Hydrodynamic performance evaluation of a novel eductor liquid–liquid extractor using CFD modeling

Accepted Manuscript Title: Hydrodynamic Performance Evaluation of a Novel Eductor Liquid–Liquid Extractor Using CFD Modeling Authors: Mostafa Hosseinzadeh, Ahad Ghaemi, Mansour Shirvani PII: DOI: Reference:

S0263-8762(17)30418-5 http://dx.doi.org/doi:10.1016/j.cherd.2017.08.006 CHERD 2781

To appear in: Received date: Revised date: Accepted date:

17-5-2017 28-7-2017 7-8-2017

Please cite this article as: Hosseinzadeh, Mostafa, Ghaemi, Ahad, Shirvani, Mansour, Hydrodynamic Performance Evaluation of a Novel Eductor Liquid–Liquid Extractor Using CFD Modeling.Chemical Engineering Research and Design http://dx.doi.org/10.1016/j.cherd.2017.08.006 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Hydrodynamic Performance Evaluation of a Novel Eductor Liquid–Liquid Extractor Using CFD Modeling Mostafa Hosseinzadeha, Ahad Ghaemia, Mansour Shirvania,* a

School of Chemical Engineering, Iran University of Science & Technology,

Narmak, Tehran, Iran *

Corresponding author. E-mail: [email protected]; PO Box: 16846-13114;

Tel.: +98-2177240496; Fax: +98-2177240495.

Graphical abstract

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Highlights:  Hydrodynamic aspect of a novel eductor-LLE system was evaluated by CFD modelling.  Some advantages of eductor-LLE system are no moving part and reduced contact volume.  The standard high surface tension water-toluene system was used in experiments.  The mixing and mixing energy efficiencies were studied as the eductor performance.  Effects of jet velocity as well as various non-dimensional parameters were studied.

Abstract The hydrodynamic aspect of a novel eductor type contacting device for liquid–liquid extraction (LLE) system has been evaluated by computational fluid dynamics (CFD) modeling. CFD results were validated by droplet rise velocity and dispersed phase holdup in water/toluene system; errors were 20.7% and 15.4%, respectively. The results of CFD simulation have shown that the existence of venturi above the nozzle-jet improves the mixing due to extension of mixing region. Educator mixing performance was investigated by the effects of the parameters: jet velocity, the throat to nozzle area ratio (At/An), the column to nozzle diameter ratio (Dc/Dn), the projection ratio (Ltn/Dt), and two phases flow ratio (Qc/Qj) on the dispersed phase holdup, the suction ratio (Rs), the mixing efficiency (ηm) and the mixing energy efficiency (ηe). A new efficiency named “overall efficiency” was defined as ηo=ηm.ηe to determine the optimum operation and design condition of the eductor. The values of important parameters were determined as a) the jet velocity less than 2 m/s; b) At/An around 100; c) the ratio of Dc/Dn<50; d) 1
Keywords: Liquid-Liquid Extraction; Eductor; CFD Modeling; Suction Ratio; Mixing Efficiency; Mixing Energy Efficiency.

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Nomenclature List of symbols An

Area of Nozzle, m2

As

Suction Area, m2

At

Area of Throat, m2

C1, C2, C3

RNG k–ϵ Turbulence Model Coefficient

Dc

Diameter of Column Diameter, mm

Dn

Diameter of Nozzle, mm

Dt

Diameter of Venturi Throat, mm

F

Body Force, N/m3

fdrag

Drag Force, N

Flift

Lift Force, N/m3

Fwl

Wall Lubrication Force, N/m3

g

Acceleration due to Gravity, m/s2

Kpq

Fluid-Fluid Exchange Coefficient

Lt

Length of Throat, mm

Ltn

Distance between Throat and Nozzle Tip, mm

P

Pressure, Pa

Pnozzle

Absolute Pressure at Nozzle, Pa

Pventuri-throat

Absolute Pressure at Throat, Pa

Pventuri-outlet

Absolute Pressure at Diffuser Outlet, Pa

Qc

Flowrate of Continuous Phase Fluid, m3/s

Qj

Flowrate of Jet Fluid, m3/s

Qs

Flowrate of Suction Fluid, m3/s

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Re

Reynolds Number

Rs

Suction Ratio

RΔp

Head Ratio

Vd

Droplet Rise Velocity, m/s

Vdr,k

Drift Velocity for Phase k, m/s

Vj

Jet Velocity, m/s

Vm

Mixture Velocity, m/s

Vmax

Jet Velocity at Maximum Jet Length, m/s

Vp

Velocity of the Primary Fluid, m/s

Vpq

Slip Velocity Between Phases p and q, m/s

Greek letters αk

Volume Fraction of Phase k

ηe

Energy Efficiency of Eductor

ηm

Mixing Efficiency of Eductor

μp

Viscosity of the Primary Fluid, kg/ms

μp

Viscosity of the Secondary Fluid, kg/ms

ρj

Density of the Jet Fluid, kg/m3

ρm

Density of the Mixture, kg/m3

ρp

Density of The Primary Fluid, kg/m3

ρq

Density of the Secondary Fluid, kg/m3

σD

Prandtl Dispersion Number

τp

Particle Relaxation Time, s

υm

Mixture Turbulent Diffusivity, m2/s

φ

Dispersed Phase Holdup

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Abbreviations ASM

Algebraic Slip Mixture

CFD

Computational Fluid Dynamics

EFCE

European Federation of Chemical Engineering

Eff.

Efficiency

Exp.

Experimental

LLE

Liquid–Liquid Extraction

RNG

Re-Normalization Group

Sim.

