A New Finite-Difference Method for General Long-Range Rotorcraft Acoustics: Initial Comparisons with Intermediate- Range Data

Transcription

1 A New Finite-Difference Method for General Long-Range Rotorcraft Acoustics: Initial Comparisons with Intermediate- Range Data Subhashini Chitta, John Steinhoff (B.H. Goethert Professor, UTSI), Andrew Wilson Wave CPC, Inc., Tullahoma, TN, Frank Caradonna, Ben W. Sim US Army Aviation Development Directorate - AFDD, Moffett Field, CA Lakshmi Sankar, Georgia Tech Fred Schmitz, University of Maryland

2 Long Range Acoustics Propagation Army SBIR: Reliable assessment of vehicle noise over long distance propagation Very long distances relative source scales!! Source Noise Refraction Atmospheric Winds & Temps Diffraction Reflection Terrain Shapes Acoustic Impedance 2

3 Outline Existing Methods Basic Concept implemented in the code Boundary Conditions Validation Reflection Diffraction Demonstration Comparison with Experiment Software Development 3

4 Existing Methods Ray Tracing Interpolation needed to compute atmospheric and ground variables at each ray location Can become chaotic even with small perturbations Fails to capture diffraction Integral Methods Require closed form propagator Homogenous medium Parabolic Method, Gaussian Difficult at treat wide angles Large angle scattering not treated High Order Discretization Eulerian (Finite Difference Time Domain) Only meaningful if significant number of cells within pulse Large grid requirements Computationally prohibitive Compatible Boundary conditions prohibitive 4

5 Basic Concept Implemented in the Code A finite-difference based approach. Propagating thin waves without dissipation by introducing Wave Confinement terms Propagation of computational wave in two steps for speed of sound, c, and background wind, U. Source Noise Refraction Atmospheric Winds & Temps t 2 φ = c 2 2 φ t φ = U φ Diffraction Reflection Terrain Shapes Acoustic Impedance Solve Propagation with Confinement Term : 2 t φ = c 2 2 φ + t 2 (μφ εφ) where Φ is the harmonic mean of the neighboring nodes and μ and ε are the confinement parameters, which are constant during the computation Can be discretized with simple low order approximations Solution stable to perturbations due to discretization i.e no dissipation/dispersion F is nonlinear and implicitly defines structure of computational wave Decouples structure relaxation from propagation dynamics Solutions are Nonlinear Solitary Waves (NSW s) *Reference: J. Steinhoff, S. Chitta, Solution of the scalar wave equation over very long distances using nonlinear solitary waves: Relation to Finite difference methods, Journal of Computational Physics, 231(19), pp ,

6 Basic Concept Implemented in the Code In reality, the acoustic waves of interest are very short and cannot be directly treated on the grid due to prohibitive grid requirements Instead, Computational waves (φ) that carry details of the physical wave (p) are propagated Wider than the physical waves Enable the use of coarser grid Computational wave Accurately compute integrals such as phase and total amplitude Physical wave Other details carried will allow the computation of physical wave forms 4 5 grid cells Computational waves Isotropic Source sphere radius is at least 10 grid cells wide and center is i 0, j 0, k 0 Centroid of the computational wave aligns with the source sphere Undergo atmospheric and ground effects Source sphere Computed using near field solver ~ (10-50) rotor radii away Pressure time history saved as a function of spatial coordinates and time The resolution on the source sphere is independent of the resolution of far field computation Acoustic field is well defined and normal to the acoustic surface 6

7 Boundary Conditions Outer boundary Perfectly matched layers 7

8 Validation (Standard Atmosphere) Elevation angle: WC (red) vs Analytical (blue) 1/r factor Source height = 250 ft Wave form at a point 3000 ft away Constant phase contours: WC (red) vs Analytical (blue) 8

9 Validation Error is less than 2% Constant elevation angle contours (WC vs ray tracing) Source height = 250ft 0.2a 9

10 Diffraction Diffraction (Preliminary results) Propagation into shadow region significant at lower frequencies Wave equation solution includes this effect WC retains the shape of the computational waves in shadow regions and conserves the integrals Total amplitude and phase computed in shadow regions (unlike ray tracing) Current work involves scaling amplitude in shadow regions for physical frequencies 10 Knife edge diffraction of plane wave Constant phase contours Propagation over a Gaussian wedge Constant amplitude contours

