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Effects of geometry and operating conditions on the mixing behavior of an in-line impinging stream mixer
Chemical Engineering Science 60 (2005) 1701 – 1708 www.elsevier.com/locate/ces
Effects of geometry and operating conditions on the mixing behavior of an in-line impinging stream mixer Chalida Niamnuy, Sakamon Devahastin∗ Department of Food Engineering, King Mongkut’s University of Technology Thonburi, 91 Pracha u-tid Road, Bangkok 10140, Thailand Received 28 May 2004; received in revised form 18 October 2004; accepted 29 October 2004
Abstract The present study investigated experimentally the effects of various geometric and operating parameters on the mixing characteristics of model liquids undergoing mixing in a novel in-line mixer, viz. an in-line impinging stream (IS) mixer. First, the mixer with one set of three inlet jets was used. Later two sets of inlet jets were used in order to increase the number of impingement zones and hence the mixing capability of the mixer. A statistical analysis was performed to indicate the best geometry of the mixer based on the data of both the mixing effectiveness and the pressure loss due to impingement of liquid streams. 䉷 2004 Elsevier Ltd. All rights reserved. Keywords: Mixing index; Pressure loss; Sucrose solution; Turbulent mixing
1. Introduction Mixing is one of the most important unit operations in the chemical and food industry since liquids must often be mixed into a homogeneous substance for easy handling and to obtain the desired characteristics of the final product. Normally, the process of mixing uses a mixing tank equipped with one or more agitators, which possesses some disadvantages, e.g., high-energy consumption and possibility of product contamination. A new type of mixer, viz. an in-line impinging stream (IS) mixer, is therefore proposed as an alternative for mixing two or more types of liquids by introducing streams of liquids into the mixer at high velocities and allowing them to impinge (or collide) against each other. As a result of the impingement a relatively narrow zone, which offers excellent conditions for transport processes is created. The streams then leave the system through the exit channel situated downstream of the impingement region(s).
∗ Corresponding author. Tel.: +662 470 9246; fax: +662 470 9240.
E-mail address: [email protected] (S. Devahastin). 0009-2509/$ - see front matter 䉷 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.10.031
The system supposedly yields a lower value of pressure drop than that encountered in a static mixer as well. Similar flow configurations have been studied recently, but the results are limited only to the laminar flow regime or are only numerical in nature. Hosseinalipour and Mujumdar (1997a, b) used temperature as a passive tracer to monitor mixing of two fluid streams in their numerical study of flow and thermal characteristics of steady two-dimensional confined laminar opposing jets. They found that by increasing the jet Reynolds number the uniformity of temperature profiles (and hence complete mixing of the two streams) was delayed. This is due to an increase in the momentum of the fluid in the exit channel (and hence shorter residence time of the fluid in the system) due to the additional mass coming into the system. Unger et al. (1998) studied flow and mixing in a semiconfined impinging jet contactor at low jet Reynolds numbers (Rej < 80) using flow visualization techniques, particle image velocimetry and three-dimensional numerical simulations. Among the reported results they observed that a substantial improvement in the mixing could be obtained by a slight modification of the impinging jet geometry that disrupted the geometric symmetry of the system.
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Johnson (2000a) performed flow visualization, LDV measurements as well as steady and unsteady three-dimensional finite volume simulations to study the flow field created by an impingement of laminar liquid jets of unequal momentum in a confined cylindrical chamber. Based on the video analysis of the flow field, this investigator found that the impingement area and the structure of the flow were more stable at higher jet Reynolds numbers for the unequal flow rate cases than those of the comparable equal flow rate cases. Unsteady numerical simulations of the flow field predicted the delay of unidirectional flow (in the downstream direction of the inlet jets) until a large value of the downstream distance had elapsed. This led to poorer mixing as compared to the equal flow cases. Johnson (2000b) then proposed alternative schemes to reduce the negative effects of flow imbalance (which is sometimes required by the stoichiometry of the reactions conducted in the equipment) such as nozzle plugging due to a high-pressure region near the lower momentum jet outlet. Three schemes were proposed and tested and it was possible to shift the impingement point toward the geometric center of the chamber by these simple modifications of the inlet nozzles. Mixing was not improved, however. Devahastin and Mujumdar (2002) studied flow and mixing characteristics of two-dimensional laminar confined impinging streams numerically. By solving time-dependent conservation equations for mass, momentum and energy they obtained the conditions beyond which the flow in impinging streams became oscillatory and even random for various geometric configurations. They also studied the effects of the inlet jet Reynolds number and system geometry on the mixing of two fluid streams impinging normally against each other. It was found that these parameters had strong effects on both the mixing of the two streams in the impingement region and the required length of the mixing channel to obtain a well-mixed condition at the exit. Devahastin and Mujumdar (2001a) proposed and tested via numerical simulation a new conceptual design of a modified in-line mixer for viscous fluids without the use of mechanical obstructions in the channel. The concept involved dividing one of the fluid streams into a multiplicity of streams, which were injected into the main flow channel as two-dimensional slot jets and impinged with another multiplicity of streams divided from another fluid stream. Effects of various key parameters, viz. inlet jet Reynolds number, the ratio of the height of the mixer exit channel to the width of an inlet jet (H/W) and the ratio of the spacing between the two inlet jets to the width of an inlet jet (S/W) on the mixing behavior of the system, were explained. Later, Devahastin and Mujumdar (2001b) extended their study of flow and mixing behavior of two-dimensional confined impinging streams to the turbulent flow regime. Using a newly proposed turbulence model they found that as the jet Reynolds number increased mixing was improved until some specific values of the dimensionless axial distance were reached. These critical values depended on both the operating conditions as well as the geometry of the system. This behavior
was quite different from what was observed in laminar impinging streams of similar geometries (Devahastin and Mujumdar, 2002). For turbulent impinging streams increase in the jet Reynolds number led to higher levels of the turbulence kinetic energy, especially in the impingement zone. The values of the turbulent viscosity were also higher at higher jet Reynolds number; this increase led to a stronger eddy mixing. The poorer mixing quality observed beyond the critical length of the main flow channel may be ascribed to the increased mean flow rate; the effect of higher turbulence kinetic energy at higher jet Reynolds number was overshadowed by the effectively shorter transit time. However, the model is yet to be extended to include the species balance equation(s) in order to use it to simulate the impingement and mixing of streams of different components. The model is not appropriate for the cases where the jet Reynolds numbers are in (or close to) the transitional region mentioned by Devahastin and Mujumdar (2002) as well. In this work a pilot-scale prototype of a novel in-line impinging stream mixer was designed and fabricated based on the conceptual mixer proposed by Devahastin and Mujumdar (2001a). The effects of various geometric and operating parameters on its mixing effectiveness were then investigated. A statistical analysis was also performed to indicate the best geometry of the mixer based on the data of both the mixing effectiveness and the pressure loss due to impingement of liquid streams.