Simulation

1. Introduction Liquid-liquid extraction (LLE) is one of the wide used separation techniques in petroleum, food, hydro-metallurgy, and chemical industries, because of its simplicity, good mass transfer rate, and wide scopes (Kislik, 2012). LLE is the combination of two basic processes: mixing and separation. The jet flow is one of the mixing processes that may be used in LLE. When a liquid is injected into another immiscible liquid then the droplets form, periodically, at low injection velocities. This is called dripping regime. By increasing the injection velocity, jetting regime appears and the length of jetting effect reaches a highest length at Vmax, where by more increase of injection velocity the jet length decreases. At higher injection velocities, the jet formation disappears, and very small and non-uniform droplets are formed. It’s called atomization regime (Clift et al., 1978). Between initial velocity of jet formation and Vmax, axisymmetric capillary waves are observed and droplets are formed uniformly, while for higher velocities the jet breaks up non-uniformly (Kitamura and Takahashi, 1986). In jet mixing systems, the jet momentum is utilized for intensive mixing, while agitation and continuous

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renewal of the interfacial area between the phases appears (Acharjee et al., 1978). The jet formation has been studied with aim to predict the length of the jet and the size of the droplets (Ahmed et al., 2013; Bright, 1985; Das, 1997; Kasyap et al., 2009; Ng et al., 2008; Parmar et al., 2015). Homma et al. (2006) performed numerical studies on the breakup of an axisymmetric liquid jet into other immiscible liquid phase and showed that there are three breakup modes including: dripping, jetting with uniform droplets, and jetting with non-uniform droplets, which can be distinguished by Weber number and viscosity ratio. For application of impinging jet technique in mixing purposes a patent was published by Carver et al. (1956). Treybal (1951) presented some industrial jet mixer applications like the Barber jet and the Elbow jet in oil refinery, nozzle and orifice mixers in crude oil desalination, DuoSol crude mixer and injector mixers in refining lubricating oils, which have good mixing results and high extraction performances, but they have some emulsion formation problems and need more time during settling down. However, no data are available on their mixing performance. The use of jet stream regime in its single form is not recommended for LLE, due to high axial mixing and it’s limited mass transfer achievement (Treybal, 1980). Recently, jet injection devices has become more interested by many researchers (Battal et al., 2003; Cavadas et al., 2012; Choo et al., 2007; Hu et al., 2009; Ibrahim et al., 2010; Inamura and Shirota, 2014). They have proposed some new designs. Tamir (1994) compared different LLE devices and reported that the impinging streams can enhance overall volumetric mass-transfer coefficients significantly. Mukherjee et al. (1988) studied on different energy losses of a liquid-jet ejector and presented some correlations to predict the pressure drop and the holdup on the basis of the physical and dynamic variables of the system. Asai et al. (1988) studied mass transfer of a cocurrent laminar flow jet apparatus in several dispersed phase systems, with different liquids including: methyl-isobutyl-ketone, n-butanol, toluene, cyclo-hexanol and water. They presented two correlations based on physical properties of the systems. Molaei-Dehkordi

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(2001) presented an impinging streams contactor with two jetting flows for extraction of succinic acid in aqueous solution by n-butanol. He reported higher overall volumetric masstransfer coefficients. Also, he presented a two-impinging-jets reactor for solid–liquid enzyme reactions and evaluated its hydrodynamic behavior by Markov chains model (MolaeiDehkordi, 2006). Saien and Moradi (2012) studied on extraction performance of butanol– succinic acid–water, which is a low interfacial tension LLE system, in a two-impinging-jets contacting device with a high jet velocity and reported 58–96% extraction efficiency. AbdelAziz et al. (2013) studied on removal of heavy metals from aqueous solutions by a jet loop contactor and reported a dimensionless correlation for calculation of mass transfer coefficient. A favored method of jet flow in mixing of two fluids is the use of ejectors. Ejectors are used in the fields of civil, mechanical, chemical and petroleum industries for suction, elevation and mixing of liquids, gases or even granular solids (Neto and Porto, 2004). The ejector mixing technique have been increasingly used in chemical and biochemical processes in gas-gas, gasliquid, and gas-liquid-solid systems (Havelka et al., 1997). Also, it is used for waste treatment of liquid-liquid systems (Garcia-Salas and Cotera-Flores, 1995). The use of ejectors as a gasliquid mixing device has been reported to give higher mass transfer rates than conventional contactors (Mandal et al., 2005), and higher rates of reaction (Leuteritz et al., 1976). The ejector technique can be used in liquid-liquid extraction due to its favorable mass transfer and mixing ability (Moresi et al., 1983; Yadav and Patwardhan, 2008). The operating principle of the ejectors is based on high kinetic energy that produces local low-pressure zones, resulting in entrainment of a secondary flow (Kandakure et al., 2005). Acharjee et al. (1978) used an ejector device to study water/n-butanol and water/methyl ethyl ketone systems, and presented some correlations between different physical and hydrodynamic variables to predict the film capacity coefficients of mass transfer. Rajagopalan et al. (1994) developed an air-pulsed ejector mixer settler for LLE application in nuclear industries. They

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reported high extraction efficiency which can be used for separation of one or more solutes from feed solutions. Suresh et al. (2004) studied uranium-thorium separation by a countercurrent ejector mixer–settler LLE device and reported a good performance of its extraction. Nosratinia et al., (2010) studied the mass transfer coefficient under jetting conditions in a liquid-liquid extraction of n-butanol/succinic acid/water system and presented a correlation for prediction of mass transfer coefficient. Computational fluid dynamics (CFD) modeling can be used, also, to understand the hydrodynamic characteristics and flow patterns in a LLE device. The studies have shown that CFD is a powerful tool in the quest to understand the mixing of two liquid phase, as it can be used to study the effect of different entrance and agitation problems (Balasubramanian et al., 2003; Dakshinamoorthy et al., 2006; Torre et al., 2008). In an eductor LLE device the CFD method provides a basis for quantifying the effects of operating conditions, using Navier– Stokes equations as well as the continuation equation, to be simulated by a finite volume method. Many researchers applied the CFD modeling methods across the ejectors to characterize the rate of gas entrainment in gas-liquid systems (Kandakure et al., 2005; Mukherjee et al., 1988). Several researchers have shown that CFD can be used for predicting the phenomena during the investigation of ejector performances (Fernandez, 2001; Giacomelli et al., 2016; Hakkaki-Fard et al., 2015; Hanafi et al., 2015; Lee et al., 2016; Marynowski et al., 2007; Palacz et al., 2017; Rusly et al., 2005; Yuan et al., 2015) and liquid jet in liquid phase systems (Bhattacharjee et al., 2017; Carcasci et al., 2016; Sandhya and Tide, 2017) as well as liquid-liquid extraction systems (Amokrane et al., 2016; Attarakih et al., 2015; Onink et al., 2010; Ye et al., 2016; Zou et al., 2016). In a CFD simulation the local pressure, flow rate and momentum associated with the fluids flow are calculated completely, while they are almost very difficult to be determined experimentally.

