A Study Of The Lagrangian PDF Method In A General Curvilinear Coordinate System And Its Application To Supersonic Combustion

The Lagrangian PDF method is capable of accurately solving turbulence/chemical reaction interactions and is expected to provide a reliable computational model for com-plex supersonic combustion simulations in scramjet engines.In this paper,a Lagrangian PDF method in general curvilinear coordinate systems is developed,and the PDF method is extended to practical scramjet configurations.It is also applied to the simulation of flow,mixing and combustion in the combustion chamber of scramjet engines.The Lagrangian PDF method in general curvilinear coordinate systems is developed.Starting from the PDF transport equation in Cartesian coordinates,a coordinate transfor-mation of the PDF position space is carried out to derive the PDF transport equation in the general curvilinear coordinate system.Particle stochastic differential equations in curvilinear coordinates are then obtained based on a system of probabilistic equivalence.Particle interpolation and estimation methods based on curvilinear coordinates are devel-oped to achieve coupled solutions for the large eddy simulation and the PDF method,and the accuracy of the mathematical equations and numerical methods is verified in the Sod tube problem.A particle tracking method in curvilinear coordinates under a multi-block structural grid is established.A coordinate conversion method of particle position and velocity be-tween multi-block partitions is proposed,and the topological information of the partitions is used for particle local coordinate conversion and communication,which solves the problem of inconsistency between local and global coordinates of particles in curvilinear coordinates and successfully achieves continuous tracking of particles in the global grid.The particle velocity correction is carried out at the partition boundary to solve the problem that the particle cannot traverse the combination point of multiple partitions.The ability of the PDF method to handle complex topology is further verified in a three-dimensional blunt case.The applicability and accuracy of the Lagrangian PDF method for compressible flows is verified in the scalar mixing problem.In the two-dimensional temporal mixing layer,the PDF method calculates significantly better statistical moments for both scalar and temperature than the conventional large eddy simulation method.And it also gives subgrid fluctuation distributions that are in good agreement with direct numerical simula-tions.In the three-dimensional spatial mixing layer,the fluctuation distribution calculated by the Lagrangian PDF method agrees well with the experimental results,indicating that the Lagrangian PDF method captures the small-scale mixing process in the supersonic flow better than the conventional large eddy simulation method method,which overesti-mates the peak mixing fraction fluctuation by about 45%.The Lagrangian PDF method is applied to the simulation of the auto-ignition prob-lem in supersonic flows.In the reacting mixing layer,the free radical predicted by PDF method is obviously better than that of well-stirred reactor model.The PDF method sim-ulates the scalar fluctuations in the subgrid through the random fluctuations of particles,promotes the mixing of fuel and oxidant in the subgrid scale,and simulating the auto-ignition process more accurately.The simulation of supersonic lifted jet flames is carried out and quantitatively compared with experimental results.The results show that in the fully developed turbulent combustion zone the PDF method gives more accurate predic-tions than the assumed PDF model.The PDF simulations of typical supersonic struct combustion problems are carried out to verify the accuracy of the curvilinear coordinate PDF method in real supersonic combustion problems.Comparison of the combustion models showed that the near-field temperatures predicted by the PDF method are essentially comparable to experimental re-sults,while the well-stirred reactor model significantly underestimated the near-field heat release,predicting temperatures 50% lower than experiment.The scalar dissipation rate of the subgrid part of the combustion chamber far exceeds that of the resolved part,and the well-stirred reactor directly ignores the subgrid scalar dissipation,thus significantly underestimating the mixing and combustion in the near-field zone.The stochastic fluctu-ations of particles in the Lagrangian PDF method promotes mixing and combustion in the near-field zone.The problem of inadequate prediction of near-field heat release in con-ventional combustion models is well addressed.The advantages of the stochastic method are demonstrated.