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Experimental and CFD study on the effect of jet position on reactant dispersion performance
International Communications in Heat and Mass Transfer 36 (2009) 1096–1102
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Experimental and CFD study on the effect of jet position on reactant dispersion performance☆ A. Parvareh a, M. Rahimi a,⁎, M. Yarmohammadi a, A.A. Alsairafi b a b
CFD Research Centre, Chemical Engineering Department, Razi University, Kermanshah, Iran Faculty of Mechanical Engineering, College of Engineering and Petroleum, Kuwait University, Kuwait
a r t i c l e
i n f o
Available online 5 September 2009 Keywords: Jet Mixing Reaction Dispersion CFD Modeling
a b s t r a c t This paper reports the effect of jet position on the acid dispersion in a neutralization process. Experiments were carried out in a continuous stirred reactor and the effect of jet nozzle position on non-reactive dye dispersion at seven layouts was studied. Consequently, the neutralization reaction mixing was carried out at the best and worst positions. The results reveal that the ways that flow pushes the acid inside the tank are quite different and the neutralization performance can significantly be affected by the jet position. The Computational Fluid Dynamics (CFD) modeling was carried out in order to analyze the experimental observations. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Mixing is one of the most important concepts in chemical, oil, petrochemical and other related industries. Mixing by a jet is one of the well known methods for fluid homogenization in the liquid phase. Jet mixers are cheaper than other mixing devices such as impellers. In the jet mixing process, a part of the liquid inside the tank is drawn out and returned back via a pump, which this circulating pattern causes liquid homogenization. Many experimental researches were carried out to study mixing by a jet with or without reaction. The main aim of use of jet as mixer is to increase heat [1] and mass transfer [2]. By development of advanced computer modeling techniques such as CFD, many studies have focused on modeling of the fluid flow hydrodynamic in laboratory scales and validating the predicted results using various experimental methods. The CFD modeling of mixing in process industries has attracted a lot of attention since 1990. Ranade [3] applied the CFD modeling using the standard k–ε model for predicting the flow pattern and the mixing time in a jet mixed tank equipped with various types of jet. The fluid flow hydrodynamics established by a jet mixer using various jet configurations in a cylindrical vessel was investigated by Jayanti [4]. He tried to find a way to reduce the mixing time by eliminating dead zones in the vessel. Patwardhan [5] compared the CFD predicted and experimental results of homogenization of a sodium chloride solution in a distinct tank. He concluded that the CFD modeling can be used for
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. Chemical Eng. Dept. Razi University, Taghe Bostan, Kermanshah, IRAN. E-mail address: [email protected] (M. Rahimi). 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.08.007
predicting the mixing time, but it is poor in predicting the homogenization progress. Mixing in confined impinging jets was numerically studied in two dimensions by Devahastin et al. [6]. They determined the critical Reynolds numbers in which the flow regime changed from laminar to transitional. It was concluded that the inlet jet Reynolds numbers and the system geometry are effective in mixing by impinging jets. Zughbi and Rakib [7] used a three dimensional CFD modeling method to study the effect of the jet angle and the number of jets on the mixing time. They showed that the angle of a jet with horizon is the most important parameter for determining the mixing time. Feng et al. [8] modeled a planar-jet reactor by the CFD method, as they were using the PIV and LIF techniques for measuring the velocity and concentration fields in the vessel. The CFD predictions were validated by the measured results and the authors reported a good agreement between them. Mixing by a jet in a pilot scale storage tank was investigated by Rahimi and Parvareh [9]. In their study, the CFD method was used to model the mixing tank using three different versions of k–ε based turbulence model. They reported the effect of these models on the predicted results. Also, Berg et al. [10] compared prediction results of modeling of a turbulent jet flow using two standard, the k–ε and k–ω, two-equation turbulence models. Their computations examined for both turbulence models using two inflow boundary conditions including; a uniform inlet velocity profile and a profiled inlet velocity fitted to experimental data. Their results showed that the k–ε model with the profiled inlet velocity succeeded in predicting the main features of the flow, including the vena contracta and the saddle-shaped velocity profiles in the nearfield region. In addition, the rate of velocity decay in the far-field region was predicted in a more efficient way by the k–ε model. Rahimi and Parvareh [11] studied the mixing progress in pilot and real scales crude oil storage tank equipped with a jet and an impeller.
