Linear stability of stratified channel flow

Abstract

Linear stability of horizontal gas-liquid stratified flow was solved using a tau spectral method that is valid for all wavenumbers. Pressures of 0.1–10 atm and liquid viscosities of 1–600 cP were examined. Comparison of these results with Kelvin-Helmholtz, integral momentum and rigorous long wave expansion approaches indicates that the approximate models do not correctly predict the point of neutral stability. The discrepancies in the models are due to more than differences in the calculation of interfacial perturbation stress components and differences in the base states. Stability predictions that include gas phase turbulence, as modeled with either a polynomial velocity profile or with imposed boundary conditions obtained from measured pressure and shear stress variations, are similar to laminar results if the interfacial stress and liquid depth are the same. The long wave stability boundary is found to correlate well for different channel height, density ratio and viscosity ratio, using a gas superficial Froude number corrected with a square root of density ratio and a liquid superficial Froude number. For gas-liquid channel flow waves that grow fastest typically have dimensionless wavenumbers of order unity. Their growth rate scales as a corrected gas Reynolds number to the first power. If the gas-liquid depth ratio is less than approximately one, long waves can be unstable before moderate wavelength waves. Under conditions where unstable moderate wavelength waves appear within a couple of meters, it can take 20–50 times this length for slowly growing long wavelength waves, which can destroy regime stability, to appear.