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Eductor is an especial design of ejectors, shown inn Fig. 1, which can serve as a liquid mixing device. It consists of a venturi located in front of a nozzle inside a column (Ludwig, 1984). The dispersed phase flow was provided from the bottom through a nozzle, entering into the venturi, and the continuous phase is the higher density phase which enters from the top section of column. When the flow leaves the venturi, a mixture of dispersed phase droplets and continuous phase is obtained in the venturi tube, which may cause a slow recirculation of continuous phase outside of the venturi. The pressure differential between the venturi inlet and the nozzle tip provides the driving force for entrainment of the continuous phase suction. The flow exiting from venturi is coaxial-flow or froth-flow.

Fig. 1. Schematic of Eductor

Some disadvantages of conventional contactors such as large space requirements, sealing and corrosion problems, and high energy input requirements, are the main reasons for developing new LLE devices which have higher efficiency with lower limitations (Sahu et al., 2016). Using of an eductor mixing devise in LLE gives some advantages such as: no requirement for moving parts; less corrosion and sealing problems; less contact time; provision of high interfacial area and higher overall mass transfer coefficients and reduced contactor volume, etc. The main objective of the present work aims at obtaining quantitative descriptive data and investigating by CFD modeling, the effects of geometry and the other design parameters of eductor mixing device; such as: venturi existence or no existence effect, throat to nozzle area ratio, column to nozzle diameter ratio, throat-nozzle distance to nozzle diameter ratio and two phase flow rates ratio. For this purpose, a novel eductor liquid–liquid extractor is designed, constructed and tested.

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2. Material and methods 2.1. Experimental Details Design of the column-type liquid-liquid contactors has been generally based on the knowledge of holdup, axial dispersion coefficients of both phases, interfacial area and coefficients of interfacial mass transfer. Since no design methodology for eductor LLE devices is available in the literature; thus, in this work we have used data extracted from several jet LLE devices, liquid gas ejectors and impinging stream reactors (Havelka et al., 1997; Kandakure et al., 2005; Moss, 1977; Neto and Porto, 2004; Palacz et al., 2017; Tamir, 1994). To achieve the aims of the work we provided a laboratory scale eductor LLE device, designed and tested for preparing data required for validation of CFD results. The following procedures were used in designing our eductor LLE device: 1 - In determining the diameter of the column the flooding velocity of the continuous phase of a water/toluene multistage column extractor was used (0.000482 m/s) (Kirou et al., 1988). According to this procedure the column diameter was calculated equal to 14 cm, for 15 L/hr of continuous feed flow rate, with the safety consideration of 70% of the above mentioned flooding velocity. 2 - The ratio of column height to diameter of jet LLE devices is proposed to be in the range of 0.5 to 3 (Tamir, 1994). Thus, the height of our column should be available between 15 to 60 cm. 3 - According to the literature (Tamir, 1994) the upper and lower limitations of nozzle diameter are 0.1 mm and 5 mm, respectively, to ensure that the jetting regime is attained. Thus, we selected 0.5, 1.0, 2.0 and 3 mm values in this respect. 4 - In order to have different ratios of venturi throat to nozzle areas we selected the values of 10, 20 and 30 mm of venturi throat diameters (Dt).

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5 - The projection ratio (throat-nozzle distance to throat diameter ratio: Lnt/Dt) is an important parameter in designing ejectors. The conventional values are 0.4 to 4.0 (Yadav and Patwardhan, 2008). In our design the range of variations for the above parameter is 0.33 to 5. On the other hand the best dispersion efficiency is achieved provided that the liquid jet breaks up at venturi throat (Cunningham, 1974). If the jet disintegration occurs before reaching to the venturi throat, then the friction energy loss resulting from the mixture flow in the region between the throat and the jet break up cross section will increase (Havelka et al., 1997). According to Asai et al. (1988) and Christiansen and hixson (1957), for a nozzles in the range of 1 to 2 mm diameter, the maximum jet length of toluene in water is about 10 to 35 mm. So, the length of nozzle to venturi through should be 10 to 30 mm. 6 - Concerning to the venturi throat length, the important notations are that the increase of throat length results in: a) increase of pressure drop inside the venturi, b) decrease of suction of continuous phase into the venturi and c) decrease of mixing energy efficiency (Bhutada and Pangarkar, 1987). For the above reasons we have preferred to select the throat length as less as possible, i.e. equal to zero. 7 - The divergence angle at discharging section of venturi is recommended of 7 degrees, for appearance of uniform velocity profile in this section (Havelka et al., 1997). According to Harrell (1977), the convergence angle is not an important parameter. However, it is important that this angle be selected such that the nozzle area does not prevent from flowing of continuous phase into the venturi. In our testing apparatus the overall length of venturis is 100 mm and the convergence angle is 45 degrees. In Fig. 2, schematic flow diagram of the experimental set-up is shown. The system includes two input and two output streams, while two flow meters were used for input streams. Another flow meter was used for continuous phase output stream for enabling the control of the position of the interphase of the two phases at a fixed level in top section of the column during experiments. Controlling of the interphase height was done manually by manipulating the output stream flow rate of the continuous phase. Separation of two phases occur at the top of 12

