Liquid wall friction in two‐phase turbulent gas laminar liquid stratified pipe flow

Abstract

AbstractThe main result of the present work is an analytic expression for the mean liquid wall shear stress in two‐phase turbulent gas/laminar liquid stratified pipe flow. The Navier‐Stokes equations are solved assuming a flat fluid‐fluid interface subject to a constant interfacial shear — approximating the interfacial drag exerted by the gas. The effect of a pipe inclination is accounted for, thereby retaining the interesting two‐phase phenomenon of backflow in upwardly inclined pipes. The corresponding expression for the wall shear stress distribution is obtained by formal differentiation. Its limiting behaviour in the triple points, where the fluid‐fluid interface meets the pipe wall, is determined by residue calculus. The expression for the mean wall shear stress is given by integration. It is found to be a linear combination of two terms. The first term accounts for the free surface liquid flow in the absence of the gas. The corresponding approximate hydraulic diameter model is found to be in surprisingly good agreement with this term. The second term represents the shear flow associated with the interfacial drag exerted by the gas (not accounted for by the hydraulic diameter approximation). The shear flow increases the flow rate near the interface on behalf of the flow rate near the pipe wall, thus reducing the wall shear stress below the free surface flow value. Expedient evaluation of the expression for the mean wall shear stress, suitable for use in a 1‐D multiphase pipe flow simulator, is facilitated by replacing certain one‐parameter integrals with highly accurate rational approximations.