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An experimental and CFD investigation of the effect of nozzle inclination and twisting in a double jet mixed tank.

Nomenclature

C1, C2       Correlation Constants of Fox and Gex (1956)
Dj           jet diameter, (m)
D            diameter of tank, (m)
d            nozzle diameter,(m)
F            mixing time factor for the correlation
               of Lane and Rice (1982)
g            acceleration due to gravity, ([m.sup.2]/s)
H            height of the tank, (m)
Qj           jet volumetric throughput, ([m.sup.3]/s)

[R.sub.ej]   jet Reynolds number
T,Tm         mixing time, (s)
x            effective jet length,(m)
y            height of the liquid in the tank,(m)
V            jet velocity, (m/s)

Greek Letters

[Phi]--Angle of inclination of the jet, (deg)

[theta]--Twist of the jet, (deg)


Introduction

Uniform composition of fluids in a tank confirms complete mixing. The time required to achieve the desired degree of mixing is an important aspect for any mixing operation.

Jet mixer has many practical applications including mixing of Tetra Ethyl Lead with petrol in large under ground tanks. There are many alternatives used to mix two fluids but jet mixing is one of the best among them due to the following reasons:

* There are no moving parts inside the tank.

* Cost of operation is less compared to others.

* Operation is easy.

Fossett and Prosser (c) (1949) conceived the original idea of jet mixing during the Second World War and described the investigation of inclined side entry jet mixer design for commercial purposes. Based on their experiments they proposed a correlation for mixing time ([T.sub.m]) in a tank of diameter 'D' with a jet nozzle diameter 'd' and jet velocity 'V' is given by

[T.sub.m] = 9.0*[D.sup.2] / (V*d) (1)

Reynolds number in the above study was in the turbulent regime although no explicit dependence on Reynolds number was included in the correlation.

Fox and Gex (d) (1956) carried out their investigations in both laminar and turbulent jet regimes and used three lobed propellers. Terminal mixing was measured using pH-based technique and their studies included other parameters that affected mixing such as jet diameter, jet velocity, tank diameter, liquid viscosity, propeller diameter, its rotational field, etc. From their studies, they concluded mixing time as a factor of momentum flux added to the tank through jets or in the form of propeller. They also concluded that mixing time was a function of Reynolds number under laminar regime and only a weak function in the case of turbulent regime. High Reynolds number had no noticeable effect on mixing time ([10.sup.6]). Their correlations governing both laminar and turbulent jet region by pH indicator technique were given as For laminar,

T = C1 * ([y.sup.0.5] *D)/ ([Rej.sup.-1.33] * V*[d.sup.0.67]* [g.sup.0.17]) (2)

For turbulent,

T = C2 * ([y.sup.0.5] *D)/ ([Rej.sup.0.17] * V*[d.sup.0.67]*[g.sup.0.17]) (3)

The above correlations were modified by Okita and Oyama [l] (1963).

In 1978, Coldrey (a) proposed a modified model for inclined side entry jets for jet mixing. He observed that, mixing time depends on the jet length (defined as the distance between the jet entry point and the point of impact on opposite wall) and formulated a mixing time equation independent of jet Reynolds number for the turbulent region.

T = 3.45 * ([D.sup.2] * y) / (x * [Q.sub.j]) (4)

Lehrer (i) (1981) formulated a model for free turbulent jet of miscible fluids of different density in which a lateral transfer of momentum was considered to be due to eddy diffusion. The eddy viscosity assumed was a product of jet Reynolds number and molecular viscosity.

Lane and Rice (g,h) (1981) investigated a vertical jet mixer in a vessel with hemispherical base. They concluded that mixing time strongly depended on Reynolds number in laminar regime but only slightly dependent on jet Reynolds number in turbulent regime. They also extended their studies in the year 1982 where they assessed the various designs of jet mixed tanks and concluded that a hemispherical bottom significantly reduced mixing time.

Maruyama, Ban and Mizushina (j) (1982) predicted that the mixing time was also dependent on the liquid depth, nozzle height and the nozzle angle.

Grenville and Tilton (e) (1996, 1997) showed that mixing time is dependent on the energy dissipation rate in the region far from the jet nozzle, where the velocities and turbulence intensities are much lower.