2. Experimental setup and procedures 2.1. Experimental setup A schematic diagram of an in-line impinging stream mixer with two pairs of three inlet jets is shown in Fig. 1 while a schematic diagram of the overall experimental setup is shown in Fig. 2. The diameter of the mixer main flow channel, the inlet jet diameter and the spacing between each pair of inlet jets are denoted by D, d and S, respectively. The main flow channel of the mixer was made of a 4-in (10-cm) PVC pipe while the inlet nozzles (of different sizes) were made of cast nylon. The inlet nozzles could be easily removed from the main flow channel and be replaced by nozzles of different sizes, so the effect of inlet jet (or nozzle) diameter on mixing could be studied. For the measurement of pressure loss due to impingement of liquid streams, a manometer was used to measure the pressure drop between a position on the first inlet jet and the three other positions on the main flow channel in each experiment. For example, in the case where S/D = A, the pressure drop was measured between point O and points 1A, 2A and 3A, while in the case where S/D = B, the pressure drop was measured between point O and points 1B, 2B and 3B as show in Fig. 3 . A and B are any arbitrary values of S/D, which were not initially specified as the exact values to be used in the pressure drop measurement were not known
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Fig. 1. A schematic diagram of an in-line impinging stream mixer studied (Fluid #1: 10 % (w/w) sucrose solution; Fluid #2: 20 % (w/w) sucrose solution; Fluid #3: water).
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a priori (since at first it was not known which S/D values would give the best mixing results). 2.2. Experimental procedure Three streams of fluid substances, i.e., 10 % (w/w) sucrose solution, 20 % (w/w) sucrose solution and water, were pumped from three storage tanks to the mixer by three centrifugal pumps each rated at 2 hp (CAE Cooperation Ltd., Taiwan) through flexible PVC hoses. The fluid streams im-
pinged against each other and left the mixer through the main flow channel. All experiments were performed at a constant temperature of 29 ◦ C (room temperature). The mixing characteristics of the mixer were quantified by sampling approximately 3 cm3 of the mixing fluid (using a syringe, see Fig. 4) at every 30 cm (8 points) along the length of the main flow channel of the mixer. Five radial positions across the channel were sampled at a particular axial position as shown in Fig. 4. The first sampling point is at x/D = 7.5, which means that for D = 10 cm (4 in) the first sampling position is located 75 cm from the first set of inlet jets. The concentration distribution of sucrose solution was analyzed using a hand-held refractometer (Atago, model ATC1E, Japan). As the three fluid streams mixed and approached the exit port the concentration profiles across the main flow channel were flattened; the well-mixed condition was satisfied when no concentration gradient existed across the channel, i.e., the concentration profile was flat. To quantify the mixing performance of the mixer at different operating conditions and geometric configurations a mixing index was defined as follows: C Mixing index = , (1) Cwell-mixed where C is the standard deviation of sucrose concentration across the channel diameter at any particular axial location along the main flow channel. Cwell-mixed is the calculated concentration (based on a simple mass balance) that should be obtained if the well-mixed condition is met. A mixing index of zero thus implies a well-mixed condition. To study the effects of various geometric parameters of an in-line impinging stream mixer on its mixing behavior, the ratio of the inlet jet diameter to the main flow channel diameter (d/D) was varied at two levels, i.e., d/D = 0.125 and d/D = 0.250. The ratio of the spacing between each set of inlet jets to the main flow channel diameter (S/D) was varied at four levels, i.e., S/D = N/A (one set of inlet jets),
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Fig. 4. A schematic diagram of sampling method and positions.
S/D = 1.5, 3 and 4.5. The effect of an inlet jet Reynolds number (Rej ) in the range of 5000–15 000 was also investigated. Experiments were designed using the full factorial design approach. Experimental data on the mixing effectiveness were analyzed statistically using the Tukey’s test at a significance level of 0.05 in order to identify the optimum geometry and operating conditions that resulted in the best mixing. Better mixing condition was defined as the condition that resulted in a shorter required length of the main flow channel to obtain a well-mixed condition. In addition, the geometry that led to the lowest pressure loss was required. An optimum geometry of an in-line impinging stream mixer is the one that yields good mixing and low pressure loss due to impingement of liquid streams.
