Wall Function Approach

This method employed successfully in many applications (Launder and Spalding (1974)) uses the Logarithmic Law of Wall , described above, as the constitutive relation between velocity and the wall shear stress. In terms of the velocity at the grid point closest to the wall surface, one assumes the law of wall to hold good. Such bridging between wall and the fully turbulent layer away from the walls allows prescription of the boundary conditions for velocity and turbulence quantities at a point placed outside the viscosity affected near wall layer. Based on the equilibrium consideration (Production of k = Dissipation of k ), k and ε or ω at the near wall node ( P ) are prescribed as following:

and

(30.1)

where C_μ is a closure coefficient. However, the Friction Velocity is not known a priori and it is an outcome of the iterative type solution algorithm where u_τ , ,k_P , U_P and ε_P or ω_P at the first near wall point are all coupled through the relevant equations. However, the logarithmic law is not strictly valid for flows where strong pressure gradients are involved and the standard wall function methods are not suitable for shear layers with strong secondary flows (spinning surface, curved ducts) or for transitional boundary layer flows.