Simon and Fonade (p) (1993) used both steady and unsteady jets and reported that alternating jets gives 15% lower mixing time at the same power input as compared to steady jets.

Orfaniotis et al (m) (1996) have done their experimental work with two side jets in a jet mixer. The Reynolds number of the jet was maintained at 3900. They used the conductivity technique to measure the mixing time. They experimented jet mixing in cylindrical vessels of varying shape and size. They located one inlet at the bottom and relatively a large outlet at the top. They used nozzle diameters ranging from 2 to 18 mm. their results did not highlight the effects of angle of jet inclination.

S.Jayanti (f) (2001) concluded that by simulating various configurations of jets, the key factor in reducing mixing time is minimizing or eliminating dead zones in the reactor. In his experiment, he used computational fluid dynamics (CFD) to simulate jet mixing inside in a cylindrical vessel. The flow circulation patterns within the reactor and their effect on the mixing of the soluble salt was studied.

H.D.Zughbi and M.A.Rakib (r) (2004) concluded that for a jet agitated tank with an aspect ratio of 1 and for a side jet injected at the bottom of a tank, the longest jet length, corresponding to an angle of injection of 45[degrees], does not give the shortest time as suggested by many previous workers but one of the longest mixing times. An angle of injection of 30[degrees] gives the shortest mixing time. These experiments were carried out for a Reynolds number between 3000 and 7000 and taking the outlet from the top of the tank.

Patwardhan.A.W and A.R.Thatte (n) (2004) found that mixing time decreases with an increase in jet length. This has been confirmed. with the help of CFD modeling also. They also proposed a correlation based on two dimensionless parameters.

S.J.Wang and A.S.Mujumdar (q) (2005) performed their experiments using low Reynolds number and k-[epsilon] turbulence models to examine the effects of unequal opposing jets on the flow pattern and mixing characteristics in a three dimensional inline static mixer utilizing confined turbulent opposing jets and compared the effects of equal and unequal jets.

Masoud Rahimi and Arsalan Parvarehk have performed a study on the flow generated and mixing time in a semi-industrial tank equipped with a side entry jet mixer. They predicted that the mixing time in the 45[degrees] jet layout was comparatively lower than all other setups investigated.

Present Study

The present study investigates the effect of jets on mixing time, by changing the inclination of the nozzle and twisting the nozzle. Twisting is defined, as the angle the jet makes with the vertical plane, perpendicular to the base passing through the nozzle axis. It is pictorially explained through figure1. The jet entries were fixed at the mid height of the tank and the out let at the bottom. The concept of twisting was arrived as an effort to find the optimum flow pattern within the tank, and hence to reduce the mixing time. Validations of the results were done using CFD simulation techniques. For this simulation, a CFD package FLUENT 6.1 was used through which flow patterns for different twists and inclinations were obtained. FLUENT 6.1 has proved to be a useful tool in simulation of such flow models and has been used by various experimenters for its compatibility and accuracy in simulating turbulent flow models. The results reveal significant progress towards reducing the mixing time, which will be explained in the following discussions.

[FIGURE 1 OMITTED]

Experimental Setup

A cylindrical open tank of 0.36 m internal diameter and 0.4 m height with a working fluid height of 0.36 m was used. A 0.02 m pipe was used to draw the liquid from the bottom of the tank through a centrifugal pump and return to the tank through two side entry jets. A schematic representation of the experimental setup is shown in figure 2.

[FIGURE 2 OMITTED]

Although liquid circulation through a centrifugal pump and the pipe line system may enhance mixing, the effect is considered to be negligible because the volume of the liquid (0.63 liters) within the recirculation pipe is very small (less than 2%) compared to the volume in the tank (36.6 liters).

The two jets enter in the opposite direction from the side of the tank at 0.18 m height from the base of the tank. The angle of inclination and twist of the jets was varied for each run. The aspect ratio of the tank was maintained constant and is equal to 1.

Tap water was used as a working fluid and sodium chloride as an electrolyte at 0.001M. Conductivity methods for evaluation of the concentration were employed. The time taken to reach 95% of the final conductivity value was taken as the time for the complete mixing time. The time for the injection of the tracer solution was considered to be negligible.