A. Parvareh et al. / International Communications in Heat and Mass Transfer 36 (2009) 1096–1102
Nomenclature C1, C2, Cµ constants of the k–ε model P pressure, Nm- 2 S source term U velocity vector, ms- 1 u, v, w, ui, uj mean velocity components, ms- 1 u′, v′, w′, ui′, uj′ turbulent fluctuating velocity component , ms- 1 xi,xj Cartesian coordinate, m Greek symbols ε dissipation rate of k; w kg- 1 µ laminar, turbulent and effective viscosities, Pas ρ density , kg m- 3 σk, σε turbulent Prandtl numbers for k–ε Φ,φ′ mean and turbulent fluctuating values of scalar property Γ scalar diffusion coefficient Subscript i, j component
They concluded that the angle between the jet and impeller has a significant effect on the mixing time. The flow and mixing characteristics of multiple and multi-set 3D confined turbulent round opposing jets were studied numerically by Wang and Mujumdar [12]. In their study, the air was used as working fluid and the fluid temperature variation was calculated to investigate the mixing performance. The standard k–ε turbulence model was applied for modeling the turbulency in the system. The effects of multiple opposing jet injection and multi-set opposing jet injections with/without offset on mixing time were studied experimentally and theoretically. The interactions between various physical and chemical processes such as mixing with reaction which occur over different times and length scales can have significant effects on the process performance. Therefore, these concepts should be well understood to improve the process efficiency or design a cost-effectively process. A CFD modeling of a fast acid–base neutralization reaction in a tubular reactor was carried out by Hjertager et al. [13]. A modified Eddy dissipation concept (EDC) model was found to be suitable for simulating liquid phase reactions. After comparing the model predictions with experimental data, they concluded that although such an approach is efficient and useful in understanding the reacting flow behavior, it might be inadequate to describe reactors involving with complex reactions. Submerged gas jets into a liquid bath are widely used in metal processing and thermal processes. These systems are classified as condensation and reaction jet systems [14]. The CFD simulations of non-reacting (steam-water) and reacting (SF6-Li) jets were carried out by Dahikar et al. [15] to understand the variation in plume dimensions of gas–liquid jet reactors. The effect different parameters on the plume dimensions were studied for both types of jets. The CFD modeling was carried out for the prediction of the flow pattern and its effect on the rate of condensation/reaction and plume dimensions for both the jet systems. In recent years, the CFD modeling of mixing with runaway reaction found some attentions [16]. An efficient way to quench such an uncontrolled chemical reaction by injection of an inhibitor using a liquid jet flow is very important for this type of reactive mixing processes. Dakshinamoorthy and Louvar [17] numerically studied the role of various factors on controlling of runaway reactions in a vessel
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equipped with a jet mixer. The computational model is solved using FLUENT commercial CFD code and their results demonstrated the value of using CFD modeling in situations that are experimentally prohibitive. In another study, mixing by a jet in a runaway reaction using CFD modeling was investigated by Torre et al. [18]. The authors reported a good agreement between the CFD predictions with experimental data for the jet trajectories. Another application of reactive jet mixer is in confined impinging jet reactors (CIJR )as devices for precipitation of nanoparticles because of its high mixing efficiency. Gavi et al. [19] studied mixing and reaction in CIJRs by means of CFD. The influence of operating conditions and reactor geometry on mixing was evaluated. The developed scale-up criterion for CIJRs showed that scaling up by means of CFD is a practicable way for further investigation. In a recent study, Marchisio [20] presented a CFD modeling of mixing and reaction in these devices using the Large Eddy Simulation (LES) approach coupled with a subgrid-scale mixing model, to take into account the effect of molecular mixing. They compared their experimental results with those of obtained from Reynolds-Averaged Navier–Stokes equations approach. In the present study, the effect of the jet position on the neutralization of an alkaline stream in a semi-industrial cubic stirred tank was investigated. The alkaline stream was neutralized with a sulfuric acid solution. This may has many industrial applications in final waste water neutralization process for controlling the environmental pollution. The efficient position of the jet for achieving this goal is the main challenge in this investigation. Experimental works in the pilot scale as well as CFD modeling were carried out for this purpose. 2. Theory The Computational Fluid Dynamics modeling involves the numerical solution of the conservation equations in laminar and turbulent fluid flow regimes. In this study, a 3D time-dependent CFD modeling was performed using the commercial CFD package, FLUENT6.2. The Navier-Stokes equations were applied to all of the control volumes and the k–ε RNG based equations [21] were used to describe the physics associated with the turbulence flow such as velocity field, pressure, turbulent kinetics energy and turbulent dissipation rate based on previous experience [9]. The Navier-Stokes equations for an incompressible flow with constant fluid properties in the Cartesian coordinate are as follows [22]: ∂ui =0 ∂xi
ρui
! " # — ∂uj ∂ui ∂P ∂ ∂ui −ρ u′i u′j =− + μ + ∂xi ∂xi ∂xi ∂xi ∂xj
ð1Þ
ð2Þ
In which ui, P, ρ and µ are mean velocity, pressure, density and dynamics— viscosity respectively. u′i and u′j are fluctuation component ′ and −ρ ui u′j is averaged Reynolds stress. The transport equation for scalar property Φ is " — — —# ∂Φ ∂u′ ϕ′ ∂v′ ϕ′ ∂w′ ϕ′ + SΦ + divðΦUÞ = divðΓΦ gradΦÞ + − − − ∂t ∂x ∂y ∂z ð3Þ In addition, in this study the following coefficients were used as the RNG turbulence model parameters [21]:
C1 = 1:42; C2 = 1:68; Cμ = 0:0845; σε = σk = 0:719; η0 = 4:8; β = 0:012
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Fig. 1. The continuous flow stirred tank and its detail.
Moreover, the Volume of Fluid (VOF) model was used to model the fluid free surface inside the tank. In this method, the interface between two phases, water and air, remains fixed [23]. In addition, by using this model the numerical stability can be obtained easily, because the flow field calculations are not coupled with identification of the free surface location. However, the viscous stresses and surface tension cannot be simulated accurately because the interface within each cell is not located precisely. This limitation has been largely overcome in this work by using very fine meshes close to the surface.
3. Pilot plant description In the present study, in order to validate the CFD modeling, a pilot plant rig was designed and fabricated. The experiments were carried out in a continuous flow stirred cubic tank with a volume of 125 lit made from Perspex. Water in the tracer mixing and an alkaline solution in the reactive study were fed into the tank from a large reservoir. In both cases, the tank inlet linear velocity was 0.045 m/s. The nozzle and suction diameters of the jet system were 6 and 8 mm respectively.
Fig. 2. A schematic view of the suction and seven nozzle positions.
Fig. 1 shows a schematic and the real views of the experimental continuous stirred tank. As can be seen in the figure, a mirror was located under the tank at an angle of 45° respect to the horizon for visualizing the tracer movement in three dimensions. As shown in the schematic view, several valves were placed between the suction and the flow meter to control the circulating flow rate. Three light sources were placed around the tank to improve the recorded film quality. The fluid in the tank was circulated from the jet suction to the nozzle via a pump. The jet linear velocity was set at 4.35 m/s in all experiments. The suction was fixed at one corner of the tank while seven positions around the tank were examined for the nozzle. In all cases the nozzle and suction were set at a fixed height of 5 cm from the tank bottom and the jet angle was fixed at an angle of 22.5° respect to the horizon. Fig. 2 shows the place of the suction as well as the seven positions of the nozzle.
Fig. 3. The meshed tank.
