Governing equation and mathematical simulation on ablation and transpiration control

This paper represents a physical model of two-dimensional transpiration cooling control system with surface heating and ablating. The governing equation is derived and the third boundary conditions are given. They constitute a two-dimensional variable-domain distributed parameter control system in which the control parameter appears in both the governing equation and the boundary conditions. Aplying time semi-step alternating direction method to difference this mathematical model, the tridiagonal difference equations are obtained. For a flying shell of electromagnetic railgun, the mathematical simulation results agree with the realistic physical process, and the control parameter not only can control the temperature of heat shield. but also can control the boundary motion effectively.