University of Greenwich Computing and Mathematical Sciences Experience of using a CFD code for estimating the noise generated by gusts along the sunroof of a car by Liang Lai Supervisors: Professor C- H Lai, Dr. G S Djambazov, Professor K A Pericleous Sponsored by University of Greenwich

Solution strategies for Computational Aeroacoustics Introduction Solution strategies for Computational Aeroacoustics Decreasing cost source + Propagation DNS/LES/RANS (Near field + far field) Direct Numerical Simulation (DNS) Large Eddy Simulation (LES or DES) Reynolds-Averaged Navier-Stokes (RANS) ¤ High-order schemes in space and time ¤ Different length scales and time scales for aeroacoustic simulation in turbulent flows ¤ Computational cost is very high even for using RANS with high-order schemes !

Introduction Coupling Methods ? The unsteady near-field is solved directly by LES or unsteady RANS, but acoustic solutions obtained by solving a set of simpler equations (e.g. wave equation, Euler equations, and other perturbation equations). + LES/RANS Simpler equations * (near field) (near field + far field) source Propagation non-linearised Euler equations Decomposition + source-retrieval techniques Other methods, e.g. Helmholtz equation? Simpler equations *

Automobile Application Examples CAA in the automotive industry

The Car Sunroof Problem Buffeting noise is due to shear-layer instability in the opening of the cavity subjected to tangential flow. Shear-layer vortices are produced and are convected downstream of the opening, eventually hitting the rear edge. When the vortex breaks, a pressure wave is produced which enters into the cavity. At a certain speed, the vortex shedding frequency in the shear layer will match an acoustic mode of the cavity leading to resonance is in the form of a standing wave. Resonance is in the form of a Helmholtz mode

Problem setup and external excitation A sinusoidal disturbance 1.2m 0.4m 1.1m 0.8m 0.03m 0.9m 0.5m Car as a Helmholtz Resonator Time step: Wave amplitude: Wave time per cycle: dt = 0.00124 s P0= -0.1 kg/s ta= 10 dt

Car as a Helmholtz Resonator Basic procedure with PHOENICS The pressure fluctuation along the open sun-roof can be calculated, where is the pressure distribution obtained by using the CFD calculation and is the background pressure distribution due to the upstream velocity.

Car as a Helmholtz Resonator Analyse Acoustic Response by using FFT Comparison to a Helmholtz Resonator therefore, resonant frequency ( = 1.45) f = 6.32Hz

Alternative Problem Description A hypothetical car with an open sun-roof *The vortex strength W = A0 sin(ωt), where A0 = 1.2 m/s t = 10-3 s , wave time per cycle ta = 20 t, f = 50 Hz 25m/s 1.28m 0.52m 1.35m 0.35m 0.05m 1.2m 0.6m 0.85m 0.3m ###Mesh

Use of nested sub-grids

9 observation points within computational domain Geometry and Observation points 7 points along sun-roof 9 observation points within computational domain

Differencing Schemes Affect Disturbance Decay | | | | ------------------------------------------------------------------------------------------------------------ | W w P | E | | -------------- | |

Effect of Differencing Scheme: (a) Hybrid Source Input (fs=50Hz)

Effect of Differencing Scheme: (b) QUICK Source Input (fs=50Hz)

Pressure time history at the sunroof LE By QUICK scheme. 6.7m

FFT of Pressure Fluctuation – Resonance at 13Hz ---- Analyse Acoustic Response f = 13Hz

Helmholtz Equation, the FT of the Wave Equation Homogeneous Wave equation Integrate with respect to time --- taking Fourier transform of the wave equation finally, one gets Apply inside car cavity – neglecting convective effects

Acoustic Pressure x-axis direction

Conclusion Coupling techniques offer a realistic alternative to a full CAA simulation A complete acoustic response can be obtained by the coupling of RANS and Helmholtz equation High order schemes are necessary to avoid numerical diffusion of fluctuations.

Acknowledgement References The Helmholtz Equation program is coded by Professor Frederic Magoules. Supported by The British Council Franco-British Alliance Programme. References [1] Z. K. Wang, “A Source-extraction Based Coupling Method for Computational Aeroacoustics”, PhD Thesis, University of Greenwich (2004) [2] S. V. Patankar, Numerical Heat Transfer and Fluid Flow, (Hemisphere, 1980) [3] G. S. Djambazov, “Numerical Techniques for Computational Aeroacoustics”, PhD Thesis, University of Greenwich (1998) [4] E. Avital, “A Computational and Analytical Study of Sound Emitted by Free Shear Flows”, PhD Thesis, Queen Mary and Westfield College (1998) [5] CFD Code PHOENICS, www.CHAM.co.uk [6] CFD Code PHYSICA, www.physica.co.uk

50Hz Disturbance Velocity Vectors [u(x,t)* - u(x,t)]