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**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

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**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 !

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**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 *

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**Automobile Application Examples**

CAA in the automotive industry

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**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

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**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 = s P0= -0.1 kg/s ta= 10 dt

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**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.

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**Car as a Helmholtz Resonator**

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

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**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

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**Use of nested sub-grids**

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**9 observation points within computational domain**

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

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**Differencing Schemes Affect Disturbance Decay**

| | | | | W w P | E | | | |

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**Effect of Differencing Scheme: (a) Hybrid**

Source Input (fs=50Hz)

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**Effect of Differencing Scheme: (b) QUICK**

Source Input (fs=50Hz)

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**Pressure time history at the sunroof LE**

By QUICK scheme. 6.7m

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**FFT of Pressure Fluctuation – Resonance at 13Hz**

---- Analyse Acoustic Response f = 13Hz

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**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

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Acoustic Pressure x-axis direction

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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.

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**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, [6] CFD Code PHYSICA,

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

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