Theoretical and Experimental Analysis of Flight-to-Ground Scaling for Axisymmetric and Planar Bodies

This paper proposes a methodology to scale the stagnation point plasma conditions of an axially symmetric body to a two-dimensional planar body. The method is required to correlate material samples tested under thermochemical loads combined with aeromechanical loads in order to relate the measurements to actual flight scenarios. The equations governing the boundary-layer and heat transfer equations are introduced and analyzed using the commonly known local heat transfer simulation concept. This technique is then adapted to the given constraints and results in a two-step flight-to-ground scaling approach. Flight conditions are first transformed to axisymmetric ground testing equivalents before being scaled to planar bodies. Thereby, the mass-specific enthalpy, total pressure, and Stanton number stay constant; and the velocity gradient doubles when scaling from axisymmetric to planar. Formulations for the velocity gradient are analyzed for both the sub- and supersonic cases. The results are compared between a theoretical approach and plasma wind-tunnel tests. Three heat flux gauges were tested at two conditions. The planar sensors were evaluated with two independent methods, and the results were scaled to a comparable condition. The results compare very well with the theoretically calculated values. The axisymmetric to planar conversion theory detailed in this paper is therefore considered experimentally verified.