August 2010 

NASA/CR–2010-216731 

Aero-Structural Assessment of an Inflatable 

Aerodynamic Decelerator 

Essam F. Sheta, Vinod Venugopalan, X. G. Tan, Peter A. Liever, and Sami D. Habchi 

CFD Research Corporation, Huntsville, Alabama 
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August 2010 

NASA/CR–2010-216731 

Aero-Structural Assessment of an Inflatable 

Aerodynamic Decelerator 

Essam F. Sheta, Vinod Venugopalan, X. G. Tan, Peter A. Liever, and Sami D. Habchi 

CFD Research Corporation, Huntsville, Alabama 
Available from: 

NASA Center for AeroSpace Information 

7115 Standard Drive 

Hanover, MD 21076-1320 

443-757-5802 

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Administration. 
i 8927/6

SUMMARY

NASA is conducting an Entry, Descent and Landing Systems Analysis (EDL-SA) Study to 

determine the key technology development projects that should be undertaken for enabling the 

landing of large payloads on Mars for both human and robotic missions. Inflatable Aerodynamic 

Decelerators (IADs) are one of the candidate technologies. A variety of EDL architectures are 

under consideration. The current effort is conducted under NASA SBIR Phase III program for 

development and simulations of computational framework for inflatable structures. 

In the Phase I study of this program, the feasibility of the CFDRC‟s Multi-Disciplinary 

Integrated Computing Environment (MDICE) was demonstrated for simulations of thin-walled 

ballute configurations. The simulations were conducted using CFDRC‟s in-house fluid dynamics 

and structural dynamics codes. In the Phase II study, selected codes were implemented and 

integrated into the MDICE framework for aeroelastic simulations of ballute configurations. The 

selected codes include NASA LaRC CFD FUN3D code, NASA JSC DSMC DAC code, and 

ABAQUS finite element structural dynamics code. The framework was validated by conducting 

aeroelastic simulations of the NASA Langley wind tunnel model for a 6-inch clamped ballute. 

The results compared fairly well with the wind tunnel data. The framework was also 

demonstrated for coupled fluid structure interaction of nonlinear model of attached ballute 

configuration supplied by Ball Aerospace. 

The objective of this Phase III effort is to provide computational aero-structural and dynamic 

analysis and simulations to support the EDL-SA assessments of IAD controllability and 

structural integrity for Mars Aerocapture and EDL. Several design configurations and analyses 

are considered to determine the candidate technology that meets the requirements. Among the 

important considerations for IADs is whether they provide the desired controllability and can 

withstand the loads induced by banking maneuvers.

Geometrical and grid models for the considered IAD configurations are developed and tested. 

NASA provided CFDRC with the geometrical models, flow conditions, the material properties, 

and other information as needed to perform the simulations. The notional model was for double 

stack Toroids configuration consists of 23 toroidal tubes. A reacting thermally perfect CO2 

model was used to simplify the Mars atmosphere. A coupled dynamic aero-structural simulations 

are performed for all cases using Euler CFD analysis, structural Finite-Element (FEM) analysis, 

and prescribed trajectory motion. Extensive FEM simulations were conducted with various 

dynamic and internal pressures and using variable fidelity CFD calculated loads. The aeroelastic 

responses of the model were computed using two-way fluid-structure interaction (FSI) coupling. 

In addition, aeroelastic responses of several cases were also computed using one-way FSI 

coupling from the fluid to the structure. The structural deformations and stresses exhibited 

mostly cyclic behavior over the model and tended to fluctuate around almost constant mean 

values. The results show dramatic decrease of the aeroelastic deformations when the effects of 

radial enforcement straps are added to the model. The von Mises stress levels on the Gores and 

Toroids were far less than the yield stress of the materials of the Gores and Toroids.
ii 8927/6

A new IAD configuration model based on single stack Toroids was also considered. The 

aerodynamic flowfield and forces of the single stack Toroids configuration were very similar to 

the double stack Toroids configuration. There were small increases in the displacements and in 

the von Mises stresses. The single stack Toroids configuration model was also tested at multiples 

of the reference dynamic pressure. The dynamic response showed an increased number of modes 

with an increase in flow dynamic pressure. The stresses were still within limits even for the case 

with 1.5 times the reference dynamic pressure.
iii 8927/6

PREFACE

This is the final report for the NASA SBIR Phase III contract entitled “Aero-Structural 

Assessment of an Inflatable Aerodynamic Decelerator”. This project is sponsored by NASA 

Langley Research Center as follow-on to Phase II SBIR (NASA Contract Number 

NNM06AA10C). The effort is performed by CFD Research Corporation (CFDRC Project 

Number 8927). The principal investigator is Dr. Essam F. Sheta, and the co-investigator was Mr. 

Vinod Venugopalan. The Project Manager is Mr. Sami D. Habchi. The technical monitor of this 

project is Dr. Jamshid Samareh (NASA Langley Research Center).
iv 8927/6

ACKNOWLEDGEMENTS 

The authors of this report would like to express their appreciation to the technical monitor Dr. 

Jamshid Samareh of NASA Langley Research Center for his close participation and discussions 

regarding the content and direction of this effort. The author would also like to thank Ms. 

Michelle Munk, Mr. Robert Dillman, and Mr. Thomas Zang of NASA Langley Research Center 

for their feedback on the direction of the effort.
v 8927/6

TABLE OF CONTENTS

1 Introduction .......................................................................................................................... 14

1.1 Background .................................................................................................................. 14

1.2 Work Scope.................................................................................................................. 15

2 Geometry Modeling And Grid Generation........................................................................... 18

2.1 Computational Grid Model for Double-Stacked IAD Configuration........................... 18

2.2 Computational Structural Dynamics Model for Double-Stacked IAD Configuration . 21

2.3 CFD Flow and Flight Conditions for the IAD Configurations..................................... 23

2.4 Aerodynamic Forces and Reference Quantities ........................................................... 23

3 Computational Methodology................................................................................................ 25

3.1 CFD Solver – CFD-FASTRAN ................................................................................... 25

3.1.1 Computational Chemistry Model for Mars Atmosphere.......................................... 25

3.2 FEM Solver – CFDRC-FEM........................................................................................ 27

3.3 MDICE Infrastructure .................................................................................................. 28

3.3.1 MDICE Controller.................................................................................................... 30

3.3.2 Multi-Physics Analysis Modules.............................................................................. 30

3.3.3 Multi-Physics Interfacing Modules.......................................................................... 31

3.4 Coupling Methods........................................................................................................ 32

4 Steady Aerodynamic Flowfield For The Double Stack IAD Configuration ........................ 34

4.1 Steady State Aerodynamic Simulation Results............................................................ 34

4.2 Computational Structural Analysis............................................................................... 40

4.2.1 Static FEM Analysis of the MIAS Model with Constant Loading........................... 40

4.2.2 Static FEM Analysis of the Modified MIAS Model ................................................ 41

4.3 Summary ...................................................................................................................... 47

5 Aeroelastic and Dynamic Analysis Of The Double Stack IAD Configuration .................... 48

5.1 Aerodynamic Forces for the Aeroelastic Dynamic Maneuver ..................................... 48

5.2 Aeroelastic Structural Deformations............................................................................ 51

5.3 Aeroelastic Structural Stresses..................................................................................... 56

5.4 Summary ...................................................................................................................... 60

6 Aeroelastic and Dynamics analysis of a Modified Double Stack IAD Configuration 

including Radial straps................................................................................................................. 61

6.1 Effect of Toroids Inflation Pressure on IAD Dynamics............................................... 61

6.2 Effect of Coarse Grid on the Solution .......................................................................... 63

6.2.1 Effect of Grid Coarsening on Aerodynamic Forces and Moments .......................... 63

6.2.2 Effect of Grid Coarsening on Structural Deformations............................................ 66

6.3 Effect of Modeling Radial Straps................................................................................. 68

6.3.1 Aerodynamic Forces and Moments.......................................................................... 68

6.3.2 Aeroelastic Structural Deformations........................................................................ 72

6.3.3 Structural von Mises Stresses................................................................................... 78

6.4 Summary ...................................................................................................................... 80

7 Aeroelastic and Dynamic analysis of a Single Stack IAD Configuration............................ 81

7.1 Computational Fluid Dynamics Model for Single Stack IAD Configuration .............. 81

7.2 Computational Structural Dynamics Model for Single Stack IAD Configuration....... 82

7.3 Steady State Aerodynamic Simulation Results of Single Stack IAD Configuration.... 84

7.4 Transient FEM Simulation of the Single Stack IAD Dynamics................................... 85
vi 8927/6

7.4.1 Comparison of Structural Deformations .................................................................. 86

7.4.2 Comparison of Structural von Mises Stress ............................................................. 90

7.5 Transient Two-Way FSI Simulation of the Single Stack IAD Dynamics.................... 91

7.5.1 Aerodynamic Forces and Moments.......................................................................... 91

7.5.2 Aeroelastic Structural Deformations........................................................................ 95

7.5.3 Aeroelastic Structural von Mises Stresses................................................................ 99

7.6 Summary .................................................................................................................... 101

8 Effect Of Dynamic Pressure on The Aeroelastic Response of A Single Stack IAD 

Configuration ............................................................................................................................. 102

8.1 Steady State CFD Results for Various Dynamic Pressures........................................ 102

8.2 Transient Two-Way FSI Simulation of the Single Stack IAD Dynamics.................. 104

8.2.1 Aerodynamic Forces and Moments........................................................................ 104

8.2.2 Aeroelastic Structural Deformations...................................................................... 108

8.2.3 Aeroelastic Structural von Mises Stresses.............................................................. 112

8.3 Modeling Failure and Collapse of a Single Stack IAD .............................................. 114

8.4 Summary .................................................................................................................... 117

9 Summary and Conclusions................................................................................................. 118

9.1 Summary and Concluding Remarks........................................................................... 118

9.2 Lessons Learnt............................................................................................................ 119

9.2.1 Flow Physics and Aeroelastic Coupling................................................................. 119

9.2.2 Structural FEM Solver............................................................................................ 119

9.2.3 Structural IAD Model............................................................................................. 120

9.3 Recommendations for Future Work ........................................................................... 120

9.3.1 Modeling Additional Flow Physics........................................................................ 120

9.3.2 Changes to Structural Model and IAD Dynamics.................................................. 120

10 References.......................................................................................................................... 122

11 APPENDIX A – CFDRC FEM Validation Against NASTRAN....................................... 123
vii 8927/6

LIST OF FIGURES

Figure 1. Notional design of an IAD............................................................................................ 14

Figure 2. Geometrical details of the MIAS model ....................................................................... 18

Figure 3. Overall computational grid boundaries of the double-stacked design. ......................... 19

Figure 4. Computational 3D grid of the MIAS overset grid model for the double-stacked design.

.............................................................................................................................................. 19

Figure 5. Three-dimensional background grid model for the double-stacked design. ................. 20

Figure 6. Close up view of the overset grid over the background grid. ....................................... 20

Figure 7. Computational FEM model of the double stack MIAS configuration.......................... 21

Figure 8. Details of the FEM model assembly (thickness exaggerated). ..................................... 22

Figure 9. Sign convention of the aerodynamic forces and moments............................................ 24

Figure 10. Axi-symmetric solution comparisons between different Chemistry models .............. 26

Figure 11 MDICE fluid structure interaction scheme. ................................................................. 28

Figure 12. Surface CFD and CSD grids overlaid over each other................................................ 32

Figure 13. Effect of chemistry model on pressure contours over the MIAS model. .................... 34

Figure 14. Steady state pressure field around the MIAS model................................................... 35

Figure 15. Steady state temperature field around the MIAS model ............................................. 35

Figure 16. Steady state Mach contours around the MIAS model................................................. 36

Figure 17. Steady state normal velocity contours around the MIAS model................................. 36

Figure 18. Surface pressure contours over the MIAS model ....................................................... 37

Figure 19. Surface pressure contours on the back of the model................................................... 37

Figure 20. Pressure and temperature distribution along the symmetry plane of the model.......... 38

Figure 21. History of lift and drag coefficients............................................................................ 39

Figure 22. History of moment coefficient. ................................................................................... 39

Figure 23. Effect of toroids inflation pressure on the model peak deflection .............................. 40

Figure 24. The convergence histories of the conducted simulations............................................ 41

Figure 25. Deformation contours for the case of inflation pressure of 15 GPa............................ 41

Figure 26. Schematic view showing the toroids structure with axial straps................................. 42

Figure 27. Predicted CFD loading over the front surface of the FEM model .............................. 43

Figure 28. Effect of toroids inflation pressure on the peak displacement of the modified model 44

Figure 29. Peak total displacement of the modified FEM model using different loading 

conditions. ............................................................................................................................ 44

Figure 30. Deformation contours over the front shield of the modified FEM model at toroids 

inflation of 15 KPa ............................................................................................................... 45

Figure 31. Deformation contours over the modified FEM model (removing the front gores skin) 

at toroids inflation of 15 KPa ............................................................................................... 45

Figure 32. Effect of toroids inflation pressure on von Mises stresses.......................................... 46

Figure 33. von Mises stresses over the modified FEM model at toroids inflation of 15 KPa...... 46

Figure 34. von Mises stress over the FEM model due to toroids internal pressure only.............. 47

Figure 35. Bank maneuver simulation period for all considered aeroelastic simulations............ 49

Figure 36. History of coefficient of lift during the aeroelastic dynamic simulation .................... 49

Figure 37. History of coefficient of drag during the aeroelastic dynamic simulation .................. 50

Figure 38. History of coefficient of side force during the aeroelastic dynamic simulation.......... 50

Figure 39. History of banking moment coefficient during the aeroelastic dynamic simulation... 51
viii 8927/6

Figure 40. History of side moment coefficients during the aeroelastic dynamic simulation ....... 51

Figure 41. Monitor Point Locations on the Model....................................................................... 52

Figure 42. Comparison of y-component of structural deformation for the conducted simulations

.............................................................................................................................................. 53

Figure 43. Comparison of x-component of structural deformation for the conducted simulations

.............................................................................................................................................. 53

Figure 44. Comparison of z-component of structural deformation for the conducted simulations

.............................................................................................................................................. 54

Figure 45. Contribution of aeroelastic deformation only for the two-way coupling simulation. . 54

Figure 46. Structural deformation of the average constant CFD loading simulation at skin 

thickness of 26.5 mil. ........................................................................................................... 55

Figure 47. Structural deformation of the average constant CFD loading simulation at skin 

thickness of 200 mil. ............................................................................................................ 55

Figure 48. Snapshots of von Mises stresses on the front surface of the toroids........................... 57

Figure 49. Snapshots of von Mises stresses on the back surface of the toroids........................... 58

Figure 50. Snapshots of von Mises stresses on the front surface of the gores.............................. 59

Figure 51. Variation of peak von Mises stress versus time .......................................................... 60

Figure 52 Comparison of y-component of structural deformation for various inflation pressures.

.............................................................................................................................................. 62

Figure 53 Comparison of x-component of structural deformation for various inflation pressures.

.............................................................................................................................................. 62

Figure 54 Comparison of aeroelastic component of structural deformation in the x-direction for 

various inflation pressures.................................................................................................... 63

Figure 55. History of coefficient of lift during the aeroelastic dynamic simulation for coarse and 

fine grids............................................................................................................................... 64

Figure 56. History of coefficient of drag during the aeroelastic dynamic simulation for coarse 

and fine grids........................................................................................................................ 64

Figure 57. History of coefficient of side force coefficient during the aeroelastic dynamic 

simulation for coarse and fine grids..................................................................................... 65

Figure 58. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for coarse and fine grids..................................................................................... 65

Figure 59. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for coarse and fine grids..................................................................................... 66

Figure 60. History of banking moment coefficient during the aeroelastic dynamic simulation for 

coarse and fine grids............................................................................................................. 66

Figure 61 Comparison of y-component of structural deformation for various inflation pressures.

.............................................................................................................................................. 67

Figure 62 Comparison of x-component of structural deformation for various inflation pressures.

.............................................................................................................................................. 67

Figure 63. History of coefficient of lift during the aeroelastic dynamic simulation for various 

radial strap models ............................................................................................................... 69

Figure 64. History of coefficient of drag during the aeroelastic dynamic simulation for various 

radial strap models ............................................................................................................... 69

Figure 65. History of side force coefficient during the aeroelastic dynamic simulation for various 

radial strap models ............................................................................................................... 70
ix 8927/6

Figure 66. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for various radial strap models ........................................................................... 70

Figure 67. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for various radial strap models ........................................................................... 71

Figure 68. History of banking moment coefficient during the aeroelastic dynamic simulation for 

various radial strap models................................................................................................... 71

Figure 69 Comparison of y-component of structural deformation for various radial strap models.

.............................................................................................................................................. 72

Figure 70 Comparison of x-component of structural deformation for various radial strap models.

.............................................................................................................................................. 73

Figure 71 Comparison of aeroelastic component of structural deformation in the x-direction for 

various radial strap models................................................................................................... 73

Figure 72 Comparison of aeroelastic component of structural deformation in the z-direction for 

various radial strap models................................................................................................... 74

Figure 73 Comparison of y-component of structural deformation for various radial strap models.

.............................................................................................................................................. 75

Figure 74 Comparison of x-component of structural deformation for various radial strap models.

.............................................................................................................................................. 75

Figure 75 Comparison of z-component of structural deformation for various radial strap models.

.............................................................................................................................................. 76

Figure 76 Comparison of aeroelastic component of structural deformation in the x-direction for 

various radial strap models................................................................................................... 76

Figure 77 Comparison of aeroelastic component of structural deformation in the z-direction for 

various radial strap models................................................................................................... 77

Figure 78 Comparison of PSD based on y-component of structural deformation for various radial 

strap models. ........................................................................................................................ 77

Figure 79 Comparison of PSD based on aeroelastic component of structural deformation in the xdirection for various radial strap models.............................................................................. 78

Figure 80 Comparison of von Mises stresses on the toroids for various radial strap models. ..... 79

Figure 81 Comparison of von Mises stresses on the cover (gores/skin) for various radial strap 

models. ................................................................................................................................. 79

Figure 82 Snapshots of peak von Mises stresses on the toroids and cover (gores/skin) for various 

radial strap models. .............................................................................................................. 80

Figure 83. Overall computational grid boundaries for the modified design................................. 82

Figure 84 Single and double stack CFD models.......................................................................... 82

Figure 85. Computational FEM model of the single stack IAD configuration compared to the 

double stack configuration. .................................................................................................. 83

Figure 86 Steady state pressure field around the single stack IAD model................................... 84

Figure 87 Steady state Mach number field around the single stack IAD model .......................... 84

Figure 88 Pressure contours on the front surface of the single stack IAD model ........................ 85

Figure 89 Comparison of pressure profiles on the back of the single stack and double stack 

models.................................................................................................................................. 85

Figure 90 Comparison of y-component of structural deformation for double and single stack 

configurations with two different inflation pressures........................................................... 86

Figure 91 Comparison of x-component of structural deformation for double and single stack 

configurations with two different inflation pressures........................................................... 86
x 8927/6

Figure 92 Comparison of z-component of structural deformation for double and single stack 

configurations with two different inflation pressures........................................................... 87

Figure 93 Comparison of aeroelastic component only of structural deformation in the x-direction 

for double and single stack configurations with two different inflation pressures............... 87

Figure 94 Comparison of aeroelastic component only of structural deformation in the z-direction 

for double and single stack configurations with two different inflation pressures............... 88

Figure 95 Comparison of PSD based on y-component of structural deformation for double and 

single stack configurations with two different inflation pressures. ...................................... 88

Figure 96 Comparison of aeroelastic component only of structural deformation in the x-direction 

with and without dynamic maneuver. .................................................................................. 89

Figure 97 Comparison of aeroelastic component only of structural deformation in the z-direction 

with and without dynamic maneuver. .................................................................................. 89

Figure 98 Comparison of von Mises stresses on the toroids for double and single stack 

configurations with two different inflation pressures........................................................... 90

Figure 99 Comparison of von Mises stresses on the cover (gores/skin) for double and single 

stack configurations with two different inflation pressures.................................................. 91

Figure 100. History of coefficient of lift during the aeroelastic dynamic simulation for single and 

double stack configurations.................................................................................................. 92

Figure 101. History of coefficient of drag during the aeroelastic dynamic simulation for single 

and double stack configurations........................................................................................... 92

Figure 102. History of side force coefficient during the aeroelastic dynamic simulation for single 

and double stack configurations........................................................................................... 93

Figure 103. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for single and double stack configurations......................................................... 93

Figure 104. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for single and double stack configurations......................................................... 94

Figure 105. History of banking moment coefficient during the aeroelastic dynamic simulation for 

single and double stack configurations................................................................................. 94

Figure 106 Comparison of y-component of structural deformation for single and double stack 

configurations....................................................................................................................... 95

Figure 107 Comparison of x-component of structural deformation for single and double stack 

configurations....................................................................................................................... 96

Figure 108 Comparison of z-component of structural deformation for single and double stack 

configurations....................................................................................................................... 96

Figure 109 Comparison of aeroelastic component of structural deformation in the x-direction for 

single and double stack configurations................................................................................. 97

Figure 110 Comparison of aeroelastic component of structural deformation in the z-direction for 

single and double stack configurations................................................................................. 97

Figure 111 Comparison of PSD based on y-component of structural deformation for single and 

double stack configurations.................................................................................................. 98

Figure 112 Comparison of PSD based on aeroelastic component of structural deformation in the 

x-direction for single and double stack configurations. ....................................................... 98

Figure 113 Comparison of von Mises stresses on the toroids for single and double stack 

configurations....................................................................................................................... 99

Figure 114 Comparison of von Mises stresses on the cover (gores/skin) for single and double 

stack configurations............................................................................................................ 100
xi 8927/6

Figure 115 Snapshots of peak von Mises stresses on the toroids and cover (gores/skin) for single 

and double stack configurations......................................................................................... 100

Figure 116 Pressure contours on the front surface of the single stack IAD model .................... 103

Figure 117 Comparison of pressure profiles on the front of the single model for various dynamic 

pressures............................................................................................................................. 103

Figure 118 Comparison of coefficient of pressure on the front of the single model for various 

dynamic pressures.............................................................................................................. 104

Figure 119. History of coefficient of lift during the aeroelastic dynamic simulation for various 

dynamic pressures.............................................................................................................. 105

Figure 120. History of coefficient of drag during the aeroelastic dynamic simulation for various 

dynamic pressures.............................................................................................................. 105

Figure 121. History of side force coefficient during the aeroelastic dynamic simulation for 

various dynamic pressures.................................................................................................. 106

Figure 122. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for various dynamic pressures.......................................................................... 106

Figure 123. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for various dynamic pressures.......................................................................... 107

Figure 124. History of banking moment coefficient during the aeroelastic dynamic simulation for 

various dynamic pressures.................................................................................................. 107

Figure 125 Comparison of y-component of structural deformation for various dynamic pressures.