3. Results and discussion As mentioned earlier, liquid streams were injected into the mixer through each pair of the three inlets. The three streams impinged in the impingement zone and then left the mixer through the main flow channel. The length of the mixing channel was extended long enough to satisfy the well-mixing condition (2.80 m) at each operating condition and for different geometric configurations. The ranges of parameters studied are inlet jet Reynolds number (Rej ) from 5000 to 15 000, the ratio of the inlet jet diameter to the main flow channel diameter (d/D) from 0.125 to 0.250, the ratio of the spacing between each set of inlet jets to the main flow channel diameter (S/D) from 1.5 to 4.5 and N/A (i.e., the case with only one set of inlet jets). 3.1. Effect of inlet jet Reynolds number (Rej ) on mixing characteristics of the mixer Fig. 5 shows the plots of the mixing index versus the dimensionless axial distance along the main flow channel (x/D) with the inlet jet Reynolds number as a parameter for the case where d/D = 0.250. It is seen that an increase in the inlet jet Reynolds number led to a better mixing in the impingement zone(s) and its (their) vicinity (or at low x/D values) because of the higher velocity of the jets. Collision of high-velocity liquid streams led to high shear rates, strong eddy mixing and hence higher transfer rates of momentum
and mass in the impingement zone and its vicinity. The mixing quality changed, however, when the critical length of the main flow channel (crossing point of lines in the plots) was reached; beyond this critical value the lower mixing index was found for lower Reynolds numbers as the effects of higher shear and turbulent viscosity were overshadowed by the effectively shorter transit time of the mixing fluid. As the inlet jet Reynolds number increased the inlet jet velocity and hence the mean flow rate of liquids increased. This led to a shorter contact time for the fluids to mix; mixing was therefore poorer. The trend is quite different at Rej = 5000, however. This is because at this Rej the flow might be close to transitional flow (Devahastin and Mujumdar, 2002); no critical length beyond which the mixing quality changed was observed in this case. In addition, using two sets of inlet jets means that the mass flow rate of liquids entering the system was doubled compared with that of the mixer having only one set of inlets. This caused the critical lengths of the mixer utilizing two sets of inlets to be less than those of the mixer utilizing only one set of inlet jets (see Figs. 5 and 6). Fig. 6 shows plots similar to those in Fig. 5 with d/D = 0.125. It was found that as the inlet jet Reynolds number increased mixing was better over a short distance of the mixer. All similar trends can be seen in Figs. 6a–d. As can be seen in these figures, when the spacing between the sets of inlet jets increased the critical length and the total length required to obtain a well-mixed condition decreased (due to the fact that the mixing fluid had longer distance to exchange momentum and mass in a region with high shear rates and strong eddies). However, the critical length and the total length required to obtain a well-mixed condition for the case where d/D = 0.125 were shorter than those of the case where d/D = 0.250. This is because the inlet jet diameter for the case where d/D = 0.125 was smaller than that of the case where d/D =0.250. The turbulence intensity of the former case was therefore stronger and hence led to a shorter distance required to obtain a well-mixed condition. 3.2. Effect of the ratio of inlet jet diameter to main flow channel diameter (d/D) on mixing characteristics of the mixer Fig. 7 shows the plots of the mixing index versus the dimensionless axial distance (x/D) with d/D as a parameter. It can be seen in this figure that for fixed values of Rej and
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3.3. Effect of the ratio of spacing between each set of inlet jets to main flow channel diameter (S/D) on mixing characteristics of the mixer
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S/D, increase in d/D led to a longer required dimensionless length (x/D) of the main flow channel to obtain a well-mixed condition. This is because when d/D increased the liquid streams had lower velocities (due to larger jet openings) and hence weaker jet interaction. The mixing was therefore poorer. In addition, when the inlet jet Reynolds number increased the mixing fluid had higher velocity so the contact time for mixing was shorter and hence a longer length of the main
The plots of the mixing index versus the dimensionless axial distance with S/D as a parameter are shown in Fig. 8. Again, it is seen that, for fixed values of the inlet jet Reynolds number and d/D, mixing was better when the spacing between sets of inlet jets increased. This is because the mixing fluid had longer time to exchange momentum and mass in the highly turbulent zone and of high shear as mentioned earlier. A similar trend can be observed for other jet Reynolds numbers and d/D values. Based on the mixing data, a statistical analysis was performed using the Tukey’s test (∝ 0.05) to identify the optimum geometry and operating conditions of the mixer. Choosing x/D = 10.5 as the sampling position as it was the position where a well-mixed condition started to be observed, the best geometry and conditions (based on the lower mixing index values over shorter distances of the main flow channel) are identified at S/D = 4.5, d/D = 0.125 and
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Rej = 5000. The other geometries and conditions that resulted in an insignificantly different mixing effectiveness are S/D = 4.5, d/D = 0.125 and Rej = 15 000; S/D = 4.5, d/D =0.250 and Rej =15 000; S/D =4.5, d/D =0.125 and Rej = 10 000; S/D = 3.0, d/D = 0.125 and Rej = 15 000; S/D = 3.0, d/D = 0.125 and Rej = 5000. From these results, it can be seen that S/D = 4.5, d/D = 0.125 are the geometric configurations of an in-line impinging stream mixer that created good mixing (well-mixed conditions over a short distance) at every value of Rej . However, mixers with S/D = 3.0, d/D = 0.125 and S/D = 4.5, d/D = 0.250 resulted in a similarly good mixing at some values of Rej .
3.4. Effect of geometry and operating conditions on pressure loss To better identify the optimum geometry of the mixer, experiments were performed to determine the pressure drop in the system due to impingement of liquid streams. Only selected geometric configurations, i.e., S/D = 3.0 and 4.5, d/D = 0.125 and 0.250, were tested since it was found from the previous statistical analysis that these geometries yielded similarly good mixing results. Combining these selections with the pressure drop data, the optimum mixer geometry could then be identified.
