A Proposed Universal Wall Function for Velocity and Temperature in Turbulent Near-Wall Flows of Low and High Prandtl Number Fluids

Abstract

Wall functions are often used in practical engineering analysis of turbulent boundary layers to approximate the near-wall mean velocity and temperature distributions and/or provide boundary conditions, by relating flow variables some distance from the wall to values of wall shear stress and heat flux. General wall functions are applicable throughout the entire inner boundary layer, including the viscous sublayer, buffer region, and logarithmic region. Several well-known general wall functions are available for mean velocity, but there are fewer options for mean temperature, especially in the form of simple algebraic expressions that require no numerical integration and which are applicable over a wide range of fluid Prandtl numbers. This technical brief presents a new general wall function formulation for mean velocity and temperature that satisfies these conditions. Because it is a relatively simple algebraic function, it is easily implemented into new or existing computational fluid dynamics (CFD) solvers. The new wall function is validated by comparison to direct numerical simulation (DNS) data for turbulent channel flow with 80 < Re < 5000 and 0.007 < Pr < 10.