NASA Technical Memorandum 107195

/

ASTROP2 Users Manual: A Program for

Aeroelastic Stability Analysis

of Propfans

T.S.R. Reddy

University of Toledo

Toledo, Ohio

and

John M. Lucero

Lewis Research Center

Cleveland, Ohio

March 1996

National Aeronautics and

Space Administration
Trade names _ manufacture_' names are used in this report for identification

only. This usage does not o0nstitute an official endot_nent, either expressed

or implied, by the National Aeronautics and Space AdministraficG.
ASTROP2 Users Manual: A Program for Aeroelastic

Stability Analysis of Propfans

Version 2.0

T.S.R. Reddy

University of Toledo

Toledo, Ohio 43606

John M. Lucero +

NASA Lewis Research Center

Cleveland, Ohio 44135

SUMMARY

This manual describes the input data required for using the second version of

the ASTROP2 ( Aeroelastic STability and Response Of Propulsion systems - 2

dimensional analysis ) computer code. In ASTROP2, version 2.0, the program

is divided into two modules: 2DSTRIP, which calculates the structural

dynamic information; and 2DASTROP, which calculates the unsteady

aerodynamic force coefficients from which the aeroelastic stability can be

determined. In the original version of ASTROP2, these two aspects were

performed in a single program. The improvements to version 2.0 include an

option to account for counter rotation, improved numerical integration,

accommodation for non-uniform inflow distribution, and an iterative scheme

to flutter frequency convergence.

ASTROP2 can be used for flutter analysis of multibladed structures such as

those found in compressors, turbines, counter rotating propellers or propfans.

The analysis combines a two-dimensional, unsteady cascade aerodynamics

model and a three dimensional, normal mode structural model using strip

theory. The flutter analysis is formulated in the frequency domain resulting

in an eigenvalue determinant. The flutter frequency and damping can be

inferred from the eigenvalues.

*NASA Resident Research Associate at Lewis Research Center

+Research Engineer
TABLE OF CONTENTS

Summary

1. Introduction ....................................................................................... 1

2. Analysis ............................................................................................ 2

. Program 2DSTRIP

3.1

3.2

3.3

3.4

3.5

3.6

3.7

3.8

ooo°°.°°oooloo Joo°.ol_.°.°°°°°°°°o°l Qol o.°°.°° °°°°°°.°°°°°°°o.°. °°°* I,o ol°° °_3

Dimension Statement for the Program ........................................... 5

Description of Input Variables ...................................................... 5

Additional Input Files .................................................................. 9

Additional Notes .......................................................................... 9

Job Run Stream on Cray YMP ..................................................... 10

Description of Output files ........................................................... 10

Example Case:

Calculation of Structural Dynamic Characteristics at Selected

Strips for SR3CX2 Propfan ..................................................... 11

Program Calling Tree ................................................................. 23

4. Program 2DASTROP ......................................................................... 24

4.1 Dimension Statement for the Program .......................................... 24

4.2 Description of Input Variables ..................................................... 24

4.3 Additional Input Files ................................................................ 28

4.4 Additional Notes ........................................................................ 28

4.5 Job Run Stream on Cray YMP ..................................................... 28

4.6 Description of Output files ........................................................... 29

4.7 Example Case:

Calculation of Unsteady Aerodynamic Forces at the Strips

and Aeroelastic Stability for SR3CX2 Propfan ............................ 29

4.8 Program Calling Tree ................................................................. 40

5. Acknowledgements ........................................................................... 41

6. References ....................................................................................... 41

ii
1. INTRODUCTION

During the last decade several aeroelastic analyses for propfans and

turbomachines have been developed at NASA Lewis Research Center. This

work has resulted in several individual codes with variations in the

aerodynamic and structural models used, Ref. 1. One of the codes is named

ASTROP2. ASTROP2 uses strip theory to integrate the aerodynamic forces

calculated using a two dimensional aerodynamic model with a three

dimensional structural model. The theoreticaldevelopment of ASTROP2 and

a user's manual for the original ASTROP2 code was given in Ref. 2. The

originalversion combined calculationof structural dynamic characteristicsof

selected blade sections called strips,and the calculation of the aeroelastic

stabilityin one large program.

In the present updated version, the original program is divided into two

programs. The firstprogram, 2DSTRIP calculates the structural dynamic

characteristicsat the required stripsfor the aeroelasticanalysis. The second

program, 2DASTROP, uses the structural data obtained from 2DSTRIP and

calculatesthe aeroelasticstability.In this way each program can be used and

modified independently. The user has to run 2DSTRIP first,and then

2DASTROP. However, for the same structuralmodel, only 2DASTROP need to

be run for differentflow conditions.

Additional improvements were made in ASTROP2 version 2.0. These include

(1) an option to account for counter rotation, (2) improved numerical

integration, (3) accommodation for nonuniform inflow distribution in the

velocity calculations, and (4) an iterative scheme for flutter convergence.

This manual will help the user in the preparation of the input data files

required for using 2DSTRIP and 2DASTROP. In the following, a brief

description of the analysis is given in section 2. In section 3, the input and

output description, followed by input and output for an example case for

2DSTRIP is given. Section 4, gives the input and output description, followed

by an actual input and output for an example case using 2DASTROP. A job

run stream for a Cray YMP computer, and the program calling tree are also

given for each program.

The codes were developed in the Structural Dynamics Branch at the NASA

Lewis Research Center. They are made available strictly as a research tool.

Neither NASA, nor any individuals who have contributed to the development of

the code, assume any liability resulting from the use of the codes beyond

research needs. Both the 2DSTRIP and 2DASTROP codes are written in

1
FORTRAN. They are operational on the Cray YMP computer at the NASA

Lewis Research Center under the UNICOS operating system.

Dr. G.V. Narayanan originally developed this program under the direction of

Dr. I_R.V. Kaza. The first author of this report was responsible for the

present version. Additional improvements and modifications were made by

Dr. A.J. Mahajan and by the second author of this report.

2. ANALYSIS

The aeroelastic analysis uses the unsteady aerodynamic forces calculated at

selected blade sections ( strips ) of a three dimensional structure. The

aerodynamic forces are calculated using a two dimensional unsteady

aerodynamic model. The aerodynamic model calculates the unsteady forces at

the selected strips for an airfoil undergoing rigid body pitching and plunging

motions. The 2DSTRIP program calculates the pitching and plunging values

for the strips, and the 2DASTROP program uses this information to calculate

the aeroelastic stability. The formulation and aeroelastic analysis are

described in detail in Ref. 2.

The three dimensional normal mode structural characteristicsare obtained

from a finiteelement analysis, and used as input to the 2DSTRIP program.

Two types of output files(to be used as input to 2DSTRIP) are used from the

finite element analysis. One, a non-linear steady state blade deflection

analysis output. The other, a free vibration analysis output in the form of

mode shapes and frequencies. 2DSTRIP can be run without the nonlinear

steady state blade deflection if its effecton the flutterstabilityis assumed

negligible. However, the effect of structural non-linearity due to blade

deflectionmust be included in the calculationof the natural frequencies and

mode shapes. The program 2DSTRIP calculates the equivalent rigid pitching

and plunging values, stagger angle, gap to chord ratio and stripwidths at the

desired strips. This information is stored as a file and used as input to

2DASTROP.

Currently, the 2DSTRIP program is set up to use the NASTRAN ( NASA

STRuctural ANalysis program) finite element analysis program. Two forms

of NASTRAN are available at NASA Lewis; one is COSMIC/NASTRAN and

the other is MSC/NASTRAN. The non-linear steady-state blade deflection

configuration of a rotating blade is obtained from a geometric nonlinear

analysis. This analysis is done in COSMIC/NASTRAN by using the available

solution sequence number 4. The normal mode vibration analysis of the blade

is done by using the solution sequence number 9. The respective solution

sequence numbers in MSC/NASTRAN are 64 and 63. See Ref. 3 for more

2
details on how to run NASTRAN for rotating flexible blades. If other finite

element programs are used in obtaining the structural characteristics, the

formats in the relevant subroutines have to be changed.

The output file from 2DSTRIP for strip data information is read by 2DASTROP

and used to calculate the unsteady aerodynamic force coefficients. The

unsteady aerodynamic forces are obtained with a two dimensional unsteady

aerodynamic model. The aerodynamic model provides unsteady aerodynamic

forces for airfoils undergoing rigid pitching (twist) and plunging (bending)

motions. For subsonic flow the Rao and Jones theory ( Ref. 4) is used. For

supersonic flow with subsonic leading edge, the Adamczyk and Goldstein

theory (Ref. 5) is used. The strip structural information along with an

assumed frequency are used to calculate the unsteady aerodynamic forces.

These unsteady aerodynamic coefficients are then used in an eigen analysis.

The eigen values determine the flutter frequency and damping. The flutter

calculations are iterated (the required number of iterations is given as input)

until the assumed frequency is close or equal to the calculated flutter

frequency. The ASTROP2 program has been used to predict flutter of the

SR3CX2 propfan observed in experiments, Ref. 6-7, and to assist in the design

of other propfans systems, Ref. 8.

The coordinate system used for both programs is shown in Fig.1. The X axis is

the axis of rotation. It is assumed to be along the direction of axial flow and

positive in the direction of flow. The blade pitch axis is the Y axis. It is taken

normal to the X axis with positive values in the direction of increasing radius.

The Z axis is then def'med to form a right-hand coordinate system. The plane

of rotation is the plane formed by the Y and Z axes. A typical strip, with mid

point, at a distance "d" is shown in Fig. 1. The axial velocity is V and the

rotational speed is "_", and Ve is the effective (relative) velocity. The tangent

(tangent to blade leading edge), chord and normal vectors ("t,c,n" respectively)

at the mid point of the strip are defined as shown. "s" denotes the arc length

measured along the leading edge. Figure 2 shows the section A-A of the strip

showing the rigid pitching (a) and plunging (h) motions for the strip,

assuming the reference axis for the aeroelastic analysis is at the leading edge.

3. PROGRAM

In this section the input and output for the 2DSTRIP program is given. The

source code is designated as 2dstrip.f, and the input data for the code is

provided in the input file 2dstrip.in. As mentioned before, in addition to this

input file, 2DSTRIP requires input files from finite element structural analysis

giving the structural dynamic characteristics of the blade. The naming and

linking of these input files is also given in the following sections.
@

X

Figure 1. • 2DSTRIP and 2DASTROP coordinate system for a

rotating propfan blade

n

/

/

Dellected

¢

t_dehcted

section A-A

Figure 2. • Section A-A showing rigid pitching (_) and plunging (h) motions

for the strip ( reference axis =leading edge)

4
3.1 Dimension Statement for the Program

The program is currently dimensioned for a maximum of 20 strips, and 500

finite elements with six degrees of freedom. It is dimensioned for reading

natural mode shape information and frequencies for six modes. If the user

needs to change these limits, the dimension statements have to be changed

globally in the source code, and compiled for execution.

3.2 Description of Input Variables

The input is given through a data file named 2dstrip.in. This file contains the

standard (unit 5) input that the 2DSTRIP code requires. Unless stated

otherwise, real values are read in 8F10.4 format and integer values are read in

8110 format.

Some lines of the input data are preceded by a line containing the names of the

variables. These lines are an aid in preparing the input file and are read by

the program but not used as data in the calculations.

The first line in the input file is the title card read in 20A4 format, used for

identification of the structure to be analyzed. The rest of the input variables

are described below in the order in which they appear in the input data file (see

section 3.7 for an example input file).

variable:

type:

description:

example:

NAEROP

integer variable

number of strips ( aero points) at which structural information

has to be generated for stability analysis (maximum 20).

10

variable:

type:

description:

example:

NMODE

integer variable

number of modes for which structural information is available

(maximum 6).

6

variable:

type:

description:

example:

ITEST

integer variable

ITEST = 0 read and check finite element structural information

and then proceed to calculate the required data for the

aeroelastic analysis

ITEST=I read and check finite element structural information

variable:

type:

I6364

integer variable
description

example:

Indicator for using MSC/NASTRAN combined solution

sequence 6364 output file

I6364 = 0

I6364 = 1 If the structural input i'de is from MSC/NASTRAN

combined solution 6364 sequence.