............................................................................................................................................ 108

Figure 126 Comparison of x-component of structural deformation for various dynamic pressures.

............................................................................................................................................ 109

Figure 127 Comparison of z-component of structural deformation for various dynamic pressures.

............................................................................................................................................ 109

Figure 128 Comparison of aeroelastic component of structural deformation in the x-direction for 

various dynamic pressures.................................................................................................. 110

Figure 129 Comparison of aeroelastic component of structural deformation in the z-direction for 

various dynamic pressures.................................................................................................. 110

Figure 130 Comparison of PSD based on y-component of structural deformation for various 

dynamic pressures. ............................................................................................................. 111

Figure 131 Comparison of PSD based on aeroelastic component of structural deformation in the 

x-direction for various dynamic pressures. ........................................................................ 111

Figure 132 Comparison of von Mises stresses on the toroids for various dynamic pressures. .. 112

Figure 133 Comparison of von Mises stresses on the cover (gores/skin) for various dynamic 

pressures............................................................................................................................. 113

Figure 134 Snapshots of peak von Mises stresses on the toroids and cover (gores/skin) for 

various dynamic pressures.................................................................................................. 113

Figure 135 Comparison of y-component of structural deformation for single stack configurations 

with various pressure loads. ............................................................................................... 114

Figure 136 Contour plots and z-cut of IAD at 60 ms for a pressure load at four times the 

reference dynamic pressure................................................................................................ 115

Figure 137 Contour plot of von Mises stress at 60 ms on the cover and toroids for a pressure load 

at four times the reference dynamic pressure..................................................................... 115

Figure 138 Comparison of y-component of structural deformation for single stack configurations 

with various pressure loads and with contact..................................................................... 116
xii 8927/6

Figure 139 Contour plots and z-cut of IAD at 60 ms for a pressure load at four times the 

reference dynamic pressure with contact model................................................................. 116

Figure 140 Contour plot of von Mises stress at 60 ms on the cover and toroids for a pressure load 

at four times the reference dynamic pressure with a contact model................................... 117
xiii 8927/6

LIST OF TABLES

Table 1. Material properties of the toroids for the double stack IAD configuration .................... 22

Table 2. Material properties of the gores for the double stack IAD configuration....................... 22

Table 3. Flow and flight conditions for the simulations............................................................... 23

Table 4. Reference conditions for the aerodynamic forces and moments.................................... 24

Table 5 Total clock time required for the three different methods of coupling on 20 CPUs....... 48

Table 6 First two modes of the IAD for various strap models..................................................... 78

Table 7. Material properties of the toroids for the single stack IAD configuration. .................... 83

Table 8. Material properties of the gores for the single stack IAD configuration........................ 83
14 8927/6

1 INTRODUCTION

1.1 Background

NASA is conducting an Entry, Descent and Landing Systems Analysis (EDL-SA) Study to 

determine the key technology development projects that should be undertaken for enabling the 

landing of large payloads on Mars for both human and robotic missions. Inflatable Aerodynamic 

Decelerators (IADs) are one of the candidate technologies. A variety of EDL architectures are 

under consideration. Taken together these architectures include IADs for aerocapture 

(hypersonic) and for the entry (hypersonic) and the descent (supersonic and subsonic) stages of 

EDL. Many aspects of IADs need to be considered, e.g., inflatability, heating, deformation, 

structural integrity, aerodynamic performance, and controllability. For each stage there are rather 

challenging requirements. Part of the EDL-SA assessment includes determining whether the 

candidate technologies meet the requirements. Among the important considerations for IADs are 

whether they provide the desired controllability and can withstand the loads induced by banking 

maneuvers. The purpose of this effort is to provide computational predictions to support the 

EDL-SA assessments of IAD controllability and structural integrity for Mars Aerocapture and 

EDL.

Figure 1. Notional design of an IAD.

Figure 1 illustrates the key components of the IADs under consideration. The Inflatable Braking 

Unit (IBU) consists of pressurized internal toroidal cells covered with a smooth surface 

containing the Thermal Protective Cover (TPC). The structural properties of the IBU are 

nonlinear. The Rigid Front Shell (RFS) is a rigid metallic structure. The payload is a cylinder

that attaches to the back portion of the RFS. In this effort, the payload is not modeled. The model 

is subject to banking maneuver that is modeled by a prescribed rotational motion of the RFS. The 

flow field and the structural response of the model are three-dimensional and exhibit no 

symmetries. The aerodynamics will be described by the Euler equations.
15 8927/6

1.2 Work Scope

The scope of this work is to conduct CFD aero-structural and dynamic simulations of Inflatable 

Aerodynamic Decelerators (IADs). The computation predictions are intended to answer the 

question: For a specific design and configuration, what range, if any, of internal pressures does 

the IBU maintain structural integrity during the banking maneuver?

The flow conditions of primary interest are Mach 18 at angles of attack of 30 degrees. The 

banking maneuver corresponds to a prescribed acceleration of the RFS of 5 deg/sec2 with

duration of 4 seconds. The computations will first determine the steady flow field at the flow 

conditions, and then conduct the banking maneuver. The predictions will include time histories 

of the aerodynamic forces and moments, the structural deformations of the IBU, and the stresses 

at the RFS–IBU attachment points.

The effort in this contract was performed under the following tasks:

Task 1: Development of Computational Models

Develop three-dimensional computational models for the aerodynamics, structural dynamics, and 

dynamics motion of the notional IAD design. A simplified Mars atmosphere chemistry model 

with an equivalent specific heat ratio is developed for the aerodynamics model. Several structural 

models are considered and tested to select the appropriate model for the rest of the effort.

Chapter 4 of this report discusses the effort conducted under Task 1.

Task 2: Aeroelastic and Dynamic Analysis of Double Stack IAD Configuration

Conduct aero-structural and dynamic simulations of the notional double stack toroids IAD 

configuration at 30 degrees angle of attack and bank angle rate of 5 deg/sec2. There are two 

subtasks are performed in this simulation:

1. Rigid body and steady flow simulation of the double stack IAD at 30 degrees angle of 

attack and no dynamic motion. The final solution of this subtask will be used as the initial 

conditions for the aeroelastic and dynamic simulations. 

2. Conduct aeroelastic and dynamic simulation of the double stack IAD at 30 degrees angle 

of attack and bank angle rate of 5 deg/sec2. Simulations will be carried out for 4 seconds.

The model and results of Task 2 simulations are discussed in details in Chapter 5 of this report.

Task 3: Aeroelastic and Dynamic Analysis of Modified Double Stack IAD Configuration at 

30

0 Angle of Attack

Conduct aero-structural and dynamic simulation of a modified design of the double stack IAD 

configuration at 30oangle of attack and bank angle rate of 5 deg/sec2. The design modifications 

included different internal tube pressures, different structural material properties, and different 

thickness dimensions based on modeling the effects of radial straps. There are two subtasks are

performed in this simulation:

1. Modify the 3D structural FEM model to account for the modified material properties, 

modified model thickness dimensions, and different internal toroidal pressures. 
16 8927/6

2. Conduct aeroelastic and dynamic simulation of the modified IAD at 30oangle of attack 

and bank angle rate of 5 deg/sec2. 

The model and results of Task 3 simulations are discussed in details in Chapter 6 of this report.

Task 4: Aeroelastic and Dynamic Analysis of Single Stack IAD Design at 30o Angle of 

Attack

Conduct aero-structural and dynamic simulation of a single stack toroids IAD design at 30oangle 

of attack and bank angle rate of 5 deg/sec2. The design modifications may include different 

internal tube pressures, different structural material and/or thickness properties, or different IAD 

shape. There are three subtasks to be performed in this simulation:

1. Modify the 3D structural FEM model and CFD computational model for the single stack 

IAD model, including the corresponding material properties, thickness dimensions, and 

internal toroidal pressures. 

2. Conduct rigid body steady flow simulation of the single stack toroids IAD at 30oangle of 

attack and no dynamic motion. 

3. Conduct aeroelastic and dynamic simulation of the single stack toroids IAD at 30oangle 

of attack and bank angle rate of 5 deg/sec2. Simulations will be carried out for 4 seconds. 

The model and results of Task 4 simulations are discussed in details in Chapter 7 of this report.

Task 5: Effect of Dynamic Pressure on the Aeroelastic Response of the Single Stack IAD 

Design at 30o Angle of Attack

Conduct aero-structural and dynamic simulation of single stack toroids IAD design at 30oangle 

of attack and bank angle rate of 5 deg/sec2. The aeroelastic simulations will be conducted at 

different dynamic pressures. There are three subtasks to be performed in this simulation:

1. Conduct rigid body steady flow simulation of the single stack toroids IAD at 30oangle of 

attack and no dynamic motion. The simulations will be conducted at different dynamic 

pressures to compute the aerodynamic flow field characteristics that are used as the initial 

conditions of the aeroelastic simulations.

2. Conduct aeroelastic and dynamic simulation of the single stack toroids IAD at 30oangle 

of attack, bank angle rate of 5 deg/sec2, and different dynamic pressures. Simulations will 

be carried out for 4 seconds. 

3. Conduct aeroelastic simulation of the single stack toroids IAD at increasing aerodynamic 

loads to determine the failure point of the model. 

The model and results of Task 5 simulations are discussed in details in Chapter 8 of this report.

Task 6: Documentations and Deliverables

A final report will be prepared and will document all the work done under the above described 

tasks. The final report will include the following;

A brief discussion of the analysis methodology
17 8927/6

A description of the analysis input information which was used to produce the analysis 

results

A description and discussion of the simulation results

Graphs, flow field pictures and other such information which describe the details of the 

flow field.

Additionally, periodic interim oral reports in the form of either MS PowerPoint slides or MS 

Word document will be prepared and delivered to NASA for discussions.
18 8927/6

2 GEOMETRY MODELING AND GRID GENERATION

The geometrical details of the MIAS model received from NASA are shown in Figure 2. The 

model has an outside diameter of 23 meters and central adapter of 3.6 meters. The inflatable 

Braking Unit (IBU) consists of a total of 23 pressurized internal toroidal cells covered with a 

smooth shield surface. The diameter of every toroidal cell is 0.92 meters. A rigid front shield is 

also shown in the figure with a diameter of 8.0 meters.

Figure 2. Geometrical details of the MIAS model

In this study, two different configurations were analyzed viz., the nominal double stacked 

configuration shown in Figure 2 and a single stack configuration with only one row of toroids. 

For each configuration, CFD-GEOM, a geometry modeling and grid generation software was 

used to create the geometry and grid. The nominal and modified IAD models were created as 

part of Task 1 and Task 4 respectively. The three-dimensional topology and grids for nominal 

and modified IAD configurations are discussed below.

2.1 Computational Grid Model for Double-Stacked IAD Configuration

The computational grid model of the MIAS was developed using the grid generator CFDGEOM. The overall computational grid is modeled using 60 zonal blocks containing about 3.6 

million grid cells. The outer boundaries of the computational grid are shown in Figure 3. As 

shown in the figure, the computational grid model of the MIAS is overset over a background grid 

to enable the dynamic bank maneuvering. The surface overset grid of the MIAS model is shown 

in Figure 4. The grid over the geometrical symmetry plane is also shown in the figure. The grid 

is fine enough for Euler solution and is clustered around the body to sharply capture the expected 

bow shock around the body. The overset grid of the MIAS model is built with a 42 zonal blocks 

consisting of about 2.4 million grid cells. 
19 8927/6

Figure 3. Overall computational grid boundaries of the double-stacked design.

Figure 4. Computational 3D grid of the MIAS overset grid model for the double-stacked design.
20 8927/6

The background grid is shown in Figure 5. The figure shows how the MIAS grid is overset the 

background. A close up view of the grid oversetting is shown in Figure 6. The background grid 

model was developed using an equivalent spacing for better Chimera interpolation near the outer 

boundaries of the overset grid. The background grid model is built with an 18 zonal blocks 

consisting of about 1.2 million grid cells. Although the geometrical model is symmetric, the 

computational grid was developed and the simulations were conducted on a full 360 degrees 

three-dimensional model due to the dynamic maneuver that will be considered in the subsequent 

chapters.

Figure 5. Three-dimensional background grid model for the double-stacked design.

Figure 6. Close up view of the overset grid over the background grid.
21 8927/6

2.2 Computational Structural Dynamics Model for Double-Stacked IAD Configuration

The computational structural dynamics FEM model of the nominal double stack MIAS 

configuration is shown in Figure 7. The model consists of 32,490 quad shell elements of nonzero thickness. A cut across the model showing the details of the model is also shown in the 

figure. The toroids are modeled with 12 quad shell elements each. The toroids are connected 

together through one of the 12 elements, and they are also connected with the gores (the outside 

skin) through on segment. The details of the geometrical FEM model are shown in Figure 8. In 

this model, the thicknesses of the model are exaggerated for clarity. 

The toroids are made of Kevlar and the gores are made of Upilex. The material properties of the 

Kevlar and the thickness of the toroids are shown in Table 1. The material properties of the 

Upilex and the thickness of the gores are shown in Table 2. A high temperature knock down 

factor of 0.5 is used for the toroids modulus of elasticity. The toroid thickness is 13.178 mil and 

the thickness of the gores is 26.536 mil. The original structural model of the MIAS configuration 

includes six circumferential straps along each of the toroids, in addition to 18 radial straps 

holding the model together. These straps are not modeled in the initial FEM model and will be 

considered in the modified FEM design model.

Figure 7. Computational FEM model of the double stack MIAS configuration 
22 8927/6

Figure 8. Details of the FEM model assembly (thickness exaggerated).

Table 1. Material properties of the toroids for the double stack IAD configuration

Kevlar Properties for Toroids

Max E 70 E+09 Pa

Design E 35 E+09 Pa

Density 1440 Kg/m3

Poisson ratio 0.1

Toroids thickness 13.178 Mil

Table 2. Material properties of the gores for the double stack IAD configuration

Upilex Properties for Gores

E 3.7 E+09 Pa

Density 1470 Kg/m3

Poisson ratio 0.34

Gores thickness 26.536 Mil
23 8927/6

2.3 CFD Flow and Flight Conditions for the IAD Configurations

The same flow and flight conditions were used for all the cases simulated in this study. These 

conditions are presented in Table 3.

Table 3. Flow and flight conditions for the simulations

Parameter Value Parameter Value

Time (sec) 2.183000000e+02 G-Load (earth g's) 3.701706979e+00 

Altitude (m) 2.674990635e+04 Pressure (N/m^2) 3.771500270e+01

Density (kg/m^3) 1.301150987e-03 Dynamic Pressure (N/m^2) 5.143675033e+03

Temperature (K) 1.768426264e+02 Bank Angle (deg) 1.087088056e+02

Atmosphere Relative 

Velocity (m/s)

2.811822563e+03 Angle of Attack (degrees) 30.0

2.4 Aerodynamic Forces and Reference Quantities

The pressure signal over the surfaces of the IAD model was integrated to compute the 

aerodynamic forces. The sign and directions of the aerodynamic forces and moments are shown 

in Figure 9. The moment reference point is about 9.2 meters from the nose of the model. The 

moment is positive in the counter clock wise direction. The aerodynamic moments are 

normalized with respect to the model reference length of 23.0 meters. The reference area is 

415.475 m2, and the reference dynamic pressure is 5143.675 N/m2. The reference quantities are 

summarized in Table 4. 
24 8927/6

Figure 9. Sign convention of the aerodynamic forces and moments.

Table 4. Reference conditions for the aerodynamic forces and moments

Parameter Value (metric)

Sref 415.475 m2

Lref 23.0 m

xmrc 0.0 m

ymrc 9.2 m 

zmrc 0.0 m 

Qref 5143.675 Pa
25 8927/6

3 COMPUTATIONAL METHODOLOGY

The Multi Disciplinary Integrated Computing Environment (MDICE1,2), developed by CFDRC 

for Air Force Research Lab and NASA, was used for the coupling between the fluid CFD solver 

and structures dynamics FEM solver. The CFD solver used in this project was the density-based 

flow solver; CFD-FASTRAN.

3 The FEM solver used was the FEM module of CFDRC‟s 

Computational Physics (CoPhy) solver.4

3.1 CFD Solver – CFD-FASTRAN

CFD-FASTRAN, a commercial well validated flow solver originally developed by CFDRC,

solves the Euler or full Navier-Stokes equations in a general curvilinear coordinate system 

employing finite-volume methods. The flow solver supports structured / unstructured, hybrid, 

multi-block, blocked and chimera grid systems, with automatic hole cutting for Chimera grid 

systems. CFD-FASTRAN is applicable for steady-state calculations or time-varying solutions 

and includes a built-in 6-DoF module for multiple interdependent moving body dynamic 

calculations. Several turbulence models are supported in CFD-FASTRAN, including the high 

Reynolds number k-ε with wall functions, Spalart-Allmaras, Baldwin-Lomax, Menter-SST and 

the k-ω turbulence models. Both flux-vector and flux-difference splitting schemes are employed 

with higher-order limiters. 

The initial conditions for most of the cases were the undisturbed uniform free stream conditions 

everywhere at 30-degree angle of attack. In some cases the flowfield was restarted from constant 

free stream conditions except in localized regions (e.g. close to the surface) where pressure and 

velocity modification were made to allow the solution to smoothly transition from startup to 

convergence. The initial local pressure close to the IAD surface was increased to allow the shock 

to form outside the cup without causing solution diverging.

Cases started from free stream conditions were begun first order and run until the forces were not 

changing by a significant amount. Roe‟s flux difference splitting was used for spatial 

discretization of all equations. All flux limiting was done with the min-mod limiter. 

All walls were modeled initially as slip adiabatic boundary conditions. The inflow and outflows 

used Riemann Invariants. CFD-FASTRAN detects when an outflow is supersonic and uses a 

more appropriate simple extrapolation in this case. The fluid was modeled with reacting CO2 

properties.

CFD-FASTRAN has been validated for numerous supersonic and hypersonic flow predictions 

similar to the flow considered under this project.

5-10

3.1.1 Computational Chemistry Model for Mars Atmosphere

The Martian atmosphere contains mostly CO2 which decomposes into CO and O across the 

hypersonic bow shock wave. Because of the shock layer chemical reactions, the post-shock 

specific heat ratio is lowered which significantly affects the shock stand-off distance. For the 

proposed preliminary design aero-elastic analysis, the computational expense of a chemically 
26 8927/6

reacting CO2 model is undesirable and unnecessary. The correct shock standoff and post-shock 

gas flow conditions (pressure, dynamic pressure, etc.) must be obtained for correct fluidstructure dynamic effects. The details of the gas composition may be important for surface 

heating effects, but are not a first order concern for the present work.

Few simplified chemistry models are analyzed to replace the fully reacting CO2 modeling. One 

model is perfect gas CO2 model with an equivalent gamma (ratio of specific heats) tuned to 

result in the correct shock jump prediction. The thermodynamic properties used for the 

equivalent perfect gas case are identical to standard carbon dioxide (transport coefficients and 

universal gas constant). One model is for a specific heat ratio of 1.33 that is based on pre-shock 

speed of sound. However, since the specific heats are function of temperature, post-shock 

properties are different than pre-shock properties. As the temperature increases behind the shock, 

so is gamma (specific heat ratio) and therefore post-shock values will be different.

