1. The Faculty of the Division of Graduate Studies
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

2. OUTLINE
Background
Approach
Results
Conclusions
Proposed Work

3. BACKGROUND
Helicopter has a wide range of military and civil applications.
However, the high noise level associated with it greatly restricts its further applications.

4. BACKGROUND Three categories of rotor noise Rotational noise
Broadband noise
Impulsive noise
High Speed Impulsive (HSI) noise
Blade Vortex Interaction (BVI) noise

5. BACKGROUND
High Speed Impulsive noise

6. BACKGROUND
Blade Vortex Interaction noise

7. 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 field
High resolution aerodynamics in the near field and Kirchhoff’s formula for radiation in far field
Fully computational aerodynamics and acoustics

8. BACKGROUND  Far Field Observer Acoustic calculation Region Blade
CFD calculation Region

9. 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.

10. 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:

11. BACKGROUND
Gaussian Pulse Distribution

12. BACKGROUND T=0 T=50 T=100 Dissipation Phenomenon
Magnitude drops as wave
propagates…
Dissipation
T=100
Dissipation Phenomenon

13. BACKGROUND T=50 T=100 T=0 Dispersion Phenomenon
Dispersion Errors- some waves travel slower than the rest.
Dispersion Phenomenon

14. 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.

15. APPROACH
The integral form of Navier-Stokes equations may be written as:
The flux across the cell boundary is split into two parts and :

16. APPROACH Data is stored at cell centers
i+1/2,j,k L R
i-1, j, k
i, j, k
Information is needed at cell faces.
i+1, j, k

17. APPROACH
Let us approximate qi+1/2 in the uniform transformed plane with three points: i
i+1
i-1
i+1/2

18. 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).

19. 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:
F.T.

20. APPROACH The following error expression should be minimized:
with respect to coefficients
This leads to an over-determined system. Solved by Least Square method.

21. APPROACH
Standard 3rd Order Monotone Upstream-centered Scheme for the Conservative Law (MUSCL Scheme):
Present Scheme:

22. RESULTS High-Speed Impulsive noise modeling
Preliminary studies of Blade-Vortex Interaction noise
Tip vortex system prediction

23. Shock Noise Test Parameters
1/7 scale model of untwisted rectangular UH-1H blades in hover condition
NACA0012 airfoil
Non-lifting case

24. Shock Noise Measurement Locations and Method
r/R=1.111
Blade
r/R=1.78 R
Microphone
Shock wave

25. Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.88, r/R=1.136, Grid size 1335535

26. Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.88, r/R=3.09, Grid size 1335535

27. Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip = 0.9, r/R=1.111, Grid size 1335535

28. Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip = 0.9, r/R=3.09, Grid size 1335535

29. Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.95, r/R=1.053, Grid size 1335535

30. Variation of Acoustic Pressure p´ with time for a Non-lifting Rotor, MTip= 0.95, r/R=3.09, Grid size 1335535

31. BLADE-VORTEX PROXIMITY NEAR FIELD MICROPHONES
Parallel BVI Study
BLADE-VORTEX PROXIMITY
VORTEX GENERATOR
NEAR FIELD MICROPHONES
+CCW VORTEX ROTATION  Y Zv X V
+v Z
Schematic of experimental set-up in wind tunnel test section

32. 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

33. Parallel BVI Study (169  45  57)
Near-field acoustic pressure for microphone 7

34. 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

35. AH-1 Forward Flight Self-induced wake Descending direction
Interaction of tip vortices with rotor disk in descending flight

36. Schematic of flow field
AH-1 Forward Flight
Tip Vortex
Inlet Flow
Advancing Side
Retreating Side 
=90
=0
=180 
Schematic of flow field

37. AH-1 Forward Flight
Blade Surface Pressure Coefficient Distribution, r/R=0.955, =0

38. AH-1 Forward Flight
Blade Surface Pressure Coefficient Distribution, r/R=0.955, =90

39. AH-1 Forward Flight
Blade Surface Pressure Coefficient Distribution, r/R=0.955, =180

40. How well does the Low Dispersion Scheme model tip vortices?
Schematic of hover rotor wake structure

41. Caradonna & Tung Rotor Test Parameters
Untwisted rectangular NACA0012 blades
Hovering condition
MTip=0.44
Collective Pitch c=8

42. Caradonna & Tung Rotor MTip=0.44
TURNS-LDFV
TURNS-MUSCL
Vorticity Magnitude Contour
Vortex I
Vortex II

43. Caradonna & Tung Rotor MTip=0.44, r/R=0.80, Grid size 79  45  31
Blade Surface Pressure Distribution

44. 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.

45. 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.

46. PROPOSED WORK
Determine the minimum number of grid points needed to predict shock noise.
Identify the contributions of different noise sources.

47. 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.