A mechanistic model for expansion loss coefficient in upward vertical annular flow

Abstract

• Differential effect of flow deceleration on gas, droplets and liquid film postulated. • Developed semi-analytical expressions for velocity profile correction factor in pipe flow. • Carried out CFD simulations of gas-droplet flow in a rough-walled pipe expansion. • Effect of droplet deceleration on pressure variation elucidated. • Mechanistic correlation developed for expansion loss coefficient for annular flow. Gas–liquid annular flow draws different responses from its three constituents, namely, the liquid film, the entrained liquid droplets and the gas core, as they flow through a diverging section in a pipe. The resulting change in the pressure profile is a combination of several effects associated with the dynamic interactions among these three fields. Accurate simulation of the response using Eulerian–Eulerian computational fluid dynamics is not feasible because the processes are inherently complex and a framework of relevant and validated constitutive relations describing the physical processes is not yet available. In the present work, a simpler approach is adopted by studying the interactions individually in idealized settings, and bringing together the separate effects into a phenomenological model for pressure loss in upward vertical annular flow. The overall pressure change is expressed as a sum of three contributors: change in area of cross-section available for gas flow, change in the effective interfacial roughness leading to peaking of the velocity profile, and droplet-gas momentum exchange in the immediate downstream of the expansion. Using air–water experimental data from two expansion ratios and three half-angles of the diverging sections, a mechanistic correlation is proposed to evaluate the overall pressure loss coefficient.