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An analysis on the proportional mixing of liquids using venturi jet mixer.

Introduction

In industrial applications, typically, when mixing processes are required the equipment that is selected is a stirred tank. However, this is not the only choice that can be done. In fact, mixing occurs, not only by mechanical agitation, but also in the pipelines connecting the existing tanks in the plant. Sometimes the pipe, especially if static mixers are inserted into, is the better place where mixing can occur [1]. Venturi jet mixer invented by Eric Halliburton in 1924 to rapidly mix a continuous supply of cementitious grout for cementing oil wells is an evolution of the idea of using simple in-line static mixer obtaining excellent mixing performances [2,3]. This choice can allow saving money, because the investment cost necessary for a static mixer is always lower than that of a dynamic agitator and because, for some applications, it allows to save energy. In fact, is worth noticing that the only power required for static mixers applications is the external pumping power necessary to compensate the pressure drops through the mixer. As these devices are characterised by short residence time and little back mixing, they can be used when the residence time required by the operation ranges is in the order of seconds to minutes. Therefore, good performances can be especially obtained when fast blending is required, when a fast chemical reaction occurs or when long hold-ups, typically associated to the use of a stirred tank, have to be avoided. A lot of industrial applications can now be identified where static mixers are used: homogenization, dispersion, emulsifying, gas/liquid and liquid/liquid contacting, co-current mass transfer, heat transfer and chemical reaction [4]. For interphase mass transfer applications, both agitated vessel and static mixers supply at the most a single equilibrium stage. Since static mixers have no moving parts they needs low maintenance costs and they have no sealing problems [5].

The difference between the mixing in a normal pipeline and in a pipeline equipped with a static mixer is apparent. In turbulent flow, static mixers create a higher degree of turbulence as compared to a normal pipe, thereby resulting in a higher degree of mixing dispersion and/or mass transfer. An empty tube working in turbulent flow regime is the simplest static mixer, however it is necessary a length nearly equal to 100 pipe diameters for complete mixing [6]. On the contrary, if static mixers are used, the complete mixing can be obtained with a length nearly equal to 4-6 diameters. Finding an effective method of mixing dates back to 1930 when Chilton and Genereaux (1930) [7] conducted a smoke visualization experiment to study the optimum mixing condition at a T-Junction. Heindel et al. (1999) [8] showed encouraging results for the inactivation of Cryptosporidium parvum oocysts using static mixers for the initial mixing of chemical ingredients. Diego et al.(2004) [9] developed analytical tools to design three-dimensional characteristics of the fuel and air flow in a venturi. Yaacob et al. (2006) [10] developed a 3d cfd model to investigate the effect of the mixing quality of venturi mixer on the cng-diesel engine performance.

In this investigation a venturi jet mixer is developed to mix two low viscous liquids. A fluid passing through smoothly varying constrictions is subject to changes in velocity and pressure in order to satisfy the conservation of mass-flux (flow rate). The reduction in pressure in the constriction can be understood by conservation of energy: the fluid (or gas) gains kinetic energy as it enters the constriction, and that energy is supplied by a pressure gradient force from behind. The pressure gradient reduces the pressure in the constriction, in reaction to the acceleration. Likewise, as the fluid leaves the constriction, it is slowed by a pressure gradient force that raises the pressure back to the ambient level. This investigation involves certain modification in the venturi design which passionate the mixing of two different liquids. Further a jet nozzle is used to accomplish the objective and this process is somewhat similar to that of atomization. The discharge of the main liquid can be varied with respect to latter's phenomenon. The venturi made of metal makes it difficult to view the details of the flow inside it. To overcome this, a clear venturi made of acrylic fiber material was used. The dimension of venturi jet mixer with jet provided at the throat is shown in Figure. 1.

[FIGURE 1 OMITTED]

Experimental Setup

The experimental apparatus consists of an assembly of a horizontal PVC pipe of diameter 20mm with a length of 1.5 m, venturi jet mixer, rotameter, pump, pressure gauges, vacuum gauges etc. The venturi jet mixer is placed at the middle of the pipe line with the help of clamps, which has a replaceable facility (unions at both ends of a replaceable horizontal pipe) so that different venturi may be used. Reynolds number Re>4000 is maintained to ensure fully developed turbulent flow in all cases. A calibrated rotameter is used to measure the discharge of main liquid. It is placed near to the inlet section of venturi. For investigation purpose potassium dichromate([K.sub.2][Cr.sub.2][0.sub.7]) of 0.1 concentrations have been used as a secondary fluid (jet), which was placed at a distance of 10cm below the axis of venturi jet mixer. The suction effect produced by the venturi arises from the flow of water through the mixing head, such that when the flow is interrupted, the suction effect disappears by itself, which stops the flow of secondary liquid toward the mixing head. To avoid any parasitic flow of secondary liquid by a siphon effect after stopping the flow of water, the level of secondary liquid in the reservoir is located at a lower level than the mixing chamber. Hence the suction of secondary liquid toward the mixing chamber will not be counter balanced by too greater a vacuum in the reservoir.

