Abstract
A two-dimensional structure of detonation waves in an 2H2+O2+X Ar mixture is numerically studied in a wide range of initial pressures and degrees of dilution. Good qualitative agreement of the numerical results with experimental data is obtained. The effect of the method of initiation (by one or several sites, symmetric or asymmetric) on the steady structure of detonation waves is studied. The changes in the wave structure induced by variation of the channel width are examined. It is shown that the behavior of the two-dimensional wave structure is qualitatively different for mixtures withX=0 andX>0.
Similar content being viewed by others
References
B. V. Voitsekhovskii, V. V. Mitrofanov, and M. E. Topchiyan,Detonation Front Structure in Gases [in Russian], Izd. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1963).
W. Fickett and W. C. Davis,Detonation, Univ. of California Press, Berkeley, CA (1979).
Ya. B. Zel'dovich and A. S. Kompaneets,Detonation Theory [in Russian], Gostekhizdat, Moscow (1955).
J. J. Erpenbeck, “Stability of idealized one-reaction detomations,”Phys. Fluids,7, 484–696 (1964).
H. I. Lee and D. S. Stewart, “Calculation of linear detonation instability: One-dimensional instability of plane detonation,”J. Fluid Mech.,216, 103–132 (1990).
S. Taki and T. Fujiwara, “Numerical analysis of twodimensional nonsteady detonations,”AIAA J.,16, No. 1, 73–77 (1978).
S. Taki and T. Fujiwara, “Numerical simulation of triple shock behavior of gaseous detonation,” in:18th Symp. (Int.) on Combustion, The Combustion Inst. (1981), pp. 1671–1680.
S. Taki and T. Fujiwara, “Numerical simulations of the establishment of gaseous detonation,” in:Progress in Astronautics and Aeronautics, Vol. 94:Dynamics of Shock Waves, Explosions, and Detonations, New York (1983), pp. 186–200.
V. V. Markov, “Numericla simulation of the formation of a multifront structure of a detonation wave,”Dokl. Akad. Nauk SSSR,258, No. 2, 314–317 (1981).
E. S. Oran, J. P. Boris, T. Young, et al. “Numerical simulations of detonations in hydrogen-air and methane-air mixtures,” in:18th Symp. (Int.) on Combustion, The Combustion Inst. (1981), pp. 1641–1649.
K. Kailasanath, E. S. Oran, J. P. Boris, and T. R. Young, “Determination of detonation cell size and the role of transverse waves in two-dimensional detonations,”Combust. Flame,61, 199–209 (1985).
E. S. Oran, K. Kailasanath, and R. H. Guirguis, “Numerical simulations of the development and structure of detonations,” in:Progress in Astronautics and Aeronautics, Vol. 114:Dynamics of Explosions, Washington (1988), pp. 155–169.
M. H. Lefebvre, E. S. Oran, K. Kailasanath, and P. J. van Tiggelen, “The influence of the heat capacity and diluent on detonation structure,”Combust. Flame,95, 206–218 (1993).
M. N. Lefebvre, E. S. Oran, K. Kailasanath, and P. J. van Tiggelen, “Simulation of cellular structure in a detonation wave,” in:Progress in Astronautics and Aeronautics, Vol. 153:Dynamics Aspects of Detonations, Washington (1993), pp. 64–77.
T. Kratzel, M. Fischer, and E. Pantow, “Vorticityinduced recoupling of a decoupled detonation wave,” in: Proc. 16th ICDERS, Cracow (1997), pp. 168–171.
E. Pantow, M. Fischer, and T. Kratzel, “Detonation front structures in hydrogen combustibles,”ibid., in: Proc. 16th ICDERS, Cracow (1997), pp. 377–380.
E. S. Oran, “Numerical simulations of unsteady combustion,” in:Combustion, Detonation, Shock Waves: Proc. of the Zel'dovich Memorial, Moscow (1994), pp. 228–247.
E. S. Oran, J. W. Weber, E. I. Stefaniw, M. H. Lefebvre, and J. D. Anderson, “A numerical study of a two-dimensional H2−O2−Ar detonation using a detailed chemical reaction model,”Combust. Flame,113, 147–163 (1998).
S. U. Schöffel and F. Ebert, “Numerical analyses concerning the spatial dynamics of an initially plane gaseous ZND detonation,” in:Progress in Astronautics and Aeronautics, Vol. 114:Dynamics of Explosions, Washington (1988), pp. 3–31.
W. Cai, “High-order hybrid numerical simulations of two-dimensional detonation waves,”AIAA J.,33, No. 7, 1248–1255 (1995).
B. Sjögreen,Numerical computation of threedimensional detonation waves on parallel computers,” Report No. 162/1994, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1994).
D. Lindström, “Numerical computation of viscous detonation waves in two space dimensions,” Report No. 178/1996, Department of Scientific Computing, Uppsala University, Uppsala, Sweden (1996).
V. A. Levin and V. P. Korobeinikov, “Strong explosion in a combustible mixture of gases,”Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 48–51 (1969).
Yu. A. Nikolaev, “Model of the kinetics of chemical reactions at high temperatures,”Fiz. Goreniya Vzryva,14, No. 4, 73–76 (1978).
P. A. Fomin and A. V. Trotsyuk, “Approximate calculation of the isentrope of a gas in chemical equilibrium,”Fiz. Goreniya Vzryva 31, No. 4, 59–62 (1995).