A. Parvareh et al. / International Communications in Heat and Mass Transfer 36 (2009) 1096–1102
4. CFD modeling In the CFD modeling part, the experimental tank with dimensions of 0.5 × 0.5 × 0.5 m3 was modeled. In the present work the modeling includes two steps. In the first step, the Navier-Stokes together with the k–ε equations was solved and the velocity profiles and the other fluid flow hydrodynamics parameters were predicted. In the second step, scalar transport equations for the tracer or reactive species were solved transiently. The SIMPLE pressure-velocity coupling algorithm, the standard pressure and the second order upwind discrimination schemes were used for determination of momentum, turbulent kinetic energy and dissipation energy, species transport and volume fraction. In addition, a convergence criterion of 10- 6 was chosen for all calculated parameters. The whole domain was divided into 821312 to 875346 numbers of unstructured tetrahedral zones. Different numbers of employed control volumes in the modeling are related to the different jet nozzle positions. These mesh layouts were found by examination of
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different cell sizes as no further significant change was obtained for finer cells. Finer meshes were used for regions with steeper gradients such as nozzle, suction and top region for increasing the precision of modeling. Fig. 3 shows an example of the meshed tank, connecting pipe in a vertical slice goes trough the tank.
5. Results and discussion 5.1. Tracer mixing In the first step of this investigation, the experiments were accomplished in a non-reactive manner and the effect of the jet position on the mixing progress of a dye inside the tank was studied. In all experiments after the fluid flow was established inside the tank, 80 ml of a dark Nigrosine solution was injected close to the inlet stream during 4 s. The front and bottom views of the tank were recorded by a digital camera during the homogenization process.
Fig. 4. Comparison between the experimental and CFD predicted contour plots of the tracer mixing.
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Table 1 The percent of the colored area at different regions of the tank. position1
position3
time(s)
top
middle
bottom
top
middle
bottom
3 21 33 40 44 47
89 85 45 49 33 24
9 11 42 41 42 49
2 4 12 10 25 27
60 27 15 28 32 33
33 44 42 33 32 33
7 29 43 39 36 34
The experimental results showed that the best performance was achieved for position3, in which the jet nozzle had an angle of 90° with respect to the tank input. However, the worst mixing performance was obtained as the jet nozzle was located at opposite side of the tank input stream, which is called position 1 in Fig. 2. The recorded front and bottom views of the tank for position1 and 3 are shown in Fig. 4. In addition, the CFD predicted concentrations of the tracer at various time steps are compared with the experiments in this figure. The visualized pictures show that as the jet was placed at position1, the injected dye solution preferred to exit from the tank outlet directly. For position1, the figure shows as the dye was going
toward the jet nozzle, it mixes with water. Consequently, the dye was dispersed by the jet outlet stream and pushed toward the top of the tank. This caused homogenization to be taken place in a more efficient way in comparison with position1 setup. The comparison between the experimental results and CFD modeling predictions shows a good qualitative agreement. In order to analyze the mixing performance in a more quantitative way, the percents of the contaminated regions by the tracer, judged from the photographs are shown in Table 1. The reported values was found using Scion Image software [24]. The table illustrates the area occupied by the dye at the top, middle and bottom regions of the tank at various time steps for both setups. As can be seen in the table, for position1 the dye was dispersed only at the top region up to 21 s. However, the dye was distributed in different regions of the tank during this period as position3 layout was employed. In second 20 s period (up to 40 s) the dye only occupied 10% of the lower regions for position1 layout, while it was 39% for the other setup. Finally, the results show that the dye distributed almost uniformly after 47 s for position3 while for another layout the dye in the middle of the tank was twice as much of other regions. This confirms that position3 setup worked more efficiently in comparison with position1. The CFD predicted fluid flow patterns in vertical and horizontal slices go through the inlet/outlet tubes are presented in Fig. 5 in
Fig. 5. Velocity vectors in vertical and horizontal slices.
A. Parvareh et al. / International Communications in Heat and Mass Transfer 36 (2009) 1096–1102
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5.2. Reactive mixing
Fig. 6. The output pH values at various time steps.
order to explain the observed experimental results. Turning to the presented flow pattern for position1, the figure illustrates that when the jet was placed in the opposite side of the inlet stream, the jet output flow hits this stream at the middle of the tank. Consequently, this stream is diverted toward the fluid free surface and goes out from the output. It is possible to see more easily this straight outgoing pattern in the related horizontal slice. Therefore, in this position the injected tracer can not move properly toward the bottom layers of the tank and goes directly to outlet and exits from the tank without suitable homogenization. Using this predicted flow pattern, it will be possible to explain why a poor mixing observed for position1 layout. On the other hand in position3, which the nozzle has an angle of 90° with the tank inlet, the jet stream hits the opposite wall close to the fluid free surface and divides into two parts. A part of fluid, which is the strong portion, circulates downward toward the nozzle. The other part circulates upward and then moves toward the tank center. Therefore, in this layout the tracer can not exit directly from the tank output. This is the main reason for the observed higher mixing performance in comparison with the other position.
