Generalized wall functions for RANS computation of turbulent flows

In the field of Computational Fluid Dynamics (CFD) a challenge is represented by the wall treatment for wall bounded turbulent flows. Indeed the so-called wall blocking effect causes a different behavior of the flow in the near-wall region. There are two methods for dealing with this challenge: Low Reynolds models and Wall Functions. The first method requires a fine near wall mesh in order to solve the entire wall affected region, but this requirement makes the computational time and costs increase. The Wall Functions method, used along with a k-ε turbulence model, allow the user to adopt a coarser near-wall mesh, but the behavior of the flow in the proximity of the wall (in terms of wall shear stress, production of turbulent kinetic energy and turbulent dissipation rate) is estimated through pre-integrated expressions. In Fluent 6.3 there are two Wall Functions available, i.e. Standard Wall Functions (SWF) and Non-Equilibrium Wall Functions (NEWF). However, the pre-integrated expressions used by these two Wall Functions are not universal. An alternative is given by Generalized Wall Functions (GWF), proposed by Popovac and Hanjalic, whose pre-integrated expressions, according to the authors, are based on more general assumptions. To be more specific, the law of the wall adopted by GWF is sensitized to the local non-equilibrium effects of the flow. First of all, a review of challenges related to wall bounded turbulent flows, of k-ε turbulence models available in Fluent 6.3 and of Wall Functions approach (including the way SWF and NEWF are implemented into Fluent 6.3) has been presented. The first work made consists of the writing of a user defined function (udf) for the implementation of GWF into Fluent 6.3 (this work includes a deep analysis of the way the macro DEFINE_WALL_FUNCTIONS works). After that, an evaluation of the quality of the results obtained with GWF has been carried out. Their performance has been tested for an axial symmetric conical diffuser geometry. In order to evaluate the goodness of the Wall Functions approach itself, sensitivity analyses (using always SWF) of near wall mesh, core mesh and turbulence model have been made. These analyses have allowed to obtain the best combination of these three parameters in terms of results obtained with a CFD simulation. This combination has been used along with GWF. A sensitivity analysis regarding the velocity scale used inside GWF law of the wall has been carried out. The slopes of the GWF log law of the wall along the diffuser are found out to have a trend similar to experimental slopes. Wall shear stress shows an improvement too, but the accordance to the experimental data is still not perfect. GWF are promising because they have a more physical background and they are easy to implement inside a commercial CFD code. However, their performance must be tested for other benchmarks different from the conical diffuser, like a backward facing step.