Abstract
The structure of flow in the vicinity of a triple point in the problem of stationary irregular reflection of weak shock waves is numerically investigated within the framework of the Euler model, including the von Neumann paradox range. To improve the accuracy of the solution near singular points a new technology including a grid contracted toward the triple point and the discontinuity fitting is applied. It is shown that in the four-wave flow pattern the curvatures of the tangential discontinuity and the Mach front at the triple point are finite. The singularity is concentrated only in a sector between the reflected wave front and the expansion fan. When the three-wave flow pattern is realized, the curvatures of the tangential discontinuity and both wave fronts at the triple point are infinite. On the range of weak and moderate shock waves the logarithmic singularity in subsonic sectors near the triple point conserves up to transition to the regular reflection.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. I. Vasil’ev, “High-Resolution Simulation for the Mach Reflection of Weak Shock Waves,” in: Proc. ECOMAS CFD 1998, Vol. 1, Pt. 1, Wiley, Hoboken (1998), p. 520.
E. I. Vasil’ev and A. N. Kraiko, “Numerical Modeling ofWeak Shock Diffraction on aWedge under the von Neumann Paradox Conditions,” Zh. Vychisl. Mat. Mat. Fiz. 39, 1393 (1999).
E. I. Vasil’ev, “Four-Wave Scheme of Weak Mach Shock Wave Interaction under von Neumann Paradox Conditions,” Fluid Dynamics 34 (3), 421 (1999).
K. G. Guderley, “Considerations of the Structure of Mixed Subsonic-Supersonic Flow Patterns,” Wright Field Report F-TR-2168-ND (1947), p. 144.
B. W. Skews and J. T. Ashworth, “The Physical Nature ofWeak ShockWave Reflection,” J. Fluid Mech. 542, 105 (2005).
B. W. Skews, G. Li, and R. Paton, “Experiments on Guderley Mach Reflection,” Shock Waves 19, 95 (2009).
A. Cachucho and B.W. Skews, “Guderley Reflection for HigherMach Numbers in a Standard Shock Tube,” Shock Waves 22, 141 (2012).
A. M. Tesdall, R. Sanders, and B. L. Keyfitz, “Self-Similar Solutions for the Triple Point Paradox in Gasdynamics,” SIAM J. Appl. Math. 68, 1360 (2008).
E. I. Vasilev, “Detailed Investigation of Guderley Shock Wave Reflections in Steady Flow,” in; Proc. 21st Int. Shock Interaction Symp., Latvia, 3–8 Aug. 2014, Univ. Latvia, Riga (2014), p. 42.
A. M. Tesdall, R. Sanders, and N. Popivanov, “Further Results on Guderley Mach Reflection and the Triple Point Paradox,” J. Scientific Computing 64, 721 (2015).
G. Ben-Dor, Shock Wave Reflection Phenomena, Springer, New York (2007).
J. Sternberg, “Triple-Shock-Wave Intersections,” Phys. Fluids 2 (2), 179 (1959).
G. Ben-Dor, T. Elperin, H. Li, E. Vasiliev, A. Chpoun, and D. Zeitoun, “Dependence of Steady Mach Reflection on the Reflecting-Wedge Trailing-Edge Angle,” AIAA J. 35, 1780 (1997).
E. I. Vasil’ev, “W-Modification of the GodunovMethod and its Application to Time-Dependent Two-Dimensional Dusty Gas Flows,” Zh. Vychisl. Mat. Mat. Fiz. 36, 122 (1996).
E. I. Vasilev, T. Elperin, and G. Ben-Dor, “Analytical Reconsideration of the von Neumann Paradox in the Reflection of a ShockWave over a Wedge,” Phys. Fluids 20, 046101 (2008).
L. F. Henderson, E. I. Vasilev, G. Ben-Dor, and T. Elperin, “The Wall-Jetting Effect in Mach Reflection: Theoretical Consideration and Numerical Investigation,” J. Fluid Mech. 479, 259 (2003).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © E.I. Vasil’ev, 2016, published in Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 2016, Vol. 51, No. 6, pp. 91–100.
Rights and permissions
About this article
Cite this article
Vasil’ev, E.I. The nature of the triple point singularity in the case of stationary reflection of weak shock waves. Fluid Dyn 51, 804–813 (2016). https://doi.org/10.1134/S0015462816060119
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0015462816060119