In the reactive experimental runs, the effect of the jet position on the mixing and neutralization reaction of an alkaline solution with an acid solution was investigated. The neutralization reaction mixing experiments were done for the best and worst positions, position3 and 1, respectively. In the experiments, the NaOH solution was diverted into the tank and the H2SO4 solution was injected from the tracer injector in order to neutralize the alkaline stream. The pH values of the input alkaline stream and the injected acid were set to be 12 and 3, respectively. In the first stage of the neutralization tests, the acid was injected during 20 s while the alkaline stream was entering the stirred tank for 40 s. During the experiments, the pH values of the output stream were recorded using an online pH-meter made by the Consort Company (C838). Fig. 6 shows the pH values of the outlet stream at various times for both jet positions. As can be seen in the figure, the initial pH of the outlet is 12 for both cases. As the acid was being injected into the tank, the alkaline stream was neutralized by the acid and the outlet pH decreased for both jet layouts. The figure shows that the pH decreasing trend for position1 layout is sharper than that of position3. This can be explained by using the CFD predicted fluid flow patterns illustrated in Fig. 5. From this pattern, it can be expected that the acid goes out directly toward the output and the neutralization process does not happen efficiently for position1 setup. Therefore, the observed pH value of 4.2 after 20 s of injection is logical. However, the measured results for position3 show that the pH decreasing trend was milder than position1. In addition, as far as more efficient neutralization reaction was happened in this layout, the pH value of 6.2 was obtained after 20 s from the acid injection. Consequently, for both setups increasing trends of the pH values were observed after the acid injection was stopped. The figure shows that the rate of increasing of the pH during the second 20 s interval was lower for position3 in comparison with that of position1. This happened as the most of the injected acid had been exited during first 20 s in position1. However, in position3 more
Fig. 7. The predicted 3D normalized reaction rate fields inside the reactor.
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A. Parvareh et al. / International Communications in Heat and Mass Transfer 36 (2009) 1096–1102
acid remained inside the tank and more alkaline was neutralized with the remained acid. In addition, regarding to the fluid flow pattern of position1, the entering alkaline stream went out directly and pH was increased quicker. In another set of tests, both acid and alkaline steams were entered the tank just for 20 s and the pH value of the remaining solutions were measured. These tests were carried out to illustrate in what jet layout more acid involved with the neutralization reaction. The pH values of 9.8 and 7.3 were obtained for position1 and 3 respectively which confirms that in position3 more base was neutralized with the acid. In the other words, the higher pH value of the remained solution of position1 means more acid directly exits from the tank and mixing was not happened efficiently. Moreover, the CFD modeling was carried out to investigate the effect of the jet position on described neutralization process. The neutralization reaction equation is as follows: H2 SO4 þ 2NaOH→Na2 SO4 þ 2H2 O
ð4Þ
The above reaction is a very fast reaction with a rate constant of 1014. Thus the mixing process controls the neutralization reaction in the reactor. The mass transfer diffusion coefficients of the reactive components were considered similar to the diffusivity of the dilute electrolyte solutions in water. Fig. 7 shows the three dimensional CFD predicted normalized reaction rates for both jet positions. The normalized reaction rate is defined as the ratio of a cell reaction rate to the maximum reaction rate, which calculated according to the entering acid and alkaline concentrations. As can be seen in this figure, the volume of regions involved with the reaction for position3 is more than those of position1. In addition, the figure illustrates that the reaction proceed more in the middle and lower regions of the tank in position3, while for position1 the reaction just happens at the top region. The more involved regions in the neutralization reaction are related to the existence of acid, and in position3 the acid reached to the alkaline in a more efficient way. These predicted results can be used to explain the reactive mixing experimental observation presented in this study. 6. Conclusions In the present work, it was tried to illustrate the role of a jet position on mixing performance, which can be very important in many industrial neutralization processes such as waste water treatment. For this purpose, the effect of the jet position on mixing performance in a continuous flow stirred tank reactor in pilot scale was investigated. The obtained passive experimental results and the way that the jet disperses the dye solution were used to select the best and worst jet positions for the reactive study. These results show how the jet position affects on the passive dye mixing efficiency. Consequently, the acid- alkaline reactive mixing experiments reveals that the way that jet diverts the reactants to the reaction zone has a significant effect on the neutralization performance. All experiments were modeled using the CFD modeling technique and the predicted results were successful to analyze the experimental observations. In addition, the results show that the CFD modeling is a powerful technique for finding an efficient jet position in continuous stirred tank reactors.
Acknowledgement The authors wish to express their thanks to the Iranian West Regional Electricity Company for the financial support of this work.
References [1] A. Pantokratoras, Horizontal penetration of inclined thermal buoyant water jets, International Communications in Heat and Mass Transfer 25 (4) (1998) 561–569. [2] O.N. Şara, J. Erkmen, S. Yapici, M. Çopur, Electrochemical mass transfer between an impinging jet and a rotating disk in a confined system, International Communications in Heat and Mass Transfer 35 (3) (2008) 289–298. [3] V.V. Ranade, Towards better mixing protocols by designing spatially periodic flows- The case of a jet mixer, Chemical Engineering Science 51 (11) (1996) 2637–2642. [4] S. Jayanti, hydrodynamics of jet mixing in vessels, Chemical Engineering Science 56 (1) (2001) 193–210. [5] A.W. Patwardhan, CFD modeling of jet mixed tanks, Chemical Engineering Science 57 (8) (2002) 1307–1318. [6] S. Devahastin, A.S. Mujumdarb, A numerical study of flow and mixing characteristics of laminar confined impinging streams, Chemical Engineering journal 85 (2–3) (2002) 215–223. [7] H.D. Zughbi, M.A. Rakib, mixing in a fluid jet agitated tank: effects of jet angle and elevation and number of jets, Chemical Engineering Science 59 (4) (2004) 829–842. [8] H. Feng, M. Olsen, Y. Liu, R.O. Fox, J.C. Hill, Investigation of turbulent mixing in a confined planar-jet reactor, AIChE Journal 51 (10) (2005) 2649–2663. [9] M. Rahimi, A. Parvareh, Experimental and CFD investigation on mixing by a jet in a semi-industrial stirred tank, Chemical Engineering journal 115 (1–2) (2005) 85–92. [10] J.R. Berg, S.J. Ormiston, H.M. Soliman, Prediction of the flow structure in a turbulent rectangular free jet, International Communications in Heat and Mass Transfer 33 (5) (2006) 552–563. [11] M. Rahimi, A. Parvareh, CFD