Examine the effect of temperature fluctuation on supersonic combustion by assumed pdf approach

An assumed probability density function (PDF) approach, developed by Girimaji and Baurle, was adopted for modeling supersonic combustion. A clipped Gauss function was used to account for turbulence-reacting interaction, which demonstrated that reaction rate constant was amplified or decreased variously by turbulence. Temperature variance was modeled from entropy variance transport equation conjugated with Wilcox's k-ω turbulent model. The approach was applied to a supersonic, co-axial H₂/air burner experiment conducted by Cheng et al. The result of the model using simplified kinetics showed improvement in predicting of turbulence effects on the initiating step which was of first-order importance because of small residence time in supersonic fluid field. Comparison was made indicating a serious problem in estimation of average rate constant using a Reynold decomposition method. A set of numerical tests showed average reaction rate constant was greatly modified by temperature fluctuation and changed the time delay of ignition sufficiently.