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Investigation of iodine removal efficiency in a venturi scrubber using mass transfer model for CFD
Progress in Nuclear Energy 121 (2020) 103243
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Investigation of iodine removal efficiency in a venturi scrubber using mass transfer model for CFD Ammar Ahmed a, Ajmal Shah b, c, Kamran Qureshi a, Khalid Waheed b, Naseem Irfan b, Waseem Siddique a, *, Masroor Ahmad b, Amjad Farooq b a b c
Department of Mechanical Engineering, Pakistan Institute of Engineering and Applied Sciences, Pakistan Department of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences, Pakistan Centre for Mathematical Sciences, Pakistan Institute of Engineering and Applied Sciences, Pakistan
A R T I C L E I N F O
A B S T R A C T
Keywords: Venturi scrubber Mass transfer model Iodine removal Filtered containment venting system
Filtered containment venting system (FCVS) is important for the ultimate safety of a nuclear power plant owing to its use in containment pressure reduction in case of severe accident. It vents a portion of containment air after removal of harmful radioactive products including iodine through venturi scrubber. The purpose of this research was to develop a mass transfer model for estimation of performance of a venturi scrubber for removal of elemental iodine using Computational Fluid Dynamics. A mathematical model for transfer of iodine from air to water was developed based on two film theory of mass transfer and experimentally validated. Simulations were performed for self-priming non-submerged circular venturi scrubber using Fluent and the results were compared with experimental ones. Experimental data was used for validation in which an aqueous solution of sodium hydroxide and sodium thiosulfate was used as scrubbing solution for removal of iodine. For simulation, only water was used instead of scrubbing solution for simplicity. Euler-Euler approach was used for two-phase modeling and realizable k-epsilon model was used for turbulence modeling. The results obtained from simula tions had a good match with the experimental ones.
1. Introduction Nuclear power plants provide clean and sustainable energy for electricity generation and heat applications. Safety of nuclear power plants along with their ability to handle severe accidents is the major concern with this technology as was highlighted from the accidents at Three Mile Island, Chernobyl and Fukushima Daiichi Nuclear Power Plants. In these accidents, containment building designed to protect the environment from harmful radioactive products was compromised. To handle such severe accidents, filtered containment venting system (FCVS) is designed which ensures containment integrity in case of core meltdown and high-pressure steam buildup inside containment. This system reduces containment pressure by venting some of the contain ment air into the atmosphere. Radioactive elemental iodine-131 is the major product among others that needs to be removed from the venting air. It has a half-life of around 8 years and is likely to cause thyroid cancer if released into the atmosphere. In FCVS, venturi scrubbers are widely used to remove the harmful
radioactive products from the venting air to prevent radioactivity release outside the plant. Therefore, it is necessary to study the phe nomenon of iodine retention in venturi scrubber to effectively improve its efficiency. Venturi scrubbers are converging diverging nozzles with facility of scrubbing solution injection at throat. Harmful gases present in air are absorbed in scrubbing solution while passing through the venturi scrubber. Generally, based on the feed mechanism of injected water, two types of venturi scrubbers are used: i.e. force-feed and selfpriming venturi scrubbers. Owing to the usage of venturi scrubber in conventional plants and industry for removal of dust and gases like SO2, some models are already available in literature for its effectiveness analysis. Uchida and Wen (1973) presented a unidimensional mass transfer and fluid flow model using heat, mass and momentum balances and formulating differential equations relating the velocity of liquid, gas concentration and its partial pressure along axial direction. They used Runge-Kutta-Gill method to numerically simulate the results of experi ments presented in three different researches and compared the overall
* Corresponding author. E-mail addresses: [email protected] (A. Ahmed), [email protected] (W. Siddique). https://doi.org/10.1016/j.pnucene.2020.103243 Received 26 April 2019; Received in revised form 26 December 2019; Accepted 6 January 2020 Available online 15 January 2020 0149-1970/© 2020 Elsevier Ltd. All rights reserved.
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efficiency for Sulfur Dioxide gas (SO2) removal. Ravindram and Pyla (1988) proposed a theoretical model to predict the efficiency for removal of gaseous pollutants from air using a venturi scrubber. Their model was based on simultaneous diffusion and irreversible chemical reaction of gases with alkaline solutions. For validation of their model, they conducted experiments for gas absorption using sodium hydroxide solution as scrubbing agent. The proposed model was found to be in agreement with the experimental results for the cases of CO2 and SO2 removal. Talaie et al. (2012) proposed a three-dimensional mathemat ical model to evaluate the removal efficiency of SO2 in venturi scrubber using alkaline solution and water. The mass transfer model presented in their study was based on physical absorption by concentration differ ence of SO2 in liquid and gaseous phases. The authors used material balance and dispersion equations to determine pollutant concentration in gaseous phase. The model calculates overall removal efficiency of SO2 considering the difference in concentration at inlet and outlet of venturi scrubber but there is no localized mass transfer phenomenon incorpo rated. Hills (1995) studied the performance of venturi scrubbers as chemical reactors and modelled the absorption of a gas with chemical reaction. In this study, Hills reported that the absorption of a gas in real venturi scrubbers can be considered as a rapid reaction and controlled by diffusion. The droplet size plays an important role in mass transfer inside venturi scrubber. Alonso et al. (2001) performed experiments for mea surement of diameter of water droplets inside cylindrical venturi scrubber using laser diffraction technique by varying the gas velocities and liquid to gas flow rate ratio. Sauter mean diameter values obtained from Nukiyama and Tansawa (Nukiyama and Tanasawa, 1938) as well as Boll et al. (1974) equations were compared with experimental results and concluded that Sauter mean diameter is well predicted using Boll et al. correlation. Also, velocity of gas has a major effect on the size of droplet instead of liquid to gas flow ratio. Costa et al. (2004) also per formed the same experiments using a rectangular venturi scrubber instead of a circular one and the results obtained agreed with the ones presented by Alonso et al. Ahmadvand and Talaie (Talaie and Ahmad vand, 2010) developed a two-dimensional mathematical model to study the droplet dispersion in cylindrical venturi scrubber using CFD. Gamisans et al. (2004) experimentally studied the effect of diameter and throat length on mass transfer in a jet-venturi scrubber for SO2 absorption in aqueous solutions. A model based on two film theory of mass transfer was proposed by incorporating diffusion with irreversible chemical reaction of SO2 with scrubbing solution. Concentration dif ference of SO2 was taken as the driving force for transfer of SO2 from air to scrubbing solution. They mentioned that the scrubbing reaction is very rapid and is diffusion controlled. Furthermore, the significance of liquid film in mass transfer was proved experimentally. Comparison of results was made for the cases considering the effect of liquid film on SO2 removal and neglecting its effect. Pak and Chang (2006) developed a three-dimensional numerical model for prediction of pressure drop as well as collection efficiency of a circular venturi scrubber for dust particle removal. Inertial impaction mechanism was considered for capturing of dust particles in water droplets. Boll correlation was used for droplet size and Eulerian-Lagrangian method for numerical simulation of dust-air-water three phase mixture. In case of severe accident in a nuclear power plant, containment is pressurized by high temperature steam mixed in air so Ali et al. (2014) experimentally studied the removal efficiency of iodine from steam in submerged venturi scrubber and concluded that removal efficiency of iodine increases with increase in flow rate of steam. Also, Ali et al. (2013) theoretically and experimentally studied the removal efficiency of iodine in a self-priming venturi scrubber for the cases of submerged and non-submerged conditions. Aqueous solution of 0.5% sodium thiosulfate and 0.2% sodium hydroxide was used to absorb iodine present in air inside venturi scrubber. A mass transfer model based on two film theory proposed by Gamisans et al. (2004) was used. Droplet diameter was calculated using Nukiyama and Tanasawa
equation whereas Steinberger and Treybal (1960) correlation was used for mass transfer coefficient of gas phase. They reported that iodine removal efficiency increases with increase in gas flow rate as well as inlet iodine concentration. They also pointed out that the scrubbing reaction is very rapid and the process is controlled by the diffusion at the gas-liquid interface. Ahmed et al. (Ahmedet al., 2018) investigated the removal efficiency of self-priming venturi scrubber for dust particles removal using computational fluid dynamics (CFD). They performed the analysis using ANSYS CFX. 1-micron size Titanium oxide particles were used as dust. They used cascade atomization and breakup (CAB) model for prediction of deformation of water droplets and Eulerian-Lagrangian method for multiphase analysis. They estimated the dust removal efficiencies for different inlet air velocities and it was concluded that removal efficiency increases with increasing air velocity. Ashfaq et al. (Ashfaqet al., 2018) studied the effect of droplet diameter of scrubbing solution on removal of elemental iodine from containment air in a venturi scrubber using CFD. They used ANSYS FLUENT to model the multiphase flow phenomenon and incorporated a user defined function for mass transfer of iodine from air to water (scrubbing). They done a tremendous job by introducing a three-dimensional mathematical model for scrubbing iodine from air and implementing the model in CFD software for the first time to the best of my knowledge. However, there were some discrepancies in the approach and mass transfer model they introduced. The work presented here is an extension of the study performed by Ashfaq et al. (Ashfaqet al., 2018). In this work an effort has been made to remove the discrepancies in the approach and CFD model for scrubbing of iodine from air. Ashfaq and his coworkers performed the simulations to study the effect of droplet diameter on the process of scrubbing. They did this by selecting various droplet diameters and running the simu lations for each case. However, the droplet diameter is a function of the air flow rate and varies as the flow rate is changed. In the present work, the droplet diameter has been calculated using the correlation of Boll et al. (1974) to overcome the discrepancy of the Ashfaq et al. (Ashfaqet al., 2018) model. Ashfaq et al. (Ashfaqet al., 2018) assumed Iodine distribution parameter equal to unity as did by Crank (1975). However, Crank (1975) has also mentioned that distribution parameter is unity only when the diffusion process is very rapid. Further, Gamisans et al. (2004) and Ali et al. (2013) have mentioned that, in the scrubbing process, reaction rate is rapid as compared to diffusion so the process is diffusion controlled. Therefore, in the present study the distribution parameter has not been taken as unity, rather it has been calculated by using the scrubbing efficiencies obtained by experiments and CFD. In this study a range of distribution parameter has been calculated and finally an average value of the distribution parameter has been pre sented. The value of the distribution parameter, reported in this work for the first time to the best of our knowledge, reflects the process of iodine diffusion from air to liquid, thus giving an insight of the governing process. Ashfaq et al. (Ashfaqet al., 2018) has not validated the scrub bing model against experimental results, therefore, in the present study the CFD results have been validated with experimental results. So, the present study presents a much-improved mathematical model of the iodine scrubbing process, which has not only been validated by exper imental results but also reflects the dynamics of the actual process by calculating the value of the distribution parameter. 2. Material and procedure In this study, Computational Fluid Dynamics analysis was performed for simulation of mass transfer phenomenon in a non-submerged cir cular venturi scrubber using Fluent module of ANSYS. A mathematical model was developed for evaluating the mass transfer of iodine from gas to liquid phase and was incorporated with the software using a user defined function (UDF). The efficiency of venturi scrubber for removal of iodine from air was obtained from the difference of concentration of 2
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Fig. 1. Experimental setup (Nawaz, 2017).