study on mixing by coupled jet-impeller mixers in a large crude oil storage tank, Computer and Chemical Engineering 31 (7) (2007) 737–744. [12] S.J. Wang, A.S. Mujumdar, Flow and mixing characteristics of multiple and multiset opposing jets, Chemical Engineering and Processing 46 (8) (2007) 703–712. [13] L.K. Hjertager, B.H. Hjertager, T. Solberg, CFD modeling of fast chemical reactions in turbulent liquid flows, Computer and Chemical Engineering 26 (4–5) (2002) 507–515. [14] S.S. Gulawani, S.K. Dahikar, J.B. Joshi, M.S. Shah, C.S.R. Prasad, D.S. Shukla, CFD simulation of flow pattern and plume dimensions in submerged condensation and reactive gas jets into a liquid bath, Chemical Engineering Science 63 (9) (2008) 2420–2435. [15] S.K. Dahikar, S.S. Gulawani, J.B. Joshi, M.S. Shah, C.S.R. Prasad, D.S. Shukla, Effect of nozzle diameter and its orientation on the flow pattern and plume dimensions in gas–liquid jet reactors, Chemical Engineering Science 62 (24) (2007) 7471–7483. [16] D. Dakshinamoorthy, A.R. Khopkar, J.F. Louvar, V.V. Ranade, CFD simulations to study shortstopping runaway reactions in a stirred vessel, Journal of Loss Prevention in the Process Industries 17 (5) (2004) 355–364. [17] D. Dakshinamoorthy, J.F. Louvar, Shortstopping and jet mixers in preventing runaway reactions, Chemical Engineering Science 63 (8) (2008) 2283–2293. [18] J.P. Torré, D.F. Fletcher, T. Lasuye, C. Xuereb, An experimental and CFD study of liquid jet injection into a partially baffled mixing vessel: A contribution to process safety by improving the quenching of runaway reactions, Chemical Engineering Science 63 (4) (2008) 924–942. [19] E. Gavi, D.L. Marchisio, A.A. Barresi, CFD modeling and scale-up of Confined Impinging Jet Reactors, Chemical Engineering Science 62 (8) (2007) 2228–2241. [20] D.L. Marchisio, Large Eddy Simulation of mixing and reaction in a Confined Impinging Jets Reactor, Computers and Chemical Engineering 33 (2) (2009) 408–420. [21] V. Yakhot, S.A. Orszag, Renormalization group analysis of turbulence, I. Basic theory, Journal of Scientific Computing 1 (1) (1986) 1–51. [22] H.K. Versteeg, W. Malalasekera, An introduction to computational fluid Dynamics, The finite volume method, first ed., Longman Limited, England, 1995, pp. 41–84. [23] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics 39 (1) (1981) 201–225. [24] http://www.scioncorp.com/pages/scion_image_windows.htm.
Contents lists available at ScienceDirect
International Communications in Heat and Mass Transfer j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Experimental and CFD study on the effect of jet position on reactant dispersion performance☆ A. Parvareh a, M. Rahimi a,⁎, M. Yarmohammadi a, A.A. Alsairafi b a b
CFD Research Centre, Chemical Engineering Department, Razi University, Kermanshah, Iran Faculty of Mechanical Engineering, College of Engineering and Petroleum, Kuwait University, Kuwait
a r t i c l e
i n f o
Available online 5 September 2009 Keywords: Jet Mixing Reaction Dispersion CFD Modeling
a b s t r a c t This paper reports the effect of jet position on the acid dispersion in a neutralization process. Experiments were carried out in a continuous stirred reactor and the effect of jet nozzle position on non-reactive dye dispersion at seven layouts was studied. Consequently, the neutralization reaction mixing was carried out at the best and worst positions. The results reveal that the ways that flow pushes the acid inside the tank are quite different and the neutralization performance can significantly be affected by the jet position. The Computational Fluid Dynamics (CFD) modeling was carried out in order to analyze the experimental observations. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Mixing is one of the most important concepts in chemical, oil, petrochemical and other related industries. Mixing by a jet is one of the well known methods for fluid homogenization in the liquid phase. Jet mixers are cheaper than other mixing devices such as impellers. In the jet mixing process, a part of the liquid inside the tank is drawn out and returned back via a pump, which this circulating pattern causes liquid homogenization. Many experimental researches were carried out to study mixing by a jet with or without reaction. The main aim of use of jet as mixer is to increase heat [1] and mass transfer [2]. By development of advanced computer modeling techniques such as CFD, many studies have focused on modeling of the fluid flow hydrodynamic in laboratory scales and validating the predicted results using various experimental methods. The CFD modeling of mixing in process industries has attracted a lot of attention since 1990. Ranade [3] applied the CFD modeling using the standard k–ε model for predicting the flow pattern and the mixing time in a jet mixed tank equipped with various types of jet. The fluid flow hydrodynamics established by a jet mixer using various jet configurations in a cylindrical vessel was investigated by Jayanti [4]. He tried to find a way to reduce the mixing time by eliminating dead zones in the vessel. Patwardhan [5] compared the CFD predicted and experimental results of homogenization of a sodium chloride solution in a distinct tank. He concluded that the CFD modeling can be used for
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. Chemical Eng. Dept. Razi University, Taghe Bostan, Kermanshah, IRAN. E-mail address: [email protected] (M. Rahimi). 0735-1933/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2009.08.007
predicting the mixing time, but it is poor in predicting the homogenization progress. Mixing in confined impinging jets was numerically studied in two dimensions by Devahastin et al. [6]. They determined the critical Reynolds numbers in which the flow regime changed from laminar to transitional. It was concluded that the inlet jet Reynolds numbers and the system geometry are effective in mixing by impinging jets. Zughbi and Rakib [7] used a three dimensional CFD modeling method to study the effect of the jet angle and the number of jets on the mixing time. They showed that the angle of a jet with horizon is the most important parameter for determining the mixing time. Feng et al. [8] modeled a planar-jet reactor by the CFD method, as they were using the PIV and LIF techniques for measuring the velocity and concentration fields in the vessel. The CFD predictions were validated by the measured results and the authors reported a good agreement between them. Mixing by a jet in a pilot scale storage tank was investigated by Rahimi and Parvareh [9]. In their study, the CFD method was used to model the mixing tank using three different versions of k–ε based turbulence model. They reported the effect of these models on the predicted results. Also, Berg et al. [10] compared prediction results of modeling of a turbulent jet flow using two standard, the k–ε and k–ω, two-equation turbulence models. Their computations examined for both turbulence models using two inflow boundary conditions including; a uniform inlet velocity profile and a profiled inlet velocity fitted to experimental data. Their results showed that the k–ε model with the profiled inlet velocity succeeded in predicting the main features of the flow, including the vena contracta and the saddle-shaped velocity profiles in the nearfield region. In addition, the rate of velocity decay in the far-field region was predicted in a more efficient way by the k–ε model. Rahimi and Parvareh [11] studied the mixing progress in pilot and real scales crude oil storage tank equipped with a jet and an impeller.
