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Energy Procedia 54 (2014) 796 - 803

4th International Conference on Advances in Energy Research 2013, ICAER 2013

Stage holdup of dispersed phase in disc & doughnut pulsed column

R K Sainia, M Bosea*

aDepartment of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai

Mumbai 400076, India

Abstract

Solvent extraction is one of the key unit operations in the process industries including the fuel recovery unit of nuclear power plants. Among various types of solvent extraction units, the pulsed column is emerging as one of the best choices because of its much smaller footprints compared to the most commonly used mixer-settler type extraction units. Optimal design of a pulsed column requires a thorough understanding of the multiphase flow dynamics as the mass transfer efficiency depends directly on the interfacial area, which is influenced by the extent of turbulent mixing in the unit. The objective of the present work is to investigate the influence of operating parameters such as frequency and amplitude of pulse on the stage wise hold up. To that end, CFD based numerical simulations are carried out on disc and doughnut pulsed column with different operating condition and for two pairs of fluids i.e. pc/pd < 1 and pc/pd >1. Both continuous and dispersed phases are treated as inter-penetrating continua. The effect of turbulence on the continuous phase is captured using low Reynolds number k-s model. Effect of the column geometry, diameter of the droplets of the dispersed phase, and operating conditions such as the frequency and amplitude of pulsation on the dispersion of the minor phase, is investigated. Simulation results are found to be in good agreement with the experimental observations reported in literature.

© 2014M.Bose.PublishedbyElsevierLtd. Thisis an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of Organizing Committee of ICAER 2013 Keywords: Solvent extraction, disc and doughnut pulsed column, CFD, pulsating flow.

1. Introduction

Hydrodynamics of fluid flow in a DDPC has been studied extensively using modeling, simulation techniques and through experiments. In a series of articles since 1990, Angelov and co-workers have investigated various aspects of fluid flow in a disc and doughnut pulsed column [1,2,3,4,5,6]. In their early papers in 1990, Angelov & co-workers

* Corresponding author. Tel: +91-22-2576-7847; fax: +91-22-2576-4890. E-mail address: manaswita.bose@iitb.ac.in

1876-6102 © 2014 M. Bose. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Selection and peer-review under responsibility of Organizing Committee of ICAER 2013 doi:10.1016/j.egypro.2014.07.323

proposed a numerical scheme to simulate the flow in a single stage of a pulsed column and determined the stream functions, liquid hold up and velocity profile. Over the years, the models have been refined and the agreement between the simulations results [1, 2] and experimental observations using LDA (Laser Doppler anemometry) has improved [7]. In their most recent papers [8], Angelov and Gourdon proposed correlation to determine stage pressure drop based on their earlier simulation and experimental results. Bujalski et al [7] have determined the velocity profile in a DDPC using PIV (Particle Image Velocimetry) and observed that the internal gap between the column and the doughnut, through small, influences the velocity distribution in a stage. The above mentioned works have considered a single stage for the simulations and used experimentally obtained velocity profile as the inlet and outlet boundary conditions.

Recently, Retieb et al.[9] have performed simulations on disc and doughnut pulsed column considering both the phases to be continua and have reported stage wise hold up distribution of the dispersed phase. Kumar et al. [10] experimentally investigated the hold-up of dispersed phase and flooding throughput in DDPC. Correlations for dispersion of organic phase in DDPC based on concept of slip velocity and characteristic velocity are developed based on the model proposed by Van Delden et al. [11,12]. Most recently, Amokrane et al.[13] have investigated the performance of two different turbulence model to predict the drop size in DDPC. They have employed coupled CFD-population based simulation technique as implemented in ANSYS Fluent. The axial velocity and turbulent kinetic energy for continuous phase is validated with results of Particle Image Velocimetry experiments.

