Numerical study of combustion effects on the development of supersonic turbulent mixing layer flows with WENO schemes

This paper mainly investigates the combustion effects on the development of supersonic turbulent mixing layer flows. Firstly, the positivity-preserving limiter proposed by Hu et al. is extended to solve the unphysical negative species mass fraction problem of traditional WENO schemes for the first time. Then, the large eddy simulation (LES)of the supersonic turbulent mixing layer flow with convective Mach number being 0.61 under the inert and combustion conditions are conducted separately to investigate the combustion effects. The LES is conducted with the extending fifth-order positivity-preserving WENO scheme and great efforts are spent to reproduce the real flow situation by adopting the three dimensional space-developing method with detailed chemical reaction mechanism. The following conclusions are drawn. It is found that the combustion will obviously change the flow structures. The kinetic energy spectra are nearly not affected by the combustion effects but the temperature fluctuations are strengthened among all the resolved scales. The decreasing mechanism of mixing layer growth rate due to combustion heat release effects is found. The combustion heat release effects decrease the production of Reynolds stress. Then the Reynolds stress is decreased, which is mainly a mean density effect. Finally, the growth rate is decreased according to the positive correlation between the growth rate and the Reynolds stress. Moreover, the old momentum thickness definition is no longer appropriate and a new one is introduced specifically for the space-developing LES. The relation between the growth rate and Reynolds stress originally deducted under the time-developing frame is also found to be valid under the space-developing frame.