Another model is based on a specific heat ratio of approximately 1.15 that is used to modify the 

values of Cv and Cp. The new value of the specific heat ratio is obtained such that the shock 

stand-off distance for the perfect gas case is similar to the one obtained for non-equilibrium 

reacting gas. The value of the equivalent gamma is determined with simple one dimensional 

normal shock relationships for the selected flight condition along the stagnation line.

In order to select the correct model for the analysis, an axi-symmetric simulations of a more 

detailed CO2 5-species reacting flow was conducted as part of Task 1. The axi-symmetric 

pressure distribution over the model is shown in Figure 10. Two more axi-symmetric simulations 

were conducted using the equivalent specific heat ratio of 1.33 and 1.15 for comparison. The 

pressure distributions from these simulations are also shown in the figure. The figure shows 

clearly that the model that takes into consideration the post-shock properties is more accurate and 

closer to the reacting CO2 model. 

Figure 10. Axi-symmetric solution comparisons between different Chemistry models
27 8927/6

Another simulation was also conducted using a thermally perfect CO2 model (single specie 

mixing of CO2) with a curve fit for specific heat Cp from Chemistry data bases. The pressure 

distribution for an axi-symmetric simulation using this model is also shown in Figure 10. The 

figure shows that the thermally perfect CO2 model gives almost similar results as the reacting 

gas model. The reason is that the reacting case showed that the chemical reactions are small and 

almost all the effect comes from the dependent of specific heat on temperature. 

3.2 FEM Solver – CFDRC-FEM

CFDRC‟s FEM code used in this project is part of a multi-physics and multi-scale computational 

physics (CoPhy) software package, written in the object-oriented language C++ and developed 

by CFDRC. It contains several modules including: pressure-based CFD, heat transfer, structures 

dynamics, electrostatics, chemistry, and several others. Each module solves physics on the same 

or different grids, and data exchanges between different modules are seamless. The code was 

successfully used to model tightly coupled aerothermoelastic problems of hypersonic vehicles.11

Only the finite element module or CFDRC-FEM was used in this project. Further information 

and validation for CFDRC-FEM is provided in Appendix A. 

CFDRC-FEM solves stress/deformation, and acoustic in a Lagrangian frame. The most relevant 

features of CFDRC-FEM are:

Both explicit and implicit FEM solver available for different time-scale applications;

Unstructured mixed element grids including tetra, hexa, pyramid, prism, octree;

Accurate finite elements such as mixed formulation for incompressible materials, and 

locking-free shell formulation and solid-shell formulation applicable for both smooth and 

folded shell structure;

Multi-rigid body dynamics with various joints and its implicit coupling with flexible 

bodies;

Various non-linear material models such as hyperelasticity, viscoelasticity and 

elastoplasticity;

Various surface interaction such as Contact-impact algorithm, tied-interface to connect 

domains with different mesh;

Acoustic model and its implicit interaction with structural dynamics;

Capable of calculate large structured/unstructured mesh movement in the fluid domain; 

Efficient large-scale parallel computing with interface to Petsc solver;

Seamless coupling with fluid dynamic module and heat transfer module.

Problems involving thin shell elements with large aspect ratios are extremely hard to solve with 

implicit solvers due to the difficulty of inverting ill-conditioned matrices. The usage of explicit 

solvers is cost-prohibitive due to the fact that the time step is driven by the small thickness. 

Therefore, we have used the mass scaling technique for shell elements involving explicit 

transient analysis. This scaling permits large critical time step size without loss of stability, 

which is particularly necessary for very thin shell structures.
28 8927/6

In CoBi-FEM, the triangular and quadrilateral shell elements are used with linear interpolation 

function, therefore the translational masses at elemental node I is

m N dAd

A

I

h

I

u

(1 )

0

The rotational masses are computed by the scaling at the node I by a factor α

A

I

h

I

mr 0N (1 ) dAd

where A and h are the area and the thickness of the element, respectively, and the scaling factor 

of 

2

1.5A/ h . 

3.3 MDICE Infrastructure

MDICE provides an environment that handles the transmission of data between different 

physical or multi-physics modules across networks and computing platforms. A fluid structure 

interaction problem can be performed between different sets of CFD and CSD codes as seen in 

Figure 11.

Figure 11 MDICE fluid structure interaction scheme.

Data transmission occurs through memory; therefore even a simulation composed of separate 

analyses and distributed across a heterogeneous network appears as a tightly coupled code. 

Existing analysis codes are integrated through an object-oriented application programming 
29 8927/6

interface (API), ensuring that modern technology can readily be implemented into the simulation 

process. The simulation modules integrated into the MDICE environment must only be modified 

to deliver and receive data and information from the MDICE system. MDICE has a full interface 

for codes written in F77, F90, C, or C++. Modules are „MDICE-compliant‟ once their 

subroutines have been equipped with appropriate MDICE calls for sending and receiving 

information. The code module must then be linked to the MDICE library and recompiled. A code 

module can also be made compliant without any modifications, but with much reduced 

efficiency, by having the MDICE wrapper script invoking module execution in a file-based mode 

(disk I/O). 

Once all necessary modules are integrated (deemed „MDICE-compliant‟), analyses are 

coordinated in a multidisciplinary simulation through a scripting language. The disciplinary 

analyses are initiated from within MDICE. Each analysis loads grid and restart information and 

then releases execution control to MDICE. Once each module is placed in a wait mode, the 

simulation is run through the scripting language, which is executed through the MDICE GUI. 

The first command usually issued to each module creates an interface object within MDICE. An 

interface object stores pointers to the grid and variable information that resides directly in the 

analysis modules‟ memory. Following, MDICE assembles the interface objects, or performs 

calculations necessary for the interpolation of quantities between the disciplinary grids.

MDICE framework has been used successfully for numerous aeroelastic applications. The most 

prominent is prediction and control of F/A-18 aircraft that is recognized by “Aerospace 

America” magazine as one of the yearly achievements in 2002.12-14 MDICE was also used to 

model and analyze different inflatable structures.15,16

Currently supported MDICE Applications include:

Distributed Computing: Codes May Be Run On Different Unix Or Windows Workstations

Parallel, Distributed Execution Of Code Solution

Network Of Heterogeneous Computer Systems (Mix Of Unix And Windows Computers)

Multi-Level Parallelism

Fluid-Fluid Interfaces: Flow Solvers Coupled With Other Flow Solvers

Code-To-Code Coupling: Incompressible To Compressible, Pressure-Based To DensityBased

Arbitrary Grid Coupling And Alignment (e.g. Structured To Unstructured Grids)

Multi-Dimensional Coupling (e.g. Axi-symmetric to 3D, 2D to 3D)

Mixing Plane Interfacing (Circumferential Averaging)

Fluid-Structure Interfaces: Communication Between Flow And Structural Solvers

Conservative And Consistent Interfacing (Force And Virtual Work Conservation)

Arbitrary Grid Coupling (e.g. Structured Fluid Grids To Unstructured Solids Grids)

Multi-Dimensional Coupling (e.g. Structural Beam Models Coupled To ThreeDimensional Fluids Flow Models)

Flow/Structural Solvers Coupled With Grid Generators

- Direct Coupling Of Grids With Analysis Codes For Optimization Problems

Computer Aided Design Codes Directly Coupled With A Grid Generation Tool

- Automated Remeshing Of Parametric Geometries
30 8927/6

The MDICE environment includes three main parts:

1. Multi-Physics Simulation Controller

2. Multi-Physics Analysis Modules

3. Multi-Physics Interfacing Modules

The first part is the MDICE controller, which controls the temporal synchronization of the data 

transfer and the multi-level parallelism of the multi-physics analysis modules and coupling 

routines. The second part is a set of multi-physics fluid, thermal (under development), and 

structure analysis modules for the analysis of the multi-physics characteristics of a hypersonic 

vehicle. The third part is the multi-physics interfacing modules such as fluid-fluid, fluidstructure, thermal-solid interfacing modules. The various parts are described in the remainder of 

this section.

3.3.1 MDICE Controller

The first component in MDICE is a central controlling process that serves as an object repository 

and provides application control via MDICE specific script language and remote procedure calls. 

The remote procedure calls are the mechanism by which MDICE controls the execution and 

synchronization of the participating applications. The controller oversees several important tasks 

such as:

Direct launching and stopping of application modules on specified hosts in the MDICE 

environment. 

Control workflow of a simulation by means of scheduling tasks to the application modules.

Facilitate data transfer between application modules. 

3.3.2 Multi-Physics Analysis Modules

The second part of the MDICE environment is a set of analysis modules for multi-physics 

analysis. In this project, the multi-physics modules used were CFD-FASTRAN for 

computational fluid dynamics, and CFDRC-FEM (CoPhy) for computational structural 

dynamics. 

These codes can interact with each other or with any multiple numbers of codes already in the 

MDICE environment. Third party tools from US govt. (AVUS, FUN3D etc), public domain and 

commercial areas (CFD-FASTRAN, CFD-ACE, AERO-F, AERO-S, ABAQUS, Matlab etc) can 

and have been integrated and fully coupled with CoPhy flow and/or FEM and/or thermal solvers 

seamlessly.
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3.3.3 Multi-Physics Interfacing Modules

The interface module consists of several interface types that let two codes communicate 

information between each other. A CFD code and a FEM code communicate through a fluid 

structure interface, a CFD code and a thermal code communicate via the fluid-thermal interface 

and the FEM and a thermal code can communicate via a volumetric interface. A CFD code can

also talk to a different CFD code through a fluid-fluid interface. None of these interfaces requires 

one to one grid connectivity. The data interpolation is done in a conservative consistent fashion. 

Fluid-Structure Interface

The fluid-structure interface algorithm is used to project forces from the fluid cells into 

equivalent forces and moments to the structure cells and to project the deflections of the structure 

to the fluid. In the developed environment, a conservative-consistent interfacing module is used 

for the fluid-structure coupling. The fluid-structure interfacing is formulated in the most general 

sense for maximum flexibility. There are no inherent assumptions that the fluid grid is matched 

with the structure grid, either through different mesh densities, mesh architecture, or through 

physical separation between the interfaces as seen with thick shell finite-element models. 

The relevant features of the fluid-structure interfacing module are: 

100% conservative and consistent.

Solid forces are directly projected from the face pressure. 

The fluid nodal forces are translated to the solid nodes 

using finite-element shape functions. 

Fluid nodal deflections are directly projected from the solid 

nodal deflections.

All grid alignment is automatic (accomplished by using fast 

ADT geometrical searching).

Unstructured and structured grids are supported.

The conservation property aims to conserve the forces and moments in the interpolation process 

between two or more grids. In this case, the sum of all forces and moments on the fluid interface 

is equivalent to the sum of all forces and moments on the structure interface. Requiring that the 

virtual work performed by the solid interface is equivalent to the virtual work performed by the 

fluid interface provides the necessary consistency or virtual work conservation. 

The surface grids of the CFD and CSD models of the IAD configuration are not identical as 

shown in Figure 12. In a typical aeroelastic analysis, the aerodynamic forces are projected into 

the surface then interpolated into the nodes of the FEM model using the fluid-structure 

interfacing module. 

Fluid-Thermal Interface

The fluid-thermal interface is used to exchange heatflux from the fluid cells to the structure cells 

and to project the temperature of the structure to the fluid. The fluid-thermal interfacing is 

formulated in the most general sense for maximum flexibility. There are no inherent assumptions 

that the fluid grid is matched with the structure grid, either through different mesh densities, 

mesh architecture, or through physical separation between the interfaces as seen with thick shell 

i

r



Ffluid



Fsolid



solid i Ffluid M r

 
32 8927/6

finite-element models. This interface was not used in this project but can be used in future work 

if the thermoelastic effects need to be simulated. 

FEM-Thermal Volumetric Interface

The FEM-thermal volumetric interface is used to exchange temperature from the thermal nodes 

to the structure nodes and to project the displacement of the structure to the thermal nodes. The 

volumetric interfacing is formulated in the most general sense for maximum flexibility. There are 

no inherent assumptions that the fluid grid is matched with the structure grid, either through 

different mesh densities, mesh architecture. The disadvantage is that it is a computationally 

expensive interpolation. This interface was not used in this project but can be used in future work 

if the thermoelastic effects need to be simulated. 

Fluid-Fluid Interface

The fluid-fluid interface is used to exchange conserved flow quantities between one set of fluid 

cells to another set of fluid cells being solved by FASTRAN. The fluid-fluid interfacing is 

formulated in the most general sense for maximum flexibility. There are no inherent assumptions 

that the fluid interfaces from each domain are matches with each other, either through different 

mesh densities, mesh architecture, or through small physical separation between the interfaces. 

The interpolated is based on conserved fluid quantities.

Figure 12. Surface CFD and CSD grids overlaid over each other

3.4 Coupling Methods

Various coupling methods and options were used through the course of this project to exchange 

CFD loads and deflections between the CFD and the Structural FEM models. The simplest 
33 8927/6

method was to divide the structural model and CFD model into a number of sections and impose 

the average pressure load of each CFD section to the corresponding structural boundary. This 

method is referred to as the “CFD averaged constant loading”. The second method is to transfer 

the pressure loads from the CFD fluid structure interface to structural FSI interface using 

MDICE interface modules to transfer the loads in a conservative consistent manner. However, in 

this method, the deformations resulting from these loads are not transferred back to the CFD 

solver. This method is referred to as “one-way coupling”. The final method is the full “two-way 

coupling” in which the pressures and deflections are both exchanged. 
34 8927/6

4 STEADY AERODYNAMIC FLOWFIELD FOR THE DOUBLE STACK IAD 

CONFIGURATION

The previously described aerodynamic model was used to simulate the aerodynamic flowfield 

around the IAD configuration. The flow and flight conditions for the simulation as well as the 

computational models and solution methodology were presented in previous chapters. 

4.1 Steady State Aerodynamic Simulation Results

The aerodynamic model described in chapters 2 and 3 was used to simulate the aerodynamic 

flowfield around the MIAS model at a specific set of conditions outlined in Table 3. Initially, 

three-dimensional simulations were conducted for both the constant specific heat ratio model and 

the CO2 thermally perfect model with Cp from curve fit. The effect of the chemistry model on 

the pressure contours over the model is shown in Figure 13. As shown in the figure, the 

thermally perfect model produced a shock that is closer to the body surfaces. Since the reacting 

CO2 chemistry model is more representative of the Mars atmosphere, this model is used for the 

remaining of the CFD simulations.

(a) C

onstant specific hear ratio = 1.33

(b) 

O2 thermally perfect model with Cp 

curve fit

Figure 13. Effect of chemistry model on pressure contours over the MIAS model.

The details of the flow field results for the case of reacting CO2 chemistry model (thermally 

perfect CO2 model) are presented next. The overall pressure and temperature contours over the 

symmetry plane of the whole computational domain are shown in Figure 14 and Figure 15, 

respectively. A maximum pressure of about 8500 Pa occurs over the front shield of the model 
35 8927/6

and in front of the oncoming flow. The Mach number contours and relative normal velocity 

contours over the symmetry plane of the whole computational domain are shown in Figure 16

and Figure 17, respectively. 

Figure 14. Steady state pressure field around the MIAS model

Figure 15. Steady state temperature field around the MIAS model
36 8927/6

Figure 16. Steady state Mach contours around the MIAS model

Figure 17. Steady state normal velocity contours around the MIAS model

The surface pressure contours over the front and back of the MIAS model surfaces are show in 

Figure 18. The maximum pressure occurs nears the windward side of the model and decreases 

toward the leeward side. The pressure in the back of the model is very small compared to the 

front side. The details of the pressure contours in the back side of the model are shown in Figure 

19 with different scale for clarity. The maximum pressure on the back side of the model is about 
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0.02 psi and it occurs near the leeward side of the model, most probably due to flow separation 

from the leeward side. The surface pressure and temperature distribution along the symmetry 

plane of the model are shown in Figure 20. The figure shows that a fairly constant pressure 

occurs almost over the whole windward side before it decreases near the leeward side. 

Figure 18. Surface pressure contours over the MIAS model

Figure 19. Surface pressure contours on the back of the model
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Figure 20. Pressure and temperature distribution along the symmetry plane of the model

The pressure signal over the surfaces of the MIAS model was integrated to compute the 

aerodynamic forces. The sign and directions of the aerodynamic forces and moments are shown 

in Figure 9. The history of the aerodynamic lift and drag coefficients are shown in Figure 21. 

The history of the moment coefficient is shown in Figure 22. The figures show that the 

aerodynamic forces converge well within 2000 iterations. The final value of the drag and lift 

coefficients are 0.869 and 0.3004, respectively. The moment coefficient converged at 

approximately -0.0561. A negative moment coefficient is necessary for the aerodynamic stability 

of the model. 
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Figure 21. History of lift and drag coefficients

Figure 22. History of moment coefficient.
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4.2 Computational Structural Analysis

4.2.1 Static FEM Analysis of the MIAS Model with Constant Loading

The model was tested first with constant loading prior to applying the predicted CFD loads. 

Several static FEM simulations were conducted at different inflation pressures from 15 KPa to 

45 KPa. A constant loading of 5000 Pa was applied over the whole front side of the model, 

including the windward and leeward sides. No loads were applied at the back side of the model. 

The effects of the toroids inflation pressure on the peak displacement of the model are shown in 

Figure 23. The figure shows the results of two simulations; one at the maximum modulus of 

elasticity, 70 GPa, and another at the knocked-down modulus of elasticity, 35 GPa. In both cases, 

the modulus of elasticity of the gores is kept the same at 3.7 GPa. The figure shows a fairly 

exponential curve with the decrease of the inflation pressure. The model at inflation pressure of 

10 KPa or less was unstable and was not able to converge. The histories of convergence of the 

performed simulations are shown in Figure 24. 

A typical deformation contours over the model for the case of toroids inflation pressure of 15 

GPa and toroids modulus of elasticity of 35 GPa is shown in Figure 25. The figure shows that the 

peak displacement occurs near the outer diameter of the model. 

The FEM cases conducted so far were with constant loading over the model. When the predicted 

CFD loads were applied to the current model, the nonlinear FEM model was not able to 

converge and sometimes collapsed. The FEM model had to be revisited to be sure that we are not 

missing important details that may affect the rigidity and stability of the model. 

Figure 23. Effect of toroids inflation pressure on the model peak deflection
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Figure 24. The convergence histories of the conducted simulations

Figure 25. Deformation contours for the case of inflation pressure of 15 GPa.

4.2.2 Static FEM Analysis of the Modified MIAS Model

As mentioned in the previous section, the original FEM model was only converging when an 

average constant loading was applied. The simulations were not converging when the predicted 

CFD loads were applied over the model. Looking back at the details of the toroids, the toroids 
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thickness was 13.178 mil and it has 6 straps running along the major circumferential direction of 

the model, as shown in Figure 26. These circumferential straps were ignored in the original 

model. The straps are made of Kevlar with maximum modulus of elasticity of 70 GPa and 

Poisson‟s ratio of 0.1. The cross sectional area of these straps is 113.37 mm2each. Obviously, 

these circumferential straps will contribute significantly to the rigidity of the model and therefore 

have to be taken into consideration. 

Since the axial straps are made of Kevlar which is the same material as the toroids, the FEM 

model can be simplified by using an equivalent toroid thickness. The equivalent toroid thickness

is adjusted based on the cross sectional areas of the toroids and axial straps together. The effect 

of the straps cross sectional area led to an equivalent toroid model with a thickness of about 24 

mil. The FEM simulations conducted in remainder of this section correspond to this modified 

FEM model.

Figure 26. Schematic view showing the toroids structure with axial straps

The predicted pressures over the front shield of the model are converted into forces and projected 

over the surface model using the MDICE interface module. The contours of the CFD loads over 

the FEM model are shown in Figure 27. Several static FEM simulations for the modified FEM 

model were conducted at different inflation pressures from 10 KPa to 35 KPa. The simulations 

were conducted using the predicted CFD loads as well as accurate constant averaging loading 

over the model for comparison. 

The effects of the toroids inflation pressure on the peak normal displacement and total 

displacement of the model are shown in Figure 28 for the cases using the predicted CFD loading. 

The total displacement is computed as follows;

The same series of simulations were conducted for an average CFD loading over the model. In 

the average CFD loading simulations, the predicted CFD loads were used to compute an average 

loading over the windward side and the leeward side of the model. The average CFD load over 

the windward side was 6706 Pa, and the average CFD load over the leeward side was 2882 Pa. 

2 2 2 Total Displacement = x y z
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The results of the total displacements for the predicted CFD loads and CFD average loading are 

compared to the cases of constant loads of 5000 Pa in Figure 29. Comparing Figure 29 (the green 

line) to the results of Figure 23 show that the addition of axial straps reduced the displacements 

by about 30%. The figure also shows that the cases of the predicted CFD loads and the cases of 

averaged CFD loading yielded close results. The averaged CFD loading on the full front shield 

under predicts the total deformation in the structure. A better averaging over several patches of 

the model may lead to even better comparison between both cases. 

The deformation contours over the front shield of the model for the predicted CFD loading and 

the averaged loading are shown in Figure 30 for the case of toroids inflation pressure of 15 KPa. 

The deformation contours over the same model, removing the front gores skin are shown in 

Figure 31. The topology of the deformation contours is similar in both cases with a larger region 

of high deformation for the case of averaged loading. 

