Reflection of a spherical blast wave from a planar surface
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Numerous authors have carried out rather extensive studies in the last twenty to thirty years of the problem of the interaction of shock and blast waves with obstacles in their paths. Owing to the complexity of the problem, they assumed certain limiting cases for the shock wave interactions in which the parameters behind the shock wave were usually taken to be constants. The first wave diffraction studies involving variable parameters behind the front were presented in [1, 2], wherein a development of the theory of “short waves” (blast waves at a substantial distance from the center of an explosion) and their reflection from a planar surface was given. The theory of short waves assumes that the jump in pressure at the wave front and the region over which the parameters vary are small. The problem concerning reflection of a blast wave from a surface was also considered in [3, 4], wherein a solution in the region behind the reflected wave was obtained at initial times. The initial stage in the reflection of a blast wave from a planar, cylindrical, or spherical surface (the one-dimensional case) was studied in . In this paper we investigate the interaction of a spherical blast wave, resulting from a point explosion, with a planar surface; we consider both regular and non-regular reflection stages. In solving this problem we use S. L. Godunov's finite-difference method. We obtain numerical solutions for various values of the shock strength at the instant of its encounter with the surface. We present the pressure fields in the flow regions, the pressure distribution over the surface at various instants of time, and the trajectories of the triple point. The parameter values at the front of the reflected wave are compared with results obtained from the theory of regular reflection of shock waves.
KeywordsShock Wave Wave Front Planar Surface Triple Point Pressure Field
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- 1.O. S. Ryzhov and S. A. Khristianovich, “Concerning nonlinear reflection of weak shock waves,” Prikl. Matem. i Mekhan.,22, No. 5 (1958).Google Scholar
- 2.A. A. Grib, O. S. Ryzhov, and S. A. Khristianovich, “Theory of short waves,” Zh. Prikl. Mekhan. i Tekh. Fiz., No. 1 (1960).Google Scholar
- 3.M. M. Vasil'ev, “On the reflection of a spherical shock wave from a plane,” in: Computational Mathematics [in Russian], Vol. 6, Izd. Akad. Nauk SSSR, Moscow (1960).Google Scholar
- 4.T. S. Chang and O. Laporte, “Reflection of strong blast waves,” Phys. Fluids,7, No. 8 (1964).Google Scholar
- 5.R. Ya. Tugazakov and A. S. Fonarev, “Initial stage in the collision of blast waves,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 5 (1971).Google Scholar
- 6.D. E. Okhotsimskii, I. L. Kondrasheva, Z. P. Vlasova, and R. K. Kazakova, “Calculation of a point explosion with counterpressure included,” Trudy Matem. Inst. im. Steklova,50, (1957).Google Scholar
- 7.V. P. Korobeinikov, P. I. Chushkin, and K. V. Sharovatova, “Gasdynamic functions of a point explosion,” Trudy Vychisl. Tsentr. Akad. Nauk SSSR (1969).Google Scholar
- 8.S. K. Godunov, “A difference method for numerically calculating discontinuous solutions of the gasdynamic equations,” Matem. Sb.,47, No. 3 (1959).Google Scholar
- 9.S. K. Godunov, A. V. Zabrodin, and G. P. Prokopov, “A difference scheme for two-dimensional nonstationary problems of gasdynamics and for flow calculations with a refracted Shock wave,” Zh. Vychisl. Matem. i Matem. Fiz.,1, No. 6 (1961).Google Scholar
- 10.A. S. Fonarev, “Calculation of the diffraction of a shock wave by a profile with a subsequent establishment of a stationary and also a transonic flow,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 4 (1971).Google Scholar
- 11.G. M. Arutyunyan, “Theory of anomalous regimes in the regular reflection of shock waves,” Izv. Akad. Nauk SSSR, Mekhan. Zhidk. i Gaza, No. 5 (1973).Google Scholar