Numerical simulations of high-speed chemically reacting flow
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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.
- Abgrall, R. (1988). Generalization of the Roe Scheme for Computing Flows of Mixed Gases with Variable Concentrations. Rech. Aérospat. 6, 31–43.
- Ben-Artzi, M. (1989). The Generalized Riemann Problem for Reactive Flows. J. Comput. Phys., 81, 70–101.
- 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.
- Chargy, D., Abgrall, R., Fezoui, L., and Larrouturou, B. (1990). Comparisons of Several Numerical Schemes for Multi-Component One-Dimensional Flows. INRIA Report 1253.
- Colella, P., Majda, A., and Roytburd, V. (1986). Theoretical and Numerical Structure for Reacting Shock Waves. SIAM J. Sci. Statist. Comput., 7, 1059–1080.
- Drummond, J.P. (1991). Mixing Enhancement of Reacting Parallel Fuel Jets in a Supersonic Combustor. AIAA Paper No. 91-1914.
- Engquist, B., and Sjogreen, B. (1991). Robust Difference Approximations of Stiff Inviscid Detonation Waves. UCLA CAM Report 91-03.
- Haas, J.-F., and Sturtevant, B. (1988). Interaction of Weak Shock Waves with Cylindrical and Spherical Gas Inhomogeneities. J. Fluid Mech., 181, 41–76.
- Harten, A. (1983). High Resolution Schemes for Hyperbolic Conservation Laws. J. Comput. Phys., 49, 357–393.
- 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.
- Jacobs, J.W. (1992). Shock-Induced Mixing of a Light-Gas Cylinder. J. Fluid Mech., 234, 629–649.
- Karagozian, A.R., and Marble, F.E. (1986). Study of a Diffusion Flame in a Stretched Vortex. Combust. Sci. Technol., 45, 65–84.
- Karni, S. (1992). Viscous Shock Profiles and Primitive Formulations. SIAM J. Numer. Anal., 29, 1592–1609.
- 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.
- Larrouturou, B. (1991). How To Preserve the Mass Fractions Positivity when Computing Compressible Multi-Component Flows. J. Comput. Phys., 95, 59–84.
- 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.
- Mass, U., and Warnatz, J. (1988). Ignition Processes in Hydrogen-Oxygen Mixtures. Combust. Flame, 74, 53–69.
- Marble, F.E., Hendricks, G.J., and Zukoski, E.E. (1987). Progress Toward Shock Enhancement of Supersonic Combustion Processes. AIAA Paper No. 87-1880.
- Picone, J.M., and Boris, J.P. (1988). Vorticity Generation by Shock Propagation Through Bubbles in a Gas. J. Fluid Mech., 189, 23–51.
- 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.
- Shu, C.W., and Osher, S.J. (1989). Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes, II. J. Comput. Phys., 83, 32–78.
- Stull, D.R., and Prophet, H. (1971). JANNAF Thermochemical Tables. National Standard Reference Data Series, U.S. National Bureau of Standards, Vol. 37.
- 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.
- 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.
- 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.
- 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.
- 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.
- Numerical simulations of high-speed chemically reacting flow
Theoretical and Computational Fluid Dynamics
Volume 6, Issue 2-3 , pp 161-179
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- 1. Department of Mechanical, Aerospace, and Nuclear Engineering, University of California, 90024-1597, Los Angeles, CA, USA
- 2. Department of Mathematics, University of California, 90024-1555, Los Angeles, CA, USA