CFD Modeling of Pulsed Disc and Doughnut Column - American

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Thermodynamics, Transport, and Fluid Mechanics

CFD Modelling of Pulsed Disc and Doughnut Column: Prediction of Axial Dispersion in Pulsatile Liquid-Liquid Two-Phase Flow Sourav Sarkar, Krishna Kumar Singh, and Kalsanka Trivikram Shenoy Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b01465 • Publication Date (Web): 11 Jul 2019 Downloaded from pubs.acs.org on July 28, 2019

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Industrial & Engineering Chemistry Research

CFD Modelling of Pulsed Disc and Doughnut Column: Prediction of Axial Dispersion in Pulsatile Liquid-Liquid Two-Phase Flow Sourav Sarkar1,2, Krishna Kumar Singh1,2,*, Kalsanka Trivikram Shenoy1 1Chemical

Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai, INDIA-400085 2Homi Bhabha National Institute, Anushaktinagar, Mumbai, INDIA-400094 *Corresponding author: [email protected]

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ABSTRACT Numerical simulations of liquid-liquid counter-current two-phase flow in Pulsed Disc and Doughnut Columns (PDDCs) are performed. The simulation methodology comprises of two steps. In the first step, Euler-Euler method is used to obtain turbulent two-phase flow field. Turbulence is simulated by using standard k- mixture model. Dispersed phase is assumed to be monodispersed. The second step comprises of solution of species transport equation together with flow equations to obtain residence time distribution (RTD) of the continuous phase. The RTD is used to estimate axial dispersion coefficient or Peclet number of the continuous phase. Experimental data of RTD for different operating conditions (pulsing velocity, dispersed phase velocity, continuous phase velocity) and different geometries (diameter of the column, spacing between the discs) are used for validation. Estimates of Peclet number by CFD model are better than the same obtained from previously reported empirical correlations.


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Keywords: Axial dispersion, CFD, holdup, numerical simulation, pulsed disc and doughnut column, Peclet number

1. INTRODUCTION Hydrometallurgical, nuclear and chemical industries extensively employ liquid-liquid extraction as separation process1-3. Various liquid-liquid contactors such as mixer-settler, rotating disc contactors, centrifugal extractor, air pulsed columns are used for liquid-liquid extraction. Among these contactors, air pulsed columns are suitable for applications involving nuclear materials as they do not have moving parts and thus are maintenance-free48.

Air pulsing is used to provide the energy to create liquid-liquid dispersion in a pulsed

column. There are several designs of air pulsed columns which basically differ in the type of internals used. Among different designs of air pulsed column, the design having sieve plates as internals and called as pulsed sieve plate column (PSPC) is the oldest design. Pulsed disc and doughnut column (PDDC), in which disc and doughnut shaped baffles are used instead of sieve plates, is relatively new compared to PSPC9-11. Better handling of feed containing solids and better mass transfer owing to higher holdup of dispersed phase resulting in lower height of transfer unit (HTU) are the advantages of PDDCs. Whereas better solid handling capability is attractive for the front-end of the nuclear fuel cycle in which feed to be processed is likely to have solids, lower HTU is particularly attractive for liquid-liquid extraction in the back-end of the nuclear fuel cycle in which a compact setup is always preferred 12,13. Several studies have been reported on PDDCs in open literature. Experimental studies on PPDC have been reported to quantify axial dispersion in single-phase flow 14,15 and two-phase flow14,13. Experimental studies focused on drop size13,16, slip velocity between continuous and dispersed phase17, flooding conditions13,16, liquid-liquid mass transfer10,13

and dispersed

phase holdup13,18-20 have been reported. Studies on computational fluid dynamics (CFD) simulations are relatively less compared to the experimental studies on PDDCs. Most of the reported CFD studies are focused on single-phase flow hydrodynamics and axial dispersion2127.

Nabli, et al 22 reported single-phase CFD simulations to quantify axial mixing for varying

operating conditions and geometrical parameters of PDDC. Bujalski, et al. reported singlephase simulations for no net flow condition in a PDDC24. Validation was performed by comparing predicted variation of velocity with time at a point with the measurements obtained by particle imaging velocimetry and laser Doppler anemometry. Charton et al carried out single-phase simulations using Reynolds Stress Model (RSM) and low-Reynolds 3 ACS Paragon Plus Environment


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number model34. Both models were found to be equally good for pulsing velocity up to 0.04 m/s. CFD simulations of PDDC focused on two-phase flow are scarce

28,29.

