Assessment of Two- and Three-Scale k–ε Models for Rotating Cavity Flows

A three-scale k–ε turbulence model was recently developed for complex flows such as the rotor–rotor and rotor–stator cavities found in gas turbine engines. The three-scale model is a logical extension of the previous two-scale k–ε model of Ko and Rhode (1990). Both multiscale turbulence models are presented and assessed via comparison with measurements for possible adoption in future cavity computations. A single computer code solving the two-dimensional axisymmetric Navier–Stokes equations with a “switch” for selecting among the various turbulence models being compared was used. It was found for both cavity cases that the three-scale model gives a marginal improvement over the two-scale model. Further, both multiscale models give a substantial improvement over the standard k–ε model for the rotor–stator case, especially in the near-wall region where different eddy sizes are found. However, the feasibility of using a multiscale model for the rotor–rotor case is unclear since it gives improved values over the standard high-Re model in some regions but worse values in other regions. In addition, the solutions provide enhanced insight concerning the large changes in flow pattern previously photographed in the rotor–rotor case as rotation increases. In particular, it is shown how: (a) the number of recirculation zones increase with increasing rotation rate and (b) the recirculation zones decrease in size with a decreasing G ratio.