Article pubs.acs.org/IECR
Research on Heat Transfer Performance of Coaxial Mixer with Inner Combined Impeller Baoqing Liu, Yikun Zhang, Jingliang Liu, Luyan Qian, Peng Li, and Zhijiang Jin* Department of Chemical and Biological Engineering, Zhejiang University, Hangzhou 310027, Zhejiang, China ABSTRACT: A novel coaxial mixer was proposed, which had an outer wall-scraping frame and a combined inner impeller consisting of a four-pitched-blade turbine paddle (PBT-4) and a Rushton turbine paddle (RT-6). Its heat transfer performance in Newtonian fluid under different operating modes (single rotation of inner impeller, corotation and counter-rotation) was experimentally investigated in a stainless steel agitated vessel with semicircle spiral jacket and ellipsoidal head by measuring the average heat transfer coefficient of the inner wall. Meanwhile, the wall temperature, the heat flow rate and the local heat transfer coefficient in the coaxial agitated vessel were determined with the help of numerical simulation. The results show that the heat transfer coefficient near the inner wall surface of the agitated vessel will increase with the increasing speed of the inner or outer impeller whether under single-shaft agitation or under coaxial agitation mode, whereas the effect of speed of the inner impeller on heat transfer is more obvious and efficient. Under the same conditions, the heat transfer of coaxial agitation is more efficient than that of single-shaft agitation, especially the local heat transfer coefficient on the upper and lower part of the agitated vessel, which is increased greatly. In addition, the local heat transfer coefficient varies with the axial position of the agitated vessel, and the heat transfer coefficient in zones between the upper and lower impeller is relatively high. The effect of the corotation mode and counter-rotation mode on heat transfer is of little difference, but the corotation mode is recommended owing to its advantage of low power consumption and good mixing performance.
1. INTRODUCTION Mixing, one of the most widely used unit operations in the processing industry, is adaptable to different kinds of materials and reaction processes with different operating conditions. Most reaction processes need extra heat input or the removal of heat generated during the reaction processes. For example, many polymerization reactions, biochemical reactions and fine chemical reactions happen with great heat effect. Misdistribution of temperature, which is caused by poor heat transfer performance of the mixing tank, usually causes the reaction process to get out of control, which has a bad effect on the quality of the product. So, the distribution of temperature field in mixing tank has a great influence on the mixing process, and it is important to know the heat transfer performance of the mixing tank. A traditional mixer is usually composed of a single-shaft paddle, which has relatively poor performance on mixing and heat transfer in systems with high or variable viscosity, so a novel mixer with wide adaptability is desirable. Against this background, a coaxial mixer is designed, which is composed of an inner high speed rotating turbine paddle and an outer low speed rotating anchor or gate paddle. Because of the cooperation between inner and outer paddles, the flow circulation characteristics in the middle of the tank and near the inner wall are improved and the mass and heat transfer of the whole tank are also enhanced. Earlier research on the performance of coaxial mixers is largely restricted to power consumption and mixing characteristics. Xie et al.,1 Jin and Pan2 and Li et al.3 experimentally studied the power consumption and mixing characteristics of a coaxial mixer with different types of impellers. Guo et al.4 performed a numerical simulation of the mixing performance of a coaxial mixer. Philippe A. Tanguy5−7 and L. Rudolph8 also studied the © 2013 American Chemical Society
mixing performance and power consumption of coaxial mixers with different configurations. However, research on heat transfer performance of the coaxial mixer is rare. Wang and Dai9 designed a coaxial mixer, composed of a double helical ribbon and a four-pitched-blade turbine paddle, based on heat transfer and mass transfer in the polymerization reaction, and established correlations of the heat transfer coefficient of the mixer through experimental methods. But the inner impeller of the coaxial mixer they used was a single-layer paddle. On the basis of our previous study on the power consumption and mixing characteristics of a coaxial mixer with a combined inner paddle;10,11 in this paper, we mainly studied the heat transfer performance of a novel coaxial mixer composed of an outer gate paddle and a combined inner paddle (consisting of a fourpitched-blade turbine impeller PBT-4 and a Rushton turbine impeller RT-6, which are widely used in industry process) with the help of experimental studies and numerical simulations.