CFD studies using

Lagrangian approach to simulate two-phase flow have been reported 30,31. Bardin-Monnier et al. carried out two-phase simulations of PDDC using Lagrangian approach30. Effects of droplet diameter, pulsing frequency and amplitude on axial dispersion and mean residence time were studied. However, there was significant deviation between the estimated and measured axial dispersion coefficient. A few studies on two-phase flow simulations of PDDCs based on Euler-Euler method have also been reported28,29. Retieb and co-workers performed Euler-Euler two-phase simulations of PDDC28. 2D axisymmetric computational domain was used. Drops of the dispersed phase were considered to be mono-dispersed. Among different drag models compared, the drag model of Wallis was shown to be good35. Column diameter was 3 inch. For validation, predicted dispersed phase holdup was compared with and measured values. Validation was done for varying operating conditions but fixed geometry. A collision model to simulate the influence of inter-drop collision on dispersed phase holdup was used. Saini and Bose also carried out two-phase CFD simulations of PDDC using Euler-Euler approach with the assumption of monodispersed drops and by using Schiller-Naumann drag model29. Validation was performed using reported experimental data18. Variations of dispersed phase holdup with density ratio of the liquids and drop size were reported. The effects of pulsing frequency and amplitude were also discussed. Effect of pulsing amplitude on dispersed phase holdup was reported to be insignificant which is in contrast to the observation reported in several experimental studies18,36,37. However, axial dispersion in two-phase flow is not studied in any of the above-mentioned studies. Most of the two-phase CFD studies focus on estimation of dispersed phase holdup in PDDC. Recently, computational fluid dynamics-population balance (CFD-PB) simulations of PDDC have been reported. In these simulations only breakage of droplets has been considered which is possible only for the condition of low dispersed phase holdup 32. To the best of our knowledge, the only CFD study on two-phase axial dispersion in disc and doughnut column based on Euler-Euler method is reported by Yi and co-workers33. However, this study is carried out for non-pulsing conditions. Though estimates of dispersed phase holdup by CFD simulations had good accuracy, significant deviation between estimated and measured Peclet number was observed. A prerequisite to correctly predict mass transfer performance of PDDC is correct estimation of hydrodynamic variables of two-phase flow which are dispersed phase holdup, axial 4 ACS Paragon Plus Environment

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dispersion coefficients and drop size distribution of the dispersed phase. If the hydrodynamic variables are correctly predicted, axial dispersion model can be used to predict mass transfer38. In our previous study we have reported CFD model of PDDC to predict dispersed phase holdup39. In the present study we focus on the next step of two-phase flow simulation of PDDC i.e. estimation of axial dispersion in PDDC. CFD model focused on estimating axial dispersion in continuous phase for two-phase in PDDCs is presented. Since the conditions of experiments done to obtain residence time distributions reported in this study are different from our previous study, dispersed phase holdup is also measured and estimated by CFD simulations. The CFD model of turbulent, pulsatile, liquid-liquid, two-phase flow is based on Euler-Euler method and standard k- mixture model. It is validated extensively with experimental data.

2. EXPERIMENTAL SETUP AND METHOD Fig. 1 shows the schematic diagram of the experimental setup details of which were reported in our previous study 39. The setup comprises of two cylindrical column sections (C1, C2) of 0.0508 m and 0.076 m diameter. Either of the two columns can be used at a time. The two liquid phases are pumped from their respective feed tanks (AT, OT) by using centrifugal pumps (PMP1 and PMP2). The flow control is by rotameters (R1, R2) and control valves installed before the rotameters. Compressed air obtained from the compressor (COM) is used as the pulsing air. Pulsing by pressurization and depressurization of pulse leg is achieved by a 3-way valve (3WV). Cylindrical section (active section) of each column, made of glass, housing the discs and doughnuts is 0.5 m long. Phase separation is ensured by SS-304L disengagement sections placed at the top and bottom of the cylindrical column section. Glass windows are provided in the disengagement sections for flow visualization. The cylindrical sections of the columns have sampling ports. The internals are such that disc spacing can be varied. Experiments are conducted for two different disc spacing (0.05 m and 0.10 m). Fractional open area of discs and doughnuts is 0.25. Experiments are conducted with water as the aqueous phase (continuous phase). Organic phase (dispersed phase) is prepared by mixing tributyl phosphate (TBP) with dodecane. The volume fraction of dodecane in the mixture is 0.7. Densities of the aqueous and organic phases are 998 kg/m3 and 816 kg/m3, respectively. Viscosities of the organic phase and aqueous phase are 0.00192 Pa.s and 0.001 Pa.s, respectively. Interfacial tension between the aqueous phase and organic phase is 0.01056 N/m. 5 ACS Paragon Plus Environment


