 2.2 will automatically correct this problem and

generate the following warning message:

NASA/CR—2002-211793 79
Two of the points on the geometry are too close together. Removing point (value) from body

(value).

This statement informs the user that one of the input points has been removed.

9.7 Body Input Backwards

LEWICE requires that the body geometry points should be input in a clockwise fashion. This

means that the points are input starting at the trailing edge and proceed sequentially toward the

leading edge along the lower surface up to the leading edge, then traverse back to the trailing edge

along the upper surface. LEWICE 2.2 will automatically correct for the case where the geometry

is input counterclockwise. If LEWICE detects this situation, the following warning message will

be generated:

Body points have been input counterclockwise. The program needs clockwise points. Reversing points. 

Note: The correction in LEWICE may not work for body geometries with an open trailing

edge.

9.8 Large Angles Between Neighboring Segments

Several errors can occur when points are typed in. These errors may cause the geometry to be

different from the one intended by the user. Some common errors include: points input in reverse

order; missing or misplaced decimal points; or mistyped numbers. LEWICE cannot check for all

possible errors in the file. The user should always check the first panel geometry printed to

“ICE1.DAT” to ensure that the body being used by LEWICE closely resembles the intended

geometry. A common consequence of geometry input errors are large angles between neighboring

segments. LEWICE will print two warning messages to aid the user in identifying potential problems. The following error will print out if this angle is greater than 45°:

You have two segments which form an angle greater than 45 degrees. Check the panel geometry and flow solution thoroughly. Check input point number (value) on body (value).

Figure 2 provides a diagram showing a 45 degree panel angle.

NASA/CR—2002-211793 80
Figure 2: Example of a 45 degree panel angle

LEWICE does not correct for this occurrence since the large angle may be intentional on the

part of the user. If this angle is intentional, the user should ensure that there are sufficient input

points in regions of high curvature. The point distribution methodology used in LEWICE will

tend to “round off” corners if an insufficient number of points are used. A more severe warning is

issued by LEWICE if the segment angle exceeds 135°:

You have two segments which form an angle greater than 135 degrees. Check the panel geometry and flow solution thoroughly. Also check that points have been entered correctly. Check

point number (value) on body (value).

Figure 3 shows an example of a 135° panel angle.

Figure 3: Example of a 135 degree panel angle

In this case, it is unlikely that the user intended to have this large of a segment angle. However, LEWICE will still not make any corrections to the input as it is possible that this large angle

was also intentional on the part of the user. If this large angle is intentional on the part of the user,

it is even more important that the user supply sufficient input points in the region around this

angle so that it does not get rounded off. The flow solution and ice accretion results should also be

thoroughly checked to ensure that an acceptable result was obtained.

Outside of body geometry

Inside of body geometry

45°Outside of body geometry

Outside of body geometry

Inside of

body

geometry

135°

Outside of body geometry

NASA/CR—2002-211793 81
9.9 Intersecting Bodies

Additional input problems may arise when the user attempts to input more than one body. One

such problem can occur when the bodies intersect. This can easily occur with multi-element airfoils if the user does not properly rotate the flap or use the proper gap settings. LEWICE cannot

correct for this problem. The following error message will be generated:

 Bodies (value) and (value) intersect. Program cannot run.

After performing the remaining checks on the geometry, the program will exit due to this

error.

9.10 Concentric Bodies

LEWICE cannot run multiple bodies where one body is completely inside another body. This

can occur if the coordinates for the bodies are supplied relative to different points of origin rather

than relative to the same point of origin. LEWICE cannot correct for this error. If this situation is

found, the following error message will be generated:

Body (value) is inside body (value). LEWICE cannot run this case.

After performing the remaining checks on the geometry, the program will exit due to this

error.

9.11 Bodies Out of Order

The logic used by the trajectory module dictates that multiple bodies need to be input in

sequential order in the x-direction. This means that the first body a particle could encounter must

be listed first, the second body it could encounter must be listed second and so on. This criteria is

based upon the leading edge of each body, not on the trailing edge as particles are most likely to

impinge on the leading edge of each body. LEWICE will correct for this problem and automatically put the bodies in the proper order. The following warning message will be generated:

NASA/CR—2002-211793 82
Bodies (value) and (value) are out of order. Bodies must be input so that the first body will be

the first to be hit by drops; the second body must be the second to be hit and so on. Putting bodies

in correct order.

If the program finds any correctable problems with the geometry file, the corrected geometry

will be written to file “FIXED.DAT”.

NASA/CR—2002-211793 83
Chapter 10: Optional Input Files

A case submitted by the user containing default values for each input in the main input file

will not read additional input files. The user can choose several flags in the main input file which

will require the input of an additional input file. An input value of 1, 2, or 3 for variable IDEICE

will read in a de-icer input file. An input value of 1 for variable IGRID will read in the files

“XY.PLT” and “Q.PLT”. An input value of 1 for variables ICP, IBETA, IHTC and IQEX will

read in values from files “RFLOW.INP”, “RBETA.INP”, “RHTC.INP” and “QEXTIN.INP”

respectively. Additionally, an input value of 1 for variables IBLEED, IQAIN and I3D in the deicer input file will read in the files “HI.INP”, “QAI.INP” and “STREAM.INP”. The formats for

all of these additional input files will now be discussed in detail.

10.1 De-icer Input File 

For IDEICE values from 1 to 3, LEWICE 2.2 will read in a de-icer input file. The name of this

file is supplied by the user interactively. This is described in more detail in Section 7.4. The deicer input consists of free-form (unformatted) ASCII text and can contain comment lines for user

comments or to improve readability. The example cases used in this manual will contain comment lines which are used to further explain the features of this module. The description of the deicer input file is divided into five sections: 1) description of the de-icer geometry and physical

properties; 2) definition of heater power and cycle times; 3) definition of boundary conditions; 4)

definition of various flags which control different features, and 5) description of time step and

input/output options. The division of the descriptions into five sections was done solely for clarity. The data is read from a single file for each body. Each of these sections will now be described

in more detail.

10.1.1 De-icer Section 1

The first section of the de-icer input file contains the definition of the internal geometry of the

body and the physical properties. The internal geometry is defined using rectangular blocks in the

NASA/CR—2002-211793 84
computational domain. This is illustrated in Figure 4. Each block contains grid spacing in the

wrap direction and the normal direction.

Figure 4: Grid block in the computational domain (left) and the physical domain (right)

Note: The de-icer geometry is specified by the user in the (rectangular) computational

domain, not in the physical domain.

10.1.1.1 LDE and NXDE

The first row of data in the de-icer file contains the number of “layers” (blocks in the normal

direction, variable named LDE) and the number of “sections” (blocks in the wrap direction, variable named NXDE). The total number of blocks simulated will be the product of these two numbers (LDE * NXDE). A sample data line is given below.

007 009

Note: In the subsequent description, the blocks in the normal direction will be referred to as

“layers” while the blocks in the wrap direction will be referred to as “sections”.

The data line given above does not have to be the first line in the data file. Comment lines can

be added for clarity. The software detects a comment line when it identifies a non-numeric character in the first 30 columns. An example is given in Table 11 below.

Table 69: First section of data file with comments

η

s

η

s

outer 

surface

inner 

surface

outer 

surface

inner 

surface

toward upper 

surface 

trailing edge

toward upper 

surface 

trailing edge

NASA/CR—2002-211793 85
________________________________________________________________________

C data for the composite body

________________________________________________________________________ 

C

C lde= total number of layers in the y-direction

C nxde= total number of heater sections in the x-direction

C

lde nxde

007 009

Note: Data is read free-form. The numbers do not have to reside in any particular column and

do not have to line up with the comments. However they must be in the prescribed order.

The number of layers and the number of sections must both be between 1 and 29. If the value

read for these variables is outside this range, the following error message will appear:

Layer number must be greater than zero (0) and less than thirty (30). Your input value of

(value) is outside this range. Blank lines are read as data with a value of zero. Check input file for

blank lines.

The software will stop because of the above error.

As the message indicates, the most common cause of this error is a blank line in the input file

which will be read as data with a value of zero.

10.1.1.2 NODE, ELDE, AK, ALP, AL, SLOPE

The next LDE number of data lines then contains six columns of numbers. The columns are:

1) the number of points in the normal direction for the layer; 2) the “thickness” of the layer (m); 3)

the thermal conductivity of the layer (W/mK) at 0 °C in the normal direction; 4) the thermal diffusivity of the layer (m2/s); 5) the anisotropy ratio; and 6) the slope of thermal conductivity with

temperature (W/mK2). The number of points defines the grid spacing in the normal direction for

that layer. All sections will have the same grid spacing in the normal direction for a given layer. 

Note: The first layer input is the innermost layer and the last layer will be the top surface.

NASA/CR—2002-211793 86
The thermal conductivity of a layer in the normal direction is defined as a function of temperature, as shown in Equation 11.

(11)

where 

k = thermal conductivity (W/mK)

kref = thermal conductivity (W/mK) at the reference temperature

m = slope of temperature dependence (W/mK2)

Tref = reference temperature = 0 °C

The user inputs the conductivity at the reference temperature as well as the slope in the equation above. For many composite materials, the conductivity can be anisotropic, which means that

it is different in the wrap direction than it is in the normal direction. Because of this, the user also

inputs a anisotropy ratio, which is the ratio of the thermal conductivity in the wrap direction to the

thermal conductivity in the normal direction. Most materials will have an anisotropy ratio of 1.

Note: The anisotropy ratio is constant, meaning that the variation of conductivity with temperature is the same in each direction.

The user also inputs the thermal diffusivity, which is defined as

(12)

where 

α = thermal diffusivity (m2/s)

k = thermal conductivity (W/mK)

ρ = density (kg/m3)

k kref mT Tref += ( ) –

α

k

ρCp

= ----------

NASA/CR—2002-211793 87
Cp = specific heat (J/kgK)

Note: Unlike thermal conductivity and density, the specific heat of materials is often difficult

to find in references. Manufacturers often do not measure (or list) this quantity in spec sheets.

However, this parameter is only important for transient (time-dependant) cases. 

An example of the data for the layers is given in Table 12 below.

Table 70: Sample data for each layer

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

Once again, the use of comment lines can be used as an aide in identifying the input, as shown

in Table 13.

Table 71: Sample data for each layer with comments

C

C Data for each layer: 

C

C nodes = # of points in that layer or section

C length = length (thickness) of layer or section

C

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

“node” “elde” “ak” “alp” “al” “slope”

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

NASA/CR—2002-211793 88
C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

Note: LDE = 7 in this example, so there are seven lines of data.

Note: The input units for LEWICE 2.2 are metric.

Note: While performing de-icing or anti-icing simulations, make certain that the top layer

contains the thermal properties of ice. If the ice melts, the software will change the properties

accordingly.

Note: For any icing, de-icing or anti-icing simulation, the thickness given to the ice layer in

this section will only be used to determine the grid spacing within the ice. The actual ice thickness

at each grid point is part of the output from this module.

Note: The total number of points in the normal direction is currently limited to 310 points.

The total number of points is the sum of the points in each individual layer minus the number of

layers, plus 2 (see equation below).

(13)

The number of points for a given layer must be at least two and less than 310. In addition, the

total number of points as given in Equation 13 must be less than 310. If the input data for a given

layer is outside this range, the following error message will occur:

Number of points in a layer must be greater than zero (0) and less than 310. Your input value

of' (value) for layer number (value) is outside this range. Blank lines are read as data with a

value of zero. Check input file for blank lines.

Ntot ( ) ∑n – 2 lde +=

NASA/CR—2002-211793 89
The software will stop because of the above error.

If the total number of points input is too high, the following error message will occur:

Total number of points in normal direction is too high. Number of points input = (value)

The software will stop because of the above error.

The thickness of each layer must be greater than zero. If the value read for this variable is outside this range, the following error message will occur:

Thickness of a layer must be greater than zero (0).Your input value of (value) for layer number (value) is outside this range.

The software will stop because of the above error.

The thermal conductivity must be greater than zero. If the value read for this variable is outside this range, the following error message will occur:

Thermal conductivity of layer must be greater than zero (0).Your input value of (value) for

layer number (value) is outside this range.

The software will stop because of the above error.

The thermal diffusivity must be greater than zero. If the value read for this variable is outside

this range, the following error message will occur:

Thermal diffusivity of layer must be greater than zero (0).Your input value of (value) for layer

number (value) is outside this range.

The software will stop because of the above error.

The anisotropic ratio must be greater than zero. If the value read for this variable is outside

this range, the following error message will occur:

NASA/CR—2002-211793 90
Anisotropic ratio of layer must be greater than zero (0).Your input value of (value) for layer

number (value) is outside this range.

The software will stop because of the above error.

10.1.1.3 NOX, ELX, AKX, ALPX, ALX, SLOPEX, ELXY, IVXY

The next NXDE number of lines contains the grid spacing and properties for each section.

The primary definition of the thermal properties was provided in the previous set of data. The

thermal properties input in this set of lines will be used only for the heater layer of an electrothermal system. For that layer, the thermal properties in this section will override those provided earlier. Each line consists of eight (8) columns of data. The columns are: 1) the number of points in

the wrap direction for each section; 2) the width of each section (m); 3) the thermal conductivity

of the layer (W/mK) at 0 °C in the normal direction; 4) the thermal diffusivity of the layer (m2/s);

5) the anisotropy ratio; 6) the slope of thermal conductivity with temperature (W/mK2); 7) the

additional thickness in the normal direction for that section; and 8) the layer number to which the

additional thickness is added.

The first six columns have the same definition as the layer data. The number of points determines the grid spacing in the normal direction. The sum of the widths should be the same as the

total wrap distance around the input geometry. The program will automatically adjust the lengths

of the two end segments so that this sum is equal to the total wrap distance. The heater locations

may have shifted during this process. The user can avoid this by manually adjusting the end segments or by using the variable OFFSET in the next section. The thermal properties identified here

will be used only in the heater layer of an electrothermal system as mentioned earlier. The last

two columns of data are used to identify one section which can have a larger thickness than the

thickness given in the layer data. This concept is illustrated in Figure 5. In this example, section 4

of layer 1 is thicker than the other sections. This feature can be used to model a nose block in an

airfoil or other geometric anomalies. Table 14 shows an example input for the section data input.

Figure 5: Additional thickness case

NASA/CR—2002-211793 91
Table 72: Sample data for each section with comments

C

C Data for each heater/gap section: 

C

 # of length cond. diff. anisotropy slope(b) of add. layer 

 nodes (m) (W/m/K) (m^2/s) of heater temp. eqn. length (m) number 

“nox” “elx” “akx” “alpx” “alx” “slopex” “elxy” “ivxy”

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C

Note: NXDE = 9 in this example, so there are nine lines of data.

Section 4 of layer 1 is thicker

than other sections.

NASA/CR—2002-211793 92
Note: Only the lines with data are used by the software. The comments included in this example are extraneous and are ignored by LEWICE 2.2. 

Note: The section data is entered from the left side of the computational domain toward the

right side. In the physical domain, data is entered starting from the lower surface trailing edge

clockwise toward the leading edge an ending back at the trailing edge.

Note: The length of the end segments will be changed so that the total segment length equals

the total wrap distance calculated by LEWICE 2.2. An identical amount will be added (or subtracted) from each end segment. Segments may be eliminated, if needed, to match the airfoil wrap

distance.

Note: The center of the middle section is not aligned with the body leading edge by default.

This can be changed in the next set of input data using variable OFFSET or by modifying the

lengths of the end segments.

The first six data columns have the same limits on the inputs that the layer data contained.

Therefore, the error messages will be the same as well. The additional thickness input cannot be

negative. If a negative value is read, the following error message will occur:

Additional length of a section must be greater than or equal to zero (0). Your input value of

(value) for section number (value) is outside this range.'

The software will stop because of the above error.

The layer number for the additional thickness must be at least 1 and no greater than the number of layers. If the value input is outside this range, the following error message will occur:

Layer number for additional thickness must be greater than zero (0) and less than or equal to

the number of layers. Your input value of (value) for section number (value) is outside this range.'

The software will stop because of the above error.

NASA/CR—2002-211793 93
10.1.1.4 Example Input

Table 15 shows an example of the complete input data for the first data section.

Table 73: Example data for first section of de-icer input.

________________________________________________________________________

C data for the composite body

________________________________________________________________________ 

C

C lde= total number of layers in the y-direction

C nxde= total number of heater sections in the x-direction

C

lde nxde

007 009

C

C Data for each layer:

C

C nodes = # of points in that layer or section

C length = length (thickness) of layer or section

C

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn.

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

NASA/CR—2002-211793 94
C

C Data for each heater/gap section: 

C

 # of length cond. diff. anisotropy slope(b) of add. layer 

 nodes (m) (W/m/K) (m^2/s) of heater temp. eqn. length (m) number 

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C

Note: It is not necessary for the input data to align on a given column. This was done in this

example to improve readability.

Note: Comment lines have been added to improve readability. The software will ignore the

comments and only read the data lines.

10.1.2 De-icer Section 2

This section of input data describes the heater power and cycle times. There are two types of

heater modes. In the first mode, a heater can be given a specific wattage, an ON time, an OFF

time and a LAG time. In the second mode, it will be temperature controlled. In this mode, the user

NASA/CR—2002-211793 95
supplies an initial wattage, an ON temperature, an OFF temperature, and the layer number which

is used to control the heaters. This means that the heater can be controlled by the surface temperature instead of the heater temperature if desired. The inputs for this section will now be discussed

in more detail.

Note: If there was an error reading data in the first section, the software will continue to read

the rest of the input file. However, an error in an earlier section can cause incorrect error messages

to appear for subsequent sections. It is highly recommended that the user fix the first errors

encountered and resubmit the case.

10.1.2.1 IJDE, OFFSET, IPAR

The first line of data in this section contains three variables: the layer number for an electrothermal heater; the offset for the parting strip heater; and the number of parameter studies. The

heater layer number defines the layer from which heat will emanate for an electrothermal system.

It also defines the layer which will use the thermal properties entered in the section data input earlier. A value for this variable must be entered even when using a hot air system. The input for this

variable must be between 1 and the total number of layers. If the value input is outside this range,

the following error message will occur:

Heater number must be greater than zero (0) and less than or equal to number of layers.

Your input value of (value) is outside this range.

Blank lines are read as data with a value of zero. Check input file for blank lines.

The software will stop because of the above error.

Additionally, if ice is the top layer, it cannot also be used as the heater layer. If this occurs, the

following error message will be generated:

The ice layer cannot be the same as the heater layer.

The software will stop because of the above error.

NASA/CR—2002-211793 96
The offset variable contains the distance, in meters, of the center of the computational domain

from the leading edge. If OFFSET = 0, then the midpoint (determined by distance) of the de-icer

sections will be aligned with the midpoint (determined by distance) of the airfoil. For values less

than 0, the midpoint will be moved toward the lower surface while for values greater than 0, it

will be moved toward the upper surface. If the absolute value of OFFSET is greater than the chord

length, the following warning message will occur:

The offset value may be past the trailing edge. OFFSET = (value) s/c

The number of parameter studies can be used to run more than one heater configuration using

the same flight and meteorological conditions. The user can also opt to run different conditions as

separate cases. The value for this variable must be between 1 and 29. If the value input is outside

this range, the following error message will occur:

Number of parameter studies must be greater than zero (0) and less than thirty (30). Your

input value of (value) is outside this range. Blank lines are read as data with a value of zero.

Check input file for blank lines.

The software will stop because of the above error.

Note: Normal operation of this software uses one parameter study per run (IPAR = 1). While

a multiple parameter study option has been included, it is possible that output from a multiple

parameter study run may be different from the output that would have been achieved if the case

were run separately. This option has seen limited testing. Section 13.1 describes a potentially better way to perform a parameter study by using external scripts.

Table 16 shows an example of this data line with comments.

Table 74: Example data line

________________________________________________________________________

C data for the heater

________________________________________________________________________

ijde offset ipar

004 0.005 1

NASA/CR—2002-211793 97
10.1.2.2 QDE, TON, TOFF, TLAG, ICFLAG

The next NXDE lines of data contain the heater power and cycle times. The user must input a

line of data for each section, even if there is no heat generation in that section. Each line must contain five columns of data. These columns represent: 1) the heater power (kW/m2); 2) heater ON

time (sec) or heater ON temperature (K) (for temperature controlled heaters); 3) heater OFF time

(sec) or heater OFF temperature; 4) heater LAG time (sec); 5) flag for using temperature controlled heaters. Figure 6 shows an example of each type of heater cycle

Figure 6: Example of heater cycle types

The heater power input can also represent the initial wall heat flux for an optimal hot air system. See IQW in de-icer section 4 input for more details. The heater power is input in units of kW/

m2 and must be ≥ 0. If the value input is outside this range, the following error message will

occur:

Heater wattage must be greater than or equal to zero (0).Your input value of (value) for layer

number (value) and parameter study (value) is outside this range.

The software will stop because of the above error.

Note: Heat flux values are input (and output) in units of kW/m2 while thermal conductivity

and heat transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively.

The heater ON time must also be ≥ 0. If the value input is outside this range, the following

error message will occur:

Heater on time must be greater than or equal to zero (0). Your input value of (value) for layer

number (value) and parameter study (value) is outside this range. Power

Time

LAG

ON

OFF

ON

Temperature

Time

ON temp.

OFF temp.

NASA/CR—2002-211793 98
The software will stop because of the above error.

The heater OFF time must also be ≥ 0. If the value input is outside this range, the following

error message will occur:

Heater off time must be greater than or equal to zero (0).Your input value of (value) for layer

number (value) and parameter study (value) is outside this range.

The software will stop because of the above error.

The heater LAG time must also be ≥ 0. If the value input is outside this range, the following

error message will occur:

Heater lag time must be greater than or equal to zero (0). Your input value of (value) for layer

number (value) and parameter study (value) is outside this range.

The software will stop because of the above error.

The temperature control flag has the following definition. If the flag = 0, then heaters are not

temperature controlled and the heater will operate with a given wattage and ON/OFF cycle time.

If the flag is > 0, then it represents the layer number which is used to control the heater cycle time.

In this mode, the wattage will be adjusted until the temperature remains between the temperature

range input. The exact temperature used will reside on the lower surface of the layer at the midpoint of the section, as illustrated in Figure 7.

Figure 7: Temperature location for temperature controlled heaters

Valid input values for this flag are then 0 up to the number of layers. Enter the top layer number to control the heater with the surface temperature. If the input value is outside this range, the

following error message will occur:

NASA/CR—2002-211793 99
Temperature control flag must be greater than or equal to zero (0) and less than or equal to

the number of layers.Your input value of (value) for layer number (value) and parameter study

(value) is outside this range.

The program will stop because of the above error.

If temperature controlled heater is used, the ON temperature must be greater than the OFF

temperature. If it is not, the following error message will occur:

Temperature control flag is on. ON temperature must be greater than OFF temperature.'

T_on = (value) T_off = (value)

In addition, if a temperature controlled heater is used, both temperatures must be greater than

the ambient temperature. To effectively de-ice the surface, these temperatures should also be

greater than freezing but this is not required for proper operation of the software. If either value is

below the ambient temperature, the following error message will occur:

Temperature for temperature controlled heater cannot be less than the ambient temperature. 

Temperature = (value)

The user should also refer to Section 10.1.4.2 for an additional use of the temperature controlled heater function.

Note: Temperature controlled heaters as modeled in this software do not necessarily determine the “optimum” heat flux. Initially, it uses the wattages input until the temperature exceeds

the ON temperature. It then turns off all heat until the temperature drops below the OFF temperature. Heat is then turned on, but at a lower wattage. This process continues until the simulation

time (TSTOP) is reached. If the simulation time is sufficiently long and the wattage has not

changed for a long time, then the wattage reported in “QOPT.DAT” may be close to the optimum

heat flux. Results to date have been inconsistent for this option.

NASA/CR—2002-211793 100
10.1.2.3 Example Input

Table 17 then gives a complete input example for the second de-icer section, including comments.

Table 75: Complete input data for de-icer section 2

________________________________________________________________________

C data for the heater

________________________________________________________________________

C

ijde offset ipar

004 0.005 1

 “QDE” “TON” “TOFF” “TLAG” “ICFLAG”

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 12.02d0 5.d0 115.d0 115.d0 0

C heater E

 11.19d0 5.d0 115.d0 115.d0 0

C heater C

 11.25d0 5.d0 115.d0 110.d0 0

C parting strip (heater A) does not turn off

 07.78d0 150.d0 0.d0 0.d0 0

C heater B

 11.68d0 5.d0 115.d0 110.d0 0

C heater D

 11.27d0 5.d0 115.d0 115.d0 0

C heater F

 11.75d0 5.d0 115.d0 115.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

Table 18 shows an example using temperature controlled heaters

NASA/CR—2002-211793 101
Table 76: Complete input data for de-icer section 2 using temperature controlled heaters

________________________________________________________________________

C data for the heater

________________________________________________________________________

C

ijde offset ipar

004 0.005 1

 “QDE” “TON” “TOFF” “TLAG” “ICFLAG”

 heater density temp on temp off lag time temp cntrl.

 (kWatts/m^2) (K) (K) (sec) flag

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 12.02d0 277.d0 275.d0 0.d0 6

C heater E

 11.19d0 277.d0 275.d0 0.d0 6

C heater C

 11.25d0 277.d0 275.d0 0.d0 6

C parting strip (heater A) 

 07.78d0 277.d0 275.d0 0.d0 6

C heater B

 11.68d0 277.d0 275.d0 0.d0 6

C heater D

 11.27d0 277.d0 275.d0 0.d0 6

C heater F

 11.75d0 277.d0 275.d0 0.d0 6

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

Note: To model a section which does not have a heater, simply input QDE = 0.

Note: To model an electrothermal anti-icing system or parting strip, set TOFF = 0.

Note: W/in2 * 1.55 = kW/m2

NASA/CR—2002-211793 102
10.1.3 De-icer Section 3

The third section of de-icer input is used to define boundary conditions for the simulation.

There are four boundary conditions which need to be defined: at the top and bottom and on both

sides. The four sides are illustrated in Figure 8.

Figure 8: Boundaries on Sample Geometry

Figure 9: Boundaries on Computational Geometry

Note: If there was an error reading data in a previous section, the software will continue to

read the rest of the input file. However, an error in an earlier section can cause incorrect error

messages to appear for subsequent sections. It is highly recommended that the user fix the first

errors encountered and resubmit the case.

10.1.3.1 IBC1, IBC2, IBC3, IBC4

The first line of this section contains four flags which represent the boundary condition on the

inside, outside, “left” and “right” boundaries as shown in the previous figure. The “left” boundary

occurs at the lower surface trailing edge while the “right” boundary occurs at the upper surface

trailing edge. Each flag can have a value from 1 to 3 where IBC = 1 represents a constant temperInside boundary (IBC1)

Outside boundary (IBC2)

Left

boundary

(IBC3)

Right

boundary

(IBC4)

Inside boundary (IBC1)

Outside boundary (IBC2)

Left

boundary

(IBC3)

Right 

boundary

(IBC4)

NASA/CR—2002-211793 103
ature boundary, IBC = 2 represents a convective boundary, and IBC = 3 represents a constant wall

flux boundary. A value outside this range will cause the following warning message to appear:

Boundary condition index must be greater than zero (0) and less than or equal to three (3)

Your input value of (value) is outside this range. Setting boundary condition = 2 (convection)'

Blank lines are read as data with a value of zero. Check input file for blank lines.

As stated in the warning, the boundary condition will be set to the default (convection) boundary.The standard boundary conditions for de-icing and anti-icing conditions are: IBC1 = 2 or 3

(IBC1 = 3 is used to model a hot air system.); IBC2 = 2; IBC3 = 2; IBC4 = 2. If a constant temperature boundary condition is used, the following warning message will appear:

Constant temperature boundary condition is not normally used in icing calculations.

If IBC2 = 3, IBC3 = 3 or IBC4 = 3, the following warning message will appear:

Constant heat flux boundary condition is not normally used in icing calculations.

10.1.3.2 TG1, TG2, TG3, TG4

The second line of data in this section also contains four values which represent the ambient

temperature (in degrees Kelvin) at the boundary. If IBC = 1 or 2, this temperature should be the

same as the ambient temperature entered in the main input file (variable TINF). If any of these

temperatures are not equal to the ambient temperature, the following warning will appear:

Temperature at boundary is not equal to the ambient temperature input from the main

LEWICE input file. Setting temperature equal to TINF.

The temperature on the inside surface (IBC1) will not be reset to the ambient temperature as

this option could be used to model a hot air anti-icer.

NASA/CR—2002-211793 104
10.1.3.3 H1, H2, H3, H4

The third line of data in this section contains the four values of the heat transfer coefficients

(W/m2/K) at the four boundaries. Each value must be ≥ 0. If the data input is outside this range,

the following error message will occur:

Heat transfer coefficient must be greater than or equal to zero (0).

The software will stop because of the above error.

Additionally, since the software is designed to emulate an enclosed boundary, the heat transfer coefficients on the “left” and “right” boundaries should be set to zero (insulated/reflective

boundary). If a value > 0 is read, the following warning message will appear:

Convective heat flux boundary condition is not normally used in icing calculations.

Note: The heat transfer coefficient input at the top surface may be overwritten using the

IBOUND flag in the next input section.

Note: The inside heat transfer coefficient, H1, can be used to model a hot air anti-icer. Section

10.1.4 provides a better way to model of this type of system.

10.1.3.4 QW1, QW2, QW3, QW4

The fourth line in this data section contains the four wall heat fluxes (kW/m2) for each boundary. These values are read even if a wall heat flux boundary is not used. These values should be ≥

0. If a negative heat flux is read, the following warning message will appear:

Negative heat flux boundary condition is not normally used in icing calculations.

The software will allow the use of this boundary condition, however negative heat flux values

have not been tested. 

NASA/CR—2002-211793 105
Note: The wall heat flux, QW1, can be used to model a hot air anti-icer. Section 10.1.4 provides a better way to model of this type of system.

Note: Heat flux values are input (and output) in units of kW/m2 while thermal conductivity

and heat transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively.

10.1.3.5 Example Input

An example of this data section is given in Table 19 below.

Table 77: Example input for boundary condition data

________________________________________________________________________

C boundary condition data

________________________________________________________________________

C

C Type of boundary condition:

C

“ibc1” “ibc2” “ibc3” “ibc4”

 2 2 2 2

C

C Temperature data for bottom, left, and side boundaries

C

 “tg1” “tg2” “tg3” “tg4”

 263.3 263.3 263.3 263.3

C

C Heat transfer coeff. in W/m^2/K

C

 “h1” “h2” “h3” “h4”

 3.d0 3.d2 0.d0 0.d0

C

C Wall heat flux in kW/m^2

C

 “qw1” “qw2” “qw3” “qw4”

 0.d0 0.d0 0.d0 0.d0

NASA/CR—2002-211793 106
10.1.4 De-icer Section 4

The fourth section of the de-icer input file contains several flags and other variables which are

used to access specialized features of the software. Since these features modify the basic way the

software operates, care should be taken to ensure that the proper flags are set for the system the

user wants to model.

Note: If there was an error reading data in a previous section, the software will continue to

read the rest of the input file. However, an error in an earlier section can cause incorrect error

messages to appear for subsequent sections. It is highly recommended that the user fix the first

errors encountered and resubmit the case.

10.1.4.1 TAIRH, AIRMD, AIRUP, XAIRMD

The first line of this section is used to input variables for an anti-icing system. There are two

ways to model a hot air system with LEWICE 2.2 in this section. In this first method, the user

specifies the internal heat transfer coefficient (using variable H1 from Section 10.3), the incoming

temperature of the bleed air (TAIRH), the mass flow rate (AIRMD), the mass fraction flowing up

from the supply location (AIRUP) and the air supply location (XAIRMD). This model is diagrammed in Figure 10.

Figure 10: First hot air model

The first variable on this input line, TAIRH, is the hot air supply temperature in degrees

Kelvin. This value should be greater than the melting point of ice (273.15 K) for this model to

work properly. If the value read is less than this, the following warning message will appear:

Temperature for bleed air is less than freezing. This is not normally used in icing calculations.

Hot air supply location

Mass fraction flowing up

Mass fraction flowing down

NASA/CR—2002-211793 107
The next variable on this line, AIRMD is the mass flow rate of the hot air supply in kg/s. This

variable must be ≥ 0. If a negative mass flow rate is entered, the following error message will

appear:

Mass flow rate for bleed air must be greater than or equal to zero (0). The software will stop

because of the above error.

The third variable on this line, AIRUP, is the mass fraction flowing up (or to the right in the

computational domain) as shown in Figure 10. The fraction flowing down is then fixed as (1 -

AIRUP). Since this variable is a fraction, its value must be 0 ≤ AIRUP ≤ 1. Values outside this

range will generate the following warning message:

Mass fraction going up must be greater than or equal to zero (0) and less than or equal to one

(1). Setting AIRUP = 0.5

As stated in the warning message, the value for AIRUP will be set to the default value of 0.5.

The user should terminate the case and change the input file if this value is unacceptable.

The last variable on this line, XAIRMD, is used to define the hot air supply location in meters

as measured from the leading edge. A negative value should be used to define a location on the

lower surface of the body and a positive value should be used to define a location on the upper

surface of the body. If the absolute value of XAIRMD is greater than the chord length of the body,

the following warning message will be generated:

Mass flow rate input location is greater than one chord length. This value will be set to the

trailing edge.

As suggested by the warning message, the supply location will be placed at the trailing edge

of the airfoil. Table 20 shows an example input for this data line with comments.

Table 78: Sample input line for hot air anti-icer

________________________________________________________________________

C miscellaneous data

________________________________________________________________________

NASA/CR—2002-211793 108
 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

10.1.4.2 I3D, IQAIN, IBLEED, IQW

The second line of data in this section defines flags which determine the type of anti-icer

which is to be modeled and a flag for reading in 3D streamline input. It is recommended that the

user only select one type of anti-icing model and not use a combination of models. The software

will accept the input, but the resulting model may not be realistic. The first variable on this line,

I3D, controls the input of a file used for performing a pseudo-3D analysis. If I3D = 0, then no

additional input data file will be read. If I3D = 1, the program will read in a file called

“STREAM.INP” (described in Section 10.2) which contains the dimensionless spanwise distance

from the current 2D cross-section to the next. The distance may also represent the axial distance

between two 2D cross-sections of an engine inlet. The program will use this data in the mass and

energy balance and is especially useful for determining the height and extent of runback ice formations. This option is often used when supplying other 2D streamline information from a 3D

flow field and 3D trajectory analysis. Valid inputs for I3D are 0 and 1. If a value outside this

range is read, the following warning message will be generated:

3D streamline flag must be zero (0) or one (1). Your value of (value) is out of range. Setting

I3D = 0

The second variable on this line, IQAIN, controls the input of a wall heat flux in kW/m2 at the

inside surface. Valid inputs for this flag are 0 (OFF) and 1 (ON). If IQAIN = 1, the software will

read a separate file called “QAIN.INP” (described in Section 10.3) which contains the wall heat

flux on the inside surface as a function of the wrap distance. Also see Section 10.1.4.8 for additional options for this input file. If a value outside the valid range (0 or 1) is input, the following

warning message will be generated:

Heat flux flag must be zero (0) or one (1) Your value of (value) is out of range. Setting IQAIN

= 0

IQAIN will then be set to the default value of 0 (no data read).

NASA/CR—2002-211793 109
The next flag on this line, IBLEED, can be used to read in a file containing heat transfer coefficients in W/m2K instead of a wall heat flux. If IBLEED = 0, no data will be read. If IBLEED =

1, the software will read in a separate file called “HI.INP” (described in Section 10.4) containing

the heat transfer coefficients on the inside surface as a function of the wrap distance. See Section

10.1.4.9 for additional options on this input file.If a value outside the valid range (0 or 1) is input,

the following warning message will be generated:

Bleed air flag must be zero (0) or one (1) Your value of (value) is out of range. Setting

IBLEED = 0

IBLEED will then be set to the default value of 0 (no data read).

Note: Heat flux values are input (and output) in units of kW/m2 while thermal conductivity

and heat transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively.

The last flag on this line, IQW, can be used to estimate the “optimal” wall heat flux for an

anti-icing system. If IQW = 0, no optimization is performed. If IQW = 1, then the software will

use the wattages input in Section 10.1.2.2 along with the temperature control information

described in that section to determine the wall heat flux required to maintain the selected temperature within the range specified. In contrast to Section 10.1.2.2, where the heat generation was

supplied from layer IJDE, the heat generation case for IQW = 1 comes from the inside wall heat

flux. For two cases which both use the temperature control option, IQW = 0 would then be used to

model an electrothermal system while IQW = 1 would be used to model a hot air system. If a

value outside the valid range (0 or 1) is input, the following warning message will be generated:

Optimum bleed air flag must be zero (0) or one (1) Your value of (value) is out of range. Setting IQW = 0

IQW will then be set to the default value of 0 (no data read). 

Note: The IQW flag does not necessarily determine the “optimum” heat flux. Initially, it uses

the wattages (or heat fluxes) input until the temperature exceeds the ON temperature. It then turns

off all heat until the temperature drops below the OFF temperature. Heat is then turned on, but at

NASA/CR—2002-211793 110
a lower value. This process continues until the simulation time (TSTOP) is reached. If the simulation time is sufficiently long and the wattage has not changed for a long time, then the wattage

reported in “QOPT.DAT” may be close to the optimum heat flux. Also see the description of temperature controlled heaters in Section 10.1.2.2. Results to date have been inconsistent for this

option.

In addition, these flags are mutually exclusive. That is, only one of these flags can be set for a

given input file. If IQAIN and IBLEED are both equal to one, the following warning message will

be generated:

Heat flux flag and bleed air flag cannot both be on. Setting IBLEED = 0

If IQW and IBLEED are both equal to one, the following warning message will be generated:

Optimum bleed flag and bleed air flag cannot both be on. Setting IBLEED = 0

 If IQAIN and IQW are both equal to one, the following warning message will be generated:

Heat flux flag and optimum bleed flag cannot both be on. Setting IQAIN = 0

An example input for this line is shown in Table 21.

Table 79: Sample input for anti-icing flags

i3d iqain ibleed iqw

 0 0 0 0 

Note: IBLEED and IQAIN flags are most often used when the input data is known. Examples

of this condition occur when experimental test data is available or when values are calculated by

another program or via correlation. IQW is most often used when this data is not available.

10.1.4.3 ICOND, IBOUND, INIT, ISH, ISTD, IGDE

The third line of this data section contains six flags which control different features within the

software. The user should consider each flag carefully to ensure that their problem is being properly modeled. The default values represent those most likely to be used to set up a de-icing or

NASA/CR—2002-211793 111
anti-icing simulation. There is, however, no “best” value for these flags as they represent ways to

model different problems.

Note: If there was an error reading data in a previous section, the software will continue to

read the rest of the input file. However, an error in an earlier section can cause incorrect error

messages to appear for subsequent sections. It is highly recommended that the user fix the first

errors encountered and resubmit the case.

The first variable on this data line, ICOND, controls the use of the slower de-icer model during an initial time lag. ICOND = 0 will turn off conduction during an initial time lag and can be

used in a de-icing simulation where the body is allowed to accrete ice before any heaters turn on.

When ICOND = 0, the software will use the standard LEWICE accretion routines for the length

of the shortest time lag input in Section 10.1.2. If ICOND = 1, the de-icer model will be used

starting at time = 0. If there is an initial accretion period as described above, the user should select

ICOND = 0 to accelerate the solution. Valid inputs for this flag are 0 and 1. If a value outside this

range is read, the following warning message will be generated:

Conduction flag must be zero (0) or one (1) Your input value of (value) is out of range. Setting

ICOND = 1

If ICOND = 0 but there is a zero second time lag on any of the heaters (or if the user selected

a wall heat flux boundary condition), the following warning message will appear:

Conduction flag must be = 1 since heaters will turn on immediately.

Setting ICOND = 1

The second variable in this data line, IBOUND, is used to refine the upper boundary condition

set with IBC2 in Section 10.1.3.1. For any of the IBOUND values, IBC2 must equal two for

IBOUND to be used. Otherwise, this flag is read in but not used by the software. If IBOUND = 1,

the convective heat transfer coefficient at the top surface is defined by the input variable H2 in

Section 10.1.3.2. This option is only useful for comparison with analytical heat transfer solutions

and is not applicable to icing simulation. If IBOUND = 2, the heat transfer coefficient is defined

NASA/CR—2002-211793 112
using the integral boundary layer equations in LEWICE 2.2 or by a user read file (if IHTC = 1 in

Section 8.3) but no ice accretion will occur. This option is useful for comparison with dry air data

with heaters on. If IBOUND = 3, the heat transfer coefficient is defined using the integral boundary layer equations in LEWICE 2.2 and ice accretion will occur. IBOUND = 3 is recommended

for any icing simulation. Valid input values are 1, 2, and 3. If a value outside this range is read,

the following warning message will appear:

Boundary flag must be one (1), two (2) or three (3) Your input value of (value) is out of range.

Setting IBOUND = 3

If IBOUND does not equal 3, the following reminder is generated:

Upper boundary is set to dry air. Ice will not form.

Note: IBOUND values are ignored by the software unless IBC2 = 2 boundary condition is

used.

The third flag on this data line determines the initial temperature profile which should be

used. If INIT = 1, all temperatures will be set equal to the ambient temperature. This option has

primarily been used for comparison with analytical heat transfer cases. If INIT = 2, the temperature distribution in the wrap direction will be set to the recovery temperature. This option should

be used when the body is initially in dry air. This occurs for dry air cases or for accretion cases

where at least one heater is on at time = 0. INIT = 2 should be used for all cases where ICOND =

1. If INIT = 3, the temperature distribution in the wrap direction will be set to the accretion temperature (wet surface temperature). This option must be used if ICOND = 0 and IBOUND = 3.

For any of these options, there is no initial temperature gradient in the body normal direction.Valid input values for INIT are 1, 2, and 3. If a value is read outside this range, the following

warning message will be generated:

Initial temperature flag must be one (1), two (2) or three (3) Your input value of (value) is out

of range. Setting INIT = 3

IF INIT = 1, the following reminder warning is generated:

NASA/CR—2002-211793 113
Initial temperature selected is not normally used in icing simulations.

This warning will also be generated when INIT = 3 and ICOND = 1 since, if conduction is

considered at the start of an accretion, the proper value for INIT is two.

Note: Most of the cases performed to date (especially those which have experimental data)

use INIT = 2 and ICOND = 1. Other combinations have seen limited testing.

The fourth and fifth flags on this data line control ice shedding behavior for a de-icing system.

The fourth flag, ISH, turns ice shedding on (ISH = 1) and off (ISH = 0) while the fifth flag, ISTD,

determined the preferred type of ice shedding. ISTD values will be read but not used if ISH = 0.

Valid input values for ISH are 0 and 1. A value outside this range will generate the following

warning message:

Ice shed flag must be zero (0) or one (1) Your input value of (value) is out of range. Setting

ISH = 1

If ISH = 0 (no ice shed), the following warning message will be generated:

Ice will not shed. This is usually too conservative.

The values of ISTD have the following meaning: if ISTD = 0, ice will only shed if the software determines that the whole ice shape will shed (conservative); if ISTD = 1, ice will shed in a

given section if the software determines that the ice in that section should shed; if ISTD = 2, ice

can shed node by node if the software determines shedding of that node is appropriate (non-conservative). The recommended value is ISTD = 1 for the cases considered thus far. The other

options are included as this result may not be universal since the number of test cases is small.

Valid inputs for ISTD are 0, 1, and 2. If a value outside this range is read, the following warning

message will be generated:

Shed type flag must be zero (0), one (1), or two (2) Your input value of (value) is out of

range.Setting ISTD = 1

NASA/CR—2002-211793 114
Additionally, if ISTD = 0 or 2, the following reminder warning is generated:

The preferred shedding mode is by sections (ISTD = 1).

The sixth and final flag on this data line, IGDE, is used to determine if phase change is considered. Phase change allows ice to melt or sublimate and allows water to evaporate. IGDE = 0 turns

phase change off and should be used only when analyzing dry air cases. Additionally, the top

layer properties entered in Section 10.1.1.2 should reflect the top layer of the de-icer or anti-icer

construction. If IGDE = 1, phase change is considered and the top layer properties entered in Section 10.1.1.2 should reflect the properties for ice.

Note: If a node of ice melts, the software will automatically change the thermal properties of

that node to water.

Note: If phase change is considered (IGDE = 1), the length (ELDE) given to the top layer in

Section 10.1.1.2 will only be used to define the normal direction grid spacing in the ice layer. In

this case, the ice thickness at time = 0 will be zero. Valid input values for IGDE are 0 and 1. If a

value is read which is outside this range, the following warning message will appear:

Phase change flag must be zero (0) or one (1) Your input value of (value) is out of range. Setting IGDE = 1

If IGDE = 0, the following reminder warning will be generated:

Phase change is not selected. This is not normally used in icing simulations.

Some combinations of the flags in this data line will result in cases which are not physically

meaningful. The software will check for these occurrences and take the following actions. If ice is

the top layer (IGDE = 1) and conduction is initially off (ICOND = 0), then the upper boundary

condition must be set so that ice accretion is considered (IBOUND = 3) and the initial temperature

distribution must be the accretion temperature (INIT = 3). If IGDE = 1 and ICOND = 0 but either

IBOUND≠3 or INIT≠3, then the following warning message will be generated:

NASA/CR—2002-211793 115
Since conduction flag is off (ICOND = 0), then the boundary condition flag (IBOUND) must

be = 3 and temperatures must be initialized to the accretion temperature (INIT = 3). Resetting

those flags.

Conversely, if ice is not the top layer (IGDE = 0) then ice accretion cannot occur and

IBOUND = 3 or INIT = 3 are not allowed. If either of these flags has an incorrect value, the following warning will be generated:

Since phase change flag is off (IGDE = 0), then the boundary condition flag (IBOUND) must

be = 2 and temperatures must be initialized to the recovery temperature (INIT = 2). Resetting

those flags.

In addition, if ice is not the top layer (IGDE = 0), then ice shedding cannot occur. If IGDE = 0

and ISH = 1, the following warning message will be generated:

Ice cannot shed without phase change. Setting ISH = 0

Finally, if ice is the top layer (IGDE = 1), it cannot also be the source of an electrothermal

heater. If IGDE = 1 and IJDE (from Section 10.1.2.1) equals the total number of layers (LDE

from Section 10.1.1.1), then the following error message will be generated:

The ice layer cannot be the same as the heater layer. The software will stop because of the

above error.

Table 22 contains a convenient cross reference showing the allowable combinations of flags.

Each row contains the valid values for selected flag in the first column. For example, the first row

shows the valid flags for that option. A cell containing the value “N/A” means “Not Applicable”

because this flag is not used by the software for the other flag values set. 

