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COBEM 2021
26th International Congress of Mechanical Engineering
A BRIEF REVIEW OF WALL SHEAR CORRELATIONS FOR HYPERSONIC FLOWS
Submission Author:
Felipe Pinheiro Maia , RN
Co-Authors:
Pedro Paulo Batista de Araújo, Felipe Pinheiro Maia, Jonatha Wallace da Silva Araújo, Ramon Carneiro, Ítalo Sabino Arrais Bezerra, Paulo Toro, Sandi Souza, Thiago Cardoso de Souza
Presenter: Pedro Paulo Batista de Araújo
doi://10.26678/ABCM.COBEM2021.COB2021-0930
Abstract
This paper adresses the problem of finding the appropriate correlation model for the estimation of drag force in aerospace vehicles that operate at hypersonic conditions. Here the analysis of the spatial variation of the local wall shear stress along a 6.28° ramp wall in a hypersonic flow is considered. Three cases corresponding to flows with Mach numbers equal to 3, 7, and 10 were analyzed. A number of correlations of the friction coefficient as proposed by Sommer and Short, Spalding and Chi, van Driest, White and Christoph, Eckert, and Meador and Smart, were applied to evaluate the wall shear using an analytical approach. The thermodynamic properties of the flow downstream of the shock wave, established at the leading edge of the ramp, were estimated using the oblique shock theory. The analytical results were compared to a reference wall shear data numerically obtained using a Reynolds-Averaged Navier-Stokes (RANS) steady-state simulation performed for the same geometry. The working fluid is air, modeled in this paper as a calorically perfect gas. For the closure of the turbulent Reynolds stresses, the k-kl-! transition model was used. The results show a quantitative comparison between the wall shear stress curves obtained for each method and correlation introduced. The results points out that most correlations models have low accuracy for the hypersonic flow, which is reasonable since these models were developed from experimental data extracted from supersonic flows. Despite this limitation, the analytical models which best predict the drag coefficient under the conditions investigated were the models derived by Eckert, the model proposed by Sommer and Short for supersonic flows and the Meador and Smart model for hypersonic flow.
Keywords
Skin Friction Drag, Wall Shear Stress, CFD, Analytical Correlations, Hypersonic Flow
