In traditional non-premixed flamelet/progress variable model, the progress variable C is introduced to replace the scalar dissipation rate χ so that, together with the mixture fraction Z, unique flamelet solutions can be determined by the value of (Z, C) along the S-curve in the flamelet solution space. However, χ can be identified as one of the most important parameters in non-premixed combustion since its mean value represents the rate of molecular scalar mixing and its fluctuation can directly influence the variance of Z. Therefore, χ should be kept as a control parameter in the flamelet model in order to correctly account for the compressive strain effects in high speed combustion. Recently, an interpolation-based progress variable implementation procedure was introduced so that (Z,χ) is still used to obtain the multiple flamelet solutions on each of the three branches of the S-curve and the unique flamelet solution is then obtained by an interpolation procedure based on C. In this study, various progress variable implementation procedures are presented and compared for supersonic combustion simulations in a scramjet model.
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