Effects of numerical techniques and near-wall modeling on the prediction of complex turbulent flows

When second-order closures are invoked, numerical treatment of the stress-gradient terms in the mean momentum equations becomes crucial to the accurate prediction of complex turbulent flows. Difficulties arise due to decoupling of the Reynolds-stress and the velocity variables and the absence of turbulent diffusion terms. These two issues are independent from each other and if they are not treated properly, physically unrealistic results and instability of the solution procedure is encountered.;Using a finite-volume method, the modeled equations are integrated around a control volume and various numerical treatments of the stress-gradient terms are tested on four different flows: developing flow inside a channel, flow over a backward-facing step, three-dimensional flow inside a square duct, and three-dimensional parallel jets issuing into a confinement. When the salient features of each flow are examined from both numerical and turbulence modeling points of view, it is seen that the numerical treatment of the stress-gradient terms in the mean momentum equations plays a role as important as the turbulence modeling. Some numerical treatments provide stability to the solution procedure but introduce considerable errors to the predictions. This partially explains why some of the results reported in the literature using second-order closures give poorer predictions than two-equation models. It is found that the predictions become more sensitive to the numerical treatment if the flow is influenced more by the Reynolds-stress than pressure gradients.;A near-wall second-order closure is developed to study the influence of different numerical methods and near-wall modeling on the prediction of complex flows. The model is formulated based on an asymptotic analysis of the high-Reynolds-number modeled and the exact time-averaged equations. Validation of the model is carried out on fully-developed Poiseuille and Couette flows. When compared with other near-wall second-order closures, the model is asymptotically more consistent and yield correct values for the near-wall asymptotes. It is able to reproduce the Reynolds number effects in the inner and outer layers of the turbulent boundary layer.