Fig. 9 shows the plots of the pressure drop versus the various measuring positions on the main flow channel (see Fig. 3) with S/D and d/D as parameters. The reason for using fixed measuring positions instead of an axial distance in Fig. 9 is to allow a direct comparison of pressure drop values of different cases at the same positions. It can be seen that when S/D and Rej were kept constant, a decrease in d/D led to a higher pressure drop. This is because the inlet jet diameter was reduced and became much smaller than the diameter of the main flow channel. When liquids flowed out from the inlet jets into the main flow channel, velocities of liquids dropped sharply; the liquid streams became turbulent and the turbulence kinetic energy in liquid streams was dispersed, which led to the loss of energy in the system. When d/D and Rej were kept constant, a decrease of S/D led to an increase in the pressure drop. This is because at low S/D, two sets of inlet jets were situated close to each other and when liquid streams entered the system through all inlet jets, strong turbulence was created and hence large pressure drop values. Comparing Figs. 9a–d, it can be seen that if d/D and S/D were kept constant, an increase of Rej would lead to a higher pressure drop because liquid streams would enter the main flow channel at higher velocities. The turbulent condition was then created, which led to higher pressure drop values (Robertson and Crowe, 1997).
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From the experimental results, it can be seen that the geometry that led to the lowest pressure drop values was S/D = 4.5, d/D = 0.250 and the second was S/D = 4.5, d/D = 0.125, which led to pressure drop of not more than 1.2 times of the former geometry at the same value of Rej . Based on the mixing characteristics and pressure drop data, a mixer with S/D =4.5, d/D =0.125 was identified as the optimum mixer that yielded both good mixing and low pressure drop due to stream impingement at every value of Rej in the range of this study. 4. Conclusions The present study examined the effects of various geometric and operating parameters on the mixing characteristics of an in-line impinging stream mixer. For a fixed value of d/D, an increase in the value of the jet Reynolds number led to a better mixing in the impingement zone and its vicinity. This mixing behavior persisted until a critical value of dimensionless axial distance (x/D) was reached beyond which the mixing quality changed. For a mixer with two sets of inlet jets it was found that a larger spacing between the two sets of inlet jets (higher S/D) resulted in a better mixing in the region between the sets of inlet jets but yielded no significant difference in the required main flow channel length to obtain a well-mixed condition. For each value of Rej and S/D, increase in d/D led to a poorer mixing and a longer dimensionless length (x/D) required to obtain a well-mixed condition. Based on the statistical analysis of the experimental mixing results, a mixer with S/D = 4.5, d/D = 0.125 yielded best mixing at every value of Rej . However, mixers with S/D=3.0, d/D=0.125 and S/D = 4.5, d/D = 0.250 also yielded good mixing at some values of Rej . To better identify the optimum geometry of the mixer, experiments were also performed to determine the values of pressure loss due to impingement of liquid streams in mixers of various geometries. For fixed values of S/D and Rej , a decrease in d/D led to larger pressure drop values the same way as when S/D was decreased or when Rej was increased while other parameters were kept constant. Based on both the mixing effectiveness and pressure loss data, the optimum geometry of an in-line mixer was identified as S/D = 4.5, d/D = 0.125. This geometry led to the good mixing characteristics and created low pressure loss at every value of Rej . Notation Cwell-mixed d D
calculated well-mixed concentration of the mixture, % w/w inlet jet diameter, cm main flow channel diameter, cm
S v x
spacing between two sets of inlet jets, cm mean flow velocity of each fluid substance, m s−1 axial distance from the first impingement zone along the main flow channel, cm
Greek letters
C
dynamic viscosity, kg m−1 s−1 kinematic viscosity, m2 s−1 density, kg m−3 standard deviation of sucrose concentration across the mixing channel, % w/w
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jet Reynolds number, dv / or dv/
Acknowledgments The authors would like to express their sincere appreciation to the Thailand Research Fund (TRF) for supporting this project financially through its Industrial Research Associate Support (IRAS) program. Our appreciation also goes to our industrial partner, Patkol Public Co., Ltd., for the generous assistance provided throughout the course of this study. References Devahastin, S., Mujumdar, A.S., 2001a. A numerical study of mixing in a novel impinging stream in-line mixer. Chemical Engineering and Processing 40, 459–470. Devahastin, S., Mujumdar, A.S., 2001b. A study of turbulent mixing of confined impinging streams using a new composite turbulence model. Industrial & Engineering Chemistry Research 40, 4998–5004. Devahastin, S., Mujumdar, A.S., 2002. A numerical study of flow and mixing characteristics of laminar confined impinging streams. Chemical Engineering Journal 85, 215–223. Hosseinalipour, S.M., Mujumdar, A.S., 1997a. Flow and thermal characteristics of steady two-dimensional confined laminar opposing jets (Part I) equal jets. International Communications in Heat and Mass Transfer 24, 27–38. Hosseinalipour, S.M., Mujumdar, A.S., 1997b. Flow and thermal characteristics of steady two-dimensional confined laminar opposing jets (Part II) unequal jets. International Communications in Heat and Mass Transfer 24, 39–50. Johnson, D.A., 2000a. Experimental and numerical examination of confined laminar opposed jets: part I. Momentum imbalance. International Communications in Heat and Mass Transfer 27, 443–454. Johnson, D.A., 2000b. Experimental and numerical examination of confined laminar opposed jets: part II. Momentum balancing. International Communications in Heat and Mass Transfer 27, 455–463. Robertson, J.A., Crowe, C.T., 1997. Engineering Fluid Mechanics, sixth ed.. Wiley, Englewood Cliffs, NJ. Unger, D.R., Muzzio, F.J., Brodkey, R.S., 1998. Experimental and numerical characterization of viscous flow and mixing in an impinging jet contactor. Canadian Journal of Chemical Engineering 76, 546–555.