the column. Actually, the dispersed phase is entering the column via the nozzle at bottom as the lighter phase. And the continuous phase enters from the top. Thus, the dispersed phase flows into the venturi and drags some amount of the continuous phase into the venturi. This results in some circulation of continuous phase around the venturi. The venturi was made of polyethylene and the nozzles from stainless steel material. Also, the glass material was used for cylindrical column to make the inside flows visible. The water/toluene system is used in this studies, which is a high surface tension standard system in LLE research literature, proposed by the European Federation of Chemical Engineering (EFCE) (Gebauer et al., 2016). The continuous phase is deionized water. Toluene is prepared from Kimia Azma Company, Tehran, Iran. For prevention from the errors resulting from initial unsaturation of the tow liquids, used in the experiments, the two phases were made saturated from each other before starting the tests. Image processing method for analyzing the video films taken for measuring the rising velocity of droplets was used in the experiments. The region selected for taking video records was the exiting region after venturi on its top. Also, for measurement of droplet sizes photos were taken from the same region. The specifications of the camera used in the experiments for preparing image processing of the data are as: a) the photo quality was 4160×3120 pixels; b) the video quality was 1920×1080 pixels with 60 frames per second. Holdup is the volume fraction of dispersed phase to the total volume of liquids inside the column under the interface between the phases, appearing at the top of the column. Measurement of holdup was done by stopping the flow rates of both phases simultaneously and letting the phases separate perfectly with change of the position of interface height at top of the column. In this way, with sufficient time given for rising up of all of the drops the accumulated dispersed phase at the top of column will show the amount of the overall holdup of dispersed phase at all the length of column.

Fig. 2. Experimental set-up 13

The details of eductor geometry and operation conditions are given in Tables 1 and 2.

Table 1. Geometrical details of eductor (named as ED-Dn-Dt-Ltn in this paper)

Table 2. Operation condition for experimental and CFD modeling

2.2. CFD modeling 2.2.1. Numerical description In CFD modeling, the Eulerian mixture model is used due to high droplet concentration of dispersed phase and it is recommended for co-axial flow in ejectors (Yadav, 2008). In Eulerian mixture model algebraic expressions are used for calculation of the relative velocities and the equations for multiphase flows are derived in mass-weighted average form. The mixture momentum equation is then derived as:   m vm  . m vm vm  m  .( m   Tm )  . Dm   m g t n               K pq  v p  v q   m pq v pq  mqp v qp    F lift ,q  F wl ,q       i 1 

(1)

The lift force, Flift, defined by Moraga et al. (1999), is created due to density difference between the two phases and the wall lubrication force, Fwl, defined by Tomiyama (1998) are used since the jet flow is relatively near to the wall of the venturi. The momentum exchange between the phases is based on the fluid-fluid exchange coefficient (Kpq), defined as: K pq 

 pq fd p Ai

(2)

6 pq

Where,

 pq   p  p   q q

(3)

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 pqd p 2  pq  18 pq

(4)

 pq   p  p   q q

(5)

f 

CD Re 24

Re 

(6)

 pqd p v p  vq   pq

(7)

0.687 24 1  0.15Re  / Re Re  1000 CD   0.44 Re  1000 

(8)

Also, the volume fraction equations are solved only for the dispersed phases. The algebraic slip mixture (ASM) model was used. It accounts for the relative velocity between the primary and secondary phases as the interfacial momentum exchange term. Since the recirculation of continuous phase flow is appearing around the venturi, thus, the Standard k–ϵ model can’t be used because during simulations it confronts with converging problems. For flows created by dispersed phase streams the RNG k–ϵ turbulence model is shown to give much better results (Manninen et al., 1996). Also, it is shown by Orszag et al. (1993), that for recirculation flows, similar to our problem, the RNG k–ϵ turbulence model renders less stability problems. The RNG k–ϵ turbulence model is defined as (Shih et al., 1995):    k    kvi     k eff k   Gk  Gb    YM t xi x j  x j 

     vi    t xi x j

2      eff    C1  Gk  C3 Gb   C 2    R  x j  k k 

(9)

(10)

Where, Gk is the generation of turbulence kinetic energy; Gb is the generation of turbulence kinetic energy resulting as the effect of buoyancy; Ym is the contribution of the fluctuating dilatation in compressible turbulence to the overall dissipation rate. The quantities ak and ae are the inverse effective Prandtl numbers for k and ε, respectively. And likewise, they are user-

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defined source terms. The values of C1, C2, C3, as well as the dispersion Prandtl number are 0.0845, 1.42, 1.68, and 0.75, respectively.

2.2.2. Computational domain Two-dimensional axisymmetric geometry with quadrilateral-meshing scheme, composed by Gambit 2.4 version was used. For saving a great deal of run time during CFD simulations, it was assumed that the effects of ring type exiting geometry of output streams at the top and bottom of the column on flow patterns around and inside the venturi and educator mixing performance are negligible. This enabled authors to use 2D instead of 3D CFD simulations. Such an assumption is conventions among all the other researchers who are engaged in simulating symmetrical geometries of LLE systems (Zhang et al., 2013; Giacomelli, et al. 2016; Onink et al., 2016). For prevention of converging problems, the smaller grid spacing, less than 0.1 mm, was used near the nozzle region, due to the intensive gradients that appear in this region. After determining the mesh independency in trial simulations, the number of mesh elements were defined as 120000. In order to reduce the computational errors at high Reynolds numbers, the standard wall functions were used near the wall regions. The boundary conditions are shown in Fig. 3.

Fig. 3. Schematic of geometry

In the procedure of CFD simulations the physical properties of pure water and toluene was taken at 25 °C and in the same way the experimental tests were done. The value of surface tension used in calculations was 0.0376 N/m. No-slip boundary condition was assumed at the walls. The second order upwind discretization scheme was used for the momentum, volume fraction, turbulent kinetic energy and turbulent energy dissipation rate calculations. SIMPLE algorithm was used for the pressure–velocity coupling. The values of relaxation factor for the pressure, momentum and volume fractions all were equal to 0.2. Also, the value of relaxation factor for slip velocity was 0.1, for the turbulent kinetic energy and turbulent energy dissipation

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rate were 0.05. About 2 days were required to obtain the converged solution for each run of CFD calculations. The accuracy of CFD simulation was evaluated by following error calculation equation: error% 

xCFD  x Exp .

