A priori evaluations and least-squares optimizations of turbulence models for fully developed rotating turbulent channel flow |
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| Affiliation: | 1. Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, Hunan 421008, People’s Republic of China;2. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and Security), MGR Knowledge City, CIT Campus, Taramani, Chennai 600 113, India;3. Department of Mathematics and Systems Analysis, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland;1. Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167 Hannover, Germany;2. Departamento de Física, Universidade Federal de São Carlos, C.P. 676, 13565-905 São Carlos (SP), Brazil;1. Nomura International Plc., 1 Angel Lane, London EC4R 3AB, UK;2. International Monetary Fund, Research Department, 700, 19th Street NW, Washington DC 20431, USA;3. University of Oxford, Oxford Centre for the Analysis of Resource-Rich Economies, Oxford, UK;4. University of Oxford, Mathematical Institute, 24–29 St Giles, Oxford OX1 3LB, UK;5. Oxford-Man Institute of Quantitative Finance, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6ED, UK |
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| Abstract: | The present study involves a priori tests of pressure-strain and dissipation rate tensor models using data from direct numerical simulations (DNS) of fully developed turbulent channel flow with and without spanwise system rotation. Three different pressure-strain rate models are tested ranging from a simple quasi-linear model to a realizable fourth order model. The evaluations demonstrate the difficulties of developing RANS-models that accurately describe the flow for a wide range of rotation numbers. Furthermore, least-squares based tensor representations of the exact pressure-strain and dissipation rate tensors are derived pointwise in space. The relation obtained for the rapid pressure-strain rate is exact for general 2D mean flows. Hence, the corresponding distribution of the optimized coefficients show the ideal behaviour. The corresponding representations for the slow pressure-strain and dissipation rate tensors are incomplete but still optimal in a least-squares sense. On basis of the least-squares analysis it is argued that the part of the representation that is tensorially linear in the Reynolds stress anisotropy is the most important for these parts. |
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