Jacques Comiti

A new model for determining mean structure parameters of fixed beds from pressure drop measurements : Application to beds packed with parallelepipedal particles

Abstract Experimental pressure drop measurements show that the behaviour of a fluid through fixed beds of parallelepipedal particles of low thickness-to-side ratio, such as wood chips used in the paper pulp making industry, is very different from that of the flow through beds packed with spherical particles. Such anisotropic porous media have a particular structure characterized by marked stratification and partial overlapping of the particles. In order to take into account the structural properties of packing, a capillary type model with wall effect corrections is proposed to determine the pressure drop through packed beds. The tortuosity factor and the dynamic specific surface area are used as mean structure parameters. This general model, checked with pressure drop data from fixed beds of spheres, is used to determine these structural parameters for packed beds of parallelepipedal particles. Correlating equations are proposed for tightly packed beds. Combined with the general equation of the model, they allow an estimation of the pressure drop as a function of the flow velocity.

Flow of non-Newtonian fluids in fixed and fluidised beds

Abstract An attempt has been made to reconcile and to critically analyze the voluminous literature available on the flow of rheologically complex fluids through unconsolidated fixed beds and fluidised beds. In particular, consideration is given to the prediction of macro-scale phenomena of flow regimes, pressure drop in fixed and fluidised beds, minimum fluidisation velocity, dispersion and liquid–solid mass transfer. Available scant results seem to suggest that flow patterns qualitatively similar to that observed for Newtonian fluids, can be expected for the flow of purely viscous non-Newtonian fluids. A Reynolds number based on the effective pore size and pore velocity is seen to be a convenient parameter for the delineation of these flow regimes. Out of the four approaches available, the generalisation of the capillary model, due to Comiti and Renaud ( Chem. Engng. Sci. 44 (1989) 1539–1545), appears to be the best for the estimation of the pressure drop through fixed beds. This method requires the flow rate – pressure drop data for the flow of a Newtonian fluid, such as air or water, through the same bed to evaluate the two key parameters, namely, the tortuosity and the dynamic surface area. While this approach can accommodate non-spherical particle shape and the wall effects and encompasses all possible flow regimes, it is limited to the situations where the polymer–wall interactions are negligible. Similarly, based on a combination of the capillary and drag models, satisfactory expressions have been identified for the prediction of the minimum fluidising velocity and velocity-voidage behaviour of uniformly expanded fluidised beds for power-law liquids and beds of spherical particles. Little is known about the effect of particle shape and column walls on these parameters. Even less work has been reported on dispersion and liquid–solid mass transfer in packed and fluidised beds, and no theoretical or experimental results seem to be available on heat transfer in these systems. Therefore, the expressions for the prediction of Peclet and Sherwood numbers presented herein must be regarded as somewhat tentative at this stage. Finally, little definitive and quantitative information is available on the role of viscoelasticity and of the effects arising from polymer/wall interactions, polymer retention, etc.

Pressure drop in non-Newtonian purely viscous fluid flow through porous media

Abstract The flow of non-Newtonian purely viscous fluids through packed beds of different structures has been investigated and a model of calculation of the pressure drop is proposed. This model takes into account the structural parameters of the porous medium: the tortuosity τ, the dynamic specific surface area a vd and the porosity e. This model has been verified experimentally for the flow of a power-law fluid through fixed beds of spherical particles, long cylinders and very flat plates. The present investigation covers a large range of Reynolds number including creeping and inertial flow regimes.

Experimental validation of a model allowing pressure gradient determination for non-Newtonian purely viscous fluid-flow through packed beds

Recently, Sabiri and Comiti (1995) proposed a model allowing the prediction of the pressure gradient for non-Newtonian purely viscous fluid flow through porous media. The aim of this work is to validate this model for beds packed with spherical and non-spherical particles in a large range of Reynolds numbers, taking into account inertial effects, even in the case when important wall effects exist.

LIQUID-SOLID MASS TRANSFER IN PACKED BEDS OF PARALLELEPIPEDAL PARTICLES : ENERGETIC CORRELATION

Abstract Mass transfer between liquid flow and anisotropic square-base parallelepipedal particles of different height-to-side ratio is investigated with an electrochemical method. The influence of axial dispersion is studied and the results analyzed by using bed structure parameters. A comparison of mass transfer performances for beds of spherical particles is made. A single energetic correlation for all types of studied parallelepipedal particles is proposed for a large range of Reynolds numbers, including creeping flow and intertial regime: where Xe is an energetic dimensionless criterion: E is the mechanical power dissipated by unit volume of fluid.