NASA/CR—2002-211793 116
Note: Some combinations of flags in this table may generate warning messages but the flag

values will not be changed

Table 80: Cross reference for allowable flags

Flag ICOND IBOUND INIT ISH ISTD IGDE

ICOND = 0 0 1,2 1,2 0 N/A 0

ICOND = 0 0 3 3 0 N/A 1

ICOND = 0 0 3 3 1 0,1,2 1

ICOND = 1 1 1,2 1,2 0 N/A 0

ICOND = 1 1 3 1,2 0 N/A 1

ICOND = 1 1 3 1,2 1 0,1,2 1

IBOUND = 1 0 1 1,2 0 N/A 0

IBOUND = 1 1 1 1,2 0 N/A 0

IBOUND = 1 0 1 3 0 N/A 1

IBOUND = 1 0 1 3 1 0,1,2 1

IBOUND = 1 1 1 1,2 0 N/A 1

IBOUND = 1 1 1 1,2 1 0,1,2 1

IBOUND = 2 0 2 1,2 0 N/A 0

IBOUND = 2 1 2 1,2 0 N/A 0

IBOUND = 2 0 2 3 0 N/A 1

IBOUND = 2 0 2 3 1 0,1,2 1

IBOUND = 2 1 2 1,2 0 N/A 1

IBOUND = 2 1 2 1,2 1 0,1,2 1

IBOUND = 3 0 3 3 0 N/A 1

IBOUND = 3 0 3 3 1 0,1,2 1

IBOUND = 3 1 3 1,2 0 N/A 1

IBOUND = 3 1 3 1,2 1 0,1,2 1

INIT = 1 0,1 1,2 1 0 N/A 0

INIT = 1 0,1 3 1 0 N/A 1

INIT = 1 0,1 3 1 1 0,1,2 1

NASA/CR—2002-211793 117
Table 23 shows an example of this data line with comments.

Table 81: Example input for the third line of the fourth de-icer input section.

 icond ibound init ish istd igde

 1 3 2 1 1 1

INIT = 2 0,1 1,2 2 0 N/A 0

INIT = 2 0,1 3 2 0 N/A 1

INIT = 2 0,1 3 2 1 0,1,2 1

INIT = 3 0 3 3 0 N/A 1

INIT = 3 0 3 3 1 0,1,2 1

ISH = 0 0,1 1,2 1,2 0 N/A 0

ISH = 0 1 3 1,2 0 N/A 1

ISH = 0 0 3 3 0 N/A 1

ISH = 1 0 3 3 1 0,1,2 1

ISH = 1 1 3 1,2 1 0,1,2 1

ISTD = 0 0 3 3101

ISTD = 0 1 3 1,2 1 0 1

ISTD = 1 0 3 1,2 1 1 1

ISTD = 1 1 3 3111

ISTD = 2 0 3 1,2 1 2 1

ISTD = 2 1 3 3121

IGDE = 0 0,1 1,2 1,2 0 N/A 0

IGDE = 1 0 3 1,2 0 N/A 1

IGDE = 1 1 3 3 0 N/A 1

IGDE = 1 0 3 1,2 1 0,1,2 1

IGDE = 1 1 3 3 1 0,1,2 1

Table 80: Cross reference for allowable flags

Flag ICOND IBOUND INIT ISH ISTD IGDE

NASA/CR—2002-211793 118
10.1.4.4 TSURF, IEVAP, ITHERM

This input data line contains variables used for the 1D anti-icing approximation (IDEICE = 1).

If IDEICE = 1, the software will use the following variables from the de-icer input file to generate

its solution: LDE (Section 10.1.1.1), ELDE and AK (Section 10.1.1.2), IJDE (Section 10.1.2.1),

the upper and lower surface boundary conditions (Section 10.1.3) and the three variables above.

The definitions for these variables are the same in version 2.2 as they were in version 2.0. The

input data format, however, conforms to the free-form format described earlier in the de-icer input

file rather than the rigid format used in version 2.0.

The first value on this input data line, TSURF, is the temperature at the airfoil surface which

the user wants to maintain. Typical running wet anti-icing systems operate in the region 278°K -

283°K while an evaporative system may operate at 320°K or even higher. The software assumes

that the user wants to perform an anti-icing analysis. The desired surface temperature should

therefore be above freezing. If a value of TSURF ≤ 273.15 is entered, the following warning message is generated:

Desired surface temperature is less than freezing. Value read in was (value) K Setting

TSURF = 273.15 K

Note: The results for a desired surface temperature at freezing will be inaccurate since the

anti-icing module does not have provisions to freeze surface water as does the LEWICE icing

module.

The second value on this input data line, IEVAP, indicates if the system is running wet

(IEVAP = 0) or evaporative (IEVAP = 1). A third option (IEVAP = 2) will use the electrothermal

wattages input. This option is convenient for direct comparison of the 1D option (IDEICE = 1)

with the 2D option (IDEICE = 2 or 3). Valid input values for IEVAP are 0, 1 or 2. If the value

input is outside this range, the following warning message will be generated:

Evaporation flag must be zero (0), one (1) or two (2). Your value of (value) is out of range.

Setting IEVAP = 0

NASA/CR—2002-211793 119
Additionally, IEVAP = 2 can only be used when wattages are read (IDEICE = 2 or 3). If

IEVAP = 2 when IDEICE = 1 in the main input file, the following warning message will be

generated:

Constant heat source for 1-D analysis can only be used for IDEICE = 2 or = 3 option. Setting

IEVAP = 0

The third value on this input data line, ITHERM, indicates whether the anti-icer is

electrothermal (ITHERM = 0) or uses hot air (ITHERM = 1). Valid input values for ITHERM are

0 and 1. If the value input is outside this range, the following warning message will be generated:

De-ice flag must be zero (0) or one (1). Your value of (value) is out of range. Setting ITHERM

= 0

Table 24 contains an example input for this data line with comments.

Table 82: Example input for 1D anti-icing approximation (IDEICE = 1)

 tsurf ievap itherm 

 278.d0 1 0 

10.1.4.5 STA, RPM, IROT

The next line in this data input section defines three variables which are used to simulate rotational effects in the de-icing system. The software does not simulate a fully rotational system

hence these options should be used with caution. The first variable, STA, defines the distance of

the 2D cross-section being simulated from the hub of the rotating device (moment arm) in meters.

Valid inputs for STA are STA ≥ 0. If a value which is outside this range is read, the following

warning message will be generated:

Span location on rotor cannot be less than zero (0) Your value of (value) is out of range. Setting STA = 0.

NASA/CR—2002-211793 120
The second variable on this data input line is the rotational speed, RPM, in revolutions per

minute. Valid inputs for RPM are RPM ≥ 0. If a value which is outside this range is read, the following warning message will be generated:

Rotor speed cannot be less than zero (0). Your value of (value) is out of range. Setting RPM =

0.

Note: To model a fixed-body problem, simply set RPM = 0.

The last variable on this data input line, IROT, contains a flag which defines the body as rotating vertically (propeller, IROT = 0) or horizontally (rotor blade, IROT = 1). Valid inputs for

IROT are 0 and 1. If a value which is outside this range is read, the following warning message

will be generated:

Rotor flag must be zero (0) or one (1). Your value of (value) is out of range. Setting IROT = 0

Note: The software uses the data input on this line for three calculations: 1) the rotational

speed is used to calculate an increase in the aerodynamic heating term in the energy balance; 2)

the rotational force is used to shed ice; and, 3) the rotational force is used to find the resultant

force of the shed ice particle, which is used to track the particle after it sheds.

Note: The rotating body information is not used by the potential flow solver in LEWICE 2.2

nor is the rotating body information used by the trajectory equation.

Note: If STA = 0 or RPM = 0, then there is no difference between IROT = 0 and IROT = 1

(rotational force is zero).

Table 25 shows an example of this data line with comments.

Table 83: Example input for rotating body information.

sta rpm irot

10.d0 0.d0 1

NASA/CR—2002-211793 121
10.1.4.6 DTAUI, NISP, DTAUM, NMSP, DTAUF, JCOUNTD

The sixth line of data input in this section defines six variables which are used to control the

de-icer time step and convergence of the solution. The de-icer time step discussed in this section

is completely different from the icing time step defined in Section 8.3. In this section, the de-icer

time step is used to calculate the transient (time-accurate) temperature distribution in the de-icer

and the ice shape. In order to accurately capture these distributions, the de-icer time step must be

much smaller than the icing time step. For example, a typical icing time step is 60 seconds while

the standard de-icer time step is 0.1 seconds. This means that during a 60 second icing cycle, the

de-icer routine will produce 600 temperature solutions, the last of which contains the local ice

growth which is then used to produce an ice shape for the next icing time. The first variable on

this line, DTAUI, defines the time step which is used at time = 0. This value must be 0.0001 ≤

DTAUI ≤ 10 and a typical value is 0.1 seconds. If the value read from the de-icer input file is outside this range, the following warning message will be generated:

Time steps less than 0.0001 or greater than 1.0 should not be used. Your value of (value) is

out of range. Setting DTAUI = 0.1 sec Blank lines are read as data with a value of zero. Check

input file for blank lines

Note: De-icer time steps less than 10-4 seconds are not allowed as the software will run very

slowly at such de-icer time steps and de-icer time steps greater than 10 second cannot accurately

capture temperature distributions even for cases where only the steady-state output (an anti-icing

case) is simulated. This occurs because convergence cannot be maintained for larger de-icer time

steps.

Note: DTAUI values other than 0.1 seconds have been used in test cases which have a large

initial transient in the temperature distribution. Smaller initial time steps were chosen in these

cases to accurately model the temperature distribution. Larger initial time steps were chosen for

steady-state anti-icing cases. Note that since the phase of each node in the ice layer must be iterated upon, a larger time step does not always provide a faster solution. 

NASA/CR—2002-211793 122
The second variable on this data input line, NISP, defines the number of time steps for which

DTAUI will be used as the time step. To use a 0.1 second time step for the first ten seconds, use

NISP = 100. To use a 0.01 second time step for the first ten seconds, use NISP = 1000. NISP must

be greater than zero. If a value is read which is outside this range, the following warning message

will appear:

Number of time steps must be greater than zero (0). Your value of (value) is out of range.Setting NISP = 1000 Blank lines are read as data with a value of zero.Check input file for blank

lines.

The third variable on this line, DTAUM, defines the time step for the period of time after

DTAUI is used. This variable has a smaller time range as DTAUI, namely 0.0001 ≤ DTAUM ≤ 1.

De-icing time steps greater than 1 should only be used in anti-icing simulations where only one

time step is needed. If a value is read which is outside this range, the following warning message

will appear:

Time steps less than 0.0001 or greater than 1.0 should not be used. Your value of (value) is

out of range. Setting DTAUM = 0.1 sec Blank lines are read as data with a value of zero. Check

input file for blank lines

The fourth variable on this line, NMSP, defines the number of time steps for which DTAUM

will be used as the time step. Valid inputs for NMSP must be > 0. If a value is read which is outside this range, the following warning message will appear:

Number of time steps must be greater than zero (0). Your value of (value) is out of range. Setting NMSP = 1000

The fifth variable on this line, DTAUF, defines the time step for the remainder of the de-icing

time, if any.This variable has the same range as DTAUM, namely 0.0001 ≤ DTAUF ≤ 1. If a

value is read which is outside this range, the following warning message will appear:

NASA/CR—2002-211793 123
Time steps less than 0.0001 or greater than 1.0 should not be used. Your value of (value) is

out of range. Setting DTAUF = 0.1 sec Blank lines are read as data with a value of zero. Check

input file for blank lines

The last variable on this line, JCOUNT, defines the number of iterations for the solution technique and the phase change iteration. The temperature distribution at each time step is solved

using the Modified Strongly Implicit Procedure (MSIP) which requires the use of some iteration.

In addition, the software must predict the phase (rime, glaze, water) of each ice node and compare

the solution to these predicted values. In most cases, JCOUNT = 10 has been found to be sufficient. The valid range for JCOUNT is 1 to 50. If a value is read which is outside this range, the

following warning message will be generated:

Number of iterations must be greater than zero (0) and less than (value). Your value of (value)

is out of range.Setting JCOUNTD = 10 Blank lines are read as data with a value of zero. Check

input file for blank lines

Table 26 shows an example of this line of data input.

Table 84: Example input for time step data input line

dtaui nisp dtaum nmsp dtauf jcountd

1.d-1 1000 1.d-1 1000 1.d-1 10

10.1.4.7 TSPRAY, TAFTER

The next line of this data input section contains two variables which control the on and off

times of the heater relative to the immersion in the cloud. The first variable, TSPRAY, is defined

as the time the heaters are on before water hits the surface. In a simulation of the real environment, this translates to the heaters being turned on before entering a cloud. In the tunnel, the heaters could also turn on before the water spray. TSPRAY = 0 has been used in the large majority of

simulations to date. This value must be ≥ 0. If a value is read which is outside this range, the following warning message is generated:

NASA/CR—2002-211793 124
Time before spray cannot be less than zero (0). Your value of (value) is out of range. Setting

TSPRAY = 0

Since TSPRAY = 0 has been used for the majority of simulations, the following reminder

warning will be generated if TSPRAY > 0:

Time before spray is greater than zero (0). Water impingement will not start until TSPRAY.

The second variable on this data input line, TAFTER, is defined as the time the heaters are on

after water stops hitting the surface. In a simulation of the real environment, it is the period of

time in which the de-icers are still on after a cloud has been exited. TAFTER = 0 has been used in

the large majority of simulations to date. This value must be ≥ 0. If a value is read which is outside this range, the following warning message is generated:

Time after spray cannot be less than zero (0).

Your value of (value) is out of range. Setting TAFTER = 0.

Since TAFTER = 0 has been used for the majority of simulations, the following reminder

warning will be generated if TAFTER > 0:

Time after spray is greater than zero (0).

Water impingement will end and de-icing will continue for (value) seconds.

Table 27 shows an example of this data input line.

Table 85: Example data for spray time data input line

tspray tafter

 0.d0 0.d0

10.1.4.8 ISCOLA, JSCOLA, KSCOLA, SSLOPA, SZEROA

The eighth line of this data input section contains variables used when reading bleed air heat

transfer coefficients (i.e. when IBLEED = 1). The data on this line is read regardless of the value

NASA/CR—2002-211793 125
of IBLEED however. The data line contains five variables which define the format of the bleed

air data. The first three numbers (ISCOLA, JSCOLA and KSCOLA) define the column numbers

in the bleed air input data file which contain the requested values. ISCOLA defines which column

contains the wrap distance. JSCOLA defines the column which contains the bleed air heat transfer

coefficients in W/m2/K, and KSCOLA defines the total number of columns in the file. A file

which contained only the necessary data would therefore have ISCOLA = 1, JSCOLA = 2, and

KSCOLA = 2. (ISCOLA = 2, JSCOLA = 1 and KSCOLA = 2 would also be valid.) This type of

data input format was used since the data probably came from a separate program and this format

style reduces the amount of reformatting needed for LEWICE 2.2. Section 10.2 contains further

information on the format of the input data file “HI.INP” which contains the bleed air heat transfer coefficient values. ISCOLA must be at least 1 and no greater than KSCOLA. If a value is read

which is outside this range, the following warning message will be generated:

Columns for 1st variable must be at least one (1) and no greater than the number of columns.

Your value of (value) is out of range. Setting ISCOLA = 1 Blank lines are read as data with a

value of zero. Check input file for blank lines.

Similarly, JSCOLA must be at least 1 and no greater than KSCOLA. It also cannot be the

same as ISCOLA. If a value is read which is outside this range, the following warning message

will be generated:

Columns for 2nd variable must be at least one (1) and no greater than the number of columns. Your value of (value) is out of range. Setting JSCOLA = 1 Blank lines are read as data with

a value of zero. Check input file for blank lines.

If the values for ISCOLA and JSCOLA are the same, the following warning message will be

generated:

Columns for 1st and 2nd variable cannot be the same. Setting ISCOLA = 1 and JSCOLA =

KSCOLA

The total number of columns, KSCOLA must be at least 2, but can be higher. If a value is read

which is outside this range, the following warning message will be generated:

NASA/CR—2002-211793 126
Number of columns must be at least two (2) Your value of (value) is out of range. Setting

KSCOLA = 2

The fourth value on this data input line, SSLOPA, defines the conversion factor which will be

applied to the wrap distance values input. LEWICE 2.2 uses wrap distances in dimensionless values (value divided by chord). The wrap distance values input can be in any set of units if the user

supplies the correct conversion to SSLOPA. The slope can be positive or negative, but not zero. If

a value of zero is read for this data input, the following warning message will be generated:

Slope cannot be zero.Blank lines are read as data with a value of zero. Check input file for

blank lines.

The last value on this data input line, SZEROA, defines the offset of the input wrap distances

from those needed for LEWICE 2.2. If SZEROA = 0., The software will assume that a wrap distance value of 0 in the input data corresponds to the lower surface of the trailing edge. If this is not

the case, the user should supply a value (in dimensionless distance) which supplies the correct

offset. The value for SZEROA should not be greater than the wrap distance from the leading edge

to the trailing edge. 

The following equation is used within LEWICE to convert wrap distance values using

SSLOPA and SZEROA:

(14)

where sLEWICE is the wrap distance used by LEWICE and sinput is the wrap distance in the

input file. If the value read is greater than 1.2 (1.2 chord lengths), the following warning message

will be generated:

Offset may be past the trailing edge. Setting SZERO = 1.

Table 28 shows an example of this data input line.

sLEWICE sinputsslopa szeroa +=

NASA/CR—2002-211793 127
Table 86: Example input for hot air data file characteristics 

input parameters for reading in hot air HTC info

iscola jscola kscola sslopa szeroa

 2 3 3 1.d0 0.d0

10.1.4.9 ISCOLQ, JSCOLQ, KSCOLQ, SSLOPQ, SZEROQ

This input data line consists of the same five variables as the previous input line, except the

variables on this line pertain to reading in heat flux data (IQAIN = 1). That is, ISCOLQ contains

the column number containing the wrap distances for heat flux data input, JSCOLQ contains the

column number containing the heat fluxes in kW/m2 and KSCOLQ contains the total number of

data columns in the input data file. Similarly, SSLOPQ and SZEROQ are the conversion factor

for the wrap distances and the offset, respectively. The limits on input and warning messages generated are the same as those listed in Section 10.1.4.8 and therefore will not be repeated here. The

relationship between the wrap distances read in Section 10.3 and the wrap distances within

LEWICE is also given by the equation in the previous section. Section 10.3 contains further information on the format of the input data file “QAI.INP” which contains the bleed air heat flux values.Table 29 shows an example of this data input line.

Note: Heat flux values are input (and output) in units of kW/m2 while thermal conductivity

and heat transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively.

Table 87: Example input for wall heat flux data file characteristics

input parameters for reading in hot air q_wall info

iscolq jscolq kscolq sslopq szeroq

 1 2 2 1.d0 0.d0

10.1.4.10 ISCOLS, JSCOLS, KSCOLS, SSLOPS, SZEROS

This input data line consists of the same five variables as the previous two input lines, except

the variables on this line pertain to reading in 3D streamline data (I3D = 1). That is, ISCOLS contains the column number containing the wrap distances for 3D streamline data input, JSCOLS

contains the column number containing the 3D streamline ratios and KSCOLS contains the total

number of data columns in the input data file. Similarly, SSLOPS and SZEROS are the converNASA/CR—2002-211793 128
sion factor for the wrap distances and the offset, respectively. The limits on input and warning

messages generated are the same as those listed in Section 10.1.4.8 and therefore will not be

repeated here. The relationship between the wrap distances read in Section 10.4 and the wrap distances within LEWICE is also given by the equation in the previous section. Section 10.4 contains

further information on the format of the input data file “STREAM.INP” which contains the 3D

streamline values. Table 30 shows an example of this data input line.

Table 88: Example input for 3D streamline data file characteristics

input parameters for reading in 3D streamline info

iscols jscols kscols sslops szeros

 1 2 2 1.d0 0.d0

10.1.4.11 Complete input section example

This completes the descriptions for the fourth input data section. Table 31 shows an example

with all of the input data read in this section.

Table 89: Complete input example for fourth data section

________________________________________________________________________

C miscellaneous data

________________________________________________________________________

C

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

C

i3d iqain ibleed iqw

 0 0 0 1 

C

icond ibound init ish istd igde

 1 3 2 1 1 1

C

 tsurf ievap itherm

 278.d0 1 0

C

sta rpm irot

NASA/CR—2002-211793 129
10.d0 0.d0 1 

C

dtaui nisp dtaum nmsp dtauf jcountd

1.d-1 1000 1.d-1 1000 1.d-1 10

C

tspray tafter

 0.d0 0.d0

C

input parameters for reading in hot air HTC info

iscola jscola kscola sslopa szeroa

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

iscolq jscolq kscolq sslopq szeroq

 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

iscols jscols kscols sslops szeros

 1 2 2 1.d0 0.d0

10.1.5 De-icer Section 5

The last section of the de-icer input file defines parameters which control how temperatures

will be output from LEWICE 2.2. There are two main styles of temperature output from the software. The first style will output temperatures in the entire domain using a specified file format.

This style is suitable for importing results into post-processor software. The second style outputs

temperatures at selected locations in space and time in column format consistent with the output

style used for the other output files generated by LEWICE 2.2.

Note: If there was an error reading data in a previous section, the software will continue to

read the rest of the input file. However, an error in an earlier section can cause incorrect error

messages to appear for subsequent sections. It is highly recommended that the user fix the first

errors encountered and resubmit the case.

NASA/CR—2002-211793 130
10.1.5.1 NPRT, NPRF

The first line of data input in this section defines how many post-processor files the user wants

and a flag defining the file format to be used. The first variable, NPRT, defines the number of

times the software will output two very large files: one containing the grid for the de-icer and ice

shape; the other containing the 2D solution file. This number must be 0 ≤ NPRT ≤ 50. If a value is

input which is outside this range, the following warning message will be generated:

Number of output files must be between zero (0) and 50.

 Your value of (value) is out of range. Setting NPRT = 0

The second variable on this line, NPRF, defines the output format for these files. If NPRF = 0,

the flies will be output in PLOT3D format. This is a standard output file format for post-processing software on Silicon Graphics and other unix platforms. If NPRF = 1, the files will be output in

TECPLOT format. TECPLOT is a widely used post-processing software on the PC. Users who

wish to have additional output file formats should contact the NASA Glenn Icing Branch. Valid

input values for NPRF are 0 and 1. If a value is input which is outside this range, the following

warning message will be generated:

Output file format flag must be zero (0) or one (1).

Your value of (value) is out of range. Setting NPRF = 0.

10.1.5.2 ITIME

The following NPRT number of lines contains the times at which this style output will be generated. Values should be input as integers (no decimal points) and cannot be negative values. If a

value is input which is outside this range, the following warning message will be generated:

Printout time number (value) must be greater than or equal to zero (0). 

Your value of (value) is out of range. Setting ITIME = 1000.

NASA/CR—2002-211793 131
Table 32 contains an example of the first series of data input for this section.

Table 90: Example input for PLOT3D style output

nprt nprf 

 10 0 

itime values (seconds)

 10

 20

 30

 40

 50

 60

 70

 80

 90

100

Note: Output times do not have to be in equal time increments as is shown in the example

input.

Note: Previous versions of the LEWICE/Thermal software used time step instead of time.

10.1.5.3 NTYPE

The next line of data input defines the number of output types the user wants. There are five

output types which can be generated by the software. These are defined as follows: 1) temperature

is output as a function of time at user-selected x,y locations (IOTYPE = 1); 2) temperature is output as a function of wrap distance at user-selected times and layer locations (IOTYPE = 2); 3)

temperature is output as a function of the normal distance at user-selected times and wrap distance

locations (IOTYPE = 3); 4) all temperatures are output in ASCII format (IOTYPE = 4); and, 5)

temperatures at every node are output at user-specified times (IOTYPE = 5). This line of data

input selects the number of output types desired. The user should select NTYPE = 1 if only one of

these output types is needed. Valid inputs for NTYPE are 1 to 4. If a value is input which is outside this range, the following warning message will be generated:

NASA/CR—2002-211793 132
Print type must be between one (1) and four (4).

Your value of (value) is out of range. Setting NTYPE = 1

Note: The last two output types (IOTYPE = 4 or 5) are intended for debugging purposes and

should not normally be needed by the user. 

10.1.5.4 IOTYPE, NPTSD

The next line of data input contains the type of output being requested (IOTYPE) and the

number of points which the user wants output (NPTSD). The output type, IOTYPE, defines

which of the five outputs will be generated. IOTYPE = 1 provides the same type of output as a

thermocouple, namely it outputs temperature at a specific location as a function of time. IOTYPE

= 2 outputs temperature as a function of wrap distance at specified times and given layers. For

example, it can provide the surface temperature as a function of wrap distance at specified times

and/or it can output heater temperatures as a function of wrap distance. IOTYPE = 3 outputs temperature as a function of the normal direction at specified wrap distance locations and times. For

example, the user could output the temperature at the parting strip for selected times as a function

of the normal distance through the heater. This output type may be useful to look for “hot spots”

in a heater section. IOTYPE = 4 outputs the temperatures at every node at all time steps and

should only be used for debugging purposes. Similarly, IOTYPE = 5 outputs the temperature at

every node, but only at user-selected times. Valid inputs for IOTYPE are 1 to 5. If a value is input

which is outside this range, the following warning message will be generated:

Printout type must be between one (1) and five (5).

Your value of (value) is out of range. Setting IOTYPE = 1

The next variable on this line, NPTSD, defines the number of points the user wants to output

for type IOTYPE. Valid inputs for NPTSD are 0 ≤ NPTSD ≤ 50. If a value is input which is outside this range, the following warning message will be generated:

Number of printouts must be between zero (0) and 50.

NASA/CR—2002-211793 133
 Your value of (value) is out of range. Setting NPTSD = 0

10.1.5.5 ILAYER, IWHERE, JLAYER, JWHERE

The user must input NTYPE number of lines which contain the values for IOTYPE and

NPTSD. These data lines are not input sequentially, however. After each data line containing values of IOTYPE and NPTSD, there must be NPTSD number of lines containing the output locations for that data type. These locations are read in as the variables ILAYER, IWHERE, JLAYER

and JWHERE. Each data type has a different input format type, each of which will be described in

this subsection. 

For IOTYPE = 1, the user must input NPTSD number of lines, each of which contains four

variables. Rather than input node numbers or distances which may be unknown, the input has

been set up to have the user input the layer and section numbers where temperature is to be output. The first variable, ILAYER, defines the section in the wrap direction where the user wants

temperature output. The second variable, IWHERE, tells the software to take the left (1), middle

(2) or right (3) side of the section. The third variable, JLAYER, defines the layer number where

the user wants temperature output and the last variable, JWHERE, tells the software to take the

bottom (1), middle (2), or top (3) side of the layer. This means of selecting temperature output is

diagramed in Figure 11. In this figure, a sample grid block is shown with 15 nodes in the wrap

direction and five in the normal direction. The open circles denote the nodes in the grid, while the

solid circles represent the locations in this block which can be output using the IOTYPE = 1 designation.

Figure 11: Potential IOTYPE = 1 (thermocouple) locations in a grid block

NASA/CR—2002-211793 134
For IOTYPE = 1, valid inputs for ILAYER are from 1 to the number of sections, NXDE (Section 10.1.1.1). If a value is input which is outside this range, the following warning message will

be generated:

 Printout section must be between one (1) and the number of sections. Your value of (value) is

out of range.Setting ILAYER = NXDE.

For IOTYPE = 1, valid inputs for JLAYER are from 1 to the number of layers, LDE (Section

10.1.1.1).If a value is input which is outside this range, the following warning message will be

generated:

 Printout layer must be between one (1) and the number of layers. Your value of (value) is out

of range. Setting ILAYER = LDE.

Valid inputs for IWHERE are from 1 to 3. If a value is input which is outside this range, the

following warning message will be generated:

Printout flag must be between one (1) and three (3) Your value of (value) is out of range. Setting IWHERE = 2

Similarly, valid inputs for JWHERE are from 1 to 3. If a value is input which is outside this

range, the following warning message will be generated:

Printout flag must be between one (1) and three (3) Your value of (value) is out of range. Setting JWHERE = 2

For IOTYPE = 2, the user must input NPTSD number of lines which contain the time and

location of temperatures for this output type. In this case, however, the user inputs only three values for each line: ILAYER, JLAYER, and JWHERE. For IOTYPE = 2, ILAYER contains the

times at which output is to take place. JLAYER and JWHERE have the same definition as for

IOTYPE = 1. For IOTYPE = 2, ILAYER need only be ≥ 0. If a value is input which is outside this

range, the following warning message will be generated:

NASA/CR—2002-211793 135
Printout time cannot be negative. Your value of (value) is out of range. Setting ILAYER =

1000

For IOTYPE = 3, the user must input NPTSD number of lines which contain the time and

location of temperatures for this output type. In this case, however, the user inputs only three values for each line: ILAYER, JLAYER, and JWHERE. For IOTYPE = 3, ILAYER contains the

times at which output is to take place. JLAYER and JWHERE now contain the section number

and location where temperature output will occur for this output type. Valid inputs are: ILAYER

≥ 0, 1 ≤ JLAYER ≤ NXDE, 1 ≤ JWHERE ≤ 3. If a value is input which is outside this range, the

warnings previously given will generated for the proper variable.

For IOTYPE = 4, the user does not input any additional lines of data, since no descriptors are

needed. For IOTYPE = 5, the user must input NPTSD number of lines which contain the time at

which temperatures will be output. In this case, the user inputs one variable on each line, namely

ILAYER. Valid inputs for ILAYER are ≥ 0 and the previously listed warning message will be

generated if the data input is outside this range. Finally, Table 33 shows an example of the data

input in this subsection.

Table 91: Example input for temperature output flags

C ntype = number of types of output 

C 

ntype

 3

C

C iotype = type of output requested 

C nptsd = number of points to be output 

C

iotype nptsd

 1 20

C section where layer where (20 data lines to follow)

 5 2 6 3

 5 2 7 3

 4 2 6 3

 4 2 7 3

NASA/CR—2002-211793 136
 6 2 6 3

 6 2 7 3

 3 2 6 3

 3 2 7 3

 7 2 6 3

 7 2 7 3

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 5 2 1 1

 4 2 1 1

 6 2 1 1

 3 2 1 1

 7 2 1 1

C

C iotype = type of output requested 

C nptsd = number of points to be output 

C

iotype nptsd

 2 10

C

C time layer where

C (sec) (10 data lines to follow)

 10 6 1

 20 6 1

 30 6 1

 40 6 1

 50 6 1

 60 6 1

 70 6 1

 80 6 1

 90 6 1

 100 6 1

C

NASA/CR—2002-211793 137
C iotype = type of output requested 

C nptsd = number of points to be output 

C

iotype nptsd

 3 10

C time section where

C (sec) (10 data lines to follow)

 10 5 2

 20 5 2

 30 5 2

 40 5 2

 50 5 2

 60 5 2

 70 5 2

 80 5 2

 90 5 2

 100 5 2

10.1.6 Complete example for de-icer input file

This completes the description of the input for the de-icer input file. Table 34 shows a complete example of an input file with comments.

Table 92: Example of complete de-icer input file

 ________________________________________________________________________

C data for the composite body

________________________________________________________________________ 

C

C lde= total number of layers in the normal direction

C nxde= total number of heater sections in the wrap direction

C

lde nxde

007 009

C

C Data for each layer:

C

NASA/CR—2002-211793 138
C nodes = # of points in that layer or section

C length = length (thickness) of layer or section

C

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn.

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

C

C Data for each heater/gap section: 

C

 # of length cond. diff. anisotropy slope(b) of add. layer 

 nodes (m) (W/m/K) (m^2/s) of heater temp. eqn. length (m) number 

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

NASA/CR—2002-211793 139
C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C

________________________________________________________________________

C data for the heater

________________________________________________________________________

C

ijde offset ipar

004 0.005 1

 “QDE” “TON” “TOFF” “TLAG” “ICFLAG”

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 12.02d0 5.d0 115.d0 115.d0 0

C heater E

 11.19d0 5.d0 115.d0 115.d0 0

C heater C

 11.25d0 5.d0 115.d0 110.d0 0

C parting strip (heater A) does not turn off

 07.78d0 150.d0 0.d0 0.d0 0

C heater B

 11.68d0 5.d0 115.d0 110.d0 0

C heater D

 11.27d0 5.d0 115.d0 115.d0 0

C heater F

 11.75d0 5.d0 115.d0 115.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

________________________________________________________________________

C boundary condition data

NASA/CR—2002-211793 140
________________________________________________________________________

C

C Type of boundary condition:

C

“ibc1” “ibc2” “ibc3” “ibc4”

 2 2 2 2

C

C Temperature data for bottom, left, and side boundaries

C

 “tg1” “tg2” “tg3” “tg4”

 263.3 263.3 263.3 263.3

C

C Heat transfer coeff. in W/m^2/K

C

 “h1” “h2” “h3” “h4”

 3.d0 3.d2 0.d0 0.d0

C

C Wall heat flux in kW/m^2

C

 “qw1” “qw2” “qw3” “qw4”

 0.d0 0.d0 0.d0 0.d0

________________________________________________________________________

C miscellaneous data

________________________________________________________________________

C

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

C

i3d iqain ibleed iqw

 0 0 0 1 

C

icond ibound init ish istd igde

 1 3 2 1 1 1

C

tsurf ievap itherm

 278.d0 1 0

NASA/CR—2002-211793 141
C

sta rpm irot

10.d0 0.d0 1 

C

dtaui nisp dtaum nmsp dtauf jcountd

1.d-1 1000 1.d-1 1000 1.d-1 10

C

tspray tafter

 0.d0 0.d0

C

input parameters for reading in hot air HTC info

iscola jscola kscola sslopa szeroa

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

iscolq jscolq kscolq sslopq szeroq

 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

iscols jscols kscols sslops szeros

 1 2 2 1.d0 0.d0

________________________________________________________________________

C input/output parameters

________________________________________________________________________

nprt nprf 

 10 1 

itime values (seconds)

 10

 20

 30

 40

 50

 60

 70

 80

 90

100

C ntype = number of types of output 

NASA/CR—2002-211793 142
C 

ntype

 3

C

C iotype = type of output requested 

C nptsd = number of points to be output 

C

iotype nptsd

 1 20

C section where layer where (20 data lines to follow)

 5 2 6 3

 5 2 7 3

 4 2 6 3

 4 2 7 3

 6 2 6 3

 6 2 7 3

 3 2 6 3

 3 2 7 3

 7 2 6 3

 7 2 7 3

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 5 2 1 1

 4 2 1 1

 6 2 1 1

 3 2 1 1

 7 2 1 1

C

C iotype = type of output requested 

C nptsd = number of points to be output 

C

iotype nptsd

 2 10

NASA/CR—2002-211793 143
C

C time layer where

C (sec) (10 data lines to follow)

 10 6 1

 20 6 1

 30 6 1

 40 6 1

 50 6 1

 60 6 1

 70 6 1

 80 6 1

 90 6 1

 100 6 1

C

C iotype = type of output requested 

C nptsd = number of points to be output 

C

iotype nptsd

 3 10

C time section where

C (sec) (10 data lines to follow)

 10 5 2

 20 5 2

 30 5 2

 40 5 2

 50 5 2

 60 5 2

 70 5 2

 80 5 2

 90 5 2

 100 5 2

10.2 Hot Air Heat Transfer Coefficient Input File (HI.INP)

LEWICE 2.2 has two methods for reading in data to be used in analyzing hot air anti-icing

performance. In this first approach, if IBLEED = 1 in the de-icer input file as specified in Section

10.1.4.2, then the program will read in a file named “HI.INP” which contains the values of the hot

NASA/CR—2002-211793 144
air heat transfer coefficients in W/m2/K. The first line of this data file contains the number of

points to be read. Subsequent lines contain at least two columns of data: one column which contains the wrap distance locations and a second column containing the hot air heat transfer coefficients. The wrap distance values are expected to be nondimensionalized by chord with the zero

wrap distance value at the lower surface trailing edge of the body, with values proceeding clockwise from that location. These defaults can be changed as described in Section 10.1.4.8 except

that the data must be input clockwise starting from the lower surface trailing edge. Since only

wrap distance locations are read in, clockwise input cannot be checked for by the software. The

heat transfer coefficients must be in units of W/m2/K. Other options on this input file are also discussed in Section 10.1.4.8.

The number of data points must be at least 2 and cannot be greater than 10000 (104). If the

value read is outside this range, the following error message will be generated:

Number of hot air values input is out of range. Fix HI.INP input and resubmit. NEL = (value)

Program will stop because of this error

If one or more of the wrap distance values do not reside on the body geometry, the following

warning message will be generated:

Wrap distance value input is out of range.srj(i) = (value) at location i = (value) limit =

(value)

The variables output are the wrap distance input (after being translated using SSLOPA and

SZEROA), the index of the wrap distance and the wrap distance limit which was exceeded. For

example if the first wrap distance value is negative after translation, then this warning will appear

since the lower wrap distance limit is zero. 

Note: It is normal for there to be a slight difference in wrap distance values between two different programs. Small differences may be ignored.

NASA/CR—2002-211793 145
Note: The user should input values for the entire wrap distance region. The program needs

values for the entire body geometry and extrapolation from the values provided can yield poor

results.

After the file has been processed, if any warning messages are issued the following confirmation will appear:

(value) warnings have been issued when reading HI values. 

Do you wish to continue (Y / N)?

The user must input the character ‘y’ or ‘Y’ to continue the run.

If any error messages were generated, the following message will appear:

(value) errors have been found when reading HI values. 

Program will stop because of this error.

The user must fix the errors and resubmit the case.

10.3 Hot Air Heat Flux Input File (QAIN.INP)

The second method of reading in data for a hot air anti-icer can be accessed by specifying

IQAIN = 1 in the de-icer input file as described in Section 10.1.4.2. In this case, the program will

read in a file named “QAIN.INP” which contains the values of the hot air heat fluxes. The first

line of this data file contains the number of points to be read. Subsequent lines contain at least two

columns of data: one column which contains the wrap distance locations and a second column

containing the heat fluxes. The wrap distance values are expected to be nondimensionalized by

chord with the zero wrap distance value at the lower surface trailing edge of the body, with values

proceeding clockwise from that location. These defaults can be changed as described in Section

10.1.4.9 except that the data must be input clockwise starting from the lower surface trailing edge.

Since only wrap distance locations are read in, clockwise input cannot be checked for by the software. The heat fluxes must be in units of kW/m2. Other options on this input file are also discussed in Section 10.1.4.9.

NASA/CR—2002-211793 146
The number of data points must be at least 2 and cannot be greater than 10000 (104). The

warning and error messages associated with this file are the same as those described in Section

10.2 and will not be repeated.

10.4 3D Streamline Input file (STREAM.INP)

LEWICE 2.2 can be used to analyze a three dimensional geometry using a pseudo-3D

approach. The user inputs a 2D cross-section in the geometry input file and then specifies in a file

named “STREAM.INP” the dimensionless distance between two cross-sections at each wrap distance location. This is diagrammed in Figure 12.

Figure 12: Representation of 3D streamline data

This input file will be read when I3D = 1 as described in Section 10.1.4.2. The first line of this

data file contains the number of points to be read. Subsequent lines contain at least two columns

of data: one column which contains the wrap distance locations and a second column containing

the spanwise distances. The wrap distance values are expected to be nondimensionalized by chord

with the zero wrap distance value at the lower surface trailing edge of the body, with values proceeding clockwise from that location. These defaults can be changed as described in Section

10.1.4.9 except that the data must be input clockwise starting from the lower surface trailing edge.

Since only wrap distance locations are read in, clockwise input cannot be checked for by the software. The spanwise distances must be nondimensionalized by the chord length. Other options on

this input file are also discussed in Section 10.1.4.10.

The number of data points must be at least 2 and cannot be greater than 10000 (104). The

warning and error messages associated with this file are the same as those described in Section

10.2 and will not be repeated.

streamline A

streamline B

spanwise distance at wrap distance loc

NASA/CR—2002-211793 147
10.5 Grid Input Files (XY.PLT and Q.PLT)

LEWICE 2.2 has the option to bypass the potential flow solution and read in a flow solution

from a grid-based flow solver. This option limits the user to a single time step. This option has

also seen very limited testing and has not been validated against the database of experimental ice

shapes. It can read up to 10 grid blocks and each block can contain up to 600x200 grid points. The

import format for the grid conforms to the PLOT3D11 format with iblanking. The input data files

must contain REAL*4 binary data. The read statements needed to create the files are as follows:

10.5.1 Grid read statements (XY.PLT)

 Read(2) mg

 Read(2) (imns(mqf),jmns(mqf),mqf=1,mg)

 Read(2) ((xg(i,j,mqf),i=1,im),j=1,jm),

1 ((yg(i,j,mqf),i=1,im),j=1,jm),

2 ((iblank(i,j,mqf),i=1,im),j=1,jm)

10.5.2 Flow solution read statements (Q.PLT)

 Read(2) mg

 Read(2) (imns(mqf),jmns(mqf),mqf=1,mg)

 Read(2) mach, alpha, reair, time 

 Read(2) ((q(i,j,1),i=1,im),j=1,jm),

1 ((q(i,j,2),i=1,im),j=1,jm),

2 ((q(i,j,3),i=1,im),j=1,jm),

3 ((q(i,j,4),i=1,im),j=1,jm)

Note: For a single body, LEWICE 2.2 assumes that the grid is in the single block format used

by PLOT3D. Therefore, the number of grid blocks (mg) is not read in.

There is no error checking of the grid and solution file. The user should independently verify that the grid and solution files are correct for the case being run. In particular, the angle of

attack and velocity should match the values input in the main input data file. The program will

also not run with a grid solution unless the grid surface geometry is very similar to the body

geometry read in from the geometry input file(s). An example case is provided in this manual

NASA/CR—2002-211793 148
which uses the grid input function. The example case will further describe errors which can occur

when using this feature.

The variables conform to the standard PLOT3D with multiple grids with IBLANKing. The

first grid variable, MG, contains the number of grid blocks being read. The second set of grid

variables, IMNS and JMNS, contain the number of grid points in each direction of the grid block.

The variables XG and YG contain the grid coordinates and the variable IBLANK is an integer

value which describes detains about that grid node. Within LEWICE, IBLANK = 1 activates the

grid node and IBLANK = 0 deactivates the node. 

The flow solution file also contains the number of grid blocks and the grid dimensions. The

following line contains ambient Mach number, angle of attack, Reynolds number, and time in

seconds. These values are not used by LEWICE with the exception of Mach number which is

used to calculate primitive variables from Eqs. 16-18. However, if these values are different from

the corresponding values read or calculated from the LEWICE main input file then the answers

obtained from the analysis may not be correct. The four flow solution variables are defined as follows:

(15)

(16)

(17)

(18)

10.6 Pressure Coefficient Input File (RFLOW.INP)

LEWICE 2.2 will read in this optional input file if ICP = 1 in the main input file, as specified

in Section 8.3.10. In this case, the program will read in a file named “RFLOW.INP” which contains the values of the pressure coefficients and bypass the calculation of this value in the software. The first line of this data file contains the number of points to be read. Subsequent lines

q1 ρ

ρ∞

= ------

q2 ρ

ρ∞

------u

a

-- ρ

ρ∞

------ u

V ∞

-------M∞ = =

q3 ρ

ρ∞

------ v

a

-- ρ

ρ∞

------ v

V ∞

-------M∞ = =

q4 P

P∞

------ 1

γ 1– ----------- 12

-- ρ

ρ∞

------ u

a

--  

  2 v

a

--  

  2

+  

  +=

NASA/CR—2002-211793 149
contain at least two columns of data: one column which contains the wrap distance locations and

a second column containing the pressure coefficients. The wrap distance values are expected to be

nondimensionalized by chord with the zero wrap distance value at the lower surface trailing edge

of the body, with values proceeding clockwise from that location. These defaults can be changed

as described in Section 8.3.10 except that the data must be input clockwise starting from the lower

surface trailing edge. Since only wrap distance locations are read in, clockwise input cannot be

checked for by the software. The pressure coefficients are by definition dimensionless. Other

options on this input file are also discussed in Section 8.3.10.

The number of data points must be at least 2 and cannot be greater than 10000 (104). The

warning and error messages associated with this file are the same as those described in Section

10.2 and will not be repeated.

Note: As stated in Section 8.3.10, surface pressures are insufficient for calculating droplet trajectories. The user must include either a grid flow solution (which makes the “RFLOW.INP” file

redundant) or supply collection efficiencies (IBETA = 1) to use this option.

10.7 Collection Efficiency Input File (RBETA.INP)

LEWICE 2.2 will read in this optional input file if IBETA = 1 in the main input file as specified in Section 8.3.11. In this case, the program will read in a file named “RBETA.INP” which

contains the values of the collection efficiencies and bypass the calculation of this value in the

software. The first line of this data file contains the number of points to be read. Subsequent lines

contain at least two columns of data: one column which contains the wrap distance locations and

a second column containing the collection efficiencies. The wrap distance values are expected to

be nondimensionalized by chord with the zero wrap distance value at the lower surface trailing

edge of the body, with values proceeding clockwise from that location. These defaults can be

changed as described in Section 8.3.11 except that the data must be input clockwise starting from

the lower surface trailing edge. Since only wrap distance locations are read in, clockwise input

cannot be checked for by the software. The collection efficiencies are by definition dimensionless. Other options on this input file are also discussed in Section 8.3.11.

NASA/CR—2002-211793 150
The number of data points must be at least 2 and cannot be greater than 10000 (104). The

warning and error messages associated with this file are the same as those described in Section

10.2 and will not be repeated.

10.8 External Heat Transfer Coefficient Input File (RHTC.INP)

LEWICE 2.2 will read in this optional input file if IHTC = 1 in the main input file as specified

in Section 8.3.12. In this case, the program will read in a file named “RHTC.INP” which contains

the values of the external heat transfer coefficients and bypass the calculation of this value in the

software. The first line of this data file contains the number of points to be read. Subsequent lines

contain at least two columns of data: one column which contains the wrap distance locations and

a second column containing the external heat transfer coefficients. The wrap distance values are

expected to be nondimensionalized by chord with the zero wrap distance value at the lower surface trailing edge of the body, with values proceeding clockwise from that location. These

defaults can be changed as described in Section 8.3.12 except that the data must be input clockwise starting from the lower surface trailing edge. Since only wrap distance locations are read in,

clockwise input cannot be checked for by the software. The external heat transfer coefficients are

expected to be in kW/m2/K. Other options on this input file are also discussed in Section 8.3.12.

The number of data points must be at least 2 and cannot be greater than 10000 (104). The

warning and error messages associated with this file are the same as those described in Section

10.2 and will not be repeated.