11 Reflection Ground reflection Solution is superposition of direct and reflected waves Flat ground: Currently, image approximation is used Complex Terrain (work in progress) φ k is set to zero every time-step inside boundary Confinement term ( t 2 F) eliminates tangential stair-case by smoothing 11

12 Reflection Demonstration Sound Pressure Levels (SPL s) on a plane 100 ft above ground when the aircraft position is at (0,0) Combined signal SPL of Direct Wave z y source height = 500ft Nose tilt = ~ 8 degrees x Only thickness noise is plotted for demonstration SPL of reflected wave Above the ground, the SPL s of the direct wave are much stronger Propagation path is shorter Attenuation factor is smaller Interference due to phase difference On the ground plane, SPL s for direct and reflected waves are identical and have no phase difference (for specular reflection) 12

13 Varying index of refraction Demonstration Sound Pressure Levels (SPL s) on ground plane when the aircraft position is at (0,0) Rays bend down Rays bend up SPL s become stronger or weaker for positive or negative gradients respectively For positive gradient, the waves bend down and more information from the rotor plane reaches the ground and so the SPL s are stronger For negative gradient, the bending is upwards and the SPLs are weaker than positive and zero gradient. z y source height = 500ft Nose tilt = ~ 8 degrees x Rays straight (c constant, no refraction) 13 Only thickness noise is plotted for demonstration

14 Effects due to background wind Demonstration No wind SPL z y Mic 3 x Mic 2 Mic 4 Mic 1 Wind SPL SPL s on ground plane 14

15 Comparison with Experiment Flight test details Aircraft MD-902 Flight 102 Test Number 273 OAT 80 F Airspeed ft/s Speed of sound 1144 ft/s Mu M_adv alpha degrees C_T over sigma Atm pressure mbar Humidity 72% Density lb/ft^3 Main rotor diameter ft No of Main rotor blades 5 ct Rotor shaft 392 RPM Blade passage frequency 32.7 Hz The dynamic flow field around the MD902 main rotor is solved for using the GT-Hybrid coupled CFD/CSD solver (using the measured airspeed, aircraft weight, weather conditions, etc. from the flight test). WOPWOP is used to integrate over the CFD solution at the rotors and generate acoustic pressure-time histories on a sphere 100 ft away from the rotorcraft. 15

16 Comparison with Experiment At a given far field location, pressure-time history (accounting for spherical spreading/geometric attenuation, time-of-flight, and Doppler Effect) is generated. At microphone 7. Helicopter is approximately 1000 ft away Atmospheric Absorption: ISO Standard , Acoustics -- Attenuation of sound during propagation outdoors -- Part 1: Calculation of the absorption of sound by the atmosphere, 1993 Ground Impedance: Empirical relationship is used 16

17 Software Development Inputs Flight Conditions Source velocity (Doppler) Source noise sphere Propagation Conditions Outputs Terrain (obstructions, impedance) Speed of sound profile Wind profile Details at receivers Pressure vs Time Sound Pressure Level Noise Spectrum SPL Map Sound Pressure Level information at every location on the ground Computational time :10 minutes on a single pc for a grid 17

18 Acknowledgements 18

19 Questions? 19

20 Computation of Small Scale Features Using WC φ 0 initialized as a thin hyperbolic secant The coordinates of the source sphere are carried using Computational waves φ 1 = i φ 0, φ 1 = j φ 0, φ 1 = k φ 0 (i, j, k) are the coordinates of the each grid cell () that lie within the computational wave, φ 0 stay invariant along the propagation path Far field point can then be associated to a point of origin on the acoustic sphere. The physical acoustic field can then be computed in the far field using Point of origin (ψ, θ) corresponding to any far field point is computed t Arrival time τ = tφ 0dt t tφ 0 dt t Attenuation factor A f = φ 0dt where A A source is source the source strength Wave form at any far field point p x, t = p ψ origin, θ origin, τ, A f May have multiple classical ray paths between field point and source due to reflections and refractions. 20