2. EXPERIMENTAL STUDY 2.1. Experimental Facility. The heat transfer experiment is performed in a stainless steel vessel with semicircle spiral jacket and ellipsoidal head, as is shown in Figure 1. Vessel diameter D is 1000 mm, overall height H is 1500 mm, and height of the free liquid surface hf is 1050 mm. A semicircle spiral jacket is welded to the outer surface of the mixing tank. Conduction oil or cooling water flows through it to heat or cool the fluid in the tank. To reduce heat loss, an insulating layer is set on the outer Received: Revised: Accepted: Published: 17285
May 10, 2013 October 29, 2013 November 7, 2013 November 7, 2013 dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
concentration. In the experiment, the maltose syrup is heated by the conduction oil in the semicircle spiral jacket, and then cooled by cooling water. As the viscosity of the maltose syrup changes rapidly when temperature changes, the viscosity of the maltose syrup at different temperatures needs to be measured with the help of rotational viscometer HAAKE VT550, which can automatically portray the viscosity-temperature curve of the maltose syrup. The results are shown in Figure 2. In the
Figure 1. Experimental facility with coaxial mixer: 1, jacket inlet; 2, thermometer; 3, semicircle spiral jacket; 4, vessel; 5, outer paddle motor; 6, torque sensor of outer paddle; 7, inner paddle motor; 8, torque sensor of inner paddle; 9, agitator drive or gearbox; 10, thermocouple; 11, jacket outlet; 12, thermal resistance sensor; 13, gate paddle; 14, PBT-4 impeller; 15, RT-6 impeller.
surface of the jacket. A coaxial mixer is vertically inserted into the mixing tank from the top of the vessel, which is composed of an inner high-speed paddle and an outer low-speed paddle. The inner paddle is a two-layer combined paddle consisting of an upper PBT-4 and a lower RT-6. The outer paddle is a gate paddle. Specific size of the experimental facility is shown in Table 1. This coaxial mixer has two independent drive systems and four operating modes: single rotation of inner or outer paddle, corotation, and counter-rotation can be achieved.
Figure 2. Viscosity−temperature curve of maltose syrup.
experiment, the heat transfer performance is inspected within a period of time when the temperature of the material reaches 323.15 K and the inlet temperature of the conduction oil is 353.15 K. All the thermophysical properties of the maltose syrup and the conduction oil are measured at 323.15 and 353.15 K respectively and listed in Table 2. 2.3. Heat Transfer Calculation. Heating and cooling of the material in the tank is an unsteady process. When conduction oil flows through the jacket, heat is transferred to the maltose syrup through the tank wall. As the heat in the tank is not dissipated, the temperature of the material will rise as long as its temperature is below the oil’s temperature at the jacket outlet. In addition, the local heat transfer coefficient is different at different places of the inner wall of the tank. So when analyzing the heat transfer performance, it is supposed that the whole heat transfer process consists of a sufficient number of short intervals, during which the temperature increment is slight enough and heat transfer process can be seen as steady. So, the average heat transfer coefficient of the inner wall hi can be calculated, which can be regarded as the instant heat transfer coefficient at 323.15 K. Detailed calculation of the heat transfer process is based on the following assumptions: the heat absorbed by the tank, jacket, and mixer is neglected; the heat dissipated by the tank is neglected because of the insulating layer of the tank; the jacket is full of heating medium all the time, and the property is the same in different places; and the material in the tank is fully mixed and the temperature is the same.12,13 In the experiment, the property parameter, operating parameter, and heat transfer parameter are monitored and captured in 10 min, 5 min before and after the moment when the material is heated to 323.15 K. According to the heat balance law, overall heat transfer coefficient Ui based on the heat transfer area of the inner wall can be calculated by the following formulas:
Table 1. Main Size Parameters of Coaxial Mixer impeller type
RT-6
PBT-4
gate paddle
