Quantitative assessment of eddy viscosity rans models for turbulent mixed convection in a differentially heated plane channel

摘要

Turbulent mixed convection between two vertical, infinite parallel plates at different temperatures is studied using various two-equation turbulence models. The numerical simulations are performed at a turbulent Reynolds number of Re_τ = 150 and a Grashof number of Gr = 9.6 × 10~5. Comparisons are made against the highly trusted DNS results. Consistent with the DNS approach, the current simulations are performed using constant properties and the Boussinesq approximation to predict the influence of buoyancy. Previous studies have provided assessments of two-equation turbulence models for various scenarios, but often rely on a qualitative "eye" test in order to determine the most appropriate model to predict a given flow. This study aims to provide a new form of quantitative assessment that accounts for both the physics captured by the turbulence model as well as the magnitude of the system response quantities (SRQ) using a modified symmetric mean absolute percent error (SMAPE) method. This method is designed to be approachable to researchers at any level and can be applied to system response quantities from multiple research fields. Uncertainty quantification is also performed to determine the discretization error for each turbulence model. Recommendations are made as to which turbulence models best capture the physics - hydrodynamically and thermally - using both local and global validation metrics. Lastly, a sensitivity analysis is performed on the damping functions used in the most accurate models. This underpins the potential of model developments and adjustments most worth pursuing for buoyant flows. Overall, this framework provides a more physics-based comparative analysis of the selected turbulence models.