Experimental Validation of a Computational Fluid...

Experimental Validation of a Computational Fluid DynamicsModel of Copper Electrowinning

MARTIN J. LEAHY and M. PHILIP SCHWARZ

The hydrodynamics that occur in the space between the electrode plates in copper electrowin-ning (EW) are simulated using a computational fluid dynamics model (CFD). The model solvesfor the phases of gas oxygen bubbles and electrolyte using the Navier–Stokes equations in aCFD framework. An oxygen source is added to the anode, which sets up a recirculation pattern.The gradients in copper near the cathode lead to buoyancy forces, which result in an uplift in theelectrolyte close to the cathode. This study investigates the experimental validation of the CFDmodel using a small/medium-scale real EW system. The predicted fluid velocity profiles arecompared with the experimental values, which have been measured along various cross sectionsof the gap between the anode and the cathode. The results show that the CFD model accuratelypredicts the velocity profile at several heights in the plate pair. The CFD model prediction of thegas hold-up and the recirculation pattern is compared with visualizations from the experiment.The CFD model prediction is shown to be good across several different operating conditionsand geometries, showing that the fundamental underlying equations used in the CFD modeltransfer to these cases without adjusting the model parameters.

DOI: 10.1007/s11663-010-9432-y� The Minerals, Metals & Materials Society and ASM International 2010

I. INTRODUCTION

COPPER electrowinning (EW) is the process ofwinning copper from an electrolyte to a solid form ona cathode by passing an electric current through theelectrolyte to attract copper ions to the cathode. CopperEW takes place in a rectangular geometry, with twoplate electrodes opposing each other; the current movesbetween the electrodes and depletes copper ions at thecathode, whereas oxygen bubbles are generated on theanode. It is well known that the oxygen bubbles cause alarge recirculation zone to develop in the space betweenthe electrodes and that this recirculation has a strongeffect on the mass transfer to the cathode because of themixing nature of the recirculation.[1] Copper EW oper-ators run at a current density well below the limitingcurrent density, and one reason for this is that thecopper deposits become rough and have a poor quality,which is evidenced by the nodules that form along partsof the cathode. It is widely known that one of the mainreason these nodules form is because of the limitingmass-transfer rate of copper to the cathode surface,[2]

whereby copper cannot be supplied locally to thecathode surface at the rate it is being depleted fromthe boundary layer solution by plating. That is to say,

the hydrodynamics are locally such that the mixing istoo poor to provide sufficient fresh copper to theboundary layer where copper is being depleted. Acomputational fluid dynamics (CFD) model of thebubble-generated recirculation can allow insights intothe hydrodynamic behavior in the plate pair to under-stand the detail of the mass transfer to different parts ofthe cathode. In particular, a CFD model can elucidatedetails of the mass transfer of copper to the cathode,which is the limiting factor in the plating of copper tothe cathode. Detailed experimental data of the hydro-dynamics are needed in both the bulk of the plate pair aswell as reasonably close to the cathode and anode. TheCFD model prediction of the velocity profile then can bevalidated and used with confidence to predict the fluiddynamics occurring in the EW process.In the copper EW literature, only a limited number

of CFD modeling studies of EW have taken place, andindeed, none has compared the model comprehensivelywith experimental data of the velocity profiles in theplate pair. Ziegler[3] and Ziegler and Evans[4] collectedlimited data of the velocity profile in a large systemand compared the velocity profiles with a simple fluiddynamics model with some success. Filzwieser’s[5,6]

studies are among the only efforts to obtain theexperimental data of the velocity profiles in an EWplate pair. Filzwieser[6] does not compare the CFDmodel developed with the experimental data but doesdiscuss some aspects of the CFD model, including thebasic recirculation zone that develops in the plate pair.Filzwieser[6,7] discusses the variation in the localcopper concentration close to the cathode, as afunction of height along the cathode, but this discus-sion is brief.

MARTIN J. LEAHY, Postdoctoral Fellow, is with CSIRO EarthSciences & Resource Engineering and with CSIRO Minerals DownUnder National Research Flagship, Clayton, Victoria, 3168 Australia.Contact e-mail: [email protected]. M. PHILIP SCHWARZ,Program Leader, is with CSIRO Mathematics, Informatics andStatistics, Clayton, Victoria, 3168 Australia, and with CSIROMinerals Down Under National Research Flagship.

Manuscript submitted May 7, 2010.Article published online September 14, 2010.

METALLURGICAL AND MATERIALS TRANSACTIONS B VOLUME 41B, DECEMBER 2010—1247

In other EW applications, such as water electrolysis,to produce hydrogen, a reasonable amount of work hasbeen done to develop a CFD model of the two-phaseflow that occurs between the electrodes.[8–12] The fluiddynamics in these systems is similar to that in copperEW, in regard to the generation of oxygen bubbles onthe anode. However, hydrogen bubbles also are gener-ated on the cathode so that in those systems theelectrolyte is forced through the plate pair at a veryfast rate (compared with copper EW); this speeddominates the overall flow, and no recirculation zoneresulting from bubbles is set up. Therefore, althoughthese systems are useful for validating the underlyingfundamentals of the CFD model, they do not have thesame recirculation hydrodynamics that determine themass transfer of copper to the cathode. Therefore, theyare only of partial relevance to copper EW.