impeller diameter d, mm blade width w, mm blade thickness e, mm distance from bottom of the tank C, mm
334 67 4 250
334 67 4 610
900 65 65 50
In the experiment, the speed of each mixer can be adjusted by the corresponding AC frequency converter and measured by the corresponding photoelectric speed sensor. Two torque sensors are mounted to the inner and outer mixing shaft, respectively. By measuring the torque of the shaft in nonload and load conditions, we can obtain the mixing power. Temperature of the heat medium at the inlet and outlet of the semicircle spiral jacket is measured with thermometers; temperatures of the fluid in different positions of the mixing tank are measured by a few thermocouples, and their average is taken as the material temperature; the wall temperatures of the tank are measured by thermal resistance sensors embedded in the inner wall with different heights, and their average is taken as the inner wall surface temperature. All the process data measured in the experiment can be read and calculated by PLC (programmable logic controller) to obtain all the needed parameters. 2.2. Experimental Material. A coaxial mixer is desirable in systems with high and variable viscosity, so high-viscosity maltose syrup is selected as the experimental material. Maltose syrup, colorless, tasteless, and nontoxic, is a typical Newtonian fluid, and its viscosity can be adjusted by changing its 17286
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
Table 2. Physical Parameters of Maltose Syrup and Conduction Oil material
temperature (K)
viscosity (Pa·s)
density (kg/m3)
specific heat (J/kg·K)
heat conductivity coefficient (W/m·K)
maltose syrup conduction oil
323.15 353.15
1.437 0.0173
1376.5 865
2596 2080
0.3681 0.1339
Q = Q w + Q p = UA i i ΔTln = Vbρb c p
ΔTln =
(Tb − T1) − (Tb − T2)
(
ln
Tb − T1 Tb − T2
)
=
dTb dt
Nu = 0.55Re 2/3 0.14 Pr Vi 1/4
(1)
Variables of the expressions on the left side of the formula 5 and 7 can be obtained by experiment, and the expression on the right side can be regarded as empirical, as it only relates to Re. Compare these data, and the result is shown in Tables 3 and 4.
T2 − T1
(
ln
Tb − T1 Tb − T2
)
(2)
The heat transfer coefficient can be obtained by the wall temperature method and Wilson graphical method.14,15 Considering the lack of correlation about the heat transfer coefficient and the deviation of the graphical method, the wall temperature method is selected to obtain the average heat transfer coefficient hi directly, as follows: hi =
Table 3. Comparison of Measured and Empirical Values of Heat Transfer Calculation under Single Rotation of Inner Combined Impeller
Q A i (TW − Tb)
(3)
Because the temperature of the inner wall of the tank is different at different positions, we select five temperature measuring points. The average temperature of the five points is used to calculate the average heat transfer coefficient hi. 2.4. Analysis and Discussion of the Results. 2.4.1. Verification of the Results. Several times of experiments were done to verify the accuracy and reliability of the experimental measurement, and the data obtained under the same condition were of no difference. The coaxial mixer has four operating modes: single rotation of the inner or outer paddle, corotation, and counter-rotation. Correlations of heat transfer coefficient of the corotation or counter-rotation and single rotation of the outer gate paddle have been proposed.16 Correlations proposed by Nagata to calculate the heat transfer coefficient are one of them.17 This correlation regards the combined paddle as a single paddle. When the outer gate paddle is still and the inner paddle rotates, the detailed correlation is:
(5)
The heat transfer coefficient of the single rotation of the gate paddle can be obtained by many correlations. On the basis of the size of the experimental apparatus, the operating parameters and the application condition of the correlations, the Bondy correlation is selected to calculate the heat transfer coefficient of the single rotation of the gate paddle,18 as shown below: Nu = 0.55Re 2/3Pr1/4Vi 0.14
wall temperature method
empirical value
deviation (%)
120 150 180 210
13.97 16.43 18.13 18.66
12.90 14.97 16.91 18.74
8.29 9.75 7.21 0.43
speed (r/min)
wall temperature method
empirical value
deviation (%)
