Error Analysis of the Surface Heat Flux Calculation for the A3 Subscale Supersonic Diffuser

Abstract

Errors associated with the application of the Cook-Feldman method calculating heat flux from experimental surface temperature are examined. This method has been applied to estimate the heat flux on the A3 subscale diffuser (SD) during a representative rocket and is reported in a parallel paper (AIAA 2009-5012). This paper studies the effects of the underlying assumptions of the method, which are not strictly satisfied in the actual test environment, and reports the corrected heat flux estimate for the structural design purposes of the full-scale A3 diffuser. The study is carried out using an existing numerical tool based on the method of space-time conservation element and solution element (CESE) for solving the 1-D transient nonlinear heat conduction equation with temperature dependent properties. The numerical analysis accurately accounts for transient boundary condition, variable material properties, finite-length domain, and backside ambient boundary condition none of which are included in Cook-Feldman method. In the CESE solver, the transient temperature boundary condition is coupled with the temperature-varying material properties so that the transient surface heat flux solution, an independent mesh-point solution variable in the CESE solution process, can be accurately resolved. Reanalysis of selective surface temperature data showed that the Cook-Feldman method based on constant properties underestimated the surface heat flux by as much as 30 percent for the extreme heating conditions observed in the A3 subscale diffuser ducts. A proper increase of the cooling capacity with the A3 full-scale diffuser ductwork is required accordingly. The effects of the other assumptions of Cook-Feldman method were not important in the at A3 subscale diffuser test conditions.