First flow of the aqueous phase is started at the desired volumetric flow rate. Then pulsing is commenced at desired amplitude and frequency. This is followed by starting of flow of the organic phase at desired volumetric flow rate. Samples of dispersion are withdrawn from the sample ports (S11, S12, S13, S21, S22, S23) to measure dispersed phase holdup after attainment of steady state40,41. Superficial velocities of the continuous phase and dispersed phase are varied in the experiments. Pulsing velocity is also varied in the experiments. Pulsing amplitude is varied to vary the pulsing velocity. Pulsing frequency is kept constant at 1 Hz. Residence time distribution studies are performed by using 3M KCl (potassium chloride) solution as the chemical tracer. Suitability of KCl as a tracer has been reported earlier14. The tracer is injected into the column using a syringe. It is ensured that complete volume of the tracer is injected quickly so that pulse injection is realized. The tracer injection point is located at a distance of 50 mm from the top of the active column section. An online conductivity meter (range of 0-5 S/cm) is placed 50 mm above the base of the cylindrical section of the column to continuously measure the continuous phase conductivity. The conductivity values are used to obtain residence time distribution (E-curve) of the continuous phase.


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Figure 1. Schematic diagram of the pulsed column setup used for the experiments. (AT: Aqueous Tank; B1, B2: Balance legs; COM: Compressor; CP: Control Panel; DAS: Data Acquisition System; L1, L2: Pulse legs; OT: Organic Tank; S11-S23: Sampling ports; PC1, PC2: Pulsed columns; R1, R2: Rotameters; PMP1, PMP2: Centrifugal Pumps; 3WV: Three-way Valve; -----------: Electrical line). [Reprinted from Separation and Purification Technology, 209, Sourav Sarkar, Krishna Kumar Singh, Kalsanka Trivikram Shenoy, Two-phase CFD modeling of pulsed disc and doughnut column: Prediction of dispersed phase holdup, 608-622, Copyright (2019), with permission from Elsevier]

3. COMPUTATIONAL APPROACH 3.1.

Governing Equations.

Numerical simulations comprise of two steps. The first step pertains to solutions of continuity and momentum equations for both the phases. Euler-Euler method, which is suitable for simulating two-phase dispersed flows having appreciable dispersed phase volume fraction, is used for the simulations reported in this work28,29,42,43. The same model was used by us in our previous work on predicting dispersed phase holdup in PDDC39. The volume fractions of the continuous phase as well as dispersed phase in all computational cells of the domain are 7 ACS Paragon Plus Environment


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computed. Interphase exchange coefficient (𝛽) is used to model interphase momentum exchange. The continuity equations are given by eqs 1 and 2. ∇.(𝜙𝑑𝑢𝑑 + 𝜙𝑐𝑢𝑐) = 0 ∂𝜙𝑑 ∂𝑡

(1)

+∇.(𝜙𝑑𝑢𝑑) = ∇.𝐷𝑚𝑑∇𝜙𝑑

(2)

Dispersed phase volume fraction and continuous phase volume fraction are represented by 𝜙𝑑 and 𝜙𝑐, respectively. 𝑢𝑑 and 𝑢𝑐 are the local velocity vectors of the dispersed phase and continuous phase, respectively. A gradient based hypothesis is used to model dispersed phase dispersion due to turbulent fluctuations. The turbulent dispersion coefficient (𝐷𝑚𝑑) is obtained from turbulent viscosity (𝜇𝑇), mixture density (𝜌𝑚) and turbulent Schmidt number ( 𝜎𝑇). The momentum equations are: ∂𝑢𝑐

