Numerical investigation of the compressible flow past an aerofoil

Abstract

Numerical investigation of the compressible flow past an 18% thick circular-arc aerofoil was carried out using detached-eddy simulation for a free-stream Mach number M∞ = 0.76 and a Reynolds number Re = 1.1 × 107. Results have been validated carefully against experimental data. Various fundamental mechanisms dictating the intricate flow phenomena, including moving shock wave behaviours, turbulent boundary layer characteristics, kinematics of coherent structures and dynamical processes in flow evolution, have been studied systematically. A feedback model is developed to predict the self-sustained shock wave motions repeated alternately along the upper and lower surfaces of the aerofoil, which is a key issue associated with the complex flow phenomena. Based on the moving shock wave characteristics, three typical flow regimes are classified as attached boundary layer, moving shock wave/turbulent boundary layer interaction and intermittent boundary layer separation. The turbulent statistical quantities have been analysed in detail, and different behaviours are found in the three flow regimes. Some quantities, e.g. pressure-dilatation correlation and dilatational dissipation, have exhibited that the compressibility effect is enhanced because of the shock wave/boundary layer interaction. Further, the kinematics of coherent vortical structures and the dynamical processes in flow evolution are analysed. The speed of downstream-propagating pressure waves in the separated boundary layer is consistent with the convection speed of the coherent vortical structures. The multi-layer structures of the separated shear layer and the moving shock wave are reasonably captured using the instantaneous Lamb vector divergence and curl, and the underlying dynamical processes are clarified. In addition, the proper orthogonal decomposition analysis of the fluctuating pressure field illustrates that the dominated modes are associated with the moving shock waves and the separated shear layers in the trailing-edge region. The results obtained in this study provide physical insight into the understanding of the mechanisms relevant to this complex flow.

Numerical analysis of shock wave and supersonic turbulent boundary interaction between adiabatic and cold walls

“…It is clear that both the turbulent boundary layer and the separated shear layer are characterised by interval of negative and positive values with large magnitude, while in the shock wave region the Lamb vector divergence is relatively small. A similar trend is also observed from numerical investigation of the compressible flow past an aerofoil [25]. The major difference in the distribution of Lamb vector convergence for different wall temperature cases is presented in the near-wall region.…”

Large-eddy simulation of the compressible flow past a wavy cylinder

“…Further, the present numerical strategy has already been applied with success to a wide range of turbulent flows such as the compressible turbulent swirling flows injected into a coaxial dump chamber (Lu et al 2005), transonic flows over a circular cylinder (Xu et al 2009a;Xu, Chen & Lu 2009b) and past an aerofoil (Chen et al 2010a) and supersonic flow past a hemispherical nose with an opposing jet (Chen, Xu & Lu 2010b). We have carefully examined the physical model and numerical approach used in this study and have verified that the calculated results are reliable.…”

“…Moreover, the resolved energy spectra obtained by the present numerical method were also examined in some previous investigations (e.g. Wang et al 2007;Chen et al 2010a).…”

“…The convective terms are discretized by a second-order central/upwind hybrid scheme for shock-capturing and the viscous terms by a fourth-order central difference (Lu et al 2005;Wang et al 2007;Chen, Xu & Lu 2010a). The temporal integration is performed using an implicit approximate-factorization method with sub-iterations to ensure the second-order accuracy (Simon et al 2007).…”

“…The spatial discretization has been constructed explicitly to be shock capturing with the upwind scheme and to revert to a central stencil with low numerical dissipation in turbulent flow regions away from shock. A binary sensor function Φ i+1/2 at cell face i + 1/2 is used for the detection of shocks; Φ i+1/2 is determined by the pressure and density curvature criteria proposed by Hill, Pantano & Pullin (2006) chosen as 0.01 (Chen et al 2010a). Based on this detection, the Roe's second-order upwind flux only operates at the cells in the vicinity of a shock wave.…”