Joint SGS Velocity-scalar Filtered Mass Density Function Of Compressible Turbulent Reacting Flows

The transported probability density function（TPDF）method has the advantage of closing chemical reaction source terms and has been successfully applied in many laboratory-scale flames involving complex turbulence/chemistry interaction.As a turbulent combustion model,the scalar filtered mass density function（SFMDF）method lacks the information of velocity.Therefore,the sub grid scale（SGS）scalar fluxes is usually modeled by the hypothesis of gradient diffusion.However,in recent years,the phenomenon of counter gradient transport（CGT）,which is contrary to common sense but has been found in engineering practice and DNS calculation,poses great challenges to the logical completeness and applicability of current turbulence models and turbulent combustion models.Counter gradient transport widely exists in turbulent combustion process and has been recognized as a consensus.Especially in the high-speed reaction flow,the combustion mode is complex and the flow field gradient is large.In this case,counter gradient transport may dominate some regions and have a profound influence on the overall combustion flow field.Aiming at the problem of closing SGS scalar fluxes,the joint SGS velocity-scalar filtered mass density function(V_SGSSFMDF)method is explored and developed in this dissertation.The transported equation of SGS velocity is also modeled by simply Langevin model（SLM）.But it is necessary to emphasize that the turbulence information required by SLM is derived from the SGS velocity field of particle evolution.In a compressible 2D mixing layer with an initial convective Mach number of 0.4,the properties of SGS velocity are studied using the data of DNS simulation.It is found that this physical quantity is greatly affected by the filter scale.At the same time,both theoretical and numerical experiments show that the updating equation of the modeled SGS velocity is not stable.And inaccurate initial value and modeling can easily lead to divergence of the calculation of the SGS velocity.By ignoring the random term in the SGS velocity equation,the V_SGSSFMDF method achieves a better agreement with the DNS data.And the SGS scalar flux modeled by this method is more accurate than that of the traditional gradient diffusion model.To quantitatively verify and analyze the performance of the new method,a 2D hydrogen/air reaction temporal development mixing layer and a 3D cold flow mixing layer are selected for simulation.The results of reaction cases are compared with DNS and LES,and it is found that the average results of hydroxyl component fraction,product component fraction and temperature are in good agreement with DNS.In addition,an obvious counter gradient transport phenomenon is found in the mixing layer ofM_c=0.8.The V_SGSSFMDF method embodies the advantages of the scalar PDF method and has better modeling of the SGS scalar flux term in the reaction flow,while the relative gradient diffusion model is completely invalid in the counter gradient phenomenon.In the case of 3D mixing layer,this method has no obvious errors and still shows obvious advantages compared with LES.Moreover,compared with the traditional SFMDF method,the V_SGSSFMDF method does not bring a significant increase in the amount of computing resources,so it has great potential in the application of compressible turbulent combustion problems.