Theoretical analysis of flamelet model for supersonic turbulent combustion

Being physically intuitionistic and computationally efficient, the flamelet model has obtained increasing attention and becomes popular in numerical simulations of supersonic combustion. However, the flamelet model was firstly built for simulations of the low-speed flows. Therefore it is still unclear whether the assumption of the flamelet model is reasonable in supersonic combustion. This paper tries to identify the existence of the flamelet mode in supersonic combustion. Firstly, the interaction of the turbulent fluctuation and the flame is discussed, based on which the combustion regime is distinguished. Then the characteristic length scale of the turbulent flows and the combustion inside the scramjet combustor are calculated and compared, which are used to identify whether the assumption of the flamelet model is reasonable in supersonic flows. The results show that for premixed combustion, due to the low fluctuation velocity in the recirculation zone and the shear layer, the assumption of the flamelet model is established for all the flight Mach numbers, while for non-premixed combustion the assumption is also established for most of the flight Mach numbers except for very high Mach number under which the slow reaction mode dominates the combustion. In order to quantitatively examine the combustion mode, numerical calculations are performed to simulate the strut-injection supersonic combustion which has been experimentally investigated in German Aerospace Center. The results show that the supersonic combustion occurs in the fully-developed turbulent regions and the assumption of the flamelet model is established in the whole flow field.