This study describes the validation of a CFD model ofthe hydrodynamics occurring in a single plate pair of acopper EW cell. The work represents the first time aCFD model of the copper EW process has beencompared with experimental data of the hydrodynamicsin a single plate pair. In addition, this is the first time acomprehensive understanding of the underlying fluiddynamics in copper EW cells has been provided. TheCFD model has been validated successfully in anelectrorefining context[13] in single phase, thus providingconfidence in the component of the model that dealswith buoyancy-driven flows related to the copperdepletion.

The article has the following structure: a descriptionof the experimental setup taken from the literature isgiven followed by a description of the CFD model andthe comparison between the CFD results and theexperimental data, and finally, conclusions are given.

II. EW EXPERIMENTAL SETUP

A. General Experimental Description

Filzwieser[6] presents both CFD modeling and theexperimental work in a copper sulfate/acid EW system.A small laboratory EW cell is used, and measurementsof the cross-sectional vertical velocity at several heightsare taken by means of laser Doppler anemometry(LDA). The scaled-down cell is transparent to allowLDA measurements to be made and to allow photos ofthe internal bubble distribution to be taken.

The cell is shown schematically in Figure 1, indicatingthat the electrodes cover most of the cell wall. Thepregnant electrolyte is fed into the cell at the basethrough glass bulbs to realize laminar flow, as shown inFigure 1. The electrolyte is removed through two off-pipes at the top of the cell, with the pipes located in themiddle of the cell and at a depth below the liquid-freesurface. It is not known to what extent the pipes affectthe fluid flow, but with the low superficial velocity used(0.04 mm s�1), they must have little effect comparedwith the velocity of the gas-bubble-driven flow (magni-tude 1 mm s�1 to 100 mm s�1). The exact dimensionand position of the in and out pipes are unknown, and

consequently, the CFD model simplifies the through-flow and ignores the pipes. As shown in Figure 1 (right),the cell is somewhat irregular in shape, with indents atthe top and bottom of the electrodes. Because of thelarge electrode thickness of 10 mm (5 mm each) out of atotal (cross section) of 40 mm, a box-like shape isapparent above the electrodes, which may affect thefluid flow significantly.A summary of the operating conditions is given as

follows:

(a) The electrolyte consisted of 0.8M copper sulfate(50 kg m�3) and 1.7M acid (165 kg m�3) and is thusa close representation of industrial cell conditions.

(b) The cell is fed continuously with electrolyte at a lowvelocity (with a cell turnover time of 2 hours or asuperficial velocity of 4 9 10�5 m s�1) to keep thecopper concentration at reasonable levels and tomaintain constant temperature.

(c) Small amounts of Cu(OH)2 are added according tothe current density to ensure the cell did not becomecopper depleted.

(d) Forty parts per million Cl– is used as an inhibitor.(e) The cell is constructed so that the cell gap could be

changed between 15 mm and 30 mm.(f) Cell dimensions include an electrode gap of 15 mm

and 30 mm, an electrode height of 190 mm, a totalcell height of 291 mm, and electrodes both 5-mmthick.

The details are summarized in Table I.

B. Experimental Results

Filzwieser[6] provided flow visualization plots that arereproduced in Figure 2, which shows photos of theexperiment at steady state. These photos are provided atthree increasing current densities. Figure 2 indicates thata fog of bubbles has developed for each current density,as shown by the darker region, with the lighter whiteregion corresponding to low or close-to-zero bubbleconcentrations in the electrolyte. In Figure 2, for200 A m�2 (on the left), bubbles are present in theupper part of the cell, and a line separating the bubblyregion is clearly visible. The bubble separation linemoves lower down the cell as the current densityincreases from 200 to 400 A m�2, to the point wherealmost all of the cell has a fog of bubbles in the400 A m�2 case. The main difference between the threecurrent densities is that the higher the current density,the more extensive the bubble fog is, which occursbecause of the following reasons: first, a higher currentdensity means a higher volume of bubbles is produced,and second, a higher down-flow velocity is present, thusthe reentrainment of more bubbles occurs, which aredragged further down in the bulk. The photos for ananode-to-cathode gap spacing of 15 mm are given inFigure 3. When comparing Figure 2 (left) and Figure 3(left), it is shown that a more extensive bubble fogdevelops when the anode–cathode gap is 15 mm, com-pared with a 30-mm gap for the same current density(200 A m�2). This outcome is a result of the smallerdistance between plates causing a faster down-flow of

1248—VOLUME 41B, DECEMBER 2010 METALLURGICAL AND MATERIALS TRANSACTIONS B

electrolyte because of the smaller space for down-flow(i.e., effective higher superficial velocity).

Filzwieser[5,6] notes the following physical aspects:

(a) The departure bubble diameter was around 50 lm.It also was noted that the largest bubble size (nearthe top of the cell) was 100 lm.

(b) The bubble-driven recirculation dominates the flow,except in a thin layer near the cathode where naturalconvection is dominant.

(c) Turbulent eddies form close to the cathode, wheredownward recirculation flow driven by gas bubblesmeets upward flow as a result of natural convection(metal depletion).

(d) A hydrodynamic boundary layer forms close to thecathode, where convection is low and diffusion

limits copper mass transport; it is expected thatcopper is depleted in the boundary layer, althoughthis was not measured experimentally by Filzwieser.

(e) Filzwieser[5,6] notes that the hydrodynamic bound-ary layer diminishes further up the cell as a result ofturbulence created by gas bubbles.