Figure 27. Predicted CFD loading over the front surface of the FEM model
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Figure 28. Effect of toroids inflation pressure on the peak displacement of the modified model

Figure 29. Peak total displacement of the modified FEM model using different loading 

conditions.
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(a) With predicted CFD loads

(b) With averaged loads

Figure 30. Deformation contours over the front shield of the modified FEM model at toroids 

inflation of 15 KPa

(a) With predicted CFD loads

(b) With averaged loads

Figure 31. Deformation contours over the modified FEM model (removing the front gores skin) 

at toroids inflation of 15 KPa

The effect of toroids inflation pressure on the von Mises stresses for the cases of predicted CFD 

loads and CFD average loading are compared to the cases of constant loads of 5000 Pa in Figure 

32. The cases simulated with the predicted CFD loading is obviously produced higher stresses 

since the highest stress is generally will be function of the high loads. The contours of von Mises

stresses over the model in both cases are shown in Figure 33 for the case of toroids inflation 

pressure of 15 KPa. The maximum stress occurs in the middle of the windward side near the 

rigid front shield. The maximum stress on the model is mostly due to the aerodynamic loading. 

To emphasize this point, a series of FEM simulations were conducted to compute the model 

response under the effect of toroids internal pressure only, i.e. no CFD loading. The distribution 
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of von Mises stresses due to the internal pressure only is shown in Figure 34. As shown in the 

figure, the stresses due to toroids internal pressure only is one-order of magnitude less than the 

total stresses over the model due to the CFD loading and internal pressure. These test cases show 

that the effect of aerodynamic loading is higher than the effect of internal pressure.

Figure 32. Effect of toroids inflation pressure on von Mises stresses

(a) With predicted CFD loads (b) With averaged loads

Figure 33. von Mises stresses over the modified FEM model at toroids inflation of 15 KPa
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Figure 34. von Mises stress over the FEM model due to toroids internal pressure only.

4.3 Summary

A three-dimensional computational CFD model for the IAD model configuration was developed. 

A reacting thermally perfect CO2 model was used to simplify the Mars atmosphere. Steady state 

Euler simulation was conducted successfully at 30 degrees angle of attack, and the aerodynamic 

forces and moments were predicted. In addition, a computational structural nonlinear FEM 

model of the IAD model was developed using quad shell elements. A modified version of the 

FEM model was also developed that takes into consideration the axial straps of the toroids. 

Extensive FEM simulations were conducted with various internal pressures and using the CFD 

calculated loads and constant averaged loads.
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5 AEROELASTIC AND DYNAMIC ANALYSIS OF THE DOUBLE STACK IAD 

CONFIGURATION

The models developed for the nominal double stack IAD configuration were used to conduct 

aero-structural and dynamic simulations at 30 degrees angle of attack and bank angle rate of 5 

deg/sec2. Simulations were carried out for up to 4 seconds. First, a dynamic moving body CFD 

simulation was conducted with an assumption that the entire IAD was rigid. This provides a set 

of baseline aerodynamic data to compare against. Then, several aero-structural simulations were 

conducted in this effort;

1. Dynamic fluid-structure interaction simulation with average constant CFD loading. In 

this case, the average CFD loads on several patches of the model are applied to the FEM 

model and the structural responses are computed during the dynamic maneuver. 

2. Dynamic fluid-structure interaction simulation with one-way coupling. In this case, the 

CFD solves for the transient aerodynamic loads and transfer them to the FEM model 

every time step to solve for structural responses. The deflections are not fed back into the 

CFD model.

3. Dynamic fluid-structure interaction simulation with two-way coupling. In this case, the 

CFD and FEM solvers are exchanging transient aerodynamic loads and aeroelastic 

deflections every time step.

The simulations for the three different coupling methods were executed over a cluster of 

computers of 20 CPU (5 nodes with 2 dual-core AMD Opteron 2218 processors each). The 

computational costs for conducting the simulations are shown in Table 6 (assuming no network 

interruptions). The computational cost is reported as time per single iteration of simulation. The 

time step for the simulations is 0.0001 s. 

Table 5 Total clock time required for the three different methods of coupling on 20 CPUs

Method Computation Time / Time Step

Averaged CFD Loading 22.68 seconds

One – Way FSI Coupling 68.04 seconds

Two-Way Coupling 75.60 seconds

5.1 Aerodynamic Forces for the Aeroelastic Dynamic Maneuver

As mentioned before, three aeroelastic dynamic simulations were conducted using average 

constant CFD loads, one-way FSI coupling, and two-way FSI coupling. All simulations assumed 

flexible structural model with banking maneuver of 5 deg/sec2. All simulations were started from 

an undeformed initial state. Figure 35 shows the simulation time period for all the conducted 

aeroelastic dynamic simulations. The aeroelastic dynamic simulation with average constant CFD 

loading was conducted for about 4 seconds of simulation. The one-way coupling simulation case 

we conducted for about 3.2 seconds of simulation. The two-way coupling simulation case we 

conducted for about 2.1 seconds of simulation.
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The histories of the aerodynamic forces and moments during the aeroelastic dynamic simulation 

are shown in Figure 36 - Figure 40. The results of the two-way coupling are compared to the 

aerodynamic coefficients of aerodynamic simulation with rigid-body motion for comparison. 

The histories of the lift and drag coefficients during the aeroelastic dynamic simulation are 

shown in Figure 36 and Figure 37, respectively. The history of the side force coefficient is shown 

in Figure 38. The figure shows that the aerodynamic loads coefficients fluctuates around mean 

values that are very close to the values of the aerodynamic forces for rigid body motion. The 

mean value of the drag coefficients is almost flat similar to the rigid body motion simulation. 

The histories of the moment coefficients during the aeroelastic dynamic simulation are shown in 

Figure 39 and Figure 40, respectively. The aerodynamic moment values are also very close to the 

values of rigid-body motion and have the same trend. 

Figure 35. Bank maneuver simulation period for all considered aeroelastic simulations

Figure 36. History of coefficient of lift during the aeroelastic dynamic simulation
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Figure 37. History of coefficient of drag during the aeroelastic dynamic simulation

Figure 38. History of coefficient of side force during the aeroelastic dynamic simulation
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Figure 39. History of banking moment coefficient during the aeroelastic dynamic simulation

Figure 40. History of side moment coefficients during the aeroelastic dynamic simulation

5.2 Aeroelastic Structural Deformations

At first, the structural deformations for the case of average constant loading on the model are 

presented. The structural deformations are monitored at three points as shown in Figure 41; one 
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on the outer edge of the model, the second on the mid surface, and the third on the inner side of 

the model. 

Figure 41. Monitor Point Locations on the Model

Comparison of the main component of structural deformation (y-component) for the three 

conducted simulations is shown in Figure 42. The contribution of the rigid body motion in this 

figure is zero as indicated previously. The figure shows that the model is fluctuating around a 

fairly constant mean. This mean value is very close to the steady state deformation value 

computed in Task 1. The results of the three simulations are comparable to each other. The mean 

value of aeroelastic deformation of the two-way coupling is slightly higher than the other two 

simulations and also shows damping over several cycles. 

Figure 43 and Figure 44 show comparisons of the x- and z- components of structural 

deformations for the three conducted simulations. The components due to rigid-body motion are 

also shown in the figures for comparison. The figures show that the aeroelastic deformations for 

the conducted simulations are comparable to each other and that they are very close to the rigidbody motion case. The two-way coupling case shows faster damping of the x-component of 

deformation. No significant change is shown in the z-component of structural deformation 

between all the considered simulations. The contribution of the aeroelastic deformation only for 

the z-component for the two-way coupling simulation is shown in Figure 45.

The previous simulations were conducted using the original thickness of the gores (skin) which 

is about 26.5 mil. However, the actual model contains 18 radial straps of 12 mm thickness and 

modulus of elasticity of 14 GPa. The structural model considered in this study do not model the 

radial straps. If the effect of straps were taken into consideration, the thickness of the gores may 

have to be increased to about 200 mil. The structural deformations for the skin thickness of 26.5 

mil are shown in Figure 46. The structural deformations for the skin thickness of 200 mil are 

shown in Figure 47. Since the model is exhibiting banking maneuver, the x- and z-components 

of deflections contain both the aeroelastic deformations and the rigid body motion contribution. 

The y-component of deflection contains only the aeroelastic deformation since the model is not 

moving in this direction. The figures show that both cases are stable and as obvious the 200 mil 

thickness case produced less aeroelastic deflections than the 26.5 mil thickness case. The effect 

of different model thickness will be discussed in more details in the next chapter.
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Figure 42. Comparison of y-component of structural deformation for the conducted simulations

Figure 43. Comparison of x-component of structural deformation for the conducted simulations
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Figure 44. Comparison of z-component of structural deformation for the conducted simulations

Figure 45. Contribution of aeroelastic deformation only for the two-way coupling simulation.
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Figure 46. Structural deformation of the average constant CFD loading simulation at skin 

thickness of 26.5 mil.

Figure 47. Structural deformation of the average constant CFD loading simulation at skin 

thickness of 200 mil.
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5.3 Aeroelastic Structural Stresses

Snapshots of von Mises stresses on the front surface of the toroids (without skin) are shown in 

Figure 48. The figure shows that the von Mises stress is cyclic, similar to the structural 

deformations, and is fluctuating between a maximum value of 4.9 E+08 N/m2and a minimum 

value of 1.5 E+08 N/m2. Since the yield stress of the Kevlar material is 35 GPa, the stress levels 

are way below the yield stress of the material. The peak stress levels occur at the windward side 

of the front surface of the toroids. Snapshots of von Mises stresses on the back surface of the 

toroids (without skin) are shown in Figure 49. Similar to the front surface, the stresses are also 

cyclic but they fluctuate around values less than those of the front surface. The peak stress levels 

occur around the inner circle of the surface, near the adapter location. Snapshots of von Mises 

stresses on the front surface of the skin are shown in Figure 50. The values of stresses on the skin 

are almost one-order of magnitude less than those values on the toroids. The von Mises stress on 

the skin is also cyclic, and is fluctuating between a maximum value of 1.4 E+08 N/m2and a 

minimum value of 5.4 E+07 N/m2. The peak values of stresses occur around the inner circle of 

the model near the location of the adapter.

The variation of the peak value of the von Mises stress versus time over the model is shown in 

Figure 51. The peak values of stresses occur over the front surface of the toroids. The figure 

shows clearly the cyclic nature of the stress variation which is in similar trend to the structural 

deformation of the model. 
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Figure 48. Snapshots of von Mises stresses on the front surface of the toroids
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Figure 49. Snapshots of von Mises stresses on the back surface of the toroids
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Figure 50. Snapshots of von Mises stresses on the front surface of the gores
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Figure 51. Variation of peak von Mises stress versus time

5.4 Summary

The aeroelastic responses of the model were computed for three simulations; using average 

constant CFD loading, using one-way FSI coupling from the fluid to the structure, and using 

two-way FSI coupling. The structural responses of the three simulations were comparable. The 

structural deformations and stresses were cyclic over the model and they fluctuates around an 

almost constant mean values. Although the von Mises stress levels on the gores and toroids were 

far less than the yield stress of the materials of the gores and toroids, it was seen that the peak tip 

deflections of the IAD were quite large (~0.7 m). We determined in consultation with the 

technical monitor that this was most likely the effect of ignoring the presence of the radial straps. 
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6 AEROELASTIC AND DYNAMICS ANALYSIS OF A MODIFIED DOUBLE STACK 

IAD CONFIGURATION INCLUDING RADIAL STRAPS

In the previous chapter, the tip deflections of the IAD were larger than expected. They were of 

the order of 0.6 to 0.7 m in the flow direction. This is most likely the effect of ignoring the 

presence of the radial straps. In this part of the study, the effect of modeling the radial straps is 

simulated. The effect of inflation pressure on the peak deflections is also simulated. Aerostructural and dynamic simulations of the IAD model at 30 degrees angle of attack and bank 

angle rate of 5 deg/sec2 were conducted. Simulations were carried out for up to 4 seconds. An 

effort was also made to speed up the computation by coarsening the CFD grid. The following 

aero-structural simulations were conducted in this effort:

1. Effect of toroid inflation pressure on the dynamic response of the using average 

constant CFD loading. In this case, the average CFD loads on several patches of the 

model are applied to the FEM model and the structural responses are computed during 

the dynamic maneuver for various toroid internal pressures. 

2. Effect of coarsening the CFD grid. In this case, the two-way coupled FSI case from task 

was re-run with a coarser CFD grid. The solutions of the fine and coarse grid were then 

compared. 

3. Effect of radial straps. In this case, the effect of radial straps was accounted for, both by 

a) increasing the thickness of the cover (skin) and b) by increasing thickness and its 

material properties.

6.1 Effect of Toroids Inflation Pressure on IAD Dynamics

In order to attempt to reduce the deflection, the effect of the increase in the toroids inflation 

pressure on the IAD dynamic was simulated. The inflation pressure of the toroids was increased 

by 50% and 100% from the baseline 15 KPa, to 22.5 KPa and 30 KPa respectively. All 

simulations were started from an undeformed initial state. The aeroelastic dynamic simulation 

with average constant CFD loading was conducted for about 4 seconds of simulation.

The plot of displacement in the y-direction (direction of flow) at the outer edge of the IAD for 

the three inflation pressures applied is shown in Figure 52. The displacement in x-direction is 

shown in Figure 53. Since the model is performing a banking maneuver, the x-component of 

deflection contains both the aeroelastic deformations and the rigid body motion contribution. The 

y-component of deflection contains only the aeroelastic deformation since the model is not 

moving in this direction. The contribution of the aeroelastic deformation only for the xcomponent is shown in Figure 54.
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Figure 52 Comparison of y-component of structural deformation for various inflation pressures.

Figure 53 Comparison of x-component of structural deformation for various inflation pressures.
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Figure 54 Comparison of aeroelastic component of structural deformation in the x-direction for 

various inflation pressures.

The results show that the overall deformation of the model is reduced by about 4 to 7 % in 

response to increase in inflation pressure of 50 to 100%. This is keeping in line with the results 

obtained in task 1 for steady state deformation response to increase in pressure. 

6.2 Effect of Coarse Grid on the Solution

In task 2, it was seen that the CFD solution with a grid of 2.4 million cells was very stable and 

robust, even during large structural deflections. However, the aeroelastic analysis with a fine 

CFD grid required about 4 weeks, on a cluster of 20 CPUs (5 nodes with 2 dual-core AMD 

Opteron 2218 processors each), assuming no network interruptions, to complete 4 seconds of 

simulations. Therefore, to speed up the solution, the CFD grid was reduced from 2.4 M to 1.6 M, 

primarily in the circumferential direction. The CSD grid was kept the same as before. Then, the 

two-way coupled FSI simulation from task 2 was rerun using the new grid to see the effect of the 

coarse grid on solution quality. 

6.2.1 Effect of Grid Coarsening on Aerodynamic Forces and Moments

The histories of the aerodynamic forces and moments during the aeroelastic dynamic simulation 

are shown in Figure 55 - Figure 60. The results of the two-way coupling methods using the fine 

and coarse CFD grids are compared with each other along with the aerodynamic coefficients of 

aerodynamic simulation with rigid-body motion for reference. The histories of the lift and drag 

coefficients during the aeroelastic dynamic simulation are shown in Figure 55 and Figure 56, 

respectively. The history of the side force coefficient is shown in Figure 57. The histories of the 
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side moment coefficients and banking moment coefficients are shown in Figure 58, Figure 59

and Figure 60. All results indicate very close agreement between the fine and coarse grid 

solutions. The coefficient of drag, which is the primary aerodynamic coefficient of interest, is 

unaffected by the reduction in grid. The effect on the magnitude, phase or frequency of the 

oscillations of all the aerodynamic coefficients was minimal. 

Figure 55. History of coefficient of lift during the aeroelastic dynamic simulation for coarse and 

fine grids

Figure 56. History of coefficient of drag during the aeroelastic dynamic simulation for coarse 

and fine grids
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Figure 57. History of coefficient of side force coefficient during the aeroelastic dynamic 

simulation for coarse and fine grids

Figure 58. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for coarse and fine grids
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Figure 59. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for coarse and fine grids

Figure 60. History of banking moment coefficient during the aeroelastic dynamic simulation for 

coarse and fine grids

6.2.2 Effect of Grid Coarsening on Structural Deformations

The plot of displacement in the y-direction (direction of flow) for the three inflation pressures 

applied is shown in Figure 61. The displacement in x-direction is shown in Figure 62. The results 
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show that the displacements using the coarse and fine grid results are nearly the same. The 

displacement in the y-direction, which is the direction of flow, is unaffected by the coarse grid. 

Figure 61 Comparison of y-component of structural deformation for various inflation pressures.

Figure 62 Comparison of x-component of structural deformation for various inflation pressures.

The coarse grid show very good agreement with the fine grid results. The coarse grid allows us 

to run the full 4 seconds of simulation in about 2 weeks on a cluster of 16 CPUs (4 nodes with 2 

dual-core AMD Opteron 2218 processors each), assuming no network interruptions. This is 
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nearly a 100% speed up improvement in the FSI simulations compared to the fine grid. The 

coarse grid is used for simulations from this point onwards. 

6.3 Effect of Modeling Radial Straps 

As mentioned before, it was seen in the previous chapter that the tip deflections of the IAD were 

larger than expected. It is strongly believed that the large deflections were due to ignoring the 

effect of radial straps. The radial straps are made of the more rigid Kevlar material and they have 

substantial mass and thickness. Therefore, an attempt was made to present a more consistent 

model with the actual design by developing an equivalent mechanical model to the radial straps. 

Instead of modeling the radial straps by adding the strap geometry to the existing structural 

model, after consultation with the program technical monitor, the effect of the radial straps was 

simulated using two methods;

a) Developing an equivalent mechanical model by increasing the thickness of the gores to 

account for both the area of the straps and higher modulus of elasticity of the straps 

Upilex material. In the model, the equivalent thickness of the gores was about 200 mil 

with Upilex E of 3.7E+9 Pa.

b) Developing an equivalent mechanical model by increasing the thickness of the gores to 

account for the area of the straps, and computing an equivalent modulus of elasticity (E) 

to account for the different E between the Upilex of the gores and Kevlar of the straps. In 

this model, the equivalent thickness of the gores was about 54 mil, and the equivalent 

modulus of elasticity was about 19.6E+9 Pa.

The dynamic FSI simulations conducted in this section were performed with an inflation 

pressure of 15 KPa. All simulations were started from an undeformed initial state. The 

aeroelastic dynamic simulations with constant averaged CFD loads and with two-way FSI 

coupling were conducted for about 4 seconds of simulation. The results were compared to the 

model without radial straps (26.5 mil) and also with the rigid body motion. 

6.3.1 Aerodynamic Forces and Moments

The histories of the aerodynamic forces and moments during the aeroelastic dynamic simulation 

are shown in Figure 63 - Figure 68. The results of the two-way coupling methods using the two 

radial strap models are compared with the case without radial straps and with the aerodynamic 

coefficients of aerodynamic simulation with rigid-body motion for reference. The histories of the 

lift and drag coefficients during the aeroelastic dynamic simulation are shown in Figure 63 and 

Figure 64, respectively. The history of the side force coefficient is shown in Figure 65. The 

histories of the side moment coefficients and banking moment coefficients are shown in Figure 

66, Figure 67, and Figure 68. 

The results show that there is a significant reduction in oscillation of the aerodynamic 

coefficients about their mean when the radial straps are taken into consideration. All the results 
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show damping of the oscillations as the simulation progresses, which may indicate that the 

structure model is aeroelastically stable. It is believed that the oscillations damping is because of 

aerodynamic damping as well as the dynamic motion of the model. The results also indicate that 

the radial strap model with the 54 mil thickness and high E is more rigid than the others and is 

consequently the closest to the reference rigid body motion solution. 

Figure 63. History of coefficient of lift during the aeroelastic dynamic simulation for various 

radial strap models

Figure 64. History of coefficient of drag during the aeroelastic dynamic simulation for various 

radial strap models
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Figure 65. History of side force coefficient during the aeroelastic dynamic simulation for various 

radial strap models

Figure 66. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for various radial strap models
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Figure 67. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for various radial strap models

Figure 68. History of banking moment coefficient during the aeroelastic dynamic simulation for 

various radial strap models
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6.3.2 Aeroelastic Structural Deformations

In this section, two sets of results are presented. First, the results obtained using CFD-averaged 

constant loads are shown. These will then be compared with the results obtained using the twoway coupling FSI to see the effects of the aerodynamic damping on the solution. 

CFD-Averaged Constant Loads

The trace of displacement in the y-direction (direction of flow) at a point on the outer edge of the 

IAD for the two radial strap models is compared with the structural model without the radial 

strap and is shown in Figure 69. The displacement in x-direction is shown in Figure 70. As 

mentioned before, since the model is performing a banking maneuver, the x- and z-components 

of deflections contain both the aeroelastic deformations and the rigid body motion contribution. 

The y-component of deflection contains only the aeroelastic deformation since the model is not 

moving in this direction. The contribution of the aeroelastic deformation alone for the xcomponent and the z-component are shown in Figure 71 and Figure 72 respectively.

