Abstract
RANS based turbulence models are still gold standard in industry despite their limitations. Traditionally, the development of turbulence models for heat transfer problems is driven by applications with either natural or forced convection dominated flows. Surprisingly, far too little attention has been paid to mixed convection problems with various buoyancy domination in the literature despite its importance for variety of engineering problems. Mixed type of flows exhibit complex flow interactions between buoyancy induced flows and inertial forces. The commonly used linear eddy viscosity and diffusivity models fail to reconstruct the Reynolds stress and turbulent flux profiles, which are mainly responsible for inaccurate heat transfer predictions, and suffer from severe convergence difficulties. Turbine casing cavity flows during different shut-down regimes, which are characterised by a wide range of mixed convection flows, are used as a platform for the development of a novel physics-based universal model to be used within RANS concept for mixed type of flows, which is presented in this paper. The model incorporates and blends a constitutive relation for Reynolds stress and a new generalised gradient diffusion hypothesis for turbulent heat fluxes. The new model, New Nonlinear RANS (NNR), has been developed to overcome the convergence difficulties with conventional RANS and to improve heat transfer predictions without having to solve any additional transport equation.
