Stability of stratified two-phase flows in horizontal channels

TL;DR

This paper investigates the linear stability of stratified two-phase flows in horizontal channels using numerical methods, revealing stability conditions, types of instabilities, and their relation to flow parameters, aligning with experimental observations.

Contribution

It introduces a numerical approach to analyze stability across all perturbation wavelengths, providing detailed stability maps and insights into instability mechanisms.

Findings

Stable stratified flow occurs only at low flow rates.

Instabilities can originate at the interface or within the bulk phases.

No clear link between instability type and perturbation wavelength.

Abstract

Linear stability of stratified two-phase flows in horizontal channels to arbitrary wavenumber disturbances is studied. The problem is reduced to Orr-Sommerfeld equations for the stream function disturbances, defined in each sublayer and coupled via boundary conditions that account also for possible interface deformation and capillary forces. Applying the Chebyshev collocation method, the equations and interface boundary conditions are reduced to the generalized eigenvalue problems solved by standard means of numerical linear algebra for the entire spectrum of eigenvalues and the associated eigenvectors. Some additional conclusions concerning the instability nature are derived from the most unstable perturbation patterns. The results are summarized in the form of stability maps showing the operational conditions at which a stratified-smooth flow pattern is stable. It is found that for gas-liquid and liquid-liquid systems the stratified flow with a smooth interface is stable only in confined zone of relatively low flow rates, which is in agreement with experiments, but is not predicted by long-wave analysis. Depending on the flow conditions, the critical perturbations can originate mainly at the interface (so-called "interfacial modes of instability") or in the bulk of one of the phases (i.e., "shear modes"). The present analysis revealed that there is no definite correlation between the type of instability and the perturbation wavelength.