Mass transfer in the membrane concentration polarization layer under turbulent cross flow

Membrane filtration has become firmly established as a primary technology for ensuring the purity, safety and/or efficiency of the treatment of water or effluents. In this paper, we review the improvements that have been achieved concerning the membranes used for microfiltration, ultrafiltration, nanofiltration/reverse osmosis processes during the last decades. More especially, we review the state of the art computational fluid dynamics (CFD) methods applied to membranes processes. Many studies have focused on the best ways of using a particular membrane process. But, the design of new membrane systems requires a considerable amount of process development as well as robust methods. Computational fluid dynamics may provide a lot of interesting information for the development of membrane processes. We review the different ways in which CFD methods are used to improve membrane performance.

Computational fluid dynamics applied to membranes: State of the art and opportunities

Techniques for computational fluid dynamics modelling of flow in membrane channels

To study the mechanism of particle deposition in crossflow filtration, hydrodynamic forces exerted on a spherical particle touching the surface of filter medium are analyzed to derive the critical selective cut-diameter of the deposited particles under various crossflow velocities and filtration rates in a crossflow filtration system. Experimental data of turbulent crossflow filtration of dilute light calcium carbonate suspension agree with the prediction of this theory within 30% error under the crossflow velocity of from 0.57 to 1.14 m/s. Equations to estimate the characteristics of crossflow filtration, such as steady-state filtration rate and average specific resistance of cake, are also presented.

Selective Particle Deposition in Crossflow Filtration

In this study, a predictive model for the separation of gases via a polydimethylsiloxane (PDMS) membrane has been developed. This model takes into account the effects of gas composition and pressure at the membrane surfaces on the gas sorption and diffusion coefficients in the membrane. Computational fluid dynamics (CFD) modeling has been employed in order to predict the behavior of a gas mixture containing C3H8, CH4, and H2 at various operating conditions and three zones (upstream, downstream, and membrane body). Artificial neural network (ANN) modeling has been applied to predict sorption and diffusion coefficients of each component of the gas mixture in the membrane. A procedure of calculation has been applied to combine the CFD modeling and the ANN modeling in order to predict sorption, diffusion, and composition of each component at various sites of the membrane. The results determined using the developed prediction model have been found to be in agreement with those determined using experimental investigations with an average error of 10.21%. POLYM. ENG. SCI., 54:215–226, 2014. © 2013 Society of Plastics Engineers

Ternary gas permeation through synthesized pdms membranes: Experimental and CFD simulation basedon sorption-dependent system using neural network model

In this paper, a fully developed turbulent flow of water in a porous-wall tube with suction or injection flow through the wall was experimentally studied. The experimental runs were executed at a fixed value of Reynolds number of inlet flow at about 25000 and with varying vw√u from -1.78×10-3 to 4.16×10-3. The radial velocity component is almost linear, but it is found that the radial distribution of shear stress becomes non-linear as the mass flux through the wall becomes larger. The mixing lengths in the flow with and without mass flux are correlated by a Reichardttype equation and the normalized values of eddy diflFusivity are also correlated with a single equation. The measurements of the local and average friction factor are in good agreement with predictions by the film theory.

Study of flow in a porous tube with radial mass flux

A theoretical and experimental study was conducted on a fully developed turbulent pipe flow with uniform fluid injection or suction through the wall. A simple model was used to analyze the effect of injection or suction on the eddy diffusivity of momentum, friction factor and pressure gradient. The model predicts that both the normalized eddy diffusivity and local friction factor are linear functions of m/(-dp*/dx*), that is), eM/vRe(-dp*/dx*)=F1(y/R)•m/(-dp*/dx*)+F2(y/R) f•(-dp*/dx*)=1/2+4m/(-dp*/dx*)and that dp*/dx*=fn (m). Functions F1(y/R), F2(y/R) and fn(m) were determined by experiment. The experimental runs were executed at Re=15, 200-95, 300 with wall flux ratio m=vW/ =-0.0042-0.00847.

https://www.jstage.jst.go.jp/article/jcej1968/8/3/8_3_217/_pdf

Eddy diffusivity in a turbulent pipe flow with uniform fluid injection and suction through the wall

A fully developed turbulent flow of an electrolyte solution in a porous-wall tube with suction or injection flow through the wall was experimentally studied. The measurements of mass transfer rates at the wall were made by an electrochemical method. Reynolds number were varied from 7900 to 21, 000 and Schmidt numbers were 750, 1100, 1920 and 2100. The mass flow ratios ρvw/ρU ranged from -2.13×10-5 to 5.59×10-5. It was recognized that mass transfer coefficients at the wall rise with increase of suction rate and fall with increase of injection rate. The results are in good agreement with predictions by film theory.

Shunji Takeshita

Papers

Study of flow in a porous tube with radial mass flux

Eddy diffusivity in a turbulent pipe flow with uniform fluid injection and suction through the wall

Study of turbulent flow in a porous tube with high mass flux to and from the wall