theoretical studies of compressor noise

110 Pages·2001·4.27 MB·English

https://ntrs.nasa.gov/search.jsp?R=19690012114 2019-05-04T17:12:17+00:00Z
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KIRTLAND AFB, N MEX
THEORETICAL STUDIES OF
COMPRESSOR NOISE
by M . V. Lowson
Prepared by
WYLE LABORATORIES
Huntsville, Ala.
for LaugZey Research Celzter
NATIONAAL E RONAUTICAS NS D P ACAE D MINISTRATION WASHINGTODN ., C. MARCH 1969
. .\
TECH LIBRARY KAFB, NM
NASA CR-1287
THEORETICAL STUDIES OF COMPRESSOR NOISE
By M. V. Lowson
Distribution of this report is provided in the interest of
informatione xchange.R esponsibilityf ort hec ontents
resides in the author or organization that prepared it.
Issued by Originator as Report No. WR 68- 15
Prepared under Contract No. NAS 1-6885 by
WYLE LABORATORIES
Huntsville, Ala.
for Langley Research Center
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
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TABLE OF CONTENTS
Page
TABLE OF CONTENTS
iii
LIST OF FIGURES v
LIST OF SYMBOLS vii
ABSTRACT
1.0 INTRODUCTION 2
2.0 MECHANISMS OF NOISE GENERATION 4
2.1 Physical Basis 4
2.2 Noise Generation by the Compressor 5
2.3 Frequency Effects in the Compressor 7
3.0 GENERAL EQUATIONS FOR SOUND GENERATION 9
3.1 The Basic Equati on 9
3.2 Solution of the Basic Equation 11
3.3 The Effects of Moti on 13
4.0 SOUND RADIATION BY MASS FLUCTUATIONS 17
4.1 Mass Fluctuations at the Stator 17
4.2 Rotor Mass Sources 21
4.3 Comments on the Resu I ts 23
4.4 Power Radiated 25
5.0 SOUND RADIATION BY FLUCTUA lING FORCES 28
5.1 Sound Radiated by Fluctuating Forces on the Stator 28
5.2 Sound Generated by Fluctuating Forces at the Rotor 31
5.3 Comments on the Resul ts 33
5.4 Power Calculations 35
6.0 DEFINITION OF SOURCE TERMS 37
6.1 Potential and Wake Interactions 37
6.2 Definition of the Fluctuating Forces in the Blades 37
6.3 Characteristics of Wakes in a Real Compressor 40
i i i
_J
TABLE OF CONTENTS (Continued)
Page
7 .O RESULTS AND 'DISCUSSION 42
7.1 General 42
7.2 Acoustic Power Levels 43
7.3 Directionality Effects 47
8 .O COMPARISON WITH EXPERIMENT 51
8.1 SounDd u e to Fluctuating Force Terms 51
8.2 Mass Source Terms 55
8.3 Discussion 57
9 .O CONCLUSIONS 59
ACKNOWLEDGEMENTS 61
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APPENDIX EFFECTS OF AXIAL MOTION 62
REFERENCES 65
BIBLIOGRAPHY ON COMPRESSOR NOISE 68
I
LIST OF FIGURES
Figure Page
1 Effects of RetardeTd im e 83
2 Effects of Source Velocity 83
3 Rotor-Stator Phase Effects 84
4 TheC ause andE ffectC haino f Compressor NoiseR adiation 84
5 Basic Wake Geometry 85
6 Model Used for Wake Mass Fluctuations 85
7 Coordinate Systems for Compressor NoiseA nalysis 86
8 Exact andA pproximate Lift Functionf ora Sinusoidal Gust 87
9 Contours of Kinetic Energy Loss at Exito f Stator Row (from Ref. 30) 88
10 Contributiont o Power of Mass and Drag Terms; 89
11 Contributiont o Poweor T f hrust Terms; 90
00 2p + 2r
A (-l)nrM
ValuOef = r ! (2p+r) ! (2p+2r+(l) 2 p+2r+3)
r=O
12 Contribution of Typical Compressor Force Term to Power; 91
A ?
Value of p2 D + (nM)2
13 Measured One-ThOir dc ta(va et Blade Passage Frequency) Radiation 92
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Patterns for Various Rotor Guide-Vane Configurations. Mt = 0.346.
