Development and Application of a New Four-Equation Eddy-Viscosity Model for Flows with Transition, Curvature and Rotation Effects

摘要

This paper presents the development and implementation of a new scalar eddy-viscosity turbulence model designed to exhibit physically correct responses to flow transition, streamline curvature and system rotation effects. The eddy-viscosity model developed herein is based on the k-ω framework and employs four transport equations in addition to the mean flow equations. The model inherits three transport equations from the transition-sensitive k-k_L-ω model and the v~2 equation from the previously documented curvature-sensitive SST k-ω-v~2 model. The new model is implemented into a commercial computational fluid dynamics (CFD) solver, and is tested on several two-dimensional (2D) problems involving flow transition, streamline curvature and rotation effects. In order to assess the model's performance, three test cases are presented: a zero-pressure-gradient flat plate, flow over a cylinder for a wide range of Reynolds numbers and flow over an elliptic airfoil test case with different angles of attack. The results obtained from the test cases are compared with experimental data and several other RANS-based turbulence models. These indicate that the new model successfully resolves both flow transition and curvature effects with reasonable engineering accuracy, for only a small increase in computational cost. Results also suggest that the new model has potential as a practical tool for the prediction of flow transition and curvature effects over blunt bodies.