Comparison Between Exact and One-Dimensional Theories for Incipient Melting in Reentry Simulation

The exact transient temperature distribution in a spherical region subjected to an axisymmetric reentry heat flux has been evaluated. The results are presented in terms of nondimensional parameters, therefore they are valid for a wide range of materials, flight conditions, and nose radii. The angular dependence of the surface temperature is given as a function of time. It is also shown that the true radial temperature distribution can be represented by an exponential function. Finally, the solution is applied to reentry ablation onset studies that are being conducted in the free-flight range of the GM Defense Research Laboratories. The exact solution and the one-dimensional theory for the stagnation temperature rise of a model simulating reentry conditions in the free-flight range are compared. It is shown that the validity of the one-dimensional solution is dependent on the flight time, material properties, and nose radius of the model. Assuming that a temperature can be assigned which corresponds to incipient ablation, the present analysis is particularly useful in the prediction of ablation onset.