Improved turbulence modeling of film cooling flow and heat transfer

Film-cooling flows are characterized by a row of jets injected at an angle from the blade surface or endwalls into the heated crossflow. The resulting flowfield is quite complex, and accurate predictions of the flow and heat transfer have been difficult to obtain using traditional two-equation turbulence models employed with ReynoldsAveraged Navier–Stokes (RANS) solvers. Recently, a four-equation model, the ε k f v − 2 model, has been shown to yield improved predictions in a wide range of applications including gas turbine flows. However, this model retains some of the drawbacks inherent with ε-based models, and in many applications exhibits significant numerical stiffness. In the present chapter, a new model is presented (the ω k f v − 2 model), which is based on ω as the relevant length scale, and provides predictive accuracy that is comparable to or better than the ε k f v − 2 , but with significantly improved numerical stability. This new model is tested on a filmcooling flow application, and computations are compared with detailed flow and cooling effectiveness measurements. It is shown that the ω k f v − 2 model provides improved flow predictions over other turbulence models, but that a variable Prandtl number formulation is necessary for improved cooling effectiveness predictions. A Prandtl number expression is proposed and shown to yield improved predictions. www.witpress.com, ISSN 1755-8336 (on-line) WIT Transactions on State of the Art in Science and Engineering, Vol 15, © 2005 WIT Press doi:10.2495/978-1-85312-956-8/04