RANS turbulence models for FENE-P viscoelastic fluids

The development of robust turbulent viscoelastic models to predict drag reducing behaviour of polymer additives within industrial flows is highly sought after. The main objective of this thesis is to develop Reynolds Averaged Navier-Stokes (RANS) models based on the Finitely Extensible Nonlinear Elastic Peterlin (FENE-P) rheological constitutive model for the polymer chains, to predict mean features of drag reducing flows. A DNS database from multiple literature sources is collated to validate the closure models \textit{a priori}, along with the performance of the models' mean field predictions. A new finite volume C++ computational solver is adapted in the OpenFOAM software to include the FENE-P parameters within the pre-existing turbulence class structure. A robust framework is developed for fully developed channel flow and square duct cases within foam-extend/4.0. A novel application of the groovyBC functionality is used to develop boundary conditions for the conformation tensor field.

Two isotropic models (k-epsilon and k-omega) are developed in the context of fully-developed channel flow which improve upon previous models. This is achieved with a modified damping function which mimics the viscoelastic effects on the turbulent redistribution process. The non-linear terms in the constitutive equation are also greatly improved with robustness and stability, by removing friction velocity dependence and reducing complexity. The model prediction span a larger DNS data set for friction Reynolds number, Re_tau_0, Weissenberg number, Wi_tau_0, maximum polymer extension, L^2, and concentration variation, beta. An anisotropic k-epsilon-v^2-f model is also developed to predict turbulent viscoelastic flow features in fully-developed channel flow and square ducts, via an extension to the Newtonian model. The non-linear closures are developed based on the premise that polymer stretching from near wall turbulent shears coincides and aligns with the mean vorticity direction, t_i, and redistributes energy to the wall normal direction, n_i, in a similar process to the Reynolds stress tensor. The predictions for the model include fully developed channel flow and square ducts, with flow features for the conformation tensor, Reynolds stresses, mean velocity (and the bending of the isolines), along with the shift of the secondary flow vorticity centre away from the wall.