Computational Fluid Dynamics Algorithms for Unsteady Shock-Induced Combustion, Part 1: Validation

Acomputational study is carried out to develop a fully implicit and time-accuratecomputational e uid dynamics code for the analysis of reactive e ow systems. Periodically oscillating shock-induced combustion around a blunt body in a stoichiometric hydrogen ‐air mixture is used as a validation problem of examining various numerical considerations. Euler equations and species conservation equations are used as the governing equations for the chemically reacting e ow. Spatial discretization of the governing equation is based on Roe’ s approximate Riemann solver with a MUSCL-type total variation diminishing scheme for higher-order spatial resolution. The secondorder-accuratetimeintegrationmethodisbasedonalower ‐uppersymmetricGauss ‐Seidelscheme,usingaNewton subiteration method and Steger ‐Warming e ux Jacobian splitting. As a e rst step of the validation procedure, simulations of experimental results were carried out to cone rm the reliability of the baseline method. In the next step, the general aspects of the baseline method were examined, including order of time integration, number of subiterations, and use of approximate e ux Jacobian splitting. Appropriateness of the grid system is also examined by using a grid ree nement study.

[1]  Meng-Sing Liou,et al.  Integration of Navier-Stokes Equations Using Dual Time Stepping and a Multigrid Method , 1995 .

[2]  A. Hertzberg,et al.  Ram accelerator - A new chemical method for accelerating projectilesto ultrahigh velocities , 1988 .

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

[4]  T. Toong.  Combustion dynamics : the dynamics of chemically reacting fluids , 1983 .

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

[6]  W. K. Anderson,et al.  Comparison of Finite Volume Flux Vector Splittings for the Euler Equations , 1985 .

[7]  C. Hirsch,et al.  Numerical Computation of Internal and External Flows. By C. HIRSCH. Wiley. Vol. 1, Fundamentals of Numerical Discretization. 1988. 515 pp. £60. Vol. 2, Computational Methods for Inviscid and Viscous Flows. 1990, 691 pp. £65. , 1991, Journal of Fluid Mechanics.

[8]  In-Seuck Jeung,et al.  Numerical study of scram accelerator starting characteristics , 1998 .

[9]  Gregory J. Wilson,et al.  Computation of unsteady shock-induced combustion using logarithmic species conservation equations , 1993 .

[10]  H. C. Yee,et al.  Hypersonic Blunt Body Computations Including Real Gas Effects , 1989 .

[11]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

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

[13]  Soogab Lee,et al.  Dimensional analysis of the effect of flow conditions on shock-induced combustion , 1996 .

[14]  Shaye Yungster,et al.  A fully implicit time accurate method for hypersonic combustion - Application to shock-induced combustion instability , 1994 .

[15]  P. Roe.  Approximate Riemann Solvers, Parameter Vectors, and Difference Schemes , 1997 .

[16]  Akiko Matsuo,et al.  Numerical simulation of shock-induced combustion around an axisymmetric blunt body , 1991 .

[17]  S. Obayashi,et al.  Numerical solutions of forward-flight rotor flow using an upwind method , 1989 .

[18]  H. C. Yee,et al.  Semi-implicit and fully implicit shock-capturing methods for nonequilibrium flows , 1989 .

[19]  K Ravi,et al.  Some aspects of high-speed blunt body flow computations with Roe scheme , 1995 .

[20]  Seong-Lyong Kim,et al.  Application of approximate chemical Jacobians for constant volume reaction and shock-induced combustion , 2001 .

[21]  Earll M. Murman,et al.  Finite volume method for the calculation of compressible chemically reacting flows , 1985 .

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

[23]  Bernard Grossman,et al.  Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation , 1990 .