Numerical Simulation of a Strongly Spanwise Modulated Wavetrain in a Compressible Mixing Layer

Abstract

Mixing layers are present in very different types of physical situations such as atmospheric flows, aerodynamics and combustion. In the current work, the temporal instability of two- and three-dimensional disturbances in the compressible mixing layer was investigated. Simulations of the Navier-Stokes equations were performed where the derivatives were discretized using a high-order compact finite-difference schemes. The time integration was performed by a fourth-order Runge-Kutta scheme. At the last step of the integration scheme, a numerical filter was applied to remove short length scales in all directions. Besides, a stretching in the normal direction was implemented with the objective of attenuating the sound waves generated by the shear region and improving the resolution near the center in the normal direction. Inspired on the work devoted to modulated waves, the current work investigates the evolution of spanwise modulated wavetrains. Modulation is often considered an important ingredient of waves in piratical circumstances. The numerical investigation starts with an analysis of the growth rate in linear regime to verify the numerical code. The results compared favorably with Linear Stability Theory. Tests were also performed in the nonlinear regime and it was possible to reproduce the vortex roll-up and pairing. Then the evolution of two-dimensional spanwise vortices subject to a flat spectrum of small disturbances was studied. For low Mach numbers, it was found that, the most amplified spanwise wavenumber was 3/2 of that of the spanwise vortices. When strongly modulated spanwise vortices were tested, the resulting spanwise wavenumbers were much smaller, suggesting a very different behavior. The effect of the Mach number was also investigated.