A computer program based on state of the art compressor and structural technologies applied to bladed shrouded discs was developed and made operational in NASTRAN level 16. The problems encompassed include aeroelastic analyses, modes, and flutter. The demonstration manual updates are described

Elchuri, V.

Gallo, A. M.

English

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NASA CR 159826
BAT Report No. D2536-941005
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	 MASIUAN L1rVLL lb
JEMONSTRAT1UM MANU/, UPt,. TES EUB ALUOELASTIC
ANALYSIS OF bLAJJLI U15CS (Textron be Al
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ASTRAN LEVEL 16 DEMONSTRATION MANUAL UPDATES
FOR AF ,cOELASTIC ANALYSIS OF BLADED DISCS
 h-r.
by
V. E:LCHURI
A. M. GALLO
*W.
BELL AEROSPACE Tr XTRON
P. O. BOX 1
Buffalo. New York 14240
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Z
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
s
CONTRACT NAS3-20382
NASA LFWIS RESEARCH CENTER 	 `^1	 AMP,^b%
CLEVELAND. OHIO	 c
MARCH 1980 ^, .
	
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NASA CR.159826
BAT Report No. D2536-941005
NASTRAN LEVEL 16 DEMONSTRATION MANUAL UPDATES
j	 FOR AEROELASTIC ANALYSIS OF BLADED DISCS
i	 ,	 by
V. ELCIIURI
A. M. GALLO
BELL AEROSPACE TEXTRON
P. 0. BOX 1
Buffalo, New York 14240
NA'T'IONAL AERONAUTICS AND SPACE ADMINISTRATIION
CONTRACT NAS3-20382
NASA LEWIS RESEARCH CENTER
CLEVELAND, OHIO
MARCH 1980
fi
.........
INTRODUCTION
A computer program based on state-of-the-art compressor and
structural technologies applied to bladed shrouded discs has been
developed and made operational in NASTRAN Level 16.
The problems encompassed include a6roelastic analyses, modes
and flutter.
The program it documented in the form of five NASA Contractor's
Reports — one Technical Report and four Updates to NASTRAN Level
16 Theoretical, User's, Programmer's and Demonstration manuals.
This report describes the Demonstration manual updates.
DEMONSTRATION MANUAL UPDATES
I
,i
RIGID FORMAT No. 16 0 Static Aerothormoelastic 'Design/Anolysis'
Aerot:'astic 'Design/Analysis' of an Axial Flow Compressor Stage (16-1)
A. Description
This problem illustrates the use of the static aeroelastic analyses of the
first stage rotor of an axial flow air compressor to determine,
i)	 the "as manufactured" b1ada shape required to produce the design point
pressure ratio ("design" problem), and
i i )
	
the operating point of the "flexible" designed blade ("analysis"
problem), The total stiffness matrix, consisting of the elastic and geometric
stiffness matrices, at Any off—design operating point is saved for use in subse-
quent modal and flutter analyses. (See Demonstration Manual example 9-1),
	
%
	 1
The 43-blade rotor is designed to develop a total pressure ratio of 1,85 at
a speed of 16043 rpm and an air flow rate of 73.15 7bm/sec,. The finite element
model of a representative sector of the rotor is ,shown in Figure 1,
B, Input
Bulk oata cards used include DTI, STRCAMLI, PARAMeters APRESS, ATCMP, FXCOOR,
FyCO R, , F1COOR, IPRTCF, IPRTC.I, IPRTCL, KTOUT, PGE014, SIGN, STREAML an.d ZORICN as
illustrated in the User's Man!uial Section 1.15,3,
C. Analysts and Results
The rigid blade of Figure 1 produces a total pressure ratio of 1.85 at
16013 rpm and 73.15 lbm/sec air flow rate (Table 1).	 Because of the elasticity
of the material, and under the action of centrifugal and aerodynamic pressure and
thermal loads, tae blade deforms and produces a total pressure ratio greater than
the design value, A "redesign" of the rigid blade, considering the elastic and
geometric properties of the bladed disc sector, enables determination of the "as
manufactured" blade :shape that, when loaded and deformed, would produce the design
16.1-1 (9/30/78)
F
Wpressure ratio. The. 'rigid" performance of the "as manufactured" blade shape
obtained at the end of the Design problem is also shown in Table 1.
This blade shape is then "Analyzed", in the current demonstration example, at
the same (design)speed and flow rate to determine the 'flexible' operating pressure
ratio. This value (1.84) can be further improved to approach the desired (1.85)
pressure ratio by reducing the Parameters FXCOOR, FYCOpR and FZC.O pR in the Design
problem (see User's Manual Section 1,15.3).
The blade shape at various stages during the Design and Analysis problems, as
reflected by the grid point coordinaes, is also shown in Tables 1 and 2. The
coordinates are expressed in the basic system of 'rigure 1.
i
16.1-2 (9/30178)
Nub
x IN
r
Blade
► u
Flow
1p,,	 Axis of Rotation
Figure 1. Finite Element Model of an Axial Flow Compressor
Rotor Sector, and the Basic. Coordinate Syscem
I
16.1a3 ( 91301 78)
i^
1I
'Ii
i
.
Table 14 Design Problem
initial ► 	 4-signed Blade "As Manufactured" Blade
'Rigid'
	 Performance `Rigid'	 Performance
!	 Total	 Pressure Ratio 1.85 1.80
Rotational
	