Model Equations and Solution Method

The equations of conservation of mass, and momentum for steady, incompressible, and viscous flow with constant fluid properties are [11]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)

At the walls no slip boundary condition is imposed and also no heat generation is assumed. At the outlet a pressure outflow boundary condition is imposed.

Finite volume discretization of the governing equation produces a set of algebraic equations, which are needed to be solved sequentially by the alternating direction implicit (ADI) method. Pressure-velocity coupling is achieved by discretisation of the continuity equation to derive an equation for pressure from the discrete continuity equation. Pressure-velocity coupling is required only for the segregated solver (FLUENT/UNS) [12]. The Semi-Implicit Pressure Linked Equations (SIMPLE) algorithm is used to solve the set of the governing equations [13]. The standard k-[epsilon] model is used in the current study. Its main advantages are rapid, stable calculation and reasonable results for many flows, especially those with high Reynolds number [14]. For pressure drop, effective viscosity and maximum axial velocity to be within 5%, the grid structure with 60000 grid points were found to be adequate.

Results and Discussion

Runs reported in this paper were carried out using 20mm venturi inlet diameter, 10mm and 9mm constriction diameter and jet of 2mm placed at inlet, centre and outlet along the throat. Jet tip were positioned at distances of 1mm, 2.5mm and 5mm from the inner wall of the mixer. Experiments with different velocities of main liquid (0.26-1.56m/s) were also carried out. Tests were done in the Reynolds number range of 6360-63600; suitable pumps were chosen to supply the main fluid with adequate flow rates. Suitable experimental set up were used to measure dynamic viscosity of main liquid, secondary liquid and mixture. Concentration of mixture obtained from the mixer was determined using spectrophotometer setup.

Our objective is to investigate the mixing process and to predict the mixer efficiency of a transverse jet with the constriction of venturi. However, most of the research has been conducted for a configuration in which the jet is normal to the mixer. Although in chemical engineering it may be desirable to have the sideissued jet contact the wall at 90o in order to enhance rapid mixing. Water at standard conditions is used as the working fluid. We studied the effect of the venturi dimensions, the jet diameter and the volumetric flow ratio. These parameters, particularly the product of the ratios of the jet -to- pipe momentum ratio, are found to be the controlling factors of the mixer.

Experimental results on moment ratio, power ratio, discharge ratio mixing parameter for various venturi sizes (20x10mm,20x9mm),jet locations along the throat (centre, outlet, inlet, top and bottom) and datum level between axis of venturi and top surface of tracer (secondary fluid) have been analyzed. The homogeneity of the cross section is assured by natural turbulence if the pipe line velocity is adequate. Where natural turbulence is insufficient, the distribution may be improved by using in -line static mixers, motor driven shear mixers or alternately jet mixers .Where flow rate rangeability is high the venturi jet mixer system provides an ideal and energy efficient solution .In pipeline with flow venturi sideways migration and shear of the fluid is always occurring the degree of shearing and mixing increases with pipeline velocity, reducing droplet size and improving the overall dispersion and distribution .

Effect of Reynolds number (Re) on discharge ratio(q/Q), and power ratio (P)

Often, the objectives in industrial mixing processes are to mix a known volume of two fluids and to achieve desired mixture uniformity within an available downstream pipeline distance. Forney and Lee (1982) [15] established the importance of the diameter and velocity ratio for geometrically similar flows. Therefore, the mixer performance based on the volumetric flow ratio (q/Q) is very important in the design and selection procedure.

The jet-to-pipe power ratio can be written for n number of jets as,

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

From Figure 2 and 3, it is observed that when the rate of discharge is less Reynolds Number was found to low, therefore less turbulence; but with increase in flow rate turbulence of main liquid increases and since change in secondary fluid flow is less than that main liquid flow, discharge ratio (q/Q) reduces which cause decrease in power ratio as given in equation (3). Figures 2 and 3 demonstrate a significant power reduction for mixer of case-5, thus the economical benefit of such geometries. In present study n=1 (1 jet) is used for both experimentation and simulation. For convenience the different cases of venturi jet mixer is indicated at the upper right hand corner of these Figures.

