Evolution of flow disturbances in cocurrent gas-liquid flows. Final report, November 1, 1993--October 31, 1994

摘要

Long-wave stability curves for two-layer laminar flow, laminar liquid and a turbulent gas (simulated with a polynomial profile) from the full differential equations and boundary conditions are compared to the standard 1-d equation methods of predicting flow regime transitions. The differential models predict instability at much less severe conditions than the integral equations -- as much as an order of magnitude when plotted on friction velocity -- liquid depth coordinates. Since this plot removes most of the base state's effects, the 1-d models clearly are not predicting linear stability of anything. So agreement between the 1-d models with observed transitions is fortuitous since either the flow is too short or convenient parameter values have been chosen; otherwise flow regimes are not linked with linear stability. A polynomial profile gas, laminar liquid model, developed for a first approximation to turbulent flow, gives growth curves near the two-layer laminar exact solutions if the interfacial friction velocity and liquid depth are matched. The main differences are that the wavelength is predicted somewhat shorter for the turbulent model and the growth rate slightly larger for a laminar gas. These linear stability studies point to a need to determine the base state before significant results are obtained. Solutions for laminar flow in a rectangular channel over a solid wavy surface show that the wavelength/channel height ratio profoundly affects the stress variations. For waves long compared to channel height, pressure is completely in phase with wave slope, not wave height, as occurs for high Re in infinitely high channels. Nonlinear effects reduce the relative magnitude of the shear stress variation and phase angle that could explain saturation in the growth of waves formed by shear variation for very thin liquid layers. But since the pressure variation and phase are increased, this is not a likely explanation wave saturation on thicker layers.