On the Hypersonic Leading-Edge Problem in the Merged-Layer Regime

by H. K. Cheng, Michael Shi-Yuan Chen, R. Mobley, Carolyn R. Huber

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A continuum description of the hypersonic flow over a sharp flat plate in the merged-layer regime (where the boundary layer and its outer flow are no longer distinct). This approach, mathematically analogous to the unsteady methods with real and/or artificial viscosities, requires that streamlines in most of the disturbed area be only slightly deflected from a main flow and that the Mach number in the undisturbed region be high. Finite-difference analyses are applied to a single set of partial differential equations that is derived from full Navier-Stokes equations. The outer boundary, an unknown in usual formulations of this problem, is eliminated, and the system is solved as an initial-value problem having only one inner boundary at the body surface. Solutions obtained for the caloric perfect gas are compared with data from air and nitrogen experiments. Calculated values for heat transfer appear to be 10 to 100 per cent higher than measured data; certain nonequilibrium effects may account for the discrepancy.

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