Speed,	 rpm 16043 15043
Air Flow Rate,	 1bmlsec 73.15 73.15
Grid Points KEin, Y,in. Z,in. X,in. Y,in. Z.in.
1 -0,8980 -0.2732 L7902 0.8901 -0.2755 3,7796
2 0.0 0.0532 3.9996 -0.0001 0.0540 3.9906
3 0.8980 -0.2499 4.1926 0_8979 ..n	 246A^....^..I A	 toeiT+18"1r
4 - C 1630 0.5004 5.4772 -0.7653 -0.4830 5.4554
5 0.0 0.0209 5.5000 -0.0005 0.0209 6,4985
6 0.7800 0.2342 5,4950 0.7799 0.2307 5.4889
7 0.6290 -0.7494 7.3620 -0.6386 -0.7217 7.3281
8 0.0 0.0131 7.4000 -0.0091 0.0155 7.3976
9 0.6290 0.6369 7.3725 0.6240 0.6123 7.3416
10 -0.4240 -0.9330 9,9564 -0.4058 -1.1351 9.8905
11 0.0 - 0.0221 10,0000 -0.0106 - 0.0236 9.9970
12 0.4240 0.7598 9.9711 U.4140 0.8134 9.9304
+1
^	 Table 3 ° Aonlysi y Problem
.	
.
^	 .
,
^	 .
.	 '
'
^
,
`
	 i
"As Manufactured" Blade "As Manufactu r -.d" Blade
'Riqfit l	Performance 'Nexiblel	 Performance
Total	 Pressure Ratio 1.80 1.84
Rotational	 Speed,	 rpm 16043 16043
Air Flow Rete,	 lbrii/sec 73.16 73.15
1 -0.8981 4,2755 3.7796 -0.8979 -0,2814 3.7712
2 -0.0001 0.0540 3.9986 0.0001 0.0616 4,0003
3 0.8979 -0.2464 41.1847 W 0701 -0.24ti 4.1795
5 -0,0005 010209 5.498$ -0.0W 0.0228 5.5033
6 0.7799 0.2307 5.4889 0.7797 0.2247 5.4889
8 -0,0091 0; 0155 7.3976 -0.0167 0,0164 7.4058
9 0.6240 C. 6123 7.3416 0,,6303 0.5962 7.3237
11 -0.0106 -0.0236 9.9970 -0.0320 -0.0656 10.0079
12 0.4140 0,8134 9.9304 0.4130 0.7329 9.9093
`
`
'
"
^
/
'
`
16,1-5 (9/30/78)
'~~~	 _	
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RIGID FORMAT No. 9 (APP AER p ), Aeroalastic Analysis
Modal, #luttor and $ubcritical Roots Analyses of an Axial Flow
Compri"sor Stage (9-6-1)
A. Descriptionip,
The problem illustrates the use of the aeroalastic cyclic modal and flutter
analyses of the first stage rotor of an axial flow air compressor to
i)	 determine the natural frequencies and mode shapes of the bladed disc
se4tor, of Figure 1, which exhiiits rotational cyclic symmetry. The total stiff-
ness matrix, including the differential stiffness effects at the ope r&tinq point
tinder considerations saved during the Static Aerothermoolastic "Analysis" (see
Demonstration Manual example 16-1) i's used for the cyclic modal analysis. 	 .,
i i )
	
