Improved Law-of-the-Wall Model for Turbulent Boundary Layer in Engineering

Abstract

Accurate prediction of mean velocity in turbulent boundary layer is an important topic from the standpoints of both physics and engineering. In the current study, a unified form of law of the wall is proposed for the mean streamwise velocity in the turbulent boundary layer with zero pressure gradient. From the physical perspective, the improved form of the law is capable of reflecting the actual weight variations between the molecular viscosity and the turbulence-eddy viscosity in the viscous, transition, and logarithmic sublayers. In the viscous sublayer, a variety of direct numerical simulation (DNS) data, including 19 groups, are used to examine the proposed law. In the transition and logarithmic sublayers, 19 groups of canonical DNS velocity profiles and 14 groups of reliable experimental data are used to confirm the applicability and accuracy of the present formula under a wider ranges of Reynolds numbers. The local and maximum relative errors are given and analyzed in detail. The results show that the improved form of the law is sufficiently accurate to represent the mean streamwise velocities in the viscous, transition, and logarithmic sublayers. The present work is helpful for prediction of mean velocity behaviors in engineering.