J.B.L.M. Campos

An experimental study of the wake of gas slugs rising in liquids

A photographic study of the wakes of slugs rising in tubes of 19 mm and 52 mm internal diameter is presented. The dependence of the flow pattern in the wake upon the Reynolds number of the rising slug, R , is established for different slug lengths. Values of R covered in this study are in the range 25 to 1.3 × 10 4 . For low values of R the flow pattern in the wake is laminar and axisymmetric and values of wake length and wake volume could be determined from the photographs: these values were correlated with the other variables in the system by means of dimensional analysis.

Coalescence of two gas slugs rising in a vertical column of liquid

Abstract This work describes an experimental investigation about the coalescence of pairs of gas slugs rising in vertical columns of liquids covering a wide range of liquid viscosities. The experiments were performed in columns with 19, 32 and 52 mm of internal diameter and slug coalescence was followed by means of a new experimental technique, based on the signals of differential pressure transducers. Important data reported in this work are: • the minimum distance between slugs above which there is no interaction, l min ; • the velocity of approach of the trailing slug as a function of its distance to the leading one. Values of l min are shown to be related to the flow pattern in the wake of liquid behind gas slugs and correlations are provided for the determination of l min ; in all cases l min is about four times the wake length, l w .

An improved numerical scheme to study mass transfer over a separation membrane

Abstract The numerical prediction of mass transfer rates in the mass boundary layer over a membrane separation requires the use of a very dense grid. In this work, a simple logarithmic variable transformation applied to the solute transport equation improves the well-known finite difference scheme, allowing the use of a larger grid spacing without loss of accuracy. This method is applied to solve laminar flow and solute transport equations in a parallel plate device with permeable walls. The concentration profiles along the membrane surface and in the mass boundary layer are predicted. For high permeate velocity, the grid spacing can increase four times without loss of accuracy. The method applied has several advantages comparatively to the optimized grid spacing method that can be used in alternative.

Mass transfer in the vicinity of a separation membrane—the applicability of the stagnant film theory

In membrane separation cells, the permeate velocity is usually predicted applying the stagnant film equation with mass transfer data from impermeable systems, Sh I . In this paper, the applicability of the stagnant film equation is discussed. Laminar momentum and solute transport equations are numerically solved in a permeable parallel plate cell and in a conical cell with a laminar jet impinging vertically to the membrane surface. Membrane surface concentration and permeate velocity predictions are applied to stagnant film equation to obtain Sh I . Sh I data are compared with Sherwood data from impermeable systems with uniform mass production at the wall, and with Sherwood data from impermeable systems with uniform concentration at the wall. This analysis is done for a wide range of the dimensionless numbers characterizing the membrane separation process: Schmidt, Reynolds (or Peclet for the parallel plate cell), Π v and Ππ0 numbers. The stagnant film equation is a quite accurate equation to predict permeate velocity, and the type of impermeable data that must be used depends on the dimensionless groups. The conclusions are identical for both cells.

Concentration polarization in a membrane placed under an impinging jet confined by a conical wall — a numerical approach

Nowadays, there is an attempt to develop new membrane separation cells to minimize the concentration polarization phenomenon. An efficient contact between the fluid and the membrane is fundamental to reach this objective. In the present study, the hydrodynamic characteristics of a liquid jet impinging perpendicularly to a flat and round shaped membrane are explored. The jet flow is confined by a conical wall extended from the jet nozzle to a short distance above the membrane. The momentum and mass transport equations in laminar regime are solved numerically by a finite difference scheme. The solution depends on Reynolds and Schmidth numbers and on two new dimensionless groups, v and 0 ; v represents the ratio between the permeate velocity through a non-polarized membrane surface and the average jet velocity at the cell inlet, and 0 the ratio between the osmotic pressure over a non-polarized membrane surface and the static pressure difference across the membrane. The concentration polarization is investigated in wide ranges of values of these groups and new indexes are defined to quantify the polarization level. For increasing values of Re, Sc, and v, the polarization level and the concentration at the membrane surface increase. For increasing values of 0 the polarization level increases, but the concentration at the membrane surface tends to the bulk concentration. The suction effects on the velocity profiles in the layer over the membrane are also analyzed. A compact module of jet cells is proposed.

Mixing induced by air slugs rising in narrow columns of water

Abstract A series of equal-sized slugs of air was injected at the bottom of water columns of internal diameters 19 and 32 mm, respectively. The dispersion of tracer initially contained in the lower half of the columns was measured. A simple physical model was developed based on the idea that dispersion is mainly due to the action of the wakes of slugs, considered to be fully mixed; this model accounts remarkably well for the experimental results observed. An alternative dispersion model, based on the analogy with one-dimensional molecular diffusion, is also presented and the relationship between the two models is discussed. Experiments were performed for a range of values of slug volume, the number of slugs injected and the frequency of slug injection.