Effects of geometry and operating conditions on the mixing behavior of an in-line impinging stream mixer Chalida Niamnuy, Sakamon Devahastin∗ Department of Food Engineering, King Mongkut’s University of Technology Thonburi, 91 Pracha u-tid Road, Bangkok 10140, Thailand Received 28 May 2004; received in revised form 18 October 2004; accepted 29 October 2004
Abstract The present study investigated experimentally the effects of various geometric and operating parameters on the mixing characteristics of model liquids undergoing mixing in a novel in-line mixer, viz. an in-line impinging stream (IS) mixer. First, the mixer with one set of three inlet jets was used. Later two sets of inlet jets were used in order to increase the number of impingement zones and hence the mixing capability of the mixer. A statistical analysis was performed to indicate the best geometry of the mixer based on the data of both the mixing effectiveness and the pressure loss due to impingement of liquid streams. 䉷 2004 Elsevier Ltd. All rights reserved. Keywords: Mixing index; Pressure loss; Sucrose solution; Turbulent mixing
1. Introduction Mixing is one of the most important unit operations in the chemical and food industry since liquids must often be mixed into a homogeneous substance for easy handling and to obtain the desired characteristics of the final product. Normally, the process of mixing uses a mixing tank equipped with one or more agitators, which possesses some disadvantages, e.g., high-energy consumption and possibility of product contamination. A new type of mixer, viz. an in-line impinging stream (IS) mixer, is therefore proposed as an alternative for mixing two or more types of liquids by introducing streams of liquids into the mixer at high velocities and allowing them to impinge (or collide) against each other. As a result of the impingement a relatively narrow zone, which offers excellent conditions for transport processes is created. The streams then leave the system through the exit channel situated downstream of the impingement region(s).
∗ Corresponding author. Tel.: +662 470 9246; fax: +662 470 9240.
E-mail address: [email protected] (S. Devahastin). 0009-2509/$ - see front matter 䉷 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2004.10.031
The system supposedly yields a lower value of pressure drop than that encountered in a static mixer as well. Similar flow configurations have been studied recently, but the results are limited only to the laminar flow regime or are only numerical in nature. Hosseinalipour and Mujumdar (1997a, b) used temperature as a passive tracer to monitor mixing of two fluid streams in their numerical study of flow and thermal characteristics of steady two-dimensional confined laminar opposing jets. They found that by increasing the jet Reynolds number the uniformity of temperature profiles (and hence complete mixing of the two streams) was delayed. This is due to an increase in the momentum of the fluid in the exit channel (and hence shorter residence time of the fluid in the system) due to the additional mass coming into the system. Unger et al. (1998) studied flow and mixing in a semiconfined impinging jet contactor at low jet Reynolds numbers (Rej < 80) using flow visualization techniques, particle image velocimetry and three-dimensional numerical simulations. Among the reported results they observed that a substantial improvement in the mixing could be obtained by a slight modification of the impinging jet geometry that disrupted the geometric symmetry of the system.
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Johnson (2000a) performed flow visualization, LDV measurements as well as steady and unsteady three-dimensional finite volume simulations to study the flow field created by an impingement of laminar liquid jets of unequal momentum in a confined cylindrical chamber. Based on the video analysis of the flow field, this investigator found that the impingement area and the structure of the flow were more stable at higher jet Reynolds numbers for the unequal flow rate cases than those of the comparable equal flow rate cases. Unsteady numerical simulations of the flow field predicted the delay of unidirectional flow (in the downstream direction of the inlet jets) until a large value of the downstream distance had elapsed. This led to poorer mixing as compared to the equal flow cases. Johnson (2000b) then proposed alternative schemes to reduce the negative effects of flow imbalance (which is sometimes required by the stoichiometry of the reactions conducted in the equipment) such as nozzle plugging due to a high-pressure region near the lower momentum jet outlet. Three schemes were proposed and tested and it was possible to shift the impingement point toward the geometric center of the chamber by these simple modifications of the inlet nozzles. Mixing was not improved, however. Devahastin and Mujumdar (2002) studied flow and mixing characteristics of two-dimensional laminar confined impinging streams numerically. By solving time-dependent conservation equations for mass, momentum and energy they obtained the conditions beyond which the flow in impinging streams became oscillatory and even random for various geometric configurations. They also studied the effects of the inlet jet Reynolds number and system geometry on the mixing of two fluid streams impinging normally against each other. It was found that these parameters had strong effects on both the mixing of the two streams in the impingement region and the required length of the mixing channel to obtain a well-mixed condition at the exit. Devahastin and Mujumdar (2001a) proposed and tested via numerical simulation a new conceptual design of a modified in-line mixer for viscous fluids without the use of mechanical obstructions in the channel. The concept involved dividing one of the fluid streams into a multiplicity of streams, which were injected into the main flow channel as two-dimensional slot jets and impinged with another multiplicity of streams divided from another fluid stream. Effects of various key parameters, viz. inlet jet Reynolds number, the ratio of the height of the mixer exit channel to the width of an inlet jet (H/W) and the ratio of the spacing between the two inlet jets to the width of an inlet jet (S/W) on the mixing behavior of the system, were explained. Later, Devahastin and Mujumdar (2001b) extended their study of flow and mixing behavior of two-dimensional confined impinging streams to the turbulent flow regime. Using a newly proposed turbulence model they found that as the jet Reynolds number increased mixing was improved until some specific values of the dimensionless axial distance were reached. These critical values depended on both the operating conditions as well as the geometry of the system. This behavior
was quite different from what was observed in laminar impinging streams of similar geometries (Devahastin and Mujumdar, 2002). For turbulent impinging streams increase in the jet Reynolds number led to higher levels of the turbulence kinetic energy, especially in the impingement zone. The values of the turbulent viscosity were also higher at higher jet Reynolds number; this increase led to a stronger eddy mixing. The poorer mixing quality observed beyond the critical length of the main flow channel may be ascribed to the increased mean flow rate; the effect of higher turbulence kinetic energy at higher jet Reynolds number was overshadowed by the effectively shorter transit time. However, the model is yet to be extended to include the species balance equation(s) in order to use it to simulate the impingement and mixing of streams of different components. The model is not appropriate for the cases where the jet Reynolds numbers are in (or close to) the transitional region mentioned by Devahastin and Mujumdar (2002) as well. In this work a pilot-scale prototype of a novel in-line impinging stream mixer was designed and fabricated based on the conceptual mixer proposed by Devahastin and Mujumdar (2001a). The effects of various geometric and operating parameters on its mixing effectiveness were then investigated. A statistical analysis was also performed to indicate the best geometry of the mixer based on the data of both the mixing effectiveness and the pressure loss due to impingement of liquid streams.