The flow rate was set with the aid of a rotameter. To maintain the precision of the rotameter, it was calibrated at regular intervals. The tracer was injected into the system at the center of the tank at the top liquid surface. It is likely for a very small axial velocity was imparted to the liquid due to tracer addition. This effect was neglected as it confines only to a small region near the liquid surface, A.W. Patwardhan (n). Diffusion effect of the tracer in the system is assumed negligible. The conductivity was monitored at five locations with the help of conductivity probes. The locations of the probes are shown in figure 3. Conductivity was monitored initially with nine probes. The mixing time monitored in five locations only differed significantly. The remaining probes were removed and only five probes were used for investigation of mixing time. These probe locations were also confirmed with the help of computational fluid dynamics simulations. These located probes were expected to have the highest mixing times.

[FIGURE 3 OMITTED]

Development of The Computational Model

CFD modeling involves the numerical simulation for flows of gases and liquids, heat and mass transfer, moving bodies, multiphase physics, chemical reaction, fluid-structure interaction and acoustics through computer modeling. CFD modeling involves a numerical solution of the conservation equations in the laminar and the turbulent flow regimes. Therefore, theoretical predictions were obtained by simultaneous solutions of continuity and Navier-Stokes equation. Fluent 6.1 (b)

The crucial difference between modeling laminar and turbulent flows is the appearance of eddying motions of wide range of length scales in the turbulent flows. The random nature of turbulent flows precludes computations based on a complete description of motion of all the fluid particles. In general, it is more attractive to characterize the turbulent flow by the mean values of flow properties and statistical properties of their fluctuations. The governing equations for a general mixing problem are the mass, momentum and the energy equations. The numerical solutions of the transport equations mainly comprise discretization of the governing equations and solving of the resulting algebraic equations.

Turbulence model was used to model the flow inside the tank. The equations were solved using a pressure implicit with the splitting up of operators (PISO) pressure velocity coupling scheme. It is to be noted that the semi-implicit method for pressure linked equations (SIMPLE) method requires an iterative procedure. To obtain solution without iterations, with large time steps and less computing effort, the PISO scheme is used. In this scheme, the conservation of mass is designed to be satisfied within the predictor--corrector steps. PISO is based upon a higher degree of approximate relation between the correction for pressure and velocity. PISO improves the efficiency of calculations when compared to SIMPLE or SIMPLEC, by performing additional corrections like neighbor and skew ness correction. PISO is recommended for transient calculations such as in this case, Fluent 6.1 (b).The residuals are monitored and the solution is converged when the residuals go below the specified value. The imbalance in each conservation equation following each iteration is defined as a Residual.

Turbulence was modeled using standard k-[epsilon] model. The k-[epsilon] model is the most frequently used model for low speed incompressible flows and also the k-[epsilon] model has been chosen because of its savings in computational time compared to various other models such as the spalart allmaras model or the k-[omega] model. The k-[epsilon] model was successfully used by many researchers including Patwardhann, S.Jayantif,H.D. Zughbi, M.A. Rakib (r), and Wang,S.J; Mujumdar,A.S (q) to predict overall mixing time. The velocity vectors and the contours for the flow using turbulence modeling were determined depending upon the twists and the inclinations of the jets, which are further explained in the document. GAMBIT, a preprocessor was used to create the geometry of the tank.

The cylindrical reactor of height and diameter 0.36m is created with an outlet and a jet as an inlet. The reactor created was 3D in nature. The entire reactor is finally created by union of all the created volumes. Since the distortion in the surface due to turbulence was negligible, the surface of the liquid was taken to be flat. Generating a good mesh is a large part of the CFD problem. Meshing is usually done to split the entire volume into small volumes or cells where parameters such as velocity vectors, stresses etc can be determined. Various meshing schemes such as TET-HYBRID, HEX/WEDGE, COOPER are available. Either one of these schemes can be used or a combination of all these schemes can also be used.

