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SELF-CONSISTENT SOLUTION OF NONLINEAR PROBLEMS IN UNSTEADY RADIATION GASDYNAMICS.
MASSACHUSETTS INST OF TECH CAMBRIDGE AEROPHYSICS LAB
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It is shown that the system of equations which governs the unsteady flow of a radiating gas in chemical nonequilibrium is hyperbolic, and standard methods are applied to the solution of situations in radiation gasdynamics RGD which are restricted neither in optical depth nor the radiation-convection parameter. Absorption of shock layer radiation by the upstream gas is included in a numerical method of characteristics, and it is proved that only a Mark-type radiation boundary condition is appropriate to the lowest order full-range differential approximation of one-dimensional radiative fields. To illustrate the method, the flow fields generated by planar and cylindrical pistons inserted into ideal gases with arbitrary absorption properties are investigated both with the differential approximation and the full transfer equation. The results obtained are believed to be the first in a realistic aerodynamic situation and show that the differential approximation predicts surface pressures and heat transfer rates very accurately and general flow fields within ten percent for the cases considered. It was found that linearized theories of piston insertions may be in error near the start of motion. In addition, nonmonotonic entropy layer induced surface pressure histories were noted, and it is observed that variable surface emissivity and wall temperature may exert blowing or suction upon entropy layers. Upstream absorption is shown to be a dominant mechanism in the evolution of unsteady flow fields, and contrary to previous predictions it is shown that the effects of radiation upon pressure and velocity may be comparable to those upon temperature in many cases. Author
APPROVED FOR PUBLIC RELEASE