Earlier simulation works on DDPC by various authors were performed on 2D axisymmetric isolated stages wherein the boundary conditions were provided based on the experimental measurements at the stage entrance. Therefore, there is a need to simulate the column including the actual inlet and outlet of the fluids to understand the issues related to design of column. Also, the effect of different operating parameters such as the amplitude and frequency of pulsation as well as the properties of fluids on the distribution of dispersion is not addressed so far. Thus, the objective of present work is to develop a numerical scheme to simulate the 3D column with the actual fluid inlet and outlet and to investigate the effect of the operating conditions as well as the geometric parameters on the distribution of hold-up in a DDPC. To that end, numerical simulations are performed on two different column geometries [9, 10] for different pairs of fluid, based on the continuum approach as implemented in ANSYS Fluent. Investigation for the influence of operating parameters such as frequency and amplitude of pulsed on the stage wise hold up is carried out. Sensitivity analysis is performed to study the effect of drop size on the hold-up distribution of dispersed phase.

2. Mathematical modeling

A disc and doughnut pulsed column can be described as a circular column with an internal fitting that has several units stacked vertically in a repeated manner as shown in Figure 1. Each unit comprises of a disc placed between two doughnuts. The height between doughnut and disc remains uniform throughout the column. All the geometric parameters such as aperture of the ring (DR), the diameter of the disc (Dd), the height between ring and disc (H), are non-dimensionalised by the column diameter.

2.1. Eulerian- Eulerian model

In the present work, both phases are assumed to be continua and the usual macroscopic mass and momentum conservation laws (equations 1 & 2) form the set of governing equations:

+v{w,)=0 (1)

d[aipiui I —\

1 ' + V.(a,pIu1u1 ) =

d( -v-^- ■j=-a1P1 VP + V-Ti +arPr8 + Fk (2)

where, i=c & d, which indicate the continuous and dispersed phase respectively. ac is the volume fraction which represents the space occupied by continuous phase, pc is the continuous phase density, uc is the continuous phase velocity, t is the stress tensor, p is the pressure shared by all phases, g is the gravitational acceleration and Fk represents the interfacial forces. In addition to equations (1&2) the constraints for the volume fractions, (ad+ ac= 1), must be satisfied.

Fig.1. Schematic diagram of DDPC considered for simulation

2.2. Turbulence k-£ model

A standard k-s model is used to capture the effect of turbulence of continuous phase. The kinetic energy (k) and energy dissipation (s) are described for continuous phase by equations 2 and 4 [14].

5(«cPckc) dt

d(ac Pcec) dt

+ V.(«cPckcuc) = V.(«c Vkc) + UcGkc -acPcg + acPc nkc

+ V.(«c Pcscuc ) = V. («c — V^c ) + «c yL (C1SGkc - C2SPcsc ) + acPc ^

where, Gk,c represents the generation of turbulence kinetic energy because mean velocity gradients, n^ and ne,c represent the influence of the dispersed phase on the continuous phase and Ci=1.44, C2=1.92, CM=0.09, ok=1.0 and oe=1.3 are closure coefficients[14,15,16].

In equation 2, the interaction force (Fk) between the continuous and dispersed phase is given by equation (5).

3 ŒcŒdMc r o - \

Fk =—-:-CD Red(ud - uc)

where, CD is the drag coefficient, and Red is the Reynolds number based on the diameter of drop. During simulation drag model proposed by Schiller-Naumann[16] is considered. In this model, the drag coefficient is given by equation(6).

(—(1 + 0.15fieS 687) ; Red < 1000 CDJ«ed d d (6)

10.44 ; Red > 1000

2.3. Boundary conditions

The continuous phase has a pulsatile motion described by u(t) = ®Af * cos(2^ft) , where A and f are amplitude (m) and frequency (Hz) of pulse. The dense phase is fed continuously. The numerical values for the turbulent kinetic energy (k) and energy dissipation rate (e) at the inlet of the continuous phase are estimated using equations 7&8 [5,17,18]

, (u*)2

k = (7)

C 0.5 K '

s = (8)

where, k=0.42 is Karman's constant, CM=0.09 is constant, k turbulence kinetic energy (m2/s2), e turbulence dissipation energy (m2/s3).

2.4. Numerical method

The set of governing equations is solved using the finite volume method as implemented in the commercial software ANSYS (FLUENT) 14.0/14.5 [16]. The second order upwind scheme is used as the discretization method for momentum, turbulent kinetic energy and dissipation rate. The absolute convergence criteria are set at 1x10-9 (unit of field variables) in the analysis. Uniform structured grid with quadrilateral mesh scheme is used to discretize the computational domain using the commercial software GAMBIT 2.2.30.