A tetrahedral mesh was used to discretize the computational domain. A coarse mesh was used for the tank and a very fine mesh was used to mesh the nozzle specifically at the inlet and at the outlet. A total of 53939 cells were used to mesh the tank, which is finer than that used by H.D. Zughbi [1]. The size of the time step of 0.5 s was chosen. Fine meshes were done on the areas where the changes in parameters are more frequent and contribute to the problem the most for example interior of the tank, outlet, inlet etc. Coarse meshes are done to areas such as side walls as in the case where they do not contribute to the flow. In the present case, the geometry is meshed with TET-HYBRID scheme of meshing where a coarse mesh is done on the outer walls of the geometry and a fine mesh inside the reactor including the inlet jet and outlet.

The meshed geometry is imported into FLUENT6.1. The grid generated using GAMBIT is first checked for its consistency. The created grid is smoothed using Laplace method. The imported mesh file is scaled to match the units created in GAMBIT. The model of the solver is selected as unsteady. An unsteady state solver is chosen since the velocity vectors are a function of time.

The ultimate goal of any numerical simulation is a convergence to the exact solution as the mesh size is reduced. A finite difference scheme is convergent if its solution approaches that of the partial difference equation as the grid size approaches zero. Both consistency and stability are prerequisites to convergence. The solutions get converged if the values of the residuals go below [10.sup.-6].

Results and Discussion

Effect of Nozzle Diameter on Mixing Time

Experiments with jet diameters of 0.004 m, 0.006 m and 0.008 m for a constant jet velocity of 3 m/s showed a trend of decrease in mixing time with increase in nozzle diameter. It's shown in Figure 4. Mixing is achieved by the transfer of momentum from the fast moving liquid to the bulk liquid. The momentum flux is proportional to the product of the square of the diameter and velocity through the nozzle. Hence as the diameter of the nozzle is increased at constant velocity the momentum increases, as a result of which the mixing time decreases.

[FIGURE 4 OMITTED]

Effect of Inclination of The Jet ([Phi])

The effect of jet inclination Refer figure 5 (the angle formed by the nozzle to the plane taken at the mid height, parallel to the base of the tank) on mixing time was studied for various jet inclinations. The mixing time required was determined for various inclinations of the jet at 15[degrees], 25[degrees], 30[degrees] and 45[degrees], for various Reynolds numbers of 4500, 5300 and 7500. This experiment need not be carried out for different nozzle diameters, for, any combination of jet diameter and velocity which produces the same flux of momentum will then produce the same mixing time. The mixing time was the least for 25[degrees] inclination of the jet for all the Reynolds numbers. The results are shown in figure 6.

[FIGURE 5 OMITTED]

When the angle of inclination was changed, a change in mixing time was observed, not only due to the change in jet length, but also due to the flow patterns created within the tank as suggested by H.D. Zughbi and M.A. Rakib (r). But the jet inclination of 25[degrees] was left unnoticed during their research. The results show that at this angle of inclination, a significant difference in the mixing time was achieved. At 45[degrees] inclination, the jet was directed away from the opposite wall and towards the bottom (figure 8, (iv)) reducing the jet length and hence the turbulence. This inclination also did not create any appealing flow patterns when compared with the other inclinations. Also at 15[degrees] inclination, the jet is directed towards the opposite wall (fig 8,(i)), losing its momentum on impingement. The flow patterns at other angles of inclinations are shown through the plots of velocity vectors in Figure 7 & 8.

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

At 25[degrees] the jet length forms the diagonal to the tank and hence the maximum figure.8 (ii), and the best flow pattern (with least dead zones) is also created and is comparatively better than all the other flow patterns created within the tank. Most of the kinetic energy is absorbed by the bulk liquid, resulting in increase in the turbulent regions and thus reducing mixing time. H.D. Zughbi and M.A. Rakib (r) have studied the effect of mixing time with single jet by having the outlet at the top and determined the angle of 30[degrees] to be the optimum for their study for a nozzle entering from the mid height of the tank. Whereas in the present investigation it was found that the jet entering at the mid height of the tank at an inclination of 25[degrees] to the horizontal was found to be the optimum which decreases the mixing time by 10% apart from handling 1.5 times of volume experimented by their volume. The tracer injected at the surface of liquid has to pass through out the bulk liquid to reach the out let which enhances proper mixing. The mixing time comparison is shown in figure 9.