A. Parvareh et al. / International Communications in Heat and Mass Transfer 36 (2009) 1096–1102
Nomenclature C1, C2, Cµ constants of the k–ε model P pressure, Nm- 2 S source term U velocity vector, ms- 1 u, v, w, ui, uj mean velocity components, ms- 1 u′, v′, w′, ui′, uj′ turbulent fluctuating velocity component , ms- 1 xi,xj Cartesian coordinate, m Greek symbols ε dissipation rate of k; w kg- 1 µ laminar, turbulent and effective viscosities, Pas ρ density , kg m- 3 σk, σε turbulent Prandtl numbers for k–ε Φ,φ′ mean and turbulent fluctuating values of scalar property Γ scalar diffusion coefficient Subscript i, j component
They concluded that the angle between the jet and impeller has a significant effect on the mixing time. The flow and mixing characteristics of multiple and multi-set 3D confined turbulent round opposing jets were studied numerically by Wang and Mujumdar [12]. In their study, the air was used as working fluid and the fluid temperature variation was calculated to investigate the mixing performance. The standard k–ε turbulence model was applied for modeling the turbulency in the system. The effects of multiple opposing jet injection and multi-set opposing jet injections with/without offset on mixing time were studied experimentally and theoretically. The interactions between various physical and chemical processes such as mixing with reaction which occur over different times and length scales can have significant effects on the process performance. Therefore, these concepts should be well understood to improve the process efficiency or design a cost-effectively process. A CFD modeling of a fast acid–base neutralization reaction in a tubular reactor was carried out by Hjertager et al. [13]. A modified Eddy dissipation concept (EDC) model was found to be suitable for simulating liquid phase reactions. After comparing the model predictions with experimental data, they concluded that although such an approach is efficient and useful in understanding the reacting flow behavior, it might be inadequate to describe reactors involving with complex reactions. Submerged gas jets into a liquid bath are widely used in metal processing and thermal processes. These systems are classified as condensation and reaction jet systems [14]. The CFD simulations of non-reacting (steam-water) and reacting (SF6-Li) jets were carried out by Dahikar et al. [15] to understand the variation in plume dimensions of gas–liquid jet reactors. The effect different parameters on the plume dimensions were studied for both types of jets. The CFD modeling was carried out for the prediction of the flow pattern and its effect on the rate of condensation/reaction and plume dimensions for both the jet systems. In recent years, the CFD modeling of mixing with runaway reaction found some attentions [16]. An efficient way to quench such an uncontrolled chemical reaction by injection of an inhibitor using a liquid jet flow is very important for this type of reactive mixing processes. Dakshinamoorthy and Louvar [17] numerically studied the role of various factors on controlling of runaway reactions in a vessel
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equipped with a jet mixer. The computational model is solved using FLUENT commercial CFD code and their results demonstrated the value of using CFD modeling in situations that are experimentally prohibitive. In another study, mixing by a jet in a runaway reaction using CFD modeling was investigated by Torre et al. [18]. The authors reported a good agreement between the CFD predictions with experimental data for the jet trajectories. Another application of reactive jet mixer is in confined impinging jet reactors (CIJR )as devices for precipitation of nanoparticles because of its high mixing efficiency. Gavi et al. [19] studied mixing and reaction in CIJRs by means of CFD. The influence of operating conditions and reactor geometry on mixing was evaluated. The developed scale-up criterion for CIJRs showed that scaling up by means of CFD is a practicable way for further investigation. In a recent study, Marchisio [20] presented a CFD modeling of mixing and reaction in these devices using the Large Eddy Simulation (LES) approach coupled with a subgrid-scale mixing model, to take into account the effect of molecular mixing. They compared their experimental results with those of obtained from Reynolds-Averaged Navier–Stokes equations approach. In the present study, the effect of the jet position on the neutralization of an alkaline stream in a semi-industrial cubic stirred tank was investigated. The alkaline stream was neutralized with a sulfuric acid solution. This may has many industrial applications in final waste water neutralization process for controlling the environmental pollution. The efficient position of the jet for achieving this goal is the main challenge in this investigation. Experimental works in the pilot scale as well as CFD modeling were carried out for this purpose. 2. Theory The Computational Fluid Dynamics modeling involves the numerical solution of the conservation equations in laminar and turbulent fluid flow regimes. In this study, a 3D time-dependent CFD modeling was performed using the commercial CFD package, FLUENT6.2. The Navier-Stokes equations were applied to all of the control volumes and the k–ε RNG based equations [21] were used to describe the physics associated with the turbulence flow such as velocity field, pressure, turbulent kinetics energy and turbulent dissipation rate based on previous experience [9]. The Navier-Stokes equations for an incompressible flow with constant fluid properties in the Cartesian coordinate are as follows [22]: ∂ui =0 ∂xi
ρui
! " # — ∂uj ∂ui ∂P ∂ ∂ui −ρ u′i u′j =− + μ + ∂xi ∂xi ∂xi ∂xi ∂xj
ð1Þ
ð2Þ
In which ui, P, ρ and µ are mean velocity, pressure, density and dynamics— viscosity respectively. u′i and u′j are fluctuation component ′ and −ρ ui u′j is averaged Reynolds stress. The transport equation for scalar property Φ is " — — —# ∂Φ ∂u′ ϕ′ ∂v′ ϕ′ ∂w′ ϕ′ + SΦ + divðΦUÞ = divðΓΦ gradΦÞ + − − − ∂t ∂x ∂y ∂z ð3Þ In addition, in this study the following coefficients were used as the RNG turbulence model parameters [21]:
C1 = 1:42; C2 = 1:68; Cμ = 0:0845; σε = σk = 0:719; η0 = 4:8; β = 0:012
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Fig. 1. The continuous flow stirred tank and its detail.
