Correlations to predict turbulent streamwise influence regions and onset of transition in supersonic flows
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Correlation functions have been developed to predict both the extent of the streamwise influence regions in supersonic turbulent flows, and the onset of transition in supersonic flow past a flat plate. These correlations are empirical relations involving a priori known flow parameters. In the turbulent flow regime, correlations that can compute the extent of the upstream and downstream regions of influence in two-dimensional compression ramp and expansion corner flowfields have been developed. The correlations were obtained by analyzing numerically computed flowfields. Regression analysis using the least squares approach was applied to the computed flowfield data to determine the correlation functions. The turbulent correlations can be used in conjunction with an iterative parabolized Navier-Stokes algorithm to minimize the region of iteration and thereby reduce the computational time. In the transitional region, correlation functions that can accurately predict the onset of transition over a flat plate have been determined in a similar manner. The transitional correlations can be used in conjunction with any flow solver in order to automatically determine the onset of transition and apply a turbulence model for closure at the appropriate location. The general form of these correlation 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 by comparing them with experimental and empirical data available in the literature.