The results show that there is a significant reduction in oscillation of the x, y, and z component 

of displacement about their mean when the radial straps are taken into consideration. The results 

also indicate that the radial strap model with the 54 mil thickness and high E is more rigid than 

the others and is consequently the closest to the reference rigid body motion solution. 

The aeroelastic deformation alone for the z-component in Figure 72 shows increasing amplitude 

of oscillations as the solution progresses. This increase is also present for both radial strap 

models although the magnitude of oscillations is smaller than the case without the radial strap. 

This increase in amplitude may be due to the effect of increasing rotational velocity of the IAD 

due to the constant acceleration of 5 deg/s2that is applied to the rigid front shield. 

Figure 69 Comparison of y-component of structural deformation for various radial strap models.
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Figure 70 Comparison of x-component of structural deformation for various radial strap models.

Figure 71 Comparison of aeroelastic component of structural deformation in the x-direction for 

various radial strap models.
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Figure 72 Comparison of aeroelastic component of structural deformation in the z-direction for 

various radial strap models.

Two-Way FSI Coupling

The trace of displacement in the y-direction (direction of flow) at a point on the outer edge of the 

IAD for the two radial strap models is compared with the structural model without the radial 

strap and is shown in Figure 73. The displacement in x-direction and z-direction are shown in 

Figure 74 and Figure 75, respectively. The contribution of the aeroelastic deformation alone for 

the x-component and the z-component are shown in Figure 76 and Figure 77, respectively.

The results show that there is a further reduction in oscillation of the x, y, and z component of 

displacement about their mean compared to the cases with averaged constant CFD loading. That 

is clearly due to aerodynamic damping. The results also indicate that the radial strap model with 

the 54 mil thickness and high E is more rigid than the others and is consequently the closest to 

the reference rigid body motion solution. 

As seen before in the test with constant CFD-averaged loads, the aeroelastic deformation alone 

for the z-component in Figure 77 shows increasing amplitude of oscillations as the solution 

progresses. However, due to the effect of aerodynamic damping, the amplitude of oscillations are 

smaller compared to the results from the constant averaged CFD loads. 

Fast Fourier Transforms (FFT) of aeroelastic component of the x-displacement and the ydisplacement were performed. The plots of the power spectral density (PSD) of all the cases 

considered in this subtask are shown in Figure 78 and Figure 79. The first and second modes of 

the IAD for the various models are shown in Table 6. 
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Figure 73 Comparison of y-component of structural deformation for various radial strap models.

Figure 74 Comparison of x-component of structural deformation for various radial strap models.
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Figure 75 Comparison of z-component of structural deformation for various radial strap models.

Figure 76 Comparison of aeroelastic component of structural deformation in the x-direction for 

various radial strap models.
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Figure 77 Comparison of aeroelastic component of structural deformation in the z-direction for 

various radial strap models.

Figure 78 Comparison of PSD based on y-component of structural deformation for various 

radial strap models.
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Figure 79 Comparison of PSD based on aeroelastic component of structural deformation in the 

x-direction for various radial strap models.

Table 6 First two modes of the IAD for various strap models

Model 26.5 mil 200 mil 54 mil, high E

1st, 2nd Frequencies (Hz) 7.069, 11.44 6.63, 11.17 10.94, 19.1

6.3.3 Structural von Mises Stresses

In this section, von Mises stress results obtained using the two-way coupling are presented. The 

time trace of von Mises stress results on the toroids is presented in Figure 80. The figure also 

shows that the von Mises stress is cyclic, similar to the structural deformations. The stress in the 

baseline 26.5 mil model is fluctuating between a maximum value of 5 E+08 N/m2and a 

minimum value of 1.5 E+08 N/m2. Since the yield stress of the Kevlar material is 35 GPa, the 

stress levels are way below the yield stress of the material. As seen in the previous sections, the 

effect of increasing the skin thickness is to reduce the overall deformation of the IAD. This is 

reflected in the factor-of-two reduction for the stress developed in the toroids for the cases with 

the thicker skin and high E.

The time history of von Mises stress results on the cover (skin/gore) is presented in Figure 81. 

The von Mises stress on the skin is also cyclic, and is fluctuating between a maximum value of 

1.5 E+08 N/m2and a minimum value of 5E+07 N/m2for the baseline 26.5 mil case. In case of 

the cover, a factor-of-ten reduction is seen in the stress for the 200 mil skin case when compared 

to the baseline 26.5 mil case. The stress developed in the 54 mil skin is higher due to the higher 
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Young‟s Modulus (E) of 19.6E+9 used in that case. Even though the strain developed in the 54 

mil case is small, the higher E implies that the stress is also numerically higher. 

Figure 80 Comparison of von Mises stresses on the toroids for various radial strap models.

Figure 81 Comparison of von Mises stresses on the cover (gores/skin) for various radial strap 

models.
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Snapshots of peak von Mises stresses on the front surface of the toroids and the cover (gore/skin) 

for the various models are shown in Figure 82. The peak stress levels occur at the windward side 

of the front surface of the toroids. For the cover, the peak values of stresses occur around the 

inner circle of the model near the location of the adapter.

Figure 82 Snapshots of peak von Mises stresses on the toroids and cover (gores/skin) for various 

radial strap models.

6.4 Summary

To speed up the computation, coarser models were developed for dynamic fluid structure 

coupling of IAD. Their fidelity was verified vs. the fine grid model. Simulations were conducted 

to investigate the effect of increasing the toroid inflation pressure. It was seen that it only has a 

small impact on overall deformation, keeping in line with the steady results obtained in Task 1. 

Aeroelastic response of the IAD was tested after adding the radial straps to the IAD by making 

changes to the thickness and material properties of the IAD Cover (gore/skin). Both CFD 

constant averaged loads and two-way FSI coupling were used. It was seen that the deflections of 

the IAD are reduced dramatically when effect of radial straps are added to the model. But as 

noted in the previous chapter, even without the straps, von Mises stresses are still far less than 

the yield stress of the Gores and toroids materials. 
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7 AEROELASTIC AND DYNAMIC ANALYSIS OF A SINGLE STACK IAD 

CONFIGURATION

In this effort, CFDRC developed three-dimensional computational models based on a modified 

design for the IAD. The main design change involved using a single row of toroids, instead of 

two rows of toroids used in the previous tasks. The new model is referred to in this report as a 

single stack(ed) model. The other design changes were to the thicknesses of the toroids and the 

cover of the IAD model. Materials and their properties were unchanged. These models were then 

used to conduct aero-structural and dynamic simulations of the IAD model at 30 degrees angle of 

attack and bank angle rate of 5 deg/sec2. Simulations were carried out for up to 4 seconds. An 

effort was also made to understand the effect of inflation pressure and the dynamic maneuver. 

The following aero-structural simulations were conducted in this effort:

4. Effect of toroid inflation pressure and banking maneuver on the dynamic response of 

the IAD the using average constant CFD loading. In this case, the average CFD loads 

on several patches of the model are applied to the FEM model and the structural 

responses are computed during the dynamic maneuver for various toroid internal 

pressures. The results were compared with the double stack model as well. 

5. Effect of the single stack IAD model on the dynamic response of the IAD using twoway aeroelastic FSI coupling. In this case, the dynamic response of single stack model 

was compared with the double stack model for the same banking maneuver and loads.

7.1 Computational Fluid Dynamics Model for Single Stack IAD Configuration

The computational grid model of the single stack IAD was developed using the grid generator 

CFD-GEOM. The overall computational grid is shown in Figure 83. As shown in the figure, the 

computational grid model of the IAD is overset over a background grid to enable the dynamic 

bank maneuvering. The computational grid of the IAD model is shown in red, while the 

background grid is shown in blue. Although the geometrical model is symmetric, the 

computational grid was developed and the simulations were conducted on a full 360 degrees 

three-dimensional model due to the banking dynamic maneuver that will be considered in this 

effort. The CFD grid of the modified single stack IAD model is compared with the nominal 

double stack model in Figure 84. 
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Figure 83. Overall computational grid boundaries for the modified design.

(a) Single stack model (b) Double stack model

Figure 84 Single and double stack CFD models

7.2 Computational Structural Dynamics Model for Single Stack IAD Configuration

The computational structural FEM model of the single stack IAD configuration is compared with 

the double stack configuration in Figure 85. The new model consists of 18,500 quad shell 

elements of non-zero thickness. The toroids are modeled with 12 quad shell elements each. The 

toroids are connected together through one of the 12 elements, and they are also connected with 

the gores (the outside skin/cover) through one segment. 

The toroids are made of Kevlar and the gores are made of Upilex. The material properties of the 

Kevlar and the thickness of the toroids are shown in Table 7. The material properties of the 
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Upilex and the thickness of the gores are shown in Table 8. A high temperature knock down 

factor of 0.5 is used for the toroids modulus of elasticity. The toroid thickness is assumed to be 

8.6 mil to take account of the 6 circumferential straps that are present in each toroid. The 

notional toroids inflation pressure is assumed to be 30 KPa. To account for the 18 radial straps 

over the cover, the thickness of the cover is set to 53.2 mil and the effective young‟s modulus 

increased to 18.5 GPa. 

Figure 85. Computational FEM model of the single stack IAD configuration compared to the 

double stack configuration.

Table 7. Material properties of the toroids for the single stack IAD configuration.

Kevlar Properties for Toroids

Max E 70 E+09 Pa

Design E 35 E+09 Pa

Density 1440 Kg/m3

Poisson ratio 0.1

Toroids thickness 5.13 Mil (w/o 

circumferential straps)

Table 8. Material properties of the gores for the single stack IAD configuration.

Upilex Properties for Gores

E 3.7 E+09 Pa

Density 1470 Kg/m3

Poisson ratio 0.34

Gores thickness 26.536 Mil
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7.3 Steady State Aerodynamic Simulation Results of Single Stack IAD Configuration

The previously described aerodynamic model with the flow and flight conditions for the 

simulation previously given in Table 3 was used to simulate the aerodynamic flowfield around 

the new single stack IAD model.

The overall pressure and mach contours over the symmetry plane of the whole computational 

domain are shown in Figure 86 and Figure 87, respectively. A maximum pressure of about 8500 

Pa occurs over the front shield of the model and in front of the oncoming flow. The surface 

pressure contours over the front of the IAD surface is shown in Figure 88. The maximum 

pressure occurs nears the windward side of the model and decreases toward the leeward side. 

The pressure profiles on the front surface for the double stack and single stack models are nearly 

identical. The pressure in the back of the model is very small compared to the front side. There 

are small differences in pressure profiles between the single and double stack models as shown 

in Figure 89. 

Figure 86 Steady state pressure field around the single stack IAD model

Figure 87 Steady state Mach number field around the single stack IAD model
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Figure 88 Pressure contours on the front surface of the single stack IAD model

Figure 89 Comparison of pressure profiles on the back of the single stack and double stack 

models

7.4 Transient FEM Simulation of the Single Stack IAD Dynamics 

In this subtask, transient FEM simulations of the single stack IAD model were conducted at 

different inflation pressures using the average constant CFD loading. The inflation pressures 

considered were 15 and 30 KPa. The results were compared against the rigid body motion and 

the double stack IAD model with the radial strap model that was developed in Task 3. All 

simulations were started from an undeformed initial state. The aeroelastic dynamic simulation 

with average constant CFD loading was conducted for about 4 seconds of simulation.
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7.4.1 Comparison of Structural Deformations

The plot of displacement in the y-direction (direction of flow) at the outer edge of the IAD for 

the three inflation pressures applied is shown in Figure 90. The displacement in x-direction and 

z-direction are shown in Figure 91 and Figure 92. Since the model is performing a banking 

maneuver, the x- and z-components of deflections contain both the aeroelastic deformations and 

the rigid body motion contribution. The y-component of deflection contains only the aeroelastic 

deformation since the model is not moving in this direction. The contribution of the aeroelastic 

deformation only for the x and z components are shown in Figure 93 and Figure 94. 

Figure 90 Comparison of y-component of structural deformation for double and single stack 

configurations with two different inflation pressures.

Figure 91 Comparison of x-component of structural deformation for double and single stack 

configurations with two different inflation pressures.
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Figure 92 Comparison of z-component of structural deformation for double and single stack 

configurations with two different inflation pressures.

Figure 93 Comparison of aeroelastic component only of structural deformation in the x-direction 

for double and single stack configurations with two different inflation pressures.
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Figure 94 Comparison of aeroelastic component only of structural deformation in the z-direction 

for double and single stack configurations with two different inflation pressures.

Just like results in previous chapters, the results show that the overall deformation of the model 

is reduced by about 4 to 7 % in response to an increase in inflation pressure of 50 to 100%. This 

is keeping in line with the results obtained in task 1 for steady state deformation response to 

increase in pressure. 

Fast Fourier Transforms (FFT) of aeroelastic component of the y-displacement were performed. 

The plots of the power spectral density (PSD) of all the cases considered in this subtask are 

shown in Figure 95. It can be seen that the frequencies are quite similar. 

Figure 95 Comparison of PSD based on y-component of structural deformation for double and 

single stack configurations with two different inflation pressures.
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The effect of the dynamic maneuver is discussed next. As seen before in previous tasks, the 

aeroelastic deformation alone for the z-component in Figure 94 shows increasing amplitude of 

oscillations as the solution progresses. To understand this, one case was run without any dynamic 

maneuver. The contribution of the aeroelastic deformation only for the x and z components are 

compared with the previous results and are shown in Figure 96 and Figure 97. 

Figure 96 Comparison of aeroelastic component only of structural deformation in the x-direction 

with and without dynamic maneuver.

Figure 97 Comparison of aeroelastic component only of structural deformation in the z-direction 

with and without dynamic maneuver.
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For the case without dynamic rotation, the magnitude of the high frequency oscillations in the z 

deflection component in Figure 97 is of the order of the thickness of the IAD cover and toroids. 

Therefore, it is clear that the increase in the mean displacement in the z-direction is primarily due 

to the effect of the dynamic maneuver. 

7.4.2 Comparison of Structural von Mises Stress

In this section, von Mises stress results obtained using the averaged constant loads are presented. 

The time history of von Mises stress results on the toroids is presented in Figure 98. The figure 

also shows that the von Mises stress is cyclic, similar to the structural deformations. The stress in 

the baseline double stacked model is fluctuating between a maximum value of 2 E+08 N/m2and 

a minimum value of 1 E+08 N/m2. Since the yield stress of the Kevlar material is 35 GPa, the 

stress levels are way below the yield stress of the material. As seen in the previous sections, the 

effect of the single stack model is to increase the overall deformation of the IAD. This is 

reflected in increase in the stress developed in the toroids for the single stack cases.

The time history of von Mises stress results on the cover (skin/gore) is presented in Figure 99. 

The von Mises stress on the skin is also cyclic, and is fluctuating between a maximum value of 

1.25 E+08 N/m2and a minimum value of 7E+07 N/m2for the baseline double stack case. In case 

of the cover, a factor-of-two increase is seen in the stress for the single stack case. 

Figure 98 Comparison of von Mises stresses on the toroids for double and single stack 

configurations with two different inflation pressures.
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Figure 99 Comparison of von Mises stresses on the cover (gores/skin) for double and single 

stack configurations with two different inflation pressures.

7.5 Transient Two-Way FSI Simulation of the Single Stack IAD Dynamics 

In this subtask, the single stack IAD model was run with a design inflation pressure of 30 KPa 

using two way FSI coupling. All simulations were started from an undeformed initial state. The 

simulations with two-way FSI coupling were conducted for 4 seconds of simulation. The results 

were compared to the double stack model with radial straps, with the rigid body motion and the 

results from the constant averaged CFD loads from the last subtask. 

7.5.1 Aerodynamic Forces and Moments

The histories of the aerodynamic forces and moments during the aeroelastic dynamic simulation 

are shown in Figure 100 - Figure 105. The results of the two-way coupling methods using the 

single stack configuration is compared with the double stack case and with the aerodynamic 

coefficients of aerodynamic simulation with rigid-body motion for reference. The histories of the 

lift and drag coefficients during the aeroelastic dynamic simulation are shown in Figure 100 and 

Figure 101, respectively. The history of the side force coefficient is shown in Figure 102. The 

histories of the side moment coefficients and banking moment coefficients are shown in Figure 

103, Figure 104 and Figure 105. 

All the results show damping of the oscillations as the simulation progresses, due to aerodynamic 

damping, indicating the structure is aeroelastically stable. The results also indicate that the single 

stack configuration shows very little difference from the double stack configuration in terms of 

aerodynamic response and that they are both close to the reference rigid body motion solution. 
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Figure 100. History of coefficient of lift during the aeroelastic dynamic simulation for single and 

double stack configurations

Figure 101. History of coefficient of drag during the aeroelastic dynamic simulation for single 

and double stack configurations
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Figure 102. History of side force coefficient during the aeroelastic dynamic simulation for single 

and double stack configurations

Figure 103. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for single and double stack configurations
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Figure 104. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for single and double stack configurations

Figure 105. History of banking moment coefficient during the aeroelastic dynamic simulation for 

single and double stack configurations
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7.5.2 Aeroelastic Structural Deformations

The history of displacement in the y-direction (direction of flow) at a point on the outer edge of 

the IAD for the single and double stack configurations are shown in Figure 106. The 

displacement in x-direction and z-direction are shown in Figure 107 and Figure 108, 

respectively. The contribution of the aeroelastic deformation alone for the x-component and the 

z-component are shown in Figure 109 and Figure 110, respectively.

The results show that there is a small increase in oscillation of the x, y, and z component of 

displacement about their mean for the single stack configurations. There is also reduction in 

amplitude as time passes due to the aerodynamic damping. The results also indicate that there are 

additional modes in the solution for the single stack configuration, especially when considering 

two-way FSI coupling. 

As seen before in the test with constant CFD-averaged loads, the aeroelastic deformation alone 

for the z-component in Figure 110 shows increasing amplitude of oscillations as the solution 

progresses. However, due to the effect of aerodynamic damping, the amplitude of oscillations is

smaller compared to the results from the constant averaged CFD loads. 

Figure 106 Comparison of y-component of structural deformation for single and double stack 

configurations.
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Figure 107 Comparison of x-component of structural deformation for single and double stack 

configurations.

Figure 108 Comparison of z-component of structural deformation for single and double stack 

configurations.
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Figure 109 Comparison of aeroelastic component of structural deformation in the x-direction for 

single and double stack configurations.

Figure 110 Comparison of aeroelastic component of structural deformation in the z-direction for 

single and double stack configurations.

Fast Fourier Transforms (FFT) of aeroelastic component of the x-displacement and the ydisplacement were performed. The plots of the power spectral density (PSD) of all the cases 

considered in this subtask are shown in Figure 111 and Figure 112. 
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Figure 111 Comparison of PSD based on y-component of structural deformation for single and 

double stack configurations.

Figure 112 Comparison of PSD based on aeroelastic component of structural deformation in the 

x-direction for single and double stack configurations.
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7.5.3 Aeroelastic Structural von Mises Stresses

In this section, von Mises stress results for the single stack configuration obtained using the twoway coupling are presented and are compared with the double stack model results and the results 

obtained using the constant averaged CFD loads. The time history of von Mises stress results on 

the toroids is presented in Figure 113. The figure also shows that the von Mises stress is cyclic, 

similar to the structural deformations. The stress in the single stack model is fluctuating between 

a maximum value of 3 E+08 N/m2and a minimum value of 2 E+08 N/m2. Since the yield stress 

of the Kevlar material is 35 GPa, the stress levels are way below the yield stress of the material.

The time history of von Mises stress results on the cover (skin/gore) is presented in Figure 114. 

The von Mises stress on the skin is also cyclic, and is fluctuating between a maximum value of 

1.5 E+08 N/m2and a minimum value of 5E+07 N/m2. Snapshots of peak von Mises stresses on 

the front surface of the IAD are shown in Figure 115. The peak stress levels occur at the 

windward side of the front surface of the toroids. For the cover, the peak values of stresses occur 

around the inner circle of the model near the location of the adapter. 

Figure 113 Comparison of von Mises stresses on the toroids for single and double stack 

configurations.
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Figure 114 Comparison of von Mises stresses on the cover (gores/skin) for single and double 

stack configurations.

Figure 115 Snapshots of peak von Mises stresses on the toroids and cover (gores/skin) for single 

and double stack configurations.
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7.6 Summary

A new configuration was modeled using a single stack of toroids instead of the double stack used 

in previous tasks. Additional changes in skin thickness and properties were incorporated into the 

new model. Steady state CFD tests were run to provide new load models. The aeroelastic 

response was then computed for two different internal pressures using constant averaged loads 

and two-way FSI coupling and compared with previous models. It was seen that the aerodynamic 

response of the single stack configuration was very similar to the double stack configuration. 

