Linear stability analysis of inclined two-layer stratified flows

International audienceTwo-layer stratified flows are commonly observed in geophysical and environmental contexts. At the interface between the two layers, both velocity shear and buoyancy interplay, resulting in various modes of instability. Results from a temporal linear stability analysis of a two-layer stratified exchange flow under the action of a mean advection are presented, investigating the effect of a mild bottom slope on the stability of the interface. The spatial acceleration is directly included in the governing stability equations. The results demonstrate that increasing the bottom slope has a similar effect on the stability of the flow as does increasing the ratio R of the thickness of the velocity mixing layer dv to that of the density layer dp as it causes the flow to be more unstable to the Kelvin-Helmholtz instabilities. The transition from Kelvin-Helmholtz modes to stable flow occurs at lower Richardson numbers and wavenumbers compared to the horizontal two-layer flow. Kelvin-Helmholtz modes are decreasingly amplified for 1 < R < v2. When 2 < R < v2, Kelvin-Helmholtz modes are first amplified and then damped as the Richardson number increases. This suggests that the behavior of the Richardson number alone is not sufficient to predict the stability tendency of the interface. © 2008 American Institute of Physics

Validating formulas for the prediction of ascent speed and mass transfer coefficient for liquid oil droplets and gas bubbles under pressure

Several different formulas exist to predict the ascent speed of gas bubbles and oil droplets released in deep waters. Similarly, different formulas are also available to predict the mass transfer coefficient of compounds dissolving into water during ascent. However, the formulas used by different authors for the modeling of the ascent and mass transfer processes of liquid oil droplets or gas bubbles under pressure can lead to widely different predictions. In this work, we investigate the abilities of different formulas to reproduce literature laboratory data for the ascent speed and mass transfer coefficient for liquid droplets and gas bubbles under pressure. We found that the ascent speed is usually well predicted by a combination of formulas by Clift et al. (1978) or by the Fan-Tsuchiya equation, with mean errors <20% and <25% for liquid CO2 droplet data by Bigalke et al. (2007). The mass transfer coefficient describing transfer of material from “dirty” droplets to water is well reproduced for droplets with diameters in the range 1.5-4 mm by a set of formulas presented in Clift et al. (1978), based on data from Thorsen and Terjesen (1962) for droplets constituted of a mixture of benzene and chlorobenzene. The formula of Kumar and Hartland (1999) behaves satisfactorily for clean droplets

Predicting the state and properties of Deepwater Horizon oil under pressure using the Peng-Robinson equation of state

Being able to estimate the partitioning behavior of the live oil mixture between a gas and a hydrocarbon liquid phase is crucial for valid modeling of the behavior of the emitted fluid. Equations of state are a well-known way to estimate the phase partitioning and phase properties of real fluids under varying pressure and temperature conditions. We used the Peng-Robinson equation of state in combination with the Lin-Duan volume translation to predict the phase partitioning and phase densities of the emitted fluid at pressures and temperatures corresponding to Gulf of Mexico water column depths ranging from 0 to 1500 m. We modeled the emitted fluid based on the 148 compounds quantified on an individual basis by Reddy et al. (2012), together with 131 pseudo-components derived from comprehensive two-dimensional gas chromatography with a flame ionization detector and simulated distillation data for the thousands of compounds not measured on an individual basis. Several correlation methods were used to estimate the required properties, when data were unavailable. The predicted density of the dead oil at surface conditions matches the measured density within <1%. Our calculations predict a partitioning of the emitted mixture at 1500 m depth of ~30% gas and ~70% liquid hydrocarbons