Thermal Protection Models And Numerical Simulation For Variable Density Charring Materials

The space vehicles are subjected to severe aerodynamic heating when they re-entry to the atmosphere.Thermal protection system is essential for the reentry of the vehicles to protect the safty of the vehicles.Due to the high enthalpy,low heat flux,low pressure,low stress and long reentry time,it is necessary to choose charring materials in the thermal protection systems of reentry vehicles.Furthermore,the heating environment of the reentry vehicles varies dramatically.The homogeneous charring materials cannot completely protect the reentry vehicles.It is important to develop novle variable density charring composites which can adapt to the changing heating environment.Based on the heat transfer theory,physicochemical theory,aerothermodynamics,combustion science,numerical heat transfer and numerical analysis,this paper researches on the thermal protection models and numerical simulation for variable density charring materialsOn the basis of the ablation mechanism of charring materials,assuming that the pyrolysis process focuses on the pyrolysis interface,the one-dimensional transient pyrolysis interface model for the variable density charring composites is developed.Based on the heat transfer theory,the heat conduction equations are built for the virgin and char layers,in which the thermophysical parameters are the functions of temperature and density.The energy conservation equation and temperature continuity equation are built at the pyrolysis interface.The energy conservation equation is built at the ablation surface,in which the surface recession rate relates with the surface temperature.Based on the numerical heat transfer method,the second order centered difference and one order forward difference is respectively used for the special and time-term discretization.Then the discretization formats of the mathematical model can be obtained.A new method to calculate the nonlinear discretization equations with moving boundary and interface is proposed:the thickness of each layer of the composite can be obtained from the results of the previous time step.Then the space grid can be renewed.The nonlinear equations at the current time step can be calculated by the diagonal matrix algorithm and the Newton iteration method.The surface recession rate then can be calculated by the results of surface temperature and its function.By the Fixed-Point Method,the moving distance of the pyrolysis interface can be obtained until that the results matches the energy conservation equation at the pyrolysis interface.Based on MATLAB,the computer codes are written to solve above equations.The thermal behaviors of homogeneous and variable density charring composites are calculated and analyzed.The numerical results show that the pyrolysis interface model for the variable density charring coomposites also can obtain the thermal behavior of homogeneous charring composites.The effective heat capacity of variable density charring composites is higher than that of homogeneous one.The variable density charring composites can effectively improve the profermance of the thermal protection system.In order to estimate the thermal responses of the charring composites more accurately,the pyrolysis layer model for the variable density composites is developed,in which the pyrolysis layer between the virgin and char layers contains both the pyrolysis reaction and the flow of the pyrolysis gases.The pyrolysis reaction leads the changing of the density in the pyrolysis layer.Meanwhile,the thermophysical parameters in the pyrolysis layer are always changing.In the pyrolysis layer model,the governing equations for the virgin and char layers and the boundary condition for the ablation surface are same with those in the pyrolysis interface model.The transient heat conduction equation is built for the pyrolysis layer.The temperature and heat flux continuity equations are built at two moving interfaces in the material.For simplifying the calculation,the density,heat capacity and thermal conductivity of the pyrolysis layer are assumed as linear interpolation from the density and thermophysical parameters of the virgin and char layers.By the finite difference method,the mathematical equations are discreted.A new method to solve the nonlinear discretization equations with moving boundary and two moving interfaces is proposed:Using the results from the previous time step,the thickness of each layer of the composite at the current time step is renewed.Then new space grids can be obtained.The nonlinear equations can be calculated by the diagonal matrix algorithm and the Newton iteration method.Using the surface recession function and the surface temperature,the surface recession can be calculated.By the Newton Secant method,two moving distances of the interfaces in the material can be calculated.The computer codes are written on MATLAB to realize above calculation processes.The thermal responses of homogeneous and variable density charring composites under constant and variable heat fluxes using the pyrolysis layer model are obtained.Also,the comparison of the results by the pyrolysis layer model and the pyrolysis interface model is presented.The numerical results show that the pyrolysis layer model for the variable density charring composites can also obtain the thermal responses of homogeneous charring composites.Under the heating environment of the reentry vehicle,the surface temperature,ablation rate,mass injection rate of the pyrolysis gases and thickness of each layer relate not only with the aerothermodynamic heating but also with the density distribution.The effective heat capacity of the variable density charring composites is higher than that of the homogeneous ones.The temperature of the pyrolysis interface is essential to the results when using the pyrolysis interface model.In above two models,the surface recession rate is assumed as the surface temperature related function without condisering the combustion of the pyrolysis gases in the shock layer.To analyze the surface ablation rate accurately,based on the aerothermodynamics,heat transfer theory,combustion science and physicochemical theory,a thermal-fluid-chemical-ablative coupled model is built.It concludes the normal shock equations,the pyrolysis layer model,the counterflow diffusion combustion model for the reactions of the pyrolysis gases with the oxidative gases in the shock layer and the surface oxidative ablation model at material's surface.Also,two concepts which are"starting reaction interface" and "critical pyrolysis gases' velocity" are proposed.By the quasi-Newton method,the FORTRAN codes are written to solve the nonlinear normal shock equations to obtain the gases' temperature and velocity behind the normal shock wave.By the calculation method for the pyrolysis layer model,the temperature and velocity of the pyrolysis gases at the material's surface can be obtained.Above calculation results can be used as the boundary conditions for the counterflow diffusion combustion model.This model can be calculated by the OPPDIF program.Then the mass concentration of oxygen near the material's surface can be obtained.It is used in the surface oxidative ablation model,together with the temperature at the material's surface,the mass ablation rate of the surface char can be calculated by the MATLAB codes.The result of the mass ablation rate then can be transfer to the pyrolysis layer model.Above calculation processes are repeated until that the iteration error for the mass ablation rate of the surface char is less than the precision.On the basis of C++,MATLAB and ACCESS,a thermal protection performance simulation software for the charring composites under severe aerothermodynamic environment is developed.Using this software,the inhibitory action of the combustion of the pyrolysis gases in the shock layer is analyzed.The numerical results show that the combustion of the pyrolysis gases can protect the charring composites' surface in a certain extent,however,this combustion has little influence on the temperature distribution in the charring materials.