10 18 26
14.82 21.65 25.34
14.07 20.81 26.59
5.33 4.04 4.70
The results of the comparison in Table 3 and Table 4 indicate that the deviation between experimental data and empirical data is within 10%, which indicates that the Yong formula and Bondy formula can be used to obtain the heat transfer coefficient and the data measured by experiment is reliable. 2.4.2. Comparison of Heat Transfer Performance under Different Operating Modes. The temperatures measured under the four rotation modes for calculating the heat transfer coefficient are listed in Tables 5−7, respectively. As can be seen from the tables, temperature increment of the material (Tb2 − Tb1) is so slight (about 1 K) that this short interval of heat transfer process (10 min) can be seen as steady. Then average heat transfer coefficient hi can be calculated through formulas 1 and 3, and Vb in formula 1 is constant 0.759 m3. Figures 3 and 4 show the average heat transfer coefficient under four different operating modes. From the pictures, it can be seen that compared to single-shaft mixing, double-shaft mixing makes the heat transfer coefficient improve obviously, whether it is corotation or counter-rotation. This is due to the optimization of the overall mixing effect caused by the double-shaft mixing, especially in the near-wall region and bottom region of the mixing tank. When the speed of the outer paddle is constant, the heat transfer coefficient increases rapidly as the speed of the inner paddle increases. The inner combined paddle plays a leading role in the mixing of the material; the increase of its speed strengthens the mixing, and then improves overall heat transfer. On the other hand, when the speed of the inner paddle is constant, the heat transfer coefficient increases as the speed of the outer paddle increases, but the increase is not obvious,
Wherein, Nu = (αDe)/λ, Re = (ρbNiD2)/μ, Pr = (cpμ)/λ, and Vi = μ/μw. By substitution of the structure parameters into the above formula and simplification of the formula, the following formula is obtained: Nu = 0.361Re 2/3 0.14 Pr Vi
speed (r/min)
Table 4. Comparison of Measured and Empirical Values of Heat Transfer Calculation under Single Rotation of Outer Gate Paddle
−0.6 ⎛ ∑ bi ⎞0.45⎛ ∑ Ci ⎞0.2 0.5 ⎛ H ⎞ Nu = 1.4Re 2/3Pr1/3Vi 0.14⎜ ⎟ ⎜ ⎟ (sin θ) ⎜ ⎟ ⎝D⎠ ⎝ D ⎠ ⎝ iH ⎠ (4)
1/3
(7)
(6)
Simplified 17287
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
Table 5. Temperatures under Single Rotation Mode of Inner and Outer Impeller speed (r/min) inner
outer
120 150 180 210 10 18 26
Tb (K)
T1 (K)
T2 (K)
Tb1 (K)
Tb2 (K)
Tw (K)
323.15 323.05 323.15 323.05 323.15 323.15 323.05
361.15 361.65 361.15 360.25 361.05 361.15 361.15
346.05 345.35 344.75 344.05 349.15 348.45 347.35
322.65 322.65 322.55 322.55 322.85 322.75 322.65
323.65 323.65 323.65 323.75 323.55 323.65 323.65
338.75 337.45 336.95 336.95 346.35 343.75 342.45
Table 6. Temperatures under Corotation Mode Ni (r/min)
No (r/min)
Tb (K)
T1 (K)
T2 (K)
Tb1 (K)
Tb2 (K)
Tw (K)
120
10 18 26 10 18 26 10 18 26
323.15 323.15 323.15 323.15 323.25 323.05 323.15 323.25 323.25
361.15 361.15 361.15 361.55 361.35 361.65 361.15 360.95 361.15
345.45 346.75 344.95 345.85 345.55 345.85 344.95 344.95 345.15
322.55 322.55 322.55 322.55 322.55 322.45 322.55 322.55 322.55
323.75 323.65 323.75 323.75 323.75 323.75 323.85 323.95 323.95
338.75 341.15 337.05 337.85 338.55 338.95 337.05 337.45 338.15
150
210
Table 7. Temperatures under Counter-rotation Mode Ni (r/min)
No (r/min)
Tb (K)
T1 (K)
T2 (K)
Tb1 (K)
Tb2 (K)
Tw (K)
120
10 18 26 10 18 26 10 18 26
323.15 323.15 323.25 323.15 323.05 323.05 323.15 323.15 323.15
361.15 361.35 361.45 361.15 361.15 361.15 359.45 361.15 361.15
346.35 346.65 345.45 345.95 345.95 345.15 345.25 345.35 344.25
322.55 322.55 322.55 322.65 322.45 322.45 322.45 322.45 322.35
323.65 323.75 323.85 323.75 323.65 323.75 323.65 323.75 323.75
338.45 339.25 338.95 338.75 338.85 338.25 337.35 337.35 336.95
150
210
Figure 3. Comparison of average heat transfer coefficient under single rotation of inner impeller and double-shaft rotation.
which is because the viscosity of maltose syrup decreases rapidly when it is heated to 323.15 K. At this time, the flow condition and heat transfer performance of the material in the near-wall region can be improved even if the speed of the outer frame is low.
