Resolving the shock-induced combustion by an adaptive mesh redistribution method

An adaptive mesh method is presented for numerical simulation of shock-induced combustion. The method is composed of two independent ingredients: a flow solver and a mesh redistribution algorithm. The flow solver is a finite-volume based second-order upwind TVD scheme, together with a lower-upper symmetric Gauss-Seidel relaxation scheme for solving the multispecies Navier-Stokes equations with finite rate chemistry. The adaptive mesh is determined by a grid generation method based on solving Poisson equations, with the monitor function carefully designed to resolve both sharp fronts and the induction zone between them. Numerically it is found that the resolution of the induction zone is particularly critical to the combustion problems, and an under-resolved numerical method may cause excessive energy release and spurious runaway reactions. The monitor function proposed in this paper, which is based on the relative rate of change of mass fraction, covered this issue satisfactorily. Numerical simulations of supersonic flows past an axisymmetric projectile in a premixed hydrogen/oxygen (or air) mixture are carried out. The results show that the spurious runaway chemical reactions appearing on coarse grids can be eliminated by using adaptive meshes without invoking any ad hoc treatment for reaction rates. The adaptive mesh approach is more effective than the fixed mesh one in obtaining grid-independent results. Finally, discrepancies between the numerical and benchmark experimental results and difficulties in simulating the detonation waves are delineated which appeal for further investigation.

[1]  Marcel Vinokur.  Flux Jacobian matrices and generaled Roe average for an equilibrium real gas , 1988 .

[2]  S. Osher,et al.  Spatially adaptive techniques for level set methods and incompressible flow , 2006 .

[3]  R. LeVeque,et al.  Adaptive Mesh Refinement Using Wave-Propagation Algorithms for Hyperbolic Systems , 1998 .

[4]  Kozo Fujii,et al.  Flow features of shock-induced combustion around projectile traveling at hypervelocities , 1993 .

[5]  Ralf Deiterding,et al.  Parallel adaptive simulation of multi-dimensional detonation structures , 2003 .

[6]  Robert D. Russell,et al.  Anr-Adaptive Finite Element Method Based upon Moving Mesh PDEs , 1999 .

[7]  Paul A. Zegeling,et al.  On Resistive MHD Models with Adaptive Moving Meshes , 2005, J. Sci. Comput..

[8]  Pingwen Zhang,et al.  An adaptive mesh redistribution method for nonlinear Hamilton--Jacobi equations in two-and three-dimensions , 2003 .

[9]  Joseph E. Shepherd,et al.  Detonation Waves and Propulsion , 1994 .

[10]  Tao Tang,et al.  Second-order Godunov-type scheme for reactive flow calculations on moving meshes , 2005 .

[11]  Robert J. Kee,et al.  CHEMKIN-III: A FORTRAN chemical kinetics package for the analysis of gas-phase chemical and plasma kinetics , 1996 .

[12]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

[13]  Elaine S. Oran,et al.  Numerical Simulation of Reactive Flow , 1987 .

[14]  H. Lehr,et al.  Experiments on Shock-Induced Combustion , 1972 .

[15]  C. J. Jachimowski,et al.  An analytical study of the hydrogen-air reaction mechanism with application to scramjet combustion , 1988 .

[16]  P. Colella,et al.  Theoretical and numerical structure for reacting shock waves , 1986 .

[17]  V. Cristini,et al.  Adaptive unstructured volume remeshing - II: Application to two- and three-dimensional level-set simulations of multiphase flow , 2005 .

[18]  Pingwen Zhang,et al.  Moving mesh methods in multiple dimensions based on harmonic maps , 2001 .

[19]  Adam P. Bruckner,et al.  Numerical simulation of hypervelocity projectiles in detonable gases , 1991 .

[20]  Richard A. Thompson,et al.  A review of reaction rates and thermodynamic and transport properties for the 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K , 1989 .

[21]  George Beckett,et al.  An r-adaptive finite element method for the solution of the two-dimensional phase-field equations , 2006 .

[22]  Pingwen Zhang,et al.  A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions , 2002 .

[23]  J. Mcvey,et al.  Mechanism of Instabilities of Exothermic Hypersonic Blunt-Body Flows , 1971 .

[24]  Seokkwan Yoon,et al.  Numerical study of chemically reacting flows using a lower-upper symmetric successive overrelaxation scheme , 1989 .

[25]  Wei Shyy,et al.  Combustion and Turbulence Effects in Hypersonic Projectile Flows , 1997 .

[26]  Dale A. Anderson.  Equidistribution schemes, poisson generators, and adaptive grids , 1987 .

[27]  T. Poinsot,et al.  Theoretical and numerical combustion , 2001 .

[28]  Barna L. Bihari,et al.  Multiresolution Schemes for the Reactive Euler Equations , 1999 .

[29]  Samuel Paolucci,et al.  Viscous detonation in H2‒O2‒Ar using intrinsic low-dimensional manifolds and wavelet adaptive multilevel representation , 2001 .

[30]  Vladimir D. Liseikin,et al.  Grid Generation Methods , 1999 .

[31]  H. C. Yee,et al.  A class of high resolution explicit and implicit shock-capturing methods , 1989 .

[32]  C. J. Schexnayder,et al.  Influence of Chemical Kinetics and Unmixedness on Burning in Supersonic Hydrogen Flames , 1980 .

[33]  Francis A. Greene,et al.  Viscous equilibrium computations using program LAURA , 1991 .

[34]  Tao Tang,et al.  Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws , 2003, SIAM J. Numer. Anal..

[35]  K. Fujii,et al.  Flow features of shock-induced combustion around projectile traveling at hypervelocities , 1993 .

[36]  E. Oran,et al.  Reaction-zone structure of a steady-state detonation wave in a cylindrical charge☆ , 1997 .

[37]  Thomas L. Jackson,et al.  Combustion in high-speed flows , 1994 .

[38]  Weizhang Huang,et al.  An error indicator monitor function for an r -adaptive finite-element method , 2001 .