3. Results and discussions

Two pairs of fluids, i.e., pc/pd < 1 & pc/pd >1, are investigated in present work. Table 1 lists the properties of systems simulated. All the simulations are performed on three dimensional columns with six stages as the minimum number of stages required to ensure periodicity at the center stage, is found to be six. The first set of simulations is carried on the column geometry reported in [9] with a pair of fluids in which the continuous phase is lighter than dispersed phase (Table 1). Figure 2(a) shows the distribution of the dispersed phase at the central stage of the column. Simulations are also performed on 1:1.5 scaled down geometry (Table 2). It is worth a mention here that with the introduction of the droplet size, it is practically impossible to have scaled systems with same Weber number (We) and dp/Dc. To understand the individual effect of these two dimensionless quantities on the distribution of the minor phases, simulations are carried out for three different cases. Figure 2(b) shows the distribution of hold up in a system where the Reynolds number (Re) is maintained same as the original case but both Weber number and density ratio are different, whereas, Figure 2(c) shows the dispersion of the minor phase where, in addition to Re, Weber number is kept constant. Figure 2(d) shows stage wise average volume fraction of the dispersed phase (hold up) against the pulsation time period for full scale and scaled down columns. A good agreement between the results of the present simulation in full 3-d column and that reported in [9] is observed; however, the stage-wise hold-up is found to be more in the scale-down columns than in the full scale geometry, which essentially indicates that scaling of DDPC based on geometric similarity, Reynolds number and either of Weber number or dp/Dc, is not sufficient.

It is worth a mention here that the diameter of the droplet of the dispersed phase has to be specified at the beginning of the simulation for determination of drag. The drop size is estimated setting the Weber number defined as We = pckc dd/y (where pc is continuous phase density, dd is drop diameter, kc, m2/s2 is turbulent kinetic energy of continuous phase and y, N/m is interfacial tension) equal to 1. Separate simulations are performed with only the continuous phase to determine the distribution of the turbulent kinetic energy in the column. The maximum value of turbulent kinetic energy is used to determine the drop size. The estimated diameter of droplet is compared with the experimental value and is found to be approximately three times of experimental value.

(c) (d)

Fig. 2. Dispersed phase hold-up distribution during for different time of a pulsation period frequency, f=0.50 Hz, Amplitude, A=0.0474 m, for pc/pd< 1; (a) Full geometry(1:1), Re=787; We=0.0396, dp/Dc = 0.02267; (b) Scaled down(1:1.5), Re=787, We=0.00602, d„/Dc = 0.02267; (c) Scaled down(1:1.5), Re=787, We=0.0396, dp/Dc = 0.01515; (d) Stage vol. avg. Hold-up distribution plotted with different moments of time for

pulsation time period for pc/pd < 1

A sensitivity analysis is carried out to investigate the influence of drop size on the distribution of stage hold up. Table 3 summaries the stage wise hold up of dispersed phase for different size of drops. The average volume fraction of the dispersed phase at the central stage is compared against the same reported in [9]. No significant dependence of the average stage wise hold up on the drop size is observed; however, the distribution of dispersed phase is clearly influenced by the size of droplet, as is evident from Figure 3.

Next, the effect of ratio of densities of the dispersed and the continuous phase on, the distribution is studied. Figure 4 shows the distribution of dispersed phase at the central stage in DDPC. The dispersed phase accumulates on the disc for the case when pc/pd<1 while for the case with pc/pd>1 the accumulation of dispersed phase is found beneath the disc.

The effect of frequency and amplitude of pulsation on distribution of dispersed phase hold up is also studied. Figure 5(a) shows the profile for hold up distribution of dispersed phase with pulsation time period at different frequencies for central stage of column. Figure 5(b) shows the time averaged holdup of dispersed phase with frequency of pulse. It is found that the time averaged hold up of dispersed phase decreases linearly with the frequency of pulse. Figure 6 shows the time average distribution of dispersed phase holdup with different pulsation period. No significant effect of pulse amplitude on the average stage-wise hold-up is observed.

