Characteristics of stratified flows of Newtonian/non-Newtonian shear-thinning fluids

Exact solutions for laminar stratified flows of Newtonian/non-Newtonian shear-thinning fluids in horizontal and inclined channels are presented. An iterative algorithm is proposed to compute the laminar solution for the general case of a Carreau non-Newtonian fluid. The exact solution is used to study the effect of the rheology of the shear-thinning liquid on two-phase flow characteristics considering both gas/liquid and liquid/liquid systems. Concurrent and counter-current inclined systems are investigated, including the mapping of multiple solution boundaries. Aspects relevant to practical applications are discussed, such as the insitu hold-up, or lubrication effects achieved by adding a less viscous phase. A characteristic of this family of systems is that, even if the liquid has a complex rheology (Carreau fluid), the two-phase stratified flow can behave like the liquid is Newtonian for a wide range of operational conditions. The capability of the two-fluid model to yield satisfactory predictions in the presence of shear-thinning liquids is tested, and an algorithm is proposed to a priori predict if the Newtonian (zero shear rate viscosity) behaviour arises for a given operational conditions in order to avoid large errors in the predictions of flow characteristics when the power-law is considered for modelling the shear-thinning behaviour. Two-fluid model closures implied by the exact solution and the effect of a turbulent gas layer are also addressed.Comment: 36 pages, 27 Figure

Predicting apparent slip at liquid-liquid interfaces without an interface slip condition

We show that if we include a density-dependent viscosity into the Navier-Stokes equations then we can describe, naturally, the velocity profile in the interfacial region, as we transition from one fluid to another. This requires knowledge of the density distribution (for instance, via Molecular Dynamics [MD] simulations, a diffuse-interface approach, or Density Functional Theory) everywhere in the fluids, even at liquid-liquid interfaces where regions of rapid density variations are possible due to molecular interactions. We therefore do not need an artificial interface condition that describes the apparent velocity slip. If the results are compared with the computations obtained from MD simulations, we find an almost perfect agreement. The main contribution of this work is to provide a simple way to account for the apparent slip at liquid-liquid interfaces without relying upon an additional boundary condition, which needs to be calculated separately using MD simulations. Examples are provided involving two immiscible fluids of varying average density ratios, undergoing simple Couette and Poisseuille flows

A slug capturing method in unconventional scenarios: The 5ESCARGOTS code applied to non-Newtonian fluids, high viscous oils and complex geometries

Abstract Previous work showed that a one-dimensional, hyperbolic, transient five-equation two-fluid model can predict automatically the formation, growth, and subsequent development of slugs in horizontal and near-horizontal flow. This method was implemented in a finite volume numerical scheme – called 5ESCARGOTS code. Comparison with experimental data showed that it can be used to predict the flow pattern and statistical characteristics (slug velocity, length, and frequency). However, the capabilities of this approach have been tested only for water-air flows in a straight horizontal pipe. In this work, we validate the application of the code to some unconventional problems. Firstly, we test the possibility of slug capturing approach to describe and predict the relevant features of air/high viscosity oils or air/non-Newtonian fluids flows. Comparisons between some slug characteristics and empirical correlations, available in literature, are discussed. Then, we move from simple geometries toward more complex conditions that may be representative of actual application cases, also employing high viscous oils as liquid phase. Comparison against experimental data shows results in reasonable agreement

Modeling the motion of a Taylor bubble in a microchannel through a shear-thinning fluid

Applications of multiphase flows in microchannels as chemical and biological reactors and cooling systems for microelectronic devices typically present liquid slugs alternated with bubbles of elongated shape, the Taylor bubbles. These occupy almost entirely the cross-section of the channel and present a hemispherical front and a liquid layer, the lubrication film, which separates the gas from the tube wall. The Taylor bubble perturbs the surrounding fluids activating many transport mechanisms in the proximity of the gas-liquid interface; therefore, the bubble motion significantly influences the heat and mass transfer rates. Although many works deeply investigate the bubble hydrodynamics in Newtonian fluids, the knowledge about the relation between bubble hydrodynamics and rheological properties is insufficient, and studies where the continuous phase exhibits a shear-thinning behavior are missing. Our numerical analysis tries to fill this gap by investigating the motion of a Taylor bubble in a non-Newtonian shear-thinning fluid, modeled by the Carreau viscosity model. First, we validate the results against the Newtonian case and a recent theory for shear-thinning fluids (Picchi et al., Journal of Fluid Mechanics, 2021, 918). Then, we investigate the bubble hydrodynamics far from the validity range of the current models. Finally, we study the scaling of the bubble velocity and lubrication film thickness, extending the current theory to shear-thinning fluids

Velocity profiles description and shape factors inclusion in a hyperbolic, one-dimensional, transient two-fluid model for stratified and slug flow simulations in pipes

In a previous work it has been shown that a one-dimensional, hyperbolic, transient five equations two-fluid model is able to numerically describe stratified, wavy, and slug flow in horizontal and near-horizontal pipes. Slug statistical characteristics can be numerically predicted with results in good agreement with experimental data and well-known empirical relations. In this model some approximated and simplified assumptions are adopted to describe shear stresses at wall and at phase interface.In this paper, we focus on the possibility to account for the cross sectional flow by inserting shape factors into the momentum balance equations of the aforementioned model. Velocity profiles are obtained by a pre-integrated model and they are computed at each time step and at each computational cell. Once that the velocity profiles are known, the obtained shape factors are inserted in the numerical resolution. In this way it is possible to recover part of the information lost due to the one-dimensional flow description.Velocity profiles computed in stratified conditions are compared against experimental profiles measured by PIV technique; a method to compute the velocity profile during slug initiation and growth has been developed and the computed velocity distribution in the liquid phase was compared against the one-seventh power law. Keywords: Multi-phase pipeline transport, Oil & gas, Hyperbolic two-fluid model, Velocity profiles, Shape factor

experimental and numerical study of multiphase flow phenomena and models in oil gas industry

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