0

variable:

type:

NASTRAN 0UPUT TYPE

character variable oflength A4 followed by a blank and then an

integer number in I2 format.

description: denotes the type of finite element structural input files for free

vibration (mode shapes and frequencies ) and steady state

solution input files followed by the file unit number.

At present COSMIC/NASTRAN and MSC/NASTRAN are

supported. Input NULL indicates that there is no input file for

steady state solution.

COSM04 NULL08

MSC04 NULL08

example: COSM04 NULL08

NOTE: Ifthe input is from any other source (otherthan COSMIC or MSC), the

formats in subroutines RDNAS, RDISP, RDMODS have to be modified.

variable:

type:

description:

example:

IPG

integer variable

controlfor printing structuralgrid data

I PG = 0 do not print

i_ = I print

1

variable:

type:

description:

example:

IPD

integer variable

control for printing structural steady data

IPD -- 0 do not print

IPD = 1 print

0

variable:

type:

description:

example:

integer variable

control for printing structural modal data

I PM = 0 do not print

IPM = i print

1

variable:

type:

description:

ISET

integer variable

defines blade coordinate axis system ofthe structuralinput

ISZT = 0 Z along span, X along velocityand chord (eg. COSMIC or

MSC NASTRAN axis system)

zszT = I Y along span, X along velocityand chord (as shown in

Fig. 1 i.e.ASTROP2 coordinate system)

6
example:

ISET = 2 X along span, Y along velocity and chord

Note: with this input, the structural data input is transformed

to ASTROP2 coordinate system, Fig. 1.

0

NOTE: If the finite element structural input axis system is other than that

described above, relevant statements in RDNAS, RDDISP and RDMODS must

be modified.

variable:

type:

description:

example:

ICONFIG

integer variable

indicatorfor counter rotation

ICONFIG = 0 no counter rotation

ZCO_ZG = 1 counter rotation

0

variable:

type:

description:

example:

BETA75

real variable

setting angle at 75% span in degrees. If this angle is different

by 0.005 degrees (0.001 radians) from the finite element

structural input the program stops. If required, this tolerance

can be increased in subroutine SETB75

61.2

variable:

type:

description:

example:

N1

integer variable

leading edge node number near and below 75% span station

157

variable:

type:

description:

example:

N2

integer variable

trailing edge node number near and below 75% span station

165

variable:

type:

description:

example:

N3

integer variable

leading edge node number near and above 75% span station

166

variable:

type:

description:

example:

N4

integer variable

trailing edge node number near and above 75% span station

174

variable:

type:

description:

example:

ZETA75

real variable

spanwise coordinate at 75% span

9.1875

Note: values of N1, N2, N3, N4 and ZETA75 are used to calculate the setting angle
from the NASTRAN output, and then checked with the input value BETA75.

variable:

type:

description:

example:

LECOY

real variable

spanwise coordinate (lowest Y-cAx_rdinate) value above which

leading edge line is effective

4.00

variable:

type:

description:

example:

TECOY

real variable

spanwise coordinate ( lowest Y-coordinate) value above which

trailing edge line is effective

4.00

variable:

type:

description:

example:

IDREAD

integer variable

option to read the node numbers of the leading and trailing edges.

IDRF_JkD=0 determine the leading and trailing edge node numbers

IDZZ_=I input the leading and trailing edge node numbers

1

variable:

type:

description:

example:

NLE

integer variable

number of leading edge nodes (required if7DREAD = I)

18

variable:

type:

description:

example:

NTE

integer variable

number of trailingedge nodes (required ifIDREAD =I)

18

NOTE: values OfNLz and _rrzare read in 215 format

variable: T.ZNODZS

type: integer variable

description: leading edge node numbers of the finiteelement structural

model with spanwsie coordinate (Y-coordinate)value greater

than LECOY in 1615 format (requiredifZD_.D =i)

example:

000670007600085_094001030011200121001300013900148001570016600175001840019300202

0021100220

variable: TENODES

type: integer variable

description: trailingedge node numbers of the finiteelement structural

model with spanwise coordinate (Y-coordinate)value greater

than TECOY in 1615 format (required ifZDRZAD =i)

example:

0007_102001110012000129001380014700156001650017400183001920020100210

002190022_
variable:

type:

description:

example:

METHOD

integer variable

METHOD =0, no steady displacements (fabricatedblade geometry)

METHOD =1,steady displacements added (deformed blade geometry)

0

variable:

type:

description:

example:

AEROPOINTS COORDINATES

character variable

this card isfollowed by the spanwise coordinate ( strip mid point)

value of the strips, equal to NAEROP values.

4.2500

4.5000

4.7500

5.6361

12.200

variable:

type:

description:

example:

C_L

real variable

indicator for calculation of rigid pitching amplitude values (a)

c_ = -1.0, read from the structural input file

CAL =0.0, calculate from displacements (h)

CAL =1.0, calculated from average rotations

1.0

3.3 Additional Input Files

The program requires that the structural dynamic characteristics data files

from a finite element analysis be linked to unit 4 and unit 8. The natural

frequencies and mode shapes input file must be linked to unit 4, and steady

displacement input file should be linked to unit 8. At present both COSMIC

and MSC NASTRAN are supported. If the structural data files are from any

other source, the formats in routines RDNAS, RDDISP, and RDMODS have to

be modified accordingly.

3.4 Additional Notes

The 2DSTRIP program is setup to work with the finite element structural

model having node numbers from root to tip, and increasing in the +ve X

direction. It also works well if the chord lines (lines parallel to X-axis) are at a

constant spanwise location. The leading edge line is taken as the reference

axis for calculating pitching and plunging values.

The program is implemented on the Cray YMP at NASA Lewis Research

Center. However, the program can be implemented on a workstation or

9
personal computer. It required about 1.1 MW memory, and took about 12

seconds to compile and about 16 seconds to execute for the example given in

section 3.7.

3.5 Job run stream on Cray YMP

A sample Cray job stream to run 2DSTRIP at the NASA Lewis Research

Center isgiven in this section. For this case,the modal information output file

(sol9cos.out)from finiteelement structural analysis is linked to unit 4. The

source code, 2dstrip.f,is compiled using cft77 with standard options. The

input to 2DSTRIP iscontained in the filenamed 2dstrip.in.The standard unit

6 output is written to a filenamed 2dstrip.out. The information required for

2DASTROP is written to unit 7 as file fort.7. This file is renamed as

fort7.2dstrip. The rest of the file contains UNICOS and Cray related

commands.

#! /bin/csh

# QSUB -r sr3cx2

# QSUB -1M 1.2Mw

#QSUB

Ibinlrm 2dstrip.out

In sol9cos.out fort.4

cft77 -V -a static 2dstrip.f

segldr -o 2dstrip 2dstrip.o

time 2dstrip<2dstrip.in>2dstrip.out

mv fort.7 fort7.2dstrip

3.6 Description of Output files

Unit 6 (2dstrip.out) output : All the output is written on to unit 6, with selected

output rewritten on to unit 7 to be used by 2DASTROP program. The user has

to check for the correctness of the following items in the output:

(1) the input file from the finite element structural output (grid and modal

values);

(2) the tangent, normal and streamline vectors for allpoints on the leading

edge;

(3)the coordinates of each of the aeropoints;

(4)the tangent, streamline and normal vectors at the aeropoints;

(5)the modal values (rigidpitching and plunging values) for each stripand for

each mode; and

lO
(6) the sweep and stagger angles, semichord (SEMICHD) values at each strip, and

strip widths (STRIPW).

Unit 7 output: This file contains the relevant information of the strips required

by the 2DASTROP program.

3.7 Example Case: Calculation of Structural Dynamic Characteristics at

Selected Strips for SR3CX2 Propfm_

In this section the actual input and output are given for the SR3CX2 propfan

which fluttered during wind tunnel testing, Refs. 6-7. The input file is named

2dstripin. The COSMIC/NASTRAN input file for six modes and frequencies

(NMODE=6) is linked to unit 4 (COSM04). There is no steady state blade deflection

input file (SVLT,).The NASTRAN grid and mode shapes are to be printed (ZPG =1,

ZPM=I), and the example is not for counter rotation (ZCONFZG=0). The setting angle

at 75% span (BZT_75) is 61.2 degrees. It is required to calculate strip data at ten

strip stations (NAZROP=I0). The strip locations along the span are given as

_ZROPOINTS COORDZNATZS. The equivalent rigid pitching (a) has to be calculated as

an average of the rotation values of the nodes on the strip (CAL=I).

Input file (2dstripAn)

READING NASTRAN OUTPUT AND PROCESSING for SR3CX2 propfan

NAEROP NMODE ITEST I6364 (READ IN MAIN)

10 6 0 0

NASTRAN OUTPUT TYPE (RDNAS)

COSM04 NULL08

IPG IPD IPM ISET ICONFIG

01 00 01 00 00

BETA75(SETTING ANGLE AT 75% SPAN)

61.20

N1 N2 N3 N4

157 165 166 174

ZBETA75

9.1875

LECOY

4.000

TECOY

4.000

I DREAD

1

NLE NTE

18 18

LENODES

00067000760008500094001030011200121001300013900148001570016600175001840019300202

0021100220

TENODES

00075000840009300102001110012000129001380014700156001650017400183001920020100210

0021900228

METHOD

0

11
AEROPOINTS COORDINATES (LOCGRI )

4.2500

4.5000

4.7500

5.6361

6.9739

8.8736

9.7114

10.8758

11.7553

12.2000

CAL (RUNAS 1 )

1.0 CAL: (=-i NODAL VALUES,=0 ALFA/DISP, =I ALFA/ALFA)

Unit 6 output rite ( 2dstrlp.out )

The output information is printed, and given here in the order mentioned in

section 3.6, and is self explanatory. In this report, most of the output is

deleted, and only key output is retained to help the user to check the output

before going through the large printed output. For easy debugging and

understanding, the output from each subroutine is identified by "entered

(subroutine) xxxx" and "leaving (subroutine) xxxxx". It is to be noted that the

rigid body pitching (a) and plunging values (h) are denoted by A-VALUE and

H-VALUE with appropriate names for their derivatives.

