Reynolds-Stress Modelling - Concepts, Advances and Challenges

Kurzfassung

The Reynolds-Averaged Navier-Stokes (RANS) equations are still the backbone of numerical flow simulations in industrial applications. Hence, a turbulence model is required for closure, which decides about the accuracy of the predictions. Many models are based on the assumption of a flow dependent eddy viscosity added to the molecular viscosity of the fluid. While agreeing with the observation of enhanced momentum transfer due to turbulent fluctuations, this is a significant simplification of the physics of turbulent flow, limiting the predictive accuracy in complex flow situations. Improvement is expected by Reynolds-stress modelling based on the transport equation for the individual components of the Reynolds-stress tensor and for an additional length-scale providing variable. In this case, the modelling is restricted to the different terms of the Reynolds-stress transport equation and the length-scale equation that is usually taken over from corresponding eddy-viscosity models and considered the weakest link of the approach. The presentation will introduce the Reynolds-stress transport equation, explain the physical significance of its terms and outline the corresponding modelling approaches. Recent advances have been achieved by developing a length-scale correction. The underlying idea will be presented and its improvement on the prediction of separated flows will be demonstrated. Turbulence modelling is challenged by the variety of flow phenomena that need to be treated. This will be underlined by a theoretical analysis of self-similar free-shear flows, predicting a layer of constant Reynolds-stress anisotropy. Experimental data confirm its existence, revealing differences in the turbulence structure between different flows. Hence, a self-adaptive modelling strategy is required, applying tailored models to automatically identified regions of the flow field. An example will be given, demonstrating the potential of such tailored modelling.