(11)

x Exp .

In CFD calculations the velocity of drops was calculated averagely for dispersed phase where exiting venturi. Indeed it is assumed that the droplet rise velocity is the calculated phase velocity exiting the venturi.

2.3. Eductor performance evaluation The main geometrical affecting parameters in an eductor are: throat area ratio (area of throat/area of nozzle: At/An); angle of converging and diverging sections of the venturi; throat aspect ratio (length of throat/diameter of throat: Lt/Dt); projection ratio (distance between nozzle tip and entry to throat/diameter of throat: Ltn/Dt), and suction chamber area ratio (the entrance area of venturi/nozzle area: As/An). According to Yadav and Patwardhan (2008), it is important that the mixing conditions be started from the input cross section of the throat of venturi. An eductor performance is evaluated by dimensional analysis using follow items: a) Suction Ratio (Rs): the suction ratio is an important parameter that affects the flow pattern inside the ejector (Zhang et al., 2013). According to (Silvester, 1961) the suction ratio in eductor systems can be defined as the ratio of continuous phase flow rate, sucked to the venturi to the dispersed phase flow rate from nozzle. It is defined as:

Rs 

Qs

(12)

Qj

b) Head Ratio (RΔp): according to Fig. 1, the head ratio is defined as (Silvester, 1961):

RP 

Pventurioutlet  Pventuriinlet 

Pnozzle  Pventurioutlet 

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(13)

c) Mixing Efficiency (ηm): the mixing efficiency, which is used as a characterizing parameter for defining the optimum condition of dissipated power during mixing is defined by Silvester (1961), as:

m  Rs RP

(14)

The mixing efficiency is the most important parameter in ejectors and the optimum configuration for ejector design should be evaluated by mixing efficiency (Neto and Porto, 2004). d) Mixing Energy Efficiency (ηe): the energy efficiency of mixing is the ratio of power imparted to the secondary fluid to the power of the fluid coming out of the nozzle (Bhutada and Pangarkar, 1987). It is defined as:

 e  Pventurioutlet  Pventurithroat Qs

 2 3   j Dn V j  8 

(15)

The higher the value of suction ratio (Eq. 12) is equivalent to better mixing of the two phases. But one should be aware that the more value of suction ratio may result in increased head ratio (Eq. 13) and reduced mixing efficiency and mixing energy efficiency. In fact Equations (14) and (15) are related to each other by Cv of the nozzle and venturi inlet and the frictional loss across the venturi. This aspect should be brought about clearly. The difference between the two eta values highlights friction. This difference is also important parameter and needs to be highlighted.

3. Results and Discussion 3.1. Validation Fig. 4 shows a comparison between CFD and experimental date for droplet rise velocity and dispersed phase holdup. The average errors according to Eq. 11 are 20.7% and 15.4%, for

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droplet rise velocity and dispersed phase holdup, respectively. In the lower values of jet velocity, Fig. 4 shows that droplets have lower rise velocity than CFD modeling results. This can be considered as venturi wall capillary effect on droplets motion, which can’t be considered in CFD modeling. Fig. 4 shows that the CFD is relatively acceptable in predicting of hydrodynamics of eductor LLE device.

Fig. 4. Validation of experimental and simulation date (φ: the dispersed phase holdup and Vd: the droplet rise velocity)

In LLE systems it is well known that the holdup of dispersed phase decreases with increase of droplet size (Kirou et al., 1988). This is also inferred from Fig. 4, in which it is seen that with increase of jet velocity the holdup increase and the droplet rise velocity decreases. These conclusions are well compatible with each other. That is with increase of jet velocity the droplet sizes reduce, resulting in increase of holdup and decrease of rising velocity of drops.

3.2. Venturi Existing Effect The effect of the venturi existing in front of nozzle on flow field distribution is shown in Fig. 5. In this figure, for all cases (a to d), the left side figures are for the condition of no venturi placed in front of nozzle and the right side figures are for the condition of existence of venturi. It is clearly visible from all the figures that in the condition of venturi, existing the recycling of continuous phase appears in a wider length in the column. That is, without the venturi a limited length of mixing zone appears at a distance from the nozzle. But, for the case of venturi existing a recycling of continuous phase appears around the venturi. Also, it is well distinguished from the figures that in the condition of venturi existence a suction of continuous phase appears from the lower sections of the column. Therefore, it is concluded that existence of venturi helps in better mixing condition.

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Fig. 5. The effect of the venturi existing in front of the nozzle: Velocity Contours: a) Vj= 1 m/s, ED-1-30-20, b) Vj= 1 m/s, ED-2-20-20 Velocity Vectors c) Vj= 1 m/s, ED-1-30-20, d) Vj= 1 m/s, ED-2-20-20 (see Table 1 for eductor configurations).

3.3. Jet Velocity Fig. 6 shows the CFD results for variations of holdup, suction ratio (Rs), mixing efficiency (ηm) and mixing energy efficiency (ηe) with jet velocity for various geometrical configurations of eductor. The corresponding configurations are given in Table 1. Firstly, it is predictable that holdup rises with increase of jet velocity (Fig. 6-a). Also, the results in Fig. 6-b show that Rs decreases by increasing of jet velocity, with higher slopes in the lower values of jet velocity, such that it becomes almost horizontal at high values of jet velocity. Concerning to the same concept investigated in liquid-gas and gas-gas ejectors, the CFD results had shown that there is almost a constant value of Rs at all values of jet velocity (Kandakure et al., 2005). On the other hand, Fig. 6-c shows that ηm increase with increase of jet velocity, but ηe (Fig. 6-d) decreases. At this point an important argument is in order. That is, while the ηm increases in a monotonic manner with increase of jet velocity, but the Rs and ηe are decreasing sharply at lower jet velocities and the continuation of decrease in these parameters appear with much lower slopes. According to fig. 6 for ηm, Rs and ηe one can see that the value of around 2 m/s for jet velocity is a boundary limit at which one can decide if it is better to operate process at higher values or lower values of this dividing limit. At lower values of 2 m/s of jet velocity one can take the benefit of higher values of Rs and ηe, but in expense of lower mixing efficiency values. On the other hand, the high values of jet velocity correspond with acceptable increase

20

of mixing efficiency with a trivial decrease of Rs and ηe. However, due to the fact that at high values of jet velocity the risk of emulation formation is possible, then one may prefer to operate jet velocities lower than 2 m/s. At this region although that the mixing efficiency is not high but the values of Rs and ηe are sufficiently high.

