PNNL

Abstract

Here we evaluate the skin coefficient of friction for steady turbulent radial wall jets across smooth and rough surfaces. Although the Colebrook equation has been used successfully to evaluate friction factors for flows through smooth and rough pipes for many decades, how roughness affects the skin friction coefficient for radial wall jets and why power-law exponents for these skin friction coefficients as a function of nozzle Reynolds number appear to vary from 1/5 to -1/2 remain unclear. Here we develop a Colebrook-type equation for skin friction coefficients associated with single-phase turbulent radial wall jets arising from orthogonally impinging circular jets. The fully iterative solution, a power-law approximation, and a non-iterative Serghides-like approximation for the friction coefficient are presented. We find the skin coefficient of friction defined on the peak radial velocity to be a function of position over rough but not smooth surfaces in contrast to pipe friction factors that remain independent of axial position. Analytical approximations for the radial velocity profile as a function of Reynolds number follow expected trends. These results have significant implications for the industrial use of jets in mixing vessels.