There were small increases in the displacements and in the von Mises stresses. The von Mises 

stresses are still far less than the yield stress of the Gores and toroids materials.
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8 EFFECT OF DYNAMIC PRESSURE ON THE AEROELASTIC RESPONSE OF A 

SINGLE STACK IAD CONFIGURATION

In this effort, CFDRC studied the effect of flow dynamic pressure on the aeroelastic response of 

the IAD. These tests will help to give NASA engineers a degree of confidence in the factor of 

safety assumptions in the model. The single stack model developed previously was used to 

conduct aero-structural and dynamic simulations of the IAD model at 30 degrees angle of attack 

and bank angle rate of 5 deg/sec2. Simulations were carried out for up to 4 seconds. An effort 

was also made to understand the effect of aero loads on buckling of the IAD and of a single 

toroid. The following aero-structural simulations were conducted in this effort:

1. Effect of dynamic pressure on the response of the IAD the using two-way FSI 

coupling. In this case, the dynamic response of single stack model at the reference 

dynamic pressure (Qref = 5143 Pa) was compared with the response for half the 

dynamic pressure and for 1.5 times the reference dynamic pressure for the same 

banking maneuver.

2. Effect of dynamic pressure and loads on the buckling tendency of the IAD. In this 

case, the average CFD loads on several patches of the model equivalent to 1.5, 2, 3 

and 4 times the reference dynamic pressure (Qref = 5143 Pa) are applied to the FEM 

model and the structural responses are computed during the dynamic maneuver. A set 

of cases was also run to find the response of a single toroid to buckling loads.

8.1 Steady State CFD Results for Various Dynamic Pressures

The previously developed aerodynamic models with the flow and flight conditions for the 

simulation given in Table 3 was used to simulate the aerodynamic flowfields around the new 

single stack IAD model at two different dynamic pressures. In order to change the dynamic 

pressure, the density of the flow was changed, in turn changing the static pressure. For the 0.5 

times reference dynamic pressure (0.5*Qref) case, the pressure used was 18.85 Pa and for the 1.5 

* Qref case, the pressure used was 56.57 Pa.

The surface pressure contours over the front of the IAD surface for the various dynamic 

pressures are shown in Figure 116. At the reference dynamic pressure case, the maximum 

pressure of about 8500 Pa occurs over the front shield of the model and in front of the oncoming 

flow. This peak value is only about 4200 Pa for the 0.5*Qref case and is 12,700 Pa for the 1.5 * 

Qref case. 

The maximum pressure occurs nears the windward side of the model and decreases toward the 

leeward side. The pressure profiles on the front surface for the various dynamic pressures are 

shown in Figure 117 The pressure differences in the back of the model is very small compared to 

the front side. The plot of coefficient of pressure shows that the profiles are near identical to each 

other as seen in Figure 118. 
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Figure 116 Pressure contours on the front surface of the single stack IAD model

Figure 117 Comparison of pressure profiles on the front of the single model for various dynamic 

pressures
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Figure 118 Comparison of coefficient of pressure on the front of the single model for various 

dynamic pressures

8.2 Transient Two-Way FSI Simulation of the Single Stack IAD Dynamics 

In this subtask, the single stack IAD model was run with a design inflation pressure of 30 KPa 

using two way FSI coupling for two different flow dynamic pressures (0.5*Qref and 1.5*Qref). All 

simulations were started from an undeformed initial state. The simulations with two-way FSI 

coupling were conducted for 4 seconds of simulation. The results were compared to the single 

stack model at the reference dynamic pressure and with the results from the rigid body motion. 

8.2.1 Aerodynamic Forces and Moments

The histories of the aerodynamic forces and moments during the aeroelastic dynamic simulation 

are shown in Figure 119 - Figure 124. The results of the two-way coupling methods using the 

single stack configuration with the two different dynamic pressures is compared with the results 

obtained using the reference dynamic pressure and also with the aerodynamic coefficients of 

aerodynamic simulation with rigid motion for reference. The histories of the lift and drag 

coefficients during the aeroelastic dynamic simulation are shown in Figure 119 and Figure 120, 

respectively. The history of the side force coefficient is shown in Figure 121. The histories of the 

side moment coefficients and banking moment coefficients are shown in Figure 122, Figure 123

and Figure 124. 
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All the results show damping of the oscillations as the simulation progresses, due to aerodynamic 

damping, indicating the structure is aeroelastically stable. Multiple modes can be seen for the 

higher dynamic pressures. Also, at higher dynamic pressures, both the variation and mean value 

of the aerodynamic coefficients is larger. 

Figure 119. History of coefficient of lift during the aeroelastic dynamic simulation for various 

dynamic pressures

Figure 120. History of coefficient of drag during the aeroelastic dynamic simulation for various 

dynamic pressures
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Figure 121. History of side force coefficient during the aeroelastic dynamic simulation for 

various dynamic pressures

Figure 122. History of side moment coefficient in the x-direction during the aeroelastic dynamic 

simulation for various dynamic pressures
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Figure 123. History of side moment coefficient in the y-direction during the aeroelastic dynamic 

simulation for various dynamic pressures

Figure 124. History of banking moment coefficient during the aeroelastic dynamic simulation for 

various dynamic pressures
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8.2.2 Aeroelastic Structural Deformations

The history of displacement in the y-direction (direction of flow) at a point on the outer edge of 

the IAD for the single stack configurations for various flow dynamic pressures are shown in 

Figure 125. The displacement in x-direction and z-direction are shown in Figure 126 and Figure 

127 respectively. The contribution of the aeroelastic deformation alone for the x-component and 

the z-component are shown in Figure 128 and Figure 129 respectively.

The results show that there is a large increase in oscillation of the x, y, and z component of 

displacement about their mean for the single stack configurations as the dynamic pressure is 

increased. There is also a reduction in amplitude as time passes due to the aerodynamic damping. 

The results also indicate that there are additional modes in the solution for the higher dynamic 

pressures. 

As seen before in the test with constant CFD-averaged loads, the aeroelastic deformation alone 

for the z-component in Figure 129 shows increasing amplitude of oscillations as the solution 

progresses. 

Figure 125 Comparison of y-component of structural deformation for various dynamic 

pressures.
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Figure 126 Comparison of x-component of structural deformation for various dynamic 

pressures.

Figure 127 Comparison of z-component of structural deformation for various dynamic 

pressures.
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Figure 128 Comparison of aeroelastic component of structural deformation in the x-direction for 

various dynamic pressures.

Figure 129 Comparison of aeroelastic component of structural deformation in the z-direction for 

various dynamic pressures.
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Fast Fourier Transforms (FFT) of aeroelastic component of the x-displacement and the ydisplacement were performed. The plots of the power spectral density (PSD) of all the cases 

considered in this subtask are shown in Figure 130 and Figure 131. The plots show a larger 

number of modes as the dynamic pressure is increased. 

Figure 130 Comparison of PSD based on y-component of structural deformation for various 

dynamic pressures.

Figure 131 Comparison of PSD based on aeroelastic component of structural deformation in the 

x-direction for various dynamic pressures.
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8.2.3 Aeroelastic Structural von Mises Stresses

In this section, von Mises stress results for the single stack configuration obtained using the twoway coupling for various flow dynamic pressures are presented. The time history of von Mises 

stress results on the toroids is presented in Figure 132. The figure also shows that the von Mises 

stress is cyclic, similar to the structural deformations. The stress in the single stack model for the 

1.5*Qref case is fluctuating between a maximum value of 5.7 E+08 N/m2and a minimum value 

of 2 E+08 N/m

2

. Since the yield stress of the Kevlar material is 35 GPa, the stress levels are way 

below the yield stress of the material. 

The time history of von Mises stress results on the cover (skin/gore) is presented in Figure 133. 

The von Mises stress on the skin is also cyclic, and is fluctuating between a maximum value of 

2.5 E+08 N/m2and a minimum value of 1E+08 N/m2for the 1.5*Qref case. 

Snapshots of peak von Mises stresses on the front surface of the IAD are shown in Figure 134. 

The peak stress levels occur at the windward side of the front surface of the toroids. For the 

cover, the peak values of stresses occur around the inner circle of the model near the location of 

the adapter. 

Figure 132 Comparison of von Mises stresses on the toroids for various dynamic pressures.
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Figure 133 Comparison of von Mises stresses on the cover (gores/skin) for various dynamic 

pressures.

Figure 134 Snapshots of peak von Mises stresses on the toroids and cover (gores/skin) for 

various dynamic pressures.
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8.3 Modeling Failure and Collapse of a Single Stack IAD

In this subtask, the loads required to induce the failure and collapse of a single stack IAD 

configuration are simulated. The single stack IAD model was run with a design inflation pressure 

of 30 KPa using average constant CFD loading. Multiple cases were run using various pressure 

loads equivalent to multiples of the reference flow dynamic pressure and were compared with 

each other. All simulations were started from an undeformed initial state. The dynamic 

simulations were conducted for about 0.4 seconds of simulation. Contact between the cover and 

skin was not modeled for this set of simulations. 

The trace of displacements in the y-direction at a point at the edge of the IAD is shown in Figure 

135. The results show that the single stack IAD begins to show signs of collapse for pressure 

loads equivalent to around three times the reference dynamic pressure.

Figure 135 Comparison of y-component of structural deformation for single stack configurations 

with various pressure loads.

The deformation of the skin at four times the reference dynamic pressure is shown in Figure 136

(a). The large deformation and wrinkling of the skin can be seen clearly. The z-cut of the IAD 

model shown in Figure 136 (b) shows a large movement of the cover and shows penetration of 

the toroids, which is clearly unphysical. This is due to the fact that contact was not modeled. The 

very large stresses developed in the model which are of the order of the yield strength of the 

materials are shown in Figure 137. 
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(a) Deformation contours in the y-direction (b) Z-cut of the windward side of IAD model

Figure 136 Contour plots and z-cut of IAD at 60 ms for a pressure load at four times the 

reference dynamic pressure.

Figure 137 Contour plot of von Mises stress at 60 ms on the cover and toroids for a pressure 

load at four times the reference dynamic pressure.

Obviously, the penetration between the skin and toroids are not physical due to the absence of 

the contact model in the previous FEM model. Addition of the contact model would enable the 

FEM model to predict more accurate response of the structural model. The disadvantage in 

contact modeling is the large amounts of simulation time required. It was seen that in order to 

model contact between the cover and toroids, the simulation time increased by a factor of 5. To 

model the self contact between toroids, the simulation time increase by a factor of 20. 

In the next test, contact between the toroid and cover was modeled for the case with four times 

the reference dynamic pressure. The trace of displacements in the y-direction at a point at the 

edge of the IAD is shown in Figure 138. The results show that the single stack IAD with contact 

models at four times the reference dynamic pressure still shows large deformations and buckling 

compared to the reference dynamic pressure case as seen in Figure 139 but that they are much 

smaller than without the contact model. The stresses developed in the model are shown in Figure 
116 8927/6

140. Animations of the structural responses and buckling of the model were created and 

submitted to NASA engineers to give insight about the dynamic response of the model.

The disadvantage in contact modeling is the large amounts of simulation time required. It was 

seen that in order to model contact between the cover and toroids, the simulation time increased 

by a factor of 5. To model the self contact between toroids, the simulation time increase by a 

factor of 20. 

Figure 138 Comparison of y-component of structural deformation for single stack configurations 

with various pressure loads and with contact.

(a) Deformation contours in the y-direction (b) Z-cut of the windward side of IAD model

Figure 139 Contour plots and z-cut of IAD at 60 ms for a pressure load at four times the 

reference dynamic pressure with contact model.
117 8927/6

Figure 140 Contour plot of von Mises stress at 60 ms on the cover and toroids for a pressure 

load at four times the reference dynamic pressure with a contact model.

8.4 Summary

In order to test the limits of the single stack configuration, simulations were run at various 

multiples of the reference dynamic pressure. Two way FSI coupled simulations were run at 0.5 

times the reference dynamic pressure and 1.5 times the reference dynamic pressure. The 

aeroelastic response was computed for an internal pressure of 30 KPa. The dynamic response 

showed an increased number of modes with an increase in flow dynamic pressure. The stresses 

were still within limits even for the case with 1.5 times the reference dynamic pressure. Further 

tests were conducted on a single stack configuration to find out the multiple of the flow dynamic 

pressure for which a collapse of the IAD occurred. It was seen that without contact modeling the 

numerical model showed signs of collapse for pressure loads equivalent to 3 times the reference 

dynamic pressure. Complete collapse was seen for four times the reference dynamic pressure. 

Once contact was modeled, collapse did not occur at that dynamic pressure, although large 

deformations and stresses were still seen. It was also observed that contact modeling has a large 

penalty associated with it in terms of computational time required. 
118 8927/6

9 SUMMARY AND CONCLUSIONS

Computational aeroelastic simulations were conducted for Inflatable Aerodynamic Decelerators 

(IAD) concepts to support the EDL-SA assessments of IAD controllability and structural 

integrity for Mars Aerocapture and EDL. Several design configurations, including double stack 

and single stack toroids, were considered to determine the candidate technology that meets the 

requirements. The following is a summary of the conclusions, lessons learned and 

recommendations for potential future work that would lead to better understanding of the 

behavior of these complex and unpredictable inflatable structures.

9.1 Summary and Concluding Remarks

A three-dimensional computational CFD model for the IAD model configuration was developed. 

A simplified non-reacting thermally perfect CO2 Mars atmosphere model was used since no 

chemical reactions occur at the Mach of 14.3 modeled. Steady state Euler simulation was 

conducted at 30 degrees angle of attack, and the aerodynamic forces and moments were 

predicted. In addition, a computational structural nonlinear FEM model of the IAD model was 

developed using quad shell elements. A modified version of the FEM model was also developed 

that takes into consideration the axial enforcement straps of the toroids. Extensive FEM 

simulations were conducted with various dynamic and internal pressures and using variable 

fidelity CFD calculated loads. The aeroelastic responses of the model were also computed for 

three simulations: 1) using averaged constant CFD predicted loading, 2) using one-way fluidstructure interaction (FSI) coupling from the fluid to the structure, and 3) using two-way FSI 

coupling. The structural responses of the three simulations were comparable. The structural 

deformations and stresses exhibited cyclic behavior over the model and they tended to fluctuate 

around almost constant mean values. The von Mises stress levels on the gores and toroids were 

far less than the yield stress of the respective materials. 

The effect of increasing the toroids inflation pressure on the aeroelastic response of the IAD 

model was also investigated. The results showed that the inflation pressure has a small impact on 

overall deformation, remaining in line with the conducted static analysis. The effects of the radial 

straps were also taken into consideration by developing an equivalent mechanical model of the 

straps, which resulted in increasing the nominal thickness and material properties of the gores. 

Both CFD constant averaged loads and two-way FSI coupling were used. The results showed

dramatic decrease of the aeroelastic deformations when the effects of radial straps are added to 

the model. von Mises stresses were still far less than the yield stress of the gores and toroids 

materials. 

Another configuration was modeled using a single stack of toroids instead of the double stack

configuration model. Additional changes in skin thickness and properties were incorporated into 

the model to account for the axial and radial straps. Steady state CFD tests were run to provide 

new load models. The aeroelastic response was then computed for two different internal 

pressures using constant averaged loads and two-way FSI coupling and compared with previous 

models. The aerodynamic flowfield and forces of the single stack configuration were very 

similar to the double stack configuration. There were small increases in the displacements and in 
119 8927/6

the von Mises stresses. The von Mises stresses were still far less than the yield stress of the gores 

and toroids materials.

In order to test the limits of the single stack configuration, simulations were run at various 

multiples of the reference dynamic pressure. Two-way FSI coupled simulations were run at 0.5 

times the reference dynamic pressure and 1.5 times the reference dynamic pressure. The 

aeroelastic response was computed for an internal pressure of 30 KPa. The dynamic response 

showed an increased number of modes with an increase in flow dynamic pressure. The stresses 

were still within limits even for the case with 1.5 times the reference dynamic pressure. More 

tests were conducted on a single stack configuration to find out the multiple of the flow dynamic 

pressure for which a collapse of the IAD occurred. The analysis was initially conducted without 

the FEM contact model between the toroids and gores. The results showed signs of collapse for 

pressure loads equivalent to three times the reference dynamic pressure. Complete collapse was 

seen for four times the reference dynamic pressure. Once contact was modeled, collapse did not 

occur at that dynamic pressure, although large deformations and stresses were still seen. It was 

also observed that contact modeling has a large penalty associated with it in terms of 

computational time required. 

9.2 Lessons Learnt

The following were the lessons learnt during this effort. They are broadly classified into three 

sections. 

9.2.1 Flow Physics and Aeroelastic Coupling

1. A thermally perfect thermophysics model (Cp=Cp(T) curve fits) for pure CO2 captures 

the important shock physics effects of the Mars atmosphere at the Mach number 

considered.

2. The temperature dependent thermophysical properties correctly account for the increased 

temperature behind the shock and the resulting effective Gamma change. Chemically 

reacting flow effects are negligible at the Mach number considered.

3. No significant changes were seen in the pressure profiles between double and single stack 

IAD configurations.

4. The pressure profile over the fluid structure interface does not change significantly for 

any of the cases tested. Therefore, a carefully calculated asymmetric CFD averaged 

constant load is sufficient to simulate the CFD loading. 

9.2.2 Structural FEM Solver

1. Nonlinear FEM modeling is necessary to correctly model the response of the very thin 

film materials.

2. Problems involving thin shell elements with large aspect ratios (>10000), coupled with 

the weak material properties are extremely hard to solve with implicit solvers due to the 

difficulty of inverting ill-conditioned matrices. 
120 8927/6

3. The usage of explicit solvers is cost-prohibitive due to the fact that the time step is driven 

by the small thickness. Therefore, we have used the mass scaling technique for shell 

elements involving explicit transient analysis. This scaling permits large critical time step 

size without loss of stability, which is particularly necessary for very thin shell structures.

4. If using solid shell FEM elements, two measures were to found to improve convergence 

and numerical stability: 1) dividing the CFD loads over the nodes top and bottom 

surfaces of an element, and 2) ramping the loads over multiple steps. 

9.2.3 Structural IAD Model

1. Modeling the presence of radial and circumferential straps is important. The IAD is much 

stiffer and more stable due to the presence of these straps. Modeling these straps also 

improves numerical stability of the models.

2. Beyond a certain value, the internal pressure has a small effect on the peak displacement 

and the frequency of the IAD. If the internal pressure is too low compared to the external 

pressure, the structure will tend towards buckling. 

3. The double stack and single stack configurations show remarkably similar frequencies. 

The single stack IAD shows slightly larger displacements. 

4. It is important to model the contact between the skin and the toroids when low inflation 

pressures or large dynamic pressures are used. However, there is a significant 

computational penalty as a result. 

9.3 Recommendations for Future Work

This Phase III effort has successfully performed all assigned tasks for the aero-structural 

assessment of different configurations of IADs. Our recommendations for future work in this 

area are presented next and can be divided into the following major areas.

9.3.1 Modeling Additional Flow Physics

1. Modeling turbulence and the full set of Navier-Stokes equations may prove to be 

important at lower altitudes. 

2. The effect of local aerothermal heating on the structural properties and aeroelastic 

responses should also be modeled instead of simply using a global knockdown factor.

3. Effects of cone-angle variation of the model should be assessed.

9.3.2 Changes to Structural Model and IAD Dynamics

1. The effects of modeling the presence of the payload and the attachment rope lines to the 

toroids. 

2. Determine aeroelastic responses with different rigid aeroshell attachments. The results 

showed that the extent of the rigid shield to which the flexible portion of the IAD attaches 

is critical in determining the peak deflections of the tip of the structure. 
121 8927/6

3. Determine the lowest possible inflation pressure for which the model will not buckle. 

4. Determine aeroelastic responses at various banking rates (1.5, 2.5, or 6 deg/sec2) and 

including the effects of gravity (due to the high mass payload). 

5. Determine aeroelastic responses of modified IAD model design and/or properties, such as 

different size of toroids, different number of toroids, different toroids assembly, etc.

6. Determine the aeroelastic responses due to puncture of single or multiple inflated 

elements. This can be done by deflation of one or two toroidal tubes in the model. The 

effect of varying the location of the toroid failure should also be considered.
122 8927/6

10 REFERENCES

1. CFD Research Corporation, “MDICE Multi-Disciplinary Computing Environment, User‟s 

Manual,” Version 6.0, December 2003.

2. CFD Research Corporation, “MDICE Multi-Disciplinary Computing Environment, 

Programmers‟s Guide,” Version 6.0, October 2001.

3. CFD Research Corporation, “CFD-FASTRAN, V2004: User's Manual,” March 2004.

4. CFD Research Corporation, “Co-Phy User‟s Manual,” 2005.

5. Sheta, E. F., Meyer, B., and Habchi, S. D., "Aerodynamic Support of the ARES Program," 

Final Report, Contract No. ATK-23525, Alliant TechSystems, Brigham City, UT, October 

2008.

6. Sheta, E. F., Meyer, B., and Habchi, S. D., "Aerodynamic Analysis of ARES I-X Upper 

Stage Wake Effect," Final Report, Contract No. 45-010003-CG, NASA Marshal Flight 

Space Center, Huntsville, AL, May 2008.

7. Liever, P.A.; Habchi, S.D.; Engelund, W.C.: Martin, J.G.: “Stage Separation Analysis of the 

X-43A Research Vehicle,” AIAA Paper 2004-4725.

8. Liever, P.A.; Habchi, S.D.: “Separation Analysis of Launch Vehicle Crew Escape Systems,” 

AIAA Paper 2004-4726.