The data presented in Figure 4 show the verticalvelocity profiles measured by LDA from Filzwieser[5,6]

at one of four heights (95 mm). Velocity also wasmeasured at heights of 20 mm, 132.5 mm, and 170 mm.The data in Figure 4 show high-velocity up-flow nearthe anode as well as slow down-flow in the bulk ofelectrolyte. Some up-flow occurs near the cathode. Thedata show little evidence of eddies, except perhaps in theslight nonuniformity of the down-flow; such features

Fig. 1—Schematic experimental setup of Filzwieser,[5,6] with the anode on the right and the cathode on the left side of each schematic. Red linesindicate LDA measurement cross section at height (H) shown. Each cross section includes approximately 70 point measurements. Reproducedwith permission from Filzwieser.[5]


may not be picked up by the measurement technique.LDA averages over turbulence, so unsteady eddies willnot show up. The data in Figure 4 is a profile from thebase case (case I in Table II) and has the mostcomprehensive data available, with velocity profilestaken at each end of the electrode.

As shown in Table II, Filzwieser[5,6] also presents datafor higher current density at 400 A m�2 (case II),including the velocity profiles as in Figure 4, but onlyat a height of 95 mm. Filzwieser[5,6] also presents datafor a cell gap of 15 mm at a current density of200 A m�2 (case III). For case III (200 A m�2), datawere taken at heights of 20 mm and 95 mm. Theconditions for which data and photos were providedby Filzwieser[5,6] are summarized in Table II.

III. EW CFD MODEL

A CFD model has been developed for the aforemen-tioned experimental configuration, accounting for two-phase bubbly flow in the EW cell. The CFD EW modelis two-dimensional in the Y-Z plane and is applied to across section of the cell, as shown in Figure 5, with theassumption that the flow is uniform in the third(horizontal) dimension (X direction) parallel to theelectrodes. The geometry modeled is split into discretecells, which are used to solve the equations. In this work,the geometry generally has the form shown in Figure 5.A standard two-phase gas–liquid CFD model is

employed in ANSYS CFX (ANSYS, Canonsburg,PA),[15] which treats the liquid phase (electrolyte) asthe continuous phase and the oxygen bubbles as the

Table I. Table of Parameters in EW Model*

Parameter Parameter

Current density i (A m�2) 200, 400Temperature (K) (oC) 323.15 K (50 �C)Superficial flow velocity (m s�1) 2.61 9 10�5

Liquid density q1 (kg m�3) 1200Oxygen density q2 (kg m�3) 1.2Liquid laminar viscosity l1 (kg m�1 s�1) 0.835 9 10�3

Oxygen viscosity l2 (kg m�1 s�1) 2.18 9 10�5

Diffusion coefficient D (m2 s�1) 8.62 9 10�10

Transport number t+ (–) 0.0849Coefficient of Expansion b (m3 kg�1) 0.0019 (copper)Reference concentration Cref (kg m�3) 50 (0.8M copper)Acid concentration (kg m�3) 165 (1.7M acid)Dimensions of cell (height 9 width 9 depth) 291 mm 9 30 mm 9 11 cm and 291 mm 9 15 mm 9 11 cmMolecular weight MCu (g mol�1) 63.546 (copper)

*Note: viscosity, density, and diffusion coefficient of expansion values are based on a source in the literature or on the tables of data from Zaytsevand Aseyev.[14]

Fig. 2—Photo of gas hold-up (dark areas indicate bubbles, and lightareas represent bubble-free regions) for an anode-to-cathode gap of30 mm for three current densities of (left) 200 A m�2, (middle)300 A m�2, and (right) 400 A m�2. Reproduced with permissionfrom Filzwieser.[5]

Fig. 3—Photo (dark areas indicate bubbles, and light areas representbubble-free regions) for an anode-to-cathode gap of 15 mm for threecurrent densities of (left) 200 A m�2, (middle) 400 A m�2, and(right) 600 A m�2. Reproduced with permission from Filzwieser.[5]


dispersed phase. The two phases can be envisaged as acontinuous liquid phase, with many gas bubbles dis-persed among the continuous phase.

A mass balance equation is solved, which ensures theconservation of mass of each phase. This process isknown as the equation of continuity, and for each phaseis given by the following:

r� ðaiqiviÞ ¼ Si ½1�

where for phase i (i = 1 is liquid and i = 2 is gas), Si

is the mass source/sink term (e.g., at the anode andfree surface where gas enters and leaves), qi is thephase density, and vi is the velocity. A momentumequation known as the Navier–Stokes equation issolved for each phase, which balances the forces pres-ent in the two-phase flow. In steady state, the Navier-Stokes equation in vector form is expressed as follows:

r� ðaiqivi � viÞ ¼ � airp0 þ r � ½aiðlL;i þ lT;iÞ� ðrvi þ ðrviÞTÞ� þMi þ Sivi ½2�

where for phase i (i = 1 is liquid and i = 2 is gas),p’ is the (modified) pressure, and Mi is the sum ofthe body forces, described subsequently. The laminarviscosity is denoted lL,i (kg m�1 s�1) and lT,i

(kg m�1 s�1) is the turbulent viscosity, which isdescribed subsequently. The sum of the body forces isgiven as follows:

Mi ¼ Bi þ Fi þ Ti þ Ai ½3�

where Bi, Fi, Ti, and Ai are the buoyancy force, dragforce, turbulent dispersion force, and concentration-re-lated buoyancy force, respectively. The forces are givenby the following:

