Numerical simulations of high-speed chemically reacting flow

  • V. T. Ton
  • A. R. Karagozian
  • F. E. Marble
  • S. J. Osher
  • B. E. Engquist
Article

Abstract

The essentially nonoscillatory (ENO) shock-capturing scheme for the solution of hyperbolic equations is extended to solve a system of coupled conservation equations governing two-dimensional, time-dependent, compressible chemically reacing flow with full chemistry. The thermodynamic properties of the mixture are modeled accurately, and stiff kinetic terms are separated from the fluid motion by a fractional step algorithm. The methodology is used to study the concept of shock-induced mixing and combustion, a process by which the interaction of a shock wave with a jet of low-density hydrogen fuel enhances mixing through streamwise vorticity generation. Test cases with and without chemical reaction are explored here. Our results indicate that, in the temperature range examined, vorticity generation as well as the distribution of atomic species do not change significantly with the introduction of a chemical reaction and subsequent heat release. The actual diffusion of hydrogen is also relatively unaffected by the reaction process. This suggests that the fluid mechanics of this problem may be successfully decoupled from the combustion processes, and that computation of the mixing problem (without combustion chemistry) can elucidate much of the important physical features of the flow.

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References

  1. Abgrall, R. (1988). Generalization of the Roe Scheme for Computing Flows of Mixed Gases with Variable Concentrations. Rech. Aérospat. 6, 31–43.Google Scholar
  2. Ben-Artzi, M. (1989). The Generalized Riemann Problem for Reactive Flows. J. Comput. Phys., 81, 70–101.Google Scholar
  3. Boris, J.P. and Book, D.L. (1973). Flux Corrected Transport I. SHASTA, a Fluid Transport Algorithm that Works. J. Comput. Phys., 11, 38–69.Google Scholar
  4. Chargy, D., Abgrall, R., Fezoui, L., and Larrouturou, B. (1990). Comparisons of Several Numerical Schemes for Multi-Component One-Dimensional Flows. INRIA Report 1253.Google Scholar
  5. Colella, P., Majda, A., and Roytburd, V. (1986). Theoretical and Numerical Structure for Reacting Shock Waves. SIAM J. Sci. Statist. Comput., 7, 1059–1080.Google Scholar
  6. Drummond, J.P. (1991). Mixing Enhancement of Reacting Parallel Fuel Jets in a Supersonic Combustor. AIAA Paper No. 91-1914.Google Scholar
  7. Engquist, B., and Sjogreen, B. (1991). Robust Difference Approximations of Stiff Inviscid Detonation Waves. UCLA CAM Report 91-03.Google Scholar
  8. Haas, J.-F., and Sturtevant, B. (1988). Interaction of Weak Shock Waves with Cylindrical and Spherical Gas Inhomogeneities. J. Fluid Mech., 181, 41–76.Google Scholar
  9. Harten, A. (1983). High Resolution Schemes for Hyperbolic Conservation Laws. J. Comput. Phys., 49, 357–393.Google Scholar
  10. Harten, A., Osher, S.J., Engquist, B.E., and Chakravarthy, S.R. (1986). Some Results on Uniformly High-Order Accurate Essentially Nonoscillatory Schemes. J. Appl. Numer. Math., 2, 347–377.Google Scholar
  11. Jacobs, J.W. (1992). Shock-Induced Mixing of a Light-Gas Cylinder. J. Fluid Mech., 234, 629–649.Google Scholar
  12. Karagozian, A.R., and Marble, F.E. (1986). Study of a Diffusion Flame in a Stretched Vortex. Combust. Sci. Technol., 45, 65–84.Google Scholar
  13. Karni, S. (1992). Viscous Shock Profiles and Primitive Formulations. SIAM J. Numer. Anal., 29, 1592–1609.Google Scholar
  14. Kee, R.J., Miller, J.A., and Jefferson, T.H. (1986). CHEMKIN: A General-Purpose, Problem-Independent, Transportable Fortran Chemical Kinetics Code Package. Report SAND 80-8003, Sandia National Laboratories, Livermore, CA.Google Scholar
  15. Larrouturou, B. (1991). How To Preserve the Mass Fractions Positivity when Computing Compressible Multi-Component Flows. J. Comput. Phys., 95, 59–84.Google Scholar
  16. LeVeque, R.J., and Yee, H.C. (1990). A Study of Numerical Methods for Hyperbolic Conservation Laws with Stiff Source Terms. J. Comput. Phys., 86, 187–210.Google Scholar
  17. Mass, U., and Warnatz, J. (1988). Ignition Processes in Hydrogen-Oxygen Mixtures. Combust. Flame, 74, 53–69.Google Scholar
  18. Marble, F.E., Hendricks, G.J., and Zukoski, E.E. (1987). Progress Toward Shock Enhancement of Supersonic Combustion Processes. AIAA Paper No. 87-1880.Google Scholar
  19. Picone, J.M., and Boris, J.P. (1988). Vorticity Generation by Shock Propagation Through Bubbles in a Gas. J. Fluid Mech., 189, 23–51.Google Scholar
  20. Rudinger, G., and Somers, L.M. (1960). Behaviour of Small Regions of Different Gases Carried in Accelerated Gas Flows. J. Fluid Mech., 7, 161–176.Google Scholar
  21. Shu, C.W., and Osher, S.J. (1989). Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes, II. J. Comput. Phys., 83, 32–78.Google Scholar
  22. Stull, D.R., and Prophet, H. (1971). JANNAF Thermochemical Tables. National Standard Reference Data Series, U.S. National Bureau of Standards, Vol. 37.Google Scholar
  23. Ton, V.T. (1993). A Numerical Method for Mixing/Chemically Reacting Compressible Flow with Finite Rate Chemistry. Ph.D. Thesis, University of California, Los Angeles.Google Scholar
  24. Ton, V.T., Karagozian, A.R., Engquist, B.E., and Osher, S.J. (1991). Numerical Simulation of Inviscid Detonation Waves with Finite Rate Chemistry. Western States Section/The Combustion Institute Fall Meeting, paper 91–101.Google Scholar
  25. Van Leer, B. (1974). Towards the Ultimate Conservative Difference Scheme. II. Monotonicity and Conservation Combined in a Second Order Scheme. J. Comput. Phys., 14, 361–370.Google Scholar
  26. Woodward, P. (1985). Simulation of the Kelvin-Helmholtz Instability of a Supersonic Slip Surface with the Piecewise-Parabolic Method (PPM). In Numerical Methods for the Euler Equations of Fluid Dynamics, edited by F. Angrand, A. Drvieux, J.A. Desideri, and R. Glowinski, SIAM, Philadelphia, PA.Google Scholar
  27. Yang, J. (1991). An Analytical and Computational Investigation of Shock-Induced Vortical Flows with Applications to Supersonic Combustion. Ph.D. Thesis, California Institute of Technology.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • V. T. Ton
    • 1
  • A. R. Karagozian
    • 1
  • F. E. Marble
    • 1
  • S. J. Osher
    • 2
  • B. E. Engquist
    • 2
  1. 1.Department of Mechanical, Aerospace, and Nuclear EngineeringUniversity of CaliforniaLos AngelesUSA
  2. 2.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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