10.9 External Heat Flux Input File (QEXTIN.INP)

LEWICE 2.2 will read in this optional input file if IQEX = 1 in the main input file as specified

in Section 8.3.13, then the program will read in a file named “QEXTIN.INP” which contains the

values of the external heat fluxes and bypass the calculation of the external heat transfer coefficient in the software. The first line of this data file contains the number of points to be read. Subsequent lines contain at least two columns of data: one column which contains the wrap distance

locations and a second column containing the external heat fluxes. The wrap distance values are

expected to be nondimensionalized by chord with the zero wrap distance value at the lower surface trailing edge of the body, with values proceeding clockwise from that location. These

NASA/CR—2002-211793 151
defaults can be changed as described in Section 8.3.13 except that the data must be input clockwise starting from the lower surface trailing edge. Since only wrap distance locations are read in,

clockwise input cannot be checked for by the software. The external heat fluxes are by expected

to be in kW/m2. Other options on this input file are also discussed in Section 8.3.13.

The number of data points must be at least 2 and cannot be greater than 10000 (104). The

warning and error messages associated with this file are the same as those described in Section

10.2 and will not be repeated.

Note: Heat flux values are input (and output) in units of kW/m2 while thermal conductivity

and heat transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively.

NASA/CR—2002-211793 152
Chapter 11: Output Files

This list contains a description of the LEWICE output files included on the distribution disk.

It will also duplicate some of the input file information where necessary. Data is output sequentially with regard to time. This means that the first set of outputs in a given file are the results for

the first time step, the second set of outputs are the results for the second time step and so on. This

is illustrated in Table 35. The values in parenthesis in the following descriptions are the titles used

for the columns of data in the output files.

Table 93: Example of Data Format in Output Files

Header Text

data from time step 1

data from time step 2

.

.

.

data from last time step

Note: All input and output file names have been presented in uppercase to make them stand

out in the manual. The actual input and output files on the CD-ROM have lower case filenames

and all output files from LEWICE 2.2 have lowercase filenames.

11.1 BETA.DAT 

This file contains collection efficiency output for each time step. Columns are dimensionless

wrap distance from the stagnation point (s/c), collection efficiency (beta), dimensionless wrap

distance as measured from the airfoil leading edge (sle/c), dimensionless x-coordinate of the airfoil (x/c) and dimensionless y-coordinate of the airfoil (y/c). This output will be generated if the

output flag BPRT is set to 1. When a drop size distribution is used, only the composite collection

efficiency is written. The collection efficiency for each individual drop size is not output.

Note: The format for this output file has changed since the validation runs were made. At that

time, the format for this file conformed to the output format specified in the LEWICE 1.6 User

Manual6. The current output format is based upon several requests from users.

NASA/CR—2002-211793 153
Note: The wrap distance from the leading edge may lose physical meaning past the first time

step.

Note: The impingement limit listed in the output file “IMP.DAT” may not match the wrap

distance location where the collection efficiency (beta) goes to zero in the output file

“BETA.DAT”. The difference is due to the resolution of surface points in the impingement limit

region. The value quoted in the file “IMP.DAT” is the computed impingement limit. The location

where the collection efficiency goes to zero is a function of both the computed impingement limit

and the body geometry coordinates.

11.2 DENS.DAT

This file contains predicted ice density at each location for each time step. Columns are: wrap

distance from stagnation (s/c) and ice density (density) in kg/m3. If the input flag MPRT is set to

1, the output from every 1/10th control volume will be generated. If this flag is set to 2, the output

from every control volume will be generated.

Note: Ice density in LEWICE is fixed at a value of 917 kg/m3. There exists two correlations

within the source code which are currently inactive due to undesirable numerical side effects.

Developers who wish to activate these correlations can do so by changing an internal flag in the

source code.

11.3 DYICE.DAT

This file contains ice thickness and other results from the mass balance. Columns are: wrap

distance from stagnation (s/c), ice height to be added at each location (dice), velocity of runback

water (vrunback) in m/s, and the ice area to be added at each location (aice) in m2. If the input flag

MPRT is set to 1, the output from every 1/10th control volume will be generated. If this flag is set

to 2, the output from every control volume will be generated.

11.4 FINAL1.DAT

This file contains the final ice shape produced by LEWICE on the first body. If the program

stopped due to an error, this file will not be output. Each line contains the dimensionless x,y coordinates of the final ice shape. This file format can also be used as input to the utility program

NASA/CR—2002-211793 154
THICK which calculates parameters of the ice shape for comparison with digitized ice shapes

from experiments.

Note: The file format has changed from the format used in LEWICE 2.0.

11.5 FINAL2.DAT, FINAL3.DAT, FINAL4.DAT, FINAL5.DAT

These files contain the final ice shape for the other bodies. “FINAL2.DAT” contains the iced

geometry for the second body, “FINAL3.DAT” contains the iced geometry for the third body and

so on. These files will be generated only if more than one body is being simulated. The data is formatted the same as for file “FINAL1.DAT”.

Note: The file format has changed from the format used in LEWICE 2.0.

11.6 FIXED.DAT

This file contains the clean airfoil geometry after the initial geometry checks. This file will

only be output if the geometry has changed as a result of this error checking. See the section on

the geometry input file for a listing and description of these checks. The data for this file consists

of the new x,y coordinates for every body. Each body is offset by the header “Body # (value)”.

The first column of the output file contains the new x-coordinates while the second column contains the y-coordinates of the changed geometry. The user should check this geometry to ensure

that the corrections made by the software are acceptable. If they are not, the user will need to fix

the geometry input file and resubmit this case.

11.7 FLOW.DAT 

This file contains the output from the potential flow solution at each time step. Columns contain the panel index (i), dimensionless x,y coordinates (x/c, y/c) at the panel center (not at the endpoints as with other files), dimensionless wrap distance as measured from the lower surface

trailing edge (s/c), dimensionless tangent velocity (vt), pressure coefficient (cp), a separate panel

index for each body (j), the panel source/sink value (sigma), and the dimensionless normal velocity (vn). One flow solution is written to disk for each time step and an additional flow solution is

generated on the final ice shape before the program exits. Prior to version 2.0, the last flow solution performed by LEWICE was on the iced geometry at the next-to-last time step. This output

NASA/CR—2002-211793 155
will be generated if the input flag FPRT is set to 1 or 2. However, no output will be generated to

this file if the user sets the grid flag on (IGRID = 1) or the flow field input flag on (ICP = 1) since

the potential flow solution will not be performed if either flag is set on. 

11.8 FRACT.DAT

This file contains mass fraction output from the LEWICE mass balance at each time step. Columns are dimensionless wrap distance from stagnation (s/c), mass fraction of incoming water

which does not freeze, evaporate, or runback (xtot), mass fraction of incoming water which

freezes (ffrac), mass fraction of incoming water which evaporates (envap), and scaling factor for

runback (xvr). The mass fraction of incoming water which freezes is commonly known as the

freezing fraction. If the input flag MPRT is set to 1, the output from every 1/10th control volume

will be generated. If this flag is set to 2, the output from every control volume will be generated.

Note: The output is generated starting from the stagnation point toward the lower surface

trailing edge. Output from the stagnation point toward the upper surface trailing edge follows this.

Output from subsequent time steps will follow after the output from the first time step, as is the

case for the other output files.

11.9 HTC.DAT 

This file contains the convective heat transfer coefficient at each time step. Columns are segment number (seg), dimensionless wrap distance from stagnation (s/c), heat transfer coefficient

(htc) in W/m2/K, and Frössling number (fr). The Frössling number output is the local Nusselt

number divided by the square root of the ambient Reynolds number. If the input flag HPRT is set

to 1, the output from every 1/10th control volume will be generated. If this flag is set to 2, the output from every control volume will be generated.

11.10 ICE1.DAT 

This file contains the ice shape for the first body at each time step. Columns contain the

dimensionless coordinates of the ice shape (x/c, y/c), dimensionless ice thickness (thick/c) and

wrap distance from the stagnation point (s/c). The first set of points contains the airfoil prior to

NASA/CR—2002-211793 156
any ice build up. Each successive set of data contains the ice shape at a specified point in time.

The last set of data contains the final ice shape, which is also output to the file “FINAL1.DAT”.

Note: The file format has changed from the format used in LEWICE 2.0.

11.11 ICE2.DAT, ICE3.DAT, ICE4.DAT, ICE5.DAT

These files contain the ice shape for the other bodies at each time step. “ICE2.DAT” contains

the iced geometry for the second body, “ICE3.DAT” contains the iced geometry for the third

body and so on. These files will be generated only if more than one body is being simulated. The

data is formatted the same as for file “ICE1.DAT”.

Note: The file format has changed from the format used in LEWICE 2.0.

11.12 IMP.DAT 

This file contains information related to the impingement limit for each time step. Columns

are droplet size (size) in microns, dimensionless x-coordinate of the lower impingement limit

(xlow), dimensionless y-coordinate of the lower impingement limit (ylow), dimensionless wrap

distance from stagnation to the lower impingement limit (slow), dimensionless wrap distance

from the leading edge to the lower impingement limit (slowle), dimensionless x-coordinate of the

upper impingement limit (xhi), dimensionless y-coordinate of the upper impingement limit (yhi),

dimensionless wrap distance from stagnation to the upper impingement limit (shi), and dimensionless wrap distance from the leading edge to the upper impingement limit (shile). This output

will be generated if the output flag BPRT is set to 1. If more than one body is being simulated,

data for the second body will be listed beneath the output for the first body and data for each subsequent body will follow this output.

Note: The wrap distance from the leading edge may lose physical meaning past the first time

step.

Note: The impingement limit listed in the output file “IMP.DAT” may not match the wrap

distance location where the collection efficiency (beta) goes to zero in the output file

“BETA.DAT”. The difference is due to the resolution of surface points in the impingement limit

NASA/CR—2002-211793 157
region. The value quoted in the file “IMP.DAT” is the computed impingement limit. The location

where the collection efficiency goes to zero is a function of both the computed impingement limit

and the number of points on the surface.

11.13 JUNK.DAT

This file contains information useful for debugging the software and any screen outputs

including warning or error messages. All of this output will be generated if the output flag IDBF

is set to 1. This flag only needs to be set on if problems occur when running the software. By

default in version 2.2, much of this printout is turned off. When the input flag IDBF is set to 0,

only the most important debug information is sent to this file.

11.14 LIMIT.DAT

This file contains the lower and upper icing limits for each time step. Due to runback or evaporation effects, this limit will be different than the impingement limit output to file “IMP.DAT”.

Columns are dimensionless coordinates of the lower icing limit (xlow/c, ylow/c), dimensionless

wrap distance of the lower icing limit from the leading edge of the clean airfoil (slow/c), dimensionless coordinates of the upper icing limit (xhi/c, yhi/c) and dimensionless wrap distance of the

upper icing limit from the leading edge of the clean airfoil (shi/c).

Note: The “LIMIT.DAT” output file was not generated in previous versions. The value for

the final time step should agree with output from the utility program THICK although roundoff

errors may cause the utility program to report an erroneous limit.

11.15 MASS.DAT

This file contains mass flux terms from the LEWICE mass balance at each time step. Columns

are dimensionless wrap distance from stagnation (s/c), mass of incoming water which freezes

(mdotf) in kg/m, mass of impinging water (mdotc) in kg/m, mass of incoming water which evaporates (mdote) in kg/m, mass of runback water (mdotri) in kg/m, mass of incoming water (mdotti)

in kg/m, mass of incoming water minus mass flux which evaporates (mdott) in kg/m, and potential mass which could be evaporated (emexs) in kg/m. If the input flag MPRT is set to 1, the outNASA/CR—2002-211793 158
put from every 1/10th control volume will be generated. If this flag is set to 2, the output from

every control volume will be generated.

Note: The output file has not changed from version 2.0. The output file description in the

LEWICE 2.0 manual were wrong.

11.16 MISC.DAT

This file contains other miscellaneous output from the software. It contains a complete copy

of the main input data file, lift results from the flow software, and individual trajectory information among other information.

11.17 PRES.DAT

This file contains the compressible flow solution at the edge of the boundary layer. Columns

are segment number (seg), dimensionless wrap distance from stagnation (s/c), dimensionless

velocity at the edge of the boundary layer (ve), dimensionless temperature at the edge of the

boundary layer (te), dimensionless pressure at the edge of the boundary layer (press) and dimensionless density at the edge of the boundary layer (ra). Reference variables which were used to

nondimensionalize these quantities are chord length, ambient velocity, freestream total temperature, freestream total pressure and freestream total density, calculated from the equation 

(19)

If the input flag HPRT is set to 1, the output from every 1/10th control volume will be generated. If this flag is set to 2, the output from every control volume will be generated.

11.18 QENER.DAT

This file contains individual terms from the energy balance. Columns are wrap distance from

stagnation (s/c), net convective heat loss (qconv), evaporative heat loss (qevap), sensible heat

loss/gain (qsens), latent heat gain (qlat), conduction heat loss/gain (qcond) and the sum of these

individual terms (qtot). The numbers in this last column should be very close to zero as an indicator that energy was balanced at that control volume. If the input flag EPRT is set to 1, the output

ρo

Po

RTo

---------=

NASA/CR—2002-211793 159
from every 1/10th control volume will be generated. If this flag is set to 2, the output from every

control volume will be generated.

11.19 TEMP.DAT

This file contains the surface temperature output from the energy balance. Columns are wrap

distance from stagnation (s/c), surface temperature (t) in degrees Kelvin, and ‘recovery’ temperature (t_rec) in degrees Kelvin. If the input flag EPRT is set to 1, the output from every 1/10th control volume will be generated. If this flag is set to 2, the output from every control volume will be

generated.

11.20 THICK.DAT

This file contains the ice thickness for each time step as measured from the clean surface. The

ice thickness output in the “ICE1.DAT” file provides the ice thickness measured from the current

ice shape. The “THICK.DAT” file was created to show the ice thickness from a common reference, i.e., the clean airfoil. This output file is similar to the ice thickness output file

“CLEAN.DAT” created by the utility program THICK. However, output is sent to

“THICK.DAT” only for every 1/10th control volume, so the output to this file will appear coarse

compared to the output from program THICK as it outputs the ice thickness at every point. Columns are the x-coordinates of the clean surface (xsav) in inches, the y-coordinates of the clean

surface (ysav) in inches, the ice thickness as measured from the clean surface (ditot) in inches, the

cumulative ice area (area) in inches and the wrap distance from the leading edge of the clean surface (s) in inches.

11.21 TRAJ1.DAT

This file contains the dimensionless x,y coordinates of individual droplet trajectories. Droplet

trajectory output is sequential. The first set of coordinates contain the coordinates of the first trajectory calculated. Subsequent output contains coordinates for each successive trajectory calculated. No indicator is present in the output file to offset trajectory output from one time step to

another. Hence, this output is only recommended for single time step cases. If the input flag

TPRT is set to 1, only droplet trajectories used for the collection efficiency calculation will be

generated. If this flag is set to 2, all droplet trajectories will be generated. Note that the definition

NASA/CR—2002-211793 160
of this flag has changed from version 1.66. These files are very large. If this information is not

needed, the user can save a great deal of disk space by not generating this file.

11.22 TRAJ2.DAT, TRAJ3.DAT, TRAJ4.DAT, TRAJ5.DAT

These files contain the droplet trajectories calculated for the other bodies at each time step.

“TRAJ2.DAT” contains the droplet trajectories for the second body, “TRAJ3.DAT” contains the

droplet trajectories for the third body and so on. These files will be generated only if more than

one body is being simulated. The data is formatted the same as for file “TRAJ1.DAT”. These files

are very large. If this information is not needed, the user can save a great deal of disk space by not

generating this file.

11.23 XKINIT.DAT

This file contains the predicted sand-grain roughness at each time step. Columns are time in

seconds (time), and two predictions for sand-grain roughness which are calculated by different

sets of equations (xkinit1) and (xkinit2). LEWICE 2.2 uses the last value listed on each line

(xkinit2) as the sand-grain roughness, which is also dimensionless.

11.24 XKINIT2.DAT

The previous file (XKINIT.DAT) contains the average sand grain roughness which is used by

LEWICE in the heat transfer coefficient calculation. LEWICE calculates a local roughness value

but uses the average for numerical purposes. The file “XKINIT2.DAT” contains the local roughness coefficients. Columns are the wrap distance from stagnation (s/c), the local sand grain roughness (xk) in millimeters, the film thickness (hflow) in millimeters, and the water bead height

(hbead) in millimeters. The user is referred to Appendix A for more details on these terms and

how they are calculated.

NASA/CR—2002-211793 161
Chapter 12: Additional Output Files

These files will be generated if nonstandard values have been selected for flags IDEICE and

IGRID in the main input file.

12.1 NOICE.DAT

This file contains output from the anti-icing calculation. Columns are dimensionless wrap

distance from stagnation (s/c), heat required at that control volume (qheat) in kW/m2, maximum

temperature (T_max) in degrees Kelvin, surface temperature (T_surf) in degrees Kelvin and

effective heat transfer coefficient in W/m2/K. The effective heat transfer coefficient can be used

to transfer information from LEWICE to other programs. It is the “effective” value which would

need to be input as the convective boundary condition for many commercial or non commercial

CFD programs in order to thermally account for icing effects. 

This output will be generated if the de-icing flag is set on (IDEICE = 1). For a multi-body

case, output for each body will be generated in succession. For a hot air anti-ice system, the maximum temperature column will contain the local temperature of the air stream. For an electrothermal system, the maximum temperature column will contain the local temperature of the heater. In

either case, the predicted temperature will be extremely high due to the simplistic assumptions

made in the solution process. The user is strongly advised to use a value of IDEICE = 3 for more

accurate prediction of these maximum temperatures.

Note: Heat flux values are input (and output) in units of kW/m2 while thermal conductivity

and heat transfer coefficients are input (and output) in units of W/m/K and W/m2/K respectively. 

12.2 CTEMP.DAT

This file contains surface velocities from the grid solution file. This output will be generated

if the grid flag is on (IGRID = 1). Columns are grid index value (i), body index value (ii), dimensionless x-coordinate (xoc), dimensionless y-coordinate (yoc), dimensionless surface velocity

(ve), and surface pressure coefficient (cp).

NASA/CR—2002-211793 162
12.3 GEOMETRY.DAT

This file contains the surface geometry of the body(s) read in from the grid solution file. The

columns are the dimensionless x,y coordinates of the surface geometry. This output will be generated if the grid flag is on (IGRID = 1). LEWICE will not run with a grid solution unless this

geometry is very similar to the one read in from the geometry input file(s). No error checking

has been added to ensure this.

12.4 FORCE.DAT

This file contains output from the ice shedding algorithm and will be output for IDEICE = 2 or

IDEICE = 3 cases. The columns are time (time), total force due to adhesion (fad), net force on the

ice shape in the x-direction (fx), net force in the y-direction (fy) and net force in the z-direction

(fz). This file will be output if ISH = 1 in the de-ice input file. Units on time are seconds and all

force units are in kN/m (kilo Newtons per meter).

12.5 FORCE2.DAT

This file contains output from the ice shed trajectories and will be output for IDEICE = 2 or

IDEICE = 3 cases where ice forms then sheds. The columns are shed time (time), trajectory time

step (tadd), x-coordinate of shed ice particle (x/c), y-coordinate of shed ice particle (y/c), z-coordinate of shed ice particle (z/c), and resultant force on the ice shape (ftot). This file will be output

if ISH = 1 in the de-ice input file. 

Units on time are seconds, distances are non-dimensionalized by chord and force is in kN/m.

Note: The shed trajectory computation assumes that shed ice particles are spheres. 

Note: The shed force data files can be extremely large and should be deleted if they are not

needed.

12.6 QOPT.DAT

This file contains output from heater optimization runs and will be output for IDEICE = 2 or

IDEICE = 3 cases where heaters are temperature controlled (including IQW = 1 cases). The columns are wrap distance index value [i], normal index value [j], temperature at control location

NASA/CR—2002-211793 163
[t(K)], and heat flux [qopt(kW/m^2)]. When the temperature control option is being used in the

de-icer input file, the software will use the wattages input by the user initially and then increase or

decrease those wattages such that the temperature at the control location remains in the range

specified. The wattages needed to maintain the heater section in that temperature range are output

to the user in this file. As noted in the file header, units of temperature are in Kelvin and wattages

are in kW/m2.

Note: There does not exist a “convergence criteria” for the heater optimization process. If the

user does not input a large enough time for the algorithm to fully converge, then the wattages output may not be optimal. Judgment is required by the user to decide if the wattages shown have

converged.

12.7 DUMMY.INP

This file contains an echo of the de-icer input data without any user comments (i.e., only the

numbers are written to this file). This file may be useful for debugging de-icer input data files.

The software reads in the de-icer input file and strips off all the comments and then writes this file

to disk. It then reads this file when it reads the variables into the program. The variables listed in

this file are described in Section 10.1.

12.8 TEMPS1.DAT, TEMPS2.DAT, TEMPS3.DAT, TEMPS4.DAT, TEMPS5.DAT, 

TEMPS6.DAT, TEMPS7.DAT

These files contain temperature output as specified by Section 10.1.5.3 to 10.1.5.5 of this

manual. If thermocouple output was specified (IOTYPE = 1), then the first column will be time

(time), and the remaining ten columns will contain the temperature in Kelvin for the first ten thermocouple locations specified. The file header will denote these temperatures with the variables

‘t1’, ‘t2’, ‘t3’, ‘4’, ‘t5’, ‘t6’, ‘t7’, ‘t8’, ‘t9’, ‘t10’. If more than ten thermocouple locations are

specified, then the next ten thermocouples will be written to the next file (for example, the first 10

will be in “TEMPS1.DAT”, the next 10 will be in “TEMPS2.DAT”, etc.). The file header for each

case will remain the same. 

If a temperature profile as a function of wrap distance was specified (IOTYPE = 2), then the

first column will contain the wrap distance (s/c) and the remaining ten columns will contain the

NASA/CR—2002-211793 164
first ten temperature profiles specified in the de-icer input file for the IOTYPE = 2 option. The file

header will denote these temperatures with the variables ‘ta’, ’tb’, ‘tc’, ’td’, ‘te’, ’tf’, ‘tg’, ’th’,

‘ti’, ’tj’ to distinguish them from the IOTYPE = 1 output. Once again, if more than ten profiles

were requested, the second ten profiles will be in the next highest number output file (for example, if the first ten profiles were output to “TEMPS3.DAT” then the second set of ten outputs

would be written to “TEMPS4.DAT” and so on).

If a normal direction temperature profile was specified (IOTYPE = 3), then the first column

will contain the normal distance (eta/c) and the remaining ten columns will contain the first ten

temperature profiles specified in the de-icer input file for the IOTYPE = 3 option. The reference

value for eta is the inside surface of the de-icer. The file header will denote these temperatures

with the variables ‘taa’, ’tbb’, ‘tcc’, ’tdd’, ‘tee’, ’tff’, ‘tgg’, ’thh’, ‘tii’, ’tjj’ to distinguish them

from the IOTYPE = 1 or IOTYPE = 2 output. Once again, if more than ten profiles were

requested, the second ten profiles will be in the next highest number output file (for example, if

the first ten profiles were output to “TEMPS3.DAT” then the second set of ten would be output to

“TEMPS4.DAT” and so on).

Note: For a case where the user selects a number which is not divisible by 10, then extraneous

data columns will be written which should be ignored. The software will always write out 11 columns in each of these files. The first column will always contain the independent variable with

the next 10 containing temperature values. Example: The user specifies 25 locations for thermocouple style output (IOTYPE = 1) and 12 locations for wrap distance style output (IOTYPE = 2).

Files “TEMPS1.DAT”, “TEMPS2.DAT”, and “TEMPS3.DAT” will contain the IOTYPE = 1

output while “TEMPS4.DAT” and “TEMPS5.DAT” will contain the IOTYPE = 2 style output. In

file “TEMPS3.DAT”, the last five columns of numbers should be ignored in this example while in

file “TEMPS5.DAT”, the last eight columns should be ignored.

If IOTYPE = 4 or IOTYPE = 5 output is specified, then the software will output the time at

the top of the output section [time (sec)] on a single line. Following this line will be the temperatures at every node. Each column of data represents one column of nodes in the wrap direction.

The first column will contain the normal distance (eta/c) and the remaining ten columns will conNASA/CR—2002-211793 165
tain temperature in Kelvin for the first ten columns of nodes. The second set of ten nodes will follow the first set and so on, as diagrammed in Figure 13.

Figure 13: Diagram of temperature output for IOTYPE = 4 and IOTYPE = 5 output

time (sec) 

eta(j) t(1,j) t(2,j) t(3,j) t(4,j) t(5,j) t(6,j) t(7,j) t(8,j) t(9,j) t(10,j)

------------------------------------------------------------------------------

eta(j) t(11,j) t(12,j) t(13,j) t(14,j) t(15,j) t(16,j) t(17,j) t(18,j) t(19,j) t(20,j)

------------------------------------------------------------------------------

eta(j) t(21,j) t(22,j) t(23,j) t(24,j) t(25,j) t(26,j) t(27,j) t(28,j) t(29,j) t(30,j)

etc

12.9 FORT.54

The file “FORT.54” contains debug information concerning the phase change convergence of

the program. The user should not need the output from this file unless the user is also a developer

looking to improve the software’s capabilities. There are 10 columns of data output to this file but

there is no file header. The columns are: wrap distance index value, normal index value, current

temperature at node, previous temperature at node, previous time step temperature at node, current phase index, previous phase index, previous time step phase index, time, and iteration number.

12.10 FORT.80, FORT.81, etc.

The file “FORT.80” will contain the de-icer grid and ice grid for the first time specified with

the variable ITIME in Section 10.1.5.2. File “FORT.81” then contains the temperature solution

file for the time specified. The format for these files will be determined by the value of the NPRF

flag entered in Section 10.1.5.1. If more than one ITIME value was specified, additional output

files will be generated. The file names for the second time specified will be “FORT.82” and

“FORT.83” respectively. If a third time is specified, the output file names will be “FORT.84” and

“FORT.85” and so on. Geometry grids are generated for each time specified since the ice grid

may change due to ice growth.

NASA/CR—2002-211793 166
Chapter 13: Utility Programs

This section will describe five utility programs which are released along with LEWICE 2.2.

The inputs and outputs to these utility programs will also be discussed. 

13.1 Program THICK

Program THICK generates an ice thickness distribution using as input a clean airfoil geometry

and an iced geometry. The iced geometry can come from LEWICE or from experiment. The program also outputs the quantitative parameters which were used for the validation tests. The results

of these tests have been published in a recent contractor report1. Only one body can be processed

for this program. A multi-body case can be processed by running THICK for each individual

body geometry.

Basically, the program calculates the minimum distance from each point on the ice shape to

the clean surface. For small ice thicknesses on the same order of magnitude as the point spacing,

the thickness is determined by using the unit normal from the surface. It is possible for complex

ice shapes to have more than one ice thickness at a given location on the clean surface. In this

case, the maximum of these individual ice thicknesses is used. The current version of THICK

included on the CD can use the same input geometry hat was used in LEWICE. There no longer

exists a need to input a refined geometry. The refined geometry will be calculated internally in the

program. The user should consult the report on the validation tests1 and Appendix A for further

details on the methodology used in this program.

13.1.1 Interactive Input for Program THICK

Input Clean Geometry File Name

The first interactive input directs the user to input the name of the input file containing the

clean geometry. The name can be up to 80 characters long. This filename length is necessary as

the user must also input the directory path of this file if it is different from the directory containing

the program. Please read the error messages in this section which describes the proper form of the

NASA/CR—2002-211793 167
input when using a directory path. If the file cannot be accessed, the following system error will

be generated:

IRIX 6.2 Message

open(name): No such file or directory

apparent state: unit 8 named

last format:

Unit 8 is a sequential formatted external file

*** Execution terminated (2) ***

Windows DOS Shell Message

forrtl: The system cannot find the file specified.

forrtl: severe (29): file not found, unit 8, file C:\Lewice\test.xyd

This error indicates that the file name input by the user does not exist, or does not exist in this

directory. Common problems: 

1) The file name was not typed correctly (remember to include the extension - use

“case1.xyd” not simply “case1”); 

2) The input file is in a different directory than the program and the user did not specify the

directory. The input file can be in a different directory than the program, but in order for THICK

to recognize the input file the path must be specified. For example, use

“inputs\naca0012\case1.xyd” instead of simply “case1.xyd” to read the input file “case1.xyd” in

the directory “inputs” and subdirectory “naca0012”. Note: The above example used the DOS

directory convention of backward slashes “\” to list subdirectories. IRIX and many other unix systems use forward slashes “/” instead.

PC Note: To get to the root directory, first type a backward slash “\”, then the path and file

name. For example, the command “\lewice\inputs\naca0012\case1.inp” can be also be used to

read the file “case1.inp” in the directory “C:\lewice\inputs\naca0012”.

Unix Note: It is common practice in unix to place all programs in a predefined directory such

as /usr/bin so that everyone using that system can run the program. The path for specifying the

NASA/CR—2002-211793 168
input file in this case is to provide the path from the directory the user is in. For example, if the

user is in their home directory and the input file is in the home directory, no path should be provided. If the user is in their home directory and the input files are in directory ../inputs/naca0012,

then the proper path to input is “inputs/naca0012/case1.inp”. If the user is in directory ../inputs/

naca0012 and the input file is in this directory, then no path needs to be provided in this case

either. P.S.: This sequence is correct based on the IRIX 6.2 operating system. Behavior for other

unix operating systems is expected to be similar, but potentially could be different.

Input Iced Geometry File Name

This interactive input directs the user to input the name of the file containing the iced geometry. The iced geometry can come from experiment or from an ice shape prediction and does not

have to be a complete airfoil. Digitized ice shapes from experiments are often supplied only up to

the end of the measured ice shape. If the file cannot be accessed, the error message listed previously for the clean geometry input file name will be generated. In this case however, the unit

number being referenced will be unit 9. The corrective measures concerning file name and directory path listed earlier for this error will also apply to errors involving the iced geometry.

This completes the section on interactive inputs for program THICK. The file format for the

input files will now be discussed.

13.1.2 File Format for Clean Geometry and Iced Geometry

The file format for the clean geometry and the iced geometry are the same. Each line of the

file contains an x,y coordinate pair for the body geometry. The x-coordinate is listed first. The format of the data is free-format for the x,y coordinates. The number of points in the geometry is

no longer input. The input file format for the clean and iced geometries is identical to the format

for the body geometry input for LEWICE. It is quite common for problems to arise when inputting a new geometry for the first time. Consult the section in this report on entering body geometries into LEWICE if there are problems with this input. There is no longer any need to create a

more refined body geometry for input into THICK. The input geometry for the clean airfoil can

(and should) be the same as the LEWICE input geometry. 

NASA/CR—2002-211793 169
Note: The units of the input variables for THICK can be any consistent set of units. The program will normalize the data for processing and then convert the data back to the original units for

output. Therefore the program should give consistent output regardless of the input units.

13.1.3 THICK output files

THICK produces five output files, each of which contains different methods for looking at the

ice thickness output. The first two output files, CLEAN.DAT and ICED.DAT, contain the ice

thickness on the clean and iced geometries. CLEAN.DAT contains four columns of data. The first

two columns contain the x,y coordinates (xsav, ysav) of the body geometry input. The number of

data points on the geometry may have changed, however. The units of the output data will be the

same units as the input data file. The third column contains the ice thickness (ditot) at that location and the fourth column contains the wrap distance (s) as measured from the leading edge

(minimum x-coordinate value). The units for these variables will be the same as the units for the

body geometry. ICED.DAT contains the x,y coordinates (xice, yice) of the iced geometry and the

ice thickness (yptot) to the body surface at each location. This output should have the same number of points and the same units as the input iced geometry.

Note: THICK does not perform any error checking on the input files. If there are any problems with the input files, then the output of THICK will be in error. The most common error

occurs when the clean body geometry and the iced geometry are in different units. 

The next output file, ECHO.DAT, contains an echo of all of the screen output from THICK,

including any program error messages. This output includes a summary of the icing parameters

which THICK has been set up to calculate. Upper and lower icing limits, horn heights, horn

angles (labeled upper and lower maximum ice thickness) are output as well as leading edge minimum thickness and ice area. The units of these variables will coincide with the units of the input

geometry (except horn angles which are in degrees). Each of these parameters were defined in the

LEWICE validation report. The definitions of horn angle and ice area have changed for this verson. The current definitions correspond to those given in an SAE Aerospace Recommended Practices (ARP) report (ref.). The current definitions are also shown in the diagram and equation 20

below. Since THICK does not input the icing parameters or chord length, the normalized variNASA/CR—2002-211793 170
ables described in the LEWICE validation report cannot be output directly. If THICK fails to find

a given parameter, it will print “N/A” for the value. The outputs from THICK cannot supplant

good engineering judgment. THICK occasionally cannot find some of the parameters which exist

and can also output erroneous information. The user is referred to the following section for

details.

Figure 14: Horn Angle Definition for THICK

(20)

where xlow = lower icing limit and xhi = upper icing limit

The fourth output file, PEAKS.DAT, was added to THICK to aid the user in correcting problems where THICK does not label the correct peak as the upper or lower horn. This file contains

all of the local maxima in ice thickness found by THICK. Experimental ice shapes will often have

several peaks due to the irregularity of the ice shape. Ice shapes from LEWICE or other programs

may have multiple peaks as well. Each peak found is labeled with the header “Found a Peak”. The

index location and x,y coordinate location (on both the clean and iced surface) are output as well

θ

θ

lower

upper

A yxd

xlow

xhi

∫  

 

 

iced

y xd

xlow

xhi

∫  

 

 

clean

–=

NASA/CR—2002-211793 171
as the ice thickness and angle (in degrees). The coordinates and thicknesses output will have the

same units as the input data. If the user believes that THICK chose the wrong location for either

the upper or lower horn, then the user can choose to select one of the peaks given in this file.

The last output file, TOTAL.TXT, contains only the eight icing parameters described in the

SAE ARP mentioned earlier. The variables output are, in order: lower icing limit, upper icing

limit, lower horn height, leading edge minimum thickness, upper horn height, ice area, lower horn

angle and upper horn angle. The numbers are output in the same units as the input data and have

not been normalized. Only the numbers are output. There do not exists any text header descriptions. The output was formatted in this manner in order to facilitate the automation of quantifying

large numbers of ice shapes and importing the results into a spreadsheet software such as

Microsoft Excel®. This option is best described by the example below.

13.1.3.1 THICK Example Case

Computation Time: Approximately 15 minutes on a 550 MHz Pentium III.

In this example, the user has a large number of data files for which the user wants the eight

quantitative icing parameters defined in the SAE report mentioned earlier. In this example, the

experimental ice shapes from the LEWICE validation CD were chosen. An ASCII text script

called “exppc.bat” was then manually generated which contains the necessary DOS commands

for running THICK for each of the data files. This script was generated in approximately one day.

An excerpt from the script is given below.

Table 94: Excerpt of Script Commands

copy GEOMETRY\C23014.XYD cgeom.xyd

copy 23014MOD\120R2.TXT exp.txt

thick < thick.inp

mkdir 23014MOD\120R2

move *.dat 23014MOD\120R2

NASA/CR—2002-211793 172
erase exp.txt

copy 23014MOD\126R8.TXT exp.txt

thick < thick.inp

mkdir 23014MOD\126R8

move *.dat 23014MOD\126R8

erase exp.txt

Each set of script commands contains the following steps:

1) The geometry file is copied to a generic name, in this case “cgeom.xyd”.

2) For each experimental data file which uses that geometry, the file name is likewise copied

to file “exp.txt”.

3) THICK is run with the interactive input coming from file “thick.inp”. “thick.inp” contains

two lines which read “cgeom.xyd” and “exp.txt” (without the quotes).

4) Appropriate subdirectories are created to organize the output

5) The output data files (excluding “total.txt”) are moved to the subdirectory.

6) File “exp.txt” is removed.

7) Steps 2-6 are repeated for each data file which uses that geometry, then Step 1 is repeated

for each airfoil in the database.

Once the script has finished, then “total.txt” will contain the output for all of the cases in a

column format which can easily be imported into a spreadsheet software such as Microsoft

Excel®. Note that in this script, the clean geometry and the iced geometry are in the same units

since no conversions have been performed. The output can then be normalized from within the

spreadsheet software. This process, including differences and percent differences has been performed for the experimental data on the LEWICE Validation CD-ROM. This spreadsheet, which

NASA/CR—2002-211793 173
contains values for Version 2.0 as well as Version 2.2 and experimental data, has been put on the

distribution CD-ROM for LEWICE 2.2 and is named “total.xls”. The astute user will notice that

several of the quantitative values generated using this process do not agree with the values given

in the LEWICE validation report spreadsheet “matrix.xls”. This demonstrates that the automated

process cannot (yet) be substituted for good engineering judgment. The following section will

describe some of the problems and potential solutions.

13.1.4 THICK Judgment Errors 

The utility program THICK performs a simplistic geometric comparison between two data

files and outputs the results. As such, it is prone to errors based upon a lack of icing knowledge. It

is possible for any (or all!) of the eight parameters to be incorrectly output. Even so, THICK has

proven to be a useful tool for reducing the amount of time needed to quantify ice shape parameters. There are two basic problems which occur repeatedly when analyzing output from THICK:

misalignment of the geometries and misidentification of the horns. 

First, the iced shape may be misaligned with the airfoil. This is illustrated in Figure 15.

Figure 15: Ice Shape Misalignment

Run 15

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.02 0.00 0.02 0.04 0.06 0.08

x/c

y/c

airfoil

LEWICE 2.0

LEWICE 2.2

exp_data

NASA/CR—2002-211793 174
This figure shows a comparison for Run 15 in the NACA 4415MOD database. It appears as

though the experimental data goes inside the airfoil on the lower surface. This will cause the

lower icing limit to be smaller than actual. The upper icing limit may also be lager than actual and

the misalignment will subtly change the area, horn heights, and possibly horn angles. This error

can possibly be fixed manually by shifting the experimental ice shape to match the airfoil as

shown in Figure 16.

Figure 16: Shifted Ice Shape Plot

The problem with this procedure is that the translation chosen has no scientific basis - it just

makes the ice shape “fit” better. This problem arises since the reference locations used for digitizing the ice shapes may not be the same reference point used for defining the airfoil coordinates.

This problem can also occur with ice shapes generated by LEWICE, although the effect is more

subtle as shown in Figure 17. Since LEWICE outputs the entire iced geometry, any misalignment

can cause the icing limits reported by THICK to be located as far back as the airfoil trailing edge. 

Run 15

-0.05

-0.03

-0.01

0.01

0.03

0.05

-0.02 0.00 0.02 0.04 0.06 0.08

x/c

y/c

airfoil

LEWICE 2.0

LEWICE 2.2

exp_data

NASA/CR—2002-211793 175
Figure 17: Expanded View of Airfoil Misalignment

Once again, the “iced” geometry resides inside the airfoil. It should be noted that the scale has

been greatly expanded in this figure to show a very small geometric discrepancy. THICK will

ignore values inside the airfoil, so in this case the THICK output may be accurate. If the discrepancy puts the iced geometry outside the airfoil, THICK may misidentify this small level as “ice”

and report an erroneous icing limit. THICK has been set up to ignore some small discrepancies,

but this tolerance cannot be set too high or else THICK will under report the limit. The icing limits reported by THICK should be checked with the icing limits output by LEWICE 2.2 to the

file“LIMIT.DAT”. Ice area can also be in error due to this type of misalignment.

The second problem which occurs occasionally with THICK is that the ice horns are not properly identified from the list of known peaks which are output to “PEAKS.DAT”. THICK identifies the “upper” surface as the region above the leading edge and the “lower” surface as the region

below the leading edge. This may not always give the correct horn locations, as illustrated in Figure 18.

0.1075

0.108

0.1085

0.109

0.1095

0.11

0.1105

0.111

0.25 0.255 0.26 0.265 0.27 0.275 0.28

NACA 4415MOD airfoil

LEWICE geometry

y/c

x/c

NASA/CR—2002-211793 176
Figure 18: THICK Horn Angle Problem

In this example, the LEWICE validation report would have listed the “upper” horn as the peak

location of the upper “finger”. The “lower” horn height would be given by the maximum thickness of the lower block feature and the leading edge minimum would have been listed as the minimum thickness between those two values. Horn angles would then be calculated from those

locations. However, since the peak thickness for each shape is below the airfoil leading edge,

THICK will identify the large “finger” feature as the lower horn and may list “N/A” for the upper

horn, since very little ice resides above the airfoil leading edge. In all cases, the LEWICE validation report numbers should be used as the reference values when comparing to an automated process such as the one described here.

13.2 Program EXPAND

Program EXPAND will read in a set of x,y coordinates from a file and output the same geometry with a different number of points. The additional points are calculated by spline interpolation.

This program had been useful for creating clean geometry input files for use with program

THICK, but may not be as useful since THICK has incorporated this feature. 

Run 072701

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

-0.09 -0.07 -0.05 -0.03 -0.01 0.01 0.03 0.05 0.07 0.09

x/c

y/c

airfoil

LEWICE 2.0

LEWICE 2.2

exp_data

NASA/CR—2002-211793 177
13.2.1 Interactive Input for Program EXPAND

Enter Input File Name

The first interactive input directs the user to input the name of the input file containing the

geometry. The name can be up to 80 characters long. This filename length is necessary as the user

must also input the directory path of this file if it is different from the directory containing the program. Please read the error messages in the previous section concerning the proper form of the

input using a directory path. If the file cannot be accessed, the following system error will be generated:

IRIX 6.2 Message

open(name): No such file or directory

apparent state: unit 8 named

last format:

Unit 8 is a sequential formatted external file

*** Execution terminated (2) ***

Windows DOS Shell Message

forrtl: The system cannot find the file specified.

forrtl: severe (29): file not found, unit 8, file C:\Lewice\test.xyd

Enter Output File Name

This interactive input directs the user to input the name of the file containing the output geometry. Note: If the file name input already exists, it will be overwritten.

Enter Number of Points

This interactive input directs the user to input the number of points for the output geometry.

The number can be free-format, but must be within the range 1 ≤ NPOINTS ≤ 10000. Input values

outside this range will generate the following warning message:

Number of points input (value) is out of range. Using default value of 5000.

NASA/CR—2002-211793 178
If a nonnumerical value is input for the number of points, it will be converted to integer for

use in the program on the SGI system. The likely result of this action is that the default number of

points will be used. On the PC, the following system error will be generated:

forrtl: severe (59): list-directed I/O syntax error, unit 5, file CONIN$

This completes the section on interactive inputs for program EXPAND. The file format for

the input files will now be discussed.

13.2.2 File Format for Input and Output Geometries

The file format for the input and output geometries are the same. Each line of the file contains

an x,y coordinate pair for the body geometry. The x-coordinate is listed first. The format of the

data is free-format for the x,y coordinates. The number of points in the geometry is no longer

input. It is quite common for problems to arise when inputting a new geometry for the first time.

Consult the section in this report on entering body geometries into LEWICE if there are problems

with this input.

Note: The input file format for this program is the same as the geometry input file format for

LEWICE 2.2. 

13.3 Program CONVERT

Input files from previous versions of LEWICE will not work with version 2.2. Program CONVERT will read in an input file from LEWICE version 1.6 and convert it for use in LEWICE version 2.2. The program will prompt the user for the name of the LEWICE 1.6 input file and the

name to be given to the LEWICE 2.2 input file. LEWICE 2.0 users simply need to add the following two lines to the end of the main input file:

&RDATA

&END

NASA/CR—2002-211793 179
13.3.1 Interactive Input for Program CONVERT

Enter Version 1.6 Input File Name

The first interactive input directs the user to enter the name of the LEWICE 1.6 input file to be

converted. The name can be up to 80 characters long. This filename length is necessary as the user

must also input the directory path of this file if it is different from the directory containing the program. Please read the error messages in the section on the main input file concerning the proper

form of the input using a directory path. If the file cannot be accessed, the following system error

will be generated:

IRIX 6.2 Message

open(name): No such file or directory

apparent state: unit 8 named

last format:

Unit 8 is a sequential formatted external file

*** Execution terminated (2) ***

Windows DOS Shell Message

forrtl: The system cannot find the file specified.

forrtl: severe (29): file not found, unit 8, file C:\Lewice\test.xyd

Enter LEWICE 2.2 Input File Name

This interactive input directs the user to input the name of the file which will contain the

LEWICE 2.2 input. Note: If the file name input already exists, it will be overwritten.

13.3.2 Format for the LEWICE 1.6 Input File

Program CONVERT will read input files which conform to the format listed in the LEWICE

1.6 User Manual6. No error checking of this input file is performed.

NASA/CR—2002-211793 180
Note: Variable IDEICE will be set to its default value (0) as it was not present in the

LEWICE 1.6 inputs.

Note: Many of the print flags in the LPRT namelist have changed definition from version 1.6

to version 2.2. Refer to those sections describing this input for a more detailed explanation.

13.3.3 Warning Message for CONVERT

The flag INCLT in the LEWICE 1.6 input file is not used in LEWICE 2.2. If the flag INCLT

= 1, then the following warning message will appear:

The flag INCLT is set to 1 in the LEWICE 1.6 input file. This means that the value of CLT in

the LEWICE 1.6 input file is probably the lift coefficient instead of the angle of attack. Since the

value of CLT was used as the value of AOA in the LEWICE 2.2 input file, make sure that the value

of AOA is the desired angle of attack.

This message serves only as a warning and the LEWICE 2.2 file will be generated.

13.4 Program TOBINARY

Naviér-Stokes solution files in PLOT3D format are read into LEWICE in binary format. This

utility program converts PLOT3D files in text format to binary. It is useful for transferring the

PLOT3D files to different hardware platforms. The program requires no interactive input. The

text file names are “XY.TXT” for the grid and “Q.TXT” for the flow solution. The binary output

files are named “XY.PLT” and “Q.PLT” respectively. If the file cannot be accessed, the following

system error will be generated:

IRIX 6.2 Message

open(name): No such file or directory

apparent state: unit 8 named

last format:

Unit 8 is a sequential formatted external file

*** Execution terminated (2) ***

NASA/CR—2002-211793 181
Windows DOS Shell Message

forrtl: The system cannot find the file specified.

forrtl: severe (29): file not found, unit 8, file C:\Lewice\test.xyd

Note: If the output files “XY.PLT” and “Q.PLT” already exist, they will be overwritten.

Note: This program was designed to be used to convert files in the PLOT3D format from text

to binary format. It is not a general purpose conversion utility.

13.5 Program TOASCII

Naviér-Stokes solution files in PLOT3D format are read into LEWICE in binary format. This

utility program converts PLOT3D files in binary format to text format. It is useful for transferring

the PLOT3D files to different hardware platforms. The program requires no interactive input. The

binary file names are “XY.PLT” for the grid and “Q.PLT” for the flow solution. The text output

files are named “XY.TXT” and “Q.TXT” respectively. If the file cannot be accessed, the following system error will be generated:

IRIX 6.2 Message

open(name): No such file or directory

apparent state: unit 8 named

last format:

Unit 8 is a sequential formatted external file

*** Execution terminated (2) ***

Windows DOS Shell Message

forrtl: The system cannot find the file specified.

forrtl: severe (29): file not found, unit 8, file C:\Lewice\test.xyd

Note: If the output files “XY.TXT” and “Q.TXT” already exists, they will be overwritten.

