Development of the Generalised Hybrid Turbulence Model for RANS simulations

Turbulence plays an important role in a broad range of engineering applications. In the industry RANS simulations are a common method for predicting turbulent flow. A broad range of RANS turbulence models have been developed over the past decades. For the assessment of complex three-dimensional flow fields Reynolds Stress Transport Models are a better choice than eddy viscosity models, even though their computational cost is higher. A hybrid model that combines the accuracy of the Reynolds Stress Transport Models with the computational speed of the eddy viscosity models could be a valuable tool in the design of structures subjected to complex three-dimensional flows. Therefore the development of such a hybrid model was the objective of this thesis. A literature study on existing RANS turbulence models showed that the Reynolds Stress Transport Models (RSTM) are the most physical but also the computationally most expensive models. The linear eddy viscosity models have a reduced computational cost, but are not capable of predicting flow features that are caused by the Reynolds stress anisotropy, since these models can not account for this anisotropy. The non-linear eddy viscosity models include extra anisotropy by means of higher order terms, but the coefficients in these models are calibrated using simple benchmark test cases, making their applicability to more complex flows uncertain. The Hybrid Turbulence Model (HTM) of Basara combines a RSTM with the formulation of the linear eddy viscosity models to reduce the computation time of the simulation. This hybrid model is also unable to account for Reynolds stress anisotropy just like the linear eddy viscosity models. The development of the Generalised Hybrid Turbulence Model (GHTM) in this thesis, was motivated by this deficiency of the HTM. This novel hybrid model combines a RSTM with the general formulation of the non-linear eddy viscosity models. By using multiple base tensors additional Reynolds stress anisotropy is included. The HTM and the Improved k-epsilon model The GHTM was implemented in OpenFOAM and three test cases were investigated with this new model. The simulations with the GHTM do not reach convergence, except when the full tensor base is considered. The simulations with the Improved k-epsilon model converge and yield more physical results for the U-bend test case, showing a recirculation zone, where the standard k-epsilon model does not predict this flow feature. A mesh refinement study showed that the grid size has no influence on the performance of the GHTM. Also the use of different gradient schemes or under-relaxation did not affect the convergence of the GHTM simulations. To improve the performance of the GHTM different smoothing techniques have been tested, since peaks in the model coefficients seemed to cause the instability of the simulations. The proposed smoothing methods are modifications of the original GHTM and are therefore not useful to improve the performance of the GHTM. A closer look at the properties of the tensors used in the GHTM for statistically two-dimensional flows showed that an error in trace of the mean rate of strain tensor cause the resulting Reynolds stress anisotropy tensor to be incorrect. This problem was solved by constructing more accurate cell face velocities which correspond to the known cell face fluxes. With these new face velocities the GHTM with N=2 converges for the two-dimensional cases, but the linear GHTM still does not converge. A further investigation of the performance of the GHTM for statistically two-dimensional flows showed that in that case the GHTM with N=2 is identical to the background RSTM. This shows that the GHTM with N>1 could only lead to a reduction in computation time for three-dimensional flows.