Numerical Benchmark of Nonconventional RANS Turbulence Models for Film and Effusion Cooling

Abstract

Over the course of the years, several turbulence models specifically developed to improve the predicting capabilities of conventional twoequations Reynoldsaveraged Navier–Stokes (RANS) models have been proposed. They have, however, been mainly tested against experiments only comparing with standard isotropic models, in single hole configuration and for very low blowing ratio. A systematic benchmark of the various nonconventional models exploring a wider range of application is hence missing. This paper performs a comparison of three recently proposed models over three different test cases of increasing computational complexity. The chosen test matrix covers a wide range of blowing ratios (0.5–3.0) including both single row and multirow cases for which experimental data of reference are available. In particular the wellknown test by Sinha et al. (1991, “FilmCooling Effectiveness Downstream of a Single Row of Holes with Variable Density Ratio,â€‌ J. Turbomach., 113, pp. 442–449) at BR = 0.5 is used in conjunction with two inhouse carried out experiments: a single row filmcooling test at BR = 1.5 and a 15 rows test plate designed to study the interaction between slot and effusion cooling at BR = 3.0. The first two considered models are based on a tensorial definition of the eddy viscosity in which the streamspan position is augmented to overcome the main drawback connected with standard isotropic turbulence models that is the lower lateral spreading of the jet downwards the injection. An anisotropic factor to multiply the off diagonal position is indeed calculated from an algebraic expression of the turbulent Reynolds number developed by Bergeles et al. (1978, “The Turbulent Jet in a Cross Stream at Low Injection Rates: A ThreeDimensional Numerical Treatment,â€‌ Numer. Heat Transfer, 1, pp. 217–242) from DNS statistics over a flat plate. This correction could be potentially implemented in the framework of any eddy viscosity model. It was chosen to compare the predictions of such modification applied to two among the most common twoequation turbulence models for filmcooling tests, namely the twolayer (TL) model and the k–د‰ shear stress transport (SST), firstly proposed and tested in the past respectively by Azzi and Lakeal (2002, “Perspectives in Modeling Film Cooling of Turbine Blades by Transcending Conventional TwoEquation Turbulence Models,â€‌ J. Turbomach., 124, pp. 472–484) and Cottin et al. (2011, “Modeling of the Heat Flux For MultiHole Cooling Applications,â€‌ Proceedings of the ASME Turbo Expo, Paper No. GT201146330). The third model, proposed by Holloway et al. (2005, “Computational Study of JetinCrossflow and Film Cooling Using a New UnsteadyBased Turbulence Model,â€‌ Proceedings of the ASME Turbo Expo, Paper No. GT200568155), involves the unsteady solution of the flow and thermal field to include the shorttime response of the stress tensor to rapid strain rates. This model takes advantage of the solution of an additional transport equation for the local effective total stress to trace the strain rate history. The results are presented in terms of adiabatic effectiveness distribution over the plate as well as spanwise averaged profiles.