2. Experimental setup and procedures 2.1. Experimental setup A schematic diagram of an in-line impinging stream mixer with two pairs of three inlet jets is shown in Fig. 1 while a schematic diagram of the overall experimental setup is shown in Fig. 2. The diameter of the mixer main flow channel, the inlet jet diameter and the spacing between each pair of inlet jets are denoted by D, d and S, respectively. The main flow channel of the mixer was made of a 4-in (10-cm) PVC pipe while the inlet nozzles (of different sizes) were made of cast nylon. The inlet nozzles could be easily removed from the main flow channel and be replaced by nozzles of different sizes, so the effect of inlet jet (or nozzle) diameter on mixing could be studied. For the measurement of pressure loss due to impingement of liquid streams, a manometer was used to measure the pressure drop between a position on the first inlet jet and the three other positions on the main flow channel in each experiment. For example, in the case where S/D = A, the pressure drop was measured between point O and points 1A, 2A and 3A, while in the case where S/D = B, the pressure drop was measured between point O and points 1B, 2B and 3B as show in Fig. 3 . A and B are any arbitrary values of S/D, which were not initially specified as the exact values to be used in the pressure drop measurement were not known
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a priori (since at first it was not known which S/D values would give the best mixing results). 2.2. Experimental procedure Three streams of fluid substances, i.e., 10 % (w/w) sucrose solution, 20 % (w/w) sucrose solution and water, were pumped from three storage tanks to the mixer by three centrifugal pumps each rated at 2 hp (CAE Cooperation Ltd., Taiwan) through flexible PVC hoses. The fluid streams im-
pinged against each other and left the mixer through the main flow channel. All experiments were performed at a constant temperature of 29 ◦ C (room temperature). The mixing characteristics of the mixer were quantified by sampling approximately 3 cm3 of the mixing fluid (using a syringe, see Fig. 4) at every 30 cm (8 points) along the length of the main flow channel of the mixer. Five radial positions across the channel were sampled at a particular axial position as shown in Fig. 4. The first sampling point is at x/D = 7.5, which means that for D = 10 cm (4 in) the first sampling position is located 75 cm from the first set of inlet jets. The concentration distribution of sucrose solution was analyzed using a hand-held refractometer (Atago, model ATC1E, Japan). As the three fluid streams mixed and approached the exit port the concentration profiles across the main flow channel were flattened; the well-mixed condition was satisfied when no concentration gradient existed across the channel, i.e., the concentration profile was flat. To quantify the mixing performance of the mixer at different operating conditions and geometric configurations a mixing index was defined as follows: C Mixing index = , (1) Cwell-mixed where C is the standard deviation of sucrose concentration across the channel diameter at any particular axial location along the main flow channel. Cwell-mixed is the calculated concentration (based on a simple mass balance) that should be obtained if the well-mixed condition is met. A mixing index of zero thus implies a well-mixed condition. To study the effects of various geometric parameters of an in-line impinging stream mixer on its mixing behavior, the ratio of the inlet jet diameter to the main flow channel diameter (d/D) was varied at two levels, i.e., d/D = 0.125 and d/D = 0.250. The ratio of the spacing between each set of inlet jets to the main flow channel diameter (S/D) was varied at four levels, i.e., S/D = N/A (one set of inlet jets),
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S/D = 1.5, 3 and 4.5. The effect of an inlet jet Reynolds number (Rej ) in the range of 5000–15 000 was also investigated. Experiments were designed using the full factorial design approach. Experimental data on the mixing effectiveness were analyzed statistically using the Tukey’s test at a significance level of 0.05 in order to identify the optimum geometry and operating conditions that resulted in the best mixing. Better mixing condition was defined as the condition that resulted in a shorter required length of the main flow channel to obtain a well-mixed condition. In addition, the geometry that led to the lowest pressure loss was required. An optimum geometry of an in-line impinging stream mixer is the one that yields good mixing and low pressure loss due to impingement of liquid streams.