Note: This program was designed to be used to convert files in the PLOT3D format from

binary to text format. It is not a general purpose conversion utility.

NASA/CR—2002-211793 182
13.6 Program ANTICON

This program reads the LEWICE3D files named “FORT.2” and “FORT.26” and outputs the

files FLOW.DAT, BETA.DAT, HTC.DAT, and STREAM.DAT which contain the 3D results

along 2D streamlines which can then be read into LEWICE using the input flags ICP, IBETA,

IHTC, and I3D. The files FLOW.DAT, BETA.DAT, HTC.DAT, and STREAM.DAT must first

be segmented into several files, each of which contains only one of the streamlines output to the

other files. For example, if the file FLOW.DAT contains five 2D streamlines, the user must first

create five separate files, each of which contains only one of the streamlines. This function can be

performed with any text editor or word processor software. These files need to have the proper

name as described in Sections 8.3 and Sections 10.5 through 10.8 in order to be read properly by

LEWICE. See the example in Section 15.18 for more details.

13.7 Program ANTICON2

This program reads the LEWICE3D files named “FORT.2” and “FORT.26” as well as the

LEWICE 2.2 output files “DYICE.DAT” and “TEMP.DAT” and outputs files named

“PLOT3D.XYZ” and “PLOT3D.Q” which can be read by the NASA software PLOT3D. If more

than one streamline exists in the “FORT.26” file, then several output files from LEWICE 2.2

must be concatenated prior to running ANTICON2. This function can be performed with any text

editor or word processor software. For example, if five 2D streamlines were output to

“FORT.26”, then the user must perform five runs of LEWICE 2.2 in order to produce output for

ANTICON2. Then the five “DYICE.DAT” output files must be combined into a single

“DYICE.DAT” file prior to running ANTICON2. See Section 15.18 for more details.

13.8 Program REDUCE

This program reads the LEWICE 2.2 output files “TEMPS1.DAT”, “TEMPS2.DAT”, and

“TEMPS3.DAT” and outputs files “TEMPS1A.DAT”, “TEMPS2A.DAT”, and

“TEMPS3A.DAT” which are more easily compared to the existing validation data. The program

converts the temperatures in these files from Kelvin to Fahrenheit and reduces the output from

one temperature every 1/10th second to once every second. The program assumes that

“TEMPS1.DAT”, “TEMPS2.DAT”, and “TEMPS3.DAT” all contain thermocouple type output

(IOTYPE = 1) and that the de-icer time step is 0.1 seconds. 

NASA/CR—2002-211793 183
Chapter 14: Runtime Errors

This section will describe errors which may occur during a run. Errors during a run are very

infrequent with this software, but may still occur if a problem arises which the software cannot

handle. The most likely cause of these errors is that the user is analyzing a case outside of the

range of data used for validation. Over 400 runs were made with LEWICE 2.2 during the validation testing phase. In one case, an error occurred because the DSMN value was too small and the

array size was exceeded. This case ran successfully with a slightly higher DSMN value. In no

other case did any error occur which caused the software to stop prior to its normal completion.

This occurred even though many of the tests were in fact selected in an attempt to create runtime

errors. Corrective actions which can be taken are discussed following the listing of each individual error message. All of the errors listed will stop the run before completion unless otherwise

noted. The runtime error which is generated will be in italics, followed by a description of the

error. Every possible error message is listed and they have been organized by type. Any error

messages which occurred during the validation testing phase are identified in this section.

14.1 Flow Solver Errors

The flow solver has encountered an error. Usually, this means that there is something wrong

with the body geometry(s) such as two bodies intersecting. Please check the last ice shape printout for problems and check that the case conforms to the recommended limits on inputs. Because

of this error, the program cannot continue.

The error listed above can only occur for multi-body simulations such as multi-element airfoils. One potential cause of this error can occur when multi-element airfoils begin to intersect

due to ice growth. It is also possible that errors occurred in the ice growth process during the previous time step. The user can run a different spacing (DSMN) on the geometry or different time

step (IFLO) for this case. However, it may be the case that this is a correct prediction and that the

elements have fused together due to ice growth. The run can only be continued from this point if

the user resubmits the case using the last iced geometry and treating the two individual bodies as

a single body.

NASA/CR—2002-211793 184
This situation can only occur when the number of panels is greater than 1001 and you have

increased both NPAF and NBF parameters. To solve this problem increase KORE in routine

SOLVIT and recompile.

If this error occurs, one of the array size dimensions has been exceeded. As stated in the error

message, this can occur only if the user has modified the program. The user should also check the

iced geometry for abnormalities.

Attempted to load the (value)th body. Maximum allowable number of bodies is (value).

Because of the above error, this run is terminated.

This error should never occur since LEWICE now checks the input for the number of bodies.

The number of elements (value) will exceed allowable storage (value) when added to the data

set.

Because of the above error, this run is terminated.

The array size had been exceeded. LEWICE should have stopped when adding ice during the

previous time step. The last iced geometry is likely bad. The user will need to increase DSMN to

run this case.

The number of elements (value) for the new body exceeds the number (value) for the body it is

replacing.

Because of the above error, this run is terminated.

The array size had been exceeded. LEWICE should have stopped when adding ice during the

previous time step. The last iced geometry is likely bad. The user will need to increase DSMN to

run this case.

NASA/CR—2002-211793 185
14.2 Errors when Using Grid Solutions

This section covers specific errors which can occur when attempting to use a grid-based flow

solution.

Cannot find the droplet position in the grid. Usually, this means the grid was read wrong or

there is a problem searching multi-block grids. Did not find interpolation stencils.

.... the point: xpt= (value) ypt= (value)

 program stop in searchpt

During the droplet trajectory calculation, LEWICE attempted to find the grid cell containing

the drop so that the air velocity at that point could be determined. This search was unsuccessful.

Check that the grid matches the airfoil input in the geometry input file and that the flight conditions in the main input file match those in the flow solution input file. The user should also refer

to the trouble shooting given for Example Case 12.

Cannot find the droplet position in the grid. Usually, this means the grid was read wrong or

there is a problem searching multi-block grids.

*****************************************

 program stop.!!! 

 subroutine: stencils! 

*****************************************

This error occurs for the same reason as the previous error but in a different subroutine.

Cannot find the droplet position in the grid. Usually, this means the grid was read wrong or

there is a problem searching multi-block grids.

   big trouble! ** ** 

This error occurs for the same reason as the previous error but in a different subroutine.

NASA/CR—2002-211793 186
14.3 Trajectory Errors

This section lists errors which can occur during the droplet trajectory calculation.

(value) trajectories are calculated in range. There is something wrong with the flow solution

for this to happen. Program cannot continue with run.

In the initial phase of the droplet trajectory routine, droplets are sent toward the model to find

an upper and lower bound for the impingement limit search. This error occurs when this range

cannot be found. Usually, there is an error in the iced geometry from the previous time step. The

user may need to adjust the point spacing (DSMN) or time step (IFLO) for this case.

 kflag= (value) difsub failed** **

Integration of trajectory stopped before a result could be found. Program will assume that

the trajectory missed which may not be correct. Please check output carefully.

During each step in the trajectory integration, the program needs to iterate on the droplet location for the next step. This message will appear if convergence was not achieved. This message

occurs very rarely. In the validation test cases, it occurred once in over 400 LEWICE runs. In that

case, the program assumed the particle had missed the body and continued the run without further

incident. If this message occurs repeatedly during a run, the user should stop the case manually

(using <ctrl> C) as a problem has occurred. This may occur for very complex ice shapes. The user

may need to adjust the point spacing (DSMN) or time step (IFLO) for this case. Below are the

definitions of the “kflag” error values.

-1 the step was taken with h = hmin, but the requested error was not achieved.

-2 the maximum order specified was found to be too large.

-3 corrector convergence could not be achieved for h.gt. hmin.

-4 the requested error is smaller than can be handled for this problem.

*** 1000*ibod steps in intig ***

Integration of trajectory stopped before a result could be found. Program will assume that the

trajectory missed which may not be correct. Please check output carefully.

NASA/CR—2002-211793 187
end point xp = (value) yp = (value)

Each trajectory is limited to no more than 1000*ibod steps, where “ibod” is the number of

bodies input by the user in the main input file. It is very rare for a trajectory to need more than 200

steps for completion. This upper limit is normally reached because the step size has gotten very

small. In certain multi-element cases, more steps are needed as the program will start the trajectories far upstream in order to obtain free stream conditions for the initial air flow around the drop.

As with the previous warning message, the program will continue as though the trajectory missed

the body. This assumption can be checked as the program prints out the last droplet location to the

screen and to the debug file. If this message occurs repeatedly during a run, the user should stop

the case manually (using <ctrl> C) as a problem has occurred. This may occur for very complex

ice shapes on multi-element airfoils. The user may need to adjust the point spacing (DSMN) or

time step (IFLO) for this case.

Newton-Raphson did not converge in vterm. minimum error = (value), last calculated value

(value), value at minimum error (value).

The program attempted to calculate the freefall (terminal) velocity of a particle to be used as

an initial condition for the trajectory integration. This error may be indicative of problems with

the flow solution. The value at the minimum error will be used and the software will continue to

run.

number of trajectories is more than (value). Flow solution is probably bad. Program cannot

continue. Check output carefully

The program is limited to 199 trajectories during a single impingement limit search. It is

highly likely that there is a problem with the iced geometry from the previous time step which

caused a poor flow solution. The user will likely need to adjust the point spacing (DSMN) or time

step (IFLO) for this case.

Impingement limit could not be found. Flow solution is probably bad. Continuing with rest of

run. Please check output thoroughly.

NASA/CR—2002-211793 188
y0max =(value), y0min = (value)

The impingement limit is determined by a binomial search algorithm. This error will occur if

the starting point for the next trajectory is the same as the last trajectory calculated. This may have

occurred if the iced geometry from the previous time step caused a poor flow solution. The program will continue as if no impingement limit exists.

Program cannot decide on path for next trajectory. Output may not be reliable. Check results

carefully.

This error can only occur if a multi-body simulation is being performed. At the end of each

trajectory, the program must decide where to start the next trajectory based on where hit trajectories have occurred and if this particle passed over or under the body for which the impingement

limit is being sought. The error occurs when the data is conflicting on the proper decision. The

program will choose one of the two possible paths and continue with the run. The user should

check for other trajectory errors and also check the iced geometry produced at the last time step.

14.4 Energy Balance Errors

This section covers errors which occur during the calculation of the mass and energy balance.

An error in this section is usually indicative of problems elsewhere in the software. The iced

geometry from the last time step and the flow solution for this time step should be checked for

possible abnormalities.

Maximum ice thickness is much too large. ymax = (value)

The calculated ice thickness at one of the control volumes is too large to be added to the ice

shape. This may indicate that the number of time steps should be increased for this case.

The temperature sent to function PVAP is outside the range for this routine. There is a problem with this case. Be careful interpreting results.

big error in pvap t = (value)

NASA/CR—2002-211793 189
This error can only occur if the calculated surface temperature is below 32 K. Obviously,

there is an error in the case for this to occur. The program will attempt to continue, but the user

should manually terminate the case (<ctrl> C) and investigate the problem with the ice shape.

In NOICE, Newton-Raphson did not converge. minimum error = (value) 

last temp. predicted = (value), temp. at min. error = (value)

The output data for anti-icing may be incorrect.

The program must iteratively solve for surface temperature for evaporative anti-icing cases.

This error occurs when convergence was not found. The program will continue with the temperature value at the minimum error.

In SOLVEW, Newton-Raphson did not converge. minimum error = (value) 

last temperature calculated (value), temperature at minimum error = (value)

The output data may be incorrect.

The program must iteratively solve for surface temperature during the energy balance. This

error occurs when convergence was not found. The program will continue with the temperature

value at the minimum error.

14.5 Ice Growth Errors

If the errors listed in this section occur, the most likely cause of the error is a problem when

the predicted ice growth is added to the current ice shape.

Stopping because nsteps too large.

nsteps = (value)

This error occurs because the software is trying to add too much ice at one time. This could be

due to a bad solution from one of the earlier routines (such as FLOW, TRAJ or ICE). Check that

your case conforms to the guidelines for time step (IFLO) and point spacing (DSMN).

NASA/CR—2002-211793 190
If it does and the case still bombs here then you have found a legitimate error in LEWICE. It

would be very helpful for future versions if we (NASA) could have a copy of the input file so this

error can be fixed. Also include what machine the software ran on and if it was recompiled.

The user most likely input fewer time steps than recommended if this message appears.

Increase the number of time steps (IFLO) for this case.

Stopping because negative nsteps.

nsteps = (value)

This error occurs because the software is trying to add too much ice at one time. This could be

due to a bad solution from one of the earlier routines (such as FLOW, TRAJ or ICE). Check that

your case conforms to the guidelines for time step (IFLO) and point spacing (DSMN).

If it does and the case still bombs here then you have found a legitimate error in LEWICE. It

would be very helpful for future versions if we (NASA) could have a copy of the input file so this

error can be fixed. Also include what machine the software ran on and if it was recompiled.

This error can also occur if too few time steps are used. Increase the number of time steps

(IFLO) for this case.

WARNING!!! The point spacing at the following location is zero. The software will attempt to

continue, but the output may be bad or the software will bomb later. This statement is in routine

NWF3 and is usually caused by a memory allocation error.

i= (value), xbtdot= (value), dsdd= (value).

This problem should never occur in LEWICE 2.2. Please consider sending this case to us

(NASA) so that this case can be investigated.

spline routine failed. doing linear interpolation

NASA/CR—2002-211793 191
The program uses a cubic spline to generate surface points. If this fails, this warning informs

the user that linear interpolation will be used. This is a minor error and the output is likely ok.

 danger you are now extrapolating. Problem in routine lntp.

i= (value) j= (value), xnl(j)= (value), xol(1)= (value), xol(no)= (value)

The program will also use linear interpolation to find new surface points. This warning

informs the user that the software needed to extrapolate to find points. This should not normally

happen. The iced geometry should be checked. Also consider changing the point spacing

(DSMN) and/or the number of time steps (IFLO) for this case.

error nwfoil (value) (value) (value) (value) (value) (value)

 The program attempted to smooth the ice shape before the next time step, but was unsuccessful. This is a minor error and the output is likely ok.

Array size exceeded. Increase npa to at least npa= (value)

The program needed more points than are currently allowed. The user should increase the

DSMN value for this case. Alternatively, the programmer may wish to consider increasing the

array size and recompiling the software.

ARRAY STORAGE EXCEEDED!!!!!

Strange things may have happened to ice shape! Do one of the following:

(1) Rerun the case with a larger DSMN input

(2) Increase the value of NPA in file param.inc

For the second option, LEWICE must be recompiled. You will need at least (value) points to

run this case.

NASA/CR—2002-211793 192
This error is the one most likely to occur during a run. It will appear when the user selects a

DSMN value which is too small for the case being run. For a typical clean airfoil, the total wrap

distance is slightly greater than 2 (dimensionless). For a DSMN value of 4*10-4, this will create

over 5000 control volumes on that shape. As the array size limits are 10000, the total wrap distance around the iced geometry needs to be more than four times greater than the chord length for

this error to appear. For a DSMN value of 8*10-4, the total wrap distance around the iced geometry needs to be more than eight times greater than the chord length. The ratio of wrap distance to

chord length for a cylinder is by definition pi (3.1415926536...). This ratio will increase as the ice

grows on the cylinder. This example shows why larger DSMN values are likely needed for a cylinder.

14.6 De-icer Routine Errors

The errors listed in this section are produced by the de-icer routine. They can only be generated for IDEICE = 1, IDEICE = 2 or IDEICE = 3 cases. Some of the errors listed in this section

are not errors, but additional information written to “JUNK.DAT” for informational purposes.

Those messages will be identified in their descriptions.

In NOICE_d, Newton-Raphson did not converge.

minimum error = (value) last temp. predicted = (value)

temp. at min. error = (value)

The output data for anti-icing may be incorrect.

This error occurs for IDEICE = 1 cases where the program could not converge on the antiicing temperature. Check the input data for possible errors, as this message did not appear during

testing of the program.

The time step is <= zero! This is usually a memory allocation problem

Check output carefully. Setting dtime = 60 sec. Current dtime = (value)

NASA/CR—2002-211793 193
This error occurs when the time step has somehow been set to zero. This should never occur,

since the time step input is checked by the program.

In SOLVEW, Newton-Raphson did not converge.

minimum error = (value) last temperature calculated (value)

temperature at minimum error = (value)

The output data may be incorrect.

This error occurs when the energy balance equations did not converge. This error occurred

during testing only after other serious warning messages listed in this section had been issued by

the program. It usually occurred during anti-icing runs with an extremely high wattage. The run

should be terminated and resubmitted with different inputs. See the recommendations below for

the error “program is having problems with this case”.

Bad stfr = (value) (value) (value) (value)

This is a warning message only which indicates possible problems with the water runback

routines. Check all output carefully, especially runback ice formations.

Bad mass flux (value) (value) (value) (value) (value) (value) (value) 

This is a warning message only which indicates possible problems with the water runback

routines. Check all output carefully, especially runback ice formations.

program is having problems with this case.

please check the output thoroughly. time = (value)

This warning message can occur when the program is having convergence problems in the

phase change algorithm. When this message is immediately followed by six numbers (5 integers

and one real number), then the program is having serious convergence problems and may soon

crash. The six numbers are: wrap distance index value, normal index value, temperature, time step

NASA/CR—2002-211793 194
index, phase change index, and previous phase change index. In any case where this message

appears, the user should check the temperature output thoroughly. If this warning message

appears more than 10 times during a run or if the user detects anomalous temperature output, the output from this run should be abandoned and the case ran again with different

inputs. The user should consider the following remedies (in recommended order): reduce or eliminate LEWICE time stepping (IFLO = 1); a larger number of iterations (JCOUNTD) and/or a

smaller time step (DTAUI, DTAUM, DTAUF); increased nodal spacing (NODE) especially in

the ice layer and the layer adjacent; simplifying the case by reducing sections, layers or other variables. 

 temp below tinf (value) (value) (value) (value) (value) (value)

This error message occurs when the de-icing module crashes (stops running prematurely). It

occurs when the temperature at a node drops below the ambient temperature, which should never

occur under normal operation. The six values are: wrap distance index value, normal index value,

temperature, time, phase change index and previous phase change index. The user should contact

the developer if this error occurs and supply a sample input file for further program debugging.

phase change algorithm did not converge

This warning message is generated if the program repeatedly fails to converge on the phase

for the problem at hand. The user should consider resubmitting this case with a larger number of

iterations (JCOUNTD) and/or a smaller time step (DTAUI, DTAUM, DTAUF).

not converged. diftemp = (value), (value), (value), (value), (value)

This warning message occurs when the matrix solver MSIP did not converge on a temperature

profile. This has occurred during testing when an anti-icing case was run with a large time step

(only the steady-state solution was desired). In this case, no action is required of the user since the

transient temperature profile was not needed. If this message occurs for a case where the transient

profile is needed (de-icing cases), then the user should resubmit the case with a smaller time step.

The user may need to examine grid refinement for this case as well. The five values output are:

NASA/CR—2002-211793 195
maximum temperature difference, temperature, previous temperature, wrap distance index value

and normal index value.

bleed air option is on but flow rate is zero

either set IBLEED = 0 in the input file, or select a value AIRMD > 0

This error message would occur if the bleed air mass flow rate was zero for a case where bleed

air was considered. This error should never occur as the program checks this when the data is

read.

 an error occurred while reading the input file

This error is generated when the program could not read the de-icer input file for some reason.

Check the de-ice input file for possible errors and resubmit the case.

14.6.1 Other de-icer routine messages

This section will describe some of the other informational messages generated by the de-icer

routine. These messages are not warnings or indicators of a problem with the output.

ice has shed (value) (value) (value) (value) (value) (value) 

This is an informational printout only and is not a warning or error message. It is written out

when the ice shape sheds The six values are: body index, net force, force in normal direction,

force in wrap direction, force in span direction and force of adhesion.

Phase has matched previous iteration

 Iteration = (value)

This message occurs during the phase change iteration when the program cannot decide on the

phase of a particular node or node(s) and is simply alternating between two values. The program

is set up to handle this occurrence, so it is not a warning or a problem with the output.

NASA/CR—2002-211793 196
(value) iterations were required at time = (value)

This message occurs when the program uses more than two iterations for a particular time

step. It can be helpful in identifying if the program used too many iterations for a given time step.

During testing, the number of iterations was almost always below 10 and usually below 5.

time = (value) sec

This message is written every 20 iterations to inform the user of the program’s progress.

NASA/CR—2002-211793 197
Chapter 15: Example Cases

The following example cases have been included to illustrate different features of LEWICE.

Many of the cases correspond to runs made for the validation report. Those examples which correspond to a particular validation case are identified. The cases are included for illustration purposes only. The user does not have to run all of the cases provided. Output for the cases are

provided on the distribution disk. A script has also been included on the distribution disk called

“EXAMPLES.BAT” which will automatically run all of the example cases. The computation

time for running the script will be the sum of the computation times for all of the individual cases.

The results shown in this section were generated using the PC executable on the distribution disk.

The validation report showed minor differences in output across platform, but the results from

two different PCs using the PC executable on the distribution disk were exactly the same.

In each of the examples, all of the possible input fields have not been specified. Those which

have not been specified will be assigned to their default value as listed in the description of the

input variables in this report. The plots for each example case show the ice shape for each time

step, the ice thickness distribution for each time step, the flow solution for the clean airfoil and the

final ice shape, the heat transfer coefficient for the clean airfoil and next-to-last ice shape and the

collection efficiency for the clean airfoil and the next-to-last ice shape. The de-icing and antiicing cases will additionally show plots for selected temperature distributions. The ice thickness

plots are the result of plotting the data in the “THICK.DAT” output file, not the thickness listed in

the ice shape file. The difference between the two outputs is the definition of wrap distance as

defined for those files. Refer to the description of these output files for further explanation. As can

be seen from the print flags in the main input files, many of the other output files were not produced. The heat transfer coefficient and collection efficiency plots show the solution on the nextto-last ice shape since the software stops after calculating the ice shape for the last time step.

15.1 Case 1: Run 072501 from Validation Report

Computation Time: Pentium III 550MHz, 1 min. 30 s.; Pentium IV 1.7GHz, 36 s.

Disk Space: 1 MB

NASA/CR—2002-211793 198
The first example case is run number 072501 from the validation report. This example case is

illustrative of the tests performed for validation against the experimental data. The run number

corresponds to the designation used by the test engineer. It is a six minute glaze ice accretion and

was the first benchmark case used to assess cross-platform variability and CPU usage in the validation report. The main input file is listed below. The main input file and geometry input file are

provided on the distribution disk as “case1.inp” and “case1.xyd” respectively.

Table 95: Main Input File for Example Case 1

 Test Case 

 &LEW20

 TSTOP = 360.

 IBOD = 1

 IFLO = 6

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

NASA/CR—2002-211793 199
Figure 19: Ice Shape for Example Case 1

Figure 20: Ice Thickness for Example Case 1

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.02 0.03 0.08 0.13 0.18 0.23

x/c

y/c

LEWICE 2.2.2

Experiment

Ice Thickness

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Thickness/c

NASA/CR—2002-211793 200
Figure 21: Heat Transfer Coefficient for Example Case 1

Figure 22: Pressure Coefficient for Example Case 1

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Clean

htc - iced

Pressure Coefficient

-12

-10

-8

-6

-4

-2

0

2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

NASA/CR—2002-211793 201
Figure 23: Collection Efficiency for Example Case 1

15.2 Case 2: Run 072504 from Validation Report

Computation Time: Pentium III 550MHz, 4 min. 59 s.; Pentium IV 1.7 GHz, 1 min.57 s.

Disk Space: 2.7 MB

This example case is taken from Run 072504 from the validation report. It is the second case

used in that report for benchmarking results on different platforms. The case is a 45 minute glaze

ice condition. This is representative of a long icing time which might be run for certification purposes. The meteorological conditions for this case are identical to Example Case 1. It is interesting to note that the experimental icing limit is less for this case than the first example even though

it has a longer exposure time. This effect is a by-product of the variability of ice formations in the

tunnel and the variability in the measurement technique. The main input file for this case is listed

in Table 38. The main input file and geometry input file are provided on the distribution disk as

“case2.inp” and “case2.xyd” respectively. 

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 202
Table 96: Main Input File for Example Case 2

 Test Case 

 &LEW20

 TSTOP = 2700.

 IBOD = 1

 IFLO = 15

 DSMN = 4.0D-4

 NPL = 24

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

NASA/CR—2002-211793 203
Figure 24: Ice Shape for Example Case 2

Figure 25: Ice Thickness for Example Case 2

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.10 -0.05 0.00 0.05 0.10 0.15

x/c

y/c

LEWICE 2.2.2

Experiment

Ice Thickness

-0.020

0.000

0.020

0.040

0.060

0.080

0.100

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Thickness/c

NASA/CR—2002-211793 204
Figure 26: Heat Transfer Coefficient for Example Case 2

Figure 27: Pressure Coefficient for Example Case 2

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

1800

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Clean

htc - iced

Pressure Coefficient

-20

-15

-10

-5

0

5

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

NASA/CR—2002-211793 205
Figure 28: Collection Efficiency for Example Case 2

15.3 Case 3: Cylinder Benchmark Case

Computation Time: Pentium III 550MHz, 24 min.37 s.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 3.9 MB

This example case uses a 6” diameter cylinder for the geometry input. This example was

included in the validation report as benchmark case number 16. It is a much longer case computationally and as such is not well suited for slower machines as the times above illustrate. The slow

execution time is due to the relative size of the ice shape to the cylinder. Slower execution times

can be expected for any small model, not just cylinders. The small chord size also causes the program to use a large number of time steps for this case if the automated time-step flag (ITIMFL) is

on. The automatic time step flag was not used for this case as the computation time would be prohibitive. The cylinder case imposes a further constraint due to the high ratio of wrap distance to

chord length. This ratio necessitates the use of a larger DSMN value than desired due to array size

limitations. The main input file for this case is listed in Table 39. The main input file and geometry input file are provided on the distribution disk as “case3.inp” and “case3.xyd” respectively.

Note that the program will warn the user that the automated time step flag is not being used. The

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 206
user should confirm this when the warning message appears on the screen. The effect of the compromises made to this case can be seen in the ice shape output as the ice shape on the cylinder is

not symmetrical. As such, this case would not be appropriate for comparison with experimental

data if such data exists.

Table 97: Main Input File for Example Case 3

 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 2700.

 IBOD = 1

 IFLO = 15

 DSMN = 0.0008

 NPL = 24

 RHOP = 1000.

 IGRID = 0

 IBOE = 0

 IDEICE = 0

 &END

 &DIST

 FLWC = 1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0

 DPD = 20.,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0

 &END

 &ICE1

 CHORD = 0.1524

 AOA = 0.0

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

NASA/CR—2002-211793 207
 BPRT = 1

 EPRT = 0

 MPRT = 0

 TPRT = 0

 IDBF = 1

 &END

 &RDATA

 &END

Figure 29: Ice Shape for Example Case 3

Ice Shape

-1.00

-0.80

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

0.80

1.00

-1.00 -0.50 0.00 0.50 1.00 1.50

x/c

y/c

LEWICE 2.2.2

NASA/CR—2002-211793 208
Figure 30: Ice Thickness for Example Case 3

Figure 31: Heat Transfer Coefficient for Example Case 3

Ice Thickness

-0.100

0.000

0.100

0.200

0.300

0.400

0.500

-0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80

s/c

Thickness/c

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

s/c

HTC (W/m2K)

htc - Clean

htc - iced

NASA/CR—2002-211793 209
Figure 32: Pressure Coefficient for Example Case 3

Figure 33: Collection Efficiency for Example Case 3

Pressure Coefficient

-20

-15

-10

-5

0

5

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 210
Figure 34: Collection Efficiency as a Function of Wrap Distance for Example Case 3

The plots for collection efficiency and pressure coefficient are quite complex due the complexity of the ice shape. For this case, it is more appropriate to plot collection efficiency as a function of wrap distance instead of x-distance. This is shown in Figure 34.

The wrap distance plotted in Figure 34 was the wrap distance from stagnation, not the wrap

distance from the leading edge. Both wrap distances are listed in the output file.

15.4 Case 4: Langmuir ‘D’ distribution

Computation Time: Pentium III 550MHz, 2 min.59 s.; Pentium IV 1.7GHz, 1 min.9 s.

Disk Space: 993 KB

This case shows an example using a drop size distribution. The conditions are identical to

Example Case 1 except for the droplet distribution. The case was originally run as part of the

Numerical Effects section in the validation report. That section showed the qualitative difference

in ice shape and ice thickness by using a droplet distribution rather than a monodispersed drop

size as was the case for the main validation runs. The main input file is listed in Table 40. The

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

-1.00 -0.80 -0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00

s/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 211
main input file and geometry input file are provided on the distribution disk as “case4.inp” and

“case4.xyd” respectively.

Table 98: Main Input File for Example Case 4

 Test Case 

 &LEW20

 TSTOP = 360.

 IBOD = 1

 IFLO = 6

 DSMN = 4.0D-4

 NPL = 24

 &END

 &DIST

 FLWC = 0.05, 0.1, 0.2, 0.3, 0.2, 0.1, 0.05

 DPD = 6.2, 10.4, 14.2, 20., 27.4, 34.8, 44.4

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

NASA/CR—2002-211793 212
Figure 35: Ice Shape for Example Case 4

Figure 36: Ice Thickness for Example Case 4

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.02 0.03 0.08 0.13 0.18 0.23

x/c

y/c

LEWICE 2.2.2

Experiment

Ice Thickness

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Thickness/c

NASA/CR—2002-211793 213
Figure 37: Heat Transfer Coefficient for Example Case 4

Figure 38: Pressure Coefficient for Example Case 4

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

1800

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Clean

htc - iced

Pressure Coefficient

-12

-10

-8

-6

-4

-2

0

2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

NASA/CR—2002-211793 214
Figure 39: Collection Efficiency for Example Case 4

15.5 Case 5: Exceedence condition

Computation Time: Pentium III 550MHz, 2 min.19 s.; Pentium IV 1.7GHz, 51 s.

Disk Space: 1.08 MB

This case shows an example using an exceedence condition as input. This condition is Run

DC-2 from the NACA4415(mod) database in the validation report1. When this case is run, a

warning message will appear to indicate that the condition is outside of the FAA certification

envelope. This warning must be confirmed by the user for this case to run. 

There are some interesting features to note on this ice accretion. First, the ice shape from the

IRT is much rougher than the one calculated by LEWICE, even more so than ice shapes generated

within the FAA Appendix C envelope. Second, the lower surface icing limit for the experiment

extends about 5 inches (6% chord) past the end of the ice shape predicted by LEWICE 2.0. This is

a curious result as water collection tests have shown the opposite trend concerning the prediction

of impingement limits12. It should be noted though that the experimental data for lower icing limit

for this particular condition ranges from 7.3 inches (9.4% chord) to 13.3 inches (17% chord)

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 215
while the predicted lower icing limit from LEWICE is 7.9 inches (10% chord) using a monodispersed drop size. Granted, there is very little ice on the ice shape from the experimental data in

this region, but it exists nevertheless. 

This example illustrates that it is the ice accretion limit which is the important parameter to

consider and not simply the water collection limit (they are not the same!). Indeed, the collection

efficiency prediction for this case shows water collection past 14% chord for this case while the

icing limit is closer to 10% chord. Another interesting observation is that although the condition

indicates a glaze ice condition, there is not a true glaze ice “horn” for this case. This observation

can be seen throughout the validation database for many of the exceedence conditions, even for

longer exposure times. The higher water collection rate for these drop sizes tends to distribute the

ice more evenly throughout the impingement region. However, the conclusions listed in these

observations may be premature due to the scarcity of data in this regime. Table 41 shows the main

input file for this case. The main input file and geometry input file are included on the distribution

disks as “case5.inp” and “case5.xyd” respectively.

Table 99: Main Input File for Example Case 5

 Test Case 

 &LEW20

 TSTOP = 420.

 IBOD = 1

 IFLO = 7

 DSMN = 4.0D-4

 NPL = 24

 &END

 &DIST

 FLWC = 1.0

 DPD = 160.0

 &END

 &ICE1

 CHORD = 1.9812

 AOA = 0.0

 VINF = 87.2

 LWC = 0.82

NASA/CR—2002-211793 216
 TINF = 266.85

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

Figure 40: Ice Shape for Example Case 5

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.02 0.03 0.08 0.13 0.18 0.23

x/c

y/c

LEWICE 2.2.2

Experiment

NASA/CR—2002-211793 217
Figure 41: Ice Thickness for Example Case 5

Figure 42: Heat Transfer Coefficient for Example Case 5

Ice Thickness

-0.001

0.000

0.001

0.001

0.002

0.002

0.003

0.003

0.004

0.004

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

s/c

Thickness/c

Heat Transfer Coefficient

0

100

200

300

400

500

600

700

800

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2K)

htc - Clean

htc - iced

NASA/CR—2002-211793 218
Figure 43: Flow Solution for Example Case 5

Figure 44: Collection Efficiency for Example Case 5

Pressure Coefficient

-1

-0.5

0

0.5

1

1.5

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 219
15.6 Case 6: Exceedence condition w/Langmuir ‘D’ distribution

Computation Time: Pentium III 550MHz, 5 min.57 s.; Pentium IV 1.7GHz, 1 min.45 s.

Disk Space: 1.14 MB

This example case uses the same input as the previous example, except that a Langmuir ’D’

drop size distribution is used instead of a monodispersed drop size. This example was provided to

show the effect of a drop size distribution for an exceedence condition. As with the previous

example, the software will print a warning concerning the input drop size. The user will have to

confirm the warning to continue the case. The collection efficiency plot for this example shows a

greater extent of water collection than the previous example as expected. However, the ice shape

comparison for this case is virtually identical to the previous example, as a comparison of the two

ice shapes shows. 

A plot of the ice thickness distribution for these two cases shows that the Langmuir ‘D’ case

extends the ice by 1 inches on the lower surface and 3 inches on the upper surface. However the

panel spacing is very course in this region for both cases. Whether this quantitative difference is

due more to the use of a drop size distribution or whether it is due to the course spacing is

unknown. The algorithms in LEWICE will place a higher density of points in regions of high curvature. This results in higher accuracy in regions where the ice thickness is greatest. Near the

icing limits, the surface curvature is flat, reducing the accuracy of the result. Table 42 shows the

main input file for this case. The main input file and geometry input file are included on the distribution disks as “case6.inp” and “case6.xyd” respectively.

NASA/CR—2002-211793 220
Table 100: Main Input File for Example Case 6

 Test Case 

 &LEW20

 TSTOP = 420.

 IBOD = 1

 IFLO = 7

 DSMN = 4.0D-4

 NPL = 24

 &END

 &DIST

 FLWC = 0.05, 0.1, 0.2, 0.3, 0.2, 0.1, 0.05

 DPD = 49.6, 83.2, 113.6, 160., 219.2, 278.4, 355.2

 &END

 &ICE1

 CHORD = 1.9812

 AOA = 0.0

 VINF = 87.2

 LWC = 0.82

 TINF = 266.85

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

NASA/CR—2002-211793 221
Figure 45: Ice Shape for Example Case 6

Figure 46: Ice Thickness for Example Case 6

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.02 0.03 0.08 0.13 0.18 0.23

x/c

y/c

LEWICE 2.2.2

Experiment

Ice Thickness

-0.001

0.000

0.001

0.001

0.002

0.002

0.003

0.003

0.004

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30

s/c

Thickness/c

NASA/CR—2002-211793 222
Figure 47: Comparison of Ice Shapes for Monodispersed and Langmuir ‘D’ Cases

Figure 48: Comparison of Ice Thicknesses for Monodispersed and Langmuir ‘D’ Cases

Ice Shape Comparison

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.02 0.03 0.08 0.13 0.18 0.23

x/c

y/c

Airfoil

Monodispersed

Distribution

Ice Thickness Comparison

-0.001

0.000

0.001

0.001

0.002

0.002

0.003

0.003

0.004

0.004

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 0.30

s/c

Thickness/c

Monodispersed

Distribution

NASA/CR—2002-211793 223
Figure 49: Heat Transfer Coefficient for Example Case 6

Figure 50: Pressure Coefficient for Example Case 6

Heat Transfer Coefficient

0

100

200

300

400

500

600

700

800

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Clean

htc - iced

Pressure Coefficient

-1

-0.5

0

0.5

1

1.5

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

NASA/CR—2002-211793 224
Figure 51: Collection Efficiency for Example Case 6

15.7 Case 7: Run 072504 without automated time step and fewer time steps

Computation Time: Pentium III 550MHz, 1 min.23 s.; Pentium IV 1.7GHz, 27 s.

Disk Space: 556 KB

This example case illustrates the problems which can occur when the user bypasses the recommended operating procedure for LEWICE. In this case, the automatic time step flag has been

set to off (ITIMFL = 0) and the number of time steps has been reduced to three. Otherwise, the

example case uses the same inputs as Example Case 2. Warning messages will be issued for this

case to inform the user that the guidelines are not being followed. This message must be confirmed by the user to run this case. Since the current example case uses fewer time steps, it runs

much faster than Example Case 2. However, an examination of the ice shape prediction shows the

pitfalls of this approach. Because the ice shape is not allowed to progress in time relative of the

proper ice accretion physics, the glaze ice horn which develops is not as large as the experimental

ice shape or the prediction from Example Case 2. Also note that there is no development of a distinctive lower horn which was observed in Case 2. Table 43 shows the main input file for this

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 225
case. The main input file and geometry input file are included on the distribution disks as

“case7.inp” and “case7.xyd” respectively.

Table 101: Main Input File for Example Case 7

 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 2700.

 IBOD = 1

 IFLO = 3

 DSMN = 4.0D-4

 NPL = 24

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

NASA/CR—2002-211793 226
Figure 52: Ice Shape for Example Case 7

Figure 53: Ice Thickness for Example Case 7

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.10 -0.05 0.00 0.05 0.10 0.15

x/c

y/c

LEWICE 2.2.2

Experiment

Ice Thickness

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Thickness/c

NASA/CR—2002-211793 227
Figure 54: Heat Transfer Coefficient for Example Case 7

Figure 55: Pressure Coefficient for Example Case 7

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

1800

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Clean

htc - iced

Pressure Coefficient

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

NASA/CR—2002-211793 228
Figure 56: Collection Efficiency for Example Case 7

15.8 Case 8: Run 072504 with Larger Point Spacing

Computation Time: Pentium III 550MHz, 1 min.26 s.; Pentium IV 1.7GHz, 29 s.

Disk Space: 1.07 MB

As with the previous example, this example case illustrates the problems which can occur

when the user bypasses the recommended operating procedure for LEWICE. In this case, the

point spacing has been increased past the recommended limits. Otherwise, the inputs for this case

also correspond to Example Case 2. A warning will be issued by the program when this example

case is run due to the large point spacing. The warning message must be confirmed by the user to

run this case. Since the point spacing is much sparser than Case 2, the program also runs much

faster, again at some cost to the accuracy of the solution. The effect on the ice shape prediction

due to the increased point spacing is not as great for this case as the time step effect, but the

effects are still noticeable. The main effect on the ice shape prediction for this case is a change in

the predicted horn angle. The upper horn tends to “droop” for this case whereas the original case

predicted a more regular horn angle throughout the run. This “drooping” effect on glaze ice horns

is typical of a case with poor numerics. The user should increase the number of points (decrease

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 229
DSMN) for this case to counter this effect. Table 44 shows the main input file for this case. The

main input file and geometry input file are included on the distribution disks as “case8.inp” and

“case8.xyd” respectively.

Table 102: Main Input File for Example Case 8

 Test Case 

 &LEW20

 TSTOP = 2700.

 IBOD = 1

 IFLO = 15

 DSMN = 1.2D-3

 NPL = 24

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

NASA/CR—2002-211793 230
Figure 57: Ice Shape for Example Case 8

Figure 58: Ice Thickness for Example Case 8

Ice Shape

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.10

-0.10 -0.05 0.00 0.05 0.10 0.15

x/c

y/c

LEWICE 2.2.2

Experiment

Ice Thickness

-0.010

0.000

0.010

0.020

0.030

0.040

0.050

0.060

0.070

0.080

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Thickness/c

NASA/CR—2002-211793 231
Figure 59: Heat Transfer Coefficient for Example Case 8

Figure 60: Pressure Coefficient for Example Case 8

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

1800

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Clean

htc - iced

Pressure Coefficient

-12

-10

-8

-6

-4

-2

0

2

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - clean

Cp - iced

NASA/CR—2002-211793 232
Figure 61: Collection Efficiency for Example Case 8

15.9 Case 9: First benchmark conditions with an evaporative hot air anti-icer.

Computation Time: Pentium III 550MHz, 18 s.; Pentium IV 1.7GHz, 5 s.

Disk Space: 420 KB

This example case illustrates the use of the IDEICE = 1 anti-ice capabilities of LEWICE. As

the procedure used in LEWICE for IDEICE = 1 anti-icing is less involved than the procedure used

for the IDEICE = 2 or IDEICE = 3 options and since this feature has not been validated with

experimental data, a warning will appear when this case is run. The user must confirm the warning message to continue the run. Also note that a second warning will be generated because the

IDEICE = 1 option is being used. The conditions for this case are the same as Example Case 1,

except the simulated icing time has been reduced to 1 minute and the de-icer flag has been set on

(IDEICE = 1). The use of a 1 minute icing time was arbitrary. The anti-ice solution provided is a

steady-state solution so the choice of time step is irrelevant to that output. Since this example was

created to illustrate the use of the anti-ice solution, a single time step was chosen for expediency. 

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.10 -0.05 0.00 0.05 0.10 0.15 0.20

x/c

Beta

Beta - clean

Beta - iced

NASA/CR—2002-211793 233
Table 45 shows the main input file for this case while Table 46 shows the de-ice input file.

The main input file and geometry input file are included on the distribution disks as “case9.inp”

and “case9.xyd” respectively. The de-ice input file is listed on the distribution disk as

“deice9.inp”. This case shows an example of an evaporative anti-icer using bleed air. Since the

input flag states that all of the water must evaporate, the wattages shown are very high. Wattages

in this range should be expected for evaporative systems. The useful outputs from “NOICE.DAT”

in this example are the heat requirements and the surface temperature. As shown in Figure 64, the

bleed air temperature solution will be inaccurate due to the simplistic assumptions used. The input

flag IDEICE should be set to 3 to predict bleed air temperatures for this case. Another output from

“NOICE.DAT” which may be useful is the effective heat transfer coefficient, heff. The effective

heat transfer coefficient can be used to transfer information from LEWICE to other programs. It is

the “effective” value which would need to be input as the convective boundary condition for

many commercial or non commercial CFD programs in order to thermally account for icing

effects. Other outputs for this case such as heat transfer coefficient, collection efficiency and pressure coefficient are the same as shown in the first example case and are not shown again here. 

Note: The full de-ice input file is read even though the program will only perform a one

dimensional steady-state analysis.

Note: The de-ice input file name no longer is fixed as “deicei.inp” as it was in version 2.0. 

Table 103: Main Input File for Example Case 9

 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 60.

 IBOD = 1

 IFLO = 1

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 1

 &END

 &DIST

 FLWC = 1.0

NASA/CR—2002-211793 234
 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

 &RDATA

 &END

Table 104: De-ice input file for Example Case 9

 l nx

 2 9 

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate(alumuinum)

 25 1.750d-3 176.530d0 4.260d-5 1.d0 0.d0

C ice

 61 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9144d0 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C heater G

 14 3.175d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C heater E

NASA/CR—2002-211793 235
 21 2.540d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C heater C

 21 2.540d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C parting strip - heater A

 36 1.905d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C heater B

 21 2.540d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C heater D

 21 2.540d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C heater F

 14 3.175d-2 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

C gap (no heat input)

 10 0.9144d0 176.56d0 4.260d-5 1.d0 0.d0 0.d0 1

ijde offset ipar

001 0.005 1 

C Q TON TOFF TLAG ICFLAG

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0 

C heater G

 00.00d0 600.d0 0.d0 0.d0 0

C heater E

 0.00d0 600.d0 0.d0 0.d0 0

C heater C

 00.00d0 600.d0 0.d0 0.d0 0

C parting strip (heater A) does not turn off

 00.00d0 600.d0 0.d0 0.d0 0

C heater B

 00.00d0 600.d0 0.d0 0.d0 0

C heater D

 00.00d0 600.d0 0.d0 0.d0 0

C heater F

 00.00d0 600.d0 0.d0 0.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0 

ibc1 ibc2 ibc3 ibc4

2 2 2 2 

NASA/CR—2002-211793 236
 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5 

 h1 h2 h3 h4 

 3.d0 3.d2 0.d0 0.d0 

 qw1 qw2 qw3 qw4

 0.d0 0.d0 0.d0 0.d0 

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

i3d iqain ibleed iopt

 0 0 1 0 

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm 

 320.d0 1 1 

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 1 2 2 1.d0 0.d0

input parameters for reading in hot air q_wall info

 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 1

iotype nptsd

 1 14

C section where layer where

 5 2 1 3

 5 2 1 1

NASA/CR—2002-211793 237
 4 2 1 3

 4 2 1 1

 6 2 1 3

 6 2 1 1

 3 2 1 3

 3 2 1 1

 7 2 1 3

 7 2 1 1

 2 2 1 3

 2 2 1 1

 8 2 1 3

 8 2 1 1

Figure 62: Heat Requirement for the Evaporative Hot Air System in Example Case 9

Required Heat Flux

-20

0

2 0

4 0

6 0

8 0

100

120

140

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

qheat(kW/m2)

NASA/CR—2002-211793 238
Figure 63: Surface Temperature for the Evaporative Hot Air System in Example Case 9

Figure 64: Hot Air Temperature for the Evaporative Hot Air System in Example Case 9

Surface Temperature

250

260

270

280

290

300

310

320

330

340

350

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Temperature (K)

Bleed Air Temperature

0

100

200

300

400

500

600

700

800

900

1000

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Temperature (K)

NASA/CR—2002-211793 239
Figure 65: Effective Heat Transfer in Example Case 9

15.10 Case 10: First benchmark condition with a running wet electrothermal anti-icer.

Computation Time: Pentium III 550MHz, 14 s.; Pentium IV 1.7GHz, 5 s.

Disk Space: 420 KB

Example Case 10 also shows an example using the IDEICE = 1 option and the de-icer input

file. The conditions for this case are the same as those shown for Example Case 9, except in this

case a running wet thermal de-icer is used instead of a hot air anti-icer as in the previous example.