9. Liever, P.A.; Habchi, S.D.; Burnell, S.I.; Lingard, S.: “CFD Prediction of the Beagle 2 

Aerodynamic Database,” AIAA Paper 2002-0683.

10. S.D. Habchi, G.S. Hufford, and T. Marquette, “Navier-Stokes Computational Analysis of 

the B-1A Escape Capsule,” 33rd Aerospace Sciences Meeting; Reno, NV; Jan. 9-12, 1995.

11. Sheta, E. F., Venugopalan, V., Tan X.G., Harrand, V. J., and Habchi, S. D., "Tightly 

Coupled Aerothermoelastic Analysis Tool for Hypersonic Vehicle Structures," Final Report, 

SBIR Phase I, Contract No. FA8650-09-M-3929, Air Force Research Laboratory, Dayton, 

OH, October 2009.

12. Sheta, E. F., Moses, R. W., and Huttsell, L. J., "Active Smart Material Control System for 

Buffet Alleviation," Journal of Sound and Vibration, Academic Press, Vol. 292, No. 5, July 

2006, pp. 854-868.

13. Sheta, E. F., "Alleviation of Vertical Tail Buffeting of F/A-18 Aircraft," Journal of Aircraft, 

Vol. 41, No. 2, March/April 2004, pp. 322-330.

14. Sheta, E. F., and Huttsell, L. J., "Characteristics of F/A-18 Vertical Tail Buffeting," Journal 

of Fluids and Structures, Academic Press, Vol. 17, No. 3, April 2003, pp. 461-477.

15. Liever, P.A.; Sheta, E. F.; Habchi, S.D.: “Aeroelastic Simulation Tool For Inflatable Ballute 

Aerocapture,” 1st JANNAF Spacecraft Propulsion Subcommittee Meeting, JPM/LPS/SPS 

Joint Meeting, Monterey, California, December 2005.

16. Liever, P. A., Venugopalan, V., Talley, C., Burns, J., Tosh, A., Sheta, E. F., and Habchi, S. 

D., "Aeroelastic Simulation Tool for Inflatable Ballute Aerocapture," Final Report, SBIR 

Phase II, Contract No. NNM06AA10C, NASA Marshal Space Center, Huntsville, AL,

November 2007.

17. Buck, G., “Testing of flexible ballutes in hypersonic wind tunnels for planetary 

aerocapture,” AIAA Paper 2006-1319, 44th AIAA Aerospace Sciences Meeting and 

Exhibit, Reno, NV, Jan. 9-12 2006.
123 8927/6

11 APPENDIX A – CFDRC FEM VALIDATION AGAINST NASTRAN

A.1 CFDRC-FEM

CFDRC‟s FEM code used in this project is part of a multi-physics and multi-scale computational 

physics (CoPhy) software package, written in the object-oriented language C++ and developed 

by CFDRC. It contains several modules including: fluid dynamics, heat transfer, structures 

dynamics, electrostatics, chemistry, and several others. All of the modules can be solved in a 

loosely or tightly coupled fashion. Each module solves physics on the same or different grids, 

and data exchanges between different modules are seamless. The modules that are most related 

to the present project is the finite element module or CFDRC-FEM.

CFDRC-FEM solves stress/deformation, and acoustic in a Lagrangian frame. The most relevant 

features of CFDRC-FEM are:

Both explicit and implicit FEM solver available for different time-scale applications;

Unstructured mixed element grids including tetra, hexa, pyramid, prism, octree;

Accurate finite elements such as mixed formulation for incompressible materials, and 

locking-free shell formulation and solid-shell formulation applicable for both smooth and 

folded shell structure;

Multi-rigid body dynamics with various joints and its implicit coupling with flexible 

bodies;

Various non-linear material models such as hyperelasticity, viscoelasticity and 

elastoplasticity;

Various surface interaction such as Contact-impact algorithm, tied-interface to connect 

domains with different mesh;

Acoustic model and its implicit interaction with structural dynamics;

Capable of calculate large structured/unstructured mesh movement in the fluid domain; 

Efficient large-scale parallel computing with interface to Petsc solver;

Seamless coupling with fluid dynamic module and heat transfer module.

A.2 Introduction and Motivation for Testing

CFD Research Corporation has developed a finite element solver CRDRC-FEM that is fully 

compliant with the Multi - Disciplinary Computing Environment (MDICE) integration tool, and 

thus used in analyzing a variety of multi disciplinary problems. 

The motivation for the development of an in house finite element solver is the ability to have a 

tight integration between the FEM solver and other codes inside the MDICE environment. This 

reason is the driving force behind CFDRC‟s development of a new code over another tool such 

as NASTRAN. While it is acknowledged that NASTRAN is the industry standard for FEM 

solvers it does not offer the hooks inside the code required to tightly integrate it with MDICE. 

Therefore, MDICE integration must be done in a loosely coupled way. This requires the creation, 
124 8927/6

passing and reading of files between NASTRAN and an MDICE compliant interface. This 

method quickly becomes computationally unacceptable for complicated nonlinear multidisciplinary simulations.

For CFDRC FEM to be accepted as a potential stand in for NASTRAN in computationally 

intensive simulations it requires comparison against NASTRAN for both static and dynamic, 

linear and nonlinear problems. Therefore, the main focus of this document is to compare the 

solutions from CFDRC FEM against NASTRAN for geometric nonlinear problems. The testing 

was conducted at AFRL by Edward Alyanak as part of an AFRL supported program on large 

non-linear aeroelastic bending of thin wings. 

A.3 CFDRC FEM Elements

CFDRC FEM‟s development is based on three degree of freedom per node elements. The basic 

elements include:

Beams

Shells

Tetrahedral

Hexagon

Pentagon

The main difference comes in the beam and shell elements. Both of these elements contain 8 

nodes per element. The beam becomes a long thin hexagon and the shell becomes a flat plate like 

hexagon. The solver contains checks to ensure that the element dimensions are consistent with 

the assumptions made in the beam and shell element formulations. 

A.4 Test Case 1 – Slender Beam Test 

The first test case is developed to test the geometric nonlinear capabilities of CFDRC FEM 

against the Nastran. The specific element formulations being analyzed will be:

NASTRAN

o CBEAM

o CHEXA

CFDRC FEM

o beam

o disp – displacement based hexa formulation

o mixed – mixed hexa formulation

- Problem Description:

The initial test case will consist of a long slender beam. The beam will have an aspect ratio of 

100. 
125 8927/6

 

Figure A.1 Test Case 1 – Long slender beam

As seen in Figure A.1, the beam is cantilevered at one end with a pressure force perpendicular to 

the beam axis applied to the bottom side of the beam. This places the beam in bending. The 

specific properties and load cases for the beam are:

Dimensions

o Length – 100.0 in

o Height – 1.0 in

o Width – 1.0 in

Material Properties

o Elastic Modulus – 10.4 x 106psi

o Poison‟s Ratio – 0.33

o Wt. Density – 0.1 lb/in3

 Wt. to Mass Factor - 0.00259 s2/in

 Mass Density – 0.00259 slinch / in3

slinch – lb · s2/ in

Pressure Load

o applied along the length of the beam

 Case 1: 1.00 psi 

 Case 2: 4.00 psi

- Static Results

The static results of the beam deflection were analyzed for two nastran elements (CHEXA, 

CBEAM) and for three CFDRCFEM elements (displacement, mixed and beam). The static 

analysis types consisted of linear, large displacement nonlinear, and follower force nonlinear 

cases. The test case will detect differences in the element formulations as well as investigate the 

accuracy of the nonlinear iterative scheme used in the solution inside CFDRCFEM. Different 

mesh refinements were created for each type of element. The mesh used for each element is as 

follows:

- CHEXA

o 900 x 3 x 3

o 400 x 2 x 2

o 10 x 1 x 1

- CBEAM

o 10 x 1 x 1

Pressure

Z

Y
126 8927/6

- displacement (disp)

o 900 x 3 x 3

o 400 x 2 x 2

- mixed

o 900 x 3 x 3

o 400 x 2 x 2

- beam

o 50 x 5 x 5

o 10 x 1 x 1

Inside CFDRCFEM the beam formulation must have a long aspect ratio. This is why a 50 x 5 x 

5 mesh was used over a 400 x 2 x 2 mesh that was used for the other brick elements. The 

CHEXA 900 x 3 x 3 mesh was selected as the “Valid” solution for comparison. This mesh of 

CHEXA proved to be a converged solution when it is compared against the CHEXA 400 x 2 x 2 

mesh. 

The results, along with percent error or deviations from the CHEXA valid mesh can be seen in 

Table A.1 and A.2. These tables represent the first and second load cases. Further results can be 

seen in Figure A.9 contained at the end of this appendix. This figure plots the beam tip 

displacement for both Y and Z deflections, where the coordinate system is defined in Figure A.1. 

From Figure A.9 and Tables 1 and 2 it is clear that the CHEXA, for all but the coarse mesh, 

CBEAM and CFDRCFEM beam elements are in very close agreement with each other. This is 

expected since the test case is a beam bending test case. The results further indicate that the 

CFDRCFEM displacement formulation for a hexagonal element is stiff for the bending case and 

the mixed formulation is flexible. This is acceptable since a beam element formulation is 

available for a hexagonal element for bending applications of long aspect ratio structural 

components. In the table, it is clear that the CFDRCFEM beam element performs very well, even 

for a 10 x 1 x 1 mesh refinement. 

Table A.1 Static results for load case 1

MESH CHEXA 900 x 3 x 3 (Valid) MESH disp 900 x 3 x 3 MESH mixed 900 x 3 x 3 MESH beam 50 x 5 x 5

0.0000 14.4078 0.0000 14.0263 0.0000 14.7965 0.0000 14.4246

-1.1808 14.3223 -1.1200 13.9507 -1.2457 14.7079 -1.1841 14.3440

-1.1609 14.2060 -1.1018 13.8407 -1.2229 14.5773 -1.1634 14.2224

MESH CHEXA 400 x 2 x 2 %Error %Error %Error %Error %Error %Error

0.0000 14.4064 0.0000 -2.6479 0.0000 2.6978 0.0000 0.1166

-1.1806 14.3214 -5.1454 -2.5946 5.5033 2.6923 0.2820 0.1515

-1.1608 14.2047 -5.0963 -2.5715 5.3384 2.6140 0.2110 0.1154

MESH CHEXA 10 x 1 x 1 MESH disp 400 x 2 x 2 MESH mixed 400 x 2 x 2 MESH beam 10 x 1 x 1

0.0000 14.2532 0.0000 13.4154 0.0000 15.2188 0.0000 14.4244

-1.1154 13.8933 -1.0250 13.3493 -1.3175 15.1227 -1.1846 14.3469

-1.0985 13.7916 -1.0099 13.2538 -1.2918 14.9798 -1.1640 14.2262

MESH CBEAM 10 x 1 x 1 %Error %Error %Error %Error %Error %Error

0.0000 14.4782 0.0000 -6.8879 -6.2500 5.6289 0.0000 0.1152

-1.1897 14.3923 -13.1902 -6.7936 11.5816 5.5881 0.3231 0.1718

-1.1643 14.2434 -13.0120 -6.7028 11.2745 5.4470 0.2653 0.1422

MESH CHEXA 900 x 3 x 3 (Valid) MESH disp 900 x 3 x 3 MESH mixed 900 x 3 x 3 MESH beam 50 x 5 x 5

0.0000 57.6311 0.0000 56.1052 0.0000 59.1858 0.0000 57.6983

-17.6152 52.5100 -16.7885 51.4028 -18.5405 53.7045 -17.6991 52.6293

-13.8149 47.2638 -13.2756 46.4025 -14.3675 48.1201 -13.8416 47.3113

MESH CHEXA 400 x 2 x 2 %Error %Error %Error %Error %Error %Error

0.0000 57.6257 -7.6923 -2.6477 0.0000 2.6977 0.0000 0.1166

-17.6123 52.5055 -4.6931 -2.1086 5.2529 2.2749 0.4766 0.2272

-13.8131 47.2602 -3.9038 -1.8222 4.0000 1.8119 0.1929 0.1005

MESH CHEXA 10 x 1 x 1 MESH disp 400 x 2 x 2 MESH mixed 400 x 2 x 2 MESH beam 10 x 1 x 1

0.0000 57.0127 0.0000 53.6617 0.0000 60.8753 0.0000 57.6974

-126647 447901 -154488 495269 -195291 549346 -177990 527676

Table 1: Static Beam Results for Load Case 1

Table 2: Static Beam Results for Load Case 2

NASTRAN RESULTS CFDRCFEM disp ELEMENT CFDRCFEM disp ELEMENT CFDRCFEM beam ELEMENT

NASTRAN RESULTS CFDRCFEM disp ELEMENT CFDRCFEM disp ELEMENT CFDRCFEM beam ELEMENT
127 8927/6

Table A.2 Static beam results for load case 2

MESH CHEXA 10 x 1 x 1 MESH disp 400 x 2 x 2 MESH mixed 400 x 2 x 2 MESH beam 10 x 1 x 1

0.0000 14.2532 0.0000 13.4154 0.0000 15.2188 0.0000 14.4244

-1.1154 13.8933 -1.0250 13.3493 -1.3175 15.1227 -1.1846 14.3469

-1.0985 13.7916 -1.0099 13.2538 -1.2918 14.9798 -1.1640 14.2262

MESH CBEAM 10 x 1 x 1 %Error %Error %Error %Error %Error %Error

0.0000 14.4782 0.0000 -6.8879 -6.2500 5.6289 0.0000 0.1152

-1.1897 14.3923 -13.1902 -6.7936 11.5816 5.5881 0.3231 0.1718

-1.1643 14.2434 -13.0120 -6.7028 11.2745 5.4470 0.2653 0.1422

MESH CHEXA 900 x 3 x 3 (Valid) MESH disp 900 x 3 x 3 MESH mixed 900 x 3 x 3 MESH beam 50 x 5 x 5

0.0000 57.6311 0.0000 56.1052 0.0000 59.1858 0.0000 57.6983

-17.6152 52.5100 -16.7885 51.4028 -18.5405 53.7045 -17.6991 52.6293

-13.8149 47.2638 -13.2756 46.4025 -14.3675 48.1201 -13.8416 47.3113

MESH CHEXA 400 x 2 x 2 %Error %Error %Error %Error %Error %Error

0.0000 57.6257 -7.6923 -2.6477 0.0000 2.6977 0.0000 0.1166

-17.6123 52.5055 -4.6931 -2.1086 5.2529 2.2749 0.4766 0.2272

-13.8131 47.2602 -3.9038 -1.8222 4.0000 1.8119 0.1929 0.1005

MESH CHEXA 10 x 1 x 1 MESH disp 400 x 2 x 2 MESH mixed 400 x 2 x 2 MESH beam 10 x 1 x 1

0.0000 57.0127 0.0000 53.6617 0.0000 60.8753 0.0000 57.6974

-12.6647 44.7901 -15.4488 49.5269 -19.5291 54.9346 -17.7990 52.7676

-10.8251 41.8062 -12.4115 44.9790 -14.9664 49.0268 -13.9169 47.4315

MESH CBEAM 10 x 1 x 1 %Error %Error %Error %Error %Error %Error

0.0000 57.9130 0.0000 -6.8876 0.0000 5.6293 0.0000 0.1150

-17.9639 53.0561 -12.2985 -5.6810 10.8651 4.6175 1.0437 0.4906

-13.7225 47.1877 -10.1586 -4.8341 8.3352 3.7301 0.7383 0.3548

Table 2: Static Beam Results for Load Case 2

NASTRAN RESULTS CFDRCFEM disp ELEMENT CFDRCFEM disp ELEMENT CFDRCFEM beam ELEMENT

When the errors are evaluated between Tables A.1 and A.2 it is important to note that the linear 

error does not change for every element type. This should be the result; any deviation would 

indicate a coding error was present. The nonlinear solution errors do slightly increase as the tip 

deflection magnitudes increase from around 15% for load case 1 and 50% for load case 2. This is 

a result of the nonlinear solution being a combination of linear solutions done in an iterative 

manner. More intermediate linear solutions were solved in determining the solution to the higher 

load deflection then the lower load. Since each individual linear solution contains some error this 

error compounds as the iteration number increases. 

- Dynamic Results

For the dynamic case only the cases that were similar in the static case were analyzed. The same 

loading was applied to an undeflected beam at t = 0.0 seconds. The response history was then 

analyzed for both the low and high load cases. 

The meshes and integration time steps used are the following:

- CBEAM

o 10 x 1 x 1

 dt = 0.0001

 dt = 0.001

- beam

o 10 x 1 x 1

 Explicit dt = 3.571 x 10 -6

 Implicit dt = 0.0001

 Implicit dt = 0.001

- Results

Figures A.2 – A.4 contain the results of the dynamic analysis test cases. The cases that were run 

were run because the agreed well in the static sense, and were somewhat less computationally 

intensive. The specific focus was the accuracy of CFDRCFEM in time integration and mass 

modeling. 
128 8927/6 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-5

0

5

10

15

20

25

30

NonLinear Large Displacement Beam Analysis

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-20

0

20

40

60

80

NonLinear Large Displacement Beam Analysis - Load Case 2

Nastran dt = 0.0001

Nastran dt = 0.001

CfdrcFEM explicit

CfdrcFEM implicit dt = 0.0001

CfdrcFEM implicit dt = 0.001

Figure A.2 Dynamic Large Displacement Analysis Results, Beam
129 8927/6 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-5

0

5

10

15

20

25

30

NonLinear Follower Beam Analysis

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-20

0

20

40

60

80

100

NonLinear Follower Beam Analysis

Nastran dt = 0.0001

Nastran dt = 0.001

CfdrcFEM explicit

CfdrcFEM implicit dt = 0.0001

CfdrcFEM implicit dt = 0.001

Figure A.3 Dynamic Follower Force Analysis Results, Beam

Form figures A.2 and A.3 it is immediately clear that the results for all of the test cases are very 

close to each other for dynamic geometric nonlinear analysis. This is critical for dynamic 

aeroelasticity analysis, since the amplitude and frequency of oscillation can have a great impact 

on aeroelastic stability prediction. 

Below, Figure A.4 just reinforces the need for nonlinear structural analysis. The results are 

generated for the high load case for the dynamic beam problem. Figure A.4 presents the same 

solution for the linear, large displacement and follower force result. While both nonlinear 

analyses have similar displacements the frequency of oscillation are different. This is because the 

deflection path is longer for the follower force case, and thus it has a longer period. This can be 

seen from the static results shown in Figure A.9. The linear solution is significantly different. 

The deflection magnitudes and frequencies are not in any type of agreement. The need for 

nonlinear structural analysis for large displacement bending applications is quite clear after 

examining this figure. 
130 8927/6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

-20

0

20

40

60

80

100

120

Comparison between geometric nonlinear analysis with and without follower force

Linear Analysis

Nonlinear Follower Analysis

Nonlinear Large Displacement Analysis

Figure A.4 Dynamic Comparison of Linear, Large Displacement and Follower Force Results for 

Example 1, Beam: Load Case 2

A.5 Test Case 2 – Plate Test Case

The second test case is developed to test the geometric nonlinear capabilities of CFDRC FEM 

against the Nastran for wing like plate structures. In the first test case the bending capabilities 

were considered. In this case a coupled bending and twisting is examined. This case is designed 

to mimic typical wing like deformations. The specific element formulations being analyzed will 

be:

Nastran

o CHEXA

CFDRC FEM

o pshell

o disp – displacement based hexa formulation

o mixed – mixed hexa formulation

- Problem Description

The test case consists of a thin plate as seen in Figure A.5. The plate is of a length 100in and a 

thickness of 1.0in. The root chord is 20in and the tip cord will be 14in. The plate is cantilevered 

at the root. 
131 8927/6

 

Figure A.5 Test Case 2 – Wing like Plate

Dimensions

o Length (y) – 100.0 in

o Height (z) – 1.0 in

o Width (x) – 20.0 in tapering to 14.0 in

Material Properties

o Elastic Modulus – 10.4 x 106psi

o Poison‟s Ratio – 0.33

o Wt. Density – 0.1 lb/in3

 Wt. to Mass Factor - 0.00259 s2/in

 Mass Density – 0.00259 slinch / in3

slinch – lb · s2/ in

Pressure Load

o applied along the bottom of the plate

 Case 1: 1.00 psi 

 Case 2: 3.00 psi

Tip Point Loading (applied along with pressure)

o Applied in the positive z – direction at leading edge

o Applied in the negative z – direction at the trailing edge

 Case 1: 200 lbs

 Case 2: 2000 lbs

- Static Results

Different mesh refinements were created for each type of element. The mesh used for each 

element is as follows:

- CHEXA

o 100 x 1 x 20

o 10 x 1 x 2

- displacement (disp)

o 100 x 1 x 20

o 10 x 1 x 2

Point Loads

Pressure

Y

X

Z
132 8927/6

- mixed

o 100 x 1 x 20

o 10 x 1 x 2

- pshell

o 100 x 1 x 20

o 10 x 1 x 2

The data format shown is for the tip of the plate or “wing”. The format is shown in Figure A.6 

below, and corresponds to the results in Tables A.3 and A.4.

