HYDROELASTIC BURSTING WAVES IN CHANNEL-SLOT STRUCTURES OF SOLID FUEL

The paper deals with questions related to a description of the propagation of nonlinear waves in homogeneous channels with elastic walls from solid fuel fi lled with solid fuel combustion products, a medium moving at a constant or space-variable velocity determined by the fuel combustion. For ease of reference, hereinafter these waves will be referred to as hydroelastic waves in a solid fuel combustion chamber. Within the framework of a long-wave approximation, a system of equations is proposed for a description of these waves. It is shown that this system is quasi-linear and hyperbolic. It is shown that the propagation velocity of hydroelastic waves is lower than the velocity of waves′ propagation across the compressible fl uid medium fi lling a channel with elastic walls. Riemann invariants have been found. Conditions on strong discontinuities have been obtained and discontinuous solutions, an analog of shock waves in a gas, have been described. It is shown that discontinuous solutions are possible with increase and decrease of pressure after the discontinuity. A Riemann equation describing the propagation of weak discontinuities of hydroelastic waves through the channel has been obtained. The Riemann equation makes it possible to determine the time and place of the occurrence of gradient catastrophes of hydroelastic waves. Numerical-analytical investigations have been conducted into the formation and propagation of strong discontinuities with a rise and drop of pressure after such discontinuities. The proposed theory of propagation of hydroelastic waves can be used for determining the location of leaks in pipeline systems and for predicting the destruction of solid-propellant rocket engines by a hydroelastic wave. An analysis has been made of the nonlinear stability of the fl ows of combustion products in a homogeneous channel with elastic walls.
   
Author:  S. V. Sukhinin, A. V. Trilis, V. S. Yurkovskii, A. A. Cheremisin
Keywords:  hydroelastic wave, quasi-linear hyperbolic systems of equations, strong discontinuity, Riccati equation, gradient catastrophe, solid-propellant rocket engine
Page:  423