Moreover, the Volume of Fluid (VOF) model was used to model the fluid free surface inside the tank. In this method, the interface between two phases, water and air, remains fixed [23]. In addition, by using this model the numerical stability can be obtained easily, because the flow field calculations are not coupled with identification of the free surface location. However, the viscous stresses and surface tension cannot be simulated accurately because the interface within each cell is not located precisely. This limitation has been largely overcome in this work by using very fine meshes close to the surface.
3. Pilot plant description In the present study, in order to validate the CFD modeling, a pilot plant rig was designed and fabricated. The experiments were carried out in a continuous flow stirred cubic tank with a volume of 125 lit made from Perspex. Water in the tracer mixing and an alkaline solution in the reactive study were fed into the tank from a large reservoir. In both cases, the tank inlet linear velocity was 0.045 m/s. The nozzle and suction diameters of the jet system were 6 and 8 mm respectively.
Fig. 2. A schematic view of the suction and seven nozzle positions.
Fig. 1 shows a schematic and the real views of the experimental continuous stirred tank. As can be seen in the figure, a mirror was located under the tank at an angle of 45° respect to the horizon for visualizing the tracer movement in three dimensions. As shown in the schematic view, several valves were placed between the suction and the flow meter to control the circulating flow rate. Three light sources were placed around the tank to improve the recorded film quality. The fluid in the tank was circulated from the jet suction to the nozzle via a pump. The jet linear velocity was set at 4.35 m/s in all experiments. The suction was fixed at one corner of the tank while seven positions around the tank were examined for the nozzle. In all cases the nozzle and suction were set at a fixed height of 5 cm from the tank bottom and the jet angle was fixed at an angle of 22.5° respect to the horizon. Fig. 2 shows the place of the suction as well as the seven positions of the nozzle.
Fig. 3. The meshed tank.
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4. CFD modeling In the CFD modeling part, the experimental tank with dimensions of 0.5 × 0.5 × 0.5 m3 was modeled. In the present work the modeling includes two steps. In the first step, the Navier-Stokes together with the k–ε equations was solved and the velocity profiles and the other fluid flow hydrodynamics parameters were predicted. In the second step, scalar transport equations for the tracer or reactive species were solved transiently. The SIMPLE pressure-velocity coupling algorithm, the standard pressure and the second order upwind discrimination schemes were used for determination of momentum, turbulent kinetic energy and dissipation energy, species transport and volume fraction. In addition, a convergence criterion of 10- 6 was chosen for all calculated parameters. The whole domain was divided into 821312 to 875346 numbers of unstructured tetrahedral zones. Different numbers of employed control volumes in the modeling are related to the different jet nozzle positions. These mesh layouts were found by examination of
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different cell sizes as no further significant change was obtained for finer cells. Finer meshes were used for regions with steeper gradients such as nozzle, suction and top region for increasing the precision of modeling. Fig. 3 shows an example of the meshed tank, connecting pipe in a vertical slice goes trough the tank.
5. Results and discussion 5.1. Tracer mixing In the first step of this investigation, the experiments were accomplished in a non-reactive manner and the effect of the jet position on the mixing progress of a dye inside the tank was studied. In all experiments after the fluid flow was established inside the tank, 80 ml of a dark Nigrosine solution was injected close to the inlet stream during 4 s. The front and bottom views of the tank were recorded by a digital camera during the homogenization process.
Fig. 4. Comparison between the experimental and CFD predicted contour plots of the tracer mixing.
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Table 1 The percent of the colored area at different regions of the tank. position1
position3
time(s)
top
middle
bottom
top
middle
bottom
3 21 33 40 44 47
89 85 45 49 33 24
9 11 42 41 42 49
2 4 12 10 25 27
60 27 15 28 32 33
33 44 42 33 32 33
7 29 43 39 36 34
The experimental results showed that the best performance was achieved for position3, in which the jet nozzle had an angle of 90° with respect to the tank input. However, the worst mixing performance was obtained as the jet nozzle was located at opposite side of the tank input stream, which is called position 1 in Fig. 2. The recorded front and bottom views of the tank for position1 and 3 are shown in Fig. 4. In addition, the CFD predicted concentrations of the tracer at various time steps are compared with the experiments in this figure. The visualized pictures show that as the jet was placed at position1, the injected dye solution preferred to exit from the tank outlet directly. For position1, the figure shows as the dye was going
toward the jet nozzle, it mixes with water. Consequently, the dye was dispersed by the jet outlet stream and pushed toward the top of the tank. This caused homogenization to be taken place in a more efficient way in comparison with position1 setup. The comparison between the experimental results and CFD modeling predictions shows a good qualitative agreement. In order to analyze the mixing performance in a more quantitative way, the percents of the contaminated regions by the tracer, judged from the photographs are shown in Table 1. The reported values was found using Scion Image software [24]. The table illustrates the area occupied by the dye at the top, middle and bottom regions of the tank at various time steps for both setups. As can be seen in the table, for position1 the dye was dispersed only at the top region up to 21 s. However, the dye was distributed in different regions of the tank during this period as position3 layout was employed. In second 20 s period (up to 40 s) the dye only occupied 10% of the lower regions for position1 layout, while it was 39% for the other setup. Finally, the results show that the dye distributed almost uniformly after 47 s for position3 while for another layout the dye in the middle of the tank was twice as much of other regions. This confirms that position3 setup worked more efficiently in comparison with position1. The CFD predicted fluid flow patterns in vertical and horizontal slices go through the inlet/outlet tubes are presented in Fig. 5 in
Fig. 5. Velocity vectors in vertical and horizontal slices.
