COMPUTER MODELING OF THE GENERALIZED NEYMAN PROBLEM OF HEAT EXCHANGE OF ROCKET FAIRING

Abstract

The choice of thermal protection of the rocket fairing is made with special care because the fairing must protect against aerodynamic heating, radiation, and temperature changes. Currents with large Mach numbers are accompanied by gas-dynamic and physicochemical effects. When flowing around the blunt body, there is formed a shock wave which departs from the body but remains in close vicinity to the frontal point almost equidistant to its surface. Physical and chemical effects are stipulated by rising temperatures caused by the inhibition of gas by the shock wave. At the same time, there occur a transition of the kinetic energy of the rushing flow into the thermal one, excitement of fluctuating degrees of gas molecules freedoms, dissociation and even ionization. Therefore, among the problems of great theoretical and practical interest, there is the problem of studying the temperature fields arising in the fairings for missiles in the form of a truncated cone that rotates around its axis, given the finiteness of the rate of heat propagation. For the first time, a mathematical model for calculating temperature fields for a truncated cone is constructed in the article. The model approximates the distribution of temperature fields that appear in rocket fairings, taking into account the angular velocity and the finite velocity of heat propagation in the form of a boundary value problem of mathematical physics for the hyperbolic equation of thermal conductivity with Neumann boundary conditions. In the paper, there is formed a new integral transformation for a two-dimensional finite space in the application of which there is found the temperature field in the form of a convergent series. The solution found can be used for computer simulation of the possible value of thermomechanical stresses, promotion of the correct choice of technological parameters, objective control, as well as for identification of the ways to improve the thermal protection of fairings for missiles.