A warning is again issued to the user to indicate that the solution provided is only a first approximation and has not been validated. The warning must be confirmed by the user to run this case.

Also note that a second warning will be generated because the IDEICE = 1 option was selected.

This warning must also be confirmed to continue the run. Table 47 shows the main input file for

this case while Table 48 lists the de-icer input file. The main input file and geometry input file are

included on the distribution disks as “case10.inp” and “case10.xyd” respectively. The de-ice input

file is listed on the distribution disk as “deice10.inp”.

Effective Heat Transfer

0

500

1000

1500

2000

2500

3000

3500

4000

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Heat Transfer Coefficient (W/m2K)

NASA/CR—2002-211793 240
The useful outputs for this case are the local heater wattages shown in Figure 66 and the effective heat transfer coefficient shown in Figure 68. For a running wet system, the assumption made

is that the surface temperature is constant and is input by the user. Therefore, a plot of surface

temperature is not provided. As was the case for the previous example, the heater temperatures

plotted are inaccurate due to the simplistic assumptions used in order to achieve a fast solution.

The input flag IDEICE should be set to 3 to predict heater temperatures for this case.

Note: The full de-ice input file is read even though the program will only perform a one

dimensional steady-state analysis.

Note: The de-ice input file name no longer is fixed as “deicei.inp” as it was in version 2.0. 

Table 105: Main Input File for Example Case 10

 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 60.

 IBOD = 1

 IFLO = 1

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 1

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 4.5

 VINF = 90.

 LWC = 0.540

 TINF = 268.30

 PINF = 100000.00

 RH = 100.0

NASA/CR—2002-211793 241
 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

Table 106: De-ice Input File for Example Case 10

 l nx

 7 9 

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 61 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

NASA/CR—2002-211793 242
 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

ijde offset ipar

004 0.005 1 

C Q TON TOFF TLAG ICFLAG

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag 

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0 

C heater G

 12.41d0 600.d0 0.d0 0.d0 0

C heater E

 8.87d0 600.d0 0.d0 0.d0 0

C heater C

 19.26d0 600.d0 0.d0 0.d0 0

C parting strip (heater A) does not turn off

 46.58d0 600.d0 0.d0 0.d0 0

C heater B

 31.95d0 600.d0 0.d0 0.d0 0

C heater D

 12.70d0 600.d0 0.d0 0.d0 0

C heater F

 11.27d0 600.d0 0.d0 0.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

ibc1 ibc2 ibc3 ibc4

2 2 2 2

NASA/CR—2002-211793 243
 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5 

 h1 h2 h3 h4 

 3.d0 3.d2 0.d0 0.d0 

 qw1 qw2 qw3 qw4

 0.d0 0.d0 0.d0 0.d0 

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

i3d iqain ibleed iopt

 0 0 0 0 

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm 

 283.15d0 0 0 

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 1

iotype nptsd

 1 21

C section where layer where

 5 2 6 3

 5 2 1 1

NASA/CR—2002-211793 244
 4 2 6 3

 4 2 1 1

 6 2 6 3

 6 2 1 1

 3 2 6 3

 3 2 1 1

 7 2 6 3

 7 2 1 1

 2 2 6 3

 2 2 1 1

 8 2 6 3

 8 2 1 1

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 2 2 4 1

 8 2 4 1

Figure 66: Heat Requirement for the Running Wet Thermal De-icer in Example Case 10

Required Heat Flux

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20

s/c

qheat(kW/m2)

NASA/CR—2002-211793 245
Figure 67: Heater Temperature for the Running Wet Thermal De-icer in Example Case 10

Figure 68: Effective Heat Transfer Coefficient in Example Case 10

Heater Temperature

280

285

290

295

300

305

310

315

320

325

330

335

-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20

s/c

Temperature (K)

Effective Heat Transfer

0

2000

4000

6000

8000

10000

12000

-0.40 -0.30 -0.20 -0.10 0.00 0.10 0.20

s/c

Heat Transfer Coefficient (W/m2 K)

NASA/CR—2002-211793 246
15.11 Case 11: Three body example

Computation Time: Pentium III 550MHz, 12 min.54 s.; Pentium IV 1.7GHz, 3 min.57 s.

Disk Space: 1.82 MB

This example case shows a condition using a multi-element airfoil instead of the single element airfoils used in the previous example and in the validation database. This condition represents one data point of only a handful of experimental data points which are available on multielement airfoils. The other data points available are for the same airfoil. A warning will be issued

to the user due to the use of multiple body input. An additional warning will be made due to the

high angle of attack used. Warnings will also be issued since the trailing edge is not closed on two

of the bodies. The user must confirm these warnings in order to run the case.

The use of a potential flow solution for this case is questionable as the flow physics clearly

indicate that a more complex flow solution should be sought. However, it is quite difficult and

time consuming even with current technology to regrid an iced airfoil multiple times in order to

obtain the more accurate solution. Icing physics dictate that in most cases a multiple time step

solution (which takes into account the change in flow due to ice accretion) is preferable to a single

time step solution which does not. In addition, parametric studies have also shown that the user

should make use of a drop size distribution for multi-element cases rather than use a monodispersed drop size as this example shows. The ice shape predicted for this case shows some of the

limitations of using the built-in flow solver for a multi-element airfoil. The ice shape predicted on

the slat shows an accuracy similar to those shown for single element airfoils. This result should be

expected, since the viscous effects are not as dominant in this region. The ice shape predicted on

the main element shows a different horn angle than the experiment, but the icing region is similar.

The largest deviation from the experimental data is shown on the flap. This result also makes

sense physically as the viscous forces are dominant in this region. Additionally, the trailing edge

of the flap is open and no corrections were made to the input angle of attack for this case as the

actual lift coefficient was not known for this case. These two corrections could make a substantial

increase in accuracy for these cases. One point which should be noted is that the ice accretion on

the aft elements is somewhat an artifact of the subscale conditions being used. Parametric studies

NASA/CR—2002-211793 247
using a full-scale airfoil at flight Reynolds numbers show much less ice accretion on aft elements.

The main input file and geometry input file are included on the distribution disks as “case11.inp”

and “case11.xyd” respectively.

Table 107: Main Input File for Example Case 11

 Test Case 

 &LEW20

 ITIMFL = 1

 TSTOP = 360.

 IBOD = 3

 IFLO = 6

 DSMN = 2.0D-4, 4.0D-4, 2.5D-4

 NPL = 24

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 8.0

 VINF = 88.5

 LWC = 0.60

 TINF = 268.15

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

NASA/CR—2002-211793 248
Figure 69: Ice Shape on Slat and Main Elements for Example Case 11

Figure 70: Ice Shape on Flap for Example Case 11

Ice Shape

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45

x/c

y/c

LEWICE 2.2.2

Experiment

LEWICE 2.2.2

Experiment

Ice Shape

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0.00

0.02

0.04

0.06

0.08

0.97 1.02 1.07 1.12 1.17 1.22

x/c

y/c

airfoil

LEWICE 2.2.2

Experiment

NASA/CR—2002-211793 249
Figure 71: Ice Thickness on Slat for Example Case 11

Figure 72: Ice Thickness on Main Element for Example Case 11

Ice Thickness

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

0.018

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

Thickness/c

Ice Thickness - Main Element

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

-0.40 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10

s/c

thickness/c

NASA/CR—2002-211793 250
Figure 73: Ice Thickness on Flap for Example Case 11

Figure 74: Slat Heat Transfer Coefficient for Example Case 11

Ice Thickness - Flap

-2.00E-03

0.00E+00

2.00E-03

4.00E-03

6.00E-03

8.00E-03

1.00E-02

1.20E-02

1.40E-02

1.60E-02

-4.00E-01 -3.00E-01 -2.00E-01 -1.00E-01 0.00E+00 1.00E-01 2.00E-01 3.00E-01 4.00E-01

s/c

thickness/c

Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

1800

2000

-0.2 -0.2 -0.1 -0.1 0.0 0.1 0.1 0.2 0.2 0.3

s/c

HTC (W/m2K)

htc - Clean (slat)

htc - Iced (slat)

NASA/CR—2002-211793 251
Figure 75: Main Heat Transfer Coefficient for Example Case 11

Figure 76: Flap Heat Transfer Coefficient for Example Case 11

Main Element Heat Transfer Coefficient

0

200

400

600

800

1000

1200

1400

1600

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

s/c

Heat Transfer Coefficient (W/m2 K)

HTC - Clean (main)

HTC - Iced (main)

Flap Heat Transfer Coefficient

0.00E+00

2.00E+02

4.00E+02

6.00E+02

8.00E+02

1.00E+03

1.20E+03

1.40E+03

1.60E+03

1.80E+03

-4.00E-01 -3.00E-01 -2.00E-01 -1.00E-01 0.00E+00 1.00E-01 2.00E-01 3.00E-01 4.00E-01

s/c

Heat Transfer Coefficient (W/m2 K)

HTC - Clean (flap)

HTC - Iced (flap)

NASA/CR—2002-211793 252
Figure 77: Pressure Coefficient for Example Case 11

Figure 78: Collection Efficiency for Example Case 11

Pressure Coefficient

-14

-12

-10

-8

-6

-4

-2

0

2

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

x/c

Cp

Cp - clean

Cp - iced

Cp - clean

Cp - iced

Cp - clean

Cp - iced

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

x/c

Beta

Beta - clean

Beta - iced

Beta - clean

Beta - iced

Beta - clean

Beta - iced

NASA/CR—2002-211793 253
15.12 Case 12: Grid input

Computation Time: Pentium III 550MHz, 24 min.37 s.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 177 KB

This example case illustrates a new feature of LEWICE. The user may import a grid and gridbased flow solution from another source in order to perform a more detailed analysis. The drawback of this feature is that since the flow solver is not integrated into the model, only a single time

step can be performed. Its use is thus limited to examining differences in water collection efficiency and heat transfer coefficient prediction. A process for integrating a flow solver into

LEWICE to perform multi-time step ice accretions using a grid-based flow solver is described in

Appendix A. This process may require modifications both to LEWICE and to the flow solver,

therefore it is best left to more advanced users or software developers to examine this feature. 

The computation times listed for this case represent the time taken for LEWICE to run. The

computation time does not include the computation time necessary to create the flow solution. In

addition, the disk space listed represents the disk space occupied by the output files from

LEWICE. The grid file and flow solution file are considered input files to LEWICE and are much

larger. Table 50 shows the main input file for this case. The complete input for this case, including the grid and flow solution are included on the distribution disk. The grid file is a single block

structured grid output by GRIDGEN13. LEWICE 2.2 can handle up to ten grid blocks, each of

which can be as large as 600 by 200 grid points. LEWICE is currently set up to use structured

grids, although a programmer familiar with unstructured grids should be able to easily modify the

software to handle unstructured grids.

The flow solution provided was generated by the Naviér-Stokes software NPARC14. The output format of the flow solution file provided is different from the original output produced by

NPARC to conform to the format needed by LEWICE. Other software packages may also be used

to generate the grid and flow solution. The programs selected for this example were chosen based

on their accessibility. This feature is quite new and may require programming knowledge on the

part of the user to get a grid solution to read in correctly. At the end of this example case, a section

NASA/CR—2002-211793 254
is provided describing some of the pitfalls encountered in reading the original flow solution into

LEWICE.

The output for this case shows that the predicted lower impingement limit has been reduced

significantly due to the use of this grid solution as compared to the output obtained by using the

potential flow solution. A parametric study should be performed on the resolution of the grid and

on the panel resolution to determine if this result is due to the flow physics or if it is an artifact of

the point spacing near the impingement limit.

Table 108: Main Input File for Example Case 12

 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 60.

 IBOD = 1

 IFLO = 1

 DSMN = 4.0D-4

 NPL = 24

 IGRID = 1

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 1.745

 AOA = 5.0

 VINF = 76.

 LWC = 0.80

 TINF = 258.00

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

NASA/CR—2002-211793 255
 HPRT = 1

 BPRT = 1

 TPRT = 0

 &END

Figure 79: Ice Shape for Example Case 12

Figure 80: Ice Thickness for Example Case 12

Ice Shape

-0.03

-0.03

-0.02

-0.02

-0.01

-0.01

0.00

0.01

0.01

0.02

0.02

-0.02 -0.01 0.00 0.01 0.02 0.03 0.04 0.05

x/c

y/c

Naviér-Stokes

Potential Flow

Ice Thickness

-0.0002

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

s/c

Thickness/c

thickness/c - Naviér-Stokes

thickness/c - Potential Flow

NASA/CR—2002-211793 256
Figure 81: Heat Transfer Coefficient for Example Case 12

Figure 82: Pressure Coefficient for Example Case 12

Heat Transfer Coefficient

0

100

200

300

400

500

600

700

800

900

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

HTC (W/m2 K)

htc - Naviér-Stokes

htc - Potential Flow

Pressure Coefficient

-2

-1.5

-1

-0.5

0

0.5

1

1.5

-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2

x/c

Cp

Cp - Naviér-Stokes

Cp - Potential Flow

NASA/CR—2002-211793 257
Figure 83: Collection Efficiency for Example Case 12

15.12.1 Grid Input Problems

This section describes the problems encountered when trying to import the NPARC flow solution into LEWICE for Example Case 12. Many of the problems do not require extensive programming knowledge to rectify. The problems encountered by the user may be different than those

described here. This section is intended to provide some general explanations which will aid the

user in reading input files.

Problem 1: Translated Grid Geometry

The airfoil for this case was the NACA23014(mod) airfoil used in the validation report.

Therefore, the geometry file originally input into LEWICE used the same airfoil geometry as the

validation cases. The grid however used a surface geometry which was offset from this geometry

file. It is necessary that the airfoil input by the user matches the surface geometry of the grid. In

order to rectify this problem, the airfoil geometry was shifted by 0.15 inches (0.0218 in nondimensional format) in the y-direction so that the airfoil is aligned with the grid surface.

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

x/c

Beta

Beta - Naviér-Stokes

Beta - Potential Flow

NASA/CR—2002-211793 258
Problem 2: Input Format

LEWICE expects the grid and flow solution to be in PLOT3D binary format with the

IBLANK feature on as described in the PLOT3D User Manual11. For a single body airfoil,

LEWICE is set up to read only single block grids. Although the original file was a single block

grid, it was written using the multi-block grid format described in the PLOT3D manual. After this

problem was corrected, it was discovered that the original input grid had the first index in the second dimension as the outer grid boundary and the last index value as the surface grid. LEWICE

expects the grid to be input such that the first index in the second dimension contains the surface

geometry. Also, LEWICE expected a ‘C’ or ‘O’ grid input clockwise in the first dimension while

the actual grid was supplied in the counterclockwise direction. These problems required that a

small utility program be written to read the file in its existing format and to output it in the desired

format.

Problem 3: Unit Conversions

The next problem which was encountered was the use by NPARC of dimensionless variables

which were nondimensionalized by different factors than those expected by LEWICE. The second and third ‘Q’ functions (ρvx and ρvy) had to be divided by the ambient Mach number while

the fourth ‘Q’ function had to be multiplied by γ (1.4) to convert the file to the quantities expected

by LEWICE. 

Problem 4: Platform Problems

Once this conversion was made, the case ran successfully on an SGI Indigo2. When the case

was repeated on a PC, it was discovered that the binary file format for SGIs and for PCs were

incompatible. The grid and flow solution files had to be converted to text format before transfer to

a PC and then reconverted to binary format on the PC before the grid and solution files could be

used on that platform. This problem also required that small utility programs be written to perform the conversion. Two such programs (TOBINARY and TOASCII) are provided on the distribution disk for conversion to and from binary format.

NASA/CR—2002-211793 259
15.12.2 LEWICE Errors Associated with Grid Input Problems

For the problems described earlier LEWICE would, for the most part, read the grid and flow

solution file and start running. The problems occurred when runtime errors were generated for

these cases. These errors usually occurred during the droplet trajectory routine as the software

attempted to interpolate air velocities from this grid. The user should review the runtime error

messages which are generated by LEWICE specific to grid usage. For the cases run thus far, the

runtime errors which were generated were caused by an incorrect interpretation of the information

in the grid and flow solution files. Once these files were converted to the file format expected by

LEWICE, the software ran without incident.

15.13 Case 13: Example Using Detailed Thermal Module

Computation Time: Pentium III 550MHz, 24 min.37 s.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 2.9 MB

This example case illustrates a feature new to version 2.2 of LEWICE. In the previous antiicing examples, a simplified analysis was employed which assumed that heat transfer was one

dimensional in the direction normal to the airfoil. This approach yielded heat flux values which

appear reasonable, but results in heater (or bleed air) temperatures which are excessive. This

result shows the importance of the chordwise component of heat transfer on the process. The

approach used in this and subsequent examples solves the two dimensional unsteady heat conduction equation within the airfoil geometry and couples this to the standard mass and energy balance

used by LEWICE for ice accretion prediction. This approach is an extension of the capabilities

which previously resided in the LEWICE/Thermal and ANTICE programs.

The first example using this approach models an electrothermal de-icer embedded within an

airfoil as illustrated in Figure 84. The airfoil is a 36” chord NACA 0012 airfoil with seven heaters

wrapped around the leading edge. The middle heater is 0.75” wide and is on for the duration of

the run which simulates a parting strip heater. The parting strip heater separates the accreted ice

into upper and lower segments for easier removal. The heaters on each side of the parting strip are

turned on for 10 seconds and are off for 110 seconds (two minute cycle time). This set of heaters

NASA/CR—2002-211793 260
will first turn on 100 seconds into the run. The remaining four heaters will also turn on for 10 seconds out of the two minute cycle, but will first engage 110 seconds into the simulation so that they

will be on immediately after the second set of heaters turn off. This heater cycle is diagrammed in

Figure 85.

The experimental data plotted in these figures comes from Run 28 from a 1996 IRT test on the

NACA0012 geometry described. Each heater zone pictured below had thermocouples just below

the airfoil surface and on the inside surface of the de-icer. An RTD was placed under the heater to

record heater temperature. For all thermocouples and RTDs, there was a set of readings at two

spanwise locations on the two dimensional model. There are over 100 cases from this test which

are available for comparison. A complete comparison of all runs has been performed and a report

on the results is currently being prepared. These comparisons show that the software underpredicts the temperatures from some of the thermocouples. This is believed to be caused by using the

standard LEWICE heat transfer coefficients which result from an assumption that ice will form on

the surface causing roughness which causes the boundary layer to turn turbulent. The next example will explore an assumption using a laminar heat transfer coefficient instead. 

Note: In this example, there is no residual ice. Therefore, only one LEWICE time step was

performed (IFLO = 1) and neither the ice shape nor ice thickness plots were included.

Note: In the IRT run of this condition, residual ice did form. Due to the fragile nature of the

runback ice formations, quantitative tracings could not be obtained and only qualitative observations of the extent of runback ice were recorded.

Note: Only the heater temperatures have been shown in this example. Surface temperature

and substrate temperature comparisons are similar.

Note: In Example Cases 13-16, the user will receive five temperature output files named

“TEMPS1.DAT” through “TEMPS5.DAT”. Since 21 locations were chosen for temperature versus time output, the first three files (“TEMPS1.DAT” to “TEMPS3.DAT”) will contain that data.

“TEMPS4.DAT” will contain the temperature versus wrap distance location at the surface of the

de-icer for 30 different times. “TEMPS5.DAT” will contain temperature as a function of the disNASA/CR—2002-211793 261
tance normal to the surface at the center of the parting strip heater for the same 30 time steps. All

of these options are controlled by the user and are discussed in Section 10.1.5. 

The 21 locations chosen for temperature versus time output correspond to the approximate

locations of the 21 thermocouples in the experimental setup. Furthermore, they are output in same

order as the original experimental data files to avoid confusion. This order is given as follows:

Section A, outer surface; Section A, inner surface; Section B, outer surface; Section B, inner surface; Section C, outer surface; Section C, inner surface; Section D, outer surface; Section D, inner

surface; Section E, outer surface; Section E, inner surface (end of “TEMPS1.DAT” file); Section

F, outer surface; Section F, inner surface; Section G, outer surface; Section G, inner surface; Section A, heater; Section B, heater; Section C, heater; Section D, heater; Section E, heater; Section

F, heater (end of “TEMPS2.DAT” file); Section G, heater. The remaining columns of

“TEMPS3.DAT” contain zero values to avoid confusion. Temperature is output to these files in

Kelvin every 0.1 seconds as specified in the input file. Experimental data was recorded in degrees

Fahrenheit once per second. The utility program REDUCE was used to convert the LEWICE 2.2

output for easier comparison to the experimental data.

Table 109: Main Input File for Example Case 13

 Example 13 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 600

 IBOD = 1

 IFLO = 1 

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 2

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

NASA/CR—2002-211793 262
 AOA = 0.

 VINF = 44.7

 LWC = 0.780

 TINF = 265.50

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 EPRT = 1

 MPRT = 1

 TPRT = 0

 IDBF = 1

 &END

 &RDATA

 &END

Table 110: De-ice Input File for Example Case 13

 l nx

 7 9 

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

NASA/CR—2002-211793 263
C ice

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9244d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

ijde offset ipar

004 0.000 1

C Q TON TOFF TLAG ICFLAG

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 11.75d0 10.d0 110.d0 110.d0 0

C heater E

 11.27d0 10.d0 110.d0 110.d0 0

C heater C

 11.68d0 10.d0 110.d0 100.d0 0

C parting strip (heater A) does not turn off

NASA/CR—2002-211793 264
 07.78d0 600.d0 0.d0 0.d0 0

C heater B

 11.25d0 10.d0 110.d0 100.d0 0

C heater D

 11.19d0 10.d0 110.d0 110.d0 0

C heater F

 12.02d0 10.d0 110.d0 110.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

ibc1 ibc2 ibc3 ibc4

2 2 2 2

 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5

 h1 h2 h3 h4 

 3.d0 3.d2 0.d0 0.d0 

 qw1 qw2 qw3 qw4

 0.d0 0.d0 0.d0 0.d0 

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

i3d iqain ibleed iopt

 0 0 0 0 

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm

 278.d0 1 0 

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

 1 2 2 1.d0 0.d0

NASA/CR—2002-211793 265
input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 3

iotype nptsd

 1 21

C section where layer where

 5 2 6 3

 5 2 1 1

 4 2 6 3

 4 2 1 1

 6 2 6 3

 6 2 1 1

 3 2 6 3

 3 2 1 1

 7 2 6 3

 7 2 1 1

 2 2 6 3

 2 2 1 1

 8 2 6 3

 8 2 1 1

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 2 2 4 1

 8 2 4 1

iotype nptsd

 2 30

C time layer where

C (sec)

 5 6 1

 10 6 1

NASA/CR—2002-211793 266
 15 6 1

 20 6 1

 25 6 1

 30 6 1

 35 6 1

 40 6 1

 45 6 1

 50 6 1

 55 6 1

 60 6 1

 65 6 1

 70 6 1

 75 6 1

 80 6 1

 85 6 1

 90 6 1

 95 6 1

 100 6 1

 105 6 1

 110 6 1

 115 6 1

 120 6 1

 125 6 1

 130 6 1

 135 6 1

 140 6 1

 145 6 1

 150 6 1

iotype nptsd

 3 30

C time section where

C (sec)

 5 5 2

 10 5 2

 15 5 2

 20 5 2

NASA/CR—2002-211793 267
 25 5 2

 30 5 2

 35 5 2

 40 5 2

 45 5 2

 50 5 2

 55 5 2

 60 5 2

 65 5 2

 70 5 2

 75 5 2

 80 5 2

 85 5 2

 90 5 2

 95 5 2

 100 5 2

 105 5 2

 110 5 2

 115 5 2

 120 5 2

 125 5 2

 130 5 2

 135 5 2

 140 5 2

 145 5 2

 150 5 2

NASA/CR—2002-211793 268
Figure 84: Schematic of Heaters for Example Case13

Figure 85: Heater Power for Example Case 13

Heater Power for Run 28

0

1

2

3

4

5

6

7

8

9

0 100 200 300 400 500 600 700

Time (sec)

Power (kW/m^2)

q(A)

q(B)

q(C)

q(D)

q(E)

q(F)

q(G)

NASA/CR—2002-211793 269
Figure 86: Heat Transfer Coefficient for Example Case 13

Figure 87: Pressure Coefficient for Example Case 13

Heat Transfer Coefficient

0

100

200

300

400

500

600

700

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

Heat Transfer Coefficient (W/m2K)

Pressure Coefficient

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

x/c

Pressure Coefficient

NASA/CR—2002-211793 270
Figure 88: Collection Efficiency for Example Case 13

Figure 89: Heater A Temperature for Example Case 13

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

s/c

Beta

Run 28 Top, Section A: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section A: Heater Temperature (Experimental) [oF] Section A: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 271
Figure 90: Heater B Temperature for Example Case 13

Figure 91: Heater C Temperature for Example Case 13

Run 28 Top, Section B: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section B: Heater Temperature (Experimental) [oF] Section B: Heater Temperature (LEWICE) [oF]

Run 28 Top, Section C: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section C: Heater Temperature (Experimental) [oF] Section C: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 272
Figure 92: Heater D Temperature for Example Case 13

Figure 93: Heater E Temperature for Example Case 13

Run 28 Top, Section D: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section D: Heater Temperature (Experimental) [oF] Section D: Heater Temperature (LEWICE) [oF]

Run 28 Top, Section E: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section E: Heater Temperature (Experimental) [oF] Section E: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 273
Figure 94: Heater F Temperature for Example Case 13

Figure 95: Heater G Temperature for Example Case 13

Run 28 Top, Section F: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section F: Heater Temperature (Experimental) [oF] Section F: Heater Temperature (LEWICE) [oF]

Run 28 Top, Section G: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section G: Heater Temperature (Experimental) [oF] Section G: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 274
15.14 Case 14: Laminar Example Using Detailed Thermal Module

Computation Time: Pentium III 550MHz, 24 min.37 s.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 3 MB

This example case was created in conjunction with the previous example. In this case, the

external heat transfer coefficient was forced to remain laminar on the airfoil. Within the icing limits, this is believed to be a more accurate assumption over the de-icer thermocouples since the deicer maintains an ice-free surface after the ice is shed. The example inputs for this case are exactly

the same as the previous example, except that IDEICE = 3 in the main LEWICE input file. The

results from this case show that while the temperatures over heater zones “B” and “C” are better

predicted using the laminar assumption, the results for heater zones “A”, “D”, “E”, “F” and “G”

were better predicted using the turbulent assumption. This indicates that the best prediction could

be obtained by forcing transition after heaters “B” and “C”. Forced transition, however, was not

included as an input option to LEWICE 2.2 as this creates user to user variability in the results

which was considered undesirable from a certification standpoint. Since the temperature in zone

“A” (parting strip) is overpredicted with this option while neighboring zones “B” and “C” are

underpredicted, this may indicate that the program may be underpredicting transverse heating in

regions of high curvature. This assumption could not be verified however.

Note: In this example, there is no residual ice. Therefore, only one LEWICE time step was

performed (IFLO = 1) and neither the ice shape nor ice thickness plots were included.

Note: In the IRT run of this condition, residual ice did form. Due to the fragile nature of the

runback ice formations, quantitative tracings could not be obtained and only qualitative observations of the extent of runback ice were recorded.

Note: Only the heater temperatures have been shown in this example. Surface temperature

and substrate temperature comparisons are similar.

NASA/CR—2002-211793 275
Table 111: Main Input File for Example Case 14

 Example 14 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 600

 IBOD = 1

 IFLO = 1 

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 2

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 0.

 VINF = 44.7

 LWC = 0.780

 TINF = 265.50

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 EPRT = 1

 MPRT = 1

 TPRT = 0

 IDBF = 1

 &END

 &RDATA

 &END

NASA/CR—2002-211793 276
Table 112: De-ice Input File for Example Case 14

 l nx

 7 9 

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9244d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

NASA/CR—2002-211793 277
 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

ijde offset ipar

004 0.000 1 

C Q TON TOFF TLAG ICFLAG

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag 

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 11.75d0 10.d0 110.d0 110.d0 0

C heater E

 11.27d0 10.d0 110.d0 110.d0 0

C heater C

 11.68d0 10.d0 110.d0 100.d0 0

C parting strip (heater A) does not turn off

 07.78d0 600.d0 0.d0 0.d0 0

C heater B

 11.25d0 10.d0 110.d0 100.d0 0

C heater D

 11.19d0 10.d0 110.d0 110.d0 0

C heater F

 12.02d0 10.d0 110.d0 110.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

ibc1 ibc2 ibc3 ibc4

2 2 2 2

 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5

 h1 h2 h3 h4

 3.d0 3.d2 0.d0 0.d0

 qw1 qw2 qw3 qw4

 0.d0 0.d0 0.d0 0.d0

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

NASA/CR—2002-211793 278
i3d iqain ibleed iopt

 0 0 0 0

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm

 278.d0 1 0

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 3

iotype nptsd

 1 21

C section where layer where

 5 2 6 3

 5 2 1 1

 4 2 6 3

 4 2 1 1

 6 2 6 3

 6 2 1 1

 3 2 6 3

 3 2 1 1

 7 2 6 3

 7 2 1 1

NASA/CR—2002-211793 279
 2 2 6 3

 2 2 1 1

 8 2 6 3

 8 2 1 1

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 2 2 4 1

 8 2 4 1

iotype nptsd

 2 30

C time layer where

C (sec)

 5 6 1

 10 6 1

 15 6 1

 20 6 1

 25 6 1

 30 6 1

 35 6 1

 40 6 1

 45 6 1

 50 6 1

 55 6 1

 60 6 1

 65 6 1

 70 6 1

 75 6 1

 80 6 1

 85 6 1

 90 6 1

 95 6 1

 100 6 1

 105 6 1

NASA/CR—2002-211793 280
 110 6 1

 115 6 1

 120 6 1

 125 6 1

 130 6 1

 135 6 1

 140 6 1

 145 6 1

 150 6 1

iotype nptsd

 3 30

C time section where

C (sec)

 5 5 2

 10 5 2

 15 5 2

 20 5 2

 25 5 2

 30 5 2

 35 5 2

 40 5 2

 45 5 2

 50 5 2

 55 5 2

 60 5 2

 65 5 2

 70 5 2

 75 5 2

 80 5 2

 85 5 2

 90 5 2

 95 5 2

 100 5 2

 105 5 2

 110 5 2

 115 5 2

NASA/CR—2002-211793 281
 120 5 2

 125 5 2

 130 5 2

 135 5 2

 140 5 2

 145 5 2

 150 5 2

Figure 96: Heat Transfer Coefficient for Example Case 14

Heat Transfer Coefficient

0

100

200

300

400

500

600

700

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

Heat Transfer Coefficient (W/m2 K)

NASA/CR—2002-211793 282
Figure 97: Pressure Coefficient for Example Case 14

Figure 98: Collection Efficiency for Example Case 14

Pressure Coefficient

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

x/c

Pressure Coefficient

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

s/c

Beta

NASA/CR—2002-211793 283
Figure 99: Heater A Temperature for Example Case 14

Figure 100: Heater B Temperature for Example Case 14

Run 28 Top, Section A: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section A: Heater Temperature (Experimental) [oF] Section A: Heater Temperature (LEWICE) [oF]

Run 28 Top, Section B: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section B: Heater Temperature (Experimental) [oF] Section B: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 284
Figure 101: Heater C Temperature for Example Case 14

Figure 102: Heater D Temperature for Example Case 14

Run 28 Top, Section C: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section C: Heater Temperature (Experimental) [oF] Section C: Heater Temperature (LEWICE) [oF]

Run 28 Top, Section D: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section D: Heater Temperature (Experimental) [oF] Section D: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 285
Figure 103: Heater E Temperature for Example Case 14

Figure 104: Heater F Temperature for Example Case 14

Run 28 Top, Section E: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section E: Heater Temperature (Experimental) [oF] Section E: Heater Temperature (LEWICE) [oF]

Run 28 Top, Section F: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section F: Heater Temperature (Experimental) [oF] Section F: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 286
Figure 105: Heater G Temperature for Example Case 14

15.15 Case 15: Running Wet Example Using Detailed Thermal Module

Computation Time: Pentium III 550MHz, 24 min.37 s.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 3.4 MB

This example case uses the same NACA0012 de-icer model as used in the previous two cases.

In this example, however, the heaters are on for the duration of the simulation. The wattages used

were high enough in the experiment (Run 22F) to keep the de-icer region free of ice, but was not

high enough to evaporate all of the water. In this mode, the electrothermal unit operates similarly

to a hot air anti-icing system, albeit with specified heat fluxes instead of specified flow rates. In

this example, the laminar heat transfer assumption was used since the de-icer region was completely free of ice. 

The results show an excellent comparison to the experimental results using the laminar

assumption. A case using the turbulent heat transfer assumption was also ran (but not shown)

which again resulted in an underprediction of the temperatures. Similar results were obtained for

all of the anti-icing cases in this database, although many of the laminar cases showed an overpreRun 28 Top, Section G: Heater Temperature

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section G: Heater Temperature (Experimental) [oF] Section G: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 287
diction of temperature. This would seem to indicate that the actual heat transfer coefficient lies

between the two predicted values. A second explanation would be a physical effect not modeled

which would cause an increase of the convective heat transfer coefficient due to the evaporation

of water above and beyond that which is already modeled. In either case, this increased heat transfer coefficient can be reverse-engineered from the experimental data. However, since the database

contains only NACA0012 airfoils, most cases of which are at 0° AOA, it is unknown how applicable this experimentally adjusted coefficient would be outside this region. As a result, the

adjusted coefficient was left out of the LEWICE 2.2 model.

Another feature modeled in this example is the comparison of the 1D anti-icing model to the

2D anti-icing model. This comparison can be achieved for any anti-icing case using the IEVAP =

2 option in the de-icer input file. Many users have requested this option, as the 1D anti-icing

model is known to overpredict heater temperatures. This comparison is shown in Figure 116.

While the temperatures are higher in the 1D model, the difference is not as great as some have

suggested.

Table 113: Main Input File for Example Case 15

 Example 15 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 600

 IBOD = 1

 IFLO = 1

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 3

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 0.

NASA/CR—2002-211793 288
 VINF = 44.7

 LWC = 0.780

 TINF = 265.50

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 EPRT = 1

 MPRT = 1

 TPRT = 0

 IDBF = 1

 &END

 &RDATA

 &END

Table 114: De-ice Input File for Example Case 15

 l nx

 7 9 

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

NASA/CR—2002-211793 289
C ice

 21 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9244d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

ijde offset ipar

004 0.000 1

C Q TON TOFF TLAG ICFLAG

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag 

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 2.27d0 600.d0 0.d0 0.d0 0

C heater E

 3.40d0 600.d0 0.d0 0.d0 0

C heater C

 2.94d0 600.d0 0.d0 0.d0 0

C parting strip (heater A) does not turn off

NASA/CR—2002-211793 290
 4.82d0 600.d0 0.d0 0.d0 0

C heater B

 3.84d0 600.d0 0.d0 0.d0 0

C heater D

 2.95d0 600.d0 0.d0 0.d0 0

C heater F

 2.59d0 600.d0 0.d0 0.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

ibc1 ibc2 ibc3 ibc4

2 2 2 2 

 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5 

 h1 h2 h3 h4 

 3.d0 3.d2 0.d0 0.d0 

 qw1 qw2 qw3 qw4

 0.d0 0.d0 0.d0 0.d0 

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

i3d iqain ibleed iopt

 0 0 0 0 

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm 

 298.d0 2 0 

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

 1 2 2 1.d0 0.d0

NASA/CR—2002-211793 291
input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 3

iotype nptsd

 1 21

C section where layer where

 5 2 6 3

 5 2 1 1

 4 2 6 3

 4 2 1 1

 6 2 6 3

 6 2 1 1

 3 2 6 3

 3 2 1 1

 7 2 6 3

 7 2 1 1

 2 2 6 3

 2 2 1 1

 8 2 6 3

 8 2 1 1

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 2 2 4 1

 8 2 4 1

iotype nptsd

 2 30

C time layer where

C (sec)

 5 6 1

 10 6 1

NASA/CR—2002-211793 292
 15 6 1

 20 6 1

 25 6 1

 30 6 1

 35 6 1

 40 6 1

 45 6 1

 50 6 1

 55 6 1

 60 6 1

 65 6 1

 70 6 1

 75 6 1

 80 6 1

 85 6 1

 90 6 1

 95 6 1

 100 6 1

 105 6 1

 110 6 1

 115 6 1

 120 6 1

 125 6 1

 130 6 1

 135 6 1

 140 6 1

 145 6 1

 150 6 1

iotype nptsd

 3 30

C time section where

C (sec)

 5 5 2

 10 5 2

 15 5 2

 20 5 2

NASA/CR—2002-211793 293
 25 5 2

 30 5 2

 35 5 2

 40 5 2

 45 5 2

 50 5 2

 55 5 2

 60 5 2

 65 5 2

 70 5 2

 75 5 2

 80 5 2

 85 5 2

 90 5 2

 95 5 2

 100 5 2

 105 5 2

 110 5 2

 115 5 2

 120 5 2

 125 5 2

 130 5 2

 135 5 2

 140 5 2

 145 5 2

 150 5 2

NASA/CR—2002-211793 294
Figure 106: Heat Transfer Coefficient for Example Case 15

Figure 107: Pressure Coefficient for Example Case 15

Heat Transfer Coefficient

0

5 0

100

150

200

250

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

Heat Transfer Coefficient (W/m2K)

Pressure Coefficient

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

x/c

Pressure Coefficient

NASA/CR—2002-211793 295
Figure 108: Collection Efficiency for Example Case 15

Figure 109: Heater A Temperature for Example Case 15

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

s/c

Beta

Run 22F Top, Section A: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section A: Heater Temperature (Experimental) [oF] Section A: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 296
Figure 110: Heater B Temperature for Example Case 15

Figure 111: Heater C Temperature for Example Case 15

Run 22F Top, Section B: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section B: Heater Temperature (Experimental) [oF] Section B: Heater Temperature (LEWICE) [oF]

Run 22F Top, Section C: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section C: Heater Temperature (Experimental) [oF] Section C: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 297
Figure 112: Heater D Temperature for Example Case 15

Figure 113: Heater E Temperature for Example Case 15

Run 22F Top, Section D: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section D: Heater Temperature (Experimental) [oF] Section D: Heater Temperature (LEWICE) [oF]

Run 22F Top, Section E: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section E: Heater Temperature (Experimental) [oF] Section E: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 298
Figure 114: Heater F Temperature for Example Case 15

Figure 115: Heater G Temperature for Example Case 15

Run 22F Top, Section F: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section F: Heater Temperature (Experimental) [oF] Section F: Heater Temperature (LEWICE) [oF]

Run 22F Top, Section G: Heater Temperature

-10

0

1 0

2 0

3 0

4 0

5 0

6 0

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section G: Heater Temperature (Experimental) [oF] Section G: Heater Temperature (LEWICE) [oF]

NASA/CR—2002-211793 299
Figure 116: Comparison of One-Dimensional Assumption to 2D Result

15.16 Case 16: Evaporative Example Using Detailed Thermal Module

Computation Time: Pentium III 550 MHz, 34 min., 52 sec.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 2.6 MB

This example case uses the same NACA0012 de-icer model as used in the previous two cases.

In this example, however, the heaters are on for the duration of the simulation. The wattages used

were high enough in the experiment (Run 22E) to completely evaporate all of the water within the

de-icer region. In this mode, the electrothermal unit operates similarly to a hot air anti-icing system, albeit with specified heat fluxes instead of specified flow rates. In this example, the laminar

heat transfer assumption was used since the de-icer region was completely free of ice. 

The LEWICE results show an underprediction of the experimental results on the lower surface despite using the laminar assumption. The prediction on the upper surface and at the parting

strip are reasonable considering the fluctuation of the heater wattages in the experiment. Since the

heaters are offset slightly from the leading edge, the results will not be symmetric. Evaporative

results were also obtained for all of the anti-icing cases in this database. While many of these

1D vs. 2D Comparison

250

260

270

280

290

300

310

320

330

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

s/c

Temperature (K)

1D Result

2D Result

NASA/CR—2002-211793 300
cases show a similar result to this example, other cases showed an overprediction of temperature

by a similar amount as the underprediction indicated in this case. This discrepancy would seem to

indicate a physical effect which is not modeled that would account for this behavior. One possible

cause is a change in the convective heat transfer coefficient due to the evaporation of water

beyond that which is already modeled. The necessary heat transfer coefficient can be reverseengineered for each case from the experimental data. However, the resulting values do not follow

a known physical trend which could be placed in the model. Additionally, since the database contains only NACA0012 airfoils, most cases of which are at 0° AOA, it is unknown how applicable

this experimentally adjusted coefficient would be outside this region. As a result, the adjusted

coefficient was left out of the LEWICE 2.2 model.

Another feature modeled in this example is the comparison of the 1D anti-icing model to the

2D anti-icing model. This comparison can be achieved for any anti-icing case using the IEVAP =

2 option in the de-icer input file. Many users have requested this option, as the 1D anti-icing

model is known to overpredict heater temperatures. This comparison is shown in Figure 127.

While the temperatures are higher in the 1D model, the difference is not as great as some have

suggested, at least within the impingement limits.

Table 115: Main Input File for Example Case 16

 Example 16 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 600

 IBOD = 1

 IFLO = 1

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 3

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

NASA/CR—2002-211793 301
 CHORD = 0.9144

 AOA = 0.

 VINF = 44.7

 LWC = 0.780

 TINF = 265.50

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 EPRT = 1

 MPRT = 1

 TPRT = 0

 IDBF = 1

 &END

 &RDATA

 &END

Table 116: De-ice Input File for Example Case 16

 l nx

 7 9 

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

NASA/CR—2002-211793 302
 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 61 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9244d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

ijde offset ipar

004 0.000 1

C Q TON TOFF TLAG ICFLAG

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag 

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 12.41d0 600.d0 0.d0 0.d0 0

C heater E

 8.87d0 600.d0 0.d0 0.d0 0

C heater C

 19.26d0 600.d0 0.d0 0.d0 0

NASA/CR—2002-211793 303
C parting strip (heater A) does not turn off

 46.58d0 600.d0 0.d0 0.d0 0

C heater B

 31.95d0 600.d0 0.d0 0.d0 0

C heater D

 12.70d0 600.d0 0.d0 0.d0 0

C heater F

 11.27d0 600.d0 0.d0 0.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

ibc1 ibc2 ibc3 ibc4

2 2 2 2

 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5 

 h1 h2 h3 h4

 3.d0 3.d2 0.d0 0.d0

 qw1 qw2 qw3 qw4

 0.d0 0.d0 0.d0 0.d0

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

i3d iqain ibleed iopt

 0 0 0 0 

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm 

 328.d0 2 0

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

NASA/CR—2002-211793 304
 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 3

iotype nptsd

 1 21

C section where layer where

 5 2 6 3

 5 2 1 1

 4 2 6 3

 4 2 1 1

 6 2 6 3

 6 2 1 1

 3 2 6 3

 3 2 1 1

 7 2 6 3

 7 2 1 1

 2 2 6 3

 2 2 1 1

 8 2 6 3

 8 2 1 1

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 2 2 4 1

 8 2 4 1

iotype nptsd

 2 30

C time layer where

C (sec)

 5 6 1

NASA/CR—2002-211793 305
 10 6 1

 15 6 1

 20 6 1

 25 6 1

 30 6 1

 35 6 1

 40 6 1

 45 6 1

 50 6 1

 55 6 1

 60 6 1

 65 6 1

 70 6 1

 75 6 1

 80 6 1

 85 6 1

 90 6 1

 95 6 1

 100 6 1

 105 6 1

 110 6 1

 115 6 1

 120 6 1

 125 6 1

 130 6 1

 135 6 1

 140 6 1

 145 6 1

 150 6 1

iotype nptsd

 3 30

C time section where

C (sec)

 5 5 2

 10 5 2

 15 5 2

NASA/CR—2002-211793 306
 20 5 2

 25 5 2

 30 5 2

 35 5 2

 40 5 2

 45 5 2

 50 5 2

 55 5 2

 60 5 2

 65 5 2

 70 5 2

 75 5 2

 80 5 2

 85 5 2

 90 5 2

 95 5 2

 100 5 2

 105 5 2

 110 5 2

 115 5 2

 120 5 2

 125 5 2

 130 5 2

 135 5 2

 140 5 2

 145 5 2

 150 5 2

NASA/CR—2002-211793 307
Figure 117: Heat Transfer Coefficient for Example Case 16

Figure 118: Pressure Coefficient for Example Case 16

Heat Transfer Coefficient

0

5 0

100

150

200

250

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

Heat Transfer Coefficient (W/m2K)

Pressure Coefficient

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2

x/c

Pressure Coefficient

NASA/CR—2002-211793 308
Figure 119: Collection Efficiency for Example Case 16

Figure 120: Heater A Temperature for Example Case 16

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

s/c

Beta

Run 22E Top, Section A: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section A: Heater Temperature (Experimental) [oF] Section A: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

NASA/CR—2002-211793 309
Figure 121: Heater B Temperature for Example Case 16

Figure 122: Heater C Temperature for Example Case 16

Run 22E Top, Section B: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section B: Heater Temperature (Experimental) [oF] Section B: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

Run 22E Top, Section C: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

290

310

330

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section C: Heater Temperature (Experimental) [oF] Section C: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

NASA/CR—2002-211793 310
Figure 123: Heater D Temperature for Example Case 16

Figure 124: Heater E Temperature for Example Case 16

Run 22E Top, Section D: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section D: Heater Temperature (Experimental) [oF] Section D: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

Run 22E Top, Section E: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section E: Heater Temperature (Experimental) [oF] Section E: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

NASA/CR—2002-211793 311
Figure 125: Heater F Temperature for Example Case 16

Figure 126: Heater G Temperature for Example Case 16

Run 22E Top, Section F: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section F: Heater Temperature (Experimental) [oF] Section F: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

Run 22E Top, Section G: Heater Temperature

-10

10

30

50

70

90

110

130

150

170

190

210

230

250

270

0 50 100 150 200 250 300 350 400 450 500 550 600

Time (s)

Temperature (°F)

Section G: Heater Temperature (Experimental) [oF] Section G: Heater Temperature (LEWICE) [oF]

Scale enlarged to show all data points.

NASA/CR—2002-211793 312
Figure 127: Comparison of 2D Anti-Icing Results to 1D Anti-Icing Results

15.17 Case 17: Hot Air Evaporative Example Using Detailed Thermal Module

Computation Time: Pentium III 550 MHz, 35 min., 57 sec.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 2.6 MB

This example case uses a NACA0012 airfoil as the previous thermal cases, but in this example the electrothermal de-icer is replaced by a hot air model shown in Figure 128. This model was

designed by NASA Glenn specifically to validate the bleed air capabilities and does not resemble

existing bleed air capabilities. The plenum section of the bleed air occupies most of the inside

area of the airfoil within the impingement region. The air is then propelled to the inside surface

via small holes which provide jet flow perpendicular to the surface. The bleed air then flows

chordwise through a small channel to the exit. The test hardware has many more holes than a typical piccolo tube anti-icing system and the flow rates were well below choked flow. The advantage of this model was that it made measurement of the internal heat transfer coefficients easier.