B2 ¼ �B1

¼ aiðqi � qrefÞg Phase-related buoyancy force ½4�

F2 ¼ �F1 ¼ �3

4

CD

dq1a2 v2 � v1j jðv2 � v1Þ Drag force

½5�

T2 ¼ �T1 ¼ Ctdqikra2 Turbulent dispersion force

½6�

A1 ¼ a1½�q1gbðC�CrefÞ�;A2 ¼ 0

Concentration-related buoyancy force liquid ði¼ 1Þ½7�

where g (m s�2) is the gravity vector, v2 – v1 (m s�1) isthe slip velocity, |v2 – v1| is the size (modulus) of the slipvelocity, qref (kg m�3) is the reference density taken asthat of the electrolyte (i = 1), CD is the drag coefficient,Ctd is the turbulent dispersion coefficient (taken as 1),k (m2 s�2) is the turbulence kinetic energy, C (kg m�3) isthe concentration of copper, Cref (kg m�3) is thereference concentration of copper (initial and inletconcentration), and b (m3 kg�1) is the coefficient ofexpansion for the copper species.The turbulent viscosity in Eq. [2] is determined by

solving turbulence transport equations using the well-known k–x model.[16] This model originally was derivedfor single-phase flows, but it can be used for multiphaseflows by solving the k–x model for the continuous liquidphase and by using the same turbulence quantities (k, x)for the dispersed gas phase. Typically, the gas turbulentviscosity (lT;2) is multiplied by the ratio of the phases’density difference and then by dividing by the turbulentPrandtl number r (taken as 1 when the particlerelaxation time is short compared with the turbulencedissipation time scales, such as with small dispersedparticles, as in this work). We adopt this method[15] inthis work; in particular, we use the following relation-ship to define the turbulent eddy viscosity for the gasphase:

lT;2 ¼q2

q1

lT;1

r½8�

Fig. 4—Example of velocity profile experimental data from Filzwie-ser[5,6] that shows the three main parts of the velocity profile, includ-ing the up-flow near the anode, down-flow in bulk, and up-flow nearthe cathode.

Table II. Cases Where Data From Filzwieser[6] is Used

ElectrodeGap (mm)

CurrentDensity (A m�2)

No. VelocityProfiles

Height from Baseof Electrode (mm)

Photo and StreakVectors Provided?

Case I (base case) 30 200 4 20, 95, 132.5, 170 YesCase II 30 400 1 95 YesCase III 15 200 2 20, 95 Yes


The drag coefficient is dependent on the bubble size,and for small bubbles, this dependency is describedwell by the following Schiller–Nauman equation:

CD ¼24

Reb1þ 0:15Re0:687b

� �½9�

where Reb (–) is the bubble Reynolds number given bythe following:

Reb ¼dbq1 v2 � v1j j

l1

½10�

where db (m) is the characteristic length scale (bubblediameter). For 50-lm diameter bubbles, as noted in theexperiment by Filzwieser,[5,6] the bubble Reynolds num-ber is Reb~0.1 causing CD to be large, which means thatthe Stokes drag regime is prevalent, where the drag is sohigh the two phases have almost the same velocity.

A closure equation is required for the volume fractionequations, and is given by the following:

a1 þ a2 ¼ 1 ½11�

The additional transport equation for the copper spe-cies (Cu2+) in the liquid phase is expressed in steadystate as follows:

r�ða1Cv1Þ¼r� a1 q1DþlT;1

ScT

� �r C

q1

� �� þSCu ½12�

where SCu (kg m�3 s�1) is the source term, whichdescribes the flux of copper at the cathode or the sourceor sink of copper at the inlet and outlet, respectively,D (m2 s�1) is the diffusion coefficient of copper ions, andScT (–) is the turbulent Schmidt number, which typicallyis given a value of 0.9, as in this work.

A. Boundary Conditions on the Anode

The geometry shown in Figure 5 is useful to describethe boundary conditions used. On the anode side whereoxygen is produced, the following boundary conditionfor the superficial gas velocity in the Y direction v2,Y(m s�1) is based on Faraday’s Law. If we assume allcurrent is converted to oxygen gas at the anode wallsurface, then the superficial gas production rate is givenby the following:

v2;Y ¼1

4

iRT

PatmF½13�

where R (J K�1mol�1) is the gas constant, T is thetemperature (K), Patm (Pa) is the atmospheric pressure,F (A s mol�1) is Faraday’s constant, and i (A m�2) isthe current density, which is assumed constant at allpoints in the cell and along the electrodes; in futurework, this assumption could be addressed to include avariable current density.

Fig. 5—Schematic CFD geometry at the side and cross section and the cross-section mesh view. High aspect ratio of the geometry causes a highcell aspect ratio. A much larger number of cells than shown actually is used in the model.


The oxygen mass flow rate _moxygen can be calculatedbased on the superficial velocity from Eq. [13] asfollows:

_moxygen ¼ v2;YAanq2 ½14�

where Aan (m2) is the area of the anode.