𝜌𝑐 ∂𝑡 + 𝜌𝑐(𝑢𝑐.∇)𝑢𝑐 = ∇.[ ―𝑝𝐼 + 𝜏𝑐] + ∂𝑢𝑑

∇𝜙𝑐

𝜙𝑐 𝜏𝑐

𝜌𝑑 ∂𝑡 + 𝜌𝑑(𝑢𝑑.∇)𝑢𝑑 = ∇.[ ―𝑝𝐼 + 𝜏𝑑] +

+ 𝜌𝑐𝑔 +

∇𝜙𝑑

𝐹𝑚,𝑐 𝜙𝑐

𝜙𝑑 𝜏𝑑 + 𝜌𝑑𝑔 +

𝐹𝑚,𝑑 𝜙𝑑

(3) (4)

where 𝜏𝑐 and 𝜏𝑑 represent the stress tensors and expressed by eqs 5 and 6.

( + 𝜇 )(∇𝑢

𝑇

)

2

2

𝜏𝑐 = (𝜇𝑐 + 𝜇𝑇) ∇𝑢𝑐 + (∇𝑢𝑐) ― 3(∇.𝑢𝑐)𝐼 ― 3𝜌𝑐𝑘𝐼 𝜏𝑑 = (𝜇𝑑

𝑇

𝑑+

𝑇

(∇𝑢𝑑)

2

)

(5)

2

― 3(∇.𝑢𝑑)𝐼 ― 3𝜌𝑑𝑘𝐼

(6)

p represents pressure which is same for both phases. Continuous phase dynamic viscosity is represented by 𝜇𝑐. Dispersed phase dynamic viscosity is denoted by 𝜇𝑑. Turbulent mixture viscosity, which is evaluated for the two-phase mixture, is denoted by 𝜇𝑇 . The closure of the momentum equations requires quantification of interphase forces denoted by 𝐹𝑚,𝑐 and 𝐹𝑚,𝑑. These forces may depend on several interphase interactions but they must satisfy the conditions that 𝐹𝑚,𝑐 = ― 𝐹𝑚,𝑑. In the simulations carried out in this study, the interphase momentum exchange is attributed solely to drag force. This assumption is generally considered suitable for dispersed liquid-liquid flows in different equipment28,29. The interphase momentum exchange term is defined by using an interphase exchange coefficient ( 𝛽) as given by eq 7. 𝐹𝑚,𝑐 = 𝛽(𝑢𝑑 ― 𝑢𝑐)

(7)

Interphase exchange coefficient is defined by using drag coefficient (CD) as given by eq 8. 𝛽=

3𝜌𝑐𝐶𝑑(|𝑢𝑑 ― 𝑢𝑐|)

(8)

4𝑑32


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Schiller-Naumann drag model used for evaluating drag coefficient is given by eq 9. 𝑅𝑒𝑝 represents drop Reynolds number and is defined by eq 10.

{

𝐶𝑑 = 𝑚𝑎𝑥

24

(1 + 0.15𝑅𝑒0.687 );0.44} 𝑝

(9)

𝑅𝑒𝑝

(

)

𝜙𝑐𝑑32𝜌𝑐 |𝑢𝑑 ― 𝑢𝑐|

𝑅𝑒𝑝 =

(10)

𝜇𝑐

Mixture k- model of turbulence is used to model turbulence. Thus, trubuelnce equations are not phase specific but solved for the mixed phase. The turbulence model is expressed by eqs 11 and 12. ∂𝑘

[( + 𝜌 (𝑢 .∇)𝜀 = ∇.[(𝜇

) ] )∇𝜀] + 𝐶

𝜇𝑇

𝜌𝑚 ∂𝑡 + 𝜌𝑚(𝑢𝑚.∇)𝑘 = ∇. 𝜇𝑚 + 𝜎𝑘 ∇𝑘 + 𝑃𝑘 ― 𝜌𝑚𝜀 ∂𝜀

𝜌𝑚∂𝑡

𝑚

𝜇𝑇 𝑚 + 𝜎𝜀

𝑚

𝜀 1𝜀𝑘𝑃𝑘 ―

(11) 𝜀2

(12)