Non-Newtonian fluidisation of spherical particles

This work presents the development of a new model based on the submerged object concept in order to characterise the expansion of spherical particles fluidised by non-Newtonian purely viscous liquids, especially at intermediate and high bed void fractions values. In order to take the interactions between the particles into account a parameter called hydraulic tortuosity is introduced which is a function of the Reynolds number and porosity. A method allowing its evaluation is proposed. Based on the test of a lot of experimental data from our laboratory and from previous works, this model is shown to give satisfactory results for porosities values larger than 0.6. In order to cover the entire range of porosities corresponding to the particles expansion a capillary-type model is proposed for the lower values of the porosities. This model is found to give satisfactory results in the range of bed void fraction comprised between the value corresponding to the minimum of fluidisation emf and e=0.65. The combination of the two models tested on 21 independent sets of data concerning viscoinelastic shear-thinning liquids leads to a mean error of 16%. It is also shown to give accurate predictions for Newtonian liquids. A comparison is also presented with the prediction of some of the widely used equations available in literature.

Pressure drops for purely viscous non-newtonian fluid flow through beds packed with mixed-size spheres

Extensive new measurements on pressure drop for the flow of purely viscous non-Newtonian fluids through packed beds made up of binary-and-quaternary size spheres are reported herein. These results have been interpreted using the previously available Sabiri and Comiti capillary model (1995), which has been quite successful in correlating the pressure drop data for the beds of uniform size spherical and nonspherical particles. The resulting predictions are also very good for mixed beds if some results are available for a Newtonian fluid, thereby enabling the evaluation of the tortuosity factor. However, since such data is always not available, an empirical scheme for estimating the tortuosity that allows the prediction of pressure drop with a mean relative error of about 10% is also presented. This sort of accuracy is quite acceptable for process engineering design calculations.

PRESSURE DROPS OF NON-NEWTONIAN PURELY VISCOUS FLUID FLOW THROUGH SYNTHETIC FOAMS

This work aims at giving a first insight of non-Newtonian fluid flow through synthetic foams. At first, a review of experimental pressure drops measured with Newtonian fluids through various foams is proposed as well as a recall of a capillary-type flow model used to determine structural parameters. In this particular case of Newtonian fluid flow, a single equation is shown to correlate experimental data whatever the grade of the foam. Results of an image analysis study are also given; they allow to give a physical sense to the value of the equivalent diameter of pore given by the flow model. In a second part, results of pressure drops measured with a non-Newtonian fluid are reported. A model allowing the determination of the pressure drops for non-Newtonian purely viscous fluid flow through packed beds of particles, based on the same capillary representation of porous media, is tested in the case of fluid flow through synthetic foams. The model predictions are acceptable for foams of high grades, but a d...

Characterisation of Flow and Mass Transfer in Cross Shape and T-Shape Micromixers

The understanding of physical phenomena such as flow behaviour and mass transfer performance is needed in order to develop appropriate micromixers for industrial or biomedical applications. In this work, CFD is used to characterize the flow and the liquid mixing quality in a micromixer as a function of the Reynolds number. Two micromixers are studied in steady flow conditions; they are based on two geometries, respectively T-shaped (⊤) and cross-type (+). Simulations allow, in the case of ⊤ micromixers, to chart the topology of the flow and to describe the evolution of species concentration downstream the crossing. The streamlines layout and the mixing quality curves reveal three characteristic types of flow previously reported in the literature, depending on Reynolds number: stratified, vortex and engulfment flows. In the case of cross-type micromixers, the structure of the flow is strongly three-dimensional and is characterized by symmetrical vortices in both output channels. The results show that the + shaped system can improve the mixing process in comparison with the micromixers having ⊤ geometry. The second part of the study is experimental. Two cells are constructed, for both geometries (T-shaped and cross) using square channels with 400 μm hydraulic diameter. In order to use particle image velocimetry (PIV), a system has been adapted to measure velocity fields for various channel plans at different channel depths. This allows observing the evolution of the flow and the vortices development along the microchannels. A second experimental technique, the electrochemical one involving microelectrodes implemented at several positions on the channel wall located near the crossing, has been used. The electrochemical method can locally characterize the formation of swirling flows. These two complementary experimental results will be analysed and a comparison with the CFD results will be performed.Copyright