Absolute linear instability in laminar and turbulent gas/liquid two-layer channel flow

TL;DR

This paper investigates the conditions under which two-layer gas/liquid flows become absolutely unstable, using stability theory to analyze laminar and turbulent gas flows and their implications for oil/gas pipeline safety.

Contribution

It introduces a combined linear modal and ray analysis approach to identify absolute instability boundaries in stratified two-phase flows with turbulent and laminar gas layers.

Findings

Absolute instability occurs in large parameter regions for turbulent gas flow at high density ratios.

Absolute instability persists in laminar gas layers at high density ratios, with boundaries depending on viscosity ratios.

Additional unstable modes can suppress absolute instability in certain conditions.

Abstract

We study two-phase stratified flow where the bottom layer is a thin laminar liquid and the upper layer is a fully-developed gas flow. The gas flow can be laminar or turbulent. To determine the boundary between convective and absolute instability, we use Orr--Sommerfeld stability theory, and a combination of linear modal analysis and ray analysis. For turbulent gas flow, and for the density ratio r=1000, we find large regions of parameter space that produce absolute instability. These parameter regimes involve viscosity ratios of direct relevance to oil/gas flows. If, instead, the gas layer is laminar, absolute instability persists for the density ratio r=1000, although the convective/absolute stability boundary occurs at a viscosity ratio that is an order of magnitude smaller than in the turbulent case. Two further unstable temporal modes exist in both the laminar and the turbulent cases, one of which can exclude absolute instability. We compare our results with an experimentally-determined flow-regime map, and discuss the potential application of the present method to non-linear analyses.