Computational Fluid Dynamics Simulations and Experimental

Article pubs.acs.org/IECR

Computational Fluid Dynamics Simulations and Experimental Validation of Macromixing and Flow Characteristics in Low-Density Polyethylene Autoclave Reactors Haijun Zheng, Zhengliang Huang, Zuwei Liao, Jingdai Wang,* Yongrong Yang, and Yuliang Wang State Key Laboratory of Chemical Engineering, Department of Chemical and Biochemical Engineering, Zhejiang University, Hangzhou 310027, P. R. China ABSTRACT: The macromixing and flow characteristics of a low-density polyethylene autoclave reactor stirred with 32 impellers were investigated by experiments and computational fluid dynamics simulations. The simulation results were validated using the experimental data. The mixing curves show an excellent agreement with the experimental results. The flow field, distribution of velocity, and mass flux obtained from the simulations were further analyzed, and the results show that the reactor can be divided into two reaction zones. In each reaction zone, two axial flows form a big circulation loop. The downward flows near the reactor wall decrease along the flow direction, while the upward flows near the shaft increase. In each big circulation loop there are many small radial circulation loops that are similar to those encountered in continuous stirred-tank reactors. Finally, a more accurate macromixing model was proposed, which is helpful to reveal the multizone phenomenon and flow characteristics in reactors. reaction zones to be introduced. Marini and Georgakis et al.19,20 and later Ochs et al.21 used a three-compartment model that was essentially one large CSTR and two small CSTRs with some recycle streams from the large CSTR to the small ones. This model was a compartmental representation of the imperfect mixing of the inlet jet with the liquid bulk. Topalis and Pladis et al.22 also employed macromixing models, namely the external recycle and backflow models, to describe the complicated mixing patterns. Chan et al.23 used a CSTR followed by a PFR to model each section of a multicompartment autoclave. There were recycle flows between each section of the model. Each PFR could be modeled as a series of small volume CSTRs to avoid the need to solve partial differential equations. With the rapid development of computational fluid dynamics (CFD), this model has been used in many studies on LDPE autoclave reactors.24−26 Tosun and Bakker et al.24 modeled a typical commercial scale autoclave reactor by CFD. The results showed that the CFD model predicted significant differences from CSTR behavior. On the basis of the three-dimensional flow field, it was tentatively concluded that commercial-scale LDPE autoclave reactors had significant macrosegregation effects. Read and Zhang et al.25 used CFD to study the macromixing, distributions of temperature, and concentration in a LDPE autoclave reactor. The results showed that the reactor was definitely not a CSTR as was commonly assumed in the literature. Although much work has been done on LDPE autoclave reactors, there are some aspects that need improvement. Most of the literature had simplified LDPE autoclave reactors as stirred vessels with four impellers; however, the flows are much different from the actual flows in complicated industrial reactors. The

1. INTRODUCTION Mixing processes are commonly encountered in chemical, food, and bioengineering processes. The degree of mixing not only determines the reaction rate and efficiency of the operation process, but also affects the product properties, for example, molecular weight and particle size distribution.1 The levels of mixing are distinguished by three length scales:2−5 macromixing, mesomixing, and micromixing. Macromixing is the process of mixing on the scale of the whole vessel. It is the main part in the mixing process and determines the environment concentrations for mesomixing and micromixing. Therefore, macromixing is the foundation not only for further study of mesomixing and micromixing, but also for the simulations coupled with reaction kinetics.3,6,7 The industrial low-density polyethylene (LDPE) autoclave reactor is a constantly stirred vessel with multiple impellers of different types. The flow behavior generated by the impellers in the reactor deviates significantly from ideal flow patterns (i.e., plug flow reactor (PFR) and continuous stirred-tank reactor (CSTR)).8,9 The complicated macromixing pattern not only affects the conversions and reaction rates of the free-radical polymerization, but also it affects the molecular weight distributions and the degrees of long chain branches (LCB) and short chain branches (SCB).8,9 In the industrial process, some special LDPE resins for the extrusion coating can only be produced in autoclave reactors rather than in tubular reactors, which is closely related to the flow characteristics in autoclave reactors. Many papers on the mathematical simulations of LDPE autoclave reactors have been published since the 1970s.10−18 A number of macromixing models were proposed in the literature to describe the nonideal flow patterns.19−23 The reactor was usually subdivided into a number of reaction zones, each of which was divided into a sequence of ideal flow patterns (i.e., PFR and CSTR). The back mixing promoted by the impeller blades was considered, which allows the recycle streams between the © XXXX American Chemical Society

Received: June 24, 2014 Revised: August 26, 2014 Accepted: August 26, 2014

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dx.doi.org/10.1021/ie502551c | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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nonideal flow, such as the multizone phenomenon, and backmixing in industrial reactors that result from multiple impellers have not been studied. Therefore, the previous results cannot provide more accurate information about the flow characteristic, such as the multizone phenomenon or backing-mixing resulted from multiple impellers, for the scale-up and optimization of industrial reactors. In addition, the literature mainly focused on the method for how to couple with reaction kinetics rather than the macromixing of the industrial reactors. The macromixing for industrial reactors has not been studied by the experiment in those works; therefore, the macromixing results obtained from the CFD simulations need to be further validated by the macromixing experiment. Consequently, the main concern of this work is the macromixing behavior of industrial LDPE autoclave reactors. An experimental tank stirred with 32 impellers of different types was used, which is a close approximation to an industrial reactor. The macromixing characteristics (including the homogenization curve and mixing time) were studied by experiment and CFD simulations. The simulation results were compared with the experimental data for a wide range of operating conditions, which are tracer injection points, conductivity probe positions, and impeller speeds. Furthermore, the flow field, distribution of velocity, and mass flux obtained from the simulations were used to analyze the macromixing behavior in the reactor. This work aims to contribute to the further understanding of the macromixing and flow characteristics in a LDPE autoclave reactor and thus provide guidance for the scale-up and optimization of industrial reactors.

