The flow field near the triple point in steady shock reflection
Tóm tắt
This paper investigates the flow field near three intersecting shock waves appearing in steady Mach reflection. Results of numerical computations reveal a “von Neumann Paradox”—like feature for weak shock waves, in which the flow field between the reflected and the Mach stem is smooth with no distinct slip flow region and changes rather smoothly. An analytical solution of the Navier–Stokes equations constructed using a polar–coordinate system gives a flow field with the same properties as the numerical simulation.
Tài liệu tham khảo
Birkoff G.: Hydrodynamics: A Study in Logic, Fact, and Similitude, 1st ed. Princeton University Press, Princeton (1950)
Bleakney W., Taub A.H.: Interaction of shock waves. Rev. Mod. Phys. 21(4), 584–605 (1949)
Sternberg J.: Triple-shock-wave interactions. Phys. Fluids 2(2), 172–206 (1959)
Sakurai A.: On the problem of weak Mach reflection. J. Phys. Soc. Jpn. 19, 1440–1450 (1964)
Khotyanovsky, D., Kudryavtsev, A., Bonder, Y., Shoev, G., Ivanov, M.: Viscosity effects on weak shock wave reflection. In: Proceedings of 26th ISSW, vol. 2, pp. 1555–1560. Springer (2009)
Sakurai A., Takahashi S.: An analytical solution for weak Mach reflection and its application to the problem of the von Neumann paradox. J. Phys. Soc. Jpn. 74, 1490–1495 (2005)
Ivanov, M.S., Markelov, G.N., Gimelshein, S.F.: Statistical Simulation of Reactive Rarefied Flows: Numerical Approach and Application. AIAA Paper 98-2669 (1998)
Tesdall M., Sanders R., Keyfitz L.: Self-similar solutions for the triple point paradox in gas dynamics. SIAM J. Appl. Math. 68, 1360–1377 (2008)