Tomographic X-ray particle tracking velocimetry

We investigate the feasibility of in-laboratory tomographic X-ray particle tracking velocimetry (TXPTV) and consider creeping flows with nearly density matched flow tracers. Specifically, in these proof-of-concept experiments we examined a Poiseuille flow, flow through porous media and a multiphase flow with a Taylor bubble. For a full 360$$^\circ$$ ∘ computed tomography (CT) scan we show that the specially selected 60 micron tracer particles could be imaged in less than 3 seconds with a signal-to-noise ratio between the tracers and the fluid of 2.5, sufficient to achieve proper volumetric segmentation at each time step. In the pipe flow, continuous Lagrangian particle trajectories were obtained, after which all the standard techniques used for PTV or PIV (taken at visible wave lengths) could also be employed for TXPTV data. And, with TXPTV we can examine flows inaccessible with visible wave lengths due to opaque media or numerous refractive interfaces. In the case of opaque porous media we were able to observe material accumulation and pore clogging, and for flow with Taylor bubble we can trace the particles and hence obtain velocities in the liquid film between the wall and bubble, with thickness of liquid film itself also simultaneously obtained from the volumetric reconstruction after segmentation. While improvements in scan speed are anticipated due to continuing improvements in CT system components, we show that for the flows examined even the presently available CT systems could yield quantitative flow data with the primary limitation being the quality of available flow tracers. Graphic abstract

Numerical simulation of the surfactants effect on the Taylor bubble in the PHP

Numerical simulation of the motion of a Taylor gas bubble in a heated small-diameter tube is carried out. Two models are used to describe the dependence of surface tension on temperature. In the first model, the surface tension decreases with temperature, and in the second, it increases, which corresponds to pure water and an aqueous surfactant solution. It is shown that the derivative sign affects the thickness of the liquid film around the bubble.

Finite Element Simulation of a Taylor Bubble in Two-Phase Gas-Liquid Slug Flows using Petrov-Galerkin Formulation

Petrov-Galerkin finite element scheme for systematic analysis of the dynamics of a rising Taylor bubble and general free surface flow problems is derived and implemented. The validity of the scheme is confirmed by simulating the buoyancy-driven motion of a Taylor bubble through a stagnant Newtonian liquid in a vertical pipe characterised by dimensionless inverse viscosity number and Eötvös number of magnitude 111 and 189, respectively. Comparison of the numerical results for the steady state features defining the nose, film, and bottom regions around the bubble with the experiment shows a good agreement between the numerical simulation and the experiment. The percentage deviation of the numerical computed rise velocity, equilibrium film thickness, and stabilisation length ahead of the bubble from the experimental determined values are 8.4%, 2.3%, and 9.5%, respectively.

The Drag Forces on a Taylor Bubble Rising Steadily in Vertical Pipes

By the adoption of a drag-buoyancy equality model, analytical solutions were obtained for the drag coefficients (CD) of Taylor bubbles rising steadily in pipes. The obtained solutions were functions of the geometry of the Taylor bubble and the gas volume fraction. The solutions were applicable at a wide range of Capillary numbers. The solution was validated by comparison with experimental data of other investigators. All derived drag formulas were subject to the condition that Bond number >4, for air-water systems.

COMPUTATIONAL FLUID DYNAMICS SIMULATIONS OF TAYLOR BUBBLE RISE IN FLOWING LIQUIDS

Systematic analysis of the effect of gravitational, interfacial, viscous and inertia forces acting on a Taylor bubble rising in flowing liquids characterised by the dimensionless Froude (Uc), inverse viscosity (Nf ) and Eötvös numbers (Eo) is carried out using computational fluid dynamic finite element method. Particular attention is paid to cocurrent (i.e upward) liquid flow and the influence of the characterising dimensionless parameters on the bubble rise velocity and morphology analysed for Nf, Eo and Uc ranging between [40, 100], [20, 300] and [−0.20, 0.20], respectively. Analysis of the results of the numerical simulations showed that the existing theoretical model for the prediction of Taylor bubble rise velocity in upward flowing liquids could be modified to accurately predict the rise velocity in liquids with high viscous and surface tension effects. Furthermore, the mechanism governing the change in morphology of the bubble in flowing liquids was shown to be the interplay between the viscous stress and total curvature stress at the interface. Keywords: Taylor bubble, finite element, slug flow, CFD, rise velocity

Computational simulation of a single Taylor bubble rising in a vertical column with stagnant liquid

This work presents a computational simulation of a single Taylor bubble rising in a vertical column of stagnant liquid. The computational simulation was based on the Navier-Stokes equations for isothermal, incompressible, and laminar flow, solved by using the open source software OpenFOAM. The two fluids were assumed immiscible. The governing equations were discretized by the volume-of-fluid (VOF) method and solved using the Gauss iteration method. Parametric mesh was used in order to improve the modeling of curvilinear geometry. Numerical solutions were obtained for the rise velocities and shapes of the bubbles which are in excellent agreement with experimental data and correlations from literature.