Numerical analysis for heat shield ablation law in transpiration cooling system

The transpiration cooling control system of the thermal protective shield with surface ablation is a nonlinear control system of distributed parameter with moving boundary. As far as the boundary conditions the third kind and a one-dimensional incompressible coolant flow under constant transpiration mass flux are concerned, this paper transforms the definite solution problem into the second-type Volterra integral equations, and applies them directly to compute the shield ablation law. Investigation of the system’s control by transpiration mass flux, ablation amount and ablation velocity varying with time, time of the ablation’s beginning and ending, etc., are presented.