Fig. 6. Effect of jet velocity on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, and d) Energy efficiency in different eductor configuration (see table 1).

3.4. Throat to Nozzle Area Ratio (At/An) Fig. 7 shows the holdup, suction ratio, mixing efficiency and mixing energy efficiency for different throat to nozzle area ratios (At/An). Concerning to Fig. 7-a, the holdup is higher in low At/An values. This is due to the low values of sucked continuous phase, which corresponds to higher values of dispersed phase holdup. In another description, when the value of At/An is low the value of Rs is, also, low (Fig. 7-b). Fig. 7-b shows that at low values of At/An the increase of suction ratio (Rs) is very sharp. An appropriate argument in this respect is that as the jet flow leaves the nozzle, it passes through the center of the throat, while the sucked continuous phase is flowing into the annular space. Thus, the momentum transfer by the jet flow depends on the cross-sectional area (At) and the velocity of the jet depends on the nozzle area (An). In low At/An ratios, venturi throat area is low and the nozzle flow can’t suck the continuous phase into the venturi appropriately. Thus, with increase of At/An ratio, the Rs increases sharply. Also, Fig 7-b infers that at higher At/An ratios a maximum point appears, after which the negative slope of the curve is much lower than its positive slope at low values of At/An.

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The argument for describing the low negative slope of the Rs curve at higher values of At/An may be done with the consideration of the fact that with increase of throat area the suction pressure inside the venturi will decrease, because of reduction in velocity through the throat area, which is in accordance to the Bernoly equation. Fig. 7-b shows that the maximum suction ratio is around At/An = 100. In fact the similar phenomena is also reported for liquid-gas ejectors, i.e., a maximum point appears in the curve of suction ratio versus At/An, which is around 2.8 to 9.0 (Bando et al., 1990; Kandakure et al., 2005; Bhutada and Pangarkar, 1987; Rylek and Zahradnik, 1984). Concerning to Fig. 7-c it is seen that the mixing efficiency (ηm) increases in a monotonic trend with At/An. Fig. 7-d shows that the variations in mixing energy efficiency (ηe) appears with high negative slope at lower values of At/An ratio but the slope reduces sharply at higher At/An ratio values. According to the CFD simulation results, given in Fig. 7, we can select the most appropriated value for At/An around 100. An argument regarding the above selection is that at higher values of At/An, although that the mixing efficiency is still increasing and the mixing energy efficiency is not decreasing severely, but since the suction ratio is starting to decrease, thus we prefer to design and operate the equipment at around the maximum points in suction ratio curve, around the value of 100 for At/An.

Fig. 7. Effect of At/An ratio on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency in different jet velocities (Vj= 0.5, 1, 2, & 5 m/s).

3.5. Column Diameter to Nozzle Diameter Ratio (Dc/Dn) Fig. 8 shows the effect of variations of Dc/Dn on the parameters: dispersed phase holdup, suction ratio, mixing efficiency and mixing energy efficiency. Fig. 8-a shows a severe reduction in holdup at lower values of Dc/Dn. This can be explained by noticing that with

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increase of the diameter of the column the continuous phase content inside the column increases sharply, while the dispersed phase content remains almost constant. In Figs. 8-b, 8-c and 8-d we notice a slow variations of suction ratio, mixing efficiency and mixing energy efficiency with increase of Dc/Dn. However, the suction ratio is decreasing while the other two show increasing trend. The increasing trend in mixing efficiency and mixing energy efficiency can be explained with the consideration that, when the column diameter increases then, there would be more cross sectional area around the venturi for continuous phase recirculation. This in turn results in reduction of pressure drop for recirculation of continuous phase and increase in energy efficiencies. From the results shown in Fig. 8, one can reach to an important decision in selecting the appropriate holdup for better operation/design of the extractor. i.e., since the sharp holdup reduction in low values of Dc/Dn shows that high values of Dc/Dn is not appropriate. On the other hand, selection of very low values of Dc/Dn corresponds to attainment of lowest values of mixing efficiency and mixing energy efficiency. Thus, we conclude that the amount of Dc/Dn less than 50 is more appropriate. This is because the higher values of holdup is important in LLE systems

Fig. 8. Effect of Dc/Dn on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency, in different jet velocities (Vj= 0.5, 1, 2, & 5 m/s).

3.7. Projection Ratio (Ltn/Dt) The projection ratio is the ratio of distance between the nozzle and throat to throat diameter (Lnt/Dt). The effect of this parameter on dispersed phase holdup, suction ratio, mixing efficiency and mixing energy efficiency are shown in Fig. 9, respectively. Fig. 9-a shows that the holdup decreases with increase of projection ratio. In the same way the suction ratio and mixing

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efficiency are reducing with increase of projection ratio (Fig. 9-b and Fig. 9-c). However, Fig. 9-d shows that the mixing energy efficiency increases with increasing of projection ratio, but with higher slope at lower projection ratios. Therefore, in order to select an appropriate value for projection ratio one can infer that a difficult problem is confronted. That is, at low projection ratio the holdup and mixing efficiency are giving higher values, but on the other hand at this range of projection values the mixing energy efficiency is severely low. This makes the approach to final decision somehow difficult. In order to resolve this problem, the Fig. 9-e is provided with the idea of determining the variation of product of mixing efficiency and mixing energy efficiency with At/An. This is called as the overall efficiency. Fig. 9-e presents the overall efficiency curve. It is seen that a maximum point appears around the values between 1 and 2 of projection ratio. Therefore, this can be considered as the optimum projection ratio to be selected for the eductor LLE device, since it includes both increasing and decreasing trends of these two efficiencies.

