Numerical simulations of compressible mixing layers with a discontinuous Galerkin method

Discontinuous Galerkin（DG） method is known to have several advantages for flow simulations,in particular,in fiexible accuracy management and adaptability to mesh refinement. In the present work,the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer,both the instantaneous fiow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer,large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous fiow field for a three-dimensional compressible mixing layer is also reported,which shows the development of largescale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear fiows.

A symmetry-based length model for characterizing the hypersonic boundary layer transition on a slender cone at moderate incidence

The hypersonic boundary layer(HBL)transition on a slender cone at moderate incidence is studied via a symmetry-based length model:the SED-SL model.The SED-SL specifies an analytic stress length function(which defines the eddy viscosity)describing a physically sound two-dimensional multi-regime structure of transitional boundary layer.Previous studies showed accurate predictions,especially on the drag coefficient,by the SED-SL for airfoil flows at different subsonic Mach numbers,Reynolds numbers and angles of attack.Here,the SED-SL is extended to compute the hypersonic heat transfer on a 7∘half-angle straight cone at Mach numbers 6 and 7 and angles of attack from 0∘to 6∘.It is shown that a proper setting of the multi-regime structure with three parameters(i.e.a transition center,an after-transition near-wall eddy length,and a transition width quantifying transition overshoot)yields an accurate description of the surface heat fluxes measured in wind tunnels.Uniformly good agreements between simulations and measurements are obtained from windward to leeward side of the cone,implying the validity of the multi-regime description of the transition independent of instability mechanisms.It is concluded that a unified description for the HBL transition of cone is found,and might offer a basis for developing a new transition model that is simultaneously of computational simplicity,sound physics and greater accuracy.