Stability of stratified two-phase flows in inclined channels

TL;DR

This paper analyzes the linear stability of stratified two-phase flows in inclined channels, identifying conditions for stability and the existence of multiple steady states, with implications for flow pattern prediction.

Contribution

It provides a comprehensive stability analysis for all wavenumber perturbations in inclined stratified flows, including multiple solution regions and their stability characteristics.

Findings

Existence of two stable stratified configurations at low flow rates in countercurrent flows.

Upper solutions are always unstable in the triple solution region for upward inclines.

Downward flows in the triple solution region are unstable for all solutions with respect to short-wave perturbations.

Abstract

Linear stability of stratified gas-liquid and liquid-liquid plane-parallel flows in inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict parameter regions in which stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of steady state solutions are presented on the flow pattern map and are accompanied by critical wavenumbers and spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of two stable stratified flow configurations in a region of low flow rates in countercurrent liquid-liquid flows. These configurations become unstable with respect to shear mode of instability. It was revealed that in slightly upward inclined flows the lower and middle solutions for the holdup are stable in a part of the triple solution region, while the upper solution is always unstable. In the case of downward flows, in the triple solution region, none of the solutions are stable with respect to short-wave perturbations. These flows are stable only in the single solution region at low flow rates of the heavy phase, where long-wave perturbations are the most unstable ones.