From Crigler and Copeland (Ref. 7).
14 Acoustic Power Radiation by a Compressor Variatiown ith Stator Vane 93
Number
V
LIST OF FIGURES (Continued)
Figure Page
15 Effect of Mach Number on Acoustic Power 94
16 Effect of Number of Rotor Blades on Acoustic Power 95
17 Directivity Patterns for Fluctuating Force Terms in Stator-Rotor 96
<
Interactions. Up is forward for X n.
18 Directivity Patterns for Mass Source (also Drag) Terms in Stator-Rotor 97
Interaction
19 Directivity Patterns from an Open Circular Duct (First Radial Mode) 98
20 Comparison of "Theory" and Experiment. Maximum Fan Discharge 99
Noise in Octave Band Containing Fundamental Blade Passage
Frequency (After Wintermeyer and McKaig, Ref. 32)
21 Basic Geometry for Moving Source Transformation 100
vi
LIST OF SYMBOLS
A Compressor area = T :R
A Arbitrary constant
Area of blades
AB
Effective area of compressor = T R2
Complex Fourier coefficient of wake velocity (see Equation 18)
B Number of rotor blades
CD Drag coefficient
D Compressor diameter in inches
D Drag (circumferential force component)
= DAR+ i D complex drag hurmonic (see Equations 50 and 51)
XI
F. Force (three component vector)
I
Component of force in the direction of the observer
Fr
Bessel function of first kind and nth order
Jn
K Modified Bessel function of second kind and nth order
n
L Lift per unit span
M Mach number and rotational Mach number in compressor
Component of convection Mach number in direction of observer
Mr
Q Mass source intensity (q = aQ/at)
R Effective radius of action of point source
Compressor tip radius
RT
S Lift response function (see Equations 77 and 79)
vii
LIST OF SYMBOLS (Continued)
T Thrust
= T' + i T complex thrust harmonic (see Equations 50 and 51)
TX XR XI
Relative velocity at blades
"I
V Number of stator vanes
Rotational velocity at effective radius R
vR
Mechanical tip velocity of rotor blades (feet per second)
vT
W Power I eve I
Power in nth sound harmonic due to X harmonic source input
Wnx
a Speed of sound in free air
0
Harmonic components of thrust and drag (see Equation 51)
aXT' bXTf 'AD' bAD
b Blade spacing = 2s R/V
C Blade chord
f function Arbitrary
h Typical dimension for velodcei( tfwye actk e displacement thickness)
fl
I andf osru ffix tensor notation
j for S uffix tensor notation
k Order of compressos ourr ce input harmonic (X = kV)
m Orodf e r compressosu onr d harmonic (n = me)
n Sound harmonic number (n = mB)
P Fluctuating pressure (at p)
9 Mass source intensity (second ratein o trfo ductoiof n mass)
viii
-
LIST OF SYMBOLS (Continued)
r Distance from observer to source
r Power summation parameter
Distance from observer to compressor hub
‘1
S Blade span
t Tim e
V Upwash
W Velocity of wake (in direction of mean flow)
Cartesian coordinates, x along compressor axis out of compressor
Xi’ Y; Cartesian coordinates of observer and source locations, respectively
Greek Symbols
CY MYh
a! Angle of blade to x-axis (see Figure 5)
P Angle of blade to wake flow (see Figure 5)
= a! x + i x complexF ourier coefficient ofw ake velocity (see Eq. 18)
‘1 Coordinates following source
(e
0 Angle around rotor = 0 on y axis)
x
Source input harmonic (X = kV)
I
x( ,
Modal order = n- and phase factor
Summation parameter over stator vanes
Circumferential coordinate
...
3.141
ix
I
LIST OF SYMBOLS (Continued)
P Density perturbation
Density of free air
Non-dimensional frequency over blade = o c/U
-
T Retarded time T = t r/ao
Reference angle befween observer and zeroth blade
Angle around source (u' = 0 along x-axis)
w Circular frequency
R Angular velocity of compressor rotor
Suffices
Indicates vector quantity
Modulus of
Refers to result for nth harmonic sound only
Refers to result for Xth source harmonic only
Refers to result for pth mode input only
X