Flow in the negative wake of a Taylor bubble rising in viscoelastic carboxymethylcellulose solutions: particle image velocimetry measurements

A simultaneous technique employing particle image velocimetry (PIV) and shadowgraphy was used to study vertical slug flow in non-Newtonian fluids. Two aqueous solutions of 0.8 and 1.0 wt% carboxymethylcellulose (CMC) were studied and the flow field around individual Taylor bubbles fully characterized. The rheological fluid properties and pipe dimension yielded Reynolds numbers of 8 and 4 and Deborah numbers of 0.2 and 0.4. A negative wake was found downstream of the Taylor bubbles in both fluids. Below the bubble trailing edge, along the axis region, the fluid flows in the opposite direction to the bubble (negative wake), originating rotational liquid movements in adjacent regions. Even far downward from the bubble, rotational liquid movements are clearly seen and measured. In the 1.0 wt% CMC solution, the bubble trailing edge has the shape of a two-dimensional cusp. This two-dimensional cusp, of small dimensions, is seen in different orientations during the bubble rise-indicating a fast rotational movement. The asymmetrical shape of the trailing edge is responsible for small asymmetries in the flow in the wake region (three-dimensional flow). The asymmetrical shape associated with the rotational movement is responsible for an unsteady flow of small amplitude. In the 0.8 wt% CMC solution, the shape of the trailing edge changes during the bubble rise. An axisymmetric axial oscillation a continuous expansion and contraction of the trailing edge, is the origin of this behaviour. This oscillatory movement is responsible for an unsteady flow of small amplitude in the wake region.

Impinging jets confined by a conical wall – high Schmidt mass transfer predictions in laminar flow

Mass transfer from a soluble plate to an impinging liquid jet confined by a conical wall is investigated. The nozzle-toplate distance is very short, less than one nozzle diameter, the flow regime is laminar, Re < 1600, and the Schmidt number ranges from 960 to 50 000. Navier‐Stokes and solute transport equations are solved by a finite diAerence scheme. Numerical predictions of the average mass transfer coeAcient are compared with data obtained by measuring the dissolution rate of benzoic acid in water and in aqueous solutions of glycerol. A correlation is presented between stagnation Sherwood number, jet Reynolds number and Schmidt number, Shst=Sc 1=3 a 1:77 1=2 . The eAects on the mass transfer coeAcients of the velocity profile at the nozzle exit and of an insoluble starting length are analyzed. The onset of laminar-to-turbulent transition is identified using mass transfer data. The mass transfer coeAcients in the conical cell are compared with those in a radial cell confined by parallel plates. ” 2001 Elsevier Science Ltd. All rights reserved.

GAS HOLD-UP IN AERATED SLUGGING COLUMNS

Gas hold-up is one of the most important parameters characterizing the hydrodynamics of bubble columns. A study is presented about the gas hold-up in gas-liquid slugging columns. Expansion of liquid columns is measured for a wide range of superficial velocities of bubbling gas, and the data are compared with available theory. The experiments were performed with liquids of different kinematic viscosities, in columns of 22 mm, 32 mm and 52 mm internal diameters and the initial liquid heights were greater than 2.5 m. A discussion is presented based on the effects of the flow pattern in the wakes of the Taylor bubbles and on coalescence of bubbles. When the flow regimes in the liquid and in the wake are both turbulent or both laminar, the theory predicts the gas hold-up. When the flow in the wake is turbulent and in the main liquid is laminar, the experimental gas hold-up is higher than predictions. This disagreement is explained by the shape of the liquid velocity profile emerging from the wake and by the long length, between bubbles, needed to restore the laminar profile in the liquid.

Drag force on the particles at the upstream end of a packed bed and the stability of the roof of bubbles in fluidised beds

Abstract A study is reported on the “bed support experiment” in which measurements of the minimum supporting velocity are performed for a wide range of conditions. Values of the drag coefficient for the particles at the upstream end of a packed bed are then calculated, and the data are seen to be well represented by The analysis of drag forces is applied to a study of stability of the roof of bubbles in fluidised beds. It is concluded that gas throughflow is sufficient to hold up the particles on the roof of spherical bubbles in 3D- beds, but that it is insufficient to prevent particles from raining down across cylindrical bubbles in 2D-beds.