B. Boundary Conditions on the Cathode for Copper

The flux of copper at the anode and cathode walls_mCu (kg m�2 s�1) based on Faraday’s Law is expressedas follows:

_mCu ¼ �i

zF

MCu

1000½15�

where i (A m�2) is the current density, F (A s mol�1)is Faraday’s constant, z (–) is the valency, and MCu

(g mol�1) is the molecular weight of copper. Theboundary condition for Eq. [15] at the cathode wall(Figure 5) is essentially the diffusional flux of copperions, which for a binary electrolyte or a dilute solutionof copper in a sulfuric-acid-supporting electrolyte, canbe expressed approximately as follows[17]:

_mCu ¼ið1� tþÞ

zF

MCu

1000½16�

where t+ (�) is the transference number (t+ ~8.49 pct inTable I), which is defined as the proportion of currentcarried by copper ions in a uniform solution withoutconcentration gradients.[17] At all walls, no slip bound-ary conditions are applied, whereas at the top freesurface, a wall boundary with a free slip (no friction)boundary condition is applied to simulate a quiescentfree surface. At the walls, the grid resolution is such thatY+ = 1, and therefore, in the k–x formulation, inte-gration in the CFD solver is carried out to the wall.

C. Wall and Free Surface Boundary Conditions

At all walls, no slip boundary conditions are appliedfor the liquid phase, whereas free slip boundaryconditions are applied for the gas phase. At the freesurface, a free slip (no friction) boundary condition isapplied to the liquid phase, whereas for the gas phase,a degassing boundary condition is used. The degassingboundary condition allows gas bubbles to leave theliquid through the surface at the rate at which theyarrive at the surface.

D. Inlet and Outlet Boundary Conditions

An inlet and outlet is added near the base to thegeometry to allow through-flow and for the introduc-tion of copper to avoid depletion. This is not exactlythe same through-flow configuration as in the exper-iment (Figure 1), but the details of the experimentalarrangement are difficult to ascertain, and as men-tioned previously, through-flow velocities are muchsmaller than those generated by the bubbles, so theexact through-flow configuration is unlikely to have asignificant effect on the simulation results. At a current

density of 400 A m�2, a higher through-flow velocity(increase by a factor of two) is used in the CFD modelto avoid copper depletion. However, in the experiment,this is not the case; instead, small amounts of Cu(OH)2are added according to the current density. Thisdiscrepancy in the experimental flow rate and theCFD flow rate for this high current density case hasinsignificant effects on the flow because of the low flowrates compared with the gas-generated flow rates,which are several orders of magnitude higher; thissetup merely simulates the CFD-predicted coppertopped up, which could have been done in anothernominal way. The parameters used are shown inTable I.

IV. VALIDATION OF CFD EW MODEL

The experimental data of Filzwieser[5,6] were discussedin Section II and now are used to compare with the CFDmodel. The computational mesh used for the simulationhas a cell spacing that is finer near the walls than in themiddle to resolve the higher velocity gradients near thewalls. The operating conditions are the same as thoseused in the experiment, as described in Section II. Theparameters used in the CFD model, including boundaryconditions, are given in Table I.

A. Comparison with Case I LDA Data

The experimental data in case I (the base case) werethe most comprehensive (with four velocity profiles).Case I used a current density of 200 A m�2 and anelectrode gap of 30 mm. In this section, we show thecomparison of CFD results with case I data, as given inFigures 6(a) through (d), for the heights (from the baseof the electrodes) of 20 mm, 95 mm, 132.5 mm, and170 mm, respectively. These positions are shown clearlyin Figure 1. The results at the height of 20 mm (from thebase of the electrodes) in Figure 6(a) show a fairly goodagreement between the experimental data and the CFDprediction, with most parts of the profile in goodagreement, except for an overprediction of the maxi-mum velocity near the anode where the oxygen gener-ated rises quickly and drags liquid upward. In themiddle of the cell, the data indicates slow downwardflow, resulting from the electrolyte recirculation zonepresent. This flow is predicted well by the CFD model.Near the cathode, an upward flow is caused by copperdepletion and by the associated natural convectionbuoyancy, which also is predicted closely by the CFDmodel, with the shape and maximum velocity in closeagreement.At the higher positions of 95 mm, 132.5 mm, and

170 mm from the electrode base (Figures 6(b) through(d)), the agreement between CFD and the experiment isalso good, with close comparison at all parts of the crosssection, including the correct maximum velocity near theanode. In the middle section, good agreement occurs inall cases. The maximum velocity near the cathode is inclose agreement in most cases.


The highest positions of 132.5 mm and 170 mm fromthe electrode base (Figures 6(c) and (d)) experience somewavy behavior in the CFD prediction in the bulk, whichis a result of unsteady eddies that form in the bulk,whereas the data indicate that the velocity profile is flat.The data points represent an average of the eddies (andthe associated fluctuations in the velocity) that may bepresent in the bulk. Future work is required to establishwhether the CFD eddies can be averaged over time togive the same overall flat velocity profile.

Mostly, a relative difference of around 20 pct is notedbetween the data and the CFD values of the maximumvelocity near the cathode and the anode, although therelative difference often was much less than this. Thisresult is considered satisfactory given the limited knowl-edge of the operating conditions, assumptions required,possible errors in liquid velocity measurements (partic-ularly in the bubbly region), and complexity of modelingmultiphase flow.

B. Comparison between CFD and ExperimentalVisualization for Case I

The streak vector plot taken from the observations ofcase I is shown in Figure 7(a) together with theassociated CFD prediction of the vector field for caseI. The CFD vector plot in Figure 7(b) (normalized)shows that a fairly good qualitative agreement existsbetween the CFD and the schematic streak plot of theexperimental vector field in regard to the behavior andflow pattern, including a large recirculation zone andup-flow near the anode caused by the bubbles as well asan up-flow near the cathode as a result of copperconcentration gradients. Agreement also was found inthe down-flow in the bulk. The shape of the velocityprofile (as shown in Figure 6 from LDA measurements)is reflected in the schematic streak plot of the experi-mental vector field and the CFD prediction of the vectorfield in Figures 7 and 8(a) in regard to the characteristics

Fig. 6—Comparison of CFD results with case I experimental data from Filzwieser[6] for 200 A m�2 and a 30-mm gap. Vertical velocity compo-nent (mm s�1) vs distance from cathode (mm) at a height of (a) 20 mm (from base of electrode), (b) 95 mm, (c) 132.5 mm, and (d) 170 mm. In-set figure shows a close-up near the cathode.


of fast up-flow near the anode, low level of up-flow nearthe cathode, and low level of down-flow in the bulk.

