Application of the k-omega turbulence model to quasi-three-dimensional turbomachinary flows

Abstract

Many computational fluid dynamics codes for turbomachinery use the Baldwin-Lomax (B-L) turbulence model. It is easy to implement in two dimensions and works well for predicting overall turbomachinery performance. However, it is awkward to implement in three dimensions, often has difficulty finding the length scale, has a crude transition model, and neglects freestream turbulence, surface roughness, and mass injection. The kappa-omega model developed by Wilcox is an appealing alternative for several reasons. First, it is the only two-equation model that can be integrated to the wall without requiring damping functions or the distance to the wall, and hence, should behave well numerically. Second, the effects of freestream turbulence, surface roughness, and mass injection are easily included in the model. Finally, transition can be simulated using the low Reynolds number version of the model. Menter applied the kappa-model to external flows and showed very good results for flows with adverse pressure gradients. Liu and Zheng described their implementation of the kappa-model in a cascade code that included an area change term to account for endwall convergence. They validated the model for a flat plate, and compared the B-L and kappa-models to measured surface pressures for a low-pressure turbine cascade. Since they did not use the low Reynolds number version of the model, their results showed problems resulting from early transition. In this Note the low Reynolds number kappa-model was incorporated in the author's quasi-three-dimensional turbomachinery analysis code. The code includes the effects of rotation, radius change, and stream-surface thickness variation, and also includes the B-L turbulence model. The kappa-omega model was implemented using many of Menter's recommendations and an implicit approximate-factorization scheme described by Baldwin and Barth. The model was tested for a transonic compressor with rotation and variable stream-surface radius and height, and for a transonic turbine vane with transition and heat transfer. Results were compared to the B-L model and to experimental data.