Derivation, testing and application of a new multi-scale k-e̳ turbulence model

Abstract

This study discusses the derivation and assessment of a new two-scale dissipation equation, the genesis of which begins with a different fundamental equation than previous multi-scale or single-scale models. The new approach presented constitutes progress in removing shortcomings inherent in the dissipation equation of single-scale two-equation turbulence models. That is, the standard requirement of modeling the source/sink terms using physical/dimensional arguments has been circumvented at the expense of algebraic complexity in the derivation. Also, a new way of evaluating the source/sink coefficient functions, which introduces new two-point correlation physics, is utilized. Comparison of predictions with the measurements of numerous test cases reveals that the new two-scale k-ε model is preferred over the standard k-ε model. For example, the spreading rate of an axisymmetric free jet was predicted within 9 percent of the measured value versus approximately 30 % using the popular standard k-ε model. In addition, the new turbulence model is employed in a numerical parametric study of a generic enclosed rotating cavity of a gas turbine engine. The cooling flow rate supplied to the cavity must be high enough to prevent the turbine blade root or retainer from being overheated by the hot mainstream, which is critical for the reliability of the rotor and the stator. The relationships among the important flow and geometry parameters are investigated by examining the entire set of computations. Predicted velocity fields and isotherms reveal the complicated interaction of the Ekman layer, the cavity core region, the gap recirculation zone and the mainstream. Also, the study presents generalized first-order design estimates for: (a) the minimum cooling flow rate for any desired maximum disk temperature and (b) the corresponding radial temperature distribution along the disk surface. Also, the friction moment of the disk surface was calculated for various conditions.