Looking at the CFD results in Figure 9, a close up ofthe anode wall is shown where oxygen bubbles areproduced (see oxygen volume fraction in Figure 9(a))and remain extremely close to the anode, predominantlyin the first computational cell. The gas remains in thetight region close to the anode because there, onlyadvection is transporting this phase, despite a turbulentdispersion force being added to the gas phase. Gas risesupward (see superficial velocity in Figure 9(b)), whichdrags the electrolyte upward (see electrolyte velocity inFigure 9(a)). As shown in Figure 9(a), after leaving thetop of the anode, the oxygen moves into the top regionand is dispersed by advection. Figure 8(a) shows on alarger scale view that the gas then is carried upward tothe free surface; the electrolyte cannot leave the system,but gas can leave the system depending on the localhydrodynamics. However, some oxygen is carried backdown into the bulk, dragged along with the electrolyte,which occurs fairly often, and results in a gas hold-up inthe bulk of the top square block region of up to 5 pct.The gas hold-up in the bulk in the middle of the top ofthe electrode region is up to 2 pct, which decreasesdownward because of the down-flow velocity decreasingdownward and also because the bubbles tend to rise as aresult of their buoyancy.

The experimental visualization in Figure 8(c) showsthe distribution of oxygen gas hold-up (the dark regionscorrespond to high gas hold-up, and the light regionscorrespond to low gas hold-up) compared with theCFD-predicted oxygen gas hold-up (Figures 8(a) and

(b)); broadly, good agreement is found in that the hold-up is high at the top and decreases down in the bulk.CFD and experimental agreement also is noted for asharp decrease in the gas hold-up near the cathode (i.e.,a decrease occurs in the oxygen volume fraction close tothe cathode extending upward, as indicated in Figure 8).This finding is true in three cases (cases I, II, and III), asindicated on the CFD contour plot of volume fraction(Figure 10 [bottom]) vs the experimental (Figure 10[top]). Also note the line plot inset in Figure 10(a) andthe close-up in Figure 8(b). This region of low gas hold-up near the cathode is a result of the following: a closedrecirculation vortex coincides with this elongated bub-ble-free region close to the cathode, which is cut-offfrom the main large recirculation coming from theanode where bubbles originate. The recirculation in thiselongated bubble-free region close to the cathode isdriven by copper gradients and by the associated naturalconvection recirculation pattern (Figure 8(a)), which areincluded in the CFD model and predict the correct typeof behavior in approximately the correct position.

C. Comparison between CFD and ExperimentalVisualization for Cases I Through III

The photos taken during the experiment (whichindicates gas hold-up) are shown in Figure 9 in additionto the CFD prediction of the velocity and oxygenvolume fraction for cases I through III. This allows acomparison between the CFD-predicted oxygen volumefraction (gas hold-up) and the visual images taken fromthe experiment. It is shown that a reasonable agreementexists in the oxygen volume fraction (or gas hold-up) inregard to the distance the bubbly region extends towardthe bottom of the cell.The value of the oxygen volume fraction predicted by

the CFD model is higher for case II compared with caseI (as in Figure 10) because of the higher down-flowvelocity and more bubble entrainment into the bulk,which is caused by the factor of two increase in thecurrent density that provides double the oxygen flowrate up the anode (because of Faraday’s Law inEq. [13]), and thus, more reentrainment of bubblesoccurs. This is a result of the following factors: (1) ahigher gas flow increases the up-flow velocity as well asthe down-flow velocity, thus enabling more reentrain-ment of bubbles caught by the down-flow at the freesurface; and (2) a higher gas flow increases the proportionof bubbles, which then can be reentrained into the bulk.For case II, the maximum oxygen volume fraction in

the bulk predicted by the CFD model in the bulk is 0.05compared with 0.02 for case I. Qualitatively, agreementoccurs in CFD and the experiment between cases I andII in the lower penetration of the gas bubbles.Comparing cases I and III in Figures 9(a) and (c), we

observe that for the same current density but a smallergap width, greater gas hold-up occurs; this finding isconfirmed in the photos that show the gas hold-up takenduring the experiment and also in the CFD prediction ofthe oxygen volume fraction. The higher gas hold-up is aresult of the smaller gap width leading to faster down-flow, thus dragging more bubbles downward.

Fig. 7—Case I (a) experimental schematic sketch of the vector fieldfrom the experiment (reproduced with permission from Filzwieser,[5,6])and (b) the CFD vector field (with vector renormalization for clarityof all vector scales), with a close-up near the cathode (top inset,no vector renormalization) and anode (bottom inset, no vectorrenormalization).


