An improved orthogonal grid generation method for solving flows past highly cambered aerofoils with and without roughness elements

Abstract

In the present work, a new hybrid hyperbolic-elliptic orthogonal grid generation method has been proposed and its applications are demonstrated in solving incompressible Navier–Stokes equation using orthogonal grid formulation. Present method is a significant improvement over the successful hyperbolic grid generation method originally proposed in Nair and Sengupta (1998). The algorithm proposed is implemented to generate an orthogonal grid around cambered aerofoils like NACA-8504, AG24, WTEA-TE1 aerofoils. Creating a hyperbolic grid over an aerofoil with localized camber like WTEA-TE1 is very challenging to ensure smooth grid metrics, to have negligible deviation from orthogonality and at the same time grid-shocks should not degrade the solution. Orthogonal grid generation around the SHM-1 Honda aerofoil with multiple roughness elements on the top surface is also shown here. The hybrid hyperbolic-elliptic grid generation is done by marching in wall-normal direction iteratively. Importance of numerically generated orthogonal grid is demonstrated by studying flow past AG24 aerofoil using orthogonal formulation of Navier–Stokes equation. Computed results match well with available experimental results. The present grid generation algorithm, the importance of grid metrics and its control is provided here in a systematic manner.