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On the Flow and Passive Noise Control of an Open Cavity at Re = 5000

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Abstract

The interaction of turbulent flows with the external structure of ground vehicles generates uncomfortable noise and a lot of attention is devoted to find new mechanisms for its suppression. The present work is concerned with open cavity flows, very often found in the automotive industry. A three-dimensional rectangular very wide open cavity with aspect ratio \(L/D=4\) at Reynolds number \(Re_D=5000\) and Mach number \(M=0.1\) is considered. The passive control technique is based on eight different geometrical modifications: the length of the cavity, the radius of the trailing, leading and bottom edges and the difference in heights between the left and right wall of the cavity. Wall-resolved Large Eddy Simulations (LES) are used to obtain the flow fields and a post-process based on Curle’s analogy is applied to evaluate the acoustic radiation and the effectiveness of the control mechanisms. The results show that the modifications on the trailing edge are the most effective to control the flow. They allow to reduce the pressure fluctuations produced by the recirculation confined inside the cavity and the abrupt ejection of the flow at the trailing edge. As a consequence, the overall sound pressure level can be decreased up to 9 dB.

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Abbreviations

\(a_0\) :

= Speed of sound

\(C_D\) :

= Cavity drag coefficient, \(\frac{F_D}{\frac{1}{2}\rho _{\infty }U_{\infty }^2DW}\)

D :

= Cavity depth

f :

= Fundamental frequency

\(F_D\) :

= Force contribution from the cavity walls

H :

= Shape factor, \(H=\frac{\delta ^*}{\theta }\)

L :

= Cavity length

l :

= Unitary vector pointing from source point to observation point.

OASPL:

= Overall averaged sound pressure level, \(20log_{10}\left( \frac{p_{rms}'}{p_{ref}'}\right)\)

M :

= Mach number, \(\frac{U_{\infty }}{a_0}\)

p :

= Non-dimensional pressure, \(\frac{p_d}{\rho _{\infty }U_{\infty }^2}\)

\(p_d\) :

= Dimensional pressure

\(p_{rms}'\) :

= Root mean square of the acoustic pressure

\(p_{ref}'\) :

= Reference acoustic pressure, \(\sqrt{\rho _{\infty } a_0\times 10^{-12}}\)

n :

= Surface normal vector pointing to the surface

\({\mathcal {Q}}\) :

= Second invariant of the velocity gradient tensor, \(-\frac{1}{2}\frac{\partial u_i}{\partial x_j}\frac{\partial u_j}{\partial x_i}\)

r :

= Distance between an observer position and a source point

\(R_{ii}\) :

= Autocorrelation coefficient

\(Re_{D,L,\theta }\) :

= Reynolds number, \(\frac{U_{\infty }D}{\nu }\), \(\frac{U_{\infty }L}{\nu }\), \(\frac{U_{\infty }\theta }{\nu }\)

\(St_L\) :

= Strouhal number based on L, \(St_L = \frac{f L}{U_{\infty }}\)

s :

= Distance from the leading edge along the wall

t :

= Time

\({\tilde{t}}\) :

= Retarded time, \(t-r/a_0\)

TU :

= Time units, \(\frac{t U_{\infty }}{D}\)

U :

= Non-dimensional velocity, \(\frac{U_d}{U_{\infty }}\)

\(U_d\) :

= Dimensional velocity

\(u^*\) :

= Friction velocity, \(\sqrt{\frac{\tau _w}{\rho }}\)

\(U_{\infty }\) :

= Freestream velocity

W :

= Cavity width

x :

= Streamwise coordinate

y :

= Cross-stream coordinate

\(y_n\) :

= Wall normal coordinate

\(y^+\) :

= Dimensionless wall-normal distance, \(y^+=\frac{u^*y_n}{\nu }\)

z :

= Spanwise coordinate

\(\alpha\) :

= Counterclockwise angle taken from the downstream wall of the cavity

\(\delta ^*\) :

= Displacement thickness, \(\int _0^{\delta _{99}}\left( 1-\frac{\rho (y_n)u(y_n)}{\rho _{\infty }U_{\infty }}\right) {\mathrm {d}}y_n\)

\(\delta _{ij}\) :

= Kronecker delta

\(\varDelta x^+\) :

= Wall spacing in the x-axis, \(\varDelta x^+=\frac{u^*\varDelta x}{\nu }\)

\(\varDelta z^+\) :

= Wall spacing in the z-axis, \(\varDelta z^+=\frac{u^*\varDelta z}{\nu }\)

\(\theta\) :

= Momentum thickness, \(\int _0^{\delta _{99}}\frac{\rho (y_n)u(y_n)}{\rho _{\infty }U_{\infty }}\left( 1-\frac{u(y_n)}{U_{\infty }}\right) {\mathrm {d}}y_n\)

\(\mu\) :

= Dynamic viscosity

\(\nu\) :

= Kinematic viscosity

\(\rho\) :

= Density

\(\rho _{\infty }\) :

= Freestream density

\(\tau _W\) :

= Wall shear stress, \(\mu \left( \frac{\partial u }{\partial y }\right) _{y=0}\)

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Acknowledgements

The work of Rocio Martin was carried out within the framework of an Industrial Doctorate project from the government of Catalonia and was sponsored by the Agència de Gestió d’Ajuts Universitaris i de Recerca (AGAUR) and the automotive company SEAT S.A (2016 DI068). The work of Manel Soria has been partially supported by the Spanish Ministry (MEC) project FIS2016-77849-R. Oriol Lehmkuhl has been partially supported by a Ramón y Cajal postdoctoral contract (RYC2018-025949-I). The results were obtained using MareNotrum IV (FI-2019-1-0016 and IM-2019-2-0025) supercomputers of Red Española de Surpercomputación. The authors thankfully acknowledge these institutions.

Funding

This research received funding from AGAUR (2016 DI068) and the Spanish Ministry (FIS2016-77849-R, RYC2018-025949-I).

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Authors and Affiliations

  1. Universitat Politècnica de Catalunya, Terrassa, 08222, Spain

    Rocio Martin, Manel Soria & Ivette Rodriguez

  2. Barcelona Supercomputing Center, Barcelona, 08034, Spain

    Oriol Lehmkuhl

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  1. Rocio Martin
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  2. Manel Soria
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Correspondence to Manel Soria.

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Martin, R., Soria, M., Rodriguez, I. et al. On the Flow and Passive Noise Control of an Open Cavity at Re = 5000. Flow Turbulence Combust 108, 123–148 (2022). https://doi.org/10.1007/s10494-021-00265-y

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