examine if the operating point being considered is a flutter point by
analyzing the V-g and V-f plots based on user-selected combinations of densities,
inter-blade phase angles anal reduced frequencies, and in the process
i i i ) identify the subcriti+cal (stable) roots.
B. luut
Bulk data cards used include AERB, FLFACT, FLUTTER, 14KAERol, STREAMLI,
ST`REAML2 and PARA14e'ters IREf, KGGIN, LMODES, MAXMACN, MINMACH, MTYPE and PRINT as
described i n the User's Ma..ual Sections 1.15.2 and 1.15.5. Bulk data cards
CYJpiN and PARAMeters CTYPE, K1NDCX and NSEGS are discussed in Section 1.12
of the User's Manual,
C. Analyses and Results
The finite element model of the bladed disc sector analyzed is shown in
Figure 1. The first five zeroth harmonic natural frequencies and mode shapes of
the sector are noted in Table 1.. The grid points on the hub in contact with tite
compressor shaft were permitted radial translational degree of freedom only..
F
p
R
r	
r.
9.5-1 (9/30/78)
As a typical example, the first of the three frames of V-g and V-f plots out.
put requested in this demonstration problem is shown in figure 2. The density
and interblade phase angle are held coo-),Ldt,t at (0,059 x 1.507 E-6) slinch/in3
and 180 0 0 respectively, for this frame. The three reduced frequencies are identi-
fied by tha symbols *(k-0.3) 0
 0(x-0.7) and A(k=1.0). The flutter summarp for the
three (p,d, k) grou p s is presented in Table 2.
A close examination of the damping curves shows that the damping is nearly
zero in the fourth mode of frequency 1797 li=.
The implied density, velocity and reduced frequency are, respectively
(0.059 x 1,507 E-6) slinch/in 3 , 1.055 E4 in/sec and 1.0 as comp ared with the
actual values of these quantities as (0.059 x 1.507 E-6) slinch /in 3 , 1.910 E4
in /sec and 1.0, respectively.
The ratio Vimpli.ed/Vactual not being equal (or close) to 1.0 discounts the
current operating pO,ot as bein g on a flutter boundary, at which all the L)ree
implied quantities	 equal the actual quantities.
The demonstration example discussed has been presented principally for the
purpose of illustrating the procedure for axial flow compressor flutter analysis.
In order to locate the unstalled flutter boundaries over this entire region of
operation of the compressor stage, similar analysis would be required for a
series of operating points, harmonic numbers, interblade phase angles and
reduced frequencies for both the stage rotor and the stator; Appropriate super-
position of the rotor and stator resulti, would then help identify the unstalled
flutter boundaries on the compressor stage map.
9.5-2 (9/30/78)
z
Clow
.` _,,.---Axis of Rotation
"	 Nuh
01 *de
Figure 1. Finite Element Model of an Axial Flow
Compressor Rotor Sector, and the Basic
Coordinate System
9.5-3 (9/30/78)
c
Table
	
Bladed Disc Sector: Zeroth Harmonic Modes
Made Hn. 'f 2 3 4 5
Mode Frequency, Ht 471 790 977 1797 2154
Mode Shape Torsion
Chords4ise
Bending
(tiP
Circum-
terential
B ndin^_
Axial
_Bending
9.5-4 (9/30/78)
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9.5-5 (9/30/78)
k
^I
Table 2. Flutter Summary (k-Method)
pok Reduced
Group Frequency k Velocity V,	 in/sec Damping g Frequency	 f,	 iiz
9.241
	 E3 -3.199
	
E-3 472
1.549	 E4 -2.291
	
E-3 791
Pill k ) 0.3 1.911
	 E4 -3,642	 E-3 976
3.530	 E4 4.261	 E-3 1803
3.956	 E3 -9.376	 E-4 471
6.633
	 E3 -6.666	 E-4 790
o l a l k 2 0.7
8.199
	
E3 -1.379	 E-3 977
1.508	 E4 8.001	 E-4 1798
4712.769	 E3 -7.441	 E-4
4.643	 E3 -6.892	 E-4 790
p l o l k 3 1.0
5.740	 E3 -4.602	 E-4 977
1.055	 E3 -8.848	 E-5 1797


NASTRAN level 16 demonstration manual updates for aeroelastic analysis of bladed discs

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