𝐶2𝜀𝜌𝑚 𝑘

Subscript m refers to the mixed phase. The physical properties and velocity of the mixed phase are defined by eqs 13 and 14. (13)

𝜌𝑚 = 𝜙𝑐𝜌𝑐 + 𝜙𝑑𝜌𝑑 𝑢𝑚 =

𝜙𝑐𝜌𝑐𝑢𝑐 + 𝜙𝑑𝜌𝑑𝑢𝑑

(14)

𝜙𝑐𝜌𝑐 + 𝜙𝑑𝜌𝑑

Turbulent viscosity is based on the two-phase mixure and so is the turbulent kinectic energy generation term. These are evaluated by using eqs 15 and 16, respectively. 𝑘2

(15)

𝜇𝑇 = 𝜌𝑚𝐶𝜇 𝜀

[

]

2

2

𝑃𝑘 = 𝜇𝑇 ∇𝑢𝑚:(∇𝑢𝑚 + (∇𝑢𝑚)𝑇) ― 3(∇.𝑢𝑚)2 ― 3𝜌𝑚𝑘∇.𝑢𝑚

(16)

It is assumed that all the drops of the dispersed phase have same drop diameter. Drop diameter is a input to the CFD model. Correlation prescribed by Kumar-Hartland is used to estimate the drop diameter 44. This correlation is given by eq 17. C1,𝐶2,𝐶3,𝐶4, 𝑚1,𝑚2,𝑚3 and 𝑚4

are the constants of the correlations. Van Delden and coworkers have suggested the values of these constants 45. Thease values are listed in Table 1. 𝛥𝜌 is the difference of the densities of the two phases. 𝛾 represents interfacial tension. 𝜌 ∗ represents reference density. 𝜎 ∗ is a refrence suface tension. Density of water at 298 K (997 kg/m3) and surface tension of water (0.0728 N/m) are used as the reference density and reference surface tension 11. 𝑑32 𝛾 𝛥𝜌𝑔

(

= 𝐶1(𝑇𝑟)𝑚1

2

𝜎∗

𝑚2

)(

ℎ 𝜌∗𝑔

𝜎∗

𝜇𝑑𝑔0.25

[

𝛾 𝑚4

)()

0.75 ∗ 0.25

𝜌

𝑚3

𝜎∗

𝐶2 + exp

{( )( ) }] 𝐶3𝐴𝑓

𝜌∗

𝑇𝑟

𝜎∗𝑔


0.25

(17)


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Table 1. Values of constants of the correlation for the Sauter mean diameter given by eq 17

Constant

𝐶1

𝐶2

𝐶3

𝑚1

𝑚2

𝑚3

𝑚4

Values

2.84

0.16

-2.59

0.30

0.18

0.14

0.06

When the holdup of the dispersed phase is appreciable, it is necessary to consider the interaction between drops. In a PDDC, drops have tendency to accumulate below the internals of the column. For high dispersed phase holdup condition, collisions among drops can create an effect which tends to reduce phase accumulation. The standard equations of Euler-Euler method do not account for this and tend to over-predict dispersed phase holdup at locations where there is probability of accumulation of the dispersed phase. These dense medium interactions, can be accounted by incorporating a collision model in the momentum equation. The collision model has its genesis in the kinetic theory of granular flows. He and Simonin proposed a model to account inter-particle collisions via an additional diffusion-type term in the momentum balance of the dispersed phase for simulating gas-solid flows46. This model has been used for estimating holdup of dispersed phase for liquid-liquid two-phase flow in PDDC 28. Accounting for these interactions, the dispersed phase turbulence stress term is modified as given by eq 18. 𝜏𝑡𝑑, 𝑚𝑜𝑑𝑖𝑓𝑖𝑒𝑑 = 𝜏𝑡𝑑(1 + 𝜙𝑑(1 + 𝑒𝑐)𝑔𝑜)

(18)

Here 𝑔𝑜 is the pair correlation function which accounts the increase of collisions probability due to an increased number of particles, and 𝑒𝑐 (0

CFD Modeling of Pulsed Disc and Doughnut Column - American

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