Figure 5 gives the comparison of the heat transfer coefficient under corotation and counter-rotation modes when the temperature of the material is heated or cooled to 323.15 K. Figure 5 indicates that all the data is distributed around the 45° diagonal, which means the effect of corotation and counter17288
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
Figure 4. Comparison of average heat transfer coefficient under single rotation of outer paddle and double-shaft rotation.
the time,19,20 and these simplifications will sometimes cause large deviation in accuracy. So to improve the accuracy and show the real heat transfer between the heating medium and the material through the tank wall, the integrated modeling method of tank, jacket, heating medium, and material was used in this numerical simulation. The whole computation model is divided into four regions: the moving region and static region of the material in the tank, wall of the mixing tank and conduction oil region in the jacket. The inner paddle region and outer paddle region belong to the moving region, while other parts in the mixing tank belong to the static region. Mesh generation uses hybrid grid technique. Because of the existence of the mixers, the material region in the tank becomes irregular. Thus unstructured tetrahedral meshes are used in this region. While structured hexahedral meshes are used in the tank wall region and the conduction oil region, as is shown in Figure 6. Meanwhile, a boundary layer is attached to the wall surface in contact with the fluid to guarantee the computational accuracy of heat transfer. On the basis of these conditions, the appropriate number of cells is determined as 1259914 through grid independence test. 3.2. Calculation Methods. The heat transfer process in the mixing tank is unsteady. The temperature and heat transfer coefficient in the tank change all the time. Solving the continuity equation, momentum equation, and energy conservation equation at the same time in unsteady conditions require large computation storage and long computation time. But if the flow field and temperature field are calculated separately, this problem can be solved. And results of these two methods agree with each other. So we choose the method combining the steady-state method and the transient method. First, the steady-state MRF (multireference frame) method is used to calculate the flow field, which is used as the original data to calculate the heat transfer coefficient. Then the transient method is used to simulate the heat transfer, which can be solved through the energy conservation equation. On the basis of the Reynolds number calculated according to the operating conditions, it can be determined that mixing occurs in a laminar flow regime, so a laminar flow model is used for calculation, and no other equation is needed.
Figure 5. Comparison of average heat transfer coefficient under corotation and counter-rotation.
rotation on heat transfer is of little difference. The advantage of corotation in heat transfer is not as obvious as in power consumption.
3. NUMERICAL SIMULATION Fluid flow and heat transfer process in the coaxial mixing tank are very complicated. With the help of the experimental test, only the temperature data from limited measuring points can be obtained to calculate the average heat transfer coefficient. Moreover, it costs much money and time. To get detailed information about the distribution of the temperature field and heat flux field, the heat transfer performance of the coaxial mixer with semicircle spiral jacket was analyzed with the help of CFD numerical simulation. 3.1. Computational Regions and Meshes. There are very few reports on the numerical simulation of heat transfer in mixing tanks, most of which did much simplification, such as no outer jacket and inner spiral tube was modeled or the temperature of wall surface was regarded as constant. While actually the temperature and heat flux of wall surface changes all 17289
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
Figure 7. Distribution of inner wall temperature Tw under counterrotation mode.
