Evolution of singular surface and interaction with a strong shock in reacting polytropic gases using Lie group theory. (November 2019)

• Record Type: Journal Article
• Authors: Shah, Sarswati; Singh, Randheer
• Is Part Of: International journal of non-linear mechanics. Volume 116(2019)
• Page Start: 173
• Page End: 180
• Publication Date: 2019-11
• Subjects: 76V05 -- 76M60 -- 74J30 -- 35L67 -- 76B15; Group theoretic method -- Exact solution -- Singular surface theory -- Strong shock -- Interaction of waves; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.06.013
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: We apply the Lie group method, which leaves the partial differential equations (PDEs) for the plane and radially symmetric flow of reacting polytropic gases invariant, to obtain an exact solution. Using the singular surface theory and compatibility conditions, we derive an evolution equation that governs the amplitude of the singular surface. The interaction between a singular surface and a strong shock is considered. The amplitudes of reflected and (or) transmitted wave and the jump in shock acceleration after the interaction are determined. Highlights: The paper concerns with the evolution of singular surface wave in reacting gases via Lie group analysis. First and second kind compatibility conditions are used to derive the transport equation. Influence of exponent of ambient density, reaction rate exponent and energies of the formation of the burnt and unburnt gas on the discontinuities is analyzed. The interaction of the singular surface wave with strong shock is considered. After the interaction the amplitudes of reflected waves and jump in shock acceleration are obtained.