Application of the turbulent potential model to unsteady flows: Numerical implementation and analysis
Unsteady turbulent flows are common in many engineering applications. In some of these flow situations, the turbulence does not have time to reach equilibrium with the mean flow. Previous research has indicated that two equation models are not accurate for non-equilibrium flows. Reynolds stress transport models can accurately predict non-equilibrium flows but tend to be more expensive. The turbulent body force potential model is able to capture non-equilibrium situations at a cost comparable to two equation models. In addition, this model naturally transits to a subgrid model or DNS in the appropriate mesh limits.
To apply the turbulent body force potential model to unsteady flows, an unstructured staggered mesh scheme for solving incompressible Navier-Stokes equations is proposed. This method has very good conservation properties. It requires low memory storage, uses very compact interpolation and discretizing operators. A detailed analysis of the discretization procedure is given. The numerical tests of some conservation properties and accuracy of some interpolations are presented. The mesh quality is very important to the implementation of this scheme. The issues such as mesh smoothing, flipping and adaptation are also discussed.
A CFD code is developed based on this numerical scheme. Unsteady vortex shedding in flows over two-dimensional obstacles (triangular and rectangular cylinders) at high Reynolds number are studied using this code. Comparisons with experimental data and other numerical simulations are presented. A full developed three-dimensional channel flow is also simulated at varies mesh resolutions. This test demonstrates the turbulent potential model's ability to transit from RANS to LES or DNS.