Yu. A. Nikolaev and D. V. Zak, “Agreement of models of chemical reactions in gases with the second law of thermodynamics,”Fiz. Goreniya Vzryva,24, No. 4, 87–90 (1988).
Yu. B. Rumer and M. Sh. Ryvkin,Thermodynamics, Statistical Physics, and Kinetics [in Russian], Nauka, Moscow (1977).
Yu. A. Nikolaev, and P. A. Fomin, “Analysis of equilibrium flows of chemically reacting gases,”Fiz. Goreniya Vzryva,18, No. 1, 66–72 (1982).
Yu. A. Nikolaev and P. A. Fomin, “Approximate equation of kinetics in heterogeneous systems of the gas-condensed-phase type,”Fiz. Goreniya Vzryva,19, No. 6, 49–58 (1983).
D. R. White, “Density induction times in very lean mixtures of D2, H2, C2H2, and C2H4 with O2,” in:11th Symp. (Int.) on Combustion, Berkeley (1966), pp. 147–154.
S. K. Godunov (ed.),Numerical Solution of Multidimensional Problems of Gas Dynamics [in Russian], Nauka, Moscow (1976).
S. Yamamoto and H. Daiguji, “Higher-order-accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations,”Computer Fluids,22, Nos. 2/3, 259–270 (1993).
H. Daiguji, X. Yuan, and S. Yamamoto, “Stabilization of higher-order high-resolution schemes for the compressible Navier-Stokes equation,”Int. J. Num. Meth. Heat Fluid Flow,7, Nos. 2/3, 250–274 (1997).
S. R. Chakravarthy and S. Osher, “A new class of high-accuracy TVD schemes for hyperbolic conservation laws,” in: AIAA 23rd Aerospace Sciences Meeting, Reno, Nevada (1985). (AIAA Paper No. 850363.)
S.-Y. Lin and Y.-S. Chin, “Comparison of higherresolution Euler Schemes for aeroacoustic computations,”AIAA J.,33, No. 2, 237–245 (1995).
P. L. Roe, “Approximate Riemann solvers, parameter vectors, and difference schemes,”J. Comput. Phys.,43, 357–372 (1981).
P. L. Roe and J. Pike, “Efficient construction and utilization of approximate Riemann Solutions in: R. Glowinski and J.-L. Lions (eds.),Computing Methods in Applied Sciences and Engineering. VI, North-Holland, Amsterdam (1984), pp. 499–513.
B. van Leer, “Flux-vector splitting for the Euler equations,” ICASE Report No. 82-30 (1982). [Lecture Notes in Physics, Vol. 170, Springer-Verlag, Berlin-New York (1982), pp. 507–512].
W. K. Anderson, J. L. Thomas, and B. van Leer, “A comparison of finite volume flux vector splitting for the Euler equations,” in: AIAA 23rd Aerospace Sciences meeting, Reno, Nevada (1985). (AIAA Paper No. 85-0122.)
M. Vinokur and J.-L. Montagné, “Generalized fluxvector splitting and Roe average for an equilibrium real gas,”J. Comput. Phys.,89, 276–300 (1990).
M. Vinokur, “An analysis of finite-difference and finite-volume formulations of conservation laws,”J. Comput. Phys.,81, 1–52 (1989).
A. harten and J. M. Hyman, “Self-adjusting grid methods for one-dimensional hyperbolic conservation laws,”J. Comput. Phys.,50, 235–269 (1983).
J. W. Shen and X. Zhong, “Semi-implicit Runge-Kutta schemes for non-autonomous differential equations in reactive flow computations,” AIAA Paper No. 96-1996 (1996).
Yu. A. Nikolaev and M. E. Topchiyan, “Calculation of equilibrium flows in detonation waves in gases,”Fiz. Goreniya Vzyva,13, No. 3, 393–404 (1977).
R. A. Strehlow and C. D. Engel, “Transverse waves in detonations. II. Structure and spacing in H2−O2, C2H2−O2, C2H4−O2, CH4−O2 systems,”AIAA J.,7, No. 3, 492–496 (1969).
R. A. Strehlow, “Gas phase detonations: recent developments,”Combust. Flame,12, No. 2, 81–101 (1968).
V. I. Manzhalei, V. V. Mitrofanov, and V. A. Subbotin, “Measurement of inhemogeneities of a detonation front in gas mixtures at elevated pressures,”Fiz. Goreniya Vzryva,10, No. 1, 102–110 (1974).
D. H. Edwards, G. Hooper, E. M. Job, and D. J. Parry, “The behavior of the frontal and transverse shocks in gaseous detonation waves,”Astronaut. Acta,15, No. 5-6, 323–333 (1970).
M. H. Lefebvre, J. W. Weber, and E. S. Oran, “Fluid mechanics and applications,” in: B. Deshaies and L. F. da Silva (eds.),Proc. of the IUTAM Symp., Vol. 39, Kluwer Academic Publ. (1997), pp. 347–358.
Author information
Authors and Affiliations
Additional information
Translated fromFizika Goreniya i Vzryva, Vol. 35, No. 5, pp. 93–103, September–October 1999.
Rights and permissions
About this article
Cite this article
Trotsyuk, A.V. Numerical simulation of the structure of two-dimensional gaseous detonation of an H2-O2-Ar mixture. Combust Explos Shock Waves 35, 549–558 (1999). https://doi.org/10.1007/BF02674500
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02674500