r/min, No = 20 r/min), in which negative values mean heat absorption. It is not difficult to see from Figure 8 that the heat flux distribution is similar to the temperature distribution. In addition, Figure 8 also indicates that the heat flux of doubleshaft mixing is larger than that of single-shaft mixing, which is more obvious in the region around the head and the free surface. The reason is that the rotation of the outer paddle strengthens the flow of material near the wall surface, thus improving the heat transfer performance in these two regions. Ten equispaced ring surfaces from the inner wall surface of the tank are chosen in the axial direction and the local heat transfer coefficient of every ring surface under three different operating modes are calculated. The distance between every two neighboring rings is 90 mm and the value “0” on horizontal axis in Figure 9 represents the junction position of the shell and the ellipsoidal head. The result is shown in Figure 9 that the heat transfer coefficient is relatively large only in the region between two paddles (axial coordinates = 0−400 mm) when the inner combined impeller rotates individually. The reason is that in systems with high and variable viscosity, the region between two paddles has direct contact with the inner combined impeller, where flow speed is high and heat transfer performance is good. In addition, Figure 9 indicates that the heat transfer performance under double-shaft mixing is better than that under single-shaft mixing, especially in the region above the upper inner paddle (axial coordinates = 400−600 mm). This is because the single inner impeller cannot work effectively in this region under single-shaft mixing. However under double-shaft mixing, rotation of the outer gate paddle strengthens the disturbance to the material near the inner wall, where the heat transfer plays an important role, thus improving the heat transfer performance in this region. Furthermore, the result of the numerical simulation indicates that the corotation and counter-rotation modes of double-shaft mixing have similar influence on the heat transfer performance and the difference between the two modes is not obvious in the region under the upper inner paddle (axial coordinates = −200−400 mm), however counter-rotation mode is much more effective than corotation mode in the region above the upper inner impeller
Figure 6. Finite element mesh.
3.3. Boundary Conditions. The surface of the material in the mixing tank is a free surface, whose normal velocity is zero. The surface of the tank wall, shaft and paddle are defined as noslip wall boundary conditions, and the shafts and paddles are also set to be corresponding speed. In addition, the entrance and exit of the jacket is applied the velocity-inlet boundary condition of 0.18 m/s and exit boundary, respectively. The outer wall, which has direct contact with the conduction oil in the jacket and inner wall of the tank, satisfy coupling boundary conditions. Because of the existence of the insulating layer, the convection heat loss between the tank and air is neglected. All outer wall surface of the jacket and the outer wall surface of the tank with no jacket covered are regarded as an adiabatic boundary. The border between moving region and static region is set as the interface. 3.4. Numerical Simulation Results and Analysis. Figure 7 shows the temperature distribution of the inner surface of the tank under counter-rotation mode, when material in the tank is heated to 323.15 K. According to Figure 7, it can be seen that the wall temperature of the head is relatively low, though still over the temperature of the material, because there is no jacket outside the head. The temperature of the inner wall surface of the tank attached with the jacket decreases as the height increases, from the border of the head and shell to the free surface, due to the upward flow of heating conduction oil in the jacket. This result agrees with data obtained from experiment. Figure 8 gives the heat flux distribution of the inner surface under different operating modes with the same speed (Ni = 240 17290
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
Figure 9. Distribution of heat transfer coefficient hi of inner wall surface.
3.5. Verification of the Results of Numerical Simulation. To verify the accuracy and reliability of the numerical simulation, the average heat transfer coefficient hi of numerical simulation was compared with that of the experiment, as shown in Table 8. It can be seen that the average heat transfer Table 8. Comparison of Average Heat Transfer Coefficient between Simulation and Experiment rotation mode
single rotation of inner impeller
counterrotation
corotation
simulation hi (W/(m2·K)) experiment hi (W/(m2·K)) deviation (%)
109.6 117.8 6.96
124.1 137.0 9.42
121.5 144.4 15.86
coefficient of the simulation is a bit lower than that of the experiment with deviations no more than 16%. The reason is that the calculation of heat transfer is separated from that of flow field in the simulation while they are processing simultaneously in the actual experiment, and simplifications, such as constant material properties, also bring deviations in the simulation against the experiment. From the above discussion, we can conclude that computational model and method used in the numerical simulation is reliable, which can meet the accuracy requirement and can be used to predict the heat transfer performance of the novel coaxial mixer.
4. CONCLUSIONS As a novel mixer with wide adaptability, this coaxial mixer, which has an outer wall-scraping frame and inner combined impeller consisting of a four-pitched-blade turbine paddle and a Rushton turbine paddle, has good performance on power consumption and mixing. To synergistically strengthen the flow and heat transfer performance of the novel coaxial mixer, it is necessary to study its heat transfer performance. In a stainless agitation vessel with semicircle spiral jacket and ellipsoidal head, various parameters of heat transfer in Newtonian fluid under different operating modes (single rotation of inner paddle, corotation and counter-rotation) were measured and the average heat transfer coefficient of the wall surface of the tank was also calculated. What’s more, to obtain more detailed information about local heat transfer, with the help of an
Figure 8. Distribution of heat flux qw of inner wall surface under different operating modes.
