School of Aerospace Engineering CERT Prediction of Rotorcraft Noise with A Low-Dispersion Finite Volume Scheme A Thesis Proposal Presented to The Faculty of the Division of Graduate Studies By Gang Wang Advisor: Dr. T. C. Lieuwen
School of Aerospace EngineeringSchool of Aerospace Engineering
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Prediction of Rotorcraft Noise with A Low-Dispersion Finite
Volume SchemeA Thesis Proposal
Presented toThe Faculty of the Division of Graduate Studies
ByGang Wang
Advisor: Dr. T. C. Lieuwen
School of Aerospace EngineeringSchool of Aerospace Engineering
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OUTLINE
Background
Approach
Results
Conclusions
Proposed Work
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BACKGROUND
Helicopter has a wide range of military and civil applications.
However, the high noise level associated with it greatly restricts its further applications.
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BACKGROUND
Three categories of rotor noiseRotational noiseBroadband noiseImpulsive noise
High Speed Impulsive (HSI) noise Blade Vortex Interaction (BVI) noise
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BACKGROUND
High Speed Impulsive noise
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BACKGROUND
Blade Vortex Interaction noise
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BACKGROUND
Many efforts have been spent on quantifying and minimizing rotorcraft noise.
Three noise prediction techniques:High resolution aerodynamics in the near field
and acoustic analogy for radiation in far fieldHigh resolution aerodynamics in the near field
and Kirchhoff’s formula for radiation in far fieldFully computational aerodynamics and acoustics
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BACKGROUND
Blade
Acoustic calculation Region
Far Field
Observer
CFD calculation Region
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BACKGROUND
Much progress has been made during the past two decades in understanding and predicting rotorcraft noise characteristics with the aid of Computational Fluid Dynamics.
However, dispersion and dissipation errors accompanied with conventional CFD methods alter the observed noise characteristics even a short distance away from the rotor.
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BACKGROUND
Significant computing resources are needed to reduce these errors. This precludes the prediction methodology from use in engineering design and development.
Dispersion and dissipation phenomena can be simply shown by tracking rectilinear propagation of a Gaussian sound pulse:
2
0
52exp0.10
xxp
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BACKGROUND
-2
0
2
4
6
8
10
12
-20 -15 -10 -5 0 5 10 15 20
Gaussian Distribution
Gaussian Pulse Distribution
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BACKGROUND
-2
0
2
4
6
8
10
12
-50 -30 -10 10 30 50 70 90 110
Magnitude drops as wavepropagates…Dissipation
Dissipation Phenomenon
T=0 T=5
0
T=100
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BACKGROUND
-2
0
2
4
6
8
10
12
-50 -40 -30 -20 -10 0 10 20 30 40 50 60 70 80 90 100
Dispersion Errors- some waves travel slower than the rest.
Dispersion Phenomenon
T=0
T=50 T=1
00
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OBJECTIVES
Develop an improved algorithm with low dispersion and dissipation errors.
The schemes should be simple enough so that they can find immediate use in CFD codes which are widely used in industry.
It should not sacrifice aerodynamic resolution for acoustic resolution, and vice versa.
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APPROACH
The integral form of Navier-Stokes equations may be written as:
The flux across the cell boundary is split into two parts and :
dSnkTjSiRdSnkGjFiEdVqt SV S
RqF LqF
RL qFqFFn)kGjFiE(
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APPROACH
L Ri, j, k i+1, j,
k
i-1, j, k
i+1/2,j,k
Data is stored at cell centers
Information is needed at cell faces.
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APPROACH
Let us approximate qi+1/2 in the uniform
transformed plane with three points:
i i+1
i-1
i+1/2
1101121
21
~ iiiii qaqaqaqq
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APPROACH
Using classical Taylor series method, we can obtain three expansion equations of qi+1, qi, and qi-1 about i+1/2, for example:
With these three equations, we can determine coefficients ai+1, ai, and ai-1
(Traditional Method).
11 2
1
!2
1
21
m
mmi
ii m
qqq
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APPROACH In our approach, we impose a further restriction to
match the Fourier transformation (in space) of approximation for qi+1/2 with its exact
transformation. The Fourier transformation of approximate
expression for qi+1/2 is:
1
1 2
1exp1
kk kiaQ
1101121
21
~ iiiii qaqaqaqq
F.T.
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APPROACH
The following error expression should be minimized:
with respect to coefficients .
This leads to an over-determined system. Solved by Least Square method.
