Turbulent flows developing along the corners are studied numerically for two different geometries : straight square duct and wing-body junction. The secondary flow is generated in the corners mainly due to the Reynolds stress, which is main interest of this paper. Initially, in the case of duct flow, uniform flow conditions are given to predict secondary flow. Experimental data for the initial longitudinal vortical flow fields are used in the case of wing-body junction flow.
The numerical procedure incoporate a finite volume method using a strong conservation form of the partially-parabolized Navier-Stokes equation.
The non-linear $k-\epsilon$ turbulence model developed by Speziale is employed for the prediction of developing turbulent flow in a straight square duct. Turbulent flow in the corner region of the wing-body junction is calculated by using both the standard $k-\epsilon$ model and the non-linear $k-\epsilon$ model.
For the straight duct, mean velocity field and turbulent kinetic energy are calculated and the results are compared with available experimental data, which show favorable agreements. For the wing-body junction, the results obtained by using the non-linear $k-\epsilon$ model show better qualitative agreement with the experimental data than those obtained by the standard $k-\epsilon$ model. However, more considerations about the numercal scheme, the initial conditions and the boundary conditions as well as turbulence model are necessary to improve the results quantitatively.