3. Results and discussion As mentioned earlier, liquid streams were injected into the mixer through each pair of the three inlets. The three streams impinged in the impingement zone and then left the mixer through the main flow channel. The length of the mixing channel was extended long enough to satisfy the well-mixing condition (2.80 m) at each operating condition and for different geometric configurations. The ranges of parameters studied are inlet jet Reynolds number (Rej ) from 5000 to 15 000, the ratio of the inlet jet diameter to the main flow channel diameter (d/D) from 0.125 to 0.250, the ratio of the spacing between each set of inlet jets to the main flow channel diameter (S/D) from 1.5 to 4.5 and N/A (i.e., the case with only one set of inlet jets). 3.1. Effect of inlet jet Reynolds number (Rej ) on mixing characteristics of the mixer Fig. 5 shows the plots of the mixing index versus the dimensionless axial distance along the main flow channel (x/D) with the inlet jet Reynolds number as a parameter for the case where d/D = 0.250. It is seen that an increase in the inlet jet Reynolds number led to a better mixing in the impingement zone(s) and its (their) vicinity (or at low x/D values) because of the higher velocity of the jets. Collision of high-velocity liquid streams led to high shear rates, strong eddy mixing and hence higher transfer rates of momentum
and mass in the impingement zone and its vicinity. The mixing quality changed, however, when the critical length of the main flow channel (crossing point of lines in the plots) was reached; beyond this critical value the lower mixing index was found for lower Reynolds numbers as the effects of higher shear and turbulent viscosity were overshadowed by the effectively shorter transit time of the mixing fluid. As the inlet jet Reynolds number increased the inlet jet velocity and hence the mean flow rate of liquids increased. This led to a shorter contact time for the fluids to mix; mixing was therefore poorer. The trend is quite different at Rej = 5000, however. This is because at this Rej the flow might be close to transitional flow (Devahastin and Mujumdar, 2002); no critical length beyond which the mixing quality changed was observed in this case. In addition, using two sets of inlet jets means that the mass flow rate of liquids entering the system was doubled compared with that of the mixer having only one set of inlets. This caused the critical lengths of the mixer utilizing two sets of inlets to be less than those of the mixer utilizing only one set of inlet jets (see Figs. 5 and 6). Fig. 6 shows plots similar to those in Fig. 5 with d/D = 0.125. It was found that as the inlet jet Reynolds number increased mixing was better over a short distance of the mixer. All similar trends can be seen in Figs. 6a–d. As can be seen in these figures, when the spacing between the sets of inlet jets increased the critical length and the total length required to obtain a well-mixed condition decreased (due to the fact that the mixing fluid had longer distance to exchange momentum and mass in a region with high shear rates and strong eddies). However, the critical length and the total length required to obtain a well-mixed condition for the case where d/D = 0.125 were shorter than those of the case where d/D = 0.250. This is because the inlet jet diameter for the case where d/D = 0.125 was smaller than that of the case where d/D =0.250. The turbulence intensity of the former case was therefore stronger and hence led to a shorter distance required to obtain a well-mixed condition. 3.2. Effect of the ratio of inlet jet diameter to main flow channel diameter (d/D) on mixing characteristics of the mixer Fig. 7 shows the plots of the mixing index versus the dimensionless axial distance (x/D) with d/D as a parameter. It can be seen in this figure that for fixed values of Rej and
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S/D, increase in d/D led to a longer required dimensionless length (x/D) of the main flow channel to obtain a well-mixed condition. This is because when d/D increased the liquid streams had lower velocities (due to larger jet openings) and hence weaker jet interaction. The mixing was therefore poorer. In addition, when the inlet jet Reynolds number increased the mixing fluid had higher velocity so the contact time for mixing was shorter and hence a longer length of the main
The plots of the mixing index versus the dimensionless axial distance with S/D as a parameter are shown in Fig. 8. Again, it is seen that, for fixed values of the inlet jet Reynolds number and d/D, mixing was better when the spacing between sets of inlet jets increased. This is because the mixing fluid had longer time to exchange momentum and mass in the highly turbulent zone and of high shear as mentioned earlier. A similar trend can be observed for other jet Reynolds numbers and d/D values. Based on the mixing data, a statistical analysis was performed using the Tukey’s test (∝ 0.05) to identify the optimum geometry and operating conditions of the mixer. Choosing x/D = 10.5 as the sampling position as it was the position where a well-mixed condition started to be observed, the best geometry and conditions (based on the lower mixing index values over shorter distances of the main flow channel) are identified at S/D = 4.5, d/D = 0.125 and
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Rej = 5000. The other geometries and conditions that resulted in an insignificantly different mixing effectiveness are S/D = 4.5, d/D = 0.125 and Rej = 15 000; S/D = 4.5, d/D =0.250 and Rej =15 000; S/D =4.5, d/D =0.125 and Rej = 10 000; S/D = 3.0, d/D = 0.125 and Rej = 15 000; S/D = 3.0, d/D = 0.125 and Rej = 5000. From these results, it can be seen that S/D = 4.5, d/D = 0.125 are the geometric configurations of an in-line impinging stream mixer that created good mixing (well-mixed conditions over a short distance) at every value of Rej . However, mixers with S/D = 3.0, d/D = 0.125 and S/D = 4.5, d/D = 0.250 resulted in a similarly good mixing at some values of Rej .
3.4. Effect of geometry and operating conditions on pressure loss To better identify the optimum geometry of the mixer, experiments were performed to determine the pressure drop in the system due to impingement of liquid streams. Only selected geometric configurations, i.e., S/D = 3.0 and 4.5, d/D = 0.125 and 0.250, were tested since it was found from the previous statistical analysis that these geometries yielded similarly good mixing results. Combining these selections with the pressure drop data, the optimum mixer geometry could then be identified.