Experimental data has been taken on the internal heat transfer coefficients for this model and are

shown in Figure 129. The peaks in this curve show the locations of the air jets. The bleed air flow

rate for this example was 0.11 kg/s at a supply temperature of 440°F. This data is then used as an

Surface Temperature Profile at 150 sec

0.00

50.00

100.00

150.00

200.00

250.00

300.00

350.00

400.00

-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20

s/c

Temperature (°F)

2D Result @ 150 sec

1D Result

Experiment

NASA/CR—2002-211793 313
input to LEWICE 2.2. This example case uses the same LEWICE input case as the previous

example, so that a direct comparison of the bleed air case could be made to the electrothermal

case. No data is currently available for comparison for this type of anti-icing case.

Note: The external heat transfer coefficients, pressure coefficients and collection efficiencies

are identical to the values in Example 16 and are not shown again in this example.

Note: All anti-icing cases are ran until TSTOP is reached or until steady-state convergence is

achieved. This example case stops prior to the TSTOP value because the latter criteria was

reached.

Figure 128: Jet Locations on Bleed Air Model

Jet Locations on Bleed Air Model

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

x(in)

y(in)

Arrows indicate 

et locations

Plenum containing supply air

NASA/CR—2002-211793 314
Figure 129: Internal Heat Transfer Coefficients for Bleed Air Case

Figure 130: Surface Temperature Distribution for Bleed Air Case

Internal Heat Transfer Coefficient

0

2 0

4 0

6 0

8 0

100

120

140

160

-0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1

s/c

Heat Transfer Coefficient (W/m2K)

Surface Temperature

260

265

270

275

280

285

290

295

300

305

310

315

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

s/c

Temperature (K)

NASA/CR—2002-211793 315
15.18 Case 18: Hot Air Example Interfaced with LEWICE3D

Computation Time: Pentium III 550 MHz, 56 min., 27 sec.; Pentium IV 1.7GHz, 8 min.41 s.

Disk Space: 15.6 MB

This example case uses five 2D cross sections of an engine inlet as the body geometries. The

first of these cross-sections is shown in Figure 131. This model was taken from a LEWICE3D

example case. The surface pressure coefficients, collection efficiencies, and external heat transfer

coefficients were supplied from a LEWICE3D output file at each 2D cross-section shown. The

computation time shown included only the time needed to run the LEWICE 2.2 cases and does

not include the computation time needed to generate the flow solution or the collection efficiencies. The internal heat fluxes for this model were selected such that residual ice would form. A

plot of these values are shown in Figure 132. These values were then used for each cross-section.

Since the inputs and results for each cross-section are very similar, only the inputs and results for

the first section are shown in this report. The CD containing LEWICE 2.2 also contains the complete input and output files for this case as well as the previous cases. Figure 133 shows surface

temperature predictions for the first section. The temperatures and the resultant residual ice can

then be loaded into the utility program ANTICON2 for the generation of a simulated 3D residual

ice shape. The simulated 3D ice shape is shown in Figure 134. The resolution of the ice shape in

this figure can be improved by the addition of more streamlines to the model or by interpolation

from the existing results. Since LEWICE 2.2 also contains a prediction of rivulet formation in its

model, it should be possible to display that information as well. That process would require a

much more sophisticated utility program than ANTICON2 and has not been developed yet. 

Note: The computation time and disk space listed above includes only the resources needed to

run the five thermal anti-icing cases. It does not include the resources needed to perform the 3D

flow solution or collection efficiency analysis.

Note: If the bleed air is shut off, the user should get similar results to using the LEWICE3D

program directly. A detailed discussion of the procedure and problems with this type of analysis

follow this example case.

NASA/CR—2002-211793 316
Note: Although pressure coefficients, heat transfer coefficients and collection efficiencies are

inputs in this example, they are plotted and not tabulated like the other input files.

Table 117: Main Input File for Example Case 18-1

 Example 18 Test Case 

 &LEW20

 ITIMFL = 0

 TSTOP = 600

 IBOD = 1

 IFLO = 1

 DSMN = 4.0D-4

 NPL = 24

 IDEICE = 3

 &END

 &DIST

 FLWC = 1.0

 DPD = 20.

 &END

 &ICE1

 CHORD = 0.9144

 AOA = 0.

 VINF = 44.7

 LWC = 0.780

 TINF = 265.50

 PINF = 100000.00

 RH = 100.0

 &END

 &LPRNT

 FPRT = 1

 HPRT = 1

 BPRT = 1

 EPRT = 1

 MPRT = 1

 TPRT = 0

 IDBF = 1

 &END

NASA/CR—2002-211793 317
 &RDATA

 &END

Table 118: De-ice Input File for Example Case 18-1

 l nx

 7 9

 # of length conductivity diffusivity anisotropy slope (b) of

 nodes (m) (W/m/K) (m^2/s) factor temp. eqn. 

C substrate

 15 3.430d-3 0.120d0 1.652d-7 1.d0 0.d0

C insulation

 08 8.900d-4 0.294d0 1.045d-7 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C heater

 07 1.300d-5 41.000d0 1.194d-5 1.d0 0.d0

C insulation

 18 2.800d-4 0.256d0 1.473d-7 1.d0 0.d0

C abrasion shield

 08 2.030d-4 16.270d0 4.035d-6 1.d0 0.d0

C ice

 61 2.540d-3 2.232d0 1.151d-6 1.d0 0.d0

 # of length cond. diff. anis. slope of add. layer 

 nodes (m) (W/m/K) (m^2/s) temp. eqn. thick. number 

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

C heater G

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater E

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater C

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C parting strip - heater A

 36 1.905d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater B

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

NASA/CR—2002-211793 318
C heater D

 21 2.540d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C heater F

 14 3.175d-2 41.000d0 1.194d-5 1.d0 0.d0 0.d0 3

C gap (no heat input)

 10 0.9144d0 0.256d0 1.637d-7 1.d0 0.d0 0.d0 3

ijde offset ipar

004 0.000 1

C Q TON TOFF TLAG ICFLAG

 heater density time on time off lag time temp cntrl.

 (kWatts/m^2) (sec) (sec) (sec) flag 

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0

C heater G

 12.41d0 600.d0 0.d0 0.d0 0

C heater E

 8.87d0 600.d0 0.d0 0.d0 0

C heater C

 19.26d0 600.d0 0.d0 0.d0 0

C parting strip (heater A) does not turn off

 46.58d0 600.d0 0.d0 0.d0 0

C heater B

 31.95d0 600.d0 0.d0 0.d0 0

C heater D

 12.70d0 600.d0 0.d0 0.d0 0

C heater F

 11.27d0 600.d0 0.d0 0.d0 0

C gap (no heat input)

 0.0d0 0.d0 0.d0 0.d0 0 

ibc1 ibc2 ibc3 ibc4

2 2 2 2 

 tg1 tg2 tg3 tg4

 265.5 265.5 265.5 265.5 

 h1 h2 h3 h4 

 3.d0 3.d2 0.d0 0.d0 

 qw1 qw2 qw3 qw4

NASA/CR—2002-211793 319
 0.d0 0.d0 0.d0 0.d0 

 tairh airmd airup xairmd

 5.d2 0.1d0 0.5d0 0.d0

i3d iqain ibleed iopt

 0 0 0 0 

icond ibound init ish istd igde

 1 3 2 1 1 1

 tsurf ievap itherm 

 328.d0 2 0 

sta rpm irot

10.d0 0.d0 1 

dtaui nisp dtaum nmsp dtauf jcount

1.d-1 1000 1.d-1 1000 1.d-1 10

tspray tafter

 0.d0 0.d0

iscol jscol kscol sslope szero

input parameters for reading in hot air HTC info

 2 3 3 1.d0 0.d0

input parameters for reading in hot air q_wall info

 1 2 2 1.d0 0.d0

input parameters for reading in 3D streamline info

 1 2 2 1.d0 0.d0

nprt nprf

 0 0

ntype

 3

iotype nptsd

 1 21

C section where layer where

 5 2 6 3

 5 2 1 1

 4 2 6 3

 4 2 1 1

 6 2 6 3

 6 2 1 1

 3 2 6 3

NASA/CR—2002-211793 320
 3 2 1 1

 7 2 6 3

 7 2 1 1

 2 2 6 3

 2 2 1 1

 8 2 6 3

 8 2 1 1

 5 2 4 1

 4 2 4 1

 6 2 4 1

 3 2 4 1

 7 2 4 1

 2 2 4 1

 8 2 4 1

iotype nptsd

 2 30

C time layer where

C (sec)

 5 6 1

 10 6 1

 15 6 1

 20 6 1

 25 6 1

 30 6 1

 35 6 1

 40 6 1

 45 6 1

 50 6 1

 55 6 1

 60 6 1

 65 6 1

 70 6 1

 75 6 1

 80 6 1

 85 6 1

 90 6 1

NASA/CR—2002-211793 321
 95 6 1

 100 6 1

 105 6 1

 110 6 1

 115 6 1

 120 6 1

 125 6 1

 130 6 1

 135 6 1

 140 6 1

 145 6 1

 150 6 1

iotype nptsd

 3 30

C time section where

C (sec)

 5 5 2

 10 5 2

 15 5 2

 20 5 2

 25 5 2

 30 5 2

 35 5 2

 40 5 2

 45 5 2

 50 5 2

 55 5 2

 60 5 2

 65 5 2

 70 5 2

 75 5 2

 80 5 2

 85 5 2

 90 5 2

 95 5 2

 100 5 2

NASA/CR—2002-211793 322
 105 5 2

 110 5 2

 115 5 2

 120 5 2

 125 5 2

 130 5 2

 135 5 2

 140 5 2

 145 5 2

 150 5 2

Figure 131: Engine Inlet Cross-Section for Example Case 18-1

-4

-2

0

2

4

-4 -2 0 2 4 6 8 10

y(in)

x(in)

NASA/CR—2002-211793 323
Figure 132: Internal Heat Transfer Coefficient for Example Case 18-1

Figure 133: Surface Temperature Distribution for Example Case 18-1

Internal Heat Transfer Coefficient

0

100

200

300

400

500

600

700

800

900

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

s/c

Heat Transfer Coefficient (W/m2K)

Surface Temperature Distribution at t = 150 sec.

0

5

1 0

1 5

2 0

2 5

3 0

3 5

4 0

4 5

5 0

-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4

s/c

Temperature (°F)

NASA/CR—2002-211793 324
Figure 134: Ice Shape for Example Case 18-1

Figure 135: Ice Thickness for Example Case 18-1

Ice Shape

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

-0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

x/c

y/c

Ice Thickness

-0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

s/c

Thickness/c

thickness/c

NASA/CR—2002-211793 325
Figure 136: Heat Transfer Coefficient for Example Case 18-1

Figure 137: Pressure Coefficients for Example Case 18-1

External Heat Transfer Coefficient

0

100

200

300

400

500

600

700

800

900

-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0

s/c

Heat Transfer Coefficient (W/m2 K)

Pressure Coefficient

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

-1.5 -1 -0.5 0 0.5 1 1.5

x/c

Pressure Coefficient

NASA/CR—2002-211793 326
Figure 138: Collection Efficiency for Example Case 18-1

Collection Efficiency

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

-0.1 -0.05 0 0.05 0.1 0.15 0.2

x/c

Beta

NASA/CR—2002-211793 327
.

Figure 139: 3D Engine Inlet (Half-model) Surface Grid (Ice is Shaded)

15.18.1 Procedure for 2.5D Anti-Icing and De-Icing Analysis

This procedure will describe, in general, the process for obtaining a pseudo-3D anti-icing

analysis using NASA software. The emphasis in this document is on the details of the anti-icing

interface to the 3D software already used for icing analysis. These steps will not describe how to

run a particular software. The user is referred to the User Manuals for the respective programs for

details. 

NASA/CR—2002-211793 328
Step 1: Create a 3D surface model of your geometry. This is often performed by commercial

software. Depending upon the requirements of your flow solver, you may need to use a CAD

model, equations or points for this geometry

Step 2: Create a grid in 3D around the model. If using a potential flow solver, it may only be

necessary to construct a “trajectory grid” for the particle trajectory program LEWI3DGR. Trajectory grids can be generated using programs supplied by NASA, while grids for Euler or NaviérStokes are often generated using commercial software such as GRIDGEN.

Step 3: Create a 3D flow solution for the model. This flow solution can be potential flow,

Euler, or Naviér-Stokes depending upon your needs. The flow solvers can be commercial software packages such as VSAERO or FLUENT.

Step 4: Create a 3D collection efficiency distribution using LEWI3DGR. This may require

using supplemental utility programs supplied by NASA to create “trajectory grids” or otherwise

translate data from the flow module for use with NASA’s 3D trajectory modules.

Step 5 (optional): Calculate the wall heat flux or convective heat transfer coefficient on the

surface of the model. This can either be calculated directly from a Naviér-Stokes solution from

(21)

(22)

or from using a 3D boundary layer program to get the convective heat transfer coefficient “h”

or by using a 2D boundary layer program along streamline “cuts” as described in Step 6. This step

is optional, as LEWICE 2.2 can generate “h” on the streamline “cuts”.

Step 6: Run the conversion program ANTICON to create input files compatible with

LEWICE 2.2. This requires the files “FORT.2” and “FORT.26” from the LEWI3DGR solution. 

qw k η∂

∂T

 

 

η 0=

–=

h

k η∂

∂T

 

 

η 0=

–

T η 0= T ∞ ( ) – = --------------------------------

NASA/CR—2002-211793 329
Note: For inlets, a customized version of this program was required to obtain the 2D “cuts”

normal to the local geometry, not simply taking the ‘X’ and ‘Z’ coordinates as is normally done

by that software. The customized utility ANTICON is on the distribution disk. This program creates the files geom.xyd, FLOW.DAT, BETA.DAT, HTC.DAT, and STREAM.DAT.

STREAM.DAT contains the spanwise distance between streamlines at each chord location.

Step 7: Using a text editor, separate the ANTICON output into several files, one for each 2D

“cut” and file type. For example, if there are five 2D “cuts” generated, the user will need to generate five geometry files, five flow solution files and so on. Each of these files must contain only the

output data. Any text headers must be removed prior to running LEWICE 2.2. The general format

for each file is as follows:

(number of points)

wrap distance1(s1) data value1

wrap distance2(s2) data value2

wrap distance3(s3) data vaulle3

...

Step 8 (optional): Create a CFD model of the internal hot air bleed flow using a procedure

similar to Steps 1-3 which are used for generating the external flow field. For each of the 2D

“cuts” defined in Step 6, generate a file containing either the wall heat flux or wall heat transfer

coefficient calculated by the internal flow software. These are defined by Equations 21 and 22

earlier. This step is optional, as the user may be modelling an electrothermal system or using the

“optimum” heat flux flag in LEWICE 2.2.

Step 9: Create a 2D anti-icing model for each of the “cuts” generated in the previous step.

Since the same system in each section is probably being modeled, the input files may be identical,

but they are not required to be so. 

Step 10: Run LEWICE 2.2 for each of the 2D “cuts” which have been created. Create directories to store each of the cases, as the output files generated by LEWICE 2.2 will be the same for

each case. Set the flags in the LEWICE 2.2 input file to bypass calculation of the flow field (ICP

= 1), collection efficiency (IBETA = 1) and heat transfer coefficient (both external [IHTC = 1]

NASA/CR—2002-211793 330
and internal [IBLEED = 1] if desired). Move the output for each run into the directory created for

it prior to the next case.

Step 11: Concatenate the output files “DYICE.DAT” and “TEMP.DAT” created from each of

the streamline “cuts”. These files must also be called “DYICE.DAT” and “TEMP.DAT”. Run the

conversion program ANTICON2 which will combine the outputs from LEWICE 2.2 and

LEWI3DGR and create a PLOT3D output file for the surface geometry, the iced geometry, and

the temperature distribution on the surface. This requires the “FORT.2” and “FORT.26” output

files used in Step 6.

Step 12: Plot the output files PLOT3D.XYZ and PLOT3D.Q in PLOT3D or a program which

can read those files. Since PLOT3D was designed to visualize a flow solution, not a temperature

solution, temperature is output from ANTICON2 in the “density” field as density and temperature

are both scalar variables. The other PLOT3D information in PLOT3D.Q contains garbage values.

The output files are read in PLOT3D using the string “read/mg/blank/form/xyz=PLOT3D.XYZ/

q=PLOT3D.Q”. An advanced user/developer could also write a small utility program to convert

these output files into a different format such as the format used by TECPLOT.

NASA/CR—2002-211793 331
Chapter 16: User Tips and Notes

Many of the tips and notes provided in this section are listed in this manual in the description

of the input and output files. They are summarized here for convenient reference by the user. Each

paragraph may contain a user note which is not directly related to other notes in that section. This

section differs from Chapter 6 which list user notes considered most important for accurate use of

the software.

16.1 Old Input Files

Input files from previous versions of LEWICE will not work ‘as is’ with this version. Please

follow the examples provided or see Chapter 5 for a summary of the differences.

16.2 Input File Errors

An error reading the input file indicates that the file name input does not exist, or does not

exist in this directory. Common problems: 

1) The file name was not typed correctly (remember to include the extension - use “case1.inp”

not simply “case1”); 

2) The input file is in a different directory than the program. The input file can be in a different directory than the program, but in order for LEWICE to recognize the input file the path must

be specified. For example, use “inputs\naca0012\case1.inp” instead of simply “case1.inp” to read

the input file “case1.inp” in the directory “inputs” and subdirectory “naca0012”. Note: The above

example used the DOS directory convention of backward slashes “\” to list subdirectories. IRIX

and many other unix systems use forward slashes “/” instead.

PC Note: To get to the root directory, first type a backward slash “\”, then the path and file

name. For example, the command “\lewice\inputs\naca0012\case1.inp” can also be used to read

the file “case1.inp” in the directory “C:\lewice\inputs\naca0012”.

Unix Note: It is common practice in unix to place all programs in a predefined directory such

as /usr/bin so that everyone using that system can run the program. The path for specifying the

input file in this case is to provide the path from the directory the user is in. For example, if the

NASA/CR—2002-211793 332
user is in their home directory and the input file is in the home directory, no path should be provided. If the user is in their home directory and the input files are in directory ../inputs/naca0012,

then the proper path to input is “inputs/naca0012/case1.inp”. If the user is in directory ../inputs/

naca0012 and the input file is in this directory, then no path needs to be provided in this case

either. P.S.: This sequence is correct based on the IRIX 6.2 operating system. Behavior for other

unix operating systems are expected to be similar, but potentially could be different.

16.3 Porting ASCII Files

The LEWICE input files are ASCII text. PCs, Macs and Unix workstations all have different

formats for treating line breaks with ASCII files which may cause problems when transferring

input files to different platforms. Specifically, when PC ASCII files are moved to an SGI with

IRIX 6.2, there is an extraneous character (^M) at the end of each line. This character must be

removed from each line to use the file on the SGI.

The conversion programs provided were designed to be used to convert files in the PLOT3D

format from text to binary format and from binary to text format. They are not general purpose

conversion utilities.

16.4 PC Application

When run from Windows, a console shell opens for interactive input and output. This console

shell disappears when the run is finished. For this reason, it is highly recommended that the user

run the PC executable from a DOS Shell instead of from the console shell.

Most of the output data is provided in columns of text, with a text header identifying the variable. This file format can be easily imported into any spreadsheet package for plotting. The program takes about 650 KB of hard disk space for the executable, and several megabytes for output

files. The second example case shows the program’s potential to produce large output files. The

output files for this case takes only 3.3 MB of disk space. However, several of the larger output

files were not printed in this example and output was further reduced using the print flags in the

main input file. If this same case were to be run with all of the outputs activated, the output for

this case would occupy over 45 MB of disk space.

NASA/CR—2002-211793 333
All input and output file names have been presented in uppercase to make them stand out in

the manual. The actual input and output files on the CD-ROM have lower case filenames and all

output files from LEWICE 2.2 have lowercase filenames.

16.5 Listing Variables in a Namelist

Variables in namelist format are input on separate lines. Each line contains a unique variable

which is listed in that namelist. The line should contain the variable name followed by an equal

sign (=) followed by the value to be assigned to that variable. The value can be in integer, real or

exponential format regardless of the definition used within the program. For example, an integer

variable does not have to be input as an integer. The value will be truncated for use in the program. In addition, the user is not required to list every variable in the namelist. If a variable is not

listed in the input file, the program will use the default value. Default values are listed in this section for each variable. Examples of valid inputs are provided for each namelist section. Common

causes for errors occur when the user mistypes the variable name or when the user enters a variable from a previous LEWICE version which is no longer input into that namelist.

At a minimum, the user must add the following two lines to the end of the main input file for

existing LEWICE 2.0 input files for them to work with LEWICE 2.2:

&RDATA

&END

See Section 8.7 for details of the new namelist.

16.6 Multiple Bodies / Multi-Element Airfoils

LEWICE 2.2 can run multiple body simulations including multi-element airfoils. A report of

its capabilities in this region shows very encouraging results7. However, much of the development effort for version 2.2 has centered on validating the existing features of the program. Even

though the results to date have been encouraging, there is not enough data available to consider

LEWICE 2.2 validated for multi-body flows.

NASA/CR—2002-211793 334
16.7 Grid-Based Flow Solutions

Some cases have been made using a grid solution as input to verify that the routines function

as designed. This option has seen very limited testing and has not been validated against the

database of experimental ice shapes. This procedure may still contain errors and is not recommended unless the user is willing to customize the software for their use. Since only one time step

can be used with this option, the use of this feature is limited to collection efficiency and heat

transfer coefficient prediction. Even for these uses, the user should perform grid resolution studies

in the impingement region before drawing any conclusions.

There is no error checking of the grid and solution file. The user should independently verify that the grid and solution files are correct for the case being run. In particular, the angle of

attack and velocity should match the values input in the main input data file. The program will

also not run with a grid solution unless the grid surface geometry is very similar to the body

geometry read in from the geometry input file(s). Similarly, the variables in the user’s PLOT3D

file may not be the variables the program expects. Refer to Section 10.5 for the correct format.

16.8 Chord Length

CHORD is the distance from the leading edge to the trailing edge in meters. For a cylinder,

this represents the cylinder diameter. For airfoils, it is the standard chord length. For a multi-body

simulation, CHORD represents the reference length used to normalize the coordinates input. A

typical value used for multi-element airfoils is the length of the airfoil in the stowed configuration.

16.9 Multiple Stagnation Points

A main cause of error in LEWICE occurs when multiple stagnation points are predicted by the

flow solution. The criteria used by the program is to select the value closest to the stagnation point

from the previous time step. If it finds more than one stagnation point on the first time step, the

point closest to the leading edge is used. If this is not satisfactory, the user should lower the

DSMN input variable or increase the number of points in the input data so as to produce a single

stagnation point value.

NASA/CR—2002-211793 335
16.10 Flow Module Limitation

For glaze ice shapes at high subsonic velocities, it is possible for the software to compute a

pressure coefficient which would lead to a negative local static pressure. If this occurs, the program will compute the static pressure needed for a local Mach number of 0.8, hence ‘rounding

off’ the solution. The subsequent ice shape may not be an accurate representation. If a validated

Euler/Naviér-Stokes program capable of handling transonic conditions becomes available, the

user is encouraged to use it for this case. In addition, no experimental data is available for Mach

Numbers above M = 0.45. Therefore the software has not been validated against experimental

data above this value. Problems may exist with the solution due to the limitations of potential

flow.

Potential flow cannot model stall or post-stall behavior. The user should also note that in the

validation test procedure, the angle of attack input into the software was sometimes different from

the actual angle of attack value. This difference was made to compensate for the difference in predicted lift using a potential flow module and an estimate of the actual lift on the clean airfoil.

16.11 Ice Density

Ice density in LEWICE is fixed at a value of 917 kg/m3. There exists two correlations within

the source code which are currently inactive due to undesirable numerical side effects. Developers

who wish to activate these correlations can do so by changing an internal flag in the source code.

16.12 Icing Limit

The “LIMIT.DAT” output file was not generated in previous versions. The value for the final

time step should agree with output from the utility program THICK although roundoff errors may

cause the utility program to report an erroneous limit.

NASA/CR—2002-211793 336
Chapter 17: Procedure for Acquiring LEWICE or other NASA Icing Software

Funding for LEWICE development comes from the NASA budget which is provided for by

US tax dollars. LEWICE is therefore provided free of charge to US corporations, universities or

individuals. A request letter such as that provided in the next section should be sent to the Icing

Branch Chief. The letter may be sent by regular mail, electronic mail or fax. A current mailing

address is provided below.

17.1 Current Address for Icing Software Requests

Mr. Thomas H. Bond

Branch Chief, Icing Branch

NASA Glenn Research Center

21000 Brookpark Rd.

MS 11-2

Cleveland OH 44135

E-mail: Thomas.H.Bond@grc.nasa.gov

Phone: (216) 433-3900

FAX: (216) 977-1269

NASA/CR—2002-211793 337
Chapter 18: Sample Software Request Letter

Dear Sir,

Our company/university would like to request the ice accretion software LEWICE 2.2 for use

in design and/or certification of our products for flight in icing conditions. We are a US corporation with offices in ___________ (place). Our immediate need is for the certification of ____ (fill

in blank). The software will be run primarily on _________ (name the system) and it is preferred

that the software be distributed on __________ (preferred media). Thank you. 

Sincerely, 

Note: Software requests are normally filled 2-3 weeks from the request date on average.

Note: As of March 1, 1999, the NASA Lewis Research Center has been renamed to the John

H. Glenn Research Center at Lewis Field. The address listed above reflects this change.

Note: The software developers are involved only in technical support of the programs and are

not directly involved in the distribution process. Questions concerning distribution should be sent

to the branch office.

NASA/CR—2002-211793 338
Chapter 19: Technical Support

Technical support is available from 9 AM to 5 PM Eastern time from the software developer(s). Questions on running the software or how to simulate difficult problems with LEWICE

should be sent to:

William Wright

NASA Glenn Research Center

21000 Brookpark Rd.

MS 11-2

Cleveland OH 44135

E-mail: William.B.Wright@grc.nasa.gov

Phone: (216) 433-2161

FAX: (216) 977-1269

E-mail and fax are the preferred methods of communication. The user should provide a

description of the problem and error messages obtained and also provide an input file (including

geometry) so the error can be reproduced. If correspondence is confidential, please mark it as

such. Software improvements including bug fixes which result from this correspondence will be

incorporated into future versions which can be released by NASA.

NASA/CR—2002-211793 339
References

1. Wright, W. B., “User Manual for the NASA Glenn Ice Accretion Code LEWICE Version

2.0,” NASA CR 209409, Sept. 1999.

2. Miller, D, et. al., “Validation of NASA Thermal Ice Protection Computer Codes Part 1 -

Program Overview,” NASA TM 107397, Jan. 1997.

3. Wright, W. B. and Rutkowski, A., “Validation Results for LEWICE 2.0,” NASA CR

208690, Nov. 1998.

4. Hess, J. L. and Smith, A. M. O., “Calculation of Potential Flow About Arbitrary Bodies,”

Progress in Aeronautical Sciences, 8:1-138, (D. Kuchemann, editor), Pergamon Press, Elmsford,

New York, 1967.

5. Frost, W., Chang, H., Shieh, C. and K. Kimble, “Two Dimensional Particle Trajectory Computer Program,” Interim Report for Contract NAS3-224488, 1982.

6. Messinger, B. L., “Equilibrium Temperature of an Unheated Icing Surface as a Function of

Air Speed,” J. Aeronaut. Sci., vol. 20, no. 1, Jan. 1953, pp. 29-42.

7. Masiulaniec, K. C. and Wright, W. B., “User’s Manual for the NASA Lewis Ice Accretion/

Heat Transfer Prediction Code with Electrothermal Deicer Input”, NASA CR 4530, 1994.

8. Al-Khalil, K. M., “Numerical Simulation of an Aircraft Anti-Icing System Incorporating a

Rivulet Model for the Runback Water,” PhD Dissertation, University of Toledo, Toledo, Ohio,

Jan. 1991.

NASA/CR—2002-211793 340
9. Wright, W.B., “Users Manual for the Improved NASA Lewis Ice Accretion Code LEWICE

1.6,” NASA CR 198355, June 1995.

10. Wright, W.B., “Capabilities of LEWICE 1.6 and Comparison with Experimental Data,”

AHS International Icing Symposium, Montreal, Canada, pp. 347-61, Sept. 1995.

11. Wright, W.B., and Potapczuk, M. G., “Computational Simulation of Large Droplet Icing,”

Proceedings of the FAA International Conference on Aircraft Inflight Icing, pp. 545-55, Aug.

1996.

12. Walatka, P. P., et. al., “PLOT3D User Manual,” NASA TM 101067, Mar. 1990.

13. Papadakis, M., et. al., “Progress in Measuring Water Impingement Characteristics on Aircraft Surfaces,” AIAA98-0488, Jan. 1998.

14. Chawner, J. and Steinbrenner, J., “Automatic Grid Generation Using GRIDGEN,” NASA

CP-3291, Surface Modeling, Grid Generation, and Related Issues in CFD Solutions, May 1995. 

15. NPARC Version 3.0 User’s Manual, NPARC Alliance, Sept. 1996

NASA/CR—2002-211793 341
 Appendix A 

 Functional Requirements for LEWICE version 2.2

This section has been included by the request of several users. It will define the equations and

other functional requirements of LEWICE 2.2 so that users can increase their understanding of the

underlying physics being solved. Note that the equations are simply defined, not derived. Users

who wish to understand how these equations are arrived at are directed to the references to this

report. The sections are organized by module, but the modules themselves are not presented in

any particular order.

NASA/CR—2002-211793 342
1 Geometry Smoothing

1.1 Description/Purpose

1.1.1 The purpose of geometry smoothing is to smooth the body 

geometry(s) supplied according to the requirements listed below.

1.2 Smoothing Requirements

1.2.1 The program shall modify the body geometry(s) such 

that the angle between any two adjoining segments is no greater 

than 0.001 degrees.

1.2.2 The program shall modify the body geometry(s) such 

that the size of any segment is no greater than or less 

than 5% of the size of an adjoining segment.

1.2.3 The program shall modify the body geometry(s) such 

that the minimum size of any segment is not less than the size 

criteria input by the user. 

1.2.4 The maximum value which the user may input for the minimum

segment size is 0.0008 times the chord length. 

1.2.5 The program shall modify the body geometry(s) such 

that the maximum size of any segment is not greater than two times 

the minimum segment size input by the user. 

1.2.6 Each 5% section (measured by wrap distance) of the body 

geometry(s) shall not have an overall curvature which is greater 

than the curvature of a circle whose radius is 0.2 times the geometry 

chord length. 

1.2.7 The 5% sections of the body geometry(s) given in 1.2.6 shall 

overlap each other by 1% of the total surface wrap distance.

1.2.8 The modified body geometry(s) shall not differ from the original 

body geometry(s) by more than 5% based on the quantified ice 

measurement scale defined in NASA TM 208690.

1.2.9 The program shall transfer the variables for interim ice thickness 

and wrap distance to the modified body geometry(s).

1.2.10 The program shall store the modified values for body geometry(s), 

wrap distance, interim ice thickness and number of points

into new variables and shall not overwrite the original values.

NASA/CR—2002-211793 343
2 Point Generation

2.1 Description/Purpose

2.1.1 The purpose of the point generation function is to calculate surface 

points and the surface wrap distance of those points for a given 

body geometry(s) according to the requirements listed below.

2.2 Point Generation Requirements

2.2.1 The program shall modify the body geometry(s) such that the

 angle between any two adjoining segments is no greater than

 0.001 degrees.

2.2.2 The program shall modify the body geometry(s) such that the 

size of any segment is no greater than 5% greater or less than a 

neighboring segment.

2.2.3 The program shall modify the body geometry(s) such that the 

minimum size of any segment is not less than the criteria input 

by the user. 

2.2.4 The maximum value which the user may input for the minimum

segment size is 0.0008 times the geometry chord length. 

2.2.5 The program shall modify the body geometry(s) such that the 

maximum size of any segment is not greater than two times 

the minimum segment size input by the user. 

2.2.6 The modified body geometry(s) for this step shall not differ from 

the original body geometry(s) by more than 1% based on the 

quantified ice measurement scale defined in NASA TM 208690.

2.2.7 The program shall transfer the variables for interim ice thickness 

and surface wrap distance to the modified body geometry(s).

NASA/CR—2002-211793 344
3 Ice Addition

3.1 Description/Purpose

3.1.1 The purpose of ice addition is to add a previously calculated ice 

thickness distribution to the existing body geometry(s) according to 

the requirements listed below.

3.2 Ice Addition Requirements

3.2.1 The program shall add the ice thickness such that the area of ice 

added to each segment is within 0.1% of the calculated amount. 

3.2.2 The program shall add the ice thickness such that the total area of 

ice added to the surface is within 0.1% of the calculated amount. 

* 3.2.3 The program shall add the ice thickness in a direction methodology 

which is chosen by the user.

* 3.2.4 The program shall allow the user to choose from the following three

direction methodologies:

3.2.4.1 Normal to each segment

3.2.4.2 Normal to the flow direction

3.2.4.3 Normal to the trajectory impact direction

3.2.5 During the ice addition, the program shall not use those surface 

points for which no ice is to be added.

3.2.6 During the ice addition, the program shall add and remove surface 

points as necessary in accordance with the point generation 

requirements listed above.

3.2.7 The program shall output to file(s) the body geometry(s) after the 

new body geometry(s) have been calculated.

* Not active in LEWICE 2.2 Beta Release

NASA/CR—2002-211793 345
4 Trajectory Integration

4.1 Description/Purpose

4.1.1 The purpose of trajectory integration is to numerically integrate the 

equations of motion of a water particle through a surrounding 

airstream.

4.2 Trajectory Integration Requirements

4.2.1 The program shall integrate the following equations:

4.2.1.1

4.2.1.2

4.2.2 The terms in these equations have the following definitions:

4.2.2.1

4.2.2.2

4.2.2.3

4.2.2.4

4.2.2.5

 for cd ≤ 100

4.2.2.6

 for cd ≥ 100

4.2.2.7

4.2.2.8

mx p

 ̇ ̇ Dcos– γ Lsin– γ mgsin+= α

my p

 ̇ ̇ Dsin– γ Lcosγ mgcos–+= α

γ

y ̇p Vy –

x ̇p Vx – -----------------atan=

D cd

ρaV2

2 ------------Ap =

L cl

ρaV2

2 ------------Ap =

V x ̇p Vx ( ) – 2y ̇p Vy ( ) – 2+=

cd

24

Re

------ 0.4 6

1 + Re = + + -------------------

cd

24

Re

------ 0.3 6

1 + Re = + + -------------------

Re

V dp

νa

----------=

NASA/CR—2002-211793 346
4.2.2.9

m = particle mass (kg)

g = gravitational constant = 9.8 m/s2

xp = x-location of water particle (m)

yp = y-location of water particle (m)

 = first derivative of x-location of water particle with respect to 

time (x-component of particle velocity) (m/s)

 = first derivative of y-location of water particle with respect to 

time (y-component of particle velocity) (m/s)

 = second derivative of x-location of water particle with respect 

to time (x-component of particle acceleration) (m/s2)

 = second derivative of y-location of water particle with respect 

to time (y-component of particle acceleration) (m/s2)

Vx = x-component of local air velocity at particle location (m/s)

Vy = y-component of local air velocity at particle location (m/s)

ρa = local air density at particle location (kg/m3)

Ap = cross-sectional area of particle (m2)

dp = particle diameter (m)

cl = coefficient of lift = 0

cd = coefficient of drag (dimensionless)

Re = Reynolds number (dimensionless)

α = angle of attack (degrees)

 = drag force (kg*m/s2)

 = lifting force (kg*m/s2)

γ = angle difference between particle velocity vector and 

air flow velocity vector (degrees)

ν = kinematic viscosity of air m2/s

π = 3.1415926536...

4.2.3 The integration shall start at a location specified in Section 8 

and with an initial velocity as specified in Section 8

4.2.4 The integration shall end when one of the following two conditions 

have been met:

4.2.4.1 

The particle path intersects one of the body geometry(s).

4.2.4.2 

Ap

πdp

2

4 = ---------

x p

 ̇

y p

 ̇

x p

 ̇ ̇

y ̇ ̇p

D

L

NASA/CR—2002-211793 347
The particle has travelled past the end of all of the body 

geometry(s) as measured in the x-direction.

* 4.2.5 The program shall model the breakup of water drops as defined in 

Section 5.

* 4.2.6 The program shall determine if droplets whose path intersects the 

body geometry(s) will fully impinge, partially impinge or bounce in 

accordance with Section 6.

4.2.7 The program shall output to file(s) the starting and ending location 

of the trajectory and the end condition met by Section 4.2.4.

4.2.8 The program shall output to file(s) the entire path of each trajectory 

or each trajectory whose path intersects the body geometry(s) if 

desired by the user. 

* Not implemented in LEWICE 2.2 Beta Release

NASA/CR—2002-211793 348
5 Droplet Breakup *

5.1 Description/Purpose

5.1.1 Droplet breakup occurs when fluid particles are moving at high 

velocities. The droplet will first deform from a spherical shape to an 

ellipsoid. This is modeled in the coefficient of drag in Sections 

4.2.2.5 and 4.2.2.6. After this deformation, the droplet 

continues to deform until it breaks apart. The purpose of this 

section is to describe the requirements for modeling the physical 

processes of droplet breakup.

5.2 5.2 Droplet Breakup Requirements

5.2.1 The program shall determine if droplet breakup occurs after each 

step of the droplet trajectory integration as described in 

Section 4.

5.2.2 The program shall calculate the Weber number as defined by

where σ = surface tension between air and water (kg/s2).

5.2.3 Where the Weber number of Section 5.2.2 exceeds a value of 10, 

the droplet shall be broken into 10 equally sized smaller particles 

where the total mass of the 10 smaller particles equals the mass of 

the original particle.

5.2.4 If droplet breakup has occurred, the program shall continue to 

integrate the trajectories of the smaller particles until one of the 

conditions in Section 4.2.4 has been met.

5.2.5 The droplet breakup routines shall not cause the execution time of 

the trajectory integration to increase by more than 25% over the 

execution time of the LEWICE 2.2 Beta Release when the 

benchmark test cases are ran.

* Not implemented in LEWICE 2.2 Beta Release

We ρaV2

dp

σ ------------------=

NASA/CR—2002-211793 349
6 Droplet Splashing *

6.1 Description/Purpose

6.1.1 Droplets whose path intersects the body geometry(s) may fully 

impinge, partially impinge and partially bounce or may fully 

bounce off the body geometry(s). The purpose of this section is to 

describe requirements for modeling the physical phenomena 

involved.

6.2 Droplet Splashing Requirements

6.2.1 When the path of a droplet intersects a body geometry, the program 

shall determine the fraction of water which bounces from the 

following equations:

** 6.2.1.1

Nb = 0 for K ≤ 57.7

 for 57.7 < K < 282.7

Nb = 0.2 for K ≥ 282.7

6.2.1.2

The terms in these equations have the following definitions:

Nb = mass fraction of water lost due to bouncing (dimensionless)

6.2.1.3

 (dimensionless)

6.2.1.4

 = Ohnesorge number (dimensionless)

6.2.1.5

 = Droplet Reynolds number (dimensionless)

6.2.1.6

μp = particle viscosity (kg/m/s)

ρp = particle density (kg/m3)

σ = surface tension between air and water (kg/s2)

dp = particle diameter (m)

V = particle velocity (m/s) as given in 4.2.2.4

6.2.2 For this function, the program shall subtract the local mass fraction 

of water lost due to splashing from the local collection efficiency 

defined in Section 8

* Not implemented in LEWICE 2.2 Beta Release

** This requirement shows an empirical equation which has not been rigorously verified and may

change as a result of future tunnel data.

Nb 0.8 ( ) K 57.7–

3600 = -------------------------

K OhRe p

1.25 =

Oh μp

ρpσdp

= --------------------

Re p

ρpV dp

μp

= ----------------

NASA/CR—2002-211793 350
7 Impingement Limits

7.1 Description/Purpose

7.1.1 Impingement limits are the uppermost and lowermost locations on 

the body geometry(s) where water droplets impinge upon the 

surface. The purpose of this section is to provide the requirements 

for determining upper and lower impingement limits for the body 

geometry(s).

7.2 Impingement Limit Requirements

7.2.1 The program shall integrate trajectories as listed in Section 4

starting from the same x-location as determined in Section 9 

but different y-locations until two trajectories meet the following 

criteria:

7.2.1.1

Their starting locations are within 5*10-5(dimensionless) distance.

7.2.1.2

One of the trajectories passes above the target body geometry while 

the other trajectory intersects the target body geometry.

7.2.1.3

The same criteria as listed in 7.2.1.1 and 7.2.1.2 are met 

except that the missed trajectory must pass below the target body 

geometry.

7.2.2 The program shall output to file(s) the starting and ending locations 

of the trajectories which intersect the target body geometry in the 

requirement above.

NASA/CR—2002-211793 351
8 Collection Efficiency

8.1 Description/Purpose

8.1.1 The collection efficiency is the efficiency with which any location 

on the body geometry(s) will collect water droplets. The purpose of 

this section is to provide the requirements for calculating the 

collection efficiency on the body geometry(s).

8.2 Collection Efficiency Requirements

8.2.1 The program shall take as input from the user a number of 

trajectories for the collection efficiency calculation. This number 

shall be greater than or equal to 12 less than 50.

8.2.2 The program shall integrate the number of trajectories listed in 

8.2.1 by the requirements listed in Section 4

starting from the same x-location as determined in Section 9 

but different y-locations which are evenly spaced between the 

starting locations determined by the impingement limit 

requirements as given in Section 7.

8.2.3 The program shall determine the local collection efficiency at each 

point on the body geometry(s) by the following equation:

8.2.3.1

8.2.3.2

The terms in the previous equation have the following definition:

β = local collection efficiency (dimensionless)

y0 = y-value of the starting locations of the collection efficiency 

trajectories (m)

s = surface wrap distance on target body geometry where the 

droplet intersects (m)

8.2.4 The local collection efficiency from the previous requirement shall 

be reduced due to splashing as described in Section 6

8.2.5 The program shall output to file(s) the starting and ending locations 

of the trajectories which intersect the target body geometry in the 

requirement above.

β sd

dyo =

NASA/CR—2002-211793 352
9 Other Droplet Trajectory Requirements

9.1 Description/Purpose

9.1.1 This section shall describe requirements for droplet trajectory and 

collection efficiency calculation not covered by the previous 

sections.

9.2 Other Droplet Trajectory Requirements

9.2.1 The droplets shall start at an initial x-location and y-location where 

the local velocity is within 10-3 of the flight velocity input by the 

user.

9.2.2 The initial velocity of the droplet shall be the flight velocity input 

by the user plus the terminal velocity of the droplet as given by the 

equation:

9.2.2.1

9.2.2.2

The terms in the above equation have the following definitions:

ρw = density of water droplet (kg/m3)

= terminal velocity Reynolds number (dimensionless)

Vt

 = terminal droplet velocity (m/s)

other variables were defined in Section 4.2.2

9.2.3 The program shall calculate droplet trajectories, impingement 

limits and collection efficiencies for up to 5 body geometries and up 

to 10 drop sizes.

9.2.4 The program shall calculate an overall local collection efficiency 

from the individual collection efficiencies in Section 8 by the 

following equation:

9.2.4.1

9.2.4.2

The terms in the above equation have the following definitions:

βo = overall local collection efficiency (dimensionless)

βi

 = local collection efficiency for droplet size i (dimensionless)

4gdp ρw ρa ( ) –

3υa

2

ρa

----------------------------------- cdRet

2 =

Ret

Vtdp

υa

-----------=

βo β ∑ i

Ni =

NASA/CR—2002-211793 353
Ni

 = mass fraction contained in droplet size i (dimensionless)

(Ni is input by the user)

9.2.5 The program shall output to file(s) the overall local collection 

efficiency.

NASA/CR—2002-211793 354
10 Potential Flow

10.1 Description/Purpose

Potential flow describes a specific equation which provides flow variables such 

as velocity, pressure, and pressure coefficient on the surface of the body 

geometry(s) assuming that the flow field is inviscid, incompressible and 

irrotational. The purpose of this section is to provide the requirements for a 

potential flow solution.

10.2 Potential Flow Requirements

10.2.1 The program shall use potential flow as the flow solution when this 

input option is selected by the user.

10.2.2 The program shall solve the following equation:

10.2.2.1

The terms in this equation have the following definitions:

10.2.2.2

Φ = velocity potential (m2/s)

r = distance from an arbitrary point (m)

S = surface area (m2)

n = unit normal direction (dimensionless)

ξ = source strength per unit area (m/s)

ς = dipole strength per unit area (m/s)

10.2.2.3

The velocity potential is related to the velocity by the following 

equations:

10.2.3 The velocity at an arbitrary point in space shall be determined from 

the following equation:

10.2.3.1

10.2.3.2

Φ ξ

r

-- ∂n

∂ ς

r

--  

  + Sd ∫ =

Vx ∂x

∂Φ =

Vy ∂y

∂Φ =

V ξ p gra

1

r

--  

  d Sd

p

∫ =

NASA/CR—2002-211793 355
The subscript p in the previous equation refers to the panel (body 

segment)

10.2.4 The equation listed above shall be used to calculate air velocities 

during the droplet trajectory integration as listed in Section 4 

when potential flow has been selected by the user.

10.2.5 The source strengths shall be calculated from the following 

equation:

10.2.5.1

V∞ = flight velocity (m/s)

 = source strength (m/s)

ξi

2π

------ ξ j

2π

------ ni ∂

∂ 1

r

--  

  Sd ∫

i j ≠

n

+ ∑ V ∞ ni –= •

ξi

NASA/CR—2002-211793 356
11 Grid-based Flow

11.1 Description/Purpose

Grid-based flow describes flow equations which provides flow variables such 

as velocity, pressure, and pressure coefficient on the surface of the body 

geometry(s) and on predetermined locations on a structured grid. The purpose 

of this section is to provide the requirements for a grid-based flow solution.

11.2 Grid-based Flow Requirements

11.2.1 The program shall use grid-based flow as the flow solution when 

this input option is selected by the user.

11.2.2 The program shall read the grid-based flow solution from file(s) 

when this input option is selected by the user.

11.2.3 The two input options given above shall be considered separate 

inputs.

11.2.4 The format of the file(s) used shall be specified by the format used 

by the grid-based flow module which generated the flow solution.

