| A complementary set of RANS equations has been developed for an incompressible fluid flow. The method is based on a decomposition of the velocity vector field into a viscous flow and a potential flow. The decomposition introduces a new complementary velocity and two additional convection terms involving viscous and potential solutions to the conventional RANS equations.; The proposed complementary RANS equations have been validated for steady laminar and turbulent flows. The laminar flow cases include the flow in a three-dimensional square duct at Re = 790, the flow over a two-dimensional flat plate at Re = 7900, and the flow over a two-dimensional NACA 0010 airfoil at Re = 7900. The turbulent flow cases include the flow over a two-dimensional flat plate at Re = 1.6E6, and the flow over a two-dimensional NACA 0012 airfoil at Re = 2.8E6. The computational results indicate that the smoothness of a potential solution is important to reduce the numerical errors in the evaluation of the two extra terms in the complementary RANS solver. The feasibility of the new method is shown by the good agreement between the predictions of the complementary RANS solver (u*-code) and the results from a conventional RANS solver (u-code) as well as other experimental and numerical data. The u*-code shows less grid-dependency than the u-code, which opens the possibility to save computational time by using less resolved grids. |