(axial coordinates = 400−600 mm) because of the generated independent swirl in this region. 17291
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
integrated modeling method and computational method combining steady-state method and transient method, the numerical simulation of the heat transfer characteristics of the novel coaxial mixer was performed, and the distribution of temperature, heat flux and local heat transfer coefficient in the mixing tank were obtained. The results from experimental test and numerical simulation agree well with each other, the details of which are shown in the following: (1) The heat transfer coefficient near the inner wall surface of the tank increases as the speed of the inner paddle or outer paddle increases, whether it is single-shaft mixing or double-shaft mixing, but the speed of the outer paddle has little influence on heat transfer coefficient. So we can strengthen heat transfer in the tank and lessen power consumption by increasing the speed of the inner impeller and decreasing the speed of the outer gate paddle, while mixing effect is also considered. (2) The heat transfer performance of double-shaft mixing is much better than that of single-shaft mixing, which is because overall mixing effect is optimized by double-shaft mixing, especially the mixing effect in the near-wall region or at the bottom of the tank. (3) The local heat transfer coefficient varies as the axial position changes. When the inner combined impeller rotates alone, the heat transfer coefficient is relatively large in the region between the two paddles, while the heat transfer coefficient in other regions is not that good. Overall heat transfer performance is good when both inner and outer paddles rotate, as the rotation of the outer frame paddle improves the flow characteristic in the upper region of the tank. (4) The heat transfer performance under corotation mode and counter-rotation mode is of little difference. But under the same conditions, the power consumption is lower and the mixing performance is better under corotation mode. So corotation mode of the novel coaxial mixer is preferred.
■
■
Q = overall rate of heat transfer, W Qw = rate of heat transfer by heating medium through wall of the tank, W Qp = heat producing rate from the friction between agitator and material, W qw = wall heat flux, W/m2 Re = Reynolds number Tb = temperature of the material, K T1 = temperature of heating medium at entrance of the jacket, K T2 = temperature of heating medium at exit of the jacket, K Tw = temperature of the material close to inner wall surface, K ΔTln = logarithmic temperature difference between heating medium and material, K t = time, s Ui = overall heat transfer coefficient, W/(m2·K) Vi = viscosity correction factor Vb = volume of the material, m3 w = blade width, mm α = convection heat transfer coefficient, W/(m2·K) λ = thermal conductivity, W/(m·K) ρb = density of the material, kg/m3 θ = tilt angle of agitator, deg μ = viscosity of the liquid at bulk temperature, Pa·s μW = viscosity of the liquid at inner wall surface temperature, Pa·s
REFERENCES
(1) Xie, Y.; Bao, Y. Y.; Liu, T.; Zhang, Z. D.; Gao, X. H. Power Demand and Mixing Performance of Coaxial Mixers in Newtonian Liquids. Chin. J. Process. Eng. 2010, 10, 424. (2) Jin, Z. W.; Pan, J. Z. The Mixed Property of a New Type of Combined Impeller. Yunnan Chem. Technol. 2006, 33, 50. (3) Li, P. Study of Mixing, Heat Transfer and Power Consumption Performance of a Coaxial Mixer. Thesis, Zhejiang University, Hangzhou, PRC, 2012. (4) Guo, W. H.; Pan, J. Z.; Xu, H. P.; Tan, G. W. Numerical Simulation for Performance of Coaxial Stirred Tank. J. East China Univ. Sci. Technol. 