[FIGURE 9 OMITTED]

Effect of Twisting of the Nozzle on Mixing Time

After experimentally verifying the effect of jet length, on mixing time, alternate ways of changing the flow pattern was tried by twisting the nozzle. The twisting of the jets

are pictorially represented in the figure 1. The jets inclined at an angle of 25[degrees], which is the optimum angle for the proposed system, were twisted through various angles at the height of 0.18 m from the base. The twist was varied from 0[degree] through 45[degrees], 90[degrees], 135[degrees]and 180[degrees] for both the jets and the mixing time was measured. The results that were obtained for these investigations are presented in figure10. These results were also predicted by FLUENT and can be seen with the help of the flow patterns from figure 11.(i) to Figure (v).These obtained flow patterns were taken in a plane to show the optimum configuration of the jets.

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

The mixing time was found to be the least when jet1 is at 0[degree] twist with respect to the vertical (the nozzle facing the bottom of the tank) and the jet2 is at 180[degrees] twist (the nozzle facing the top of the tank). At this twist of the jets (Figure11(i)), the mixing time was the lowest compared to all other twists experimented (Fig.10), because of the maximum jet length achieved by both the jets and also the best flow patterns were achieved at this configuration. The jet 1 which is twisted to an angle of 0[degrees] accounts for the turbulence and hence the flow patterns created in the lower part of the tank and the jet 2 which is twisted to an angle of 180[degrees] accounts for the turbulence created on the upper surface of the tank. Hence the lowest mixing time for a double jet mixed tank can be achieved by having such a combination of the jets.

The mixing time is comparatively higher for other twists because, say for the twist of jet1 at 0[degrees] and jet2 at 0[degree] (Fig 11(ii)), the jet length does not attain the maximum possible because the jets collides with each other and the turbulence is created only in the bottom region, which results in more dead zones in the upper part of the tank. This ultimately results in poor mixing and results as one of the highest mixing times investigated. Hence the nozzles with this type of arrangement does not contribute to the reduction in mixing time. In case of the jet twist of jet1 at 0[degree] and jet2 at 45[degrees], the jet length is minimized since the jet2 hits the wall of the tank and loses much of its momentum which eventually results in increase of mixing time. This combination of the jets also results in a lot of dead zones in the upper regions of the tank which is not desired. For a combination of jet 1 at 135[degrees] and jet 2 at 45[degrees], though both jets are directed at different directions the jet looses its momentum on impingement and also more dead zones were visualized.

In this case the dead zones are visualized in the centre of the tank. Similarly for combinations such as 135[degrees], 0[degree] or 90[degrees], 45[degrees] for jet1 and jet2 there were no significant changes in flow patterns. These combinations resulted as one of the highest mixing times and did not contribute to the reduction in the mixing time. Even though some marginal changes were observed for the jets having a twist of 90[degrees] and 90[degrees] (Fig 11.(v) viewed from the top for better visualization of flow pattern), 135[degrees] and 135[degrees], 90[degrees] and 135[degrees], they do not contribute to the decrease in mixing time appreciably. The flow patterns for these combinations shows maximum dead zones. Incase of the jet combination with 90[degrees] and 90[degrees] the dead zones were visualized in the upper region as well as the bottom region of the tank. The flow patterns were also not appreciable when compared to that of the optimum twist which is 0[degree] twist for jet 1 and 180[degrees] twist for jet 2. The above discussion is further reinstated by the flow patterns existing within the tank in fig 11.

Conclusion

An experiment was conducted to study the effects of nozzle diameter, jet inclination of a single jet and compared with the previous results. The effect of twisting on mixing time for double jets was also studied. The results show that the angle of the jet inclination has also a strong influence on the mixing time. When the angle of inclination was changed, a change in mixing time was observed, not only due to the change in jet length, but also due to the flow patterns created within the tank as suggested by H.D. Zughbi and M.A. Rakibr. The results show that at this angle of inclination, a significant difference in the mixing time was achieved. The optimum angle of inclination for a nozzle entering at the mid height of a tank and the outlet from the centre of the bottom, whose aspect ratio is 1, is 25[degrees].

Using two jets reduces the mixing time to a greater extent. Mixing time was found to be the least by twisting double jets at an optimum angle. The best combination of twist is found to be when jet 1 is at a twist of 0[degree] and the jet 2 is at a twist of 180[degrees].This combination of the jets provide the least dead zones with the maximum possible jet lengths and ultimately the best flow patterns that can be created with a double jet mixed tank. The results are presented through flow visualizations with the suitable CFD simulation techniques. The results are universal for all cylindrical tanks with an aspect ratio of one.