READING NASTRAN OUTPUT AND PROCESSING for SR3CX2 propfan

*** ENTERED RDNAS ***

ECHO PRINT OF FINITE ELEMENT ANALYSIS OUTPUT

IN ASTROP2 COORDINATE SYSTEM

GRID 1

GRID 2

GRID 3

GRID 4

GRID 5

GRID 6

GRID 7

IPG= 1 IPD= 0 IPM= 1 ISETUP= 0

NUMBER OF GRID POINTS = 228

-0.699 1.700 -0.038

-0.399 1.700 -0.022

-0.200 1.700 -0.011

0.000 1.700 0.000

0.200 1.700 0.011

0.399 1.700 0.022

0.699 1.700 0.038

*******linesdeleted for brevity ***

GRID 220 1.905 12.250 -1.739

GRID 221 2.079 12.250 -1.885

GRID 222 2.253 12.250 -2.023

GRID 223 2.426 12.250 -2.159

GRID 224 2.600 12.250 -2.291

GRID 225 2.772 12.250 -2.422

GRID 226 2.945 12.250 -2.550

GRID 227 3.118 12.250 -2.674

GRID 228 3.291 12.250 -2.791

12
GIVEN SETTING ANGLE = 61.20000

ZI,Z2,XI,X2 IN SETB75 BETA1=

2.47060 -0.49308

ZI,Z2,XI,X2 IN SETB75 BETA1=

2.47060 1.07772

SAME AS ABOVE IN SETB75 BETA2=

2.64270 -0.51862

SAME AS ABOVE IN SETB75 BETA2=

2.64270 1.05217

CALCULATED SETTING ANGLE = 61.19985

GIVEN SETTING ANGLE = 61.20000 DIFF.=

GRID COORDINATES IN ROUTINE SETB75

RETURNING FROM ROUTINE SETB75

***ENTERED RDDISP{NGP,NFC) *** 228 1

***ENTERED RDMODS***

DIFF.=

0.76110

0.76110

0.54020

0.54020

0.00000

-1.31350

-1.31350

-1.53350

-1.53350

-0.00015

FREQ IN HZ= 0.221082E+03 GEN. MASS = 0.100000E+01

FREQ IN HZ= 0.402129E+03 GEN. MASS = 0.100000E+01

FREQ IN HZ= 0.698200E+03 GEN. MASS = 0.100000E+01

FREQ IN HZ= 0.816943E+03 GEN. MASS = 0.100000E+01

FREQ IN HZ= 0.I06519E+04 GEN. MASS = 0.100000E+01

FREQ IN HZ= 0.I15721E+04 GEN. MASS = 0.100000E+01

-1.39020

-1.39020

-0.99070

-0.99070

NUMBER OF EIGENVALUES EXTRACTED = 6

NOTE THAT MAX. NO. OF EIGENVALUES RETAINED IS 6

FREQUENCY(OMEGA**2) = 0.192960E+07

FREQUENCY(OMEGA**2) = 0.638395E+07

FREQUENCY(OMEGA**2) = 0.192451E+08

FREQUENCY(OMEGA**2) = 0.263477E+08

FREQUENCY(OMEGA**2) = 0.447934E+08

FREQUENCY(OMEGA**2) = 0.528671E+08

** MODAL DISPLACEMENTS AT EACH NODE *** 6

*** LEAVING RDMODS ***

** MODAL DISPLACEMENTS AT EACH NODE *** 6

MODE NUMBER 1 FREQENCY 0.1929603E+07

NODE 1 0.000000E+00 0.000000E+00 0.000000E+00 0.000000E+00

0.000000E+00 0.000000E+00

*NOTE: grids 1 thru 7 are fixed at the base thus displacement = 0

NODE 8 -0.304607E-02-0.806913E-03 0.147851E-02 0.120198E-01 0.181593E01 0.000000E+00

NODE 9 -0.333980E-02-0.933904E-03-0.138738E-02-0.109695E-01 0.916673E02 0.000000E+00

NODE 10 -0.312842E-02-0.986026E-03-0.315005E-02-0.305093E-01 0.912233E02 0.000000E+00

NODE 11 -0.206363E-02-0.127986E-02-0.420668E-02-0.410897E-01 0.337328E02 0.000000E+00

NODE 12 -0.650327E-03-0.238605E-03-0.413737E-02-0.414708E-01-0.374381E02 0.000000E+00

NODE 13 -0.100480E-03 0.137419E-02-0.319257E-02-0.311352E-01-0.489164E02 O.O00000E+O0

NODE 14 -0.508570E-03 0.153128E-02-0.568214E-03-0.110998E-01-0.200406E01 0.000000E+00

NODE 15 -0.834550E-02-0.226911E-02-0.755601E-03-0.270103E-02 0.347927E13
01 0.000000E+00

NODE 16 -0.816145E-02-0.205379E-02-0.667316E-02-0.354511E-01 0.368838E01 0.000000E÷00

NODE 17 -0.715473E-02-0.211537E-02-0.132772E-01-0.675880E-01 0.261375E01 0.000000E÷00

NODE 18 -0.510992E-02-0.274521E-02-0.164227E-01-0.805298E-01 0.116495E01 0.000000E÷00

NODE 19 -0.261430E-02-0.125851E-02-0.169016E-01-0.848442E-01-0.545229E02 0.000000E÷00

NODE 20 -0.392116E-03 0.277116E-02-0.144540E-01-0.778615E-01-0.216500E01 0.000000E+00

*******_nes deleted for brevity ***

NODE 219 -0.I16350E+03-0 407301E÷02-0 201573E÷03

0.811890E+02 0.124330E+01

NODE 220 -0.538991E+02-0 193324E÷02-0 116813E+03

0.397867E+02 0.226917E+01

NODE 221 -0.603932E+02-0 213408E+02-0 124651E÷03

0.546571E÷02 0.268687E÷02

NODE 222 -0.674061E÷02-0 236378E+02-0 133485E+03

0.553667E+02-0.150818E+01

NODE 223 -0.752087E+02-0 261159E+02-0 143511E+03

0.693699E÷02 0.322665E÷02

NODE 224 -0.833544E+02-0 288660E+02-0 154295E+03

0.662551E÷02-0.212215E÷01

NODE 225 -0.920327E+02-0

0.703865E+02-0.420867E+01

NODE 226 -0.I00975E÷03-0

0.751524E÷02 0.000000E÷00

NODE 227 -0.110112E÷03-0

0.735406E+02-0.175985E+02

NODE 228 -0.I19026E÷03-0

0.815080E+02-0.802315E÷00

*****shmlar output for modes 2 thru 6 has been deleted***

FINISHED ECHOING FEA OUTPUT

*** LEAVING RDNAS***

0.000000E÷00

0.000000E+00

0.217392E+02

0.000000E÷00

0.264773E+02

0.000000E+00

317458E÷02-0.165770E+03-0.117279E+01

348671E÷02-0.177933E+03 0.135083E+01

380907E÷02-0.190600E÷03-0.110234E+02

414257E+02-0.203769E+03 0.000000E+00

4.5000 0.8019 85

6.0000 1.1372 112

7.5000 1.1335 139

9.0000 0.7611 166

10.5000 -0.0689 193

12.0000 -1.4427 220

4.5000 -0.3132 93

ENTERED ROUTINE ASTROP ***

ENTERED_SI

NUMBER OF MODES USED= 6

** ENTERED LETEDG (NGP, IDREAD) ** 228 1

ENTERED ROUTINE RDLTNS 18 18

67 -2.4215 4.0000 0.6462 76 -2.5971

-2.7349 5.0000 0.9417

94 -2.8152 5.5000 1.0565 103 -2.8205

-2.7366 6.5000 1.1770

121 -2.5662 7.0000 1.1750 130 -2.3366

-2.0649 8.0000 1.0540

148 -1.7488 8.5000 0.9309 157 -1.3902

-0.9907 9.5000 0.5402

175 -0.5511 10.0000 0.2666 184 -0.0704

0.4520 11.0000 -0.4692

202 1.0024 11.5000 -0.9262 211 1.5822

1.9048 12.2500 -1.7386

75 1.9588 4.0000 -0.3136 84 1.8736

1.8326 5.0000 -0.3335

14
102 1.8060 5.5000 -0.3760

1.8282 6.5000 -0.5280

129 1.9023 7.0000 -0.6402

2.1567 8.0000 -0.9348

156 2.3066 8.5000 -1.1140

2.6427 9.5000 -1.5335

183 2.8139 10.0000 -1.7726

3.1039 11.0000 -2.2645

210 3.2148 11.5000 -2.4990

3.2906 12.2500 -2.7913

*******lines deleted for brevity ***

LEADING EDGE(REF. AXIS) GRID

1 67 -2.4215

2 76 -2.5971

3 85 -2.7349

4 94 -2.8152

5 103 -2.8205

6 112 -2.7366

7 121 -2.5662

8 130 -2.3366

9 139 -2.0649

I0 148 -1.7488

Ii 157 -1.3902

12 166 -0.9907

13 175 -0.5511

14 184 -0.0704

15 193 0.4520

16 202 1.0024

17 211 1.5822

18 220 1.9048

TRAILING EDGE GRID COORDINATES

1 75 1.9588

2 84 1.8736

3 93 1.8326

4 102 1.8060

5 111 1.8005

6 120 1.8282

7 129 1.9023

8 138 2.0190

9 147 2.1567

i0 156 2.3066

11 165 2.4706

12 174 2.6427

13 183 2.8139

14 192 2.9716

15 201 3.1039

16 210 3.2148

17 219 3.2915

18 228 3.2906

*** LEAVING ROUTINE LETEDG ***

111 1.8005 6.0000 -0.4404

138 2.0190 7.5000 -0.7770

165 2.4706 9.0000 -1.3135

192 2.9716 10.5000 -2.0215

219 3.2915 12.0000 -2.7131

COORDINATES:

4.0000

4.5000

5.0000

5.5000

6.0000

6.5000

7.0000

7.5000

8.0000

8.5000

9.0000

9.5000

i0.0000

10.5000

11.0000

11.5000

12.0000

12.2500

: KYT =

4.0000

4.5000

5.0000

5.5000

6.0000

6.5000

7.0000

7.5000

8.0000

8.5000

9.0000

9.5000

10.0000

10.5000

ii.0000

11.5000

12.0000

12.2500

KYL

18

18

0.6462

0.8019

0.9417

1.0565

1.1372

1.1770

1.1750

1.1335

1.0540

0.9309

0.7611

0.5402

0.2666

-0.0689

-0.4692

-0.9262

-1.4427

-1.7386

-0.3136

-0.3132

-0.3335

-0.3760

-0.4404

-0.5280

-0.6402

-0.7770

-0.9348

-1.1140

-1.3135

-1.5335

-1.7726

-2.0215

-2.2645

-2.4990

-2.7131

-2.7913

*** LEAVING ROUTINE LETEDG ***

NUMBER OF MODES USED= 6

I-TH MODAL FREQUENCY(OMEGA:RAD/SEC)

2-TH MODAL FREQUENCY(OMEGA:RAD/SEC)

1929603.00

6383953.00

120

147

174

201

228

15
3-TH MODAL FREQUENCY(OMEGA:RAD/SEC)

4-TH MODAL FREQUENCY(OMEGA:RAD/SEC)

5-TH MODAL FREQUENCY (OMEGA: RAD / SEC )

6-TH MODAL FREQUENCY(OMEGA:RAD/SEC)

