| Turbulent mixing layers exhibit striking compressibility effects. In particular, at modest Mach numbers, the growth rate of compressible mixing layers is significantly reduced from that of incompressible mixing layers. In this research, the relationship of this growth rate reduction to the commonly observed large-scale structures in the mixing layer is investigated. This goal is accomplished by performing direct numerical simulations of compressible time-developing mixing layers. Two fields from the fully developed incompressible mixing-layer simulations of Rogers and Moser are used to construct initial conditions, one from the natural (unforced) simulation and one from the ‘strongly forced’ simulation, which has much more prominent two-dimensional mixing-layer structures. Cases were run at convective Mach numbers of 0.4, 0.8, and 1.2.; It is found that significant compressible growth rate reductions occur only in the cases in which two-dimensional flow structures are prevalent. Flow visualization reveals that large spanwise vortices are stretched and pairing is suppressed, leading to a reduction in mixing layer growth. Structural change of large-scale structures induces a decrease in cross-stream velocity fluctuations, Reynolds shear stress, and magnitude of pressure fluctuations, consistent with the growth suppression mechanism proposed by Vreman et al. and Freund et al.; Direct numerical simulations of turbulent flows require numerical schemes with high resolution and grid flexibility. Resolution properties of B-spline and compact finite-difference schemes are evaluated using Fourier analysis in periodic domains, and tests based on solution of the wave and heat equations in finite domains, with uniform and non-uniform grids. Results show that compact finite-difference schemes have a higher convergence rate and in some cases better resolution on uniform grids. However, B-spline schemes have more consistent behavior on non-uniform grids, and a more straightforward and robust formulation. |
