Assessing turbulence models for large-eddy simulation using exact solutions to the Navier–Stokes equations
Bachelor's thesis. University of Groningen, The Netherlands (2016).
We study the behaviour of turbulent fluid flows, behaviour that is governed by the Navier–Stokes equations. Due to the extensive detail entailed in a turbulent flow, it is diffcult to solve the Navier–Stokes equations numerically. A large-eddy simulation (LES), using a filtering operation, solves for the large-scale motions in a flow and smooths over small-scale motion, hence requiring a turbulence model for these small-scale motions. Using conditions derived from, and exact solutions to, the Navier–Stokes equations we investigate a number of turbulence models for LES both with and without explicit filtering. We found that the Vortex-Stretching-based eddy-viscosity model was most endorsed in the case without explicit filtering, and that the Vreman, QR, Gradient, and Vortex-Stretching-based models were equally endorsed by the case with explicit filtering, with the Smagorinsky model being the least endorsed. To reduce the bias that may arise when exact solutions are similar, we then considered classes of flows to further determine which models are the most endorsed. We considered classes based on Vreman's flow classes, and on the principal and combined invariants of flows. Once again the Vortex-Stretching-based eddy-viscosity model was usually the most endorsed. As more exact solutions to the Navier–Stokes equations are found, they can be easily added to the report to further endorse or oppose the models. We also considered Vreman's paper (2004) and did not find anything to contradict his results. We did extend his results slightly by finding a solution outside of his zero-subfilter-dissipation classes with zero subfilter dissipation.