= 19245060.00

= 26347720.00

= 44793420.00

= 52867090.00

STEADY DISP. NOT ADDED: METHOD= 0

NUMBER OF MODES USED= 6

*** ENTERED TSNFAL***

TANGENT VECTOR AT GRIDPOINT 67 ARE

-0.3467 0.8915 0.2917

TANGENT VECTOR AT GRIDPOINT 76 ARE

-0.2941 0.9157 0.2738

TANGENT VECTOR AT GRIDPOINT 85 ARE

-0.2233 0.9426 0.2485

TANGENT VECTOR AT GRIDPOINT 94 ARE

-0.0991 0.9751 0.1986

TANGENT VECTOR AT GRIDPOINTI03 ARE

0.0717 0 9898 0.1233

TANGENT VECTOR AT GRIDPOINTII2 ARE

0.2622 0 9644 0.0357

TANGENT VECTOR AT GRIDPOINTI21 ARE

0.3873 0 9210 -0.0419

TANGENT VECTOR AT GRIDPOINTI30 ARE

0.4499 0 8868 -0.1057

TANGENT VECTOR AT GRIDPOINTI39 ARE

0.4994 0 8498 -0.1685

TANGENT VECTOR AT GRIDPOINTI48 ARE

0.5449 0 8055 -0.2330

TANGENT VECTOR AT GRIDPOINTI57 ARE

0.5778 0.7610 -0.2950

TANGENT VECTOR AT GRIDPOINTI66 ARE

0.6018 0.7173 -0.3512

TANGENT VECTOR AT GRIDPOINTI75 ARE

0.6187 0.6728 -0.4056

TANGENT VECTOR AT GRIDPOINTI84 ARE

0.6309 0.6240 -0.4610

TANGENT VECTOR AT GRIDPOINT193 ARE

0.6328 0.5871 -0.5048

TANGENT VECTOR AT GRIDPOINT202 ARE

0.6270 0.5605 -0.5411

TANGENT VECTOR AT GRIDPOINT211 ARE

0.6283 0.5233 -0.5756

TANGENT VECTOR AT GRIDPOINT220 ARE

0.6447 0.4755 -0.5986

TESTP = 2.7952 PLEQC = 4.5939

TESTP = 3.2706 PLEQC = 4.5939

TESTP = 3.7246 PLEQC = 4.5939

TESTP = 4.1672 PLEQC = 4.5939

TESTP = 4.5960 PLEQC = 4.5939

VALI = 5.5000 VAL2 = 6.0000

YVAL = 5.7500 DY = 0.2500

VALI = 5.7500 VAL2 = 6.0000

YVAL = 5.8750 DY = 0.3750

VALI = 5.8750 VAL2 = 6.0000

YVAL = 5.9375 DY = 0.4375

VALI = 5.9375 VAL2 = 6.0000

16
YVAL = 5. 9688

STREAMLINE VECTOR AT

STRUCTURAL PRE-TWIST OF BLADE AT

NORMAL VECTOR AT 67 -TH GRIDPOINT =

TESTP = 3.0011 PLEQC =

TESTP = 3.4841 PLEQC =

TESTP = 3. 9485 PLEQC =

TESTP = 4.4025 PLEQC =

TESTP = 4. 8444 PLEQC =

TESTP = 5. 2701 PLEQC =

VALI = 6.0000 VAL2 =

YVAL = 6.2500 DY =

STREAMLINE VECTOR AT

DY = 0.4688

67 -TH GRIDPOINT = 0.8828 0.4117 -0.2262

67 -TH GRIDPOINT = 76.9241

-0.3218 0.1791 -0.9297

5.1040

5.1040

5.1040

5.1040

5.1040

5.1040

6.5000

0.2500

0.8971

76 -TH GRIDPOINT

76 -TH GRIDPOINT =

STRUCTURAL PRE-TWIST OF BLADE AT

NORMAL VECTOR AT 76 -TH GRIDPOINT =

*******lines deleted for brevity ***

TESTP = 3.3524 PLEQC =

TESTP = 3.5350 PLEQC =

TESTP = 3.7585 PLEQC =

TESTP = 4.0045 PLEQC =

TESTP = 4.2773 PLEQC =

TESTP = 4.5853 PLEQC =

TESTP = 4.9380 PLEQC =

TESTP = 5.3329 PLEQC =

TESTP = 5.7538 PLEQC =

TESTP = 6.1955 PLEQC =

TESTP = 6.6584 PLEQC =

TESTP = 7.1388 PLEQC =

TESTP = 7.6300 PLEQC =

TESTP = 8.1184 PLEQC =

VALI = I0.0000 VAL2 =

YVAL = 10.2500 DY =

VALI = 10.2500 VAL2 =

YVAL = 10.3750 DY =

VALI = 10.3750 VAL2 =

YVAL = 10.4375 DY =

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

8.0934

10.5000

0.2500

10.5000

0.3750

10.5000

0.4375

-0.3368

STREAMLINE VECTOR AT 220 -TH GRIDPOINT = 0.4970

STRUCTURAL PRE-TWIST OF BLADE AT 220 -TH GRIDPOINT

NORMAL VECTOR AT 220 -TH GRIDPOINT = -0.5713

*** LEAVING TSNFAL***

NUMBER OF MODES USED= 6

ENTERED LOCGRI

* NO. OF AEROELASTIC PTS FOR "LOCGRI"*= i0

(DEFAULT: INPUT 7 AEROPOINTS)

0.3563 -0.2612

= 74.8562

0.1688 -0.9263

-0.8595 -0.1195

= 83.1355

-0.2205 -0.7904

Y - COORDINATE

Y - COORDINATE

Y - COORDINATE

Y - COORDINATE

Y - COORDINATE

Y - COORDINATE

OF I-TH AEROELASTIC POINT:

OF 2-TH AEROELASTIC POINT:

OF 3-TH AERO_STIC POINT:

OF 4-TH AEROF/._STIC POINT:

OF 5-TH AEROELASTIC POINT:

OF 6-TH AERO_STIC POINT:

Y - COORDINATE OF 7-TH AEROEI_STIC POINT:

Y - COORDINATE OF 8-TH AEROELASTIC POINT:

Y - COORDINATE OF 9-THAEROELASTIC POINT:

Y - COORDINATE OFI0-TH AEROEI_STIC POINT:

*** ENTERED LOCXZ***

4.25000

4.50000

4.75000

5.63610

6.97390

8.87360

9.71140

10.87580

11.75530

12.20000

17
*******lines deleted for brevity ***

POINT 1 X-C0 =

POINT 2 X-CO =

POINT 3 X-CO =

POINT 4 X-CO =

POINT 5 X-CO =

POINT 6 X-CO =

POINT 7 X-CO =

POINT 8 X-C0 =

POINT 9 X-C0 =

POINT i0 X-CO =

-2.513537 Y-C0 =

-2.597100 Y-CO =

-2.671259 Y-CO =

-2.825452 Y-CO =

-2.577051 Y-CO =

-1.484797 Y-CO =

-0.809747 Y-CO =

0.319148 Y-CO =

1.293340 Y-C0 =

1.837465 Y-CO =

***  lines deleted for brevity ** *

4.250000 Z-CO

4.500000 Z-CO

4.750000 Z-CO

5.636100 Z-CO

6.973900 Z-CO

8.873600 Z-CO

9.711400 Z-CO

10.875800 Z-CO

11.755300 Z-CO

12.200000 Z-CO

POINT 1 X-CO =

POINT 2 X-CO =

POINT 3 X-CO =

POINT 4 X-CO =

POINT 5 X-CO =

POINT 6 X-CO =

POINT 7 X-CO =

POINT 8 X-CO =

POINT 9 X-CO =

POINT i0 X-CO =

1.909270 Y-CO =

1.873600 Y-CO =

1.850524 Y-CO =

1.801821 Y-CO =

1.896989 Y-CO =

2.427798 Y-CO =

2.715210 Y-CO =

3.073039 Y-CO =

3.260289 Y-CO =

3.294167 Y-CO =

*** LEAVING LOCXZ***

4.250000 Z-CO

4.500000 Z-CO

4.750000 Z-CO

5.636100 Z-CO

6.973900 Z-CO

8.873600 Z-CO

9.711400 Z-CO

10.875800 Z-CO

11.755300 Z-CO

12.200000 Z-CO

ENTER CUBE DIMEN. ALONG STACKING AXIS,IN INCHES, TO

STRUCTURAL GRID NOS. AND HENCE, ITS X-,Y-0Z-

(DEFAULT CUBE DIMENSION = 2.0)

ENTER CONTROL VALUE TO PRINT GRID CONNECTION ARRAY

TYPE 1 TO USE THIS PRINT OPTION

*** LEAVING LOCGRI***

NUMBER OF MODES USED= 6

ALFA VALUES FROM AVERAGE ALFA

NUMBER OF MODES USED= 6

= 0.725816

= 0.801900

= 0.874009

= 1.082509

= 1.176128

= 0.808617

= 0.431453

= -0.364181

= -1.181533

= -1.676337

= -0.310858

= -0.313200

= -0.320663

= -0.391327

= -0.633688

= -1.261101

= -1.632949

= -2.204533

= -2.612417

= -2.778188

LOCATE

COORDINATES.

