Potential Turbulence Model Predictions of Flow past a Triangular Cylinder Using an Unstructured Staggered Mesh Method

Numerical simulation of the turbulent flow around a triangular cylinder at Reynolds number of 45,000 is presented in this paper. A body force potential model is used to model the turbulent motion. This approach is able to model non-equilibrium turbulence accurately at a cost and complexity comparable to k-ε models. The numerical method used in this calculation is an unstructured staggered mesh scheme. The Strouhal number and timeaveraged velocity profiles obtained from this simulation agree with experiments. INTRODUCTION The flow around a triangle provides an example of bluff body flow with fixed separation points. If the Reynolds number is not too small the flow is inherently unsteady and a Von Karman vortex street appears with a well-defined frequency. If the Reynolds number is sufficiently high the flow will be turbulent and a turbulence model must be included to model the turbulent fluctuations. The large-scale motions of the vortices are not turbulence, so they should be resolved by the numerical scheme and only the small-scale fluctuations are modeled. LDA measurement by Sjunnesson et al. [1] of vortex shedding flow past a triangular cylinder in a duct at ReD=45,000 is a useful test case for unsteady turbulent flow of this kind. Their experimental study was motivated by the application to flame holders. Johansson et al [2] carried out numerical simulation of this flow using a k-ε model. Durbin [3] (1994) carried out a simulation using a k-ε2 v model. In some similar simulations by Franke et al. [4], they compared the ability of different models to predict turbulent vortex shedding from a rectangular cylinder. Franke’s conclusion is that some k-ε models do not predict the right shedding frequency and Reynolds stress transport models can produce results in good agreement with the experiments. It is hypothesized that this is because the turbulence is not in equilibrium with the mean flow. The proposed turbulent potential model is a simplified Reynolds stress transport model, which has the ability of modeling non-equilibrium turbulence with the computing cost and complexity comparable to k-ε model. EQUATIONS Mean Flow Equations R u u p u u t u T r r r r r r ⋅ ∇ − ∇ + ∇ ⋅ ∇ + − ∇ = ⋅ ∇ + ∂ ∂ ) ( ) ( ν