Fig. 2. Geometry of venturi scrubber (Nawaz, 2017).
iodine in air at inlet and outlet of venturi scrubber.
�
2.1. Multiphase model and governing equations
� m_ qp þ Sq
þ
n � X ! _ R pq þ mpq ! v pq
m_ qp ! v qp
qp
(1)
(3)
q
lift;q
wl;q
vm;q
td;q
� � ∂ ∂pq α ρ h þ r: αq ρq hq ! u q ¼ αq þ τq ∂t q q q ∂t : r! uq
r:! q q þ Sq þ
n X
Qpq þ m_ pq hpq
m_ qp hqp
�
(4)
p¼1
Where hq , ! q q and Sq represent specific enthalpy, heat flux and source term of qth phase respectively. Qpq and hpq show intensity of heat ex change between pth and qth phases and interphase enthalpy respectively. Iodine was treated as a chemical specie in air and scrubbing solution phases. It was modelled by specie transport model with following con servation equation for iodine in any phase q,
αq rp þ r:τq þ αq ρq ! g �
� 2 v qI μq r:! 3
represent external body force, lift force, wall lubrication force, virtual mass force and turbulent dispersion force respectively. Interaction force ! between phases is shown by R pq and pressure shared by all phases represented by p. The conservation of energy equation in Eulerian model is written as
Where mass transfer from pth to qth phase is shown by m_ pq and from qth to pth phase by m_ qp . The momentum balance equation for a phase q is given by � � ∂ αρ! v þ r: αq ρq ! v q! vq ¼ ∂t q q q
T
Where μq and λq represent shear and bulk viscosity of phase q. ! v pq and ! ! ! ! ! ! v show interphase velocities. F ; F ; F ; F and F
Eulerian-Eulerian approach was used for solution of complex twophase flow consisting of air-water-iodine mixture. The Eulerian model solves a set of continuity and momentum equations for each phase. In this model, continuity equation for a generic phase q flowing with velocity ! v q is n � � X ∂ m_ pq αq ρq þ r: αq ρq ! vq ¼ ∂t p¼1
�
�
v q þ r! τq ¼ αq μq r! v q þ αq λ q
(2)
p¼1
! ! ! ! ! � þ F q þ F lift;q þ F wl;q þ F vm;q þ F td;q Where τq represents stress-strain tensor of qth phase given by 3
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Table 1 Experimental data reported by Nawaz (2017) and used for benchmarking. Sr. #
Mass Flow Rate of Air (m3/s)
Inlet I2 Concentration (ppm)
Outlet I2 Concentration (ppm)
Removal Efficiency (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1.389 � 10 3
50.1 34.6 27.9 42.0 48.6 69.7 44.0 39.5 34.0 37.6 32.7 35.6 49.4 45.1 41.4 37.2
4.9 5.2 5.0 5.1 4.8 5.6 4.9 4.7 2.5 2.5 2.4 2.5 2.5 2.5 2.5 2.4
90.2 85.0 82.1 87.9 90.1 92.0 88.9 88.1 92.6 93.4 92.7 93.0 94.9 94.5 94.0 93.5
1.528 � 10 3 1.667 � 10 3 1.806 � 10 3
∂ q q q q v Y qÞ ¼ ðρ α Y Þ þ r:ðρq αq ! ∂t
n X !q m_ pq r:αq J þ αq Rq þ αq Sq þ
m_ qp
�
p¼1
þR (5) 2.2. Mass transfer model The mathematical model developed for mass transfer of iodine from air to droplets of water is based on two film theory. The driving force for mass transfer is the iodine’s concentration difference (diffusion) and takes place at interface of air and water films. It is assumed that the reaction is kinetically rapid and hence, rate of mass transfer is gas-film controlled (Gamisans et al., 2004). Furthermore, all droplets of water are spherical and represented by a Sauter mean diameter. Mass transfer rate of iodine in a single droplet of water is given by the following relation (Gamisans et al., 2004), Nl ¼ 4πr2 kg mðCin
Ci Þ
(6)
The distribution factor (m) in Equation (5) was assumed by Crank (1975) and Ashfaq (Ashfaqet al., 2018) as unity considering the same concentration of solute present in film as well as in solution. However, it was mentioned that in reality, the concentration of solute in liquid film is m times the concentration of solute in the gas phase (Crank, 1975) i.e. m¼
Equilibrium Concentration of iodine in liquid phase Equilibrium Concentration of iodine in gaseous phase
Fig. 3. Meshed Geometry (a) Complete (b) Outlet region (c) Throat region (d) Inlet region.
Since the scrubbing process is diffusion controlled (Gamisans et al., 2004; Ali et al., 2014), the value of distribution parameter cannot be assumed unity as mentioned by Crank (1975). Therefore, the distribu tion parameter becomes very important to understand the process of diffusion in iodine scrubbing. To determine the mass transfer rate at local computational cell, it is required to find the number of droplets (n) in the cell, which is calculated by considering volume of water and volume of spherical droplets in the computational cell. n¼
3αl Vc 4π r 3
3αl kg mCin M_ ¼ r 2.3. The mass transfer coefficient is calculated using sherwood number formula
(7)
Sh ¼
Rate of mass transfer in a unit cell of domain in Equation (8) can be obtained by the product of Equations (6) and (7). m_ ¼
3αl kg mðCin r
Ci Þ Vc
(9)
kg dd Dg
(10)
Where Sherwood number is calculated using Steinberger and Treybal correlation (Steinberger and Treybal, 1960) �0:62 Sh ¼ 2 þ 0:347 Re Sc0:5 (11)
(8)
And Reynolds and Schmidt number are given by Equations (12) and (13).
With the assumption of reaction being gas film controlled, Ci ¼ 0 for this case (Ali et al., 2013). On per unit volume of cell basis, the rate of mass transfer is given by Equation (9). 4
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Fig. 6. Distribution parameter values.
Fig. 4. Mesh independence study. Table 2 CFD models and boundary conditions used in simulation. Multiphase model Turbulence model Specie transport Phase-1 (Gas phase) Phase-2 (Liquid phase) Mass Transfer Venturi scrubber inlet Orifice inlets at throat Venturi scrubber outlet Wall
Eulerian-Eulerian Realizable k-epsilon Iodine taken as specie in gas and liquid phase Air-Iodine mixture Water-Iodine mixture From phase-1 iodine to phase-2 iodine at a user defined rate using UDF Boundary Conditions Mass Flow Inlet of Phase-1 with certain concentration of I2 Pressure Inlet of Phase-2 with no concentration of I2 Pressure Outlet at atmospheric pressure No slip conditions at wall
Fig. 7. Comparison of simulation and experimental removal efficiency of iodine.
Re ¼
ρg vg dd μg
(12)
Sc ¼
μg ρg D g
(13)
The diameter of water droplet is calculated using correlation of Boll et al. (1974) � �1:932 l 4:22 � 10 2 þ 5:77 � 10 3 1000Q Qg dd ¼ (14) v1:602 r 2.4. Experimentation The validation of a computational model generally requires experi mental results for comparison. As part of this ongoing project Nawaz (2017) performed some experimental work, which has been used as validation data in this current study. The details of Nawaz (2017) experimental work are mentioned below.
Fig. 5. Variation in distribution parameter values.
