An implicit numerical solution for the laminar and turbulent flow of an incompressible fluid along the axis of a 90-degree corner

Abstract

A method of solving the equations for the three–dimensional, incompressible laminar and turbulent flow along the intersection of two planes at ninety-degrees has been developed. The Alternating Direction Implicit (ADI) finite-difference method was applied for both types of flow. The turbulent stresses in the corner region were modeled with an eddy-viscosity model which was obtained from mixing length theory. The method was compared with other types of solutions for the laminar case and good agreement was achieved. For the turbulent case, the method was compared with experimental data and good agreement was obtained.

The three momentum equations were solved simultaneously and the continuity equation was used to verify the method. The method appeared to predict the velocity components correctly since the continuity equation residual approached zero as the solution proceeded from the leading edge in the mainstream flow direction.

No analysis was presented for the convergence or stability of the finite-difference equations and no convergence or stability problems solved were encountered when the finite-difference equations were solved. The method predicted symmetry about the corner bisector in all cases and gave the expected u-velocity profile along the bisector for both the laminar and turbulent cases.