Advanced turbulence models for recirculating flows

The standard k-e model has been widely used due to the simplicity and realistic predictions it makes. However, the standard k-e model has its disadvantage. It can only be applied in the high Reynolds number region of the flow where the viscous effect is less important. For flow close to a wall, where local Reynolds number is low and viscous effect dominates, the standard k-e model will not perform satisfactorily. The drawback has limited the first grid adjacent to the wall to be placed in the fully turbulent region which is not close enough to the wall to predict the wall effect on the flow. To tackle this near wall region, the common practice is to use an empirical wall function to approximate turbulence quantities for the grid adjacent to the wall and the standard k-e model for the rest of the grids. The wall function is a logarithmic profile correlated from boundary layer data.

Moreover, most of the success of the standard k-e model is limited to simple turbulent flows, such as boundary layer flows and flows in a plane duct with no recirculation. However, industrially, the most important flow, the turbulent flow, is separated in the presence of adverse pressure gradient, creating a recirculating region. In recirculating flows where the flow at a point is influenced by flow conditions upstream and downstream, the standard k-e model is known for underpredicting the recirculation region. This drawback in the standard k-e model has led researchers to look for a better turbulence model to predict recirculating flow.

In this study, some efforts were made to move from the standard k-e model to the higher level turbulence models that can predict recirculating flows. Basically, there are two ways to approach this purpose. Both approaches were pursued in this study. The first way is an easier approach, and this approach modifies the standard k-e model so that it works on both viscous and fully turbulent regions. The second way is to get rid of the unrealistic eddy-viscosity concept and study the multi-equation Reynolds stress model. A new Reynolds stress model, the SSG model of Speziale, Sarkar and Gatski [8], was investigated in this study. The original version of SSG model cannot predict recirculating flow. After a simple modification was made, it can work for predicting recirculating flow. However, the modified SSG model still has very poor performance in predicting recirculating flow. Further efforts are made to improve the SSG model, and a new SSG model is proposed in this study.