SWIRLING STREAMLINE-CURVATURE LAW OF THE WALL FROM A NOVEL PERTURBATION ANALYSIS

Abstract

A new law of the wall for swirling axial boundary layers is derived analytically, which accounts for local streamline curvature effects. Compared to previous derivations, the new law covers a wider range of streamline curvature, y+, and the axial-to-swirl shear stress ratio. Incorporation of the local streamline curvature physics gave greatly increased mathematical difficulty. The difficulty was handled by developing a novel perturbation solution approach, which is thoroughly presented. This new solution approach allows a closed-form analytical solution to many similar nonlinear problems which heretofore required numerical techniques. To demonstrate the worst-case scenario for swirl prediction (computational fluid dynamics, CFD) improvement, the new law of the wall was implemented in the standard k-epsilon model as a wall function. The new law gives CFD solutions in closer agreement with measurements than does the classical log law.