Fig. 9. Effect of Lnt/Dt on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Mixing energy efficiency in different eductor configuration.

3.7. Two phase ratio Fig. 10 shows the effect of two phase ratio parameter on the dispersed phase holdup, suction ratio, mixing efficiency, and mixing energy efficiency. It is seen that the effect of this parameter is trivial on the holdup and suction ratio (Figs. 10-a and 10-b), However, the other two figures show both of the efficiencies are decreasing with increase of the two phase ratio. On the other hand, the slopes of decreasing are varying with variations in two phase ratios.

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Fig. 10. Effect of Lnt/Dt on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency in different jet velocity (Vj= 0.5, 1, 2, & 5 m/s).

5. Conclusions In this work, hydrodynamic aspect of application of eductor in LLE systems on mixing performance is investigated. The experimental set up designed and tested for the effect of geometrical and operational parameters. In order to improve and extend the results of experimental investigations, CFD simulations were also done on the eductor LLE system. In the first stage the CFD model is validated by the droplet rise velocity and the dispersed phase hold experimental data. The overall conclusions are as: 1. As of the most important concluding remark, it was found that the existence of venturi in front of the jet flow helps in extension of mixing region inside the column. Actually, in the literature of jetting flow processes (without venturi) there is no definition for suction ratio, mixing efficiency and mixing energy efficiency. 2. The low jet velocities result in higher suction ratio and mixing energy efficiency. But, it affects mixing efficiency inversely. So, the appropriate jet velocity is recommended as 2 m/s. 3. Concerning to the effect of throat to nozzle area ratio (At/An) it is concluded that mixing efficiency increases with increase of At/An, but the mixing energy efficiency decreases. However, the CFD results of suction ratio curve show a maximum point around the value of 100 for At/An. Therefore, this can be considered as the optimum point. 4. Another important affecting geometrical parameter is the ratio of column diameter to nozzle diameter (Dc/Dn). Both of the mixing efficiency and mixing energy efficiency are increasing with increase of Dc/Dn. However, the dispersed phase holdup severely

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decrease with increase of Dc/Dn. Therefore, for prevention of missing the higher values of dispersed phase hold up, it would be reasonable to select the ratio of column to nozzle diameter as Dc/Dn<50. 5. Concerning to the geometrical parameter of projection ratio (Lnt/Dt), the overall efficiency definition is much useful to determine the optimum value for projection ratio. The optimum value obtained by this method was between 1 and 2. 6. Comparing to the other parameter effects, the ratio of the two phases has the lowest effect on the holdup, suction ratio, mixing and mixing energy efficiencies. Both of the two efficiency parameters are decreasing (particularly at low values of two phase ratio) with increase of Qc/Qj. The eductor extractor is a new design for LLE processes. It is more reduced size in comparison to other extraction columns, without any moving parts inside it. Instead of using any moving part, jet type stream and venturi channel are used for improving two phases contacting performance inside the system. Investigation of its hydrodynamics in the first stage, and its performances in the next stage, as well as theoretical analysis and dimensional analysis for scaling purposes and etc., seem to be incentive from the view point of industrial applications.

6. Acknowledgements This work was supported by the scientific and technological department of presidential office, Tehran, Iran.

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Figures: Fig. 1. Schematic of Eductor Fig. 2. Experimental set-up Fig. 3. Schematic of geometry Fig. 4. Validation of experimental and simulation date (φ: the dispersed phase holdup and Vd: the droplet rise velocity) Fig. 5. The effect of the venturi existing in front of the nozzle: Velocity Contours: a) Vj= 1 m/s, ED-1-30-20, b) Vj= 1 m/s, ED-2-20-20 Velocity Vectors c) Vj= 1 m/s, ED-1-30-20, d) Vj= 1 m/s, ED-2-20-20 (see Table 1 for eductor configurations). Fig. 6. Effect of jet velocity on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, and d) Energy efficiency in different eductor configuration (see table 1). Fig. 7. Effect of At/An ratio on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency in different jet velocities (Vj= 0.5, 1, 2, & 5 m/s). Fig. 8. Effect of Dc/Dn on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency, in different jet velocities (Vj= 0.5, 1, 2, & 5 m/s). Fig. 9. Effect of Lnt/Dt on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Mixing energy efficiency in different eductor configuration. Fig. 10. Effect of Lnt/Dt on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency in different jet velocity (Vj= 0.5, 1, 2, & 5 m/s).

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34

Discharge

Venturi Venturi Divergence Angle

Venturi Outlet

Throat Length

Venturi Throat

Nozzle to Throat Distance

Venturi Convergence Angle Suction Liquid Flow

Venturi Inlet

Nozzle

Jet Liquid Flow

Fig. 1. Schematic of Eductor

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Continuous Phase Feed Tank (50 L)

Top Section of column

F

Column D=14 cm L=50 cm V=5 L

Flowmeter Continuous Phase Disposal Tank (20 L) Pump

Dispersed Phase Disposal Tank (20 L)

F

F

Flowmeter

Flowmeter

Fig. 2. Experimental set-up

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Dispersed Phase Feed Tank (50 L) Pump

Pressure Outlet (Dispersed Phase Discharge)

Axis of Symmetry

Velocity Inlet (Continuous Phase Entrance)

Venturi

Velocity Outlet (Continuous Phase Discharge)

Velocity Inlet (Dispersed Phase Entrance)

Fig. 3. Schematic of geometry

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0.3

0.2

0.015 0.012 0.009 0.006

0.1 0.003 0

Holdup [volume fraction]

Droplet Rise Velosity [m/s]

Vd (Exp.) Vd (Sim.) φ (Exp.) φ (Sim.)

