The numerical simulation of variable-density compressible shear layers

In the pursuit of a better understanding of hydrogen/oxygen mixing in the shear layers within a SCRAMJET engine, we seek to gain insight into the effects of compressibility and variable density on free shear layers in the absence of combustion. We first consider a self-similar solution to the laminar, binary mixture (hydrogen/nitrogen), compressible boundary layer equations at various convective Mach numbers. Although the solution incorporates no turbulence effects, it is in qualitative agreement with experiments that show a transverse shift between velocity and density profiles. Using these profiles for an inflow boundary condition gives rise to regions of high density and concentration gradients that may not be coincident with regions of high velocity gradient. A dissipative, high-order finite-difference scheme is developed (RKLW-Rusanov, Kutler, Lomax, and Warming) to cope with these regions of high gradients while retaining computational stability. The RKLW scheme is third-order accurate in time and (2n)th order accurate in space for both viscous and inviscid terms. A family of explicit filters is also developed to enhance stability. For simulations where significant dissipation is not as important, a five-stage, fourth-order Runge-Kutta integrator has been developed that maximizes stability with typical spatial derivative operators and minimizes storage requirements.; Two-dimensional simulations are considered using both the similarity inflow profiles and the (3-6T) RKLW scheme, producing a number of new results. Vorticity and dilatation are both affected by the presence of density gradients. Large-scale vorticity is suppressed by compressibility and density gradients act to accentuate vorticity in the braid region while generating a large reverse vorticity region at the species interface. Dilatation is characterized by a "quadrupole" type pattern surrounding the large vortical structures. Density-gradient effects may be seen to create a striated dilatation structure. Through the use of the transport equations for both the vorticity and dilatation, various specific terms giving rise to the respective flowfields are identified.