Prediction of separation induced transition on thick airfoil using non-linear URANS based turbulence model

Abstract

Most of the turbulence models in practice are based on the assumption of a linear relation between Reynolds stresses and mean flow strain rates which generally provides a good approximation in case of attached and fully turbulent flows. However, this is seldom the need in most of the engineering problems; the majority of the engineering problems observe flow separation or flow transition. Recent developments in non-linear turbulence models have proven significant improvement in prediction of separated flow due to better resolution of anisotropy in modeled Reynolds stress. The domain of application of this improved RANS model can be extended to flow transitions as well, where the resolution of anisotropy in Reynolds stress is required. For a validation of such kind, a two-dimensional numerical study has been carried out over NACA 0021 with k-ω SST model with non-linear correction at Re = 120000 for various angles of attack which experiences the formation of a laminar separation bubble (LSB). A correct prediction of LSB requires an accurate resolution of anisotropy in Reynolds stresses. For comparison with other linear models, the simulations are also performed with k-k_l-ω (a 3-equation linear transition model), k-ω SST (a 2-equation linear model) and Spalart-Allmaras (a 1-equation model). The performance of these models is assessed through aerodynamic lift, drag, pressure and friction coefficients. It is found that the non-linear k-ω SST and k-k_l-ω transition model provide comparable quality of prediction in lift and drag coefficients (in spite of the fact that non-linear k-ω SST involves solving less number of transport equation than the transition model) as observed in the experiments whereas k-ω SST and SA models under predict the drag coefficient value at low angle of attack due to inability to capture the separation induced transition. It is also observed that the location of laminar separation bubble is captured accurately when non-linear or transition model is used as opposed to the SA or linear SST models, which lack in the ability to predict the same.