Correlations to predict the streamwise influence regions of two-dimensional turbulent shock separated flows

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Ramesh, Manohari D.
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Tannehill, John C.
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In the present study, correlation functions which can accurately predict the extent of the streamwise regions of influence in a two-dimensional shock separated turbulent boundary-layer flow have been developed. These correlations are empirical relations involving known flow parameters that can predict the streamwise influence regions of a turbulent flow in the presence of a disturbance. This information is particularly useful in the modeling of turbulent flows where the numerous turbulent models still rely heavily on experiment. As the functions have been developed to depend entirely on known flow variables, with no dependence, implicit or explicit, on the random turbulent fluctuations or on the turbulent closure parameters, they do not depend upon the turbulent model used to provide closure of the governing equations. In addition, correlations can be used to greatly improve the speed and efficiency of a numerical procedure which iterates over the region of streamwise influence to obtain accurate results. The shock impingement flowfields were computed using an iterated parabolized Navier-Stokes algorithm and the turbulent flow is modeled using the relaxation eddy viscosity model of Shang and Hankey. The correlations were obtained by regression analysis of the numerically computed data points, using the least squares method. The general form of these functions, the wide range of applicability, and their ease of calculation makes them a handy tool for engineering design purposes. The accuracy of these functions is demonstrated, and they were found to be excellent in predicting the upstream influence region and were quite adequate in predicting the downstream influence region. The correlation functions developed in this study are the only known correlations (theoretical or empirical) that can predict the streamwise extent of the interaction in a 2D turbulent boundary-layer flow, separated by an impinging shock.