prediction of rotorcraft noise with a low-dispersion finite volume scheme

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


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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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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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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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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






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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






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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.


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PROPOSED WORK

Repeat forward flight BVI calculation on fine grid; Incorporate trim effects.

Further investigation of BVI noise investigated in Higher harmonic control Aeroacoustic Rotor Test (HART) program.

prediction of rotorcraft noise with a low-dispersion finite volume scheme

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