Multidimensional Assessment of Modeling Error in Typical High-Speed Wind-Tunnel Heat-Transfer Data-Reduction Schemes

Abstract

R IGOROUS validation of computational tools places stringent demands on the accuracy of measured experimental data. This is increasingly the case in fluid dynamics, in which computational approaches havematured to the point at which certain propertiesmay be predicted to the same level of accuracy that can be measured. In such a situation, a discrepancy between computation and experiment cannot simply be assumed to lie exclusively in either the computational or experimental result. Rather, a thorough evaluation of both the computational and experimental techniques is required. Such is the case for perfect-gas wind-tunnel measurements of surface heat transfer for a simple body in an attached laminar flow. A standard technique for measuring the heat-transfer rate to a surface is via thermocouple instrumentation. The thermocouples may be subjected to an unknown heat flux for some period of time, and temperature histories may be obtained. This surface temperature history can then be used as a boundary condition in a transient thermal analysis from which the heat-transfer rate may be inferred. This technique is often employed in wind-tunnel tests that seek to quantify the aerothermodynamic environment for a given geometry. In such applications, the thermocouple instrumentation is typically too sparse to determine a true multidimensional surface temperature distribution, which could then be used in a three-dimensional thermal analysis. Consequently, the thermocouple temperature histories are often used in conjunction with a one-dimensional heat-transfer analysis, which only considers conduction normal to the surface. For geometries with regions of tight curvature and/or substantial lateral gradients in heat-flux distribution, the validity of the onedimensional assumption comes into question. This Note investigates the modeling error induced by the combined factors of lateral heat-flux distribution and multidimensional curvature for a specific geometry that was recently tested in the Arnold Engineering Development Center’s Hypervelocity Wind Tunnel no. 9. A purely analytical approach is used that combines steady computational fluid dynamics simulation, transient threedimensional thermal analysis, and the standard transient onedimensional thermal analysis technique to quantify the modeling error introduced through the data-reduction process for each gauge. The remainder of the Note is organized as follows: Section II provides an overview of the experimental test series that provides the motivation for this work, Sec. III describes the analytical approach used to predict the external convective heat-transfer and the transient thermal analysis, Sec. IV presents results for the specific case of a scaled Orion Crew Module model at wind-tunnel conditions, and some general conclusions are discussed in Sec. V.