| Summary: | The filtered mass density function (FMDF) model has been employed for large-eddy simulations (LES) of compressible high-speed turbulent mixing and reacting flows. However, the mixing model remains a pressing challenge for FMDF methods, especially for compressible reactive flows. In this work, a temporal development mixing layer with two different convective Mach numbers, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">M</mi><mi mathvariant="normal">c</mi></msub><mrow><mo>=</mo><mn>0.4</mn></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="normal">M</mi><mi mathvariant="normal">c</mi></msub><mrow><mo>=</mo><mn>0.8</mn></mrow></mrow></semantics></math></inline-formula>, is used to investigate the mixing models. A simplified one-step reaction and a real hydrogen/air reaction are employed to study the mixing and turbulence-chemistry interaction. Two widely used mixing models, interaction by exchange with the mean (IEM) and Euclidean minimum spanning tree (EMST), are studied. Numerical results indicate that no difference is observed between the IEM and EMST models in simple reaction flows. However, for hydrogen/air reactions, the EMST model can predict the reaction more accurately in high-speed flow. For mixing models in compressible reactive flows, the requirement of localness preservation tends to be more essential as the convective Mach number increases. With the increase of compressibility, the sensitivity of the mixing model coefficient is reduced significantly. Therefore, the appropriate mixing model coefficient has a wider range. Results also indicate that a large error may result when using a fixed mixing model coefficient in compressible flows.
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