Perspectives on Reynolds Stress Modeling. Part I: General Approach

Abstract

RANS models are still the backbone of contemporary CFD methods because of their lower simulation cost compared to scale-resolving methods at acceptable prediction accuracy for attached flow. The current trend towards a fully simulation-based design challenges this philosophy because the accuracy requirements are extended to off-design conditions associated with separation. It is assumed that the RANS approach is still valid at incipient and mild separation and that the observed failure is due to model-simplifications, like the Boussinesq hypothesis, or to limitations of the calibration approach. Therefore, Reynolds stress models (RSM) based on the transport equations for the individual Reynolds stresses are considered as a possibility for improvement. Such models are numerically demanding, but have shown to be applicable to industrial problems at moderate cost (e.g. SSG/LRR-omega). Reynolds stress models constitute the highest level within the RANS context, having the advantage that the production mechanism is described exactly in terms of given quantities. Their key-element is the modeling of the re-distribution mechanism of kinetic turbulence energy between the different components, where a wide variety of models can be constructed, and the equation that models the rate of dissipation of turbulent kinetic energy. This, in principle, allows for a specific calibration of the respective model. The presentation will briefly describe the different components of Reynolds stress models and the approaches for modeling them. A zonal approach is suggested, allowing a model to adapt to the respective flow situation, e.g. strong pressure gradients, separation and reattachment. Such development could be supported by advanced methods of data analytics and machine learning. The need for compressibility corrections, including necessary experimental support, is considered as an open question that should be addressed in the general discussion. An effort towards a zonal model improvement for flows subjected to adverse pressure gradients will be addressed in a companion presentation by T. Knopp.