11.2.5 When the user has selected a grid-based flow solution but did not 

select the read option, the program shall run a user-supplied script 

file which runs the grid-based flow solver.

11.2.6 The requirements for the grid-based flow solver shall be specified in 

the requirements document for the program being used and shall 

not be specified herein.

11.2.7 For either grid-based option, the program shall accept structured 

grids and flow solutions of up to 10 grid blocks.

11.2.8 When requested by the droplet trajectory requirements of Section 

4, the program shall calculate velocities at locations which are 

not at grid points.

NASA/CR—2002-211793 357
12 Compressibility Correction

12.1 Description/Purpose

12.1.1 A compressibility correction will adjust an incompressible flow 

solution for compressibility effects. The purpose of this section is to describe 

the requirements for this function.

12.2 Compressibility Requirements

12.2.1 The program shall apply standard corrections to the potential flow 

solution described in Section 10 and the grid-based flow 

solution of Section 11 to account for compressibility effects.

12.2.2 The following equation shall be used as the correction for the 

pressure coefficient:

12.2.2.1

The terms in this equation have the following definition:

12.2.2.2

 = incompressible pressure coefficient at a given location 

(dimensionless)

 = compressible pressure coefficient at the same location 

(dimensionless)

M∞ = flight Mach number

12.2.3 The static pressure at a given location shall be calculated from the 

pressure coefficient using the equation:

12.2.3.1

The terms in the above equation are defined as follows:

12.2.3.2

p = static pressure at a given location (N/m2)

p∞ = ambient static pressure (N/m2)

ρ∞ = ambient air density (kg/m3)

V∞ = flight velocity (m/s)

12.2.4 The Mach number at a given location shall be calculated using the 

equation:

c pcomp

c pinc

1 M∞

2 – c pinc

2

--------- M∞

2

1 1 M∞

2

–+

+ ------------------------------

---------------------------------------------------------------------=

c pinc

c pcomp

c p

p p∞ –

1

2

--ρ∞V ∞

2 -----------------=

NASA/CR—2002-211793 358
12.2.4.1

The terms in this equation have the following definitions:

12.2.4.2

γ = specific heat ratio = 1.4 for air (dimensionless)

M = Mach number at a given location (dimensionless)

p = static pressure at a given location (N/m2)

po = ambient total pressure (N/m2)

12.2.5 The ambient total pressure in Section 12.2.4 is defined by the

equation:

12.2.5.1

The variables in this equation have been previously defined in this 

section.

12.2.6 The static air temperature at a given location shall be defined by the 

equation:

12.2.6.1

The variables in this equation have the following definitions:

12.2.6.2

T = static air temperature at a given location (°K)

To = ambient total temperature (°K) which is defined as

po

p

----- 1 γ 1–

2 + -----------M  

 

γ

γ 1– -----------

=

po p∞

1

2

--ρ∞V ∞

2

+=

To

T

----- po

p

-----  

 

γ 1–

γ -----------

=

To

T ∞

------ po

p∞

------  

 

γ 1–

γ -----------

=

NASA/CR—2002-211793 359
* 12.2.7 The corrected velocity at a given point shall be calculated from the 

following equation:

12.2.7.1

The terms in the above equation have the following definitions:

12.2.7.2

V = corrected velocity at a given location

R = ideal gas constant = 287.5 m2/s2/°K

* The implementation in the LEWICE 2.2 Beta Release defines the corrected velocity from the 

equation:

where Vinc = incompressible velocity (m/s). It then calculates the local Mach number from the 

equation:

The maximum local Mach number allowed is M = 0.8. The velocity is also adjusted downward if the equation above gives a Mach number greater than 0.8. Other quantities are then calculated from the local Mach number as given earlier. The discrepancy between this implementation

and the isentropic equations given earlier is due to numerical error in the calculated incompressible pressure coefficient. For large negative pressure coefficients, the equation in 12.2.3.1 will

give a negative static pressure, an impossible result. For smaller negative pressure coefficients or

for positive pressure coefficients, the two methodologies give approximately equal answers.

(For the following inputs: P∞ = 100,000 N/m2; ρ∞ = 1.3 kg/m3; V∞ = 150 m/s, corrected pressure coefficients less than [more negative than] cp = -6.84 will give negative static pressures. This

result is a consequence of the physical limitations of potential flow when applying the equation in

12.2.2.1)

V M = γRT

V

Vinc( ) 1 – γ

1 γVinc

2 –

= ---------------------------

M V

RT γ 1–

2 -----------V2 –

------------------------------------=

NASA/CR—2002-211793 360
13 Stagnation Point

13.1 Description/Purpose

13.1.1 The flow solution specified in Sections 11 and 12 will have one or

more locations where the surface velocity changes sign (direction). The purpose of this section is

to describe the requirements for this function.

13.2 Stagnation Point Requirements

13.2.1 The program shall use the minimum x-location on the body 

geometry as the initial stagnation point estimate.

13.2.2 The program shall determine the location(s) on the body 

geometry(s) where the surface velocity changes sign or is equal to 

zero.

13.2.3 If only one stagnation point occurs on a body geometry, it shall be 

designated as the main stagnation point.

13.2.4 If more than one stagnation point occurs on a body geometry, the 

program shall select the main stagnation point as the location 

nearest to the previous value for the main stagnation point.

NASA/CR—2002-211793 361
14 Roughness Height

14.1 Description/Purpose

14.1.1 Ice growth will have a characteristic surface roughness which is 

based on the specific conditions input by the user. The purpose of 

this section is to describe the requirements for determining this 

height.

14.2 Roughness Height Requirements

14.2.1 The surface roughness height shall be determined from the 

following empirical correlation:

14.2.1.1

*

The terms in this equation have the following definitions:

14.2.1.2

xk = surface roughness height (dimensionless); also known as 

equivalent sand-grain roughness height

 = freezing fraction at stagnation point (dimensionless)

14.2.2 The freezing fraction at stagnation point shall be calculated in 

accordance with the requirements given in Section 17.

* This empirical equation was determined from experimental measurements of roughness heights 

as a function of the calculated freezing fraction at the stagnation point. It was not reverse-engineered in order to match ice shape predictions.

xk

1

2

-- 0.15 0.3

N f stag

------------+=

N f stag

NASA/CR—2002-211793 362
15 Heat Transfer Coefficient

15.1 Description/Purpose

15.1.1 The convective heat loss from the surface is characterized by a heat 

transfer coefficient which is calculated from a flow solution. The 

purpose of this section is to provide requirements for the 

calculation of this parameter.

15.2 Heat Transfer Coefficient Requirements

15.2.1 The program shall calculate the heat transfer coefficient on the 

surface of the body geometry(s) using an integral boundary layer 

approach when it is not supplied from a grid-based flow solution. 

The integral boundary layer approach involves the following steps:

15.2.1.1

Calculation of critical Reynolds number for transition from the 

following empirical equation:

Rec = 1022 when at stagnation point

when ≤ 3.5% chord and Rec ≥ 600

Rec = 600 when > 3.5% chord or Rec < 600 in the equation 

above.

15.2.1.2

Calculation of shape factors Z, Λ and K from the equations:

15.2.1.2.1

15.2.1.2.2

The terms in these equations have the following definitions:

15.2.1.2.3

15.2.1.2.4

15.2.1.2.5

Rec 3834.2 1.9846 5 – 3.2812 ×10 s

6

×10 s

2 6.9994 6

×10 s

3

–+=

s

s

sd

dZ F K( )

V ------------=

K Z sd

dV =

Z

δ2

2

ν

-----=

F K( ) 2 37

315 -------- Λ

945 --------– Λ2

9072 -----------–  

  2 116

315 – --------Λ 2

945 -------- 1

120 --------+  

 Λ2 2

9072 -----------Λ3 = + +

Λ δ

2

ν

----- sd

dV =

NASA/CR—2002-211793 363
15.2.1.2.6

δ = boundary layer thickness (m)

δ2 = momentum thickness (m)

V = surface velocity at a given location (m/s)

s = surface distance from stagnation point (m)

ν = kinematic viscosity of air (m2/s)

15.2.1.3

Calculation of the roughness Reynolds number from the equation:

15.2.1.3.1

The terms in this equation have the following definition:

15.2.1.3.2

xk = roughness height (m) from Section 14

ν = kinematic viscosity of air (m2/s)

Vk = velocity at the roughness height as found by the equation:

15.2.1.3.3

The term ηk is defined as:

15.2.1.3.4

 if xk ≤ δ and ηk = 1 if xk > δ

15.2.1.4.5

The solution procedure is as follows:

1) The flow function U(s) together with its derivative dU/ds are 

known (Sections 10 and 11);

2) Integration of the above equations gives the shape factors Z(s) 

and K(s) so that displacement thickness δ2 can be calculated;

3)The first shape factor Λ(s) is found;

4) The boundary layer thickness δ(s) is found;

5) Finally, the velocity distribution is found.

15.2.1.4

Assigning a transition location to the first wrap distance from the 

stagnation point where the roughness Reynolds number has 

exceeded the critical Reynolds number.

15.2.1.5

Calculation of the laminar heat transfer coefficient prior to the 

transition location from the equation:

15.2.1.5.1

Rek

Vk xk

ν = -----------

Vk

V

------ 2ηk 2ηk

3 – ηk4 ( ) +

Λ

6

--- ηk 3ηk

2 – 3ηk3

ηk

4

+= ( ) –+

ηk

xk

δ

----=

NASA/CR—2002-211793 364
The terms in this equation have the following definitions:

15.2.1.5.1

δT = thermal boundary thickness (m) as given by the equation:

15.2.1.5.1.1

15.2.1.5.2

c = chord length of body geometry(s)

k = thermal conductivity of air (W/m/°K)

hl

 = laminar heat transfer coefficient (W/m2/°K)

V = velocity at a given surface location (m/s)

s = surface distance from stagnation point (m)

ν = kinematic viscosity of air (m2/s)

V∞ = flight velocity (m/s)

15.2.1.6

Calculation of the turbulent heat transfer coefficient after the 

transition location from the equation:

15.2.1.6.1

The terms in this equation have the following definitions:

15.2.1.6.2

ht

 = turbulent heat transfer coefficient (W/m2/°K)

ρ = air density at a given surface location (kg/m3)

V = air velocity at a given surface location (m/s)

Cp = specific heat of air (J/kg/°K)

Pr = Prandtl number (dimensionless) = 

k = thermal conductivity of air (W/m/°K)

μ = viscosity of air (kg/m/s)

 = turbulent roughness Reynolds number as given by

15.2.1.6.3

hl

2k

δT

-----=

δT

c

-----  

  2V ∞c

ν

---------- 46.72

V

V ∞

-------  

  2.87 -------------------- V

V ∞

-------  

  1.87 s

c

--  

  d

0

s

c

--

∫ =

ht

1

2

--c f ρV Cp

0.9

c f

2

-----0.52Rekt

0.45Pr0.8

+

= --------------------------------------------------------------

Cpμ

k

----------

Rekt

NASA/CR—2002-211793 365
15.2.1.6.4

cf = skin friction coefficient (dimensionless) as given by the 

empirical expression:

The terms in this equation have the following meaning

15.2.1.6.5

xk = roughness height (m) from Section 14

θt = turbulent momentum thickness (m) as given by the equation:

Terms in this equation which have not been previously defined in 

this section are defined as follows:

15.2.1.6.6

st

 = wrap distance from stagnation point to transition location (m)

 = laminar momentum thickness at transition location (m) as 

calculated in Section 15.2.1.4.5

15.2.2 When the program performs an integral boundary layer integration, 

a separate integration shall be made for each body geometry.

15.2.3 If the heat transfer coefficient is supplied by a grid-based flow 

solution, its definition and requirements are a function of that gridbased flow module and is not specified by this document.

Rekt

Vc

ν

------ c f

2

-----=

c f

0.3362

864θt

xk

------------- 2.568+  

  log    2 = -------------------------------------------------------

θt

0.36ν

0.2

V3.29 ------------------- V3.86ds

st

s

∫

 

 

  0.8

δ2 st+=

δ2 st

NASA/CR—2002-211793 366
16 Energy Balance Equation

16.1 Description/Purpose

16.1.1 The energy balance equation determines the amount of heat gain 

and loss from different factors and determines the energy available 

at each location for freezing the available water. The purpose of this 

section is to describe the requirements for this equation.

16.2 Energy Balance Equation Requirements

16.2.1 The program shall solve the following equation for the temperature 

distribution on the surface of the body geometry(s):

16.2.1.1

The terms in this equation have the following definitions:

16.2.1.2

kφ = thermal conductivity of body in direction normal to the surface 

(W/m/°K)

T = temperature at a given location on the body geometry(s) (°K)

φ = direction normal to body surface (m)

q ̋nc = net convective heat loss from body (W/m2)

q ̋evap = evaporative heat loss from surface water (W/m2)

q ̋ke = kinetic heat gain to body from impinging droplets (W/m2)

q ̋lat = latent heat gain to body from freezing (W/m2)

q ̋sens = sensible heat loss (or gain) from surface water (W/m2)

16.2.2 The net convective heat loss shall be determined by the equation:

16.2.2.1

The terms in this equation have the following definition:

16.2.2.2

q ̋conv = convective heat loss (W/m2) as defined by the equation:

The terms in this equation have the following definitions:

16.2.2.2.1

h = convective heat transfer coefficient (W/m2) as determined from 

Section 15

Ts = temperature at a given surface location on a body 

geometry (°K).

T∞ = ambient static temperature (°K)

16.2.2.3

kφ φ∂

∂T

 

 

φ 0=

– q''nc q''evap q''ke – q''lat – q''sens += ±

q''nc q''conv q'' fh ( ) – Aratio =

q''conv h Ts T ∞ = ( ) –

NASA/CR—2002-211793 367
q ̋fh = heat gain on surface from frictional heating (W/m2) as 

defined by the equation:

Trec has the following definition:

16.2.2.3.1

Trec = recovery temperature (°K) at a given surface location on a 

body geometry as given by the equation:

The terms in this equation have the following definitions:

16.2.2.3.2

γ, M and To were previously defined in Section 12

r = recovery factor (dimensionless) = Pr1/2 if the boundary layer is 

laminar as defined in Section 15 and r = Pr1/3 if the 

boundary layer is turbulent as defined in Section 15. 

Pr = Prandtl number (dimensionless) as given in 15.2.1.6.2

16.2.2.4 The area ratio (Aratio) is defined as the ratio of the 

surface area of a bead on the surface with respect to the surface area 

of the control volume and has the following definition:

The terms in this equation have the following definitions:

16.2.2.4.1

θc = contact angle (radians) = π/90 * (Tmp - Ts)

Tmp = melting point temperature for ice (°K)

wf = wetness factor constant (dimensionless) = 1 in impingement 

region and = 0.3 elsewhere

zf = wetness factor = 1 in impingement region and

 elsewhere

16.2.3 The evaporative heat loss shall be defined by the equation:

16.2.3.1

The terms in this equation have the following definitions:

16.2.3.2

Aratio = area ratio as defined above

Lv = latent heat of vaporization (J/kg)

q''fh h Trec T∞ = ( ) –

Trec

To 1 r

γ 1–

2 -----------M2

+  

 

1 γ 1–

2 -----------M2

+  

 

= --------------------------------------------

Aratio

2

1 θc cos+ ----------------------- 1 wfzf = ( ) –

zf 1

θc

θc sin ------------–  

  =

q''evap

AratioLvhm( ) MW w

Rˆ --------------------------------------------- es

Ts

----- ee

Te

-----–  

  =

NASA/CR—2002-211793 368
hm = mass transfer coefficient (m/s)

(MW)w = molecular weight of water = 18 kg/kg-mole

 = molar ideal gas constant = 8337.5 kg*m2/kg-mole/s2/°K

Ts = temperature at a given surface location on a body

geometry (°K).

Te = Temperature at the edge of boundary layer (°K) as given 

in Section 12.2.6.1

es = saturated evaporative pressure at a given surface location on a 

body geometry (N/m2)

ee = saturated evaporative pressure at the edge of boundary layer

(N/m2)

16.2.3.3

The saturated evaporative pressure shall be defined by the following 

empirical equations:

for T < Tmp = 273.15°K

for T ≥ Tmp

Tmp = melting point temperature for ice (°K)

16.2.3.4

The mass transfer coefficient shall be defined by the following 

empirical equation:

16.2.3.4.1

The terms in this equation have the following definitions:

16.2.3.4.2

ρair = density of air (kg/m3) at a given location as given 

in Section 12.

Cp,air = specific heat of air (J/kg/°K)

L = Lewis number (dimensionless) which is defined by the 

equation:

The terms in this equation have the following definitions:

16.2.3.4.3

ρair = density of air (kg/m3) at a given location as given 

in Section 12.

Rˆ

e 6894.7 20.15247167 11097.16963

1.8T – -------------------------------  

  exp=

e 6894.7 14.56594634 7129.219482

1.8T 72– – -------------------------------  

  exp=

hm

h

ρCp ( )airL

2 3⁄ = ---------------------------------

L

kair

ρairCp, airDaw

----------------------------------=

NASA/CR—2002-211793 369
Cp,air = specific heat of air (J/kg/°K)

kair = thermal conductivity of air (W/m/°K)

Daw = mass diffusivity between water and air (m2/s)

16.2.4 The kinetic heat gain from the impinging droplets shall be defined 

by the following equation:

16.2.4.1

The terms in this equation have the following definitions:

16.2.4.2

βo = local collection efficiency as defined in Section 9.2.4

LWC = ambient liquid water content (kg/m3)

V∞ = flight velocity (m/s)

16.2.5 The latent heat gain shall be defined by the following equation:

16.2.5.1

The terms in this equation which have not been defined in this 

sections are defined as follows:

16.2.5.2

Lf = latent heat of fusion (J/kg)

Nf = mass fraction of incoming water which does not freeze 

[freezing fraction] (dimensionless) as defined 

in the following equation:

∆Tr = temperature range between water and ice phases (°K)

16.2.6 The sensible heat transfer shall be defined by the following 

equations:

16.2.6.1

This equation shall be used when Ts < Tmp (rime ice)

The terms which have not been defined in this section have the 

following definitions:

 = mass flux of impinging water = βoLWCV∞ (kg/m2s)

 = mass flux of runback water entering a given 

section (kg/m2s) as defined in Section 17

Trb = temperature at previous surface location on a body geometry 

q''ke

βoLWCV ∞

3

2 --------------------------=

q''lat N f βoLWCV ∞L f =

N f

T mp ∆Tr Ts –+

∆Tr

= -------------------------------------

qsens m ̇im Cpw T mp T ∞ ( ) – Cpi Ts T mp – ( ) + ( ) – m ̇rbin Cpw T mp Trb ( ) – Cpi Ts T mp –= ( ) + ( ) –

m ̇im

m ̇rbin

NASA/CR—2002-211793 370
(runback temperature) (°K)

Cpw = specific heat of water (J/kg/°K)

Cpi = specific heat of ice (J/kg/°K)

16.2.6.2

This equation shall be used when Tmp ≤ Ts ≤ Tmp + ∆Tr

16.2.6.3

This equation shall be used when Ts > Tmp + ∆Tr

qsens m ̇imCpw T mp T ∞ – ( ) – m ̇rbinCpw T mp Trb –= ( ) –

qsens m ̇imCpw Ts T ∞ – ( ) – m ̇rbinCpw Ts Trb –= ( ) –

NASA/CR—2002-211793 371
17 Mass Balance Equation

17.1 Description/Purpose

17.1.1 The mass balance equation determines the amount of mass gain 

and loss from different factors and determines the mass of water 

which freezes at each location. The purpose of this section is to

describe the requirements for this equation.

17.2 Mass Balance Equation Requirements

17.2.1 The program shall solve the following equation for the mass flux of 

runback water leaving at each location on a body geometry:

17.2.1.1

The terms in this equation have the following definitions:

17.2.1.2

 = mass flux of impinging water = βoLWCV∞ (kg/m2s)

 = mass flux of runback water entering a given 

section (kg/m2s)

 = mass flux of evaporating water (kg/m2s)

 = mass flux of runback water leaving a given 

section (kg/m2s)

 = mass flux of water freezing in a given 

section (kg/m2s)

 = mass flux of water shedding (kg/m2s) in a given section.

This physical phenomena is different from droplet splashing 

as given in Section 6

 = mass flux of standing water (kg/m2s) due to 

surface tension effects

 = surface distance spacing at next location (m)

 = surface distance spacing at current location (m)

17.2.2 The mass flux of runback water entering the stagnation point shall 

be equal to 0 (no mass flow).

17.2.3 The direction of runback mass flow shall be in the surface direction 

away from the stagnation point. (Therefore the calculation of 

17.2.1.1 is initiated at the stagnation point and is calculated 

going away from this point on either side so that is a known 

quantity at each location.)

m ̇im m ̇rbin + me

 ̇ m f ̇ m ̇rbout

∆snext

∆scurrent

-------------------- m ̇sh m ̇st = ++ + +

m ̇im

m ̇rbin

me

 ̇

m ̇rbout

m ̇ f

m ̇sh

m ̇st

∆snext

∆scurrent

m ̇rbin

NASA/CR—2002-211793 372
17.2.4 The mass flux of evaporating water shall be defined from the 

following equations:

17.2.4.1

 when 

17.2.4.2

 when in the previous 

equation

17.2.5 In the case cited by Section 17.2.4.2, the other mass fluxes on 

the right hand side of 17.2.1.1 are identically zero.

* 17.2.6 The mass flux lost by water shedding shall be determined by the 

empirical equations:

17.2.6.1

 for We ≥ Wec

17.2.6.2

 for We < Wec

The terms in these equations have the following definitions:

17.2.6.3

Wec = critical bead Weber number (dimensionless) which shall be 

determined from the following empirical expression:

xk = surface roughness (m) as defined in Section 14

c = chord length of the body geometry(s)

17.2.6.4

We = bead Weber number (dimensionless) which shall be defined 

by the equation:

The terms in this equation have the following definitions:

17.2.6.5

ρ = air density (kg/m3) at a given location at the edge of the 

boundary layer as defined in Section 12

V = air velocity (m/s) at a given location at the edge of the 

boundary layer as defined in Section 12

σ = surface tension between water and air (kg/s2)

me

 ̇ qevap

Lv

= ------------ me

 ̇ mim ̇ mrbin ̇ < +

me

 ̇ mim ̇ mrbin ̇ += me ̇ mim ̇ mrbin ̇ ≥ ( ) +

msh

 ̇ mrbout ̇ 1

W ec

We – ----------  

  =

msh

 ̇ 0=

W ec 200 50000

xk

c

+= ----

We ρV2

db

σ ---------------=

NASA/CR—2002-211793 373
db = diameter of a bead of surface water (m) which shall be defined 

from the equation:

The terms in this equation have the following definitions:

17.2.6.6

 = standing water from previous time step (kg/m2)

∆t = current time step (sec)

ρw = water density (kg/m3)

17.2.7 The mass flux of standing water shall be determined by the 

following equation:

17.2.7.1

where hb = height of water bead = 

17.2.8 The mass flux of water freezing shall be determined from the 

following equation:

17.2.8.1

The terms in this equation have been previously defined 

in this section.

* Not implemented in LEWICE 2.2 Beta Release

db

mst ( )t t –= ∆t mim +  ̇ ∆t

ρw

= ---------------------------------------------------

mst ( )t t –= ∆t

mst

 ̇ hbρw

∆t ----------- mst ( )t t –= ∆t +=

1

2

--db

m f

 ̇ N f mim ̇ mrbin ̇ = ( ) +

NASA/CR—2002-211793 374
18 One Dimensional Anti-Icing

18.1 Description/Purpose

18.1.1 The purpose of anti-icing is to determine the amount of heat 

required to keep the surface of the body geometry(s) free of ice by 

supplying bleed air from a compressor. or by supplying heat from 

an electrothermal heater pad inside the body geometry using a one 

dimensional steady-state heat transfer analysis.

18.2 One Dimensional Anti-Icing Requirements

18.2.1 The program shall determine the heat requirements for either a

bleed air system or an electrothermal system based on an input 

surface temperature or based on an assumption that all of the 

impinging water evaporates.

18.2.1.1 The four options stated above (bleed air evaporative, 

bleed air running wet, electrothermal evaporative and 

electrothermal running wet) shall be determined by 

the user.

18.2.2 For an input surface temperature, the program shall solve for the 

surface heat flux from the equation:

18.2.2.1

The terms in this equation are defined in Section 16 with the 

additional definition:

18.2.2.1.1

 = heat flux at the surface (W/m2)

18.2.2.2

The mass fluxes needed for the previous equation shall be 

calculated from Section 17 with the stipulation that = 0

18.2.3 For an evaporative system, the surface heat flux shall be solved for 

as stated in Section 18.2.2 with the following alterations:

18.2.3.1

The mass flux equation of Section 17 reduces to the following 

equation:

18.2.3.2

The surface temperature shall be calculated from the equation in 

18.2.3.1 noting the definitions of these terms from Sections 

17 and 16.

q''surf q''nc q''evap q''ke – q''sens += ±

q''surf

m f

 ̇

mim

 ̇ me ̇ =

NASA/CR—2002-211793 375
18.2.4 For a bleed air system, the required heat flux shall be equal to the 

surface heat flux as defined in Sections 18.2.2 and 18.2.3.

18.2.5 For an electrothermal system, the required heat flux shall be 

calculated from the following equation:

18.2.5.1

18.2.5.2

The terms in this equation are defined as follows:

 = required heat flux (W/m2)

Ts = surface temperature (K)

T∞ = ambient temperature (K)

 = surface heat flux (W/m2)

∆yh = thickness of heater (m)

kh = thermal conductivity of heater material (W/mK)

∆yj

 = thickness of layer j in body structure (m)

kj = thermal conductivity of material in layer j (W/mK)

n = number of layers in body structure

h = index number of heater layer in body structure as counted from 

the inside surface of the body structure

hinside = convective heat transfer coefficient on inside surface of 

body structure (W/m2K). For a bleed air system, this is the 

heat transfer coefficient supplied by the bleed air. For an 

electrothermal system, this is the natural convection heat 

transfer coefficient.

18.2.6 For a bleed air system, the program shall calculate the local bleed 

air temperature from the following equation:

18.2.6.1

18.2.6.2

The terms in the previous equation have already been defined in this 

section with the addition:

q''required q''surf

Ts T ∞ q''surf

∆yh

2kh

-------- ∆y j

k j

--------

j h 1+=

n

+ ∑  

 

  ––

1

hinside

-------------- ∆yh

2kh

-------- ∆y j

k j

--------

j 1=

h 1–

+ + ∑

-------------------------------------------------------------------------------------–=

q''required

q''surf

Tair Ts q''surf

1

hinside

-------------- y ∆ j

k j

--------

j 1=

n

++= ∑

NASA/CR—2002-211793 376
Tair = local bleed air temperature (°K)

18.2.7 For an electrothermal system, the program shall calculate the 

temperature at the top of the heater layer from the following 

equation:

18.2.7.1

18.2.7.2

The terms in this equation have been previously defined in this 

section with the addition:

 = temperature at top of the heater layer (°K)

18.2.8 For an electrothermal system, the program shall calculate the 

temperature at the bottom of the heater layer from the following 

equation:

18.2.8.1

18.2.8.2

The terms in the following equation have been defined previously in 

this section with the addition:

 = temperature at bottom of the heater layer (K)

18.2.9 For an one-dimensional electrothermal system which uses the heat 

fluxes specified for use in Section 19, the program shall instead 

calculate the unknowns and Ts using the known heat fluxes 

for the values of d in the above equations.

Thtop Ts q''surf

∆y j

k j

--------

j h 1+=

n

–= ∑

Thtop

Thbot Thtop

2q''surf q''required ( ) – y ∆ h

2kh

-----------------------------------------------------------–=

Thbot

q''surf

q''required

NASA/CR—2002-211793 377
19 Effective Heat Transfer Coefficient

19.1 Description/Purpose

19.1.1 The purpose of this module is to calculate the effective heat transfer 

coefficient for use when interfacing LEWICE 2.2 with other 

software such as an internal flow solver for bleed air applications. 

19.2 Effective Heat Transfer Requirements

19.2.1 The effective heat transfer coefficient is defined by the equation:

19.2.1.1

19.2.1.1.1 q”surface is determined from Section 18.

19.2.1.1.2Trec is defined in Section 16.2.2.3.1

19.2.2 First, a temporary value using heff,temp and a reference 

temperature, Tref, are obtained without evaporation. For a 

mixed phase, heff,temp and Tref are defined by the following 

equations: 

19.2.2.1

19.2.2.2

19.2.2.3 The effective heat transfer coefficient is then calculated from 

the following equation:

19.2.2.4 The estimated freezing fraction at each location on the body 

geometry shall be calculated from the following equation:

19.2.2.4.1

19.2.2.4.2 The terms in this equation are defined in Sections 16 and 17

19.2.2.4.3 The evaporative term shall be evaluated using Ts = Tmp

19.2.3 For a solid (rime ice) condition, heff,temp and Tref are defined by the 

following equations: 

19.2.3.1

q''surface heff Ts Trec = ( ) –

heff temp h mim

 ̇ mrbin ̇ ( ) + Cpw +=

Tref

hTrec mim

 ̇ Cpw

T ∞ mrbin

 ̇ Cpw

Trb + +

heff temp

= ----------------------------------------------------------------------------------

heff heff temp N f L f mim

 ̇ mrbin ̇ ( ) + q''evap –+=

N f

– '' q surface h T mp Trec ( ) – q''evap m ̇imCpw T mp T ∞ ( ) – m ̇rbinCpw T mp Trb + ++ + ( ) –

L f m ̇im m ̇rbin ( ) + = ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

heff temp h mim

 ̇ mrbin ̇ ( ) + Cpi +=

NASA/CR—2002-211793 378
19.2.3.2

19.2.3.2.1 The term is determined by the following equation:

19.2.3.2.2 Other terms (including those in 19.2.3.2.1) are defined in 

Sections 16 and 17

19.2.3.2.3 The effective heat transfer coefficient is then calculated from 

the following equation:

19.2.4 For a liquid phase condition (including fully evaporative cases), 

heff,temp and Tref are defined by the following equations:

19.2.4.1

19.2.4.2

19.2.4.3 For a fully evaporative condition, is defined by the 

following equation:

19.2.4.3.1

19.2.3.2.3 The effective heat transfer coefficient is then calculated from 

the following equation:

Tref

hTrec q''sens +

heff temp

---------------------------------=

q''sens

q''sens m ̇imCpw T ∞ T mp ( ) – m ̇rbinCpw Trb T mp ( ) – CpiT mp m ̇im m ̇rbin = + + ( ) +

heff heff temp L f mim

 ̇ mrbin ̇ ( ) + q''evap –+=

heff temp h mim

 ̇ mrbin ̇ ( ) + Cpw +=

Tref

hTrec mim

 ̇ Cpw

T ∞ mrbin

 ̇ Cpw

Trb + +

heff

= ----------------------------------------------------------------------------------

q''evap

q''evap mim

 ̇ mrbin ̇ ( ) + Lv =

heff heff temp q''evap –=

NASA/CR—2002-211793 379
20 Two Dimensional De-icing/Anti-Icing

20.1 Description/Purpose

20.1.1 The purpose of this module is to calculate the temperatures on a

two dimensional grid inside the body geometry(s) using a given 

amount of heat from bleed air or an electrothermal heater pad inside 

the body geometry. This module can also be used to determine the 

heat required to keep the surface of the body geometry(s) at a 

specified surface temperature using the same type of heat input as 

described earlier.

20.2 Two Dimensional De-Icing Requirements

20.2.1 The program shall solve the following equation within the airfoil 

geometry:

20.2.1.1

20.2.1.2 The terms in this equation are defined as follows:

ρk = density of material k (kg/m3)

Cp,k = specific heat of material k (J/kg/°K)

T = temperature at each location in material k (°K)

kx = thermal conductivity of material k in direction parallel to surface (W/m/K)

ky = thermal conductivity of material k in direction normal to surface (W/m/K)

 = volumetric heat source emanating from material k (W/m3)

t = time (s)

x = direction parallel to surface (m)

y = direction normal to surface (m)

20.2.1.3 In the ice/water region, the above equation shall be replaced with 

the following expression:

20.2.1.4 The additional terms are defined as follows:

H = enthalpy in ice/water region (J/m3)

ki,w = thermal conductivity of ice or water (changed as needed) (W/m/K)

20.2.2 The program shall solve the above equation for up to 29 different 

materials in the parallel direction and for up to 29 different materials in the 

direction normal to the surface.

20.2.3 The program shall use the following relationships at the interface 

ρCp ( )k

∂T

∂t

------ kx k, x2

2

∂

∂ T ky k, y2

2

∂

∂ T q'''k = + +

q'''k

∂H

∂t

------- ki w, x2

2

∂

∂ T ki w, y2

2

∂

∂ T

+=

NASA/CR—2002-211793 380
between materials within the airfoil geometry:

20.2.3.1

 at every interface between different materials

20.2.3.2

 at interfaces normal to the surface

20.2.3.3

 at interfaces parallel to the surface

20.2.4 The program shall be able to use any of the following boundary 

conditions for each external interface of the airfoil geometry:

20.2.4.1

20.2.4.2 The temperature constant (Tconst) can be different for each 

external boundary

20.2.4.3

 for an external boundary normal to the 

surface (at interior of de-icer or at airfoil (or ice) external surface).

20.2.4.4

 for an external boundary parallel to the 

surface (at ends of airfoil)

20.2.4.5 The temperature constant (Tconst) and heat transfer coefficient (h) 

can be different for each external boundary.

20.2.4.6

 for an external boundary normal to the surface

20.2.4.7

 for an external boundary parallel to the surface

20.2.4.8 The surface heat flux (qsurface) can be different for each external 

boundary.

20.2.4.9 In place of the boundary conditions specified above, the outer 

surface boundary of the airfoil geometry shall be also able to use 

the equations in Section 16 as the external boundary condition.

20.2.4.10 In place of the boundary conditions specified above, the outer

surface boundary of the airfoil geometry shall be also able to use 

the following boundary condition:

20.2.4.10.1

T material1 T material2 =

kx∂x

∂T – 



material1

kx∂x

∂T – 



material2

=

ky∂y

∂T – 



material1

ky∂y

∂T – 



material2

=

T )surface Tconst =

kx∂x

∂T – 



surface

h Tsurface Tconst = ( ) –

ky∂y

∂T – 



surface

h Tsurface Tconst = ( ) –

kx∂x

∂T – 



surface

q''surface =

ky∂y

∂T – 



surface

q''surface =

NASA/CR—2002-211793 381
where Trec is defined in Section 16.2.2.3.1

20.2.4.11 The heat transfer coefficient for the external boundary parallel

 to the surface may be defined in three ways:

20.2.4.11.1 A user-specified constant

20.2.4.11.2 A user-specified array as a function of wrap distance

20.2.4.11.2 From the equations listed in Section 15

20.2.4.12 The heat transfer coefficient for the internal boundary parallel

 to the surface may be defined in two ways:

20.2.4.12.1 A user-specified constant

20.2.4.12.2 A user-specified array as a function of wrap distance

20.2.4.13 The surface heat flux for the boundaries parallel to the surface 

 may be defined in two ways:

20.2.4.13.1 A user-specified constant

20.2.4.13.2 A user-specified array as a function of wrap distance

20.2.5 The ice layer shall be allowed to shed (be removed from the 

computation) when the following condition is met:

20.2.5.1

The terms in this equation have the following definitions:

Fad = adhesion force (Pascals) as defined by the empirical equations *

 when 267.7K ≤ Ts ≤ Tmp

 when 258.15K ≤ Ts ≤ 267.7K

 when Ts ≤ 258.15K

Tmp = melting point of ice = 273.15K

Ts = surface temperature (K)

Fp = component of force parallel to the ice as provided by the flow solution in 

Sections 10 or 11 

Fn = component of force normal to the ice as provided by the flow solution in 

Sections 10 or 11 

Fr = component of force on the ice as provided by a rotating airfoil (rotor or 

propeller) as defined by

 where

ρair = air density (kg/m3)

Vr = rotor velocity (RPM) (=0 for fixed wing simulations)

r = distance of airfoil section from rotor hub (m)

* These empirical equations were derived from experimental data with a reported error rate of

±100%. Caveat emptor.

ky∂y

∂T – 



surface

h Tsurface Trec = ( ) –

Fad Fn

2 Fr2 Fp2

≤ ( ) –+

Fad 14583 T mp Ts = ( ) –

Fad 34475 1.5 267.3 Ts = ( ) ( ) – 4+

Fad 34475 3.79 258.15 Ts = ( ) ( ) – 12.5+

Fr

ρairVr

2

r

2 3600 ( ) -------------------=

NASA/CR—2002-211793 382
20.2.5.2

Only ice is shed by these mechanisms. If the ice/water layer contains only 

water, it is shed by the equations in Section 17.2.6 or it is subjected to 

runback or standing water as defined in Section 17

20.2.5.3 The shedding formula provided above can be applied by using one 

of three user-specified options:

20.2.5.3.1 It is applied independently at each grid location

20.2.5.3.2 It is applied as a summation of forces for each section in the 

direction parallel to the surface with each section shedding independent of the 

others. (default)

20.2.5.3.1 It is applied as a summation of forces for the entire ice shape, 

meaning that the entire ice shape must shed as a whole unit or not at all.

20.2.6 The equations in this section shall be discretized into a 

two-dimensional grid with implicit central differencing (second order accuracy 

of Taylor series) in the spatial direction and first-order differencing in time.

NASA/CR—2002-211793 383
21 Error Checking

21.1 Description/Purpose

21.1.1 The variables input by the user must be checked for errors and for 

the ranges imposed by the available test data. 

21.2 Error Checking Requirements

21.2.1 The program shall check the following input data and issue a 

warning message for the following inputs:

21.2.1.1

The automated time step procedure was not selected.

21.2.1.2

The simulation time is > 45 minutes (data limit).

21.2.1.3

The number of body geometries is > 1 and ≤ 5

21.2.1.4

The number of flow solutions is < the number calculated for the 

automated time step procedure.

21.2.1.5

The point spacing for any body geometry is ≥ 8*10-4

21.2.1.6

The number of trajectories is < 10 or > 50

21.2.1.6.1

The warning message for number of trajectories < 10 

shall indicate that this number is insufficient and the 

program shall set this variable equal to 24.

21.2.1.6.2

The warning message for number of trajectories > 50

shall indicate that this number is unnecessarily high.

21.2.1.7

The particle density is ≤ 980 kg/m3 or ≥ 1020 kg/m3.

21.2.1.8

A grid-based flow solution is selected.

21.2.1.9

An additional warning if an interactive grid-based flow solution is 

selected.

21.2.1.10

The anti-icing option is selected.

21.2.1.11

The sum of the particle distribution is ≠ 1.

21.2.1.11.1

The program shall adjust the individual particle 

fractions such that their sum is =1 by the following 

equation:

NASA/CR—2002-211793 384
21.2.1.11.2

The terms in this equation are defined as follows:

 = fraction liquid water content (dimensionless)

 = fraction liquid water content input

(dimensionless)

n = number of drop sizes input

j = index value for a given drop size in distribution

21.2.1.12

The volume median drop size of the distribution is > 50 μm which 

acknowledges that the distribution is outside the FAA certification 

range.

21.2.1.13

An additional warning if the volume median drop size of the 

distribution is > 270 μm (data limit).

21.2.1.14

The angle of attack is < -6 or > +6 to indicate possible flow 

separation.

21.2.1.15

The ambient Mach number calculated in Section 21.2.2.13.1 is

≥ 0.6 to reflect limits of incompressible flow.

21.2.1.16

The ambient liquid water content is > 2 g/m3 (data limit).

21.2.1.17

The ambient temperature is < 240 °K (outside meteorological 

probability) or ≥ 273.15 °K (no ice will form).

21.2.1.18

Output files which are estimated > 100 kB will be generated.

21.2.1.19

Blank lines are found in a body geometry input file.

21.2.1.19.1

The program shall otherwise ignore the blank lines in

a body geometry input file.

21.2.1.20

A body geometry is not enclosed (first and last input data points are 

different).

21.2.1.21

Two consecutive body geometry points are the same.

21.2.1.21.1

The program shall remove one of the duplicate points 

from the body geometry.

ηLWCj

ηLWCinputj

ηLWCinputj

j 1=

n

∑

= --------------------------------

ηLWC

ηLWCinput

NASA/CR—2002-211793 385
21.2.1.22

The body geometry points are input counter-clockwise.

21.2.1.22.1

The program shall reverse the body geometry points 

so they are clockwise.

21.2.1.23

The angle between two adjacent body segments is > 45°.

21.2.1.24

An additional warning is issued if the angle between two adjacent 

body segments is > 145°.

21.2.1.25

Number of thermal time steps must be > 0

21.2.1.26

Number of thermal iterations must be 0 < N < 50

21.2.1.27

Time before spray cannot be < 0

21.2.1.28

Time after spray cannot be < 0

21.2.1.29

Time before spray is > 0

21.2.1.30

Time after spray is > 0

21.2.1.31

Number of thermal output files must be 0 ≤ N < 50

21.2.1.32

Printout time number must be ≥ 0

21.2.1.33

Printout type must be 1 ≤ N ≤ 5

21.2.1.34

Number of printouts must be between 0 ≤ N < 50

21.2.1.35

Printout flag must be 1 ≤ N ≤ 3

21.2.1.36

Second printout flag must be 1 ≤ N ≤ 3

21.2.1.37

Printout layer must be 1 ≤ N ≤ number of layers.

21.2.1.38

Printout section must be 1 ≤ N ≤ number of sections

21.2.1.39

Printout time must be ≥ 0

21.2.1.40

Total number of columns for external data files must be ≥ 2

21.2.1.41

Column for 1st variable in external data files must be 1 ≤ N ≤

number of columns.

21.2.1.42

NASA/CR—2002-211793 386
Column for 2nd variable in external data files must be 1 ≤ N ≤

number of columns.

21.2.1.43

Columns for 1st and 2nd variable in external data files 

cannot be the same. 

21.2.1.44

Offset may be past the trailing edge.

21.2.1.45

Output file format flag must be 0 or 1

21.2.1.46

Constant heat source for 1-D analysis can only be used

for IDEICE = 2 or = 3 option.

21.2.1.47

The offset value may be past the trailing edge

21.2.1.48

Boundary condition index must be 0 < N ≤ 3

21.2.1.49

Constant temperature boundary condition is not

normally used in icing calculations.

21.2.1.50

Constant heat flux boundary condition is not

normally used in icing calculations.

21.2.1.51

Temperature at boundary is not equal to the ambient

temperature input from the main LEWICE input file.

21.2.1.52

Convective heat flux boundary condition is not

normally used in icing calculations.

21.2.1.53

Negative heat flux boundary condition is not

normally used in icing calculations.

21.2.1.54

Temperature for bleed air is less than freezing.

This is not normally used in icing calculations.

Mass flow rate for bleed air must be ≥ 0

21.2.1.55

Mass fraction going up must be 0 ≤ N ≤ 1

21.2.1.56

Mass flow rate input location is greater than one chord length. 

21.2.1.57

Heat flux flag must be 0 or 1

21.2.1.58

Bleed air flag must be 0 or 1

21.2.1.59

“Optimum” bleed air flag must be 0 or 1

21.2.1.60

NASA/CR—2002-211793 387
Heat flux flag and bleed air flag cannot both be on. 

21.2.1.61

“Optimum” bleed flag and bleed air flag cannot both be on.

21.2.1.62

Heat flux flag and “optimum” bleed flag cannot both be on.

21.2.1.63

Conduction flag must be 0 or 1

21.2.1.64

Boundary flag must be 0 < N ≤ 3

21.2.1.65

Initial temperature flag must be 0 < N ≤ 3

21.2.1.66

Ice shed flag must be 0 or 1

21.2.1.67

Shed type flag must be 0 < N ≤ 2

21.2.1.68

Phase change flag must be 0 or 1

21.2.1.69

For anti-icing case, conduction flag must be = 1 since heaters 

will turn on immediately.

21.2.1.70

Since conduction flag is off (ICOND = 0), then the

boundary condition flag (IBOUND) must be = 3 and

temperatures must be initialized to the accretion

temperature (INIT = 3).

21.2.1.71

Since phase change flag is off (IGDE = 0), then the

boundary condition flag (IBOUND) must be = 2 and

temperatures must be initialized to the recovery

temperature (INIT = 2). 

21.2.1.72

Upper boundary is set to dry air. Ice will not form.

21.2.1.73

Initial temperature selected is not normally used 

in icing simulations.

21.2.1.74

Ice will not shed. This is usually too conservative.

21.2.1.75

The preferred shedding mode is by sections (ISTD = 1).

21.2.1.76

Phase change is not selected. This is not

normally used in icing simulations.

21.2.1.77

Ice cannot shed without phase change.

21.2.1.78

3D streamline flag must be 0 or 1

NASA/CR—2002-211793 388
21.2.1.79

Desired surface temperature is less than freezing.

21.2.1.80

Evaporation flag must be 0 < N ≤ 2

21.2.1.81

De-ice flag must be 0 or 1

21.2.1.82

Span location on rotor cannot be < 0

21.2.1.83

Rotor speed cannot be < 0

21.2.1.84

Rotor flag must be 0 or 1

21.2.1.85

Thermal time steps < 0.0001 or > 1.0 should not be used.

21.2.2 The program shall check the following input data and issue an

error message for the following inputs: 

21.2.2.1

The simulation time input is less than or equal to zero.

21.2.2.2

The number of body geometries is < 1 or > 5.

21.2.2.3

The number of flow solutions is ≤ 0.

21.2.2.4

The point spacing for any body geometry is ≤ 0.

21.2.2.5

The particle density is ≤ 0.

21.2.2.6

Any drop size in the distribution is ≤ 0.

21.2.2.7

The chord length is ≤ 0.

21.2.2.8

The ambient velocity is ≤ 0.

21.2.2.9

The ambient liquid water content is < 0.

21.2.2.10

The ambient static temperature is ≤ 0.

21.2.2.11

The ambient static pressure is ≤ 0.

21.2.2.12

The ambient relative humidity is < 0% or > 100%.

21.2.2.13

The ambient Mach number is ≥ 1

21.2.2.13.1

The ambient Mach number is calculated from the 

equation:

NASA/CR—2002-211793 389
21.2.2.13.2

The terms in this equation are defined as follows:

M∞ = ambient Mach number (dimensionless)

V∞ = ambient velocity (m/s)

T∞ = ambient temperature (°K)

γ = heat capacity ratio = 1.4 (dimensionless)

R = ideal gas constant = 1430 m2/s2/°K

21.2.2.14

A given body geometry contains no data points.

21.2.2.15

One body geometry lies completely inside any other body 

geometry.

21.2.2.16

Any two body geometries intersect.

21.2.2.17

Blank lines are read as data with a value of zero.

Check input file for blank lines.

21.2.2.18

Layer number must be 1 < N < 30. 