Effect of Reynolds number (Re) on viscosity ratio

Mixing is said to be more effective and of higher degree of homogeneity if degree of viscosity reduces. Viscosity of the fluid mixture can be calculated using,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

With the increase in velocity, Reynolds number increases that cause more amount of secondary fluid to enter into throat region, but the flow rate of secondary fluid is less than that of the main fluid, therefore viscosity ratio decreases. Figure 4 indicates that viscosity ratio decreases with the increase in Reynolds number. From Figure 4 it can be approximated that case-3 and case-5 give better result compared to other venturi jet mixer.

[FIGURE 4 OMITTED]

Figures 5 and 6 show a comparison of the experimental viscosity for Re (6300-63000) for different venturi jet mixer with those numerically predicted for the physical mixing of two liquid streams. The predicted values of viscosity of mixture depicted in Figure 6 agree well with the experimental data shown in Figure 5.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Effect of second moment(M) on mixing parameter([zeta])

Furthermore we characterise the homogeneity of the mixture by determining the second moment of tracer concentration, M for the venturi cross section area. For better mixing quality the second moment value should be less. Second moment directly depends on negative power of mixing parameter as given in equation (5), therefore with increase in mixing parameter second moment reduces which indicates uniform mixing which can be observed in Figures 7 and 8.

In practice, the design procedure is to fix q/Q and then to determine the jet-topipe diameter ratio that provides the desired degree of mixing. The latter is accomplished with equation (5) and Figure 7.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

The plot of M[(x/D).sup.En] Vs [Mo.sup.-1] in Figure 9 show a consistent mixing pattern. It also suggests that by modifying the variable 1/Mo, one can obtain a common curve. From Figure 8 one may approximate mixer performance and the plot may yield very important information to select and design the venturi jet mixers.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

From these plots it is clear that all configurations have a similar mixing pattern with downstream distance, which is expected since the mixing quantity M decreases (i.e the mixture uniformity increases) with an increase in Reynolds number (Re) and decrease in discharge ratio (q/Q).

Effect of concentration ratio(Co/C) on moment ratio (M/Mo)

Sroka and Forney (1989) [16] derived a scaling law for the second moment of the tracer concentration within the pipeline when the turbulent jet injection is normal to the pipeline. Furthermore Mo is defined as the initial second moment of the cross-sectional concentration in the main and the jet before mixing with respect to the final average concentration C and it can be expressed as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

where, [C.sup.m] is the initial main pipe tracer concentration. From Figure 10, it can be observed that with the increase in concentration ratio, moment ratio decreases and for venturi jet mixer of case 5 it reduces uniformly.

[FIGURE 10 OMITTED]

Mixing parameter ([zeta]) for different venturi jet mixers

For mixture to be more uniform the value of mixing parameters has to be more. Mixing parameter mainly depends upon discharge ratio and jet-to-pipe diameter [17]. Since for a particular venturi mixer configuration, jet-to-pipe diameter ratio remains constant and hence mixing parameter is dependent on volumetric flow ratio (q/Q) as shown in equation 7.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)

Amongst the modified venturies the value of mixing parameter ([zeta]) is maximum for venturi mixer of case 5 as indicated in the Figure 11. Figures 12 and 13 shows pressure and velocity contours obtained from the current CFD simulations. For R of 0.35, and um of 0.6m/s Figure 13 shows that the jet impinges the opposite wall and an eddy is formed at the exit of the mixer.

Variation coefficient (CoV) of different venturi jet mixers

Ger and Holley (1976) [18] and Holley (1981) [19] conducted experiments and compared co-efficient of variation (CoV) of measured tracer concentration far down the mixer and proposed the CoV as an indicator of mixing quality. The homogeneity requirement differs according to the particular mixing task and should be specified by the final user in terms of variation coefficient CoV. Usually a CoV lies in the range of 0.6 to 0.9 is a reasonable target for more applications. Lower the value of CoV the better the mixture quality. Finally the variation coefficient is shown for different venturi jet mixers in Figure 14 represent that the experimental values of CoV are within the range.

[FIGURE 11 OMITTED]

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

Conclusion

Venturi-jet mixers have a variety of application in chemical and biological processes, becoming an important component in mixing systems. The detailed mixing behaviors of venturi jet mixer have been developed by experimental analysis and numerical analysis, which ultimately facilitates efficient mixer design. A systematic experimental method has been developed enabling quantification of mixing performance in venturi jet mixers. The numerical simulations approve the appearance of vortex-like structures, and the phenomenon of engulfment at higher velocity near the outlet of the mixer. From the current study by comparing the various performance parameters between the five cases of venturi jet mixer imply that the mixing quality obtained in case-5 is the most optimal. Thus by having venturi with minimum throat diameter and positioning the jet near to the wall of venturi, the mixing performance can be optimized.

