Conservation laws and invariant solutions of the non-linear governing equations associated with a thermodynamic model of a rotating detonation engines with Korobeinikov׳s chemical source term

Abstract

Cite this article as: R.N. Ibragimov, N.H. Ibragimov and L.R. Galiakberova, Conservation laws and invariant solutions of the nonlinear governing equations associated with a thermodynamic model of a rotating detonation engines with Korobeinikov's chemical source term, International Journal of Non-Linear Mechanics, http://dx. AbstractThe nonlinear governing gas dynamics equations that are used as a descriptor of a rotating detonation engine are investigated from the group theoretical standpoint. The equations incorporate approximation of the Korobeinkov's chemical reaction model that are used to describe the two-dimensional detonation field on a surface of a two-dimensional cylindrical chamber without thickness. The transformations that leave the equations invariant are found. On the basis of these transformations, the conservation equations were constructed and the invariant solutions were obtained for specific form of the equation of state, for which the equations are nonlinearly self-adjoint. The invariant solutions are given in terms of the functions that satisfy nonlinear ordinary differential equations. The above reduction simplifies the analysis of the original nonlinear system of partial differential equations on a surface of rotating cylinder.