21.2.2.19

Number of points in a layer must be 1 < N < 310

21.2.2.20

Length of a layer must be > 0.

21.2.2.21

Thermal conductivity of layer must be > 0.

21.2.2.22

Thermal diffusivity of layer must be > 0.

21.2.2.23

Anisotropic ratio of layer must be > 0.

21.2.2.24

Total number of points in normal direction is > 310.

21.2.2.25

Number of points in a section must be 1 < N < 310

21.2.2.26

Length of a section must be > 0

21.2.2.27

Thermal conductivity of section must be > 0

21.2.2.28

Thermal diffusivity of section must be > 0

21.2.2.29

Anisotropic ratio of section must be > 0

21.2.2.30

M∞

V ∞

γRT ∞

-----------------=

NASA/CR—2002-211793 390
Additional length of a section must be ≥ 0

21.2.2.31

Layer number for additional thickness must be 0 < N ≤

number of layers.

21.2.2.32

Total number of points in wrap direction < 310

21.2.2.33

Heater number must be 0 < N ≤ number of layers.

21.2.2.34

Number of parameter studies must be 0 < N < 30

21.2.2.35

Heater wattage must be ≥ 0

21.2.2.36

Heater on time must be ≥ 0

21.2.2.37

Heater off time must be ≥ 0

21.2.2.38

Heater lag time must be ≥ 0

21.2.2.39

Temperature control flag must be 0 ≤ N ≤ number of layers

21.2.2.40

Temperature control flag is on. ON temperature

must be > OFF temperature.

21.2.2.41

Temperature for temperature controlled heater

cannot be < the ambient temperature.

21.2.2.42

Slope cannot be zero.

21.2.2.43

Number of beta values input is out of range

21.2.2.44

Wrap distance value input is out of range.

21.2.2.45

Number of hot air values input is out of range

21.2.2.46

Number of streamline values input is out of range

21.2.2.47

The ice layer cannot be the same as the heater layer.

21.2.2.48

Heat transfer coefficient must be ≥ 0

NASA/CR—2002-211793 391
 References for Appendix A

Abbott, I. H., and A. E. von DoenHoff, “Theory of Wing Sections,” Dover Publications, New

York, 1959.

Al-Khalil, K. M., Keith, T. G., and K. J. De Witt, “Development of an Improved Model for

Runback Water on Aircraft Surfaces”,: AIAA 92-0042, Jan. 1992.

Anderson, D. A., Tannehill, J. C., and R. H. Pletcher, “Computational Fluid Mechanics and

Heat Transfer,” McGraw-Hill Book Company, New York, 1984.

Anderson, J. D., “Modern Compressible Flow with Historical Perspective,” McGraw-Hill

Book Company, New York, 1982.

Bilanin, A. J. “Proposed Modifications to Ice Accretion/Icing Scaling Theory,” AIAA88-

0203, Jan. 1988.

Bird, R.B., Stewart, W. E., and E. N. Lightfoot, “Transport Phenomena”, John Wiley & Sons,

Inc., New York, 1960.

Cansdale, J. T. and R. W. Gent, “Ice Accretion on Aerofoils in Two-Dimensional Compressible Flow - A Theoretical Model,” Royal Aircraft Establishment Technical Report 82128, 1983.

Carlson, D.J. and Haglund, R.F. “Particle Drag and Heat Transfer in Rocket Nozzles.” AIAA

Journal, Vol. 2, No. 11, 1964, pp. 1980-1984.

Chang, H., Frost, W., and Shaw, R.J. “Influence of Multidroplet Size Distribution on Icing

Collection Efficiency.” AIAA-83-0110, 1983.

Clift, R., “Bubbles, Drops and Particles”, Academic Press, New York, 1978.

Crowe, C., Sommerfeld, M., and Y. Tsuji, “Multiphase Flows with Droplets and Particles,”

CRC Press 1998.

NASA/CR—2002-211793 392
Dipprey, D. F., and R. H. Sabersky, “Heat and Momentum Transfer in Smooth and Rough

Tubes at Various Prandtl Numbers,” Int. J. Heat and Mass Transfer vol. 6, pp. 329-353, 1963.

Frost, W., Chang, H., Shieh, C. and K. Kimble, “Two Dimensional Particle Trajectory Computer Program,” Interim Report for Contract NAS3-224488, 1982.

Gent, R.W., and Cansdale, J.T.: “One-Dimensional Treatment of Thermal Transients in Electrically Deiced Helicopter Rotor Blades”, Technical Report 80159, Royal Aircraft Establishment,

Procurement Executive, Ministry of Defense, Farnborough, Hunts, England, 1980.

Hansman, R. J., A. Reehorst, and J. Sims, “Analysis of Surface Roughness Generation in Aircraft Ice Accretion,” AIAA-92-0298, Jan. 1992.

Hess, J. L. and Smith, A. M. O., “Calculation of Potential Flow About Arbitrary Bodies,”

Progress in Aeronautical Sciences, 8:1-138, (D. Kuchemann, editor), Pergmon Press, Elmsford,

New York, 1967.

Gear, C.W. “The Automatic Integration of Ordinary Differential Equations.” Comm. ACM

14, 1971, pp. 176-179.

Hobbs, P.V., “Ice Physics”, Oxford University Press, Ely House, London, 1974.

Hollworth, B. R., and R. D. Berry, “Heat Transfer from Arrays of Impinging Jets with Large

Jet-to-Jet Spacing,” J. of Heat Transfer, v. 100, pp. 352-7, May 1978.

Jones, K. F., “The Density of Natural Ice Accretions,” Fourth International Conference on

Atmospheric Icing of Structures, 1988, pp. 114-117.

Kays, W. M. and M. E. Crawford, “Convective Heat and Mass Transfer”, 2nd Edition,

McGraw-Hill Book Company, New York, 1980.

Kim, J. J., “Computational Particle Trajectory Analysis on a 3-Dimensional Engine Inlet,”

AIAA 85-0411, Jan. 1985.

NASA/CR—2002-211793 393
Macklin, W. C., and G. S. Payne, “A Theoretical Study of the Ice Accretion Process,” Quarterly Journal of the Royal Meteorological Society, 1967, Vol. 93, pp. 195-213.

Messinger, B. L.: “Equilibrium Temperature of an Unheated Icing Surface as a Function of

Air Speed”, J. Aeronaut. Sci., vol. 20, no. 1, Jan. 1953, pp. 29-42.

Miller, D., et. al, “Validation of NASA Thermal Ice Protection Computer Codes, Part 1: Program Overview,” AIAA 97-0049, Jan. 1997

Mills, A. F., “Heat and Mass Transfer,” ISBN 0-256-11443-9, 1995. 

Olsen, W., Shaw, R., and Newton, J. “Ice Shapes and the Resulting Drag Increase for an

NACA 0012 Airfoil.” NASA Technical Memorandum 83556, 1984.

Olsen, W. and E. Walker, “Experimental Evidence for Modifying the Current Physical Model

for Ice Accretion on Aircraft Surfaces,” NASA TM 87184, 1986.

Olsen, W., “Close-up Movies of the Icing Process on the Leading Edge of an Airfoil.” NASA

Lewis Research Center Movie C-313, 1985.

Perry, R. H., Green, D. W., and J. O. Maloney, “Perry’s Chemical Engineer’s Handbook,”

McGraw-Hill Book Company, 1984.

Press, W. H., Teukolsky, S. A., Vettering, W. T., and B. P. Flannery, “Numerical Recipes in

Fortran - The Art of Scientific Computing,” Second Edition, Cambridge University Press, New

York, 1992.

Reehorst, A. L., Ratvasky, T. P. and J. Sims, “Close-Up Analysis of Inflight Ice Accretion,”

AIAA 94-0804, 1994.

Rios, M., “Icing Simulations Using Jones’ Density Formula for Accreted Ice,” AIAA-91-

0556.

NASA/CR—2002-211793 394
Roache, P. J., “Verification and Validation in Computational Science and Engineering,” ISBN

0-913478-08-3, 1998. 

Scavuzzo, R. J. and Chu, M. L., “Structural Properties of Impact Ices Accreted on Aircraft

Structures”, NASA CR 179580, 1987.

Scavuzzo, R. J., Chu, M. L. and Kellackey, C. J., “Impact Ice Stresses in Rotating Airfoils”,

AIAA Paper 90-0198, 1990.

Schneider, G. E. and Zedan, M. “A Modified Strongly Implicit Procedure for the Numerical

Solution of Field Problems,” Numer. Heat Transfer, vol. 4, 1981, pp. 1-19.

Schneider, G. E. and Raw, M. J. ,“An Implicit Solution Procedure for Finite Difference Modeling of the Stefan Problem,” AIAA J., vol. 22, Nov. 1984, pp. 1685-1690.

Schlichting, H., Boundary-Layer Theory. F. J. Cerra, ED. New York, New York: McGrawHill, 1979.

Shin, J., “Characteristics of Surface Roughness Associated With Leading Edge Ice Accretion,” NASA TM106459 (AIAA-94-0799), Jan. 1994.

Steger, J.L., “Implicit Finite Difference of Flow About Arbitrary Geometries with Application

to Airfoils,” AIAA-77-665, 1977.

Tribus, M.V., et al. “Analysis of Heat Transfer Over a Small Cylinder in Icing Conditions on

Mount Washington.” American Society of Mechanical Engineers Transactions, Vol. 70, 1949, pp.

871-876.

Von Doenhoff, A. E. and E. A. Horton, “Low-Speed Experimental Investigation of the Effect

of Sandpaper Type Roughness on Boundary-Layer Transition,” NACA TN 3858, 1956.

White, F. M., “Viscous Fluid Flow,” McGraw-Hill, Inc., 1974.

NASA/CR—2002-211793 395
A

adhesion 172, 205, 391

AIRMD 116, 117, 118, 138, 150, 205

AIRUP 116, 117, 118, 138, 150

AK 95, 97, 128

AKX 100, 101

AL 95, 97

ALP 95, 97

ALPX 100, 101

ALX 100, 101

angle 42, 89, 90, 179, 180, 181, 186, 238, 256, 352, 353, 356, 377, 395

angle of attack 42, 60, 157, 158, 190, 256, 344, 345, 356, 394

anisotropy 95, 96, 97, 99, 100, 101, 103, 104, 148, 399

ANTICE iii, 21, 269

ANTICON 192, 338, 339

ANTICON2 192, 325, 340

anti-ice iii, 11, 12, 17, 21, 22, 27, 29, 30, 31, 48, 49, 69, 72, 74, 76, 98, 111, 113, 114, 115, 116,

118, 119, 120, 121, 128, 129, 131, 153, 171, 199, 202, 203, 204, 207, 242, 243, 249, 269, 296, 297,

309, 310, 322, 323, 325, 337, 339, 349, 384, 389, 393, 397

AOA 81, 190

array size 18, 20, 42, 44, 45, 88, 193, 194, 201, 202, 215

ASCII 37, 93, 141, 181, 342

automatic 17, 19, 38, 39, 40, 43, 215, 234

B

benchmark 16, 208, 211, 215, 242, 249, 358

BETA.DAT 23, 162, 163, 166, 192, 339

binary 157, 190, 191, 268, 342

bleed air iii, 11, 116, 117, 119, 120, 134, 137, 205, 243, 269, 322, 323, 324, 325, 339, 384, 385,

386, 387, 389, 396, 397

body iii, 10, 11, 18, 19, 20, 21, 22, 25, 26, 28, 30, 33, 34, 35, 41, 42, 45, 48, 49, 50, 60, 68, 82, 87,

88, 89, 90, 91, 92, 93, 95, 102, 103, 117, 121, 122, 130, 147, 154, 155, 156, 157, 159, 160, 163,

164, 165, 166, 170, 171, 172, 176, 178, 179, 188, 193, 194, 196, 197, 198, 256, 268, 325, 343, 344,

352, 353, 354, 356, 357, 359, 360, 361, 362, 364, 365, 366, 370, 372, 374, 375, 376, 377, 378, 379,

381, 382, 384, 385, 387, 389, 393, 394, 395, 398, 399

boundary condition 30, 93, 112, 113, 114, 115, 121, 122, 124, 125, 128, 149, 150, 171, 243, 390,

396, 397

boundary layer 52, 53, 54, 122, 168, 270, 338, 372, 373, 375, 377, 378, 382

BPRT 66, 162, 166

C

CD-ROM 13, 14, 16, 182

certification 10, 57, 211, 224, 284, 347, 394

CHORD 59, 344

chord 12, 19, 20, 21, 39, 43, 44, 59, 60, 71, 73, 75, 76, 77, 78, 81, 106, 117, 136, 154, 155, 156,

159, 160, 168, 172, 179, 202, 215, 224, 225, 269, 339, 344, 352, 353, 372, 374, 382, 396, 398

NASA/CR—2002-211793 396
CLEAN.DAT 169, 179

CLT 190

collection efficiency 21, 22, 23, 46, 47, 51, 52, 63, 66, 68, 72, 159, 162, 163, 166, 169, 207, 211,

215, 219, 220, 224, 225, 228, 229, 234, 238, 242, 243, 262, 263, 267, 280, 292, 305, 318, 323, 325,

326, 336, 338, 339, 344, 359, 361, 362, 379, 401

computation time 27, 50, 65, 181, 207, 211, 215, 220, 224, 229, 234, 238, 242, 249, 256, 263, 269,

284, 296, 309, 322, 325

computational domain 27, 28, 94, 102, 106, 117

conduction 11, 12, 121, 123, 124, 125, 168, 269, 397

control volume 11, 18, 20, 44, 45, 65, 66, 67, 163, 165, 168, 169, 171, 198, 202, 377

convergence 30, 131, 173, 175, 196, 199, 203

CONVERT 188, 189, 190

CTEMP.DAT 171

cycle time 93, 104, 107, 108, 269

cylinder 11, 18, 19, 20, 21, 43, 44, 45, 59, 202, 215, 216, 344, 404

D

debug 31, 36, 68, 87, 142, 167, 173, 175, 197, 204

default 16, 19, 20, 28, 36, 38, 40, 41, 42, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 56, 59, 60,

61, 62, 63, 64, 65, 66, 67, 68, 93, 102, 113, 117, 118, 119, 120, 154, 155, 156, 159, 160, 161, 167,

187, 188, 190, 207, 343, 392

de-ice 11, 12, 17, 21, 26, 27, 30, 34, 35, 48, 49, 93, 94, 98, 103, 104, 106, 107, 109, 110, 112, 113,

116, 120, 121, 123, 124, 127, 128, 129, 131, 132, 134, 139, 147, 153, 155, 171, 172, 173, 174, 175,

192, 202, 204, 205, 207, 242, 243, 244, 249, 250, 251, 254, 255, 269, 270, 272, 284, 286, 296, 297,

298, 309, 310, 311, 322, 327, 337, 389, 390, 398

de-icing iii

DENS.DAT 67, 163

density 19, 27, 39, 47, 96, 97, 110, 111, 149, 163, 168, 229, 340, 345, 356, 359, 362, 367, 374, 378,

382, 383, 389, 391, 393, 398, 402, 403

design 10, 48, 51, 52, 53, 54, 114, 191, 208, 322, 340, 342, 344, 347, 370

disk space 15, 24, 65, 170, 207, 211, 215, 220, 224, 229, 234, 238, 242, 249, 256, 263, 269, 284,

296, 309, 322, 325, 342

distribution iii, 12, 16, 22, 23, 26, 30, 31, 46, 55, 56, 57, 59, 90, 122, 124, 131, 133, 162, 176, 207,

220, 229, 256, 268, 324, 333, 338, 340, 347, 354, 373, 376, 393, 394, 398, 401

distribution disk 15, 16, 32, 162, 183, 207, 208, 211, 215, 221, 225, 229, 235, 239, 243, 249, 257,

263, 339

DOS 14, 16, 32, 33, 37, 38, 177, 181, 187, 189, 191, 341, 342

DPD 56, 59

drop 10, 22, 23, 24, 47, 55, 56, 57, 58, 59, 62, 63, 67, 92, 159, 162, 166, 169, 170, 195, 196, 197,

220, 225, 229, 256, 269, 350, 357, 358, 359, 360, 361, 362, 363, 365, 366, 376, 379, 381, 394, 398,

401

DSMN 18, 20, 21, 25, 44, 45, 87, 193, 194, 196, 197, 199, 200, 201, 202, 215, 239, 344

DTAUF 131, 132, 133, 139, 151, 204

DTAUI 31, 131, 132, 133, 139, 151, 204

DTAUM 131, 132, 133, 139, 151, 204

DUMMY.INP 173

NASA/CR—2002-211793 397
DYICE.DAT 67, 163, 192, 340

E

ELDE 30, 95, 97, 124, 128

electrothermal iii, 11, 17, 21, 29, 100, 105, 111, 119, 125, 128, 129, 171, 249, 269, 296, 309, 322,

323, 339, 349, 384, 385, 386, 389

ELX 100, 101

ELXY 100, 101

energy balance 30, 67, 118, 130, 168, 169, 198, 199, 203, 269, 376

EPRT 67, 168, 169

error 25, 26, 28, 32, 33, 34, 35, 36, 37, 40, 41, 42, 44, 45, 47, 48, 55, 56, 57, 59, 60, 61, 62, 63, 64,

65, 69, 71, 74, 76, 78, 82, 87, 89, 91, 95, 98, 99, 100, 102, 105, 106, 107, 108, 109, 112, 114, 116,

117, 121, 125, 139, 154, 155, 156, 157, 158, 159, 160, 161, 163, 164, 167, 172, 176, 178, 179, 183,

184, 185, 187, 189, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 269, 341, 343,

344, 345, 348, 369, 391, 393, 398

Euler 338, 345

evaporative 22, 128, 168, 199, 242, 243, 247, 248, 309, 322, 376, 377, 378, 384, 387, 388

example 17, 20, 21, 22, 28, 29, 32, 33, 36, 41, 43, 45, 46, 54, 56, 58, 59, 63, 65, 68, 78, 82, 88, 90,

94, 97, 98, 100, 101, 102, 103, 104, 106, 107, 110, 115, 117, 120, 125, 127, 129, 130, 133, 134,

136, 137, 138, 141, 142, 145, 147, 154, 162, 173, 174, 177, 178, 181, 186, 192, 202, 283, 336, 339,

341, 343

example case iii, 15, 24, 31, 33, 79, 93, 157, 195, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216,

217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 235, 236, 237,

238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 250, 251, 254, 255, 256, 257, 258, 259, 260, 261,

262, 263, 264, 265, 266, 267, 269, 270, 271, 272, 278, 279, 280, 281, 282, 284, 285, 286, 291, 292,

293, 294, 295, 296, 297, 298, 304, 305, 306, 307, 308, 309, 310, 311, 317, 318, 319, 320, 321, 322,

325, 326, 327, 332, 333, 334, 335, 342

EXAMPLES.BAT 207

exceedence 23, 57, 58, 62, 224, 225, 229

EXPAND 186, 188

experiment iii, 11, 23, 29, 30, 41, 44, 57, 60, 61, 63, 81, 120, 123, 157, 164, 176, 178, 180, 181,

182, 183, 184, 208, 211, 216, 224, 225, 234, 242, 256, 270, 271, 296, 297, 309, 310, 322, 344, 345,

350, 371, 391, 403, 404

external heat flux 53, 54, 76, 160

F

file name 14, 26, 32, 33, 34, 35, 82, 153, 155, 156, 158, 159, 160, 162, 175, 176, 177, 178, 182,

187, 189, 190, 191, 243, 250, 341, 343

FINAL1.DAT 163, 164, 166

FINAL2.DAT 164

FINAL3.DAT 164

FINAL4.DAT 164

FINAL5.DAT 164

FIXED.DAT 92, 164

flow iii, 10, 11, 12, 18, 25, 42, 44, 51, 60, 61, 65, 69, 76, 88, 89, 90, 118, 157, 158, 159, 164, 165,

168, 190, 191, 193, 195, 196, 197, 198, 207, 228, 256, 263, 264, 267, 268, 269, 322, 325, 338, 339,

NASA/CR—2002-211793 398
340, 343, 344, 345, 354, 356, 366, 367, 370, 372, 373, 375, 381, 387, 391, 393, 394, 398, 401, 404

FLOW.DAT 65, 164, 192, 339

FLUENT 338

FLWC 22, 23, 55, 56, 59

FORCE.DAT 172

FORCE2.DAT 172

FORT.2 192, 338, 340

FORT.26 192, 338, 340

FORT.54 175

FORT.80 175

FORT.81 175

FPRT 65, 66, 165

FRACT.DAT 67, 165

freezing fraction 165, 371, 379, 387

Frössling number 165

G

geometry iii, 10, 11, 14, 18, 19, 20, 22, 23, 25, 26, 27, 33, 34, 35, 44, 45, 49, 50, 51, 52, 53, 54, 66,

82, 87, 88, 89, 90, 91, 92, 93, 94, 100, 112, 154, 155, 156, 157, 163, 164, 172, 175, 176, 178, 179,

182, 185, 186, 187, 188, 193, 195, 208, 211, 215, 221, 225, 229, 235, 239, 243, 249, 257, 267, 268,

269, 270, 338, 339, 340, 344, 348, 352, 353, 354, 356, 357, 359, 360, 361, 364, 366, 370, 372, 374,

375, 376, 377, 378, 379, 381, 382, 384, 387, 389, 390, 393, 394, 395, 398, 399

GEOMETRY.DAT 172

glaze ice 18, 19, 23, 133, 208, 211, 225, 234, 238, 345

grid iii, 12, 27, 30, 47, 48, 51, 53, 94, 95, 98, 100, 124, 140, 143, 157, 159, 165, 171, 172, 175, 190,

191, 195, 204, 256, 263, 264, 267, 268, 269, 337, 338, 344, 350, 366, 367, 372, 375, 389, 392, 393

GRIDGEN 263, 338, 350

H

H1 29, 114, 115, 116, 121, 150

H2 114, 115, 150

H3 114, 115, 150

H4 114, 115, 150

heat flux 11, 21, 27, 29, 49, 53, 54, 76, 107, 109, 113, 114, 115, 118, 119, 120, 121, 137, 150, 155,

160, 161, 171, 173, 269, 296, 309, 325, 338, 339, 384, 385, 386, 390, 391, 396, 397

heat transfer coefficient 11, 22, 27, 29, 48, 50, 52, 53, 54, 66, 74, 107, 114, 115, 116, 119, 121, 122,

134, 135, 137, 150, 153, 154, 160, 161, 165, 170, 171, 207, 210, 214, 218, 223, 227, 233, 237, 241,

243, 250, 255, 260, 261, 263, 266, 270, 279, 284, 291, 297, 304, 310, 317, 322, 323, 324, 325, 326,

333, 335, 338, 339, 344, 372, 373, 374, 375, 376, 385, 387, 388, 390, 391, 400

heater 11, 12, 29, 35, 48, 49, 93, 95, 98, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 120,

121, 122, 125, 133, 142, 147, 148, 149, 171, 172, 173, 244, 245, 250, 251, 252, 255, 269, 270, 271,

272, 273, 274, 278, 280, 281, 282, 283, 284, 286, 287, 293, 294, 295, 296, 297, 298, 300, 305, 306,

307, 308, 309, 310, 311, 312, 318, 319, 320, 321, 327, 328, 384, 385, 386, 389, 397, 400

HI.INP 93, 119, 135, 153

hot air iii, 12, 17, 21, 29, 49, 105, 107, 113, 114, 115, 116, 117, 119, 129, 137, 139, 151, 153, 155,

171, 242, 246, 247, 248, 249, 253, 274, 288, 296, 300, 309, 313, 322, 325, 329, 339, 400

NASA/CR—2002-211793 399
HPRT 66, 165, 168

HTC.DAT 66, 165, 192, 339

I

I3D 93, 118, 120, 137, 138, 150, 156, 192

IBC1 112, 113, 115, 150

IBC2 30, 112, 113, 115, 121, 122, 150

IBC3 112, 113, 115, 150

IBC4 112, 113, 115, 150

IBETA 51, 52, 72, 93, 159, 192, 339

IBLEED 29, 93, 118, 119, 120, 134, 135, 138, 150, 153, 340

IBOUND 29, 30, 114, 120, 121, 122, 124, 125, 126, 127, 138, 150, 397

ice accretion iii, 10, 11, 20, 21, 22, 24, 26, 39, 45, 47, 48, 49, 50, 51, 52, 53, 54, 64, 90, 121, 122,

124, 125, 208, 224, 225, 234, 256, 257, 263, 269, 347, 349, 350, 401, 402, 403, 404

ice growth ii, iii, 10, 131, 175, 193, 199, 371

ice shape iii, 12, 15, 17, 18, 19, 20, 21, 22, 40, 43, 45, 47, 48, 49, 123, 131, 140, 157, 163, 164,

165, 166, 169, 172, 176, 178, 180, 181, 183, 184, 193, 196, 197, 198, 199, 201, 205, 207, 209, 213,

215, 216, 217, 220, 222, 224, 225, 226, 229, 231, 232, 234, 236, 238, 240, 256, 258, 265, 270, 284,

325, 334, 344, 345, 371, 392, 403

ice thickness iii, 10, 27, 30, 98, 124, 163, 165, 169, 176, 179, 180, 181, 198, 207, 209, 213, 218,

220, 222, 227, 229, 231, 232, 236, 240, 259, 260, 265, 270, 284, 334, 352, 353, 354

ICE1.DAT 25, 26, 87, 89, 165, 166, 169

ICE2.DAT 166

ICE3.DAT 166

ICE4.DAT 166

ICE5.DAT 166

iced geometry 11, 20, 164, 166, 176, 178, 179, 182, 184, 185, 193, 194, 196, 197, 198, 201, 202,

340

ICFLAG 107, 110, 111, 149

icing iii, 10, 11, 12, 20, 22, 27, 40, 41, 44, 48, 59, 62, 74, 98, 113, 114, 116, 121, 122, 124, 128,

131, 171, 179, 181, 183, 211, 224, 229, 242, 243, 256, 346, 347, 349, 350, 396, 397, 401, 402, 403,

404

icing limit 167, 179, 180, 181, 184, 185, 211, 224, 225, 284, 345

ICOND 30, 120, 121, 122, 123, 124, 126, 127, 138, 150, 397

ICP 50, 51, 69, 93, 158, 165, 192, 339

IDBF 68, 167

IDEICE 17, 21, 26, 27, 35, 48, 49, 50, 93, 128, 129, 171, 172, 190, 202, 242, 243, 249, 250, 284,

396

IEVAP 128, 129, 138, 150, 297, 310

IFLO 38, 39, 40, 42, 43, 48, 51, 52, 53, 54, 193, 196, 197, 199, 200, 201, 204, 270, 284

IGDE 30, 120, 124, 125, 126, 127, 138, 150, 397

IGRID 47, 48, 51, 93, 165, 171, 172

IHTC 52, 53, 54, 74, 93, 122, 160, 192, 339

IJDE 105, 106, 110, 111, 119, 125, 128, 149

ILAYER 143, 144, 145

IMP.DAT 23, 163, 166, 167

NASA/CR—2002-211793 400
impingement iii, 10, 21, 134, 166, 225, 322, 344, 350, 377

impingement limit 22, 23, 46, 163, 166, 167, 196, 197, 198, 224, 264, 310, 360, 361, 362

INIT 30, 120, 122, 123, 124, 125, 126, 127, 138, 150, 397

input file 12, 13, 14, 15, 17, 18, 20, 21, 22, 25, 26, 28, 32, 33, 34, 35, 36, 37, 45, 47, 48, 49, 50, 69,

71, 74, 76, 78, 79, 82, 87, 88, 93, 95, 98, 105, 106, 112, 113, 116, 117, 118, 119, 120, 121, 128,

129, 131, 132, 133, 135, 136, 139, 147, 153, 155, 156, 157, 158, 159, 160, 161, 162, 164, 171, 172,

173, 174, 176, 177, 178, 187, 188, 189, 190, 195, 197, 200, 204, 205, 207, 208, 211, 212, 215, 216,

220, 221, 225, 229, 230, 234, 235, 239, 243, 244, 249, 250, 251, 257, 263, 264, 267, 271, 272, 284,

286, 297, 298, 310, 311, 326, 327, 339, 341, 342, 343, 344, 348, 394, 396, 399

interpolation 186, 195, 200, 201, 325

IOTYPE 31, 141, 142, 143, 144, 145, 146, 147, 152, 153, 173, 174, 175, 192

IPAR 28, 105, 106, 110, 111, 149

IQAIN 29, 93, 118, 120, 137, 138, 150, 155

IQEX 53, 54, 76, 93, 160

IQW 29, 107, 118, 119, 120, 138, 150, 172

IRIX 15, 16, 32, 33, 36, 37, 38, 87, 177, 178, 187, 189, 190, 191, 341, 342

IROT 30, 129, 130, 138, 151

IRT ii, 64, 224, 270, 284

ISCOLA 134, 135, 137, 139, 151

ISCOLB 71, 72

ISCOLC 69, 70

ISCOLH 74, 75

ISCOLQ 137, 139, 151

ISCOLS 137, 138, 139, 151

ISCOLX 76, 77

ISH 120, 123, 125, 126, 127, 138, 150, 172

ISTD 120, 123, 124, 126, 127, 138, 150, 397

ITHERM 128, 129, 138, 150

ITIME 140, 141, 151, 175

ITIMFL 38, 39, 40, 43, 215, 234

IVXY 100, 101

IWHERE 143, 144

J

JCOUNT 133

JCOUNTD 131, 133, 139, 151, 204

JLAYER 143, 144, 145

JSCOLA 134, 135, 137, 139, 151

JSCOLB 71, 72

JSCOLC 69, 70

JSCOLH 74, 75

JSCOLQ 137, 139, 151

JSCOLS 137, 138, 139, 151

JSCOLX 76, 77

JUNK.DAT 36, 38, 68, 87, 167, 202

JWHERE 143, 144, 145

NASA/CR—2002-211793 401
K

KSCOLA 134, 135, 137, 139, 151

KSCOLB 71, 72, 73

KSCOLC 69, 70

KSCOLH 74, 75

KSCOLQ 137, 139, 151

KSCOLS 137, 138, 139, 151

KSCOLX 76, 77

L

LAG time 104, 107, 108, 400

laminar 26, 48, 50, 270, 284, 296, 309, 373, 374, 375, 377

layer 11, 21, 27, 28, 30, 31, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 119,

124, 125, 131, 141, 143, 145, 146, 147, 148, 152, 153, 204, 385, 386, 391, 392, 395, 399, 400

LDE 94, 95, 103, 125, 128, 144, 147

leading edge 23, 25, 26, 28, 50, 59, 71, 73, 75, 78, 89, 91, 102, 106, 117, 136, 162, 163, 166, 167,

169, 179, 181, 185, 186, 220, 269, 309, 344, 403, 404

LEWI3DGR 72, 74, 338, 340

LEWICE/Thermal iii, 21, 31, 269

LEWICE3D 192, 325

LIMIT.DAT 167, 185, 345

LWC 10, 19, 39, 61, 62, 81, 379, 381

M

Mach number 61, 81, 158, 268, 345, 367, 368, 369, 394, 398, 399

mass balance 67, 163, 165, 167, 381

mass diffusivity 379

MASS.DAT 67, 167

meteorological ii, 10, 59, 106, 211, 394, 403

MISC.DAT 38, 168

monodispersed 59, 220, 225, 229, 232, 256

MPRT 67, 163, 165, 167

MSIP 133, 204

multi-body 20, 41, 42, 45, 48, 59, 171, 176, 193, 198, 343, 344

multi-element 11, 12, 21, 22, 26, 42, 49, 59, 91, 193, 197, 256, 343, 344

MVD 22, 23, 56, 57, 58, 59, 62, 81

N

namelist 17, 36, 37, 38, 40, 54, 55, 58, 59, 65, 68, 69, 78, 190, 343

Naviér-Stokes iii, 12, 69, 74, 76, 190, 191, 263, 338, 345

Newton-Raphson 197, 199, 202, 203

NISP 131, 132, 133, 139, 151

NMSP 131, 132, 133, 139, 151

NODE 95, 97, 103, 148, 204

node 30, 31, 101, 123, 124, 131, 133, 141, 142, 143, 148, 158, 174, 175, 204, 205

NOICE.DAT 27, 50, 171, 243

NASA/CR—2002-211793 402
normal direction 28, 30, 94, 95, 96, 98, 99, 100, 122, 124, 142, 143, 147, 174, 205, 364, 399

note 17, 19, 25, 31, 33, 35, 37, 43, 44, 45, 46, 49, 50, 59, 60, 63, 64, 67, 68, 82, 89, 94, 95, 96, 97,

98, 101, 102, 104, 105, 106, 107, 109, 111, 112, 114, 115, 116, 119, 120, 121, 122, 123, 124, 126,

128, 130, 131, 137, 139, 141, 142, 154, 155, 157, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169,

171, 172, 173, 174, 177, 179, 182, 185, 187, 188, 189, 190, 191, 215, 224, 234, 242, 243, 249, 250,

256, 270, 284, 323, 325, 339, 341, 345, 347, 351

NOX 100, 101

NPARC 263, 267, 268, 350

NPL 46

NPRF 140, 141, 151, 175

NPRT 140, 141, 151

NPTSD 142, 143, 144, 145, 146, 147, 152, 153

NTYPE 141, 142, 143, 145, 151

Nusselt number 165

NXDE 94, 95, 100, 103, 107, 144, 145, 147

O

OFF temperature 29, 105, 107, 109, 119, 400

OFF time 104, 107, 108, 400

OFFSET 28, 100, 102, 105, 106, 110, 111, 149

ON temperature 29, 105, 107, 109, 119, 400

ON time 104, 107, 400

operating system 13, 32, 33, 178, 342

P

panel iii, 18, 20, 21, 25, 26, 44, 45, 46, 47, 50, 66, 87, 88, 89, 90, 164, 194, 229, 264, 365

parting strip 29, 101, 104, 105, 110, 111, 142, 148, 149, 269, 271, 284

PC 13, 14, 15, 16, 32, 33, 37, 140, 177, 188, 207, 268, 341, 342

PEAKS.DAT 180, 185

phase change 30, 124, 125, 133, 175, 203, 204, 205, 397

physical domain 27, 28, 94, 102

physical property 35, 93

PINF 63, 64

platform 16, 32, 37, 140, 190, 191, 207, 208, 211, 268, 342

PLOT3D 12, 47, 140, 141, 157, 158, 190, 191, 192, 268, 340, 342, 344, 350

PLOT3D.Q 192, 340

PLOT3D.XYZ 192, 340

points 18, 19, 20, 23, 25, 26, 28, 33, 41, 45, 47, 62, 87, 88, 89, 90, 91, 95, 97, 98, 99, 100, 103, 142,

145, 146, 148, 152, 153, 154, 155, 156, 157, 158, 159, 160, 163, 164, 165, 166, 167, 178, 179, 186,

187, 188, 201, 229, 238, 256, 263, 338, 339, 344, 352, 353, 354, 366, 394, 395, 399, 400

potential flow iii, 12, 18, 30, 47, 48, 50, 51, 60, 61, 130, 157, 164, 165, 256, 264, 338, 345, 349,

364, 365, 367, 369, 402

PRES.DAT 65, 168

pressure 10, 24, 63, 64, 159, 168, 345, 364, 366, 367, 368, 378, 398

pressure coefficient 50, 51, 69, 158, 159, 164, 171, 210, 214, 219, 220, 223, 233, 237, 241, 243,

262, 266, 279, 292, 304, 317, 323, 325, 326, 335, 345, 364, 366, 367, 369

NASA/CR—2002-211793 403
Q

Q.PLT 47, 93, 157, 190, 191

Q.TXT 190, 191

QAI.INP 93, 137

QAIN.INP 118, 155

QDE 29, 107, 110, 111, 149

QENER.DAT 67, 168

QEXTIN.INP 53, 78, 93, 160

QOPT.DAT 29, 109, 120, 172

QW1 29, 114, 115, 150

QW2 114, 115, 150

QW3 114, 115, 150

QW4 114, 115, 150

R

RBETA.INP 51, 74, 93, 159

RDATA 17, 69, 78, 188, 343

REDUCE 192, 271

relative humidity 10, 24, 64, 65, 398

request 346, 347

Reynolds number 61, 81, 158, 165, 257, 356, 359, 362, 372, 373, 374

RFLOW.INP 50, 71, 93, 158, 159

RH 64

RHOP 47

RHTC.INP 52, 76, 93, 160

rivulet 12, 325, 349

rotational 30, 129, 130

roughness 170, 270, 371, 373, 374, 375, 382, 402, 404

RPM 30, 129, 130, 138, 151, 391

runback 11, 12, 118, 163, 165, 167, 203, 270, 284, 349, 379, 380, 381, 392, 401

running wet 22, 128, 249, 250, 254, 255, 296, 384

runtime error 17, 45, 193, 269

S

section 11, 28, 29, 94, 95, 97, 100, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 123, 124, 142,

143, 144, 145, 147, 148, 152, 153, 173, 271

SGI 16, 32, 37, 87, 188, 268, 342

shed iii, 11, 12, 30, 31, 123, 124, 125, 130, 172, 205, 284, 381, 382, 391, 392, 397

SLOPE 95, 97, 148

slope 71, 73, 75, 77, 78, 95, 96, 97, 100, 101, 103, 104, 136, 244, 400

SLOPEX 100

SLOPX 101

specific heat 27, 97

SSLOPA 134, 136, 137, 139, 151, 154

SSLOPB 71, 73

SSLOPC 69, 71

NASA/CR—2002-211793 404
SSLOPH 74, 75, 76

SSLOPQ 137, 139, 151

SSLOPS 137, 138, 139, 151

SSLOPX 76, 77, 78

STA 30, 129, 130, 138, 151

stagnation 50, 162, 163, 165, 166, 167, 168, 169, 170, 171, 220, 344, 370, 371, 372, 373, 374, 375,

381

STREAM.DAT 192, 339

STREAM.INP 93, 118, 138, 156

streamline 69, 118, 137, 138, 139, 151, 156, 192, 325, 338, 340, 397, 400

Sun 16

system error 32, 36, 37, 38, 87, 177, 187, 188, 189, 190, 191

SZEROA 134, 136, 137, 139, 151, 154

SZEROB 71, 73

SZEROC 69, 71

SZEROH 74, 75, 76

SZEROQ 137, 139, 151

SZEROS 137, 138, 139, 151

SZEROX 76, 78

T

TAFTER 133, 134, 139, 151

TAIRH 116, 118, 138, 150

technical support 347, 348

TECPLOT 12, 140, 340

TEMP.DAT 67, 169, 192, 340

temperature iii, 10, 11, 12, 21, 22, 24, 26, 29, 30, 31, 49, 50, 54, 62, 63, 81, 95, 96, 100, 104, 105,

107, 108, 109, 110, 112, 113, 115, 116, 119, 120, 122, 123, 124, 125, 128, 131, 133, 139, 141, 142,

143, 144, 145, 150, 168, 169, 171, 172, 173, 174, 175, 192, 198, 199, 202, 203, 204, 205, 207, 243,

248, 250, 255, 269, 270, 271, 280, 281, 282, 283, 284, 293, 294, 295, 296, 297, 305, 306, 307, 308,

310, 318, 319, 320, 321, 322, 324, 325, 333, 340, 349, 368, 376, 377, 378, 379, 380, 384, 385, 386,

389, 390, 391, 394, 396, 397, 398, 399, 400, 403

TEMPS1.DAT 173, 174, 192, 270, 271

TEMPS1A.DAT 192

TEMPS2.DAT 173, 174, 192, 271

TEMPS2A.DAT 192

TEMPS3.DAT 173, 174, 192, 270, 271

TEMPS3A.DAT 192

TEMPS4.DAT 173, 174, 270

TEMPS5.DAT 173, 174, 270

TEMPS6.DAT 173

TEMPS7.DAT 173

TG1 113, 115, 150

TG2 113, 115, 150

TG3 113, 115, 150

TG4 113, 115, 150

NASA/CR—2002-211793 405
thermal 11, 12, 26, 27, 30, 50, 98, 100, 105, 124, 249, 254, 255, 269, 284, 296, 309, 322, 325, 349,

374, 395, 398, 402, 403

thermal conductivity 27, 95, 96, 97, 99, 100, 101, 103, 104, 107, 115, 119, 137, 148, 161, 171, 374,

376, 379, 385, 389, 399

thermal diffusivity 95, 96, 97, 99, 100, 101, 103, 104, 148, 399

thermocouple 142, 143, 173, 174, 192, 270, 271, 284

THICK 164, 167, 169, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 345

THICK.DAT 169, 207

time step iii, 12, 17, 18, 19, 20, 22, 23, 24, 30, 31, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 51, 52,

53, 54, 93, 131, 132, 133, 141, 142, 157, 162, 163, 164, 165, 166, 167, 169, 170, 172, 175, 192,

193, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204, 206, 207, 215, 234, 238, 242, 256, 263, 270,

284, 344, 345, 383, 393, 395, 398

TINF 62, 63, 113

TLAG 107, 110, 111, 149

TOASCII 191, 268

TOBINARY 190, 268

TOFF 29, 107, 110, 111, 149

TON 107, 110, 111, 149

TOTAL.TXT 181

TPRT 25, 67, 68, 169

trailing edge 25, 26, 28, 50, 59, 71, 73, 75, 76, 78, 88, 89, 91, 102, 106, 112, 117, 136, 154, 155,

156, 159, 160, 161, 164, 165, 184, 256, 344, 396

TRAJ1.DAT 67, 68, 169, 170

TRAJ2.DAT 67, 170

TRAJ3.DAT 67, 170

TRAJ4.DAT 67, 170

TRAJ5.DAT 67, 170

trajectory iii, 10, 21, 23, 24, 26, 30, 31, 46, 47, 48, 51, 52, 67, 68, 72, 74, 91, 118, 130, 159, 168,

169, 170, 172, 195, 196, 197, 198, 269, 338, 349, 354, 355, 357, 358, 360, 361, 362, 365, 366, 393,

402

transient 21, 27, 31, 48, 97, 131, 204, 402

TSPRAY 133, 134, 139, 151

TSTOP 29, 40, 41, 109, 120, 323

TSURF 128, 129, 138, 150

turbulent 270, 284, 296, 374, 375, 377

U

unix 13, 16, 32, 33, 37, 140, 177, 178, 341, 342

V

validation iii, 15, 16, 17, 18, 19, 20, 22, 23, 25, 39, 41, 43, 44, 45, 46, 57, 58, 60, 61, 62, 63, 64,

81, 82, 162, 176, 179, 180, 181, 182, 186, 192, 193, 196, 207, 208, 211, 215, 220, 224, 225, 256,

267, 345, 349, 403, 404

variability 16, 19, 39, 208, 211, 284

velocity 10, 19, 39, 47, 60, 61, 63, 81, 157, 163, 164, 168, 171, 195, 197, 344, 356, 359, 362, 364,

365, 366, 367, 369, 370, 373, 374, 379, 382, 391, 398, 399

NASA/CR—2002-211793 406
VINF 60, 61

VSAERO 338

W

warning 15, 23, 30, 34, 35, 36, 39, 40, 41, 42, 43, 45, 46, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 60,

61, 62, 64, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 87, 88, 89, 90, 91, 106, 113, 114,

116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 128, 129, 130, 131, 132, 133, 134, 135, 136,

137, 138, 140, 141, 142, 144, 145, 154, 155, 156, 159, 160, 167, 187, 190, 197, 200, 201, 203, 204,

205, 216, 224, 229, 234, 238, 242, 249, 256, 393, 394, 395

wattage 29, 35, 104, 107, 108, 109, 119, 120, 128, 129, 173, 203, 243, 250, 296, 309, 400

WIND 69, 76

Windows 14, 15, 32, 37, 38, 177, 187, 189, 191, 342

wrap direction 94, 96, 100, 122, 143, 147, 174, 205, 400

wrap distance 20, 21, 23, 28, 45, 50, 51, 52, 53, 54, 69, 71, 72, 73, 74, 75, 76, 77, 78, 100, 102,

118, 135, 136, 137, 138, 141, 142, 154, 155, 156, 159, 160, 162, 163, 164, 165, 166, 167, 168, 169,

170, 171, 172, 173, 174, 175, 179, 202, 203, 204, 205, 207, 215, 220, 270, 339, 352, 353, 361, 373,

375, 391, 400

X

XAIRMD 116, 117, 118, 138, 150

XKINIT.DAT 170

XKINIT2.DAT 67, 170

XY.PLT 47, 93, 157, 190, 191

XY.TXT 190, 191

NASA/CR—2002-211793 407
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

REPORT DOCUMENTATION PAGE

2. REPORT DATE

19. SECURITY CLASSIFICATION

 OF ABSTRACT

18. SECURITY CLASSIFICATION

 OF THIS PAGE

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources,

gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this

collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson

Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

Form Approved

OMB No. 0704-0188

12b. DISTRIBUTION CODE

8. PERFORMING ORGANIZATION

 REPORT NUMBER

5. FUNDING NUMBERS

3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE

6. AUTHOR(S)

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS

17. SECURITY CLASSIFICATION

 OF REPORT

16. PRICE CODE

15. NUMBER OF PAGES

20. LIMITATION OF ABSTRACT

Unclassified Unclassified

Final Contractor Report

Unclassified

1. AGENCY USE ONLY (Leave blank)

10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington, DC 20546–0001

Available electronically at http://gltrs.grc.nasa.gov

August 2002

NASA CR—2002-211793

E–13488

WU–708–20–13–00

NAG3–00145

413

User Manual for the NASA Glenn Ice Accretion Code LEWICE

Version 2.2.2

William B. Wright

Aircraft icing; Deicing

Unclassified -Unlimited

Subject Categories: 02, 34, and 64 Distribution: Nonstandard

QSS Group, Inc.

21000 Brookpark Road

Cleveland, Ohio 44135

A research project is underway at NASA Glenn to produce a computer code which can accurately predict ice growth under

a wide range of meteorological conditions for any aircraft surface. This report will present a description of the code inputs

and outputs from version 2.2.2 of this code, which is called LEWICE. This version differs from release 2.0 due to the

addition of advanced thermal analysis capabilities for de-icing and anti-icing applications using electrothermal heaters or

bleed air applications. An extensive effort was also undertaken to compare the results against the database of electrothermal

results which have been generated in the NASA Glenn Icing Research Tunnel (IRT) as was performed for the validation

effort for version 2.0. This report will primarily describe the features of the software related to the use of the program.

Appendix A of this report has been included to list some of the inner workings of the software or the physical models used.

This information is also available in the form of several unpublished documents internal to NASA. This report is intended

as a replacement for all previous user manuals of LEWICE. In addition to describing the changes and improvements made

for this version, information from previous manuals may be duplicated so that the user will not need to consult previous

manuals to use this code.

Project Manager, Thomas Bond, Turbomachinery and Propulsion Systems Division, NASA Glenn Research Center,

organization code 5840, 216–433–3900.