In summary, the overall trend of the CFD model is inagreement with the experimental photos. However, thepenetration of the gas bubbles toward the bottom of thebulk as predicted by the CFD is not as extensive asthe photos for the three cases in Figure 9 indicate. Thisshortcoming may be a result of the CFD model for thefollowing reasons:

(a) The assumption of a single bubble size and/oroverestimating the average size chosen (50 micron)

(b) Underpredicting the bubble dispersion into thebulk, which does not occur significantly along theanode but mainly near the top of the free surface

(c) Ignoring three-dimensional side-wall effects thatwere present in the experiment, as this may beaffecting the fluid flow significantly.

D. Comparison of Case II LDA Data

We now show the comparison between the CFD ver-tical velocity and the experimental LDA measurements

for case II (summarized in Table II) in which the anode–cathode gap is 30 mm and a current density of400 A m�2 is used. Figure 11 shows the comparisonbetween the CFD and the experimental data, indicatinga fairly good agreement between the CFD and theexperiment in the maximum value in the velocity at theanode and cathode sides as well as in the down-flowvelocity in the middle section. A higher velocity isobserved near the anode and in the bulk in both theexperiment and the CFD compared with case I for200 A m�2 (compare the velocity profile for case I inFigure 6(b) with case II in Figure 11). This followsbecause of the doubled current density (and doubled gasflow rate) for the same gap width, which causes a fastervelocity near the anode and in the bulk.

E. Comparison of Case III LDA Data

We now show the comparison for case III (summa-rized Table II) in which the electrode gap is 15 mm andthe current density is 200 A m�2. Figures 12(a) and (b),

Fig. 8—Case I (a) streamlines of electrolyte flow, electrolyte vector plot, and volume fraction showing recirculation patterns as well as a(b) close-up of the box in (a), and an (c) experimental visualization for comparison. Bold arrows indicate similar bubble-free regions near thecathode, indicating qualitative agreement between the experiment and CFD. Streamlines show that a closed recirculation region coincides withthis bubble-free region.


show the comparison at positions of 20 mm and 95 mmfrom the base of the electrode, respectively. The CFDresults for both heights show a close comparison withthe experimental data at all parts of the profile, exceptfor an underprediction close to the anode. The up-flownear the cathode is predicted well by the CFD model.

V. CONCLUSIONS

A CFD model has been developed to simulate flowand copper distribution in an EW cell consisting of asingle anode–cathode pair. The model incorporates thetransport of oxygen bubbles generated on the anodeand copper in the electrolyte, including the deple-tion of copper at the cathode and density-relatedbuoyancy forces resulting from metal concentrationgradients.

The experimental setup used by Filzwieser[5,6]

involves a copper sulfate and acid mixture in a mediumsized cell with through-flow; thus, the experiment is agood representation of a scaled-down real EW cell.Data from three cases with different current densitiesand interelectrode gaps compared well with the CFDmodel.The conclusions of the study are as follows:

1. The CFD model closely can predict the behavior inthe scaled EW cell across a range of operating con-ditions and electrode spacings.

2. The CFD-predicted velocity profile is close toexperimental data in most parts of the cross section,with flow near the anode and cathode in goodagreement. For the base case, a relative difference ofaround 20 pct was noted between the data and theCFD values in the maximum velocity near the cath-ode and anode, although often, the relative difference

Fig. 9—Close-up near the anode (near top), depicting the (a) fill contours of the oxygen volume fraction (–), electrolyte vector plot, and stream-lines of electrolyte and (b) the filled contours of the oxygen superficial velocity (mm s�1), oxygen superficial velocity vectors (mm s�1), and astreamline of the oxygen phase.


Fig. 10—Comparison of a photo indicating gas hold-up (top) (Reproduced with permission from Filzwieser[5,6]) and CFD-predicted gas hold-up(or oxygen volume fraction) (bottom) for the following cases: (a) case I (CD200 EA30) with an inset of a line plot of the oxygen volume fractionat a height of 170 mm, (b) case II (CD400 EA30), and (c) case III (CD200 EA15). Th figure indicates that CFD predicts bubble behaviorreasonably well across three operating conditions. In CFD, the scale is shown with a maximum of 0.15, although the maximum oxygen volumefraction is 0.88 at the top of anode.


was much less than this. This outcome is consid-ered satisfactory given the unknowns, assumptionsrequired, possible errors in the data, and complexityof modeling multiphase flow.

3. Some differences in the overlay of CFD results andexperimental data of the velocity are attributed tocomplicating issues including,

(a) Wall effects that were present in the experiment,which may be affecting the fluid flow significantly

(b) TheCFDmodel exhibits someunsteady behavior,with eddies present in the bulk

(c) The through-flow conditions in the CFD modelare not set up exactly the same as in the experiment

because of a lack of information about the exactexperimental configuration.

4. Photos from the experiments of the voidage werecompared with the CFD model, which establishedthe following:

(a) Trends in the CFD-predicted gas hold-up are inagreement with the experiments, with the highercurrent densities and a smaller gap width lead-ing to greater gas hold-up

(b) Good agreement was noted in the existence of avertically elongated bubble-free region close to thecathode, resulting from a closed recirculationvortex that is cut off from the main large recir-culation coming from the anode where bubblesoriginate. The recirculation in this elongatedbubble-free region close to the cathode is drivenby copper gradients and the associated naturalconvection recirculation pattern.

