Non-Linear k-ε-ζ-f Model Sensitized to Rotation for Blade Turbine Internal Cooling

Abstract

The need to study flow and heat transfer in turbine blade cooling design calls to develop appropriate modelling approaches able to return accurate predictions at a reduced computational costs. Here we propose and scrutinize a quadratic version of the well-known k-ε-ζ-f RANS turbulence models, aiming at sensitizing the model to the effect of rotation in configurations mimicking the flow in turbine internal cooling. Starting from the evidence that rotation modified turbulent flow through a turbulence suppression (enhancement) on the stabilized (destabilized) surface, we modified the Cμ coefficient present in the formulation of turbulent viscosity introducing a dependence on the strain and vorticity tensors, the latter explicitly including solid body rotation. The proposed model was tested on plane channel and square-sectioned duct flows, and then used for simulating a rib-duct rotating channel. Results are assessed against DNS literature data and properly developed LES computations, by examining flow variables, heat transfer and turbulence budgets. We demonstrate that, as for the channel flows, the proposed quadratic model is able to accurately reproduce velocity, temperature and turbulent variables at various angular velocity regimes. In the duct flow the flow is subjected to the mutual influence vorticity induced by rotation and turbulence anisotropy developing close the walls. In particular, the non-linear rotation-sensitized model is able to reproduce the near-wall turbulent kinetic energy distribution close to the suction side, returning a zero value in the mid-span and a small peak close to the wall on the suction side. Turbulent kinetic energy and temperature budgets analysis demonstrates the capabilities of the model in describing all the terms in the equations. Also if some tuning of the model is required, these analysis showed very encouraging results. In fact if the basic mechanisms of turbulence and heat transfer are properly predicted, then it can be expected that the model can be successfully applied to a set of different cases. For such reason, the model was applied to the analysis of flow and heat transfer in a rotating ribduct with reasonably results.