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DIFFERENT EXPLICIT ALGEBRAIC REYNOLDS STRESS MODEL REPRESENTATIONS AND THEIR PREDICTIONS OF FULLY DEVELOPED TURBULENT ROTATING PIPE FLOW

Olaf Grundestam
Department of Mechanics, Royal Institute of Technology, KTH SE-100 44 Stockholm, Sweden

Stefan Wallin
Linne FLOW Center, Department of Mechanics Royal institute of technology Osquars Backe 18, Stockholm, Sweden

Arne V. Johansson
Linne FLOW Centre, Dept. of Mechanics, Royal Institute of Technology SE-100 44 Stockholm, Sweden

Abstract

The least square projection method is used for obtaining optimal EARSMs for different incomplete sets of basis tensors. The possible singular behaviour depending on the choice of the basis tensors has been investigated. It is demonstrated that many of the incomplete representations, expressed in general 3D mean flows, have singularities in some specific flows, such as general 2D mean flows or more specifically, strain and/or rotation free 2D mean flows.
The different representations are investigated by computing fully developed rotating pipe flow. It is demonstrated that EARSMs containing basis tensors of odd powers higher than one, of the mean velocity gradients, do indeed predict a parabolic mean azimuthal velocity profile. The predcitions made by the incomplete representations deviate significantly from those by the complete representations, and the actual choice of basis tensors as well as the model parameters have a significant effect on the predictions.