Fig. 3. Effect of drop size on dispersed phase hold-up distribution during for different time of a pulsation period, frequency, f=0.50 Hz, amplitude, A=0.0474 m for all case (pc/pd< 1) at (a) dp = 1.7 mm; (b) dp = 15.6 mm

Table 1.Physical properties of systems simulated .

Property

pc/pd<1 [9]

pc/pd > 1 [10]

Continuous phase

Dispersed phase

Continuous phase

Dispersed phase

Composition 33.5vol% (Tributyl Nitric acid solution, Aqueous phase, Organic phase, [30%T

phosphate) diluted in HTP 1.95 Mol/L 0.5N HNO3 BP/NHP (normal paraffinic

(hydrogen Tetrapropylene) hydrocarbon)]

Density, p, kg/m3 842 1062 1015.5 808.5

Viscosity, Pa.s 0.0019 0.0011 0.00105 0.00209

Interfacial tension, 0.0203 0.00995

Y, N/m

Drop diameter, dp 1.7, 4, 10, 15.6 6.67

Table 2. Design parameters based on column diameter.

Design parameters

Non-dimensionalised

Number Dc =75 mm , [9]

Non dimensional ratio (1:1.5)

Dc =25mm , [10]

Column diameter

Ratio of thickness of disc &doughnut to column diameter

Ratio of disc and doughnut space doughnut to column diameter

Ratio of diameter of disc doughnut to column diameter

Ratio of diameter of aperture to column diameter

Dc/Dc 8/ Dc

H/ Dc Dd/ Dc

Dr/ Dc

Table 3.Drop sensitivity-analysis [9]_

Drop size Hold-up (Avg. Vol. fraction *Difference % in Hold-up (Avg. Vol.

(dp),mm single stage, 0s) (%) A0s (stage hold-up) fraction total, 0t ) (%)

1.7 2.73[9] 0 9.746[9]

4 2.695 1.282 9.805

10 2.939 7.656 9.78

15.6 2.82 3.296 9.82

* Difference % in A0 = ° 0ref' x 100

®re/.

1/1=0.25

Fig. 4. Dispersed phase hold-up distribution during for different time of a pulsation period frequency, f=1 Hz, for dp = 6.67 mm (a) (pc/pd)> 1 ; (b) (pc/pd)< 1

t/T f, Hz

(a) (b)

Fig. 5. Stage wise average hold-up distribution plotted with different moments of time for pulsation time period; Amplitude,

A=0.0474, dp = 1.7 mm, frequency, f=0.5, 1,1.5, 2 Hz for pc/pd < 1

Fig. 6. Stage wise average hold-up distribution plotted with different moments of time for pulsation time period; frequency, f=0.5 Hz, dp = 1.7 mm, Amplitude, A=0.0474, 0.0674,0.0774, 0.0874 m for pc/pd < 1

4. Conclusions

Flow of two pairs of immiscible fluids in a disc and doughnut pulsed column (DDPC) is investigated using CFD based numerical simulation techniques. Simulations are performed on three dimensional columns with six units, the

minimum number required to ensure periodicity at the central stage. Distribution of the hold-up of the dispersed phase is compared with earlier results [9] and is found to be in good agreement with each other. A sensitivity analysis is carried out to investigate the influence of drop size on the distribution of stage hold up. It is observed that there is no significant dependence of the average stage wise hold up on the drop size; however, the distribution of dispersed phase is influenced by the droplet size. The effect of density ratios i.e., pc/pd<1 & pc/pd>1, on the holdup distribution of dispersed phase are investigated. Dispersed phase is found to accumulate on the disc for the case when pc/pd<1 while for the case with pc/pd>1 the accumulation of dispersed phase is beneath the disc. The effect of amplitude and frequency of pulsation on hold up distribution of dispersed phase is also studied. Average stage-wise holdup of dispersed phase is found to decrease linearly with the frequency of the pulsation, whereas, no significant effect of the amplitude on the hold-up is observed in the simulation.

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