 

Figure A.6 Data format for Static Results Case 2

Table A.3 contains the results for the lower loading magnitudes applied to the plate. The error 

calculations are relative to the Nastran solution with the same mesh. The same mesh is used 

since a direct comparison is being carried out. The formulation for the percent error for each 

element is shown below.

nastran

cfdrc nastran

LEtip

nastran

TEtip

nastran

TEtip

cfdrc

LEtip

nastran

LEtip

nastran

LEtip

cfdrc

LEtip

nastran

TEtip

nastran

TEtip

cfdrc

LEtip

nastran

LEtip

nastran

LEtip

cfdrc

LEtip

nastran

TEtip

nastran

TEtip

cfdrc

LEtip

nastran

LEtip

nastran

LEtip

cfdrc

z

z z

z

z z

y

y y

y

y y

x

x x

x

x x

Error

7

100%

%

Point 1

Mid Point 2

Point 3

Point 2

Point 4

Twist

- Before Deflection

- After Deflection

Mid Point 1
133 8927/6

Table A.3 Static Plate Results for Load Case 1

dX (in) dY (in) dZ (in) dX (in) dY (in) dZ (in) dX (in) dY (in) dZ (in) dX (in) dY (in) dZ (in)

MESH CHEXA 100 x 1 x 20 MESH disp 100 x 1 x 20 MESH mixed 100 x 1 x 20 MESH pshell 100 x 1 x 20

LINEAR LINEAR LINEAR LINEAR

LE Tip 0.00 0.00 11.84 0.00 0.00 7.55 0.00 0.00 14.77 0.00 0.00 11.84

TE Tip 0.00 0.00 11.61 0.00 0.00 7.33 0.00 0.00 14.53 0.00 0.00 11.61

Twist (deg) 0.97 0.89 % Error = -11.6217 0.99 % Error = 7.4177 0.97 % Error = 0.0043

LGDISP LGDISP LGDISP LGDISP

LE Tip 0.04 -0.79 11.70 0.02 -0.33 7.51 0.05 -1.22 14.50 0.04 -0.79 11.71

TE Tip 0.04 -0.76 11.47 0.02 -0.31 7.30 0.05 -1.18 14.27 0.04 -0.76 11.47

Twist (deg) 0.95 0.88 % Error = -41.4391 0.97 % Error = 30.5498 0.95 % Error = -0.0049

FOLLOWER FOLLOWER FOLLOWER FOLLOWER

LE Tip 0.04 -0.80 11.76 0.02 -0.33 7.52 0.06 -1.24 14.63 0.04 -0.80 11.77

TE Tip 0.04 -0.77 11.53 0.02 -0.31 7.31 0.05 -1.21 14.39 0.04 -0.77 11.53

Twist (deg) 0.95 0.89 % Error = -41.5062 0.97 % Error = 31.1321 0.95 % Error = -0.0551

MESH CHEXA 10 x 1 x 2 MESH disp 10 x 1 x 2 MESH mixed 10 x 1 x 2 MESH pshell 10 x 1 x 2

LE Tip LINEAR LINEAR LINEAR LINEAR

TE Tip 0.00 0.00 11.81 0.00 0.00 0.38 0.00 0.00 0.39 0.00 0.00 11.82

Twist (deg) 0.00 0.00 11.57 0.00 0.00 0.24 0.00 0.00 0.25 0.00 0.00 11.59

0.96 0.57 % Error = -33.6207 0.57 % Error = -33.6030 0.95 % Error = -0.1180

LE Tip LGDISP LGDISP LGDISP LGDISP

TE Tip 0.04 -0.75 11.41 0.00 0.00 0.38 0.00 0.00 0.39 0.04 -0.79 11.67

Twist (deg) 0.04 -0.73 11.19 0.00 0.00 0.24 0.00 0.00 0.25 0.04 -0.76 11.44

0.93 0.57 % Error = -90.2443 0.57 % Error = -90.2244 0.93 % Error = 3.4615

LE Tip FOLLOWER FOLLOWER FOLLOWER FOLLOWER

TE Tip 0.04 -0.76 11.47 0.00 0.00 0.38 0.00 0.00 0.39 0.04 -0.79 11.72

Twist (deg) 0.04 -0.74 11.25 0.00 0.00 0.24 0.00 0.00 0.25 0.04 -0.77 11.49

0.93 0.57 % Error = -90.1231 0.57 % Error = -90.0871 0.94 % Error = 3.4285

NASTRAN RESULTS CFDRCFEM disp ELEMENT CFDRCFEM mixed ELEMENT CFDRCFEM pshell ELEMENT

As expected the CFDRCFEM pshell element performs very well relative to NASTRAN results. 

The displacement and mixed formulation elements again are not good choices for these types of 

problems. Their main use is for modeling of solid structures as opposed to structures with 

bending deformation. They are shown in the comparison for the purpose of completeness. Table 

A.4 is the same format as Table A.3 and contains the results for the high load case. The higher 

load produces significantly more nonlinear deflection behavior then the low load.

Table A.4 Static Plate Results for Load Case 2

dX (in) dY (in) dZ (in) dX (in) dY (in) dZ (in) dX (in) dY (in) dZ (in) dX (in) dY (in) dZ (in)

MESH CHEXA 100 x 1 x 20 MESH disp 100 x 1 x 20 MESH mixed 100 x 1 x 20 MESH pshell 100 x 1 x 20

LINEAR LINEAR LINEAR LINEAR

LE Tip 0.00 0.00 36.33 0.00 0.00 23.38 0.00 0.00 45.11 0.00 0.00 36.33

TE Tip 0.00 0.00 34.38 0.00 0.00 21.50 0.00 0.00 43.14 0.00 0.00 34.38

Twist (deg) 7.93 7.64 % Error = -10.9631 8.01 % Error = 7.2425 7.92 % Error = -0.0182

LGDISP LGDISP LGDISP LGDISP

LE Tip 0.77 -6.26 32.51 0.51 -2.85 22.15 0.97 -9.01 38.70 0.77 -6.26 32.51

TE Tip 0.66 -5.68 30.87 0.40 -2.45 20.44 0.86 -8.33 37.09 0.66 -5.68 30.87

Twist (deg) 6.75 7.04 % Error = -35.2387 6.60 % Error = 26.2132 6.75 % Error = -0.0015

FOLLOWER FOLLOWER FOLLOWER FOLLOWER

LE Tip 0.87 -6.85 33.92 0.55 -2.95 22.54 1.15 -10.36 41.24 0.87 -6.86 33.93

TE Tip 0.76 -6.25 32.25 0.43 -2.55 20.81 1.04 -9.63 39.61 0.76 -6.26 32.27

Twist (deg) 6.82 7.12 % Error = -37.2492 6.67 % Error = 31.0110 6.82 % Error = 0.0595

MESH CHEXA 10 x 1 x 2 MESH disp 10 x 1 x 2 MESH mixed 10 x 1 x 2 MESH pshell 10 x 1 x 2

LE Tip LINEAR LINEAR LINEAR LINEAR

TE Tip 0.00 0.00 36.20 0.00 0.00 1.63 0.00 0.00 1.65 0.00 0.00 36.24

Twist (deg) 0.00 0.00 34.30 0.00 0.00 0.24 0.00 0.00 0.26 0.00 0.00 34.34

7.77 5.65 % Error = -31.7271 5.67 % Error = -31.6758 7.74 % Error = -0.0252

LE Tip LGDISP LGDISP LGDISP LGDISP

TE Tip 0.64 -5.46 30.28 0.04 -0.01 1.62 0.04 -0.01 1.64 0.74 -6.18 32.30

Twist (deg) 0.55 -4.94 28.72 -0.02 0.00 0.25 -0.03 0.00 0.26 0.64 -5.63 30.70

6.41 5.60 % Error = -86.3296 5.63 % Error = -86.2472 6.56 % Error = 10.9936

LE Tip FOLLOWER FOLLOWER FOLLOWER FOLLOWER

TE Tip 0.71 -5.87 31.33 0.05 -0.01 1.61 0.05 -0.01 1.63 0.83 -6.75 33.65

Twist (deg) 0.61 -5.34 29.76 -0.02 0.00 0.25 -0.02 0.00 0.26 0.73 -6.17 32.03

6.45 5.59 % Error = -86.2475 5.62 % Error = -86.1343 6.62 % Error = 12.3333

NASTRAN RESULTS CFDRCFEM disp ELEMENT CFDRCFEM mixed ELEMENT CFDRCFEM pshell ELEMENT
134 8927/6

The general comments for this load case are similar then for load case 1. However, it is 

important to recognize that the percent error calculations are against the NASTRAN solution 

with the same mesh. This is significant when looking at the pshell element solution for a 10 x 1 

x 2 mesh size. The coarse NASTRAN solution is relatively stiff and the pshell element is not. 

The error relative to the 100 x 1 x 20 NASTRAN solution for the pshell 10 x 1 x 2 mesh is: -

0.40%, -1.80%, and -2.18% respectively for the linear, large displacement and follower force 

solutions. This further emphasizes the solid performance of the pshell element in CFDRCFEM 

for modeling of geometrically nonlinear structural behavior in wing like structures. 

 

Figure A.7 Result Format for Plate Displacement Plots A2 and A4

Plots of the results contained in Tables A.3 and A.4 are contained at the end of this appendix in 

Figures A.9 – A.12. Plots A.9 and A.111 are results as if the plate tip was projected onto a plane 

generated at a constant Y-axis location. Figure A.7 above shows the plate tip projection onto the 

viewing plane that these plots are generated from.

Projected Result 

show in FiguresA2 

and A4
135 8927/6

Figure A.8 Static Tip Displacements for Beam Test Case

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2

13

13.5

14

14.5

15

15.5

TIP DISPLACEMENT FOR BEAM LOAD CASE 1

Y - Tip Displacement Z - Tip Displacement

NASTRAN Linear 900 x 3 x 3

NASTRAN follower 900 x 3 x 3

NASTRAN LgDisp 900 x 3 x 3

NASTRAN Linear 400 x 2 x 2

NASTRAN follower 400 x 2 x 2

NASTRAN LgDisp 400 x 2 x 2

NASTRAN CHEXA linear 10 x 1 x 1

NASTRAN CHEXA follower 10 x 1 x 1

NASTRAN CHEXA LgDisp 10 x 1 x 1

NASTRAN beam linear 10 x 1 x 1

NASTRAN beam follower 10 x 1 x 1

NASTRAN beam LgDisp 10 x 1 x 1

CFDRCFEM disp element Linear 900 x 3 x 3

CFDRCFEM disp element follower 900 x 3 x 3

CFDRCFEM disp element LgDisp 900 x 3 x 3

CFDRCFEM disp element Linear 400 x 2 x 2

CFDRCFEM disp element follower 400 x 2 x 2

CFDRCFEM disp element LgDisp 400 x 2 x 2

CFDRCFEM mixed element Linear 900 x 3 x 3

CFDRCFEM mixed element follower 900 x 3 x 3

CFDRCFEM mixed element LgDisp 900 x 3 x 3

CFDRCFEM mixed element Linear 400 x 2 x 2

CFDRCFEM mixed element follower 400 x 2 x 2

CFDRCFEM mixed element LgDisp 400 x 2 x 2

CFDRCFEM beam element linear 50 x 5 x 5

CFDRCFEM beam element follower 50 x 5 x 5

CFDRCFEM beam element LgDisp 50 x 5 x 5

CFDRCFEM beam element linear 10 x 1 x 1

CFDRCFEM beam element follower 10 x 1 x 1

CFDRCFEM beam element LgDisp 10 x 1 x 1

-20 -15 -10 -5 0 5

40

45

50

55

60

65

TIP DISPLACEMENT FOR BEAM LOAD CASE 2

Y - Tip Displacement

Z - Tip Displacement
136 8927/6

-2 0 2 4 6 8 10 12 14 16

0

5

10

15

Plate Leading and Trailing Edge x and z Tip Displacement Load Case 1: Low

In-plane X - displacement (inches) Vertical Z - displacement (inches)

NASTRAN CHEXA linear 100 x 1 x 20

NASTRAN CHEXA follower 100 x 1 x 20

NASTRAN CHEXA Lgdisp 100 x 1 x 20

NASTRAN CHEXA linear 10 x 1 x 2

NASTRAN CHEXA follower 10 x 1 x 2

NASTRAN CHEXA Lgdisp 10 x 1 x 2

CFDRCFEM disp linear 100 x 1 x 20

CFDRCFEM disp follower 100 x 1 x 20

CFDRCFEM disp Lgdisp 100 x 1 x 20

CFDRCFEM disp linear 10 x 1 x 2

CFDRCFEM disp follower 10 x 1 x 2

CFDRCFEM disp linear 10 x 1 x 2

CFDRCFEM mixed linear 100 x 1 x 20

CFDRCFEM mixed follower 100 x 1 x 20

CFDRCFEM mixed Lgdisp 100 x 1 x 20

CFDRCFEM mixed linear 10 x 1 x 2

CFDRCFEM mixed follower 10 x 1 x 2

CFDRCFEM mixed Lgdisp 10 x 1 x 2

CFDRCFEM pshell linear 100 x 1 x 20

CFDRCFEM pshell follower 100 x 1 x 20

CFDRCFEM pshell Lgdisp 100 x 1 x 20

CFDRCFEM pshell linear 10 x 1 x 2

CFDRCFEM pshell follower 10 x 1 x 2

CFDRCFEM pshell Lgdisp 10 x 1 x 2

Figure A.9 Static Tip Displacements for Plate, Load Case 1, z-x plane

-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2

0

5

10

15

Plate Leading Edge y and z Tip Displacement Load Case 1: Low

Axial Y - displacement (inches) Vertical Z - displacement (inches)

NASTRAN CHEXA linear 100 x 1 x 20

NASTRAN CHEXA follower 100 x 1 x 20

NASTRAN CHEXA Lgdisp 100 x 1 x 20

NASTRAN CHEXA linear 10 x 1 x 2

NASTRAN CHEXA follower 10 x 1 x 2

NASTRAN CHEXA Lgdisp 10 x 1 x 2

CFDRCFEM disp linear 100 x 1 x 20

CFDRCFEM disp follower 100 x 1 x 20

CFDRCFEM disp Lgdisp 100 x 1 x 20

CFDRCFEM disp linear 10 x 1 x 2

CFDRCFEM disp follower 10 x 1 x 2

CFDRCFEM disp linear 10 x 1 x 2

CFDRCFEM mixed linear 100 x 1 x 20

CFDRCFEM mixed follower 100 x 1 x 20

CFDRCFEM mixed Lgdisp 100 x 1 x 20

CFDRCFEM mixed linear 10 x 1 x 2

CFDRCFEM mixed follower 10 x 1 x 2

CFDRCFEM mixed Lgdisp 10 x 1 x 2

CFDRCFEM pshell linear 100 x 1 x 20

CFDRCFEM pshell follower 100 x 1 x 20

CFDRCFEM pshell Lgdisp 100 x 1 x 20

CFDRCFEM pshell linear 10 x 1 x 2

CFDRCFEM pshell follower 10 x 1 x 2

CFDRCFEM pshell Lgdisp 10 x 1 x 2

Figure A.10 Static Tip Displacements for Plate, Load Case 1, z-y plane
137 8927/6

0 2 4 6 8 10 12 14 16

0

5

10

15

20

25

30

35

40

45

50

Plate Leading and Trailing Edge x and z Tip Displacement Load Case 2: High

In-plane X - displacement (inches) Vertical Z - displacement (inches)

NASTRAN CHEXA linear 100 x 1 x 20

NASTRAN CHEXA follower 100 x 1 x 20

NASTRAN CHEXA Lgdisp 100 x 1 x 20

NASTRAN CHEXA linear 10 x 1 x 2

NASTRAN CHEXA follower 10 x 1 x 2

NASTRAN CHEXA Lgdisp 10 x 1 x 2

CFDRCFEM disp linear 100 x 1 x 20

CFDRCFEM disp follower 100 x 1 x 20

CFDRCFEM disp Lgdisp 100 x 1 x 20

CFDRCFEM disp linear 10 x 1 x 2

CFDRCFEM disp follower 10 x 1 x 2

CFDRCFEM disp Lgdisp 10 x 1 x 2

CFDRCFEM mixed linear 100 x 1 x 20

CFDRCFEM mixed follower 100 x 1 x 20

CFDRCFEM mixed Lgdisp 100 x 1 x 20

CFDRCFEM mixed linear 10 x 1 x 2

CFDRCFEM mixed follower 10 x 1 x 2

CFDRCFEM mixed Lgdisp 10 x 1 x 2

CFDRCFEM pshell linear 100 x 1 x 20

CFDRCFEM pshell follower 100 x 1 x 20

CFDRCFEM pshell Lgdisp 100 x 1 x 20

CFDRCFEM pshell linear 10 x 1 x 2

CFDRCFEM pshell follower 10 x 1 x 2

CFDRCFEM pshell Lgdisp 10 x 1 x 2

Figure A.11 Static Tip Displacements for Plate, Load Case 2, z-x plane

-12 -10 -8 -6 -4 -2 0 2

0

5

10

15

20

25

30

35

40

45

50

Plate Leading Edge y and z Tip Displacement Load Case 2: High

Axial Y - displacement (inches) Vertical Z - displacement (inches)

NASTRAN CHEXA linear 100 x 1 x 20

NASTRAN CHEXA follower 100 x 1 x 20

NASTRAN CHEXA Lgdisp 100 x 1 x 20

NASTRAN CHEXA linear 10 x 1 x 2

NASTRAN CHEXA follower 10 x 1 x 2

NASTRAN CHEXA Lgdisp 10 x 1 x 2

CFDRCFEM disp linear 100 x 1 x 20

CFDRCFEM disp follower 100 x 1 x 20

CFDRCFEM disp Lgdisp 100 x 1 x 20

CFDRCFEM disp linear 10 x 1 x 2

CFDRCFEM disp follower 10 x 1 x 2

CFDRCFEM disp Lgdisp 10 x 1 x 2

CFDRCFEM mixed linear 100 x 1 x 20

CFDRCFEM mixed follower 100 x 1 x 20

CFDRCFEM mixed Lgdisp 100 x 1 x 20

CFDRCFEM mixed linear 10 x 1 x 2

CFDRCFEM mixed follower 10 x 1 x 2

CFDRCFEM mixed Lgdisp 10 x 1 x 2

CFDRCFEM pshell linear 100 x 1 x 20

CFDRCFEM pshell follower 100 x 1 x 20

CFDRCFEM pshell Lgdisp 100 x 1 x 20

CFDRCFEM pshell linear 10 x 1 x 2

CFDRCFEM pshell follower 10 x 1 x 2

CFDRCFEM pshell Lgdisp 10 x 1 x 2

Figure A.12 Static Tip Displacements for Plate, Load Case 2, z-y plane
138 8927/6

In addition to fully parallelized FSI within CoPhy, its FEM module, CFDRC-FEM can be used 

in serial or parallel mode with third party CFD codes through the Multi Disciplinary Integrated 

Computing Environment (MDICE). In the following example, a FSI coupled problem between 

CFD-FASTRAN, a density based CFD solver and COBI‟s FEM module is presented for Mach 

5.6 flow over a thin film ballute structure. A ballute (balloon- parachute) is a flexible, inflatable 

device made from thin film material with thickness on the order of 1 to 10mil, which is deployed 

to increase the drag of the vehicle to which it is attached during reentry/aerocapture maneuvers. 

As seen in Figure A.13, the clamped ballute consisted of a clamped, rigid nose section and a 

fixed outer support and a 1-mil thick kapton film was stretched in between them. Details of the 

model can be seen in [Gregory M. Buck, 2006]. This problem was run using the explicit solver in 

COBI. The results can be seen in Figure A.14. 

(a) Cross section of test 

model

(b) Assembled test 

model

(c) Model during and after testing

Figure A.13 CF4 wind tunnel model [Gregory M. Buck, 2006].

(a) Displacement Contours (b) Mach Contours Around Deformed 

Ballute after FSI

Figure A.14 FSI coupling results between CFD-FASTRAN and CFDRC-FEM for a thin film 

ballute.
REPORT DOCUMENTATION PAGE Form Approved

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2. REPORT TYPE 

Contractor Report

 4. TITLE AND SUBTITLE

Aero-Structural Assessment of an Inflatable Aerodynamic Decelerator 

5a. CONTRACT NUMBER

NNM06AA10C

 6. AUTHOR(S)

Sheta, Essam F.; Venugopalan, Vinod; Tan, X. G.; Liever, Peter A.; 

Habchi, Sami D.

 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

NASA Langley Research Center

Hampton, VA 23681-2199

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National Aeronautics and Space Administration

Washington, DC 20546-0001

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CFDRC Report: 8927/6

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14. ABSTRACT

NASA is conducting an Entry, Descent and Landing Systems Analysis (EDL-SA) Study to determine the key technology 

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robotic missions. Inflatable Aerodynamic Decelerators (IADs) are one of the candidate technologies. A variety of EDL 

architectures are under consideration. The current effort is conducted for development and simulations of computational 

framework for inflatable structures.

15. SUBJECT TERMS

Inflatable structures; Descent; Landing; EDL; Toroids

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