A Study of Global-Coefficient Non-Linear Eddy Viscosity Models

Abstract

In this research a global-coefficient non-linear eddy viscosity model (NLEVM) is studied. This model stems from the inherent inability of the Boussinesq approximation to model anisotropy and therefore flow features such as: swirl, stream-line curvature and secondary motions (Lumley, 1970; Pope, 1975; Craft et al., 1996). The focus lies on the limitations of using global-coefficients calibrated on a square-duct flow when applied on a rectangular-duct and a wing-body junction. The calibration is done with the Direct Numerical Simulation (DNS) results from Pinelli et al. (2010) at a Reynolds number of Re = 1, 100. It is shown that using a global-coefficient NLEVM the velocity prediction on a square-duct and rectangular-duct is successfully corrected, i.e. secondary motions are present. On an attempt to improve the corner flow separation on a wing-body junction poor performance is observed. Stability issues led to only 3 models converge out of 21. Differently to Bordji et al. (2014) who found a large corner flow separation reduction with a Spalart-Allmaras Quadratic Constitutive Relation (SA-QCR) turbulence model when compared to a standard SA model, the global-coefficient NLEVM only showed limited corner flow separation reduction. Apart from correcting the anisotropy the near-wall resolution and treatment is found to be of large importance for flow field predictions. In the square- and rectangular-duct a wall damping function destroyed the secondary motion prediction, whilst in the wing-body junction improving the junction and corner flow prediction.