By using the compressible and permeable theory, it presents a mathematical model of closed loop control with gas transpiration and surface erosion. Its numerical solution is achieved. The series of pressure p_l as a control parameter is given. It also points out, when the pressure of the control parameter is constant or the transpiration coolant is incompressible, the problem will be back to ref.[2]

It presents the characteristics of some parameters and physical problems which are described in three kind of transpiration control equations,and provides a part of the numerical simulation results.

The transpiration cooling control system of surface thermal protection for bodies of revolution at hypersonic is studied. Not only the critical transpiration quantity equaling to plane case is obtained, but also another smaller second critical transpiration quantity is found. When the transpiration quantity is between of this two critical transpiration quantities, the ablation will appear on the shield surface, but the ablation will stop automatically, and a remainder thickness of shield will be kept at last. Numerical simulation is accomplished and yields all kinds of charactdstic curves. Three methods of ablation control for shield surface are discussed:the controls are for surface temperature, for ablation quantity and for ablation beginning time, the rules for selecting control variable are given.

A solution of transpiration control equation is investigated in this paper. It is found that the equation can be classified as the classic heat transfer equation under certain conditions by means of variable alternation and then the analytic solution can be obtained. A numerical calculation of the analytic solution by a computer has proved the existence, uniqueness and stability of the solution. The theoretical problem of this sort of control system applied in the engneering is preliminarily ascertained. A finite difference numerical calculation has shown that the smaller the difference step is, the faster the difference solution approaches the analytic one. Because of limitation of the difference method, the steady numerical solution can be gotten in the region surrounded by R=0, BT=0 and R·BT=βτ/4h. The main conclusion of reference [2] is verified again.