Modelling of turbulent energy flux in canonical shock-turbulence interaction |
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Affiliation: | 1. School of Mechanical Engineering, Andong National University, Andong 760-749, Republic of Korea;2. Department of Mechanical Engineering, Saga University, Saga, Japan;1. Università degli Studi di Bergamo, Dipartimento di Ingegneria e Scienze Applicate, viale Marconi 5 - 24044 Dalmine (BG), Italy;2. Von Karman Institute for Fluid Dynamics, Turbomachinery and Propulsion Department, Chaussée de Waterloo 72, Rhode-Saint-Genèse, Belgium;3. Università di Brescia, Dipartimento di Ingegneria Meccanica e Industriale, via Branze 38 - 25123 Brescia, Italy |
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Abstract: | High-speed turbulent flows often encounter high heat loads due to the presence of shock waves. The turbulent energy flux correlation in the mean energy conservation equation is a key unclosed term that determines the heat transfer rate. In this work, we employ existing turbulence models to predict the turbulent energy flux in canonical shock-turbulence interaction. The shortcomings of these models are highlighted, and a new heat-flux limiter model is proposed with the aid of linear theory results. We also write the transport equation for the turbulent energy flux across a shock wave and use it to develop a physics-based model for the same. It is found to predict the peak energy flux at the shock wave and its variation in the acoustic-adjustment region behind the shock. Numerical error incurred while solving the model equations at a shock wave are analyzed and a numerically robust model is obtained by eliminating the nonconservative source terms. The model predictions are compared with available direct numerical simulation data and a good match is obtained for a range of Mach numbers. |
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