FOR MODE NUMBER 1

******************

*** ENTERED A MV2***

***AVERAGE ROTATION FROM ROTATIONS AT GRID POINTS***

***   lines deleted for brevity **  *

MODE NO = 1

-3.0417

-5.2683

-5.5081

-22.1784

-29.1149 -31.2989

*** LEAVING AVEMV2***

*** ENTERED HAINTS***

THE LEADING EDGE NODES ARE

ALPHA VALUES FROM TIP TOWARDS HUB

-9.0542 -6.2417 -7.1214 -6.9717

-5.8454 -6.9008 -7.5113 -9.8267

-6.3822

-12.4296

-5.9653

-16.3741

18
67 76 85 94 103

139 148 157 166 175

211 220

*** ENTERED RLENC ***

SLEN( 1 ) = 0.000000

SLEN( 2 ) = 0.552423

SLEN( 3 ) = 1.089718

SLEN( 4 ) = 1.609389

SLEN( 5 ) = 2.116627

SLEN( 6 ) = 2.626125

SLEN( 7 ) = 3.154886

SLEN( 8 ) = 3.706856

SLEN( 9 ) = 4.281621

SLEN( 10 ) = 4.886038

SLEN( 11 ) = 5.524519

SLEN( 12 ) = 6.201727

SLEN( 13 ) = 6.921677

SLEN( 14 ) = 7.692331

SLEN( 15 ) = 8.518967

SLEN( 16 ) = 9.391846

SLEN( 17 ) = 10.315491

SLEN( 18 ) = 10.819666

*** LEAVING RLENC***

*******lines deleted for bre_4ty ***

AT GRID NO 67

AT GRID NO 76

AT GRID NO 85

AT GRID NO 94

AT GRID NO 103

AT GRID NO 112

AT GRID NO 121,

AT GRID NO 130,

AT GRID NO 139

AT GRID NO 148

AT GRID NO 157

AT GRID NO 166

AT GRID NO 175

AT GRID NO 184

AT GRID NO 193

AT GRID NO 202

AT GRID NO 211

AT GRID NO 220

112 121 130

184 193 202

H-DISP= -0.85677149E+00 A-ROT= -0.30417404E+01

H-DISP= -0.23271259E+01 A-ROT= -0.90542090E+01

H-DISP= -0.41668405E+01 A-ROT= -0.62417229E+01

H-DISP= -0.62370540E+01 A-ROT= -0.71214226E+01

H-DISP= -0.85312713E+01

H-DISP= -0.11246058E+02

H-DISP= -0.14687740E+02

H-DISP= -0.18990035E+02

H-DISP= -0.23948742E+02

H-DISP= -0.29253928E+02

H-DISP= -0.35091410E+02

H-DISP= -0.41663892E+02

H-DISP= -0.49065662E+02

H-DISP= -0.57838489E+02

H-DISP= -0.70096814E+02

H-DISP= -0.88089094E+02

H-DISP= -0.11246933E+03

H-DISP= -0.12738349E+03

A-ROT= -0.69716610E+01

A-ROT= -0.63821847E+01

A-ROT= -0.59652618E+01

A-ROT= -0.52683215E+01

A-ROT= -0.55080652E+01

A-ROT= -0.58453933E+01

A-ROT= -0.69007687E+01

A-ROT= -0.75112929E+01

A-ROT= -0.98267179E+01

A-ROT= -0.12429613E+02

A-ROT= -0.16374141E+02

A-ROT= -0.22178403E+02

A-ROT= -0.29114876E+02

A-ROT= -0.31298910E+02

IKAP =

AT POINT

IKAP =

AT POINT

IKAP =

AT POINT

AT

AT

AT

AT

AT

AT

1

= 4.250000, FUNCTION VALUE = 0.278031

1

= 0.278031, FUNCTION VALUE = -1.540085

1

= 0.278031, FUNCTION VALUE = -7.404140

I-TH AEROPOINT ,MODAL DISP = -1.54008

I-TH AEROPOINT, MODAL ROTATION = -7.40414

I-TH AEROPOINT ,MODAL DISP PRIME = -2.65048

I-TH AEROPOINT, MODAL ROTATION PRIME = -11.60601

I-TH AEROPOINT ,MODAL DISP DBLE PRIME = -1.48127

I-TH AEROPT., MODAL ROT. DBLE PRIME = 38.50773

19
*******lines deleted for brevity ***

AT 10-TH AEROPOINT ,MODAL DISP =-124.17147

AT 10-TH AEROPOINT, MODAL ROTATION = -30.99385

AT 10-TH AEROPOINT ,MODAL DISP PRIME = -30.38635

AT 10-TH AEROPOINT, MODAL ROTATION PRIME = -3.13811

AT 10-TH AEROPOINT ,MODAL DISP DBLE PRIME = -5.59814

AT 10-TH AEROPT., MODAL ROT. DBLE PRIME = 11.23637

*** LEAVING HAINTS***

FOR MODE NUMBER 1

PT. H-VALUE A-VALUE HP-VALUE

APP-VALUE HD-VALUE HDD-VALUE

AP-VALUE HPP-VALUE

1 -0.15401E+01 -0.74041E+01 -0.26505E+01 -0.11606E+02

0.38508E+02 0.00000E+00 0.00000E+00

2 -0.23271E+01 -0.90542E+01 -0.31019E+01

0.14500E+01 0.00000E+00 0.00000E+00

0.41897E+00

3 -0.32109E+01 -0.75414E+01 -0.34261E+01

-0.46401E+01 0.00000E+00 0.00000E+00

0.79799E+01

4 -0.68320E+01 -0.71166E+01 -0.44000E+01

0.21310E+01 0.00000E+00 0.00000E+00

0.32047E-01

5 -0.14485E+02 -0.59894E+01 -0.71812E+01

-0.23912E+00 0.00000E+00 0.00000E+00

0.84405E+00

6 -0.33556E+02 -0.66212E+01 -0.92709E+01 -0.19033E+01

-0.12593E+01 0.00000E+00 0.00000E+00

7 -0.44685E+02 -0.84228E+01 -0.I0287E+02 -0.32436E+01

-0.69398E+00 0.00000E+00 0.00000E+00

8 -0.66616E+02 -0.15185E+02 -0.16125E+02

-0.34197E+01 0.00000E+00 0.00000E+00

-0.53830E+01

9 -0.99850E+02 -0.25676E+02 -0.26406E+02 -0.78140E+01

0.14973E+00 0.00000E+00 0.00000E+00

10 -0. 12417E+03 -0.30994E÷02 -0.30386E+02

0. 11236E+02 0. 00000E+00 0. 00000E+00

**9:

*****similar output for modes 2 to 6 is deleted 

** * ENTERED TSNCAL ***

IKAP = 1

TANGENT X-, Y-, Z-COMPONENTS AT AEROPOINT 1 ARE

-0.3163 0.9060 0.2813

STRU. SWEEP ANGLE OF BLADE AT 1-TH AEROPOINT=

TANGENT X-, Y-, Z-COMPONENTS AT AEROPOINT 2 ARE

-0.2941 0.9157 0.2738

STRU. SWEEP ANGLE OF BLADE AT 2-TH AEROPOINT=

*******lines deleted for brevity ***

9:**

-0.31381E+01

-25.0446

-23.6928

-0.14813E+01

-0.13621E+01

-0.12149E+01

-0.I0374E+01

-0.27125E+01

-0.79620E+00

-0.73941E+00

-0.71867E+01

-0.39630E+01

-0.55981E+01
TANGENT X-,Y-,Z-COMPONENTS AT AEROPOINT 9 ARE

0.6278 0.5409 -0.5598

STRU. SWEEP ANGLE OF BLADE AT 9-TH AEROPOINT=

TANGENT X-, Y-, Z-COMPONENTS AT AEROPOINTI0 ARE

0.6444 0.4820 -0.5936

STRU. SWEEP ANGLE OF BLADE AT 10-TH AEROPOINT=

57.2568

61.1818

STRUCTURAL PRE-TWIST OF BLADE AT

STRUCTURAL PRE-TWIST OF BLADE AT

***** **lines deleted for brevity ** *

NUMBER OF

I-TH MODAL

2-TH MODAL

3-TH MODAL

4-TH MODAL

5-TH MODAL

1 -TH AEROPOINT =

2 -TH AEROPOINT =

STRUCTURAL PRE-TWIST

STRUCTURAL PRE-TWIST

*** LEAVING TSNCAL ***

*** LEAVING RDNASI ***

MODES = 6

FREQUENCY(OMEGA:RAD/SEC) = 1389.10

FREQUENCY(OMEGA:RAD/SEC) = 2526.65

FREQUENCY(OMEGA:RAD/SEC) = 4386.92

FREQUENCY(OMEGA:RAD/SEC) = 5133.00

FREQUENCY(OMEGA:RAD/SEC) = 6692.79

6-TH MODAL FREQUENCY(OMEGA:RAD/SEC) = 7270.98

NUMBER OF AEROPOINTS (NAEROP) = i0

X-,Y-,ZX-,Y-,ZOF BLADE AT 9 -TH AEROPOINT =

OF BLADE AT I0 -TH AEROPOINT =

COORD OF AEROPOINT NO. 1 =-2.513537

COORD OF AEROPOINT NO. 2 = -2.597100

*******lines deleted for brevity ***

X-, Y-, Z- COORD OF AEROPOINT NO .

X-,Y-,Z- COORD OF AEROPOINT NO. I0 =

X-,Y-,Z- COORD OF STLINE POINT 1 =

X-,Y-,Z- COORD OF STLINE POINT 2 =

*******lines deleted for brevity * **

X-, Y-, Z- COORD OF STLINE POINT

X- , Y-o Z- COOND OF S'I_INE POINT

*******lines deleted for brevity ***

REF. SEMI-CHORD (AT THE ROOT) =

4.250000

4.500000

9 = 1.293340 11.755300

1.837465 12.200000

1.803263 6.125000

1.808957 6.250000

9 = 2.685601 9.625000

i0 = 2.934168 10.375000

2.24211

0.24268E+01 0.24557E+01 0.24843E+01 0.24517E+01

0.22884E+01 0.20388E+01 0.16567E+01 0.12889E+01 0.I0740E+01

NUMBER OF NODES ON THE LEADING EDGE(KYL)= 18

NUMBER OF NODES ON THE TRAILING EDGE(KYT)= 18

*** LEAVING ROUTINE ASTROP ***

COMPONENTS OF SVEC---

0.88942 0.38632 -0.24432

0.89710 0.35631 -0.26124

0.90340 0.32706 -0.27731

0.94398 0.09971 -0.31458

0.87863 -0.36903 -0.30302

0.71770 -0.64151 -0.27088

0.65667 -0.71092 -0.25174

75.8581

74.8562

80.8365

82.4217

(chordline(streamline)

0.725816

0.801900

-1.181533

-1.676337

-0.460014

-0.481173

-1.592055

-1.959611

0.25051E+01

vector)

21
-0

-0

-0

-0

0

0

0

0

0

0

0.57670 -0.79248 -0.19847

0.54009 -0.82640 -0.15925

0.51058 -0.84965 -0.13188

COMPONENTS OF TANV ...................... (tangent vector)

31635 0.90598 0.28129

29410 0.91571 0.27382

25498 0.93145 0.25958

04845 0.98323 0.17580

38009 0.92417 -0.03800

56967 0.77225 -0.28124

60934 0.69795 -0.37625

63241 0.59567 -0.49521

62779 0.54088 -0.55976

-0

-0

-0

-0

-0

-0

-0

-0.51067

-0.54872

-0.56796

64439 0.48203 -0.59364

COMPONENTS OF NVEC .........

33002 0.17290 -0.92800

33679 0.16881 -0.92628

34320 0.16379 -0.92487

32684 0.15071 -0.93298

29406 0.08179 -0.95227

38961 -0.04753 -0.91970

44319 -0.09368 -0.89152

-0.16007 -0.84470

-0.20234 -0.81093

-0.21812 -0.79362

(normal vector)

PT. SEMICHD SETTA STAGGER SWEEP ANG

1 2.42676 75.85810

2 2.45571 74.85620

3 2.48429 73.90004

4 2.45170 71.66442

5 2.50506 72.36114

6 2.28843 74.28347

7 2.03883 75.41933

8 1.65669 78.55250

9 1.28890 80.83649

i0 1.07397 82.42165

*** ENTERED RLENCA***

****** *lines deleted for brevity ***

STRIPW 1

STRIPW_ 2

STRIPWI 3

STRIPW 4

STRIPW 5

STRIPW 6

STRIPW 7

STRIPW 8

STRIPW 9

STRIPW 10

*** LEAVING

= 0.274364

= 0.272468

= 0.598613

= 0.989694

= 1.610702

= 1.376096

= 1.591950

= 1.569312

= 1.214444

= 0.859577

RLENCA***

14.14190

15.14380

16.09996

18.33558

17.63886

15.71653

14.58067

11.44750

9.16351

7.57835

-25.04462

-23.69282

-21.33763

-10.50709

22.45675

39.44325

45.73715

53.43972

57.25675

61.18180

---(strip width)
as Program CaningTree

The following is the static calling tree for the 2DSTRIP code:

MAIN--- ASTROP--RDNAS I--ADISP I---ADDDIS

I...... AVEMV0 ...... SEQNOD

I...... AVEMV1--NORMAL-- IQHSCU--UERTST--UGETIO

I--USPKD

I...... SEQNOD

I...... AVEMV2 ....... SEQNOD

I...... HAINTS--FDDRP--FUNCD --IQHSCU--UERTST--UGETIO

I--USPKD

i-- FUNCD---IQHSCU --UERTST--UGETIO

USPKD

I---RLENC---IQHSCU---UERTST---UGETIO

USPKD

I-- SEQNOD

I---SPLINT--IQHSCU--UERTST--UGETIO

I-USPKD

I...... LETEDG ...... DETLTN ...... SORTX

I-RDLTNS ...... SEQNOD

I--SPLINT--IQHSCU--UERTST--UGETIO

I-USPKD

]SEQNOD

I SORTX

I...... LOCGRI---LOCXZ--- IQHSCU---UERTST--- UGETIO

I--USPKD

I...... TSNCAL--IQHSCU--UERTST .... UGETIO

I_USPKD

I...... TSNFAL-IQHSCU--UERTST--UGETIO

I-USPKD

I....... RDNAS ....... RDDISP

I...... RDMODS

1...... SETB75 ...... ROTATE

I....... RLENCA- ..... IQHSCU .... UERTST ...... UGETIO

I.... USPKD

23
4. PROGRAM 2DASTROP

In this section the input and output for an example problem for using the

2DASTROP program is given. The source code is designated as 2dastrop.f,

and the input data for the code is provided in the input file 2dastrop.in. In

addition to this input file, 2DASTROP requires the structural characteristic

information at the selected strips. This information was obtained by first

executing 2DSTRIP program.

4.1 Dimension Statement for the

The program is dimensioned for a maximum of 20 strips, six modes and

frequencies, and for 20 blades (phase angles). If the user needs to change

these limits, the dimension statements have to be changed globally in the

source code, and compiled for execution.

4_2 Description of Input Variables

The input is given through a data file named 2dastrop.in. This file contains

the standard (unit 5) input that the 2DASTROP code requires. Unless

otherwise stated, real values are read in 8F10.4 format and integer values are

read in 8110 format.

Some lines of the input data are preceded by a line containing the names of the

variables. These lines are an aid in preparing the input file and are read by

the program but not used as data in the calculations.

The first line in the input file is the title card read in 20A4 format, used for

identification of the structure to be analyzed. The rest of the input variables

are described below in the order in which they appear in the input data file (see

section 4.7 for an example input file).

variable:

type:

description:

example:

P0

real variable

static pressure in psi

13.1023

variable:

type:

description:

example:

SPS

real variable

speed of sound in feet per second

1130.0

variable:

type:

NMODEU

real variable (converted to integer value with in the program)

24
description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

Note: If UINFL

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

actual number of modes to be used in the flutter calculation

(NMODEU<NMODE in the 2DSTRIP run)

4.0

NSEGS

real variable (converted to integer value with in the program)

number of the first strip to be used in integration

1.0

CONFIG

real variable (converted to integer value with in the program)

indicator for counter rotation

com_IG = 0.0 front rotor in a counter rotation setup

CO,WIG -- 1.0 aft rotor in a counter rotation setup

0.0

RTIP

real variable

blade tip radius in inches

12.25

UINFL

real variable (converted to integer value with in the program)

indicator for inflow description

UINFL = 0.0 uniform inflow

UZNFL > 0.0 number of pointsin the inflowvelocitydata set

0.0

>0.0, the velocity distribution (axial, and tangential ) is read as

input from unit 11 (see section 4.7)

NONROT

integer variable

NO,mOT = 0 non-rotating blades

NO_U_OT= 1 rotating blades

1

NATHE

integer variable

indicatorfor subsonic cascade aerodynamic theory used

_WTHz = 22 Rao and Jones aerodynamic theory

22

NQUASI

integer variable

indicator for quasi-steady aerodynamics

seuAsz = 0 no quasi steady aerodynamics

NQVASI = 1 quasi steady aerodynamics used

0

25
variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

variable:

type:

description:

example:

IRF_JkD

integer variable

unit number for reading 2DSTRIP output

7

IS_

integer variable

option for isolated airfoil or cascade aerodynamic theory

ISO_L = 0 cascade aerodynamics

ISO_L = 1,isolated airfoil aerodynamics

0

IAUTO

integer variable

indicator for automatic flutteranalysis

i_vTo = 0 no auto flutteranalysis

IAUTO = i, auto flutteranalysis

0

INTEG

integer variable

indicator for numerical integration method used

z_rzG = 0 Newton-Cotes formula for spanwise integration

z1_rzQ= i trapezoidal rule used

1

FSF

real variable

frequency scalefactorson calculatedfrequencies up to _mODZU

modes in 8FI0.0 format.

