Perturbation and initial Reynolds number effects on transition attainment of supercritical, binary, temporal mixing layers

Abstract

Two- and three-dimensional (2D and 3D) numerical simulations are performed for a heptane/nitrogen (thermodynamically) supercritical mixing layer initially perturbed at different wavelengths, including the most unstable incompressible wavelength. Simulations are performed with spanwise (and streamwise, for 3D) perturbations available in the literature (for direct numerical simulations of turbulent flow) superimposed on the mean flow, and the domain length is four times the perturbation wavelength. The 2D simulations are undertaken to ascertain that perturbations having the shortest unstable wavelength obtained from a linear inviscid stability analysis are unstable for the viscous non-linear flow. For 3D layers, the purpose of the perturbations is to accelerate the growth of the layer in order to attain transitional Reynolds numbers, as well as to generate structures similar to those that have been observed in spatial mixing layers. The goal of the 3D simulations is to ascertain whether perturbing the mixing layer at different wavelengths, in contrast to the most unstable incompressible wavelength as had previously been done, will affect the transition to turbulence. In particular, we inquire whether perturbing the layer at smaller wavelengths, which requires a smaller domain, will reduce the computational time. It is found that transition can be obtained at different perturbation wavelengths, provided that they are longer than the shortest unstable wavelength as determined by the 2D linear inviscid stability analysis, and provided that the initial Reynolds number is proportionally increased as the wavelength is decreased. The transitional states thus obtained display different dynamic and mixture characteristics, and show strong departures from perfect gas, ideal mixtures. The smaller wavelength perturbations were found to have similar computational requirements for transition attainment.