5. Streak vector plots from the experiments were com-pared with the CFD model, with general agreementobserved in the following features:

(a) Large recirculation, especially in the regionabove the electrodes,

(b) Up-flow near the anode and cathode(c) Down-flow in the bulk

6. Generally, the CFD model underpredicted the gashold-up in the bulk, which may be caused by acombination of the following:

(a) The assumption of a single bubble size and/oroverestimating the average size chosen (50micron)

(b) Underestimating bubble dispersion along theanode

Fig. 11—Comparison of CFD results with the case II experimentaldata from Filzwieser.[5,6] The vertical velocity component (mm s�1)vs the distance from the cathode (mm) at a height of 95 mm fromthe base of the electrode at 400 A m�2 and a 30-mm gap.

Fig. 12—Comparison of CFD results with the case III experimental data from Filzwieser,[5,6] with 200 A m�2 and a 15-mm gap. The verticalvelocity component (mm s�1) vs distance from the cathode (mm) at a height of (a) 20 mm from the base of the electrode and at (b) 95 mm fromthe base of the electrode.


ACKNOWLEDGMENTS

The authors gratefully acknowledge funding fromthe AMIRA P705 sponsors. The authors also grate-fully acknowledge Mike Horne, for his help with theexperimental work and for his helpful discussions, andPeter Witt, Darrin Stephens, and Graeme Lane fortheir helpful CFD assistance and discussions. MikeNicol is acknowledged for his helpful discussions.

NOMENCLATURE

A area (m2)Ai concentration related buoyancy force of phase

i (N m�3)Bi natural convection buoyancy force of phase i

(N m�3)C copper concentration (kg m�3)Cref average concentration of copper over the

cathode (kg m�3)DC difference in bulk to wall concentration of

copper (kg m�3)CD drag coefficientCtd turbulent dispersion coefficientD diffusion coefficient (m2 s�1)F Faraday’s constant (A s mol�1)Fi drag force of phase i (N m�3)g gravitational acceleration vector (m s�2)H height of electrode (mm)h width of electrode (mm)i current density (A m�2)k kinetic energy (m2 s�2)_mCu flux of copper at the cathode walls

(kg m�2 s�1)_moxygen flux of oxygen at the anode and cathode walls

(kg m�2 s�1)MCu molecular weight of copper (g mol�1)Mi sum of body forces of phase i (N m�3)Patm atmospheric pressure (Pa)p pressure (Pa)p’ modified pressure (Pa)R cas constant (J/K/mol)Reb bubble Reynolds number (–)ScT turbulent Schmidt number (–)t+ transference number (–)Ti turbulent dispersion force of phase i (N m�3)T temperature (K) (�C)vi velocity vector of phase i (m s�1)X X direction coordinate (m)Y Y direction coordinate (m)Z valency (–)Z Z direction coordinate (m)Z’ effective height above base of electrodes (m)

GREEK SYMBOLS

ai volume fraction of phase ib coefficient of expansion (m3 kg�1)li liquid laminar dynamic viscosity (kg m�1 s�1)lT,i turbulent dynamic viscosity (kg m�1 s�1)qi density of phase i (kg m�3)rT turbulence Schmidt number (–)x Eddy frequency (s�1)

SUBSCRIPTS

An anodeatm atmosphericb bubbleCu copperi phase i (i = 1 water, i = 2 gas)ref referenceT turbulent

SUPERSCRIPTS

T transpose‘ modified pressure p’

REFERENCES1. J. Graydon and D. Kirk: Can. J. Chem. Eng., 2001, vol. 69,

pp. 564–70.2. G. Rigby, P. Grazier, A. Stuart, and E. Smithson: Chem. Eng. Sci.,

2001, vol. 56, pp. 6329–36.3. D. Ziegler: Ph.D. Dissertation, University of California, Berkeley,

CA, 1984.4. D. Ziegler and J. Evans: J. Electrochem. Soc., 1986, vol. 133 (3),

pp. 567–76.5. A. Filzwieser, K. Hein, G. Hanko, and H. Grogger: Proc. Copper-

Cobre 99 Vol III. – Electrorefining and Electrowinning of Copper,1999, pp. 695–709.

6. A. Filzwieser: Ph.D. Dissertation, Leoben University, Leoben,Austria, 2000.

7. A. Filzwieser, K. Hein, and G. Mori: JOM, 2002, pp. 28–31.8. K. Aldas: Appl. Math. Comput., 2004, vol. 154, pp. 507–19.9. M. Mat and K. Aldas: Int. J. Hydrogen Energ., 2005, vol. 30,

pp. 411–20.10. R. Wedin, L. Davoust, A. Cartellier, and P. Byrne: Exp. Therm.

Fluid Sci., 2003, vol. 27, pp. 685–96.11. P. Boissonneau and P. Byrne: J. Appl. Electrochem., 2000, vol. 30,

pp. 767–75.12. V. Agranat, S. Zhubrin, A. Maria, J. Hinatsu, M. Stemp, and M.

Kawaji: Proc. of FEDSM2006, 2006, pp. 1–8.13. M. Leahy and M.P. Schwarz: 16th Australasian Fluid Mechanics

Conf, Gold Coast, Australia, 2007.14. I. Zaytsev and G. Aseyev: Properties of Aqueous Solutions of

Electrolytes, CRC Press, Boca Raton, FL, 1992, pp. 1–1081.15. ANSYS, Inc.: CFX-11 Solver, www.ansys.com/cfx, 2007.16. D. Wilcox: Proc. of the 24th AIAA Aerospace Sciences Meeting,

American Institute of Aeronautics and Astronautics, Reno, NV,1986, pp. 1311–20.

17. J. Newman and K. Thomas-Alyea: Electrical Systems, 3rd ed.,Wiley, Hoboken, NJ, 2004, p. 14.


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