1.0 1.0 1.0 1.0 1.0 1.0

GDAMP

real variable

generalized structural damping ratio values for each mode up to

m_ODZU modes in 8F10.0 format.

0.0 0.0 0.0 0.0 0.0 0.0

real variable

rotor rotational speed in revolutions per minute

6080.0

FRF

real variable

estimated flutter frequency in HZ to start aeroelastic calculations.

An initial value may be equal to one of the natural frequencies of

the blade

261.0

26
variable:

type:

description:

example:

MACH

real variable

free stream Mach number

0.60

variable:

type:

description:

example:

BR

real variable

reference chord

1.0

variable:

type:

description:

example:

NBLD

real variable (converted to integer in the program)

number of phase angles to be evaluated

_rSLD = 1 calculate for the phase angle given in SIGMA

_mLD >1, calculate for all phase angles 1 through BLDN

1.0

variable:

type:

description:

example:

BLDN

real variable

number of blades on the rotor

8.0

variable:

type:

description:

example:

SIGMA

real variable

interblade phase angle in degrees, if NBLD=I. Ignored if NBLD >1

225.0

variable:

type:

description:

example:

SWEEP

real variable

user input sweep angle in degrees

0.0

variable:

type:

description:

example:

GAP /CHD

real variable

user input gap to chord ratio value

0.0

variable:

type:

description:

example:

STAG

real variable

user input stagger angle in degrees

0.0

NOTE: User input values of SWEEP, GAP/CHD, and STAG are used only if

NONROT = 0

variable:

type:

description:

example:

NITER

integer variable

number of iterations for flutter convergence

3 _usually enough if the assumed frequency is near the

natural frequency of the mode of interest).

27
4.3 Additional Input Fries

The program uses the strip data obtained from 2DSTRIP on unit 7. In

addition, if UISFL is not zero, a velocity distribution file, for example v_. IN (see

below), should be linked to unit 11.

4.4 Additional Notes

The aeroelastic analysis assumes the leading edge as the reference axis, the

axis to which values of pitching and plunging values are referred. The

iterative procedure for obtaining the flutter condition is explained in appendix

B of Ref. 2.

The program is implemented on Cray YMP at NASA Lewis Research Center.

However, the program can be implemented on a workstation or personal

computer. It required about 1.2 MW memory, and took about 27 seconds to

compile and about 32 seconds to execute for the example given in section 4.7.

4.5 Job Run Stream on Cray YMP

A sample Cray job stream to run 2DASTROP at the NASA Lewis Research

Center is given in this section. The strip data f'de, fort7.2dstrip, from 2DSTRIP

is linked to unit 7. The source code, 2dastrop.f, is compiled using cft77 with

standard options. The input is contained in the file named 2dastropin. The

standard unit 6 output is written to a file named 2dastrop.out. The rest of the

file contains UNICOS and Cray related commands.

#! /bin/csh

# QSUB -r M55

# QSUB -IM 1.2Mw

# QSUB

/bin/rm 2dastrop. out

in fort7.2dstrip fort.7***************************(file created by 2DSTRIP)

in vel.in fort.ll ******************************************** (if needed)

cft77 -V -a static 2dastrop.f

segldr -o 2dastrop 2dastrop.o

time 2dastrop<2dastrop. in>2dastrop, out

28
4.6 Description of Output file

Unit 6 (2dastrop.out) output: Only one output file, 2dastrop.out, is generated.

This output contains

(1) the atmospheric conditions;

(2) a printout of the fort.7 file ( obtained from 2DSTRIP program). This is

printed to check for proper reading by 2DASTROP. This printout includes

(a)the rigid pitching (a-value) and plunging (h-value) values ) at aeropoints

(strips) for all the modes.

(b) the leading edge coordinates, the tangent, streamline and normal

vectors at each strip, setting angles, sweep angles, semichord values and

strip width.

(c) the generalized mass, frequencies and damping values;

(3) for the given Mach number, and for the reference frequency, 2DASTROP

prints, in a tabular form

the helical Mach number, effective Mach number, reduced frequency,

semichord and gap/chord ratio, stagger and sweep angle at each strip

(aeropoint);

(4) the eigen values indicating frequency and damping.

4.7 Example case: Calculation of Unsteady Aerodynamic Forces at the

Strips and _c Stability of SR3CX2 propfan

In this section, the actual input and output are given for the SR3CX2 propfan.

This propfan fluttered in experiments, Refs. 6-7. The air static pressure (P0) is

13.1023 psi, and the speed of sound(sps) is 1130 feet per second. Four modes

(m_OD_.U=4) are used in the aeroelastic stability calculation. The example is not

for counter rotation (CONFIG=0.0). The modal data for the strips (pitching and

plunging values) are available on unit 7 (IRF_D=7). There are no scaling factors

on the frequency, and the structural damping is zero. The propfan is rotating

at 6080 RPM (RPM=6080). The free stream Mach number (m_CH) is 0.60, and the

assumed flutter frequency (FRF) is 261 HZ. The calculation of the aeroelastic

stability is required at only one (NBLD=I) inter blade phase angle (SIG_) of 225.

degrees. The propfan has eight blades (m.DN--8). The flutter calculations are

done for three iterations (NIT_.RF--3). The iterations are indicated as

i fast=l,2,3 in the output.

29
Input file (2dastrolzln)

FLUTTER ANALYSIS OF SR3CX2 PROPFAN

P0 (psi) SPS (fps) NMODEU

13.1023 1130.0 4.0

NONROT NATHE NQUASI

01 22 00

FSF(Frequency Scaling Factors,

1.0 1.00000 1.00

GDAMP (Generalized DAMPing) ratios

0.0 0.0 0.0

RPM FRF (HZ) MACH

6080. 261.00 0.60

SIGMA

225.0

SWEEP GAP /CHD STAGGER

0.0 0.0 0.0

NITERF

3

NSEGS CONFIG RTIP UINFL

1.00 0.0 12.25 0.0

IREAD ISOAFL IAUTO INTEG

07 00 0 1

I = I, NMODEU)

1.0 1.0 1.0

(I=l, NMODEU)

0.0 0.0 0.0

BR NBLD BLDN

1.0 1.0 8.0

Input file (veLin)

The following input file should be provided if UINFL is not zero. In this

example, the velocity distribution is given at 15 radial stations (UINFL=15) .

J r/R v-axial v-tang

1 0.41081017 -0.16728285 -0.05450882

2 0.44025650 -0.16872721 -0.05451032

3 0.47642539 -0.17227991 -0.05357961

4 0.51606186 -0.18472728 -0.05425016

5 0.56907335 -0.20119552 -0.05350141

6 0.62218097 -0.21676765 -0.05081225

7 0.67530677 -0.23388092 -0.04875675

8 0.73462527 -0.25145703 -0.04527572

9 0.79412632 -0.26515110 -0.03736664

10 0.85373921 -0.27467869 -0.03441140

11 0.90105147 -0.27602396 -0.04618262

12 0.94203777 -0.26435932 -0.07675376

13 0.97108997 -0.23443168 -0.10637459

14 0.98845123 -0.18557730 -0.11354895

15 1.00000000 -0.09629623 -0.02621240

Unit 6 output file ( 2dastrop_ut )

The output information is printed, and given here in the order mentioned in

section 4.6, and is self explanatory. In this report, most of the output is

deleted, and only key output is retained to help the user to check his output

before going through the large printed output. For easy debugging and

understanding, the subroutine, from which the output is generated, is

identified by statements '** ENTEREV (SUBROUTINE) **' and '**LEAVING

(SUBROUTINE) **'