References

[1] Coldrey, P. W., 1978, "Jet mixing. Industrial chemical engineering," Course Paper,University of Bradford, Bradford, U.K.,1978.

[2] FLUENT 6.1.18., 2002, "Users guide," Fluent Inc.,

[3] Fossett, H.; Prosser, L. E. 1949, "The Application of Free Jets to the Mixing of Fluids in bulk," In Proc. Inst. Mech. Eng. 160, pp. 224-251.

[4] Fox, E. A.; Gex, V. E, 1956, "Single-Phase Blending of Liquids," AIChE J. 2, pp. 539 -545.

[5] Grenville, R. K.; Tilton, J. N. 1996, "A New Theory Improves the Correlation of Blend Time Data from Turbulent Jet Mixed Vessels," Trans. Inst. Chem. Eng. Vol 74, Part A, pp. 390 -396.

[6] Jayanti, S. 2001, "Hydrodynamics of Jet Mixing in Vessels," Chem.Eng. Sci., 56, pp. 193 - 210.

[7] Lane, A. G. C.; Rice, P. 1981, "An Experimental Investigation of Liquid Jet Mixing employing a Vertical Submerged Jet," Proc. Inst.Chem. Eng. Symp. Ser. 64, pp. K1-K14.

[8] Lane, A. G. C.; Rice, P, 1982, "An Investigation of Liquid Jet Mixing employing an inclined Side Entry Jet," Trans. Inst. Chem.Eng. 60, pp. 171 - 176.

[9] Lehrer,I.H., 1981, "A new model for free turbulent jets of miscible fluids of different density and a jet mixing time criterion," Trans IchemE, Vol 59, pp. 247--252

[10] Maruyama, T.; Ban, Y.; Mizushina, T.,1982 "Jet Mixing of Fluids in Tanks,". J. Chem. Eng. Jpn. Vol 15, No.5, pp. 342 - 348.

[11] Masoud Rahimi;Arsalan Parvareh., 2005, "Experimental and CFD investigation on mixing by a jet in a semi- industrial stirred tank," Chemical Engg. Journal 115, pp. 85 - 92

[12] Okita, N.; Oyama, Y., 1963, "Mixing Characteristics in Jet Mixing,". Japanese journal of Chemical Engineers, 31(9), pp. 92 - 101.

[13] Orfaniotis, A., Fonade, C., Lalane, M., & Doubrovine, N., 1996,"Experimental Study of the fluidic mixing in a cylindrical reactor," Canadian Journal of Chemical Engineering, 74, pp. 203--212

[14] Patwardhan, A.W.; Amit R.Thatte., 2004, "Process Design aspects of Jet mixers," Canadian journal of chemical engineering, 82, pp.198-205

[15] Patwardhan, A.W., 2002, "CFD Modelling in Jet Mixed Tanks," Chemical Eng. Sci, 57, pp. 1307--1318

[16] Simon, M. and Fonade, C., 1993, "Experimental Study of mixing performances using steady and unsteady jets," Con. J. Chem. Eng, 71, pp. 507-513.

[17] Wang,S.J; Mujumdar,A.S., 2005, "A numerical study of flow and mixing characteristics of three--dimensional confined turbulent opposing jets: Unequal jets," Chem. Engg and Processing 44, pp.1068-1074

[18] (r)Zughbi, H. D and Rakib, M. A., 2004, " Investigations of Mixing in a Fluid Jet Agitated Tank: Effects of Jet Angle and elevation and Number of Jets," Chem. Eng. Sci. 59, pp. 829 -842.

Raja Thiruvengadam, *P. Kalaichelvi and N. Ananthraman

Department of Chemical Engineering, National Institute of Technology, Tiruchirappalli--620 015, Tamilnadu, India

*E-mail: kalai@nitt.edu
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Author:Thiruvengadam, Raja; Kalaichelvi, P.; Ananthraman, N.
Publication:International Journal of Applied Engineering Research
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Date:Oct 1, 2008
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