Direct numerical simulation of a compressible transitional mixing layer with combustion chemical reactions

A fifth-order upwind/sixth-order symmetriccompact hybrid difference scheme coupled with a third-order explicitRunge-Kutta time-marching method is used as a direct numerical simulationalgorithm to investigate a three-dimensional temporally-developingcompressible plane free shear mixing layer with H_2/O_2 non-premixedcombustion. The reacting mixing layer with product formation and energyrelease is perturbed by a pair of conjugate oblique waves, and henceexperiences an instable transitional evolution. At the beginning oftransition, some well-known large scale coherent structures, such as\it\Lambda vortex and horseshoe vortex, are found, and a three-dimensionalparing phenomenon of two horseshoe vortices following flow instabilities isalso revealed. Furthermore, these large scale structures are approximatelysymmetric. At the last stage of the development of this flow, large scalestructures break down continuously, and small scale structures gradually getdominant. The reacting mixing layer finally behaves very similar toturbulence and shows clear asymmetry. On the analogy of the stability theoryfor incompressible boundary layer, the large scale structures obtained hereare due to a subharmonic secondary instability mechanism, which is wellknown as Herbert type secondary instability.