30
FLUTTER ANALYSIS OF SR3CX2 PROPFAN

STATIC PRESSURE(PSI) = 13.102

SPEED OF SOUND (FT/SEC) = 1130.000

AIR DENSITY (LBF-SEC**2/IN**4) = 0.99759944E-07

*** DATA FROM 2DSTRIP PROGRAM ***

NO. OF MODES= 6

NO.OF AEROPOINTS= i0

FOR MODE NUMBER 1

PT. H-VALUE A-VALUE HP-VALUE

APP-VALUE

AP-VALUE HPP-VALUE

1 -0.15401E+01 -0.74041E+01 -0.26505E+01 -0.11606E+02 -0.14813E+01

0.38508E+02

2 -0.23271E+01 -0.90542E+01 -0.31019E+01 0.41897E+00 -0.13621E+01

0.14500E+01

3 -0.32109E+01 -0.75414E+01 -0.34261E+01 0.79799E+01 -0.12149E+01

-0.46401E+01

4 -0.68320E+01 -0.71166E+01 -0.44000E+01 0.32047E-01 -0.I0374E+01

0.21310E+01

5 -0.14485E+02 -0.59894E+01 -0.71812E+01 0.84405E+00 -0.27125E+01

-0.23912E+00

6 -0.33556E+02 -0.66212E+01 -0.92709E+01 -0.19033E+01 -0.79620E+00

-0.12593E+01

7 -0.44685E+02 -0.84228E+01 -0.10287E+02 -0.32436E+01 -0.73941E+00

-0.69398E+00

8 -0.66616E+02 -0.15185E+02 -0.16125E+02 -0.53830E+01 -0.71867E+01

-0.34197E+01

9 -0.99850E+02 -0.25676E+02 -0.26406E+02 -0.78140E+01 -0.39630E+01

0.14973E+00

I0 -0.12417E+03 -0.30994E+02 -0.30386E+02 -0.31381E+01 -0.55981E+01

0.11236E+02

 similar output for modes 2 thru 6 are deleted** **

** FREQUENCIES (OMEGA: RAD/SEC) **

0.138910E+04 0.252665E+04 0.438692E+04

0.513300E+04 0.669279E+04 0.727098E+04

** GENERALIZED MASS **

0.100000E+01 0.100000E+01 0.100000E+01

0.100000E+01 0.100000E+01 0.100000E÷01

31
** LEADING EDGE COORDINATES **

-.251354E+01 0.425000E+01 0.725820E+00

-.259710E+01 0.450000E+01 0.801900E+00

-.267126E+01 0.475000E+01 0.874010E+00

-.282545E+01 0.563610E+01 0.108251E+01

-.257705E+01 0.697390E+01 0.117613E+01

-.148480E+01 0.887360E+01 0.808620E+00

-.809750E+00 0.971140E+01 0.431450E+00

0.319150E+00 0.I08758E+02 -.364180E+00

0.129334E+01 0.I17553E+02 -.118153E+01

0.183747E+01 0.122000E+02 -.167634E+01

** TANGENT VECTOR AT AEROPOINTS **

-.316350E+00 0.905980E+00 0.281290E+00

-.294100E+00 0.915710E+00 0.273820E+00

-.254980E+00 0.931450E+00 0.259580E+00

-.484500E-01 0.983230E+00 0.175800E+00

0.380090E+00 0.924170E+00 -.380000E-01

0.569670E+00 0.772250E+00 -.281240E+00

0.609340E+00 0.697950E+00 -.376250E+00

0.632410E+00 0.595670E+00 -.495210E+00

0.627790E+00 0.540880E+00 -.559760E+00

0.644390E+00 0.482030E+00 -.593640E+00

** CHORD LINE VECTOR AT AEROPOINTS **

0.889420E+00 0.386320E+00 -.244320E+00

0.897100E+00 0 356310E+00 -.261240E+00

0.903400E+00

0.943980E+00

0.878630E+00

0.717700E+00

0.656670E÷00

0.576700E+00

0.540090E+00

0 327060E+00

0 997100E-01

- 369030E+00

- 641510E+00

- 710920E+00

- 792480E+00

- 826400E+00

-.277310E+00

-.314580E+00

-.303020E+00

-.270880E+00

-.251740E÷00

-.198470E+00

-.159250E+00

0.510580E+00 - 849650E+00 -.131880E+00

** NORMAL VECTOR AT AEROPOINTS **

-.330020E+00 0.172900E+00 -.928000E+00

-.336790E+00 0 168810E+00 -.926280E+00

-.343200E+00

-.326840E+00

-.294060E+00

-.389610E+00 -

-.443190E+00 -

-.510670E+00 -

-.548720E+00 -

-.567960E+00 -

** SETTING

0 163790E+00

0 150710E+00

0 817900E-01

475300E-01 -

936800E-01 -

160070E+00 -

202340E+00 -

-.924870E+00

-.932980E+00

-.952270E+00

.919700E+00

.891520E+00

.844700E+00

.810930E+00

218120E+00 -.793620E+00

ANGLE AT 75% SPAN **

0.611998E÷02

* REF. SEMI-CHORD AT ROOT FROM ASTROP2 *

0.224211E+01

** TRAILING EDGE COORDINATES **

0.190927E+01 0.425000E+01 -.310860E+00

0.187360E+01 0.450000E+01 -.313200E+00
0.185052E+01

0.180182E+01

0.189699E+01

0.242780E+01

0.271521E÷01

0.307304E+01

0.326029E+01

0.329417E+01

0.475000E+01

0.563610E+01

0.697390E+01

0.887360E+01

0.971140E+01

0.I08758E+02

0.I17553E+02

0.122000E+02

-.320660E+00

-.391330E+00

-.633690E+00

-.126110E÷01

-.163295E÷01

-.220453E+01

-.261242E+01

-.277819E+01

0.180896E+01

0.181735E+01

0.180326E+01

0.182500E+01

0.179999E+01

0.186792E+01

0.222998E+01

0.268560E+01

0.293417E+01

** STLP COORDINATES **

0.180326E+01 0.612500E+01 -.460010E+00

0.625000E+01 -.481170E+00

0.637500E+01 -.503850E+00

0.612500E+01 -.460010E+00

0.512500E+01 -.342020E+00

0.593750E+01 -.431150E+00

0.681250E+01 -.595070E+00

0.825000E+01 -.I02179E+01

0.962500E+01 -.159206E+01

0.I03750E+02 -.195961E+01

** SETTING ANGLES AT AEROPOINTS **

0.758581E+02 0.748562E+02 0.739000E+02

0.716644E+02 0.723611E+02 0.742835E+02

0.754193E+02 0.785525E+02 0.808365E+02

0.824217E+02

** SWEEP ANGLES AT AEROPOINTS **

-.250446E+02 -.236928E+02 -.213376E+02

-.105071E+02 0.224568E+02 0.394433E+02

0.457371E+02 0.534397E+02 0.572568E÷02

0.611818E+02

** STAGGER ANGLES AT AEROPOINTS **

0.141419E+02 0.151438E+02 0.161000E+02

0.183356E+02 0.176389E+02 0.157165E+02

0.145807E+02 0.114475E+02 0.916351E+01

0.757835E+01

** SEMICHORD VALUES AT AEROPOINTS **

0.242676E+01 0.245571E+01 0.248429E+01

0.245170E+01 0.250506E+01 0.228843E+01

0.203883E÷01 0.165669E+01 0.128890E+01

0.I07397E+01

** LENGTH BETWEEN GRID POINTS ALONG LEADING EDGE **

**********************************************************

0.00000 0.55242 1.08972 1.60939 2.11663

3.70686 4.28162 4.88604

5.52452 6.20173 6.92168 7.69233 8.51897

10.81967

** STRIP WIDTH **

0.27436 0.27247 0.59861 0.98969 1.61070

1.56931 1.21444 0.85958

*** END OF ECHOING DATA FROM 2DSTRIP ***

2.62613

9.39185

1.37610

3.15489

10.31549

1.59195

SS
FREQUENCY FACTORS 1.000 1.000 1.000 1.000

MODE. GEN. MASS FREQ(RAD/S) DAMP.

1 0.10000E+01 0.13891E+04 0.00000E+00

2 0.10000E+01 0.25266E+04 0.00000E+00

3 0.10000E+01 0.43869E+04 0.00000E+00

4 0.10000E+01 0.51330E+04 0.00000E+00

RPM = 6080.000

ST. STN SWEEP ANG. SEMICHD GAP/CHD STAGGER

SETANG

1 5.18750 -25.04462 2.42676 0.83944

75.85810

2 5.37500 -23.69282 2.45571 0.85953

74.85620

3 5.56250 -21.33763 2.48429 0.87928

73.90004

4 5.88055 -10.50709 2.45170 0.94191

71.66442

5 6.04945 22.45675 2.50506 0.94833

72.36114

6 7.40555 39.44325 2.28843 1.27081

74.28347

7 8.26195 45.73715 2.03883 1.59133

75.41933

8 9.56290 53.43972 1.65669 2.26677

78.55250

9 10.69015 57.25675 1.28890 3.25705

80.83649

10 11.28750 61.18180 1.07397 4.12729

82.42165

14 14190

15 14380

16 09996

18 33558

17 63886

15 71653

14 58067

ii 44750

9 16351

7 57835

** number of modes used in the analysis ** 4

** ENTERED SMAP(NB,NMODES) ** 1 4

*** LEAVING SMAP ***

** FLUTTER ANALYSIS **

No. of ITER. for flutter convergence 3

ifast = 1 (first iteration)

*** ENTERED PRPAN ***

FREE STREAM MACH NO = 0.60000

** ENTERED RELVEL(SPEED OF SOUND)= **

***LEAVING RELVEL* * *

REFERENCE FREQUENCY(RAD/SEC & HZ) =

IPRNT= 0

0.13560E+05

1639.91137 261.00000

PT. STN HMACH SWEEP ANG.

RED. FREQ GAP/CHD STAGGER SETANG

EFF. M SEMICHD

1 5.18750 0.63323 -25.04462 0.57369 2.42676

34
0.51157 0.83944 14.14190 76.80836

2 5.37500 0.63723 -23.69282 0.58352

0.50896 0.85953 15.14380 75.99482

3 5.56250 0.64143 -21.33763 0.59746

0.50287 0.87928 16.09996 75.20042

4 5.88055 0.65774 -10.50709 0.64671

0.45848 0.94191 18.33558 72.33271

5 6.04945 0.68577 22.45675 0.63376

0.47803 0.94833 17.63886 67.97589

6 7.40555 0.73146 39.44325 0.56488

0.48994 1.27081 15.71653 62.12168

7 8.26195 0.75388 45.73715 0.52617

0.46861 1.59133 14.58067 59.64454

8 9.56290 0.78808 53.43972 0.46943

0.42680 2.26677 11.44750 56.24627

9 10.69015 0.81715 57.25675 0.44198

0.35268 3.25705 9.16351 53.96537

i0 11.28750 0.83327 61.18180 0.40166

0.32336 4.12729 7.57835 52.89609

2.45571

2.48429

2.45170

2.50506

2.28843

2.03883

1.65669

1.28890

1.07397

** ENTERED AMAP **

W0 = 1639.911365

XMACHA = 0.600000

NUMBER OF SEGMENTS, N = 9

THE CORRESPONDING WEIGHTING MATRIX FOR INTEGRATION IS:

0.50000000

1.00000000

1.00000000

1.00000000

1.00000000

1.00000000

1.00000000

1.00000000

1.00000000

0.50000000

TRAPEZOIDAL FORMULA FOR INTEGRATION

ENTERING DEINVE

LEAVING DEINVE

LEAVING AMAP

REF FREQ = 0.164E+04 RAD/SEC, = 0.261E+03 HZ

EIGZC: INFER AND IER = 0 0

INTER BLADE PHASE ANGLE = 225.000

1 -TH DAMPING(HZ) = -0.14137E+03

1 -TH FREQ (HZ) = 0.78911E+03

2 -TH DAMPING(HZ) = -0.29494E+03

2 -TH FREQ (HZ) = 0.19294E+03

38
3 -TH DAMPING(HZ) = 0.55686E+01

3 -TH FREQ (HZ) = 0.27232E+03

4 -TH DAMPING(HZ) = -0.I0921E+03

4 -TH FREQ (HZ) = 0.36121E+03

SMALLEST DAMPING VALUE = 0.55686E+01 HZ

CORRESPONDING FREQUENCY = 0.27232E+03 HZ

CORRESPONDING INTERBLADE PHASE ANGLE = 225.0

ifast = 2

DEG

*** ENTERED PRPAN ***

FREE STREAM MACH NO = 0.60000

** ENTERED RELVEL(SPEED OF SOUND)= ** 0.13560E+05

***LEAVING REL%FEL***

REFERENCE FREQUENCY(RAD/SEC & HZ) = 1711.05389

IPRNT= 0

(second iteration)

272.32268

PT.

RED. FREQ

ST_ HMACH SWEEP ANG.

GAP/CHD STAGGER SETANG

EFF. M SEMICHD

1

0.53376

2

0.53104

3

0.52469

4

0.47837

5.18750 0.63323 -25.04462

0.83944 14.14190 76.80836

5.37500 0.63723 -23.69282

0.85953 15.14380 75.99482

5.56250 0.64143 -21.33763

0.87928 16.09996 75.20042

5.88055 0.65774 -10.50709

0.94191 18.33558 72.33271

5 6.04945 0.68577 22.45675

0.49876 0.94833 17.63886 67.97589

6

0.51120

7.40555 0.73146 39.44325

1.27081 15.71653 62.12168

7 8.26195 0.75388 45.73715

0.48894 1.59133 14.58067 59.64454

8

0.44532

9

0. 36798

i0

0.33739

9.56290 0.78808 53.43972

2.26677 11.44750 56.24627

10.69015 0.81715 57.25675

3.25705 9.16351 53.96537

11.28750 0.83327 61.18180

4.12729 7.57835 52.89609

0 57369

0 58352

0 59746

0 64671

0 63376

0 56488

0 52617

0 46943

0 44198

2.42676

2.45571

2.48429

2.45170

2.50506

2.28843

2.03883

1.65669

1.28890

0.40166 1.07397

** ENTERED AMAP **

W0 = 1711.053886
XMACHA = 0. 600000

 lines deleted for bre_/ty** * *

LEAVING AMAP

REF FREQ = 0.171E+04 RAD/SEC,

EIGZC: INFER AND IER = 0 0

INTER BLADE PHASE ANGLE = 225.000

1 -TH DAMPING(HZ) = -0.13849E+03

1-TH FREQ (HZ) = 0.79085E+03

2 -TH DAMPING(HZ) = -0.30141E+03

2 -TH FREQ (HZ) = 0.21534E+03

3 -TH DAMPING(HZ) = 0.15226E+01

3 -TH FREQ (HZ) = 0.26961E+03

4 -TH DAMPING(HZ) = -0.I0627E+03

4 -TH FREQ (HZ) = 0.36589E+03

SMALLEST DAMPING VALUE = 0.15226E+01 HZ

CORRESPONDING FREQUENCY = 0.26961E+03 HZ

CORRESPONDING INTERBLADE PHASE ANGLE =

ifast = 3

*** ENTERED PRPAN ***

FREE STREAM MACH NO = 0.60000

** ENTERED RELVEL(SPEED OF SOUND)= **

***LEAVING RELVEL***

0.272E+03 HZ

225.0 DEG

0.13560E+05

(third iteration)

REFERENCE FREQUENCY(RAD/SEC & HZ) =

IPRNT= 0

1693.98904 269.60673

PT. STN HMACH

RED. FREQ GAP/CHD STAGGER

SWEEP ANG.