Fig. 9 shows the plots of the pressure drop versus the various measuring positions on the main flow channel (see Fig. 3) with S/D and d/D as parameters. The reason for using fixed measuring positions instead of an axial distance in Fig. 9 is to allow a direct comparison of pressure drop values of different cases at the same positions. It can be seen that when S/D and Rej were kept constant, a decrease in d/D led to a higher pressure drop. This is because the inlet jet diameter was reduced and became much smaller than the diameter of the main flow channel. When liquids flowed out from the inlet jets into the main flow channel, velocities of liquids dropped sharply; the liquid streams became turbulent and the turbulence kinetic energy in liquid streams was dispersed, which led to the loss of energy in the system. When d/D and Rej were kept constant, a decrease of S/D led to an increase in the pressure drop. This is because at low S/D, two sets of inlet jets were situated close to each other and when liquid streams entered the system through all inlet jets, strong turbulence was created and hence large pressure drop values. Comparing Figs. 9a–d, it can be seen that if d/D and S/D were kept constant, an increase of Rej would lead to a higher pressure drop because liquid streams would enter the main flow channel at higher velocities. The turbulent condition was then created, which led to higher pressure drop values (Robertson and Crowe, 1997).
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C. Niamnuy, S. Devahastin / Chemical Engineering Science 60 (2005) 1701 – 1708
From the experimental results, it can be seen that the geometry that led to the lowest pressure drop values was S/D = 4.5, d/D = 0.250 and the second was S/D = 4.5, d/D = 0.125, which led to pressure drop of not more than 1.2 times of the former geometry at the same value of Rej . Based on the mixing characteristics and pressure drop data, a mixer with S/D =4.5, d/D =0.125 was identified as the optimum mixer that yielded both good mixing and low pressure drop due to stream impingement at every value of Rej in the range of this study. 4. Conclusions The present study examined the effects of various geometric and operating parameters on the mixing characteristics of an in-line impinging stream mixer. For a fixed value of d/D, an increase in the value of the jet Reynolds number led to a better mixing in the impingement zone and its vicinity. This mixing behavior persisted until a critical value of dimensionless axial distance (x/D) was reached beyond which the mixing quality changed. For a mixer with two sets of inlet jets it was found that a larger spacing between the two sets of inlet jets (higher S/D) resulted in a better mixing in the region between the sets of inlet jets but yielded no significant difference in the required main flow channel length to obtain a well-mixed condition. For each value of Rej and S/D, increase in d/D led to a poorer mixing and a longer dimensionless length (x/D) required to obtain a well-mixed condition. Based on the statistical analysis of the experimental mixing results, a mixer with S/D = 4.5, d/D = 0.125 yielded best mixing at every value of Rej . However, mixers with S/D=3.0, d/D=0.125 and S/D = 4.5, d/D = 0.250 also yielded good mixing at some values of Rej . To better identify the optimum geometry of the mixer, experiments were also performed to determine the values of pressure loss due to impingement of liquid streams in mixers of various geometries. For fixed values of S/D and Rej , a decrease in d/D led to larger pressure drop values the same way as when S/D was decreased or when Rej was increased while other parameters were kept constant. Based on both the mixing effectiveness and pressure loss data, the optimum geometry of an in-line mixer was identified as S/D = 4.5, d/D = 0.125. This geometry led to the good mixing characteristics and created low pressure loss at every value of Rej . Notation Cwell-mixed d D
calculated well-mixed concentration of the mixture, % w/w inlet jet diameter, cm main flow channel diameter, cm
S v x
spacing between two sets of inlet jets, cm mean flow velocity of each fluid substance, m s−1 axial distance from the first impingement zone along the main flow channel, cm
Greek letters
C
dynamic viscosity, kg m−1 s−1 kinematic viscosity, m2 s−1 density, kg m−3 standard deviation of sucrose concentration across the mixing channel, % w/w
Dimensionless group Rej
jet Reynolds number, dv / or dv/
Acknowledgments The authors would like to express their sincere appreciation to the Thailand Research Fund (TRF) for supporting this project financially through its Industrial Research Associate Support (IRAS) program. Our appreciation also goes to our industrial partner, Patkol Public Co., Ltd., for the generous assistance provided throughout the course of this study. References Devahastin, S., Mujumdar, A.S., 2001a. A numerical study of mixing in a novel impinging stream in-line mixer. Chemical Engineering and Processing 40, 459–470. Devahastin, S., Mujumdar, A.S., 2001b. A study of turbulent mixing of confined impinging streams using a new composite turbulence model. Industrial & Engineering Chemistry Research 40, 4998–5004. Devahastin, S., Mujumdar, A.S., 2002. A numerical study of flow and mixing characteristics of laminar confined impinging streams. Chemical Engineering Journal 85, 215–223. Hosseinalipour, S.M., Mujumdar, A.S., 1997a. Flow and thermal characteristics of steady two-dimensional confined laminar opposing jets (Part I) equal jets. International Communications in Heat and Mass Transfer 24, 27–38. Hosseinalipour, S.M., Mujumdar, A.S., 1997b. Flow and thermal characteristics of steady two-dimensional confined laminar opposing jets (Part II) unequal jets. International Communications in Heat and Mass Transfer 24, 39–50. Johnson, D.A., 2000a. Experimental and numerical examination of confined laminar opposed jets: part I. Momentum imbalance. International Communications in Heat and Mass Transfer 27, 443–454. Johnson, D.A., 2000b. Experimental and numerical examination of confined laminar opposed jets: part II. Momentum balancing. International Communications in Heat and Mass Transfer 27, 455–463. Robertson, J.A., Crowe, C.T., 1997. Engineering Fluid Mechanics, sixth ed.. Wiley, Englewood Cliffs, NJ. Unger, D.R., Muzzio, F.J., Brodkey, R.S., 1998. Experimental and numerical characterization of viscous flow and mixing in an impinging jet contactor. Canadian Journal of Chemical Engineering 76, 546–555.