2009, 35, 486. (5) Rivera, C. A.; Heniche, M.; Takenaka, K.; Tanguy, P. A. Finite Element Modeling of the Laminar and Transition Flow of the Superblend Dual Shaft Coaxial Mixer on Parallel Computers. Chem. Eng. Sci. 2009, 64, 4442. (6) Rivera, C.; Foucault, S.; Heniche, M. Mixing Analysis in a Coaxial Mixer. Chem. Eng. Sci. 2006, 61, 2895. (7) Foucault, S.; Ascanio, G.; Tanguy, P. A. Power Characteristics in Coaxial Mixing: Newtonian and Non-Newtonian Fluids. Ind. Eng. Chem. Res. 2005, 44, 5036. (8) Rudolph, L.; Schaefer, M.; Atiemo-Obeng, V.; Krame, M. Experimental and Numerical Analysis of Power Consumption for Mixing of High Viscosity Fluids with a Co-axial Mixer. Chem. Eng. Res. Des. 2007, 85, 568. (9) Wang, L. S.; Dai, G. Mixing Characteristic and Heat Transfer Performance in Combined Impeller with Twin Shafts and Two Dissimilar Paddles. China Synth. Rubber Ind. 1999, 22, 16. (10) Liu, B. Q.; Zhang, Y. K.; Liu, J. L.; Qin, F. L.; Lin, X. H.; Jin, Z. J. Numerical Simulation of Power Consumption and Mixing Characteristic in Stirred Vessel with Novel Coaxial Mixer. J. Chem. Ind. Eng. 2013, 64, 1135. (11) Liu, B. Q.; Liu, J. L.; Zhang, Y. K.; Chen, M. Q.; Qin, F. L.; Jin, Z. J. Experimental Research on the Power Consumption of a Coaxial Mixer in a Fluid with High Viscosity. Ind. Eng. Chem. Res. 2013, DOI: http://dx.doi.org/10.1021/ie4002266.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was financially supported by Zhejiang Science and Technology Plan Project (2012C21079), the Program for Zhejiang Leading Team of S&T Innovation (2011R50005), and the National Natural Science Foundation of China (21206144).
■
NOMENCLATURE Ai = heat transfer area, m2 cp = specific heat of material, J/(kg·K) C = distance from the tank bottom, mm d = impeller diameter, mm D = vessel diameter, mm De = equivalent diameter, m e = blade thickness, mm H = overall height of material, mm hi = average heat transfer coefficient of the inner wall, W/ (m2·K) Ni = speed of inner impeller, r/min No = speed of outer impeller, r/min Nu = Nusselt number Pr = Prandtl number 17292
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
Industrial & Engineering Chemistry Research
Article
(12) Kawase, Y.; Hoshino, M.; Takahashi, T. Non-Newtonian Laminar Boundary-Layer Heat Transfer in Stirred Tanks. Heat Mass Transfer 2002, 38, 679. (13) Delaplace, G.; Demeyre, J. F.; Guerin, R.; Debreyne, P.; Leuliet, J. C. Determination of Representative and Instantaneous Process Side Heat Transfer Coefficients in Agitated Vessel Using Heat Flux Sensors. Chem. Eng. Process. 2005, 44, 993. (14) Debab, A.; Chergui, N.; Bekrentchir, K.; Bertrand, J. An Investigation of Heat Transfer in a Mechanically Agitated Vessel. J. Appl. Fluid Mech. 2011, 4, 43. (15) Fernandez-Seara, J.; Uhia, F. J.; Sieres, J.; Campo, A. A General Review of the Wilson Plot Method and its Modifications to Determine Convection Coefficients in Heat Exchange Devices. Appl. Therm. Eng. 2007, 27, 2745. (16) Li, L.; Bao, Y. Y.; Yang, B.; Gao, Z. M. Power Demand and Mixing Performance of Helical Ribbon Coaxial Mixers with Newtonian Fluids. Int. J. Chem. Reactor Eng. 2012, 10. (17) Nagata, S. Mixing Principle and Application; Ma, J. S., translator; Chemical Industry Press: Beijing, 1975 (translated 1984). (18) Bondy, F.; Lippa, S. Heat Transfer in Agitated Vessels. Chem. Eng. 1983, 90, 62. (19) Delaplace, G.; Torrez, C.; Leuliet, J. C.; Belaubre, N.; Andre, C. Experimental and CFD Simulation of Heat Transfer to Highly Viscous Fluids in an Agitated Vessel Equipped with a Non Standard Helical Ribbon Impeller. Chem. Eng. Res. Des. 2001, 79, 927. (20) Zakrzewska, B.; Jaworski, Z. CFD Modeling of Turbulent Jacket Heat Transfer in a Rushton Turbine Stirred Vessel. Chem. Eng. Technol. 2004, 27, 237.
17293
dx.doi.org/10.1021/ie401499f | Ind. Eng. Chem. Res. 2013, 52, 17285−17293