SETANG

EFF. M SEMICHD

1 5.18750 0.63323

0.52844 0.83944 14.14190

2 5.37500 0.63723

0.52574 0.85953 15.14380

3 5.56250 0.64143

0.51945 0.87928 16.09996

4 5.88055 0.65774

0.47360 0.94191 18.33558

5 6.04945 0.68577

0.49379 0.94833 17.63886

6 7.40555 0.73146

0.50610 1.27081 15.71653

7 8.26195 0.75388

-25.04462

76.80836

-23.69282

75.99482

-21.33763

75.20042

-10.50709

72.33271

22.45675

67.97589

39.44325

62.12168

0.57369 2.42676

0.58352 2.45571

0.59746 2.48429

0.64671 2.45170

0.63376 2.50506

0.56488 2.28843

45.73715 0.52617 2.03883

37
0.48407 1.59133 14.58067

8 9.56290 0.78808

0.44088 2.26677 11.44750

9 10.69015 0.81715

0.36431 3.25705 9.16351

I0 11.28750 0.83327

0.33403 4.12729 7.57835

59.64454

53.43972

56.24627

57.25675

53.96537

61.18180

52.89609

0.46943

0.44198

0.40166

1.65669

1.28890

1.07397

** ENTERED AMAP **

W0 = 1693.989044

XMACHA = 0.600000

 lines deleted for brevity** * *

LEAVING AMAP

REF FREQ = 0.169E+04 RAD/SEC, = 0.270E+03 HZ

EIGZC: INFER AND IER = 0 0

INTER BLADE PHASE ANGLE = 225.000

1 -TH DAMPING(HZ) = -0.13918E+03

1 -TH FREQ (HZ) = 0.79043E+03

2 -TH DAMPING(HZ) = -0.30001E+03

2 -TH FREQ (HZ) = 0.20992E+03

3 -TH DAMPING(HZ) = 0.24343E+01

3 -TH FREQ (HZ) = 0.27027E+03

4 -TH DAMPING(HZ) = -0.I0693E+03

4 -TH FREQ (HZ) = 0.36481E+03

SMALLEST DAMPING VALUE = 0.24343E+01 HZ

CORRESPONDING FREQUENCY = 0.27027E+03 HZ

CORRESPONDING INTERBLADE PHASE ANGLE = 225.0 DEG

The calculated damping value obtained above for M (Mach number) = 0.6, and

for the phase angle of 225 degrees is positive indicating instability. The

2DASTROP program is again run for M=0.55, and the following eigen values

are obtained ai_r 3rd iteration.

ifast = 3

*** ENTERED PRPAN ***

(third iteration)

FREE STREAM MACH NO = 0.55000

** ENTERED RELVEL(SPEED OF SOUND)= ** 0.13560E+05

***LEAVING RELVEL***

REFERENCE FREQUENCY(RAD/SEC & HZ) = 1679.50802 267.30200

IPRNT= 0

PT.

RED. FREQ

STN HMACH SWEEP ANG. EFF. M SEMICHD

GAP/CHD STAGGER SETANG

38
1 5.18750 0.58607 -25.04462

0.56608 0.83944 14.14190 76.80836

2 5.37500 0.59039 -23.69282

0.56260 0.85953 15.14380 75.99482

3 5.56250 0.59492 -21.33763

0.55527 0.87928 16.09996 75.20042

4 5.88055 0.61247 -10.50709

0.50426 0.94191 18.33558 72.33271

5 6.04945 0.64248 22.45675

0.52256 0.94833 17.63886 67.97589

6 7.40555 0.69104 39.44325

0.53112 1.27081 15.71653 62.12168

7 8.26195 0.71473 45.73715

0.50622 1.59133 14.58067 59.64454

8 9.56290 0.75071 53.43972

0.45887 2.26677 11.44750 56.24627

9 10.69015 0.78118 57.25675

0.37783 3.25705 9.16351 53.96537

i0 11.28750 0.79802 61.18180

0.34580 4.12729 7.57835 52.89609

0.53097

0.54063

0.55414

0.60220

0.59376

0.53366

0.49885

0.44718

0.42252

0.38467

2.42676

2.45571

2.48429

2.45170

2.50506

2.28843

2.03883

1.65669

1.28890

1.07397

** ENTERED AMAP **

W0 = 1679.508017

XMACHA = 0.550000

LEAVING AMAP

REF FREQ = 0.168E+04 RAD/SEC, = 0.267E+03 HZ

EIGZC: INFER AND IER = 0 0

INTER BLADE PHASE ANGLE = 225.000

1 -TH DAMPING(HZ) = -0.13124E+03

1 -TH FREQ (HZ) = 0.78521E+03

2 -TH DAMPING(HZ) = -0.30854E+03

2 -TH FREQ (HZ) = 0.23974E+03

3 -TH DAMPING(HZ) = -0.25824E+01

3 -TH FREQ (HZ) = 0.26804E+03

4 -TH DAMPING(HZ) = -0.97135E+02

4 -TH FREQ (HZ) = 0.36791E+03

SMALLEST DAMPING VALUE = -0.25824E+01 HZ

CORRESPONDING FREQUENCY = 0.26804E+03 HZ

CORRESPONDING INTERBLADE PHASE ANGLE = 225.0 DEG

The calculated damping shows a negative value for M=0.55, indicating the

blade is stable. The flutter Mach number can be interpolated to zero damping,

to give about 0.575, which is very close to the experimental value of 0.58.

39
4.S Ptx,m-amCalling Tree

The following is the static calling tree for the 2DASTROP code:

MAIN ........ DATAP

[ ...... PRPAN ........... AMAP ...... ATITLE

[ ...... CTVP

[...... DEINVE

[ ...... NCOTEW

[ ...... PRMATX ...... REALMP

I...... RAO ............ GAUSSR

[..... LM

[...... SSCASC ......... AKAPM

i ....... AKAPPA

I....... AKP2

]....... ALAMDA

i ....... ASYCON

[....... DLKAPM

I....... DRKAPM

[....... EIGEN2 ...... EIGZC ...... ELZHC

[---ELZVC ...... UERTST ..... UGETIO

I---USPKD

[---UERTST ......UGETIO

I----USPKD

[...... RELVEL ...... INFLOW

I...... INTERP

[...... VCROSP

[...... QNEWTU ...... PRPAN ...... AMAP ...... ATITLE

I...... CTVP

I...... DEINVE

]...... NCOTEW

i ...... PRMATX ...... REALMP

}...... RAO ............ GAUSSR

I...... LM

I...... SSCASC ......... AKAPM

[ ....... AKAPPA

I....... AKP2

[ ...... READMV

[...... RPLACE

[...... SMAP

[ ....... ALAMDA

I....... ASYCON

I....... DLKAPM

I....... DRKAPM

[........ EIGEN2 ...... EIGZC---ELZHC

I..... ELZVC--UERTST-UGETIO

I --USPKD

l......UERTST ........... UGETIO

I ........... USPKD

I...... RELVEL ...... INFLOW

I...... INTERP

I...... VCROSP

40
5. ACKNO_EMENTS

The authors thank D. C. Jantzke and R. Srivastava for helpful suggestions in

preparing this manual. This work was supported by NASA grant NAG-1137

from NASA Lewis Research Center. O. Mehmed and G.L. Stefko are the grant

monitors.

6. REFI_RENCES

o Reddy, T.S.R., et al, "A Review of Recent Aeroelastic Analysis Methods for

Propulsion at NASA Lewis Research Center", NASA TP 3406, December

1993.

. Narayanan, G.V., and Kaza, K.R.V., "ASTROP2 Users Manual: A

Program for Aeroelastic Stability Analysis of Propfans", NASA TM 4304,

August 1991.

3. Lawrence, C., Aiello, R.A., Ernst, M.A., and McGee, O.G., "A NASTRAN

Primer for the Analysis of Rotating Flexible Blades", NASA TM 89861, 1987.

4. Rao, B.M. and Jones, W.P., "Unsteady Airloads on a Cascade of Staggered

Blades in Subsonic Flow, Unsteady Phenomena in Turbomachinery",

AGARD-CP-177, 1975, pp. 32-1 to 32-10.

5. Adamczyk, J.J., and Goldstein, M.E., "Unsteady Flow in a Supersonic

Cascade with Subsonic Leading Edge Locus", A/AA Journal, Vol. 16, No.

12, Dec. 1978, pp. 1248-1254.

o Kaza, K.R.V., Mehmed, O., Narayanan, G.V., and Murthy, D.V.,

"Analytical Flutter Investigation of a Composite Propfan Model", Journal

of Aircraft, Vol. 26, No. 8, Aug., 1989, pp. 772-780.

7. Mehmed, O., and Kaza, I_R.V., "Experimental Classical Flutter Results of

a Composite Advanced Turboprop Model", NASA TM 88792, 1986.

o Mahajan, A.J., Lucero, J., Mehmed, O., and Stefko, G., "Aeroelastic

Stability Analyses of Two Counter Rotating Propfan Designs for a Cruise

Missile Model", AIAA Paper 92-2218, Presented at 33rd AIAA/ ASME/

ASCE/ AHS /ASC Structures, Structural Dynamics, and Materials

Conference, April 13-15, 1992, Dallas, Texas, part 2, pp. 1303-1313 (also

NASA TM 105268, April 1992)

41
REPORT DOCUMENTATION PAGE I Form OMBNo. Approved 070_ISS

p=,_ r¢orUnouurdm_ mu=lUc_onofInfom'mi=i__numd - awmlwI tmu,pu.re_oon.,indud,_gm me _ m,vi_..ng.._n_u_., .m=c_t=g_i_Ingdm m

Dlv_Hl0hwly, SulD 1204, klblgtOn, VA 22202.430_ and totaled Man--and Btxl_ lperwod_ Redtg:tk)nP_fojecef0704-0188). ( ), Wal h_t_n.

1. AGENCY USE ONLY (Leave b/ank) 2. REPORT DATE

M=ch 1996

4. 11TLE AND SUBTrrLE

ASTROP2 Us=s Manual: A Program for Acroclastic Stability

Analysis of Propfans

Atrmo_s)

T.S.R. Reddy and John/vL Lucero

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space AdminisWation

Lewis Research Center

Cleveland, Ohio 44135-3191

9. SPONSORING/MONITORINGAGENCYNAME(S)ANDADDRESS(ES)

NationalAeronautics and Space Administration

Washington, D.C. 20546-0001

1 REPORT TYPE AND OA_S COVERED

Technical Memorandum

5. FUNDING NUik6ERS

WU-538-06-13

NAG-1137

8. PERFORMING ORGANIZATION

REPORT NUMBER

E- 10174

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASATM-107195

11. SIJPPLEtiENTANY NOTES

T.S.R. Reddy, University of Toledo and NASA Resident Research Associate at Lewis Research Center (work funded by

NASA Grant NAG-1137) and John M. Lucero, NASA Lewis Research Center. Responsible person, John M. Lucero,

organization code 5230, (216) 433- 6038.

12a. DiSTRIBUTION/AVAILABILITY STATEMENT

Unclassified- Unlimited

Subject Category 39

This publicatim is available from the NASA Cen_r forAeroSpace Information,(301 ) 621--0390.

12b. DISTRIBUTION CODE

13. ABSTRACT (Msxknum200 tt_rds)

This manual describes the input data required for using the second version of the ASTROP2 (Aeroelasfic STability and

Response Of Propulsion systems - 2 dimensional analysis) computer code. In ASTROP2, version 2.0, the program is

divided into two modules:2DSTR_, which calculates the s_'uctural dynamic information;and 2DASTROP, which

calculatestheunsteadyaerodynamic forcecoefficientsfrom which theaemelasticstabilitycan be determined.In the

originalversion of ASTROP2, thesetwo aspectswere performedina single program. The improvements toversion 2.0

includean optiontoaccount forcounterrotation,improved numericalintegration,accommodation fornon-uniform inflow

distribetion, and an itcntivescheme toflutterfrequencyconvergence.ASTROP2 can be used forflutteranalysisof

multibladedslructuressuch as thosefound incompressors,turbines,counterrotatingpropellerscrpropfans.The analysis

combines a two-dimensional,unsteadycascadeaerodynamicsmodel and a threedimensional,normal mode structural

model usingstriptheory.The flutteranalysisisformulatedin thefrequencydomain resultingin an eigenvaluedeterminant.The flutterfrequencyand damping can be infen'edfzom theeigenvalues.

14. SUBJECT "IIERMS

Aeroelastic stability;Huu_;, Normal modes; Cascades;NASTRAN; Finiteelement

analysis;Striptheory;Eigenvalues;Pitchingand plunging;Subsonic axialflow;Propfans

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

NSN 7540-01-280-5500

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURffY CLASSIFICATION

OF ABSTRACT

Unclassified

15. NUMBER OF PAGES

46

16. PRICE CODE

A03

20. UMITATION OF ABSTRACT

Standard Form 298 (Rev. 2-89)

l=Yescrfoed by ANSI Sld. Z39-18

298-102

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