Nomenclature

C Concentration of the liquid

[C.sub.o] Jet tracer concentration

[d.sub.j] Diameter of the jet/nozzle, m

[d.sub.th] Diameter of the throat, m

[d.sub.p] Diameter of the pipe, m

[f.sub.1] Fraction of main liquid

[f.sub.2] Fraction of secondary liquid

M Second moment of tracer concentration

Mo Initial second moment

n Number of jet

P Jet-to-pipe power ratio

q Volumetric flow rate of Secondary liquid, [m.sup.3]/s

Q Volumetric flow rate of main liquid, [m.sup.3]/s

R Velocity ratio

Re Reynolds Number

[u.sub.m] Main liquid velocity, m/s

[u.sub.j] Jet velocity, m/s

x Distance of downstream from the mixer inlet, m

Greek Symbols

[rho] Density of the liquid, kg/[m.sup.3]

[micro] Dynamic viscosity, Ns/[m.sup.2]

[micro].sub.t] Eddy viscosity

[zeta] Mixing parameter, [n.sup.2][R.sup.2][(d/D).sup.2]

References

[1] Etchells AW, Meyer CF. Mixing in Pipelines in Handbook of Industrial Mixing Science and Practice A.L. Paul VA, Atiemo- Obeng SZ, Kresta E. John Wiley & Sons, Inc., Hoboken, New Jersey 2004; p.391-477.

[2] Mathys, P., Frohofer, S.: US20036595682B2 (2003).

[3] Mathys, P., Fleischli M., Breiter A.: US20046811302B2 (2004).

[4] Aklilu T.G. Giorges, Forney L.J and Xiaodong Wang 2001. "Numerical study of multi-jet mixing", TransIChemE, Vol.79, p.515.

[5] Casey Jones S, Fotis Sotiropoules and Appiah Amirtharajah 2002. "Numerical modeling of helical static mixers for water treatment", Journal of Environmental Engineering Vol.128, No.5 p.431.

[6] Hartung HK, Hiby JW. Acceleration of Turbulent Mixing in Tubes. Chemi-Ingeneieur-Technik 1972; 18: p.1051-1056.

[7] Chilton T.H and Genereaux R.P., 1930. "The mixing of gases for reaction", AIChE Trans,25. p.102.

[8] Heindel H.L., Hardy S.A., Amirtharajah A and Arrowwood M.J 1999. "Disinfection of cryptosporidium parvum with static mixers". Proc. AWWA Water quality technology conference, Denver.

[9] Diego A. Arias and Timothy A. Shedd 2004. Proceedings of the 11th International Symposium of Flow Visualisation. p.11.

[10] Zulkefli Yaacob, Zulkifli Abdul Majid, Martin Philip King Ik Piau and Ong, Hua Long, 1990. "A Study on Exhaust Performance and Lubricating Oil Effects on Natural Gas Motorcycle." Journal Technology, 31 (F)

[11] Wilcox D.C., 1993. "Turbulence modeling for CFD" (DCW Industries Inc.).

[12] Fluent Incorporated, 1995. Computational Fluid Dynamics Software, (Fluent Inc).

[13] Patankar S.V. 1980. Numerical Heat Transfer and Fluid Flow, New York. McGraw Hill.

[14] Habib D. Zughbi, Shad W. Siddiqui and Ashraf I. Fatehi. 2006. "Reactive mixing in a pipeline with a side-tee", The Arabian Journal for Science and Engineering, Vol.31, Number 13, p.13.

[15] Foney L.J and Lee H.C 1982, Optimum dimensions for pipeline mixing at a T-junction", AIChE J. Vol. 35, p.406.

[16] Sroka L.M and Forney L.J, 1989, "Fluid mixing with a pipeline tee: Theory and experiment", AIChE J, Vol 35.p.406.

[17] Forney L.T., Nafia N and Vo H.X., 1996, "Optimum jet mixing in a tubular reactor", AIChE J 42(11).p.3113.

[18] Ger A.M and Holley E.R., 1976, "Comparison of single-point injection in pipe flow", J Hydraulics Divisions of ASCE, 102(HY 6). p.731.

[19] Fitzgerald S.D and Holley E.R., 1981, "Jet injections for optimum mixing in pipe flow", J. Hydraulics Division of ASCE, 107(Hy 10). p.1179.

S. Sundararaj (1) and V. Selladurai (2)

(1) Department of Mechanical Engineering, Sri Krishna College of Engineering & Technology, Coimbatore, Tamilnadu, India

(2) Professor and Head, Department of Mechanical Engineering, Coimbatore Institute of Technology, Coimbatore, Tamilnadu, India Email:papers.sundar@yahoo.co.in
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Author:Sundararaj, S.; Selladurai, V.
Publication:International Journal of Applied Engineering Research
Article Type:Report
Date:Jul 1, 2008
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