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5.2. Reactive mixing
Fig. 6. The output pH values at various time steps.
order to explain the observed experimental results. Turning to the presented flow pattern for position1, the figure illustrates that when the jet was placed in the opposite side of the inlet stream, the jet output flow hits this stream at the middle of the tank. Consequently, this stream is diverted toward the fluid free surface and goes out from the output. It is possible to see more easily this straight outgoing pattern in the related horizontal slice. Therefore, in this position the injected tracer can not move properly toward the bottom layers of the tank and goes directly to outlet and exits from the tank without suitable homogenization. Using this predicted flow pattern, it will be possible to explain why a poor mixing observed for position1 layout. On the other hand in position3, which the nozzle has an angle of 90° with the tank inlet, the jet stream hits the opposite wall close to the fluid free surface and divides into two parts. A part of fluid, which is the strong portion, circulates downward toward the nozzle. The other part circulates upward and then moves toward the tank center. Therefore, in this layout the tracer can not exit directly from the tank output. This is the main reason for the observed higher mixing performance in comparison with the other position.
In the reactive experimental runs, the effect of the jet position on the mixing and neutralization reaction of an alkaline solution with an acid solution was investigated. The neutralization reaction mixing experiments were done for the best and worst positions, position3 and 1, respectively. In the experiments, the NaOH solution was diverted into the tank and the H2SO4 solution was injected from the tracer injector in order to neutralize the alkaline stream. The pH values of the input alkaline stream and the injected acid were set to be 12 and 3, respectively. In the first stage of the neutralization tests, the acid was injected during 20 s while the alkaline stream was entering the stirred tank for 40 s. During the experiments, the pH values of the output stream were recorded using an online pH-meter made by the Consort Company (C838). Fig. 6 shows the pH values of the outlet stream at various times for both jet positions. As can be seen in the figure, the initial pH of the outlet is 12 for both cases. As the acid was being injected into the tank, the alkaline stream was neutralized by the acid and the outlet pH decreased for both jet layouts. The figure shows that the pH decreasing trend for position1 layout is sharper than that of position3. This can be explained by using the CFD predicted fluid flow patterns illustrated in Fig. 5. From this pattern, it can be expected that the acid goes out directly toward the output and the neutralization process does not happen efficiently for position1 setup. Therefore, the observed pH value of 4.2 after 20 s of injection is logical. However, the measured results for position3 show that the pH decreasing trend was milder than position1. In addition, as far as more efficient neutralization reaction was happened in this layout, the pH value of 6.2 was obtained after 20 s from the acid injection. Consequently, for both setups increasing trends of the pH values were observed after the acid injection was stopped. The figure shows that the rate of increasing of the pH during the second 20 s interval was lower for position3 in comparison with that of position1. This happened as the most of the injected acid had been exited during first 20 s in position1. However, in position3 more
Fig. 7. The predicted 3D normalized reaction rate fields inside the reactor.
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acid remained inside the tank and more alkaline was neutralized with the remained acid. In addition, regarding to the fluid flow pattern of position1, the entering alkaline stream went out directly and pH was increased quicker. In another set of tests, both acid and alkaline steams were entered the tank just for 20 s and the pH value of the remaining solutions were measured. These tests were carried out to illustrate in what jet layout more acid involved with the neutralization reaction. The pH values of 9.8 and 7.3 were obtained for position1 and 3 respectively which confirms that in position3 more base was neutralized with the acid. In the other words, the higher pH value of the remained solution of position1 means more acid directly exits from the tank and mixing was not happened efficiently. Moreover, the CFD modeling was carried out to investigate the effect of the jet position on described neutralization process. The neutralization reaction equation is as follows: H2 SO4 þ 2NaOH→Na2 SO4 þ 2H2 O
ð4Þ
The above reaction is a very fast reaction with a rate constant of 1014. Thus the mixing process controls the neutralization reaction in the reactor. The mass transfer diffusion coefficients of the reactive components were considered similar to the diffusivity of the dilute electrolyte solutions in water. Fig. 7 shows the three dimensional CFD predicted normalized reaction rates for both jet positions. The normalized reaction rate is defined as the ratio of a cell reaction rate to the maximum reaction rate, which calculated according to the entering acid and alkaline concentrations. As can be seen in this figure, the volume of regions involved with the reaction for position3 is more than those of position1. In addition, the figure illustrates that the reaction proceed more in the middle and lower regions of the tank in position3, while for position1 the reaction just happens at the top region. The more involved regions in the neutralization reaction are related to the existence of acid, and in position3 the acid reached to the alkaline in a more efficient way. These predicted results can be used to explain the reactive mixing experimental observation presented in this study. 6. Conclusions In the present work, it was tried to illustrate the role of a jet position on mixing performance, which can be very important in many industrial neutralization processes such as waste water treatment. For this purpose, the effect of the jet position on mixing performance in a continuous flow stirred tank reactor in pilot scale was investigated. The obtained passive experimental results and the way that the jet disperses the dye solution were used to select the best and worst jet positions for the reactive study. These results show how the jet position affects on the passive dye mixing efficiency. Consequently, the acid- alkaline reactive mixing experiments reveals that the way that jet diverts the reactants to the reaction zone has a significant effect on the neutralization performance. All experiments were modeled using the CFD modeling technique and the predicted results were successful to analyze the experimental observations. In addition, the results show that the CFD modeling is a powerful technique for finding an efficient jet position in continuous stirred tank reactors.
Acknowledgement The authors wish to express their thanks to the Iranian West Regional Electricity Company for the financial support of this work.
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