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

OUTLINE Background Approach Results Conclusions Proposed Work

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

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

BACKGROUND High Speed Impulsive noise

BACKGROUND Blade Vortex Interaction noise

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

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

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.

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:

BACKGROUND Gaussian Pulse Distribution

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

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

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.

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

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

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

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).

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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.