Large eddy simulation of transonic turbulent flow over a bump

Abstract

Transonic turbulent boundary-layer flow over a circular-arc bump has been computed by high-resolution large-eddy simulation of the compressible Navier–Stokes equations. The inflow turbulence was prescribed using a new technique, in which known dynamical features of the inner and outer part of the boundary-layer were exploited to produce a standard turbulent boundary-layer within a short distance of the inflow. This method was separately tested for a flat plate turbulent boundary-layer, for which results compared well with direct numerical simulation databases. Simulation of the bump flow was carried out using high-order methods, with the dynamic Smagorinsky model used for sub-grid terms in the momentum and energy equations. Simulations were carried out at a Reynolds number of 233,000 based on bump length and free-stream properties upstream of the bump. At a back pressure equal to 0.65 times the stagnation pressure, a normal shock was formed near the bump trailing-edge and a peak mean Mach number of 1.16 was observed. Turbulence fluctuations decayed in the favourable pressure gradient region of the flow, before being amplified due to the shock interaction and boundary-layer separation. The effect of Reynolds number on turbulence intensity upstream of the shock is discussed in connection with a laminarisation parameter. With reference to turbulence modelling, anisotropy levels are not unreasonably high in the shock interaction region and shock unsteadiness was not found to be an issue. Of more relevance to the perceived poor performance of models for this type of flow may be the extremely rapid rise and decay of turbulence levels in the separated shear layer immediately under the shock-wave.

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ORCID for N.D. Sandham: orcid.org/0000-0002-5107-0944

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