5
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form of a spectrum which gives the concentration of material present in the sample. Calibration curve was drawn for absorbance of light versus known value of concentration and later used for determination of con centration of iodine in samples. The removal efficiency was calculated using the difference in concentration of iodine at inlet and outlet of scrubbing column. Table 1 shows part of the experimental data reported by Nawaz (2017) and used as benchmark for simulating the scrubbing of iodine from containment air through venturi scrubber. Mass flow rate of air was mentioned in units of cubic meters per hour, concentration of iodine in air at inlet and outlet of venturi scrubber was mentioned in parts per million. Removal efficiency was calculated using the difference in con centration of I2 in air at inlet and outlet. Further details of the experi mental work are given in Nawaz (2017). 2.5. CFD simulation CFD simulations were performed using ANSYS Fluent version 14.0. The venturi scrubber geometry was obtained from the experiments performed by Nawaz (2017). The geometry was made in ANSYS Design Modular and meshed in ANSYS Meshing module. The geometry with dimensions is shown in Fig. 2. The venturi scrubber used in this study is of self-priming type; In order to apply pressure boundary conditions at orifices, orifices were extended 5 mm from throat. The meshed geometry with tetrahedral mesh at orifices and hexahedral elsewhere is shown in Fig. 3. The mesh independent study was performed. Variation of iodine concentration in air was obtained on axis of venturi scrubber by grad ually increasing the number of mesh elements. The concentration (mass fraction) of iodine in air became independent of mesh size at around 112875 elements as shown in Fig. 4. The Eulerian-Eulerian model was used to obtain in-depth two-phase analysis, constant droplet diameter was used by calculation using Boll correlation, realizable k-epsilon model was used for turbulence and mass transfer model was incorporated using user defined function in ANSYS Fluent. The boundary conditions used were mass flow inlet at air inlet, pressure inlet at orifices and pressure outlet at outlet of venturi scrubber. The boundary conditions were used according to the data obtained from
Fig. 8. Variation of liquid droplet diameter with flow rate of air.
The experiments were performed on a circular self-priming sub merged venturi scrubber made of brass with dimensions shown in Fig. 2. The schematic of experimental setup is shown in Fig. 1. The filtered air from compressor was passed through iodine sublimation chamber. A certain amount of solid iodine was loaded in iodine chamber before each experiment. The sublimated iodine vapors get mixed with air in iodine chamber. The amount concentration of iodine mixing in air was deter mined using iodine traps before inlet of venturi scrubber. The air-iodine mixture was passed through the venturi scrubber submerged in scrub bing solution (0.5% NaOH and 0.2% Na2S2O3). Iodine concentration in air at inlet as well as outlet of venturi scrubber was measured at 5-min intervals using traps as shown in Fig. 1. Air streams containing iodine vapors from inlet and outlet were bubbled through traps containing 0.1 M KOH solution and analyzed on UV–visible spectrophotometer that works on absorption spectroscopy principle. The amount of light absorbed as a function of wavelength is measured and plotted in the
Fig. 9. vol fraction of (a) gas phase on axial plane (b) gas phase on cross-sections along length (c) liquid phase on axial plane (d) liquid phase on cross-sections along length. 6
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Fig. 10. Zoomed contour of volume fraction of (a) Phase-1 (b) Phase-2.
the experimentation (Nawaz, 2017). Because of unavailability of iodine in the Fluent library, properties of iodine were manually entered in the software. Because of very low concentration of NaOH and Na2S2O3 in the solution, its flow was simulated using water whereas the iodine absorption of the solution was simulated by mass transfer model. The convergence criterion used for the simulation was 10 4. The CFD set tings have been summarized in Table 2.
diameter, using Boll et al. (1974) correlation. Further the experimental results of scrubbing efficiency were used to calculate the iodine distri bution parameter which was assumed unity previously by Ashfaq et al. (Ashfaqet al., 2018). In the following topics the distribution parameter, droplet diameter, validation of mass transfer model and contours of volume fraction, mass transfer, pressure and velocity have been dis cussed in detail to throw light on the scrubbing process of iodine from containment air using submerged venturi scrubber.
3. Results and discussion
3.1. Distribution parameter and validation of mass transfer model
In this study, an improved computational mass transfer model of iodine scrubbing from containment air has been presented and validated through experimental results. As mentioned earlier, this model was applied for the first time by Ashfaq et al. (Ashfaqet al., 2018) for their computational study of iodine scrubbing and the present study is an extension of the work of Ashfaq et al. (Ashfaqet al., 2018). In this work, the scrubbing model has been modified by calculating the droplet
The distribution parameter is defined as the ratio of equilibrium concentration of specie in liquid phase to its equilibrium concentration in gas phase. It is an important parameter in flows where the mass transfer is diffusion controlled as is the case in iodine scrubbing from containment air. It can be considered as unity if the diffusion process is very fast as mentioned by Crank (1975). Ashfaq et al. (Ashfaqet al., 2018) assumed the value of distribution parameter as unity in the mass transfer model of iodine scrubbing, however, in the present study a more realistic approached was used to calculate its value using the experi mental value of scrubbing efficiency. In this study, a series of simula tions were performed by keeping the experimental value of scrubbing efficiency as the bench mark to ascertain a range of distribution parameter under different operating conditions. The distribution parameter values as a function of concentration of iodine in air and air flow rate are shown in Fig. 5. The values of distribution parameter vary from 0.00144 to 0.00205 for an air flow rate of 1.389 � 10 3 m3/s to 1.806 � 10 3 m3/s and iodine concentration of 24 ppm–70 ppm in air. These results indicate that the distribution parameter is not a strong function of air flow rate and iodine concentration in air. However, these values indicate that the process of iodine scrubbing from containment air is strongly diffusion controlled as the values of distribution param eter are very small as compared to unity. These values, therefore, vali dates the assumption, employed in the mass transfer model, that the process of iodine scrubbing is diffusion controlled rightly mentioned by Gamisans et al. (2004) and Ali et al. (2013) too. The narrow band of the values of distribution parameter, under different operating conditions, as shown in Fig. 6 provoked us to search for a single value of the distribution parameter valid for the simulation of all the cases with reasonable error. So, a mean value of the distribu tion parameter was obtained from the data of Fig. 6 and it was 0.00185.
Fig. 11. The mass fraction of iodine in Phase-1 and Phase-2 on axial centerline of venturi scrubber. 7
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Fig. 12. Mass fraction of iodine in (a) gas phase on axial plane (b) gas phase on cross-sections along length (c) liquid phase on axial plane (d) liquid phase on crosssections along length.
All the simulations were performed again using this single value of the distribution parameter and the iodine removal efficiency was calculated and compared with the experimental values as shown in Fig. 7. It was found that the maximum error in the iodine removal efficiency is 6.1%, which looks acceptable.
entering the venturi scrubber. Smaller the diameter of these droplets, more will be the mass transfer because of an increased surface area as depicted by Equation (9). Ashfaq et al. (Ashfaqet al., 2018) used a constant mass flow rate of 0.09 kg/s and considered different diameters of water droplets for the same flow rate to study the effect of changing diameter on different parameters. However, droplet diameters are rep resented by a Sauter mean diameter which is a function of flow rates of gas and liquid (Alonso et al., 2001). In this improved model, the Boll et al. correlation was introduced to calculate the droplet diameter. With the edition of this correlation the model is now able to calculate the droplet diameter according to the existing flow conditions. Fig. 8 in dicates the droplet diameter variation with the air flow rate obtained through modified model. This Figure indicates that the diameter of liquid droplet depends on the air mass flow rate and decreases as the air mass flow is increased. So, the water atomizes into finer droplets as the air flow increases. The variation in droplet diameter is from 32 μm to 47
3.2. Droplet diameter Droplet diameter is an important parameter in scrubbing process of iodine from containment air because it defines the surface area offered by liquid phase to the iodine present in air. If larger surface area is offered by liquid the scrubbing will be efficient and vice versa. The droplet diameter decreases with increase in gas flow rate as reported by Alonso et al. and Costa et al. (Talaie et al., 2012; Nukiyama and Tana sawa, 1938). The liquid phase enters the venturi scrubber by pressure difference through tiny holes present at throat of venturi scrubber as shown in Fig. 3. The liquid atomizes into very small droplets after
Fig. 14. Mass transfer rate contour on (a) axial cross-section (b) radial crosssections along length (c) enlarged view near orifices of axial cross-section.
Fig. 13. Enlarged view of contour of mass fraction of I2 in Phase-1 near orifices. 8
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Fig. 15. Axial profiles of (a) pressure and (b) velocity at different flow rates of gas. 3 to 1.806 � 10 3 m3/s. The modified model is now capable of calculating the Sauter mean diameter according to the flow conditions and draw back present in Ashfaq et al. (Ashfaqet al., 2018) model was removed.
μm as the air flow rate is varied from 1.389 � 10
liquid (phase-2) phases have been shown in Fig. 9 (a and c) and on different cross sections along the length of the venture Fig. 9 (b and d), respectively. The boundary condition of mass flow inlet for gaseous phase was applied at inlet of venturi scrubber. The pressure inlet con dition (corresponding to the hydrostatic head for a column height of 0.762 m mentioned in experiments (Nawaz, 2017)) for liquid phase was used at eight orifices present at throat of venturi scrubber. The liquid enters from the orifices present at throat of venturi scrubber because of applied pressure. The volume fraction contours shown in Fig. 8 show the behavior of water entering through orifices at inlet air flow rate of 1.389 � 10 3 m3/s. At the inner walls of venturi scrubber downstream of orifices, the
3.3. Contours of volume fraction The interaction between the liquid and gas phases results in mass transfer of iodine between them. The localized mass transfer rate at any local position inside venturi scrubber is also dependent on volume fraction of liquid present there as evident from Equation (8). The con tours of volume fraction on an axial plane of gaseous (phase-1) and
Fig. 16. Contour of (a) pressure on axial plane (b) pressure on cross-sections along length (c) air velocity on axial plane (d) air velocity on cross-sections along length.
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solution entering from orifices and hence, transfer of iodine from air to scrubbing solution. On the contrary, the concentration of iodine present in liquid phase (Fig. 12 c and d) increases gradually downstream of orifices which is a proof of transfer of iodine specie from gaseous phase to liquid phase by virtue of the mass transfer model added. This behavior was also reported by Ashfaq et al. (Ashfaqet al., 2018). There is peculiar behavior of iodine concentration in air at inner wall of venturi scrubber just downstream of orifices. The iodine concentra tion decreases and then increases near the wall. The behavior has been highlighted by Fig. 13 which shows an enlarged view of iodine mass fraction in phase-1 contour near the orifice region. The reason for this behavior may be the presence of liquid film at walls as observed in Fig. 10 resulting in a large concentration of liquid phase. This means a very small amount of gas-phase is present in that region. So, concen tration of iodine drops too low in that region. It increases downstream where the film vanishes and the air from center expands to move to walls in diverging section. This behavior has been observed for the first time to the best of our knowledge. Fig. 14 shows the contours of mass transfer rate of iodine from gasphase to liquid-phase. Mass transfer rate is maximum at throat region near the orifices because concentration of iodine is maximum in this region as seen in Fig. 12 and also because volume fraction of water is highest as seen in Fig. 9. As the iodine gets transferred continuously from gas phase to liquid phase as gas moves downstream of orifices, its con centration reduces and as a result, mass transfer rate decreases as shown in Fig. 11. Ashfaq et al. (Ashfaqet al., 2018) mentioned the same effect. Fig. 14 (c) shows the enlarged view mass transfer rate contour near orifices. It has been observed that maximum mass transfer occurs at the region near the wall where the film of liquid phase is formed as observed in Fig. 10. The reason for this might be the presence of negligible amount of phase-1 at the region and a large volume fraction of phase-2.
Fig. 17. Variation of removal efficiency of iodine with throat gas velocity.
volume fraction contours show almost zero volume fraction of gas phase. The reason is the film formation of liquid phase along walls of venturi scrubber after entry and before droplet formation. Also, the momentum of air forces the incoming water to stay at the walls before droplet formation and dispersion in the whole venturi scrubber. Fig. 10 shows an enlarged view of the contour of volume fraction near orifices on an axial plane. The film formation of liquid phase can be seen clearly in Fig. 10, a phenomenon captured by CFD for the first time to the best of our knowledge. It was observed that the film of liquid phase was present in a small region just downstream of orifice and it vanishes when moving further away into diverging section. It can be concluded from the afore discussion that the film might be trapped in this localized region.
3.5. Contours of pressure and velocity The behavior related to flow physics of phases inside venturi scrubber was obtained as an additional information apart from the mass transfer. The pressure and velocity variation at an axial centerline of venturi scrubber is shown in Fig. 15 (a) and (b) respectively. The in crease in velocity and reduction in pressure downstream of inlet may be attributed to the converging section of venturi scrubber where a gradual decrease in area of flow causes such a behavior. The reduction in slope of both profiles is because of straight throat region after converging sec tion. A sharp peak in velocity profile and the corresponding valley in pressure profile may be because of water injection at orifices which reduces the area of flow for air. Downstream the orifices, is the diverging section of venturi scrubber and hence the velocity decrease and pressure recover because of increasing area of flow. With increase in flow rate the maximum pressure at inlet increases but the minimum pressure at throat further decrease because of the corresponding increase in velocity in that region. Also, the velocity change with changing flow rate of air is significant at throat but in other regions, it is little affected by it. The pressure and velocity contours are shown in Fig. 16. The con tours were plotted at an axial cross section passing through two out of eight orifices. The same behavior of velocity and pressure can be seen in these contours as mentioned above. Negative pressure present at throat of venturi scrubber causes the water to enter through orifices by pressure difference. Pressure inlet boundary condition was used at orifices so pressure decreases towards center of venturi scrubber where negative pressure maintains. Similar pressure and velocity contours were re ported by Ashfaq et al. (Ashfaqet al., 2018). The variation of removal efficiency of iodine with throat gas velocity is shown in Fig. 17. The smaller droplet diameter at higher gas velocities results in increase of mass transfer rate. Higher mass transfer rate of iodine from gas to liquid phase means higher removal efficiency.
3.4. Contours of mass transfer Since the process is assumed to be diffusion controlled, the concen tration of iodine present in both phases play a vital role in determining the mass transfer rate. Higher the concentration of iodine present in gaseous phase in any localized region of venturi scrubber, the more will be the mass transfer rate in that area, provided the scrubbing solution is present there. The mass transfer of iodine from gas phase to liquid phase is governed by Equation (8). According to Equation (9), the increase in mass flow rate of air decreases the droplet diameter of water and hence increases the mass transfer rate. In Fig. 10 the mass fraction of iodine in air as well as water has been plotted along the axis of the venture for different flow rates of the air stream. In Fig. 11 it has been observed that the mass fraction of iodine in air decreases after the throat section of venturi scrubber (where water is entered to the venturi scrubber) due to mass transfer from air to water. At the same time the mass fraction of iodine is increased in the water as a result of scrubbing process. It has also been observed that the process of scrubbing of iodine from air oc curs at a higher rate as the air flow rate is increased and vice versa. The reason is that at higher flow rate of air the water droplet size decreases as can be seen from Fig. 8, which results in increased mass transfer from air to water as can be seen from Equation (9) as well. The contour of mass fraction of iodine present in air and at axial cross-sectional plane are shown in Fig. 12 (a and c), respectively. Fig. 12 (b and d) represent the iodine mass fraction in air and water at many cross-sections downstream of orifices along the length of venturi scrubber, respectively. The iodine concentration in air (Fig. 12 a and b) was constant upstream of orifices because of no liquid present as mentioned in section 3.4 and hence no mass transfer. The mass fraction of iodine downstream of orifices gradually reduces because of scrubbing 10
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4. Conclusion
� It was observed that the removal efficiency of venturi scrubber in creases with an increase in mass flow rate of gas as well as the concentration of iodine in air at inlet
� A new model has been proposed to simulate the mass transfer phe nomenon of a gas inside venturi scrubber using computational fluid dynamics � An averaged value of distribution parameter has been proposed for which a maximum error of 6.1% was observed between simulated and experimental removal efficiency � The model was used to simulate the mass transfer phenomenon under various conditions and the behavior of trends of volume fractions, mass transfer rate, velocity and pressure inside venturi scrubber were reported � There is a decrease in mean diameter of liquid droplets with increase in flow rate of gas through venturi scrubber which results in an in crease in removal efficiency
CRediT authorship contribution statement Ammar Ahmed: Formal analysis, Writing - original draft. Ajmal Shah: Conceptualization, Supervision, Writing - original draft. Kamran Qureshi: Conceptualization, Supervision, Writing - original draft. Khalid Waheed: Conceptualization, Writing - review & editing. Naseem Irfan: Funding acquisition. Waseem Siddique: Project administration. Masroor Ahmad: Funding acquisition. Amjad Farooq: Funding acquisition.
Nomenclature
Q mf
Mass transfer rate in one droplet (kg s 1) Radius of droplet Mass transfer coefficient Distribution parameter Concentration (kg m 3) Number of droplets Volume Volume fraction Mass transfer rate in a unit cell (kg s 1) Mass transfer rate in a unit cell (kg m 3 s 1) Sherwood number Reynolds number Schmidt number Diameter Diffusion coefficient Density Velocity Dynamic viscosity Volume flow rate Mass Fraction
g in i w c l d r
Gas phase Inlet Interface Water Cell Liquid phase Droplet Relative
N r k m C n V
α
m_ M_
Sh Re Sc d D
ρ v
μ
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.pnucene.2020.103243.
References
Ashfaq, T., et al., 2018. CFD investigation of iodine mass transfer in venturi scrubbing solution of Filtered Containment Venting System. Prog. Nucl. Energy 111, 195–204. Boll, R., Flais, L.R., Maurer, P.W., Thompson, L.V., 1974. Mean drop size in a full scale venturi scrubber via transmissometer. J. Air Pollut. Control Assoc. 24, 934. Costa, M.A.M., Henrique, P.R., Gonçalves, J.A.S., Coury, J.R., 2004. Droplet size in a rectangular venturi scrubber. Braz. J. Chem. Eng. 21 (2), 335–343. Crank, J., 1975. The Mathematics of Diffusion. Oxford University Press second ed. New York, U.S. Gamisans, X., Sarr� a, M., Lafuente, F.J., 2004. The role of the liquid film on the mass transfer in venturi-based scrubbers. Chem. Eng. Res. Des. 82 (3), 372–380. Hills, J.H., 1995. Behavior of venturi scrubbers as chemical reactors. Ind. Eng. Chem. Res. 34, 4254–4259. Nawaz, S., 2017. Installation and experimentation on desktop, floor-top and pilot-scale FCVS experimental setup. MS Nuclear Engineering. Department of Nuclear
Ahmed, S., et al., 2018. Investigation of dust particle removal efficiency of self-priming venturi scrubber using computational fluid dynamics. Nuclear Engineering and Technology 50 (5), 665–672. Ali, M., Changqi, Y.A.N., Zhongning, S.U.N., Haifeng, G.U., Junlong, W., Mehboob, K., 2013. Iodine removal efficiency in non-submerged and submerged self-priming venturi scrubber. Nuclear Engineering and Technology 45 (2), 203–210. Ali, M., Changqi, Y., Haifeng, G., Mehboob, K., Rasool, A., 2014. Removal efficiency of iodine at saturated steam in submerged venturi scrubber. Presented at the Proceedings of International Conference on Nuclear Engineering, Prague, Czech Republic. July 7-11, 2014. Alonso, D.F., Gonclaves, J.A.S., Azzopardi, B.J., Coury, J.R., 2001. Dropsize measurements in venturi scrubbers. Chem. Eng. Sci. 56, 4901–4911.
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Engineering, Pakistan Institute of Engineering & Applied Sciences, Islamabad, Pakistan. Nukiyama, S., Tanasawa, Y., 1938. An experiment on the atomization of liquid by means of an air stream. Transactions of Society of Mechanical Engineers (Japan) 4, 86. Pak, S.I., Chang, K.S., Dec 1 2006. Performance estimation of a Venturi scrubber using a computational model for capturing dust particles with liquid spray. J. Hazard Mater. 138 (3), 560–573. Ravindram, M., Pyla, N., 1988. Modeling of a venturi scrubber for the control of gaseous pollutants. Ind. Eng. Chem. Process Des. Dev. 25, 35–40.
Steinberger, R.L., Treybal, R.E., 1960. Mass transfer from a solid soluble sphere to a flowing liquid system. AIChE J. 6, 227. Talaie, M.R., Ahmadvand, F., 2010. CFD modeling of droplet dispersion in a venturi scrubber. Chem. Eng. J. 160, 423–431. Talaie, M.R., Fathikalajahi, J., Taheri, M., 2012. Mathematical modeling of SO2 absorption in a venturi scrubber. J. Air Waste Manag. Assoc. 47 (11), 1211–1215. Uchida, S., Wen, C.Y., 1973. Gas absorption by alkaline solutions in a venturi scrubber. Ind. Eng. Chem. Process Des. Dev. 12 (4).
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Investigation of iodine removal efficiency in a venturi scrubber using mass transfer model for CFD Ammar Ahmed a, Ajmal Shah b, c, Kamran Qureshi a, Khalid Waheed b, Naseem Irfan b, Waseem Siddique a, *, Masroor Ahmad b, Amjad Farooq b a b c
Department of Mechanical Engineering, Pakistan Institute of Engineering and Applied Sciences, Pakistan Department of Nuclear Engineering, Pakistan Institute of Engineering and Applied Sciences, Pakistan Centre for Mathematical Sciences, Pakistan Institute of Engineering and Applied Sciences, Pakistan
A R T I C L E I N F O
A B S T R A C T
Keywords: Venturi scrubber Mass transfer model Iodine removal Filtered containment venting system
Filtered containment venting system (FCVS) is important for the ultimate safety of a nuclear power plant owing to its use in containment pressure reduction in case of severe accident. It vents a portion of containment air after removal of harmful radioactive products including iodine through venturi scrubber. The purpose of this research was to develop a mass transfer model for estimation of performance of a venturi scrubber for removal of elemental iodine using Computational Fluid Dynamics. A mathematical model for transfer of iodine from air to water was developed based on two film theory of mass transfer and experimentally validated. Simulations were performed for self-priming non-submerged circular venturi scrubber using Fluent and the results were compared with experimental ones. Experimental data was used for validation in which an aqueous solution of sodium hydroxide and sodium thiosulfate was used as scrubbing solution for removal of iodine. For simulation, only water was used instead of scrubbing solution for simplicity. Euler-Euler approach was used for two-phase modeling and realizable k-epsilon model was used for turbulence modeling. The results obtained from simula tions had a good match with the experimental ones.
1. Introduction Nuclear power plants provide clean and sustainable energy for electricity generation and heat applications. Safety of nuclear power plants along with their ability to handle severe accidents is the major concern with this technology as was highlighted from the accidents at Three Mile Island, Chernobyl and Fukushima Daiichi Nuclear Power Plants. In these accidents, containment building designed to protect the environment from harmful radioactive products was compromised. To handle such severe accidents, filtered containment venting system (FCVS) is designed which ensures containment integrity in case of core meltdown and high-pressure steam buildup inside containment. This system reduces containment pressure by venting some of the contain ment air into the atmosphere. Radioactive elemental iodine-131 is the major product among others that needs to be removed from the venting air. It has a half-life of around 8 years and is likely to cause thyroid cancer if released into the atmosphere. In FCVS, venturi scrubbers are widely used to remove the harmful
radioactive products from the venting air to prevent radioactivity release outside the plant. Therefore, it is necessary to study the phe nomenon of iodine retention in venturi scrubber to effectively improve its efficiency. Venturi scrubbers are converging diverging nozzles with facility of scrubbing solution injection at throat. Harmful gases present in air are absorbed in scrubbing solution while passing through the venturi scrubber. Generally, based on the feed mechanism of injected water, two types of venturi scrubbers are used: i.e. force-feed and selfpriming venturi scrubbers. Owing to the usage of venturi scrubber in conventional plants and industry for removal of dust and gases like SO2, some models are already available in literature for its effectiveness analysis. Uchida and Wen (1973) presented a unidimensional mass transfer and fluid flow model using heat, mass and momentum balances and formulating differential equations relating the velocity of liquid, gas concentration and its partial pressure along axial direction. They used Runge-Kutta-Gill method to numerically simulate the results of experi ments presented in three different researches and compared the overall
* Corresponding author. E-mail addresses: [email protected] (A. Ahmed), [email protected] (W. Siddique). https://doi.org/10.1016/j.pnucene.2020.103243 Received 26 April 2019; Received in revised form 26 December 2019; Accepted 6 January 2020 Available online 15 January 2020 0149-1970/© 2020 Elsevier Ltd. All rights reserved.
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efficiency for Sulfur Dioxide gas (SO2) removal. Ravindram and Pyla (1988) proposed a theoretical model to predict the efficiency for removal of gaseous pollutants from air using a venturi scrubber. Their model was based on simultaneous diffusion and irreversible chemical reaction of gases with alkaline solutions. For validation of their model, they conducted experiments for gas absorption using sodium hydroxide solution as scrubbing agent. The proposed model was found to be in agreement with the experimental results for the cases of CO2 and SO2 removal. Talaie et al. (2012) proposed a three-dimensional mathemat ical model to evaluate the removal efficiency of SO2 in venturi scrubber using alkaline solution and water. The mass transfer model presented in their study was based on physical absorption by concentration differ ence of SO2 in liquid and gaseous phases. The authors used material balance and dispersion equations to determine pollutant concentration in gaseous phase. The model calculates overall removal efficiency of SO2 considering the difference in concentration at inlet and outlet of venturi scrubber but there is no localized mass transfer phenomenon incorpo rated. Hills (1995) studied the performance of venturi scrubbers as chemical reactors and modelled the absorption of a gas with chemical reaction. In this study, Hills reported that the absorption of a gas in real venturi scrubbers can be considered as a rapid reaction and controlled by diffusion. The droplet size plays an important role in mass transfer inside venturi scrubber. Alonso et al. (2001) performed experiments for mea surement of diameter of water droplets inside cylindrical venturi scrubber using laser diffraction technique by varying the gas velocities and liquid to gas flow rate ratio. Sauter mean diameter values obtained from Nukiyama and Tansawa (Nukiyama and Tanasawa, 1938) as well as Boll et al. (1974) equations were compared with experimental results and concluded that Sauter mean diameter is well predicted using Boll et al. correlation. Also, velocity of gas has a major effect on the size of droplet instead of liquid to gas flow ratio. Costa et al. (2004) also per formed the same experiments using a rectangular venturi scrubber instead of a circular one and the results obtained agreed with the ones presented by Alonso et al. Ahmadvand and Talaie (Talaie and Ahmad vand, 2010) developed a two-dimensional mathematical model to study the droplet dispersion in cylindrical venturi scrubber using CFD. Gamisans et al. (2004) experimentally studied the effect of diameter and throat length on mass transfer in a jet-venturi scrubber for SO2 absorption in aqueous solutions. A model based on two film theory of mass transfer was proposed by incorporating diffusion with irreversible chemical reaction of SO2 with scrubbing solution. Concentration dif ference of SO2 was taken as the driving force for transfer of SO2 from air to scrubbing solution. They mentioned that the scrubbing reaction is very rapid and is diffusion controlled. Furthermore, the significance of liquid film in mass transfer was proved experimentally. Comparison of results was made for the cases considering the effect of liquid film on SO2 removal and neglecting its effect. Pak and Chang (2006) developed a three-dimensional numerical model for prediction of pressure drop as well as collection efficiency of a circular venturi scrubber for dust particle removal. Inertial impaction mechanism was considered for capturing of dust particles in water droplets. Boll correlation was used for droplet size and Eulerian-Lagrangian method for numerical simulation of dust-air-water three phase mixture. In case of severe accident in a nuclear power plant, containment is pressurized by high temperature steam mixed in air so Ali et al. (2014) experimentally studied the removal efficiency of iodine from steam in submerged venturi scrubber and concluded that removal efficiency of iodine increases with increase in flow rate of steam. Also, Ali et al. (2013) theoretically and experimentally studied the removal efficiency of iodine in a self-priming venturi scrubber for the cases of submerged and non-submerged conditions. Aqueous solution of 0.5% sodium thiosulfate and 0.2% sodium hydroxide was used to absorb iodine present in air inside venturi scrubber. A mass transfer model based on two film theory proposed by Gamisans et al. (2004) was used. Droplet diameter was calculated using Nukiyama and Tanasawa
equation whereas Steinberger and Treybal (1960) correlation was used for mass transfer coefficient of gas phase. They reported that iodine removal efficiency increases with increase in gas flow rate as well as inlet iodine concentration. They also pointed out that the scrubbing reaction is very rapid and the process is controlled by the diffusion at the gas-liquid interface. Ahmed et al. (Ahmedet al., 2018) investigated the removal efficiency of self-priming venturi scrubber for dust particles removal using computational fluid dynamics (CFD). They performed the analysis using ANSYS CFX. 1-micron size Titanium oxide particles were used as dust. They used cascade atomization and breakup (CAB) model for prediction of deformation of water droplets and Eulerian-Lagrangian method for multiphase analysis. They estimated the dust removal efficiencies for different inlet air velocities and it was concluded that removal efficiency increases with increasing air velocity. Ashfaq et al. (Ashfaqet al., 2018) studied the effect of droplet diameter of scrubbing solution on removal of elemental iodine from containment air in a venturi scrubber using CFD. They used ANSYS FLUENT to model the multiphase flow phenomenon and incorporated a user defined function for mass transfer of iodine from air to water (scrubbing). They done a tremendous job by introducing a three-dimensional mathematical model for scrubbing iodine from air and implementing the model in CFD software for the first time to the best of my knowledge. However, there were some discrepancies in the approach and mass transfer model they introduced. The work presented here is an extension of the study performed by Ashfaq et al. (Ashfaqet al., 2018). In this work an effort has been made to remove the discrepancies in the approach and CFD model for scrubbing of iodine from air. Ashfaq and his coworkers performed the simulations to study the effect of droplet diameter on the process of scrubbing. They did this by selecting various droplet diameters and running the simu lations for each case. However, the droplet diameter is a function of the air flow rate and varies as the flow rate is changed. In the present work, the droplet diameter has been calculated using the correlation of Boll et al. (1974) to overcome the discrepancy of the Ashfaq et al. (Ashfaqet al., 2018) model. Ashfaq et al. (Ashfaqet al., 2018) assumed Iodine distribution parameter equal to unity as did by Crank (1975). However, Crank (1975) has also mentioned that distribution parameter is unity only when the diffusion process is very rapid. Further, Gamisans et al. (2004) and Ali et al. (2013) have mentioned that, in the scrubbing process, reaction rate is rapid as compared to diffusion so the process is diffusion controlled. Therefore, in the present study the distribution parameter has not been taken as unity, rather it has been calculated by using the scrubbing efficiencies obtained by experiments and CFD. In this study a range of distribution parameter has been calculated and finally an average value of the distribution parameter has been pre sented. The value of the distribution parameter, reported in this work for the first time to the best of our knowledge, reflects the process of iodine diffusion from air to liquid, thus giving an insight of the governing process. Ashfaq et al. (Ashfaqet al., 2018) has not validated the scrub bing model against experimental results, therefore, in the present study the CFD results have been validated with experimental results. So, the present study presents a much-improved mathematical model of the iodine scrubbing process, which has not only been validated by exper imental results but also reflects the dynamics of the actual process by calculating the value of the distribution parameter. 2. Material and procedure In this study, Computational Fluid Dynamics analysis was performed for simulation of mass transfer phenomenon in a non-submerged cir cular venturi scrubber using Fluent module of ANSYS. A mathematical model was developed for evaluating the mass transfer of iodine from gas to liquid phase and was incorporated with the software using a user defined function (UDF). The efficiency of venturi scrubber for removal of iodine from air was obtained from the difference of concentration of 2
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Progress in Nuclear Energy 121 (2020) 103243
Fig. 1. Experimental setup (Nawaz, 2017).
Fig. 2. Geometry of venturi scrubber (Nawaz, 2017).
iodine in air at inlet and outlet of venturi scrubber.
�
2.1. Multiphase model and governing equations
� m_ qp þ Sq
þ
n � X ! _ R pq þ mpq ! v pq
m_ qp ! v qp
qp
(1)
(3)
q
lift;q
wl;q
vm;q
td;q
� � ∂ ∂pq α ρ h þ r: αq ρq hq ! u q ¼ αq þ τq ∂t q q q ∂t : r! uq
r:! q q þ Sq þ
n X
Qpq þ m_ pq hpq
m_ qp hqp
�
(4)
p¼1
Where hq , ! q q and Sq represent specific enthalpy, heat flux and source term of qth phase respectively. Qpq and hpq show intensity of heat ex change between pth and qth phases and interphase enthalpy respectively. Iodine was treated as a chemical specie in air and scrubbing solution phases. It was modelled by specie transport model with following con servation equation for iodine in any phase q,
αq rp þ r:τq þ αq ρq ! g �
� 2 v qI μq r:! 3
represent external body force, lift force, wall lubrication force, virtual mass force and turbulent dispersion force respectively. Interaction force ! between phases is shown by R pq and pressure shared by all phases represented by p. The conservation of energy equation in Eulerian model is written as
Where mass transfer from pth to qth phase is shown by m_ pq and from qth to pth phase by m_ qp . The momentum balance equation for a phase q is given by � � ∂ αρ! v þ r: αq ρq ! v q! vq ¼ ∂t q q q
T
Where μq and λq represent shear and bulk viscosity of phase q. ! v pq and ! ! ! ! ! ! v show interphase velocities. F ; F ; F ; F and F
Eulerian-Eulerian approach was used for solution of complex twophase flow consisting of air-water-iodine mixture. The Eulerian model solves a set of continuity and momentum equations for each phase. In this model, continuity equation for a generic phase q flowing with velocity ! v q is n � � X ∂ m_ pq αq ρq þ r: αq ρq ! vq ¼ ∂t p¼1
�
�
v q þ r! τq ¼ αq μq r! v q þ αq λ q
(2)
p¼1
! ! ! ! ! � þ F q þ F lift;q þ F wl;q þ F vm;q þ F td;q Where τq represents stress-strain tensor of qth phase given by 3
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Table 1 Experimental data reported by Nawaz (2017) and used for benchmarking. Sr. #
Mass Flow Rate of Air (m3/s)
Inlet I2 Concentration (ppm)
Outlet I2 Concentration (ppm)
Removal Efficiency (%)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1.389 � 10 3
50.1 34.6 27.9 42.0 48.6 69.7 44.0 39.5 34.0 37.6 32.7 35.6 49.4 45.1 41.4 37.2
4.9 5.2 5.0 5.1 4.8 5.6 4.9 4.7 2.5 2.5 2.4 2.5 2.5 2.5 2.5 2.4
90.2 85.0 82.1 87.9 90.1 92.0 88.9 88.1 92.6 93.4 92.7 93.0 94.9 94.5 94.0 93.5
1.528 � 10 3 1.667 � 10 3 1.806 � 10 3
∂ q q q q v Y qÞ ¼ ðρ α Y Þ þ r:ðρq αq ! ∂t
n X !q m_ pq r:αq J þ αq Rq þ αq Sq þ
m_ qp
�
p¼1
þR (5) 2.2. Mass transfer model The mathematical model developed for mass transfer of iodine from air to droplets of water is based on two film theory. The driving force for mass transfer is the iodine’s concentration difference (diffusion) and takes place at interface of air and water films. It is assumed that the reaction is kinetically rapid and hence, rate of mass transfer is gas-film controlled (Gamisans et al., 2004). Furthermore, all droplets of water are spherical and represented by a Sauter mean diameter. Mass transfer rate of iodine in a single droplet of water is given by the following relation (Gamisans et al., 2004), Nl ¼ 4πr2 kg mðCin
Ci Þ
(6)
The distribution factor (m) in Equation (5) was assumed by Crank (1975) and Ashfaq (Ashfaqet al., 2018) as unity considering the same concentration of solute present in film as well as in solution. However, it was mentioned that in reality, the concentration of solute in liquid film is m times the concentration of solute in the gas phase (Crank, 1975) i.e. m¼
Equilibrium Concentration of iodine in liquid phase Equilibrium Concentration of iodine in gaseous phase
Fig. 3. Meshed Geometry (a) Complete (b) Outlet region (c) Throat region (d) Inlet region.
Since the scrubbing process is diffusion controlled (Gamisans et al., 2004; Ali et al., 2014), the value of distribution parameter cannot be assumed unity as mentioned by Crank (1975). Therefore, the distribu tion parameter becomes very important to understand the process of diffusion in iodine scrubbing. To determine the mass transfer rate at local computational cell, it is required to find the number of droplets (n) in the cell, which is calculated by considering volume of water and volume of spherical droplets in the computational cell. n¼
3αl Vc 4π r 3
3αl kg mCin M_ ¼ r 2.3. The mass transfer coefficient is calculated using sherwood number formula
(7)
Sh ¼
Rate of mass transfer in a unit cell of domain in Equation (8) can be obtained by the product of Equations (6) and (7). m_ ¼
3αl kg mðCin r
Ci Þ Vc
(9)
kg dd Dg
(10)
Where Sherwood number is calculated using Steinberger and Treybal correlation (Steinberger and Treybal, 1960) �0:62 Sh ¼ 2 þ 0:347 Re Sc0:5 (11)
(8)
And Reynolds and Schmidt number are given by Equations (12) and (13).
With the assumption of reaction being gas film controlled, Ci ¼ 0 for this case (Ali et al., 2013). On per unit volume of cell basis, the rate of mass transfer is given by Equation (9). 4
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Fig. 6. Distribution parameter values.
Fig. 4. Mesh independence study. Table 2 CFD models and boundary conditions used in simulation. Multiphase model Turbulence model Specie transport Phase-1 (Gas phase) Phase-2 (Liquid phase) Mass Transfer Venturi scrubber inlet Orifice inlets at throat Venturi scrubber outlet Wall
Eulerian-Eulerian Realizable k-epsilon Iodine taken as specie in gas and liquid phase Air-Iodine mixture Water-Iodine mixture From phase-1 iodine to phase-2 iodine at a user defined rate using UDF Boundary Conditions Mass Flow Inlet of Phase-1 with certain concentration of I2 Pressure Inlet of Phase-2 with no concentration of I2 Pressure Outlet at atmospheric pressure No slip conditions at wall
Fig. 7. Comparison of simulation and experimental removal efficiency of iodine.
Re ¼
ρg vg dd μg
(12)
Sc ¼
μg ρg D g
(13)
The diameter of water droplet is calculated using correlation of Boll et al. (1974) � �1:932 l 4:22 � 10 2 þ 5:77 � 10 3 1000Q Qg dd ¼ (14) v1:602 r 2.4. Experimentation The validation of a computational model generally requires experi mental results for comparison. As part of this ongoing project Nawaz (2017) performed some experimental work, which has been used as validation data in this current study. The details of Nawaz (2017) experimental work are mentioned below.
Fig. 5. Variation in distribution parameter values.
5
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form of a spectrum which gives the concentration of material present in the sample. Calibration curve was drawn for absorbance of light versus known value of concentration and later used for determination of con centration of iodine in samples. The removal efficiency was calculated using the difference in concentration of iodine at inlet and outlet of scrubbing column. Table 1 shows part of the experimental data reported by Nawaz (2017) and used as benchmark for simulating the scrubbing of iodine from containment air through venturi scrubber. Mass flow rate of air was mentioned in units of cubic meters per hour, concentration of iodine in air at inlet and outlet of venturi scrubber was mentioned in parts per million. Removal efficiency was calculated using the difference in con centration of I2 in air at inlet and outlet. Further details of the experi mental work are given in Nawaz (2017). 2.5. CFD simulation CFD simulations were performed using ANSYS Fluent version 14.0. The venturi scrubber geometry was obtained from the experiments performed by Nawaz (2017). The geometry was made in ANSYS Design Modular and meshed in ANSYS Meshing module. The geometry with dimensions is shown in Fig. 2. The venturi scrubber used in this study is of self-priming type; In order to apply pressure boundary conditions at orifices, orifices were extended 5 mm from throat. The meshed geometry with tetrahedral mesh at orifices and hexahedral elsewhere is shown in Fig. 3. The mesh independent study was performed. Variation of iodine concentration in air was obtained on axis of venturi scrubber by grad ually increasing the number of mesh elements. The concentration (mass fraction) of iodine in air became independent of mesh size at around 112875 elements as shown in Fig. 4. The Eulerian-Eulerian model was used to obtain in-depth two-phase analysis, constant droplet diameter was used by calculation using Boll correlation, realizable k-epsilon model was used for turbulence and mass transfer model was incorporated using user defined function in ANSYS Fluent. The boundary conditions used were mass flow inlet at air inlet, pressure inlet at orifices and pressure outlet at outlet of venturi scrubber. The boundary conditions were used according to the data obtained from
Fig. 8. Variation of liquid droplet diameter with flow rate of air.
The experiments were performed on a circular self-priming sub merged venturi scrubber made of brass with dimensions shown in Fig. 2. The schematic of experimental setup is shown in Fig. 1. The filtered air from compressor was passed through iodine sublimation chamber. A certain amount of solid iodine was loaded in iodine chamber before each experiment. The sublimated iodine vapors get mixed with air in iodine chamber. The amount concentration of iodine mixing in air was deter mined using iodine traps before inlet of venturi scrubber. The air-iodine mixture was passed through the venturi scrubber submerged in scrub bing solution (0.5% NaOH and 0.2% Na2S2O3). Iodine concentration in air at inlet as well as outlet of venturi scrubber was measured at 5-min intervals using traps as shown in Fig. 1. Air streams containing iodine vapors from inlet and outlet were bubbled through traps containing 0.1 M KOH solution and analyzed on UV–visible spectrophotometer that works on absorption spectroscopy principle. The amount of light absorbed as a function of wavelength is measured and plotted in the
Fig. 9. vol fraction of (a) gas phase on axial plane (b) gas phase on cross-sections along length (c) liquid phase on axial plane (d) liquid phase on cross-sections along length. 6
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Fig. 10. Zoomed contour of volume fraction of (a) Phase-1 (b) Phase-2.
the experimentation (Nawaz, 2017). Because of unavailability of iodine in the Fluent library, properties of iodine were manually entered in the software. Because of very low concentration of NaOH and Na2S2O3 in the solution, its flow was simulated using water whereas the iodine absorption of the solution was simulated by mass transfer model. The convergence criterion used for the simulation was 10 4. The CFD set tings have been summarized in Table 2.
diameter, using Boll et al. (1974) correlation. Further the experimental results of scrubbing efficiency were used to calculate the iodine distri bution parameter which was assumed unity previously by Ashfaq et al. (Ashfaqet al., 2018). In the following topics the distribution parameter, droplet diameter, validation of mass transfer model and contours of volume fraction, mass transfer, pressure and velocity have been dis cussed in detail to throw light on the scrubbing process of iodine from containment air using submerged venturi scrubber.
3. Results and discussion
3.1. Distribution parameter and validation of mass transfer model
In this study, an improved computational mass transfer model of iodine scrubbing from containment air has been presented and validated through experimental results. As mentioned earlier, this model was applied for the first time by Ashfaq et al. (Ashfaqet al., 2018) for their computational study of iodine scrubbing and the present study is an extension of the work of Ashfaq et al. (Ashfaqet al., 2018). In this work, the scrubbing model has been modified by calculating the droplet
The distribution parameter is defined as the ratio of equilibrium concentration of specie in liquid phase to its equilibrium concentration in gas phase. It is an important parameter in flows where the mass transfer is diffusion controlled as is the case in iodine scrubbing from containment air. It can be considered as unity if the diffusion process is very fast as mentioned by Crank (1975). Ashfaq et al. (Ashfaqet al., 2018) assumed the value of distribution parameter as unity in the mass transfer model of iodine scrubbing, however, in the present study a more realistic approached was used to calculate its value using the experi mental value of scrubbing efficiency. In this study, a series of simula tions were performed by keeping the experimental value of scrubbing efficiency as the bench mark to ascertain a range of distribution parameter under different operating conditions. The distribution parameter values as a function of concentration of iodine in air and air flow rate are shown in Fig. 5. The values of distribution parameter vary from 0.00144 to 0.00205 for an air flow rate of 1.389 � 10 3 m3/s to 1.806 � 10 3 m3/s and iodine concentration of 24 ppm–70 ppm in air. These results indicate that the distribution parameter is not a strong function of air flow rate and iodine concentration in air. However, these values indicate that the process of iodine scrubbing from containment air is strongly diffusion controlled as the values of distribution param eter are very small as compared to unity. These values, therefore, vali dates the assumption, employed in the mass transfer model, that the process of iodine scrubbing is diffusion controlled rightly mentioned by Gamisans et al. (2004) and Ali et al. (2013) too. The narrow band of the values of distribution parameter, under different operating conditions, as shown in Fig. 6 provoked us to search for a single value of the distribution parameter valid for the simulation of all the cases with reasonable error. So, a mean value of the distribu tion parameter was obtained from the data of Fig. 6 and it was 0.00185.
Fig. 11. The mass fraction of iodine in Phase-1 and Phase-2 on axial centerline of venturi scrubber. 7
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Fig. 12. Mass fraction of iodine in (a) gas phase on axial plane (b) gas phase on cross-sections along length (c) liquid phase on axial plane (d) liquid phase on crosssections along length.
All the simulations were performed again using this single value of the distribution parameter and the iodine removal efficiency was calculated and compared with the experimental values as shown in Fig. 7. It was found that the maximum error in the iodine removal efficiency is 6.1%, which looks acceptable.
entering the venturi scrubber. Smaller the diameter of these droplets, more will be the mass transfer because of an increased surface area as depicted by Equation (9). Ashfaq et al. (Ashfaqet al., 2018) used a constant mass flow rate of 0.09 kg/s and considered different diameters of water droplets for the same flow rate to study the effect of changing diameter on different parameters. However, droplet diameters are rep resented by a Sauter mean diameter which is a function of flow rates of gas and liquid (Alonso et al., 2001). In this improved model, the Boll et al. correlation was introduced to calculate the droplet diameter. With the edition of this correlation the model is now able to calculate the droplet diameter according to the existing flow conditions. Fig. 8 in dicates the droplet diameter variation with the air flow rate obtained through modified model. This Figure indicates that the diameter of liquid droplet depends on the air mass flow rate and decreases as the air mass flow is increased. So, the water atomizes into finer droplets as the air flow increases. The variation in droplet diameter is from 32 μm to 47
3.2. Droplet diameter Droplet diameter is an important parameter in scrubbing process of iodine from containment air because it defines the surface area offered by liquid phase to the iodine present in air. If larger surface area is offered by liquid the scrubbing will be efficient and vice versa. The droplet diameter decreases with increase in gas flow rate as reported by Alonso et al. and Costa et al. (Talaie et al., 2012; Nukiyama and Tana sawa, 1938). The liquid phase enters the venturi scrubber by pressure difference through tiny holes present at throat of venturi scrubber as shown in Fig. 3. The liquid atomizes into very small droplets after
Fig. 14. Mass transfer rate contour on (a) axial cross-section (b) radial crosssections along length (c) enlarged view near orifices of axial cross-section.
Fig. 13. Enlarged view of contour of mass fraction of I2 in Phase-1 near orifices. 8
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Fig. 15. Axial profiles of (a) pressure and (b) velocity at different flow rates of gas. 3 to 1.806 � 10 3 m3/s. The modified model is now capable of calculating the Sauter mean diameter according to the flow conditions and draw back present in Ashfaq et al. (Ashfaqet al., 2018) model was removed.
μm as the air flow rate is varied from 1.389 � 10
liquid (phase-2) phases have been shown in Fig. 9 (a and c) and on different cross sections along the length of the venture Fig. 9 (b and d), respectively. The boundary condition of mass flow inlet for gaseous phase was applied at inlet of venturi scrubber. The pressure inlet con dition (corresponding to the hydrostatic head for a column height of 0.762 m mentioned in experiments (Nawaz, 2017)) for liquid phase was used at eight orifices present at throat of venturi scrubber. The liquid enters from the orifices present at throat of venturi scrubber because of applied pressure. The volume fraction contours shown in Fig. 8 show the behavior of water entering through orifices at inlet air flow rate of 1.389 � 10 3 m3/s. At the inner walls of venturi scrubber downstream of orifices, the
3.3. Contours of volume fraction The interaction between the liquid and gas phases results in mass transfer of iodine between them. The localized mass transfer rate at any local position inside venturi scrubber is also dependent on volume fraction of liquid present there as evident from Equation (8). The con tours of volume fraction on an axial plane of gaseous (phase-1) and
Fig. 16. Contour of (a) pressure on axial plane (b) pressure on cross-sections along length (c) air velocity on axial plane (d) air velocity on cross-sections along length.
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solution entering from orifices and hence, transfer of iodine from air to scrubbing solution. On the contrary, the concentration of iodine present in liquid phase (Fig. 12 c and d) increases gradually downstream of orifices which is a proof of transfer of iodine specie from gaseous phase to liquid phase by virtue of the mass transfer model added. This behavior was also reported by Ashfaq et al. (Ashfaqet al., 2018). There is peculiar behavior of iodine concentration in air at inner wall of venturi scrubber just downstream of orifices. The iodine concentra tion decreases and then increases near the wall. The behavior has been highlighted by Fig. 13 which shows an enlarged view of iodine mass fraction in phase-1 contour near the orifice region. The reason for this behavior may be the presence of liquid film at walls as observed in Fig. 10 resulting in a large concentration of liquid phase. This means a very small amount of gas-phase is present in that region. So, concen tration of iodine drops too low in that region. It increases downstream where the film vanishes and the air from center expands to move to walls in diverging section. This behavior has been observed for the first time to the best of our knowledge. Fig. 14 shows the contours of mass transfer rate of iodine from gasphase to liquid-phase. Mass transfer rate is maximum at throat region near the orifices because concentration of iodine is maximum in this region as seen in Fig. 12 and also because volume fraction of water is highest as seen in Fig. 9. As the iodine gets transferred continuously from gas phase to liquid phase as gas moves downstream of orifices, its con centration reduces and as a result, mass transfer rate decreases as shown in Fig. 11. Ashfaq et al. (Ashfaqet al., 2018) mentioned the same effect. Fig. 14 (c) shows the enlarged view mass transfer rate contour near orifices. It has been observed that maximum mass transfer occurs at the region near the wall where the film of liquid phase is formed as observed in Fig. 10. The reason for this might be the presence of negligible amount of phase-1 at the region and a large volume fraction of phase-2.
Fig. 17. Variation of removal efficiency of iodine with throat gas velocity.
volume fraction contours show almost zero volume fraction of gas phase. The reason is the film formation of liquid phase along walls of venturi scrubber after entry and before droplet formation. Also, the momentum of air forces the incoming water to stay at the walls before droplet formation and dispersion in the whole venturi scrubber. Fig. 10 shows an enlarged view of the contour of volume fraction near orifices on an axial plane. The film formation of liquid phase can be seen clearly in Fig. 10, a phenomenon captured by CFD for the first time to the best of our knowledge. It was observed that the film of liquid phase was present in a small region just downstream of orifice and it vanishes when moving further away into diverging section. It can be concluded from the afore discussion that the film might be trapped in this localized region.
3.5. Contours of pressure and velocity The behavior related to flow physics of phases inside venturi scrubber was obtained as an additional information apart from the mass transfer. The pressure and velocity variation at an axial centerline of venturi scrubber is shown in Fig. 15 (a) and (b) respectively. The in crease in velocity and reduction in pressure downstream of inlet may be attributed to the converging section of venturi scrubber where a gradual decrease in area of flow causes such a behavior. The reduction in slope of both profiles is because of straight throat region after converging sec tion. A sharp peak in velocity profile and the corresponding valley in pressure profile may be because of water injection at orifices which reduces the area of flow for air. Downstream the orifices, is the diverging section of venturi scrubber and hence the velocity decrease and pressure recover because of increasing area of flow. With increase in flow rate the maximum pressure at inlet increases but the minimum pressure at throat further decrease because of the corresponding increase in velocity in that region. Also, the velocity change with changing flow rate of air is significant at throat but in other regions, it is little affected by it. The pressure and velocity contours are shown in Fig. 16. The con tours were plotted at an axial cross section passing through two out of eight orifices. The same behavior of velocity and pressure can be seen in these contours as mentioned above. Negative pressure present at throat of venturi scrubber causes the water to enter through orifices by pressure difference. Pressure inlet boundary condition was used at orifices so pressure decreases towards center of venturi scrubber where negative pressure maintains. Similar pressure and velocity contours were re ported by Ashfaq et al. (Ashfaqet al., 2018). The variation of removal efficiency of iodine with throat gas velocity is shown in Fig. 17. The smaller droplet diameter at higher gas velocities results in increase of mass transfer rate. Higher mass transfer rate of iodine from gas to liquid phase means higher removal efficiency.
3.4. Contours of mass transfer Since the process is assumed to be diffusion controlled, the concen tration of iodine present in both phases play a vital role in determining the mass transfer rate. Higher the concentration of iodine present in gaseous phase in any localized region of venturi scrubber, the more will be the mass transfer rate in that area, provided the scrubbing solution is present there. The mass transfer of iodine from gas phase to liquid phase is governed by Equation (8). According to Equation (9), the increase in mass flow rate of air decreases the droplet diameter of water and hence increases the mass transfer rate. In Fig. 10 the mass fraction of iodine in air as well as water has been plotted along the axis of the venture for different flow rates of the air stream. In Fig. 11 it has been observed that the mass fraction of iodine in air decreases after the throat section of venturi scrubber (where water is entered to the venturi scrubber) due to mass transfer from air to water. At the same time the mass fraction of iodine is increased in the water as a result of scrubbing process. It has also been observed that the process of scrubbing of iodine from air oc curs at a higher rate as the air flow rate is increased and vice versa. The reason is that at higher flow rate of air the water droplet size decreases as can be seen from Fig. 8, which results in increased mass transfer from air to water as can be seen from Equation (9) as well. The contour of mass fraction of iodine present in air and at axial cross-sectional plane are shown in Fig. 12 (a and c), respectively. Fig. 12 (b and d) represent the iodine mass fraction in air and water at many cross-sections downstream of orifices along the length of venturi scrubber, respectively. The iodine concentration in air (Fig. 12 a and b) was constant upstream of orifices because of no liquid present as mentioned in section 3.4 and hence no mass transfer. The mass fraction of iodine downstream of orifices gradually reduces because of scrubbing 10
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4. Conclusion
� It was observed that the removal efficiency of venturi scrubber in creases with an increase in mass flow rate of gas as well as the concentration of iodine in air at inlet
� A new model has been proposed to simulate the mass transfer phe nomenon of a gas inside venturi scrubber using computational fluid dynamics � An averaged value of distribution parameter has been proposed for which a maximum error of 6.1% was observed between simulated and experimental removal efficiency � The model was used to simulate the mass transfer phenomenon under various conditions and the behavior of trends of volume fractions, mass transfer rate, velocity and pressure inside venturi scrubber were reported � There is a decrease in mean diameter of liquid droplets with increase in flow rate of gas through venturi scrubber which results in an in crease in removal efficiency
CRediT authorship contribution statement Ammar Ahmed: Formal analysis, Writing - original draft. Ajmal Shah: Conceptualization, Supervision, Writing - original draft. Kamran Qureshi: Conceptualization, Supervision, Writing - original draft. Khalid Waheed: Conceptualization, Writing - review & editing. Naseem Irfan: Funding acquisition. Waseem Siddique: Project administration. Masroor Ahmad: Funding acquisition. Amjad Farooq: Funding acquisition.
Nomenclature
Q mf
Mass transfer rate in one droplet (kg s 1) Radius of droplet Mass transfer coefficient Distribution parameter Concentration (kg m 3) Number of droplets Volume Volume fraction Mass transfer rate in a unit cell (kg s 1) Mass transfer rate in a unit cell (kg m 3 s 1) Sherwood number Reynolds number Schmidt number Diameter Diffusion coefficient Density Velocity Dynamic viscosity Volume flow rate Mass Fraction
g in i w c l d r
Gas phase Inlet Interface Water Cell Liquid phase Droplet Relative
N r k m C n V
α
m_ M_
Sh Re Sc d D
ρ v
μ
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.pnucene.2020.103243.
References
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