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Numerical Simulation of the Transition Region in Hypersonic Flow
McKeel, Scott Andrew
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The current state of transition region modeling is investigated through a literature search. The six most promising transition region models from the literature search were implemented in the Navier-Stokes code GASP. Baldwin-Lomax is an algebraic turbulence model in which the authors discuss how it can be used to simulate the transition region. Wilcox developed a procedure to use the low-Reynolds number k - w model as a transition region model where a roughness strip is used to fix the transition point. Schmidt and Patankar developed production term modifications for low-Reynolds number k - e models to correct for the problems these models have in simulating the transition region. Warren, Harris and Hassan developed a one equation turbulence model that accounts for the first and second mode disturbances in the transition region. The algebraic transition region model of ONERA/CERT controls the amount of eddy viscosity added to the molecular viscosity. The linear combination model of Dey and Narasimha combines a fully laminar and fully turbulent flow field through the indeterminacy to form the transitional flow field. GASP is a compressible Navier-Stokes code which has a practical lower working limit of M = .1. The majority of experimental data for transitional flow exists below this limit. The test cases found above this limit and used here were all in the hypersonic regime. The results from the six transition region models were compared against the experimental test cases found for a variety of cones and ramps. Two models produced inadequate results on these test cases. The Wilcox model did not function as it was intended. The algebraic transition region model overpredicted the heat transfer in the turbulent region for several cases and did not transition in regions of large adverse pressure gradients. Several models performed adequately. The Baldwin and Lomax model provide fast estimates of the transition region. The Warren, Harris and Hassan model, the Schmidt and Patankar model, and the linear combination model produced adequate results on the test cases for this work and are worthy of attention on other test cases. Modifications were made to the Schmidt and Patankar model and the algebraic transition region model to improve their predictions on the current test cases. A turbulent spot was introduced into the boundary layer for the Schmidt and Patankar model which facilitated in the use of the model. Also, the maximum production allowed was recalibrated and allowed to grow exponentially to improve transition region simulating for the test cases presented here. The empirical transition function from the algebraic transition region model was recalibrated for the hypersonic test cases used in this work.
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