0 0

1

2

3

Jet Velosity [m/s]

Fig.

4.

Validation

of

experimental

and

phase holdup and Vd: the droplet rise velocity)

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simulation

date

(φ:

the

dispersed

(a)

(b)

Velocity Contours (m/s) (d)

(c)

Velocity Vectors (m/s)

Fig. 5. The effect of the venturi existing in front of the nozzle: Velocity Contours: a) Vj= 1 m/s, ED-1-30-20, b) Vj= 1 m/s, ED-2-20-20 Velocity Vectors c) Vj= 1 m/s, ED-1-30-20, d) Vj= 1 m/s, ED-2-20-20 (see Table 1 for eductor configurations).

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(b) 15

ED-2-20-10

0.005

ED-2-20-20

0.004

12

Suction Ratio

Holdup [volume fraction]

(a)

ED-2-20-30

0.003 0.002

9 ED-2-20-10

6

ED-2-20-20 3

0.001 0

ED-2-20-30

0 0

1

2

3

4

5

0

1

Jet Velocity [m/s]

3

4

5

(d)

0.6 0.4 ED-2-20-10 ED-2-20-20 ED-2-20-30

0.2 0 0

1

2

3

4

Mixing Energy Efficiency

(c) 0.8

Mixing Efficiency

2

Jet Velocity [m/s]

ED-2-20-10 ED-2-20-20 ED-2-20-30

0.03 0.02 0.01

5

0 0

1

Jet Velocity [m/s]

2

3

4

Jet Velocity [m/s]

Fig. 6. Effect of jet velocity on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, and d) Energy efficiency in different eductor configuration (see table 1).

40

5

Vj [m/s] 0.5 1 2 5

0.005 0.004 0.003 0.002

(b) 15 12

Suction Ratio

Holup [volume fraction]

(a)

0.001

9 Vj [m/s] 0.5 1 2 5

6 3

0

0 0

100

200

300

400

0

100

At/An

0.8 0.6

300

(d) 0.07

Vj [m/s] 0.5 1 2 5

Mixing Energy Efficiency

Mixing Efficiency

(c) 1

200

400

At/An

0.4 0.2

Vj [m/s] 0.5 1 2 5

0.06 0.05 0.04 0.03 0.02 0.01

0

0 0

100

200

300

400

0

100

At/An

200

At/An

Fig. 7. Effect of At/An ratio on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency in different jet velocities (Vj= 0.5, 1, 2, & 5 m/s).

41

300

400

0.012 0.008

8 6

2

0

0 30

60

90

Dc/Dn

120

Vj [m/s] 0.5 1 2 5

4

0.004

0

0

150

30

(d)

0.4 0.3 Vj [m/s] 0.5 1 2 5

0.2 0.1 0 0

30

60

90

60

90

120

150

120

150

Dc/Dn

(c) 0.5

Mixing Efficiency

(b) 10

Suction Ratio

Vj [m/s] 0.5 1 2 5

0.016

120

Mixing Energy Efficiency

Holdup [volume fraction]

(a)

Vj [m/s] 0.5 1 2 5

0.12 0.1 0.08 0.06 0.04 0.02 0

150

0

Dc/Dn

30

60

90

Dc/Dn

Fig. 8. Effect of Dc/Dn on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency, in different jet velocities (Vj= 0.5, 1, 2, & 5 m/s).

42

Vj [m/s] 0.5 1 2 5

0.006 0.004 0.002 0

(b)

8 4 0

0

1

2

3

4

5

0

Lnt/Dt

0.4 0.2 0 0

1

2

3

Lnt/Dt

4

(e)

2

3

0.02 0.015

0.08 0.06 0.04 0.02

5

0 0

1

0.01 0.005 0 0

1

2

3

Lnt/Dt

4

5

Fig. 9. Effect of Lnt/Dt on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Mixing energy efficiency in different eductor configuration.

43

5

Vj [m/s] 0.5 1 2 5

0.1

Vj [m/s] 0.5 1 2 5

0.025

4

Lnt/Dt

(d)

Vj [m/s] 0.5 1 2 5

0.6

1

Mixing Energy efficiency

Mixing efficiency

(c)

Overal efficiency

Vj [m/s] 0.5 1 2 5

12

Suction Ratio

Holdup [volume fraction]

(a)

2

3

Lnt/Dt

4

5

Vj [m/s] 0.5 1 2 5

Holdup [volume fraction]

0.005 0.004 0.003 0.002

(b) 15 12

Suction Ratio

(a)

0.001

9 Vj [m/s] 0.5 1 2 5

6 3

0

0 0

1

2

3

4

5

0

1

2

Vj [m/s] 0.5 1 2 5

1

0.8 0.6 0.4 0.2 0 0

1

2

3

4

5

4

(d)

Mixing Energy Efficiency

Mixing Efficiency

(c)

3

Qc/Qj

Qc/Qj

Vj [m/s] 0.5 1 2 5

0.16 0.12 0.08 0.04

5

0 0

Qc/Qj

1

2

3

Qc/Qj

Fig. 10. Effect of Lnt/Dt on eductor mixing performance: a) Holdup of dispersed phase, b) Suction ratio, c) Mixing efficiency, d) Energy efficiency in different jet velocity (Vj= 0.5, 1, 2, & 5 m/s).

44

4

5

Tables: Table 1. Geometrical details of eductor (named as ED-Dn-Dt-Ltn in this paper) Table 2. Operation condition for experimental and CFD modeling

Table 1. Geometrical details of eductor (named as ED-Dn-Dt-Ltn in this paper) Dn (mm)

Dt (mm)

Ltn (mm)

1

10

10

2

20

20

3

30

30

45

Table 2. Operation condition for experimental and CFD modeling Vj (m/s)

Qc/Qj

0.5

0.25

1

0.5

2

1

3

2

5

4 6

46