Figure 1. Schematic diagram of experimental apparatus for the determination of the mixing time. (1) Tracer injection; (2) variable frequency drive; (3) motor; (4) reactor; (5) stirring shaft; (6) conductivity probe; (7) bearing; (8) outlet valve; (9) conductivity meter; (10) computer.

2. EXPERIMENTAL APPARATUS AND METHODS Figure 1 is a schematic diagram of the experimental apparatus for the determination of the mixing time. The reactor is a 2150 mm in height, 210 mm in diameter plexiglass tank stirred with 32 impellers. The shaft is 60 mm in diameter while the impellers are 190 mm in diameter. These 32 sets of impellers can be classified into four types: one Impeller A, one Impeller B, one Impeller C, and 29 Impeller Ds. Impeller A and Impeller B are straight-blade turbines, which are set at the top and middle of the tank. Impeller C is set at the bottom of the tank and is an anchor impeller. Impeller D is a kind of two-blade oblique impeller with a blade angle of around 10 degrees, located between Impeller A and Impeller B and between Impeller B and Impeller C. There is a bearing above Impeller B that covers about 75% of the crosssectional area. The tracer method was used in the experiment to measure the mixing time. Water at 25 °C (density = 998 kg/m3, dynamic viscosity = 9.10 × 10−4 Pa·s) was taken as the test fluid. The liquid level in the stirred tank is 2.0 m, and the liquid volume is 67.0 L. The impeller speed (N) is controlled by variablefrequency drive. When the stirred tank reaches a steady state, a volume of 25 mL of an inert chemical tracer (saturated solution of KCl in water) was transiently injected into the tank at time zero. The online conductivity meter detects the salt concentration by measuring the conductivity. The conductivity data obtained from the experiment was normalized as follows: Ct* =

Ct − Ct = 0 Ct =∞ − Ct = 0

The mixing time,27,28 θ95, is the time when the tracer concentration at the probe position reaches and remains within a value of ±5% of the final value.29−33 The locations of the tracer injection points and conductivity probes are shown in Table 1. H is the height of the tank, and L is Table 1. Locations of Tracer Injection Points and Conductivity Probes tracer injection point

L/H (mm)

conductivity probe

L/H (mm)

L1 L2 L3

0.87 0.52 0.23

M1 M2 M3

0.79 0.41 0.09

the height of the tracer injection points or conductivity probes. The tracer injection points represent the initiator injection points in industrial LDPE autoclave reactors for the study of the effects of the initiator injection points on mixing time. These three conductivity probes are used to study the mixing time in the different heights of the reactor.

3. NUMERICAL MODEL 3.1. Governing Equations. The governing equations that describe the flow of fluids consist of the continuity and momentum equations. The fluid in the mixing process is supposed to be incompressible Newtonain fluid. Without any heating or cooling (neglecting the temperature rise due to viscous dissipation), the flow is governed by the simplified set of continuity and Navier−Stokes equations as follows.34−39 Continuity equation

(1)

where Ct is the conductivity at any time, Ct=0 is the conductivity at time zero, Ct=∞ is the conductivity after infinite time, that is, the final steady-state value, and Ct* is the normalized conductivity. B



∂ui =0 ∂xi

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Step 3: In the unsteady simulations, the sliding mesh is activated to solve the concentration field of the tracer. A time step of 1.0 × 10−4 s is adopted at the preliminary stage of iteration, but a larger time step is used at the later stage in order to reduce the computing time. A simulation of a rather long time period is made to ensure that the final concentration is sufficiently approached. The simulations of LDPE autoclave reactors are carried out using the CFD package of Fluent 6.3 (Ansys Inc.). The geometry of the stirrer is shown in Figure 2, panel a, and the reactor is

(2)

Momentum equation ∂uiuj ∂ 2u ∂ui 1 ∂p =− + v 2i + ∂xj ∂t ρ ∂xi ∂xj

(3)

where u is the velocity, ρ is the density, p is the pressure, and ν is the kinematic viscosity of the fluid. The concentration, or to be exact, the mass fraction of tracer is governed by the following scalar transport equation: ∂ ∂ ∂ (ρYm) + (ρ ·ui ·Ym) = − Jm , i + Sm ∂t ∂xi ∂xi

(4)

where Ym is the mass fraction of species m, Jm,i is the diffusion flux of species m, and Sm is the source term due to the chemical reactions. ⎛ μ ⎞ Jm , i = −⎜ρDm , i + t ⎟∇Ym Sct ⎠ ⎝

Figure 2. (a) Geometry of the stirrer; (b) geometry of the LDPE autoclave reactor. (5)

where Dm,i is the molecular diffusivity, and Sct is the turbulent Schmidt number. Sct is defined as follows: μ Sct = t ρDt (6) where μt is the turbulent viscosity, and Dt is the turbulent diffusivity. In the turbulent regime, eq 3 can be written on the basis of the average velocities and the fluctuating components that follow the Reynolds-averaged Navier−Stokes (RANS) equation for momentum. The Renormalization Group (RNG) k-ε model is used to close the Reynolds stress term because of the features cited in the literature.26,36,40,41 First, the effect of swirl on turbulence is included in the RNG k-ε model, which enhances the accuracy for swirling flows. Second, the RNG theory accounts for a wider range of Reynolds-number effects, because it provides an analytically-derived differential formula for the effective viscosity. 3.2. Solve Technique. The multiple reference frame (MRF) and the sliding mesh approach are both used to model flows in moving zones, that is, the flows in a stