Lagrangian transported MDF methods for compressible high speed flows

This paper deals with the application of thermochemical Lagrangian MDF (mass density function) methods for compressible sub- and supersonic RANS (Reynolds Averaged NavierStokes) simulations. A new approach to treat molecular transport is presented. This technique on the one hand ensures numerical stability of the particle solver in laminar regions of the flow field (e.g. in the viscous sublayer) and on the other hand takes differential diffusion into account. It is shown in a detailed analysis, that the new method correctly predicts first and second-order moments on the basis of conventional modeling approaches. Moreover, a number of challenges for MDF particle methods in high speed flows is discussed, e.g. high cell aspect ratio grids close to solid walls, wall heat transfer, shock resolution, and problems from statistical noise which may cause artificial shock systems in supersonic flows. A Mach 2 supersonic mixing channel with multiple shock reflection and a model rocket combustor simulation demonstrate the eligibility of this technique to practical applications. Both test cases are simulated successfully for the first time with a hybrid finite-volume (FV)/Lagrangian particle solver (PS).

[1]  Sunil James,et al.  Lagrangian PDF Transport Method for Simulations of Axisymmetric Turbulent Reacting Flows , 2005 .

[2]  Andrew T. Hsu,et al.  A study of hydrogen diffusion flames using PDF turbulence model , 1991 .

[3]  Budugur Lakshminarayana,et al.  Stability of explicit navier-stokes procedures using k-ε and k - ε/algebraic reynolds stress turbulence models , 1992 .

[4]  T. J. Coakley,et al.  TURBULENCE MODELING FOR HIGH SPEED FLOWS , 1992 .

[5]  James C. McDaniel,et al.  Transverse injection into Mach 2 flow behind a rearward-facing step - A 3-D, compressible flow test case for hypersonic combustor CFD validation , 1991 .

[6]  Jean-Pierre Minier,et al.  Stochastic modelling of conjugate heat transfer in near-wall turbulence , 2006 .

[7]  Zhaorui Li,et al.  Large-Eddy Simulations of Compressible Turbulent Reacting Flows , 2010 .

[8]  Peter Gerlinger.  Numerische Verbrennungssimulation : effiziente numerische Simulation turbulenter Verbrennung , 2005 .

[9]  S. Osher,et al.  Weighted essentially non-oscillatory schemes , 1994 .

[10]  D. Brüggemann,et al.  An implicit multigrid method for turbulent combustion , 2001 .

[11]  D. Brüggemann,et al.  Comparison of Eulerian and Lagrangian Monte Carlo PDF methods for turbulent diffusion flames , 2001 .

[12]  J. Shuen,et al.  Upwind differencing and LU factorization for chemical non-equilibrium Navier-Stokes equations , 1992 .

[13]  M. S. Raju,et al.  PDF approach for compressible turbulent reacting flows , 1993 .

[14]  Stephen B. Pope,et al.  Calculations of subsonic and supersonic turbulent reacting mixing layers using probability density function methods , 1998 .

[15]  Sharath S. Girimaji,et al.  Modeling turbulent/chemistry interactions using assumed pdf methods , 1992 .

[16]  Haifeng Wang,et al.  Numerical implementation of mixing and molecular transport in LES/PDF studies of turbulent reacting flows , 2011, J. Comput. Phys..

[17]  Peter Gerlinger,et al.  Influence of spatial discretization and unsteadiness on the simulation of rocket combustors , 2015 .

[18]  D. Haworth,et al.  Probability density function approach for multidimensional turbulentflow calculations with application to in-cylinder flows in reciprocating engines , 1991 .

[19]  Wolfgang Kollmann,et al.  Pdf prediction of supersonic hydrogen flames , 1993 .

[20]  Stephen B. Pope,et al.  Local Time-Stepping Algorithm for Solving Probability Density Function Turbulence Model Equations , 2002 .

[21]  Stephen B. Pope,et al.  EPVS-FMDF for les of high-speed turbulent flows , 2012 .

[22]  Dieter Brüggemann,et al.  Multigrid Convergence Acceleration for Turbulent Supersonic Flows , 1997 .

[23]  Peyman Givi,et al.  Scalar-Filtered Mass-Density-Function Simulation of Swirling Reacting Flows on Unstructured Grids , 2012 .

[24]  Antony Jameson,et al.  Lower-upper implicit schemes with multiple grids for the Euler equations , 1987 .

[25]  Stephen B. Pope,et al.  TURBULENT PREMIXED FLAMES , 1987 .

[26]  S. Pope.  The probability approach to the modelling of turbulent reacting flows , 1976 .

[27]  Stephen B. Pope,et al.  A particle formulation for treating differential diffusion in filtered density function methods , 2006, J. Comput. Phys..

[28]  Manfred Aigner,et al.  Modeling of heat transfer and differential diffusion in transported PDF methods , 2014 .

[29]  Dieter Brüggemann,et al.  Scalar and joint scalar-velocity-frequency Monte Carlo PDF simulation of supersonic combustion , 2003 .

[30]  A. Leonard,et al.  Applications of a coupled Monte Carlo PDF/finite volume CFD method for turbulent combustion , 1994 .

[31]  Stephen B. Pope,et al.  A Monte Carlo Method for the PDF Equations of Turbulent Reactive Flow , 1981 .

[32]  Stephen B. Pope,et al.  Application of PDF methods to compressible turbulent flows , 1997 .

[33]  M. Aigner,et al.  Influence of reaction mechanisms, grid spacing, and inflow conditions on the numerical simulation of lifted supersonic flames , 2009 .

[34]  J. Heimerl,et al.  A comparison of transport algorithms for premixed, laminar steady state flames , 1980 .

[35]  Daniel C. Haworth,et al.  A general mass consistency algorithm for hybrid particle/finite-volume PDF methods , 2004 .

[36]  P. Spalart,et al.  A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities , 2008 .

[37]  Stephen B. Pope,et al.  Filtered mass density function for large-eddy simulation of turbulent reacting flows , 1999, Journal of Fluid Mechanics.

[38]  Peter Gerlinger,et al.  Multi-dimensional limiting for high-order schemes including turbulence and combustion , 2012, J. Comput. Phys..

[39]  Stephen B. Pope,et al.  Turbulent dispersion from line sources in grid turbulence , 2008 .

[40]  P. Spalart,et al.  A New Version of Detached-eddy Simulation, Resistant to Ambiguous Grid Densities , 2006 .

[41]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[42]  Meng-Sing Liou,et al.  A sequel to AUSM, Part II: AUSM+-up for all speeds , 2006, J. Comput. Phys..

[43]  K. Kuo.  Principles of combustion , 1986 .

[44]  E. Turkel,et al.  An effective multigrid method for high-speed flows , 1992 .

[45]  P. Stoll,et al.  An Implicit Multigrid Method for the Simulation of Chemically Reacting Flows , 1998 .

[46]  Rodney O. Fox,et al.  Computational Models for Turbulent Reacting Flows: PDF methods for turbulent reacting flows , 2003 .

[47]  Roger Woodward,et al.  Benchmark Wall Heat Flux Data for a GO2/GH2 Single Element Combustor , 2005 .

[48]  Peter Gerlinger,et al.  High-Order Multi-Dimensional Limiting for Turbulent Flows and Combustion , 2011 .

[49]  P. Gerlinger,et al.  Numerical Investigation of Hydrogen Strut Injections into Supersonic Airflows , 2000 .

[50]  Zhaorui Li,et al.  Compressible Scalar Filtered Mass Density Function Model for High-Speed Turbulent Flows , 2011 .

[51]  M. Liou.  A Sequel to AUSM , 1996 .

[52]  S. Pope.  PDF methods for turbulent reactive flows , 1985 .

[53]  A. T. Hsu,et al.  Probability density function approach for compressible turbulent reacting flows , 1994 .

[54]  Asghar Afshari,et al.  Large-eddy simulations of turbulent flows in internal combustion engines , 2013 .

[55]  S. Pope,et al.  Time-averaging strategies in the finite-volume/particle hybrid algorithm for the joint PDF equation of turbulent reactive flows , 2008 .

[56]  S. M. Correa,et al.  Joint PDF calculations of a non-equilibrium turbulent diffusion flame , 1988 .

[57]  Chongam Kim,et al.  Multi-dimensional limiting process for three-dimensional flow physics analyses , 2008, J. Comput. Phys..

[58]  Eli Turkel,et al.  Effect of artificial viscosity on three-dimensional flow solutions , 1990 .

[59]  Peter Gerlinger,et al.  Monte Carlo pdf simulation of compressible turbulent diffusion flames using detailed chemical kinetics , 1999 .

[60]  H H Fernholz,et al.  A Critical Compilation of Compressible Turbulent Boundary Layer Data , 1977 .