Visualization of compressibility effects on large-scale structures in compressible mixing layers

Vorticity, x; velocity divergence, r u ~; and the magnitude of pressure gradient, rp j j are visualized in a same flow domain, to reveal large-scale, dilatation and shocklet structures in a compressible mixing layer from direct numerical simulation results. We simulated 2-dimensional (2-D) and 3-dimensional (3-D) compressible mixing layers with a third-order Discontinuous Galerkin method (Cockburn and Shu 1998) and a third order explicit Runge–Kutta time advancement scheme. The grid numbers are 5:04 10 for 2-D cases, and 4:6 10 for 3-D case. The resulting variants are normalized with the density q; the speed of sound a and qa of the free streams. A perturbation signal with a broadband spectrum and a peak at the most unstable frequency in incompressible case, in conjunction with a hyperbolic tangent mean velocity profile are imposed Fig. 1 Vorticity, x; velocity divergence, r u ~; and the magnitude of pressure gradient, rp j j; from DNS of 2-D compressible mixing layers. The mixing layer convects from left to right. The higher speed stream is at the upper portion of the flow field, and the lower speed stream is at the lower side of the flow field. x is plotted by contour, the colors of which represent velocity divergence. Pressure waves are identified by rp j j with blue contours. a Mc = 0.4. The contour levels for x range from -1.24 to 0.01 with 30 levels. The color levels for r u ~range from -0.001 to 0.001. b Mc = 0.8. The contour levels of x range from -1.24 to 0.01 with 30 levels. The color levels for r u ~ range from -0.005 to 0.005. The boundary for rp j j is determined by 0.1