2
2
21
1 2
1exp1
dkiaE
kk
ka
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APPROACH
Standard 3rd Order Monotone Upstream-centered Scheme for the Conservative Law (MUSCL Scheme):
Present Scheme:
11 3333.08333.01666.0 iiiL qqqq
11 3872.07257.01129.0 iiiL qqqq
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RESULTS
High-Speed Impulsive noise modeling
Preliminary studies of Blade-Vortex Interaction noise
Tip vortex system prediction
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Shock Noise Test Parameters
1/7 scale model of untwisted rectangular UH-1H blades in hover condition
NACA0012 airfoil
Non-lifting case
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Shock Noise Measurement Locations and Method
r/R=1.111
Blade
r/R=1.78
R
Microphone
Shock wave
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Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.88, r/R=1.136,
Grid size 1335535
-3000
-2500
-2000
-1500
-1000
-500
0
500
1000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time(msec)
Pre
ssur
e(P
a)
TURNS-MUSCL Result
TURNS-LDFV Result
Experiment Data
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Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.88, r/R=3.09,
Grid size 1335535
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time(msec)
Pre
ssur
e(kP
a)
TURNS-MUSCL Result
TURNS-LDFV Result
Experimental Data
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Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip = 0.9, r/R=1.111,
Grid size 1335535
-7000
-6000
-5000
-4000
-3000
-2000
-1000
0
1000
2000
0 0.5 1 1.5 2
Time(msec)
Pressure(Pa)
TURNS-MUSCL Result
TURNS-LDFV Result
Experimental Data
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Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip = 0.9, r/R=3.09,
Grid size 1335535
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time(msec)
Pressure(kPa)
TURNS-MUSCL Result
TURNS-LDFV Result
Experimental Data
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Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.95, r/R=1.053,
Grid size 1335535
-20
-15
-10
-5
0
5
10
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time(msec)
Pressure(kPa)
TURNS-MUSCL Result
TURNS-LDFV Result
Experimental Data
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Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.95, r/R=3.09,
Grid size 1335535
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time(msec)
Pressure(kPa)
TURNS-MUSCL Result
TURNS-LDFV Result
Experimental Data
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Parallel BVI Study
Schematic of experimental set-up in wind tunnel test section
BLADE-VORTEX PROXIMITY
VORTEX GENERATOR
NEAR FIELD MICROPHONES
+CCW VORTEX
ROTATION
YZv
X
V+v
Z
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Parallel BVI Test Parameters
Untwisted, rectangular blade NACA 0012 airfoil Mtip=0.71, Advance ratio=0.2 Vortex 0.25 chord below blade Non-lifting case
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Parallel BVI Study(169 45 57)
-1500
-1250
-1000
-750
-500
-250
0
250
500
120 135 150 165 180 195 210 225 240
Azimuth Angle
So
un
d P
ress
ure
Lev
el(P
a)
TURNS-MUSCL ResultTURNS-LDFV ResultExperimental Data
Near-field acoustic pressure for microphone 7
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AH-1 Forward Flight Test Parameters
1/7 scale model of Operational Load Survey (OLS) blades
Rectangular blades with 8.2 of twist from root to tip
Mtip=0.664, Advance ratio=0.164 Grid size 110 45 40
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AH-1 Forward Flight
Descending direction
Self-induced wake
Interaction of tip vortices with rotor disk in descending flight
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AH-1 Forward Flight
Schematic of flow field
Tip Vortex
Inlet Flow
Advancing Side
Retreating Side
=90
=0
=180
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AH-1 Forward Flight
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
X/C
-Cp
Numerical Result(Upper Surface)
Numerical Result(Lower Surface)
Experimental Data(Upper Surface)
Blade Surface Pressure Coefficient Distribution, r/R=0.955, =0
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AH-1 Forward Flight
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
X/C
-Cp
Numerical Result(Upper Surface)
Numerical Result(Lower Surface)
Experimental Data(Upper Surface)
Blade Surface Pressure Coefficient Distribution, r/R=0.955, =90
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AH-1 Forward Flight
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
X/C
-Cp
Numerical Result(Upper Surface)
Numerical Result(Lower Surface)
Experimental Data(Upper Surface)
Blade Surface Pressure Coefficient Distribution, r/R=0.955, =180
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How well does the Low Dispersion Scheme model tip vortices?
Schematic of hover rotor wake structure
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Caradonna & Tung Rotor Test Parameters
Untwisted rectangular NACA0012 blades Hovering condition MTip=0.44
Collective Pitch c=8
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Caradonna & Tung RotorMTip=0.44
TURNS-LDFV TURNS-MUSCL
Vorticity Magnitude Contour
Vortex I
Vortex II
Vortex I
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Caradonna & Tung RotorMTip=0.44, r/R=0.80, Grid size 79 45 31
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
-0.2 0 0.2 0.4 0.6 0.8 1 1.2
x/C
-Cp
TURNS-MUSCL
TURNS-LDFV
Experimental Data
Blade Surface Pressure Distribution
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CONCLUSIONS
A Low-Dispersion Finite Volume scheme has been developed and implemented into TURNS, a finite volume CFD code.
Encouraging agreement between the predicted results and experiment data has been obtained for shock noise on coarse grid.
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CONCLUSIONS
Basic characteristics of BVI noise are predicted with satisfactory accuracy.
TURNS-LDFV can capture main features of the tip vortex system with good resolution on coarse grids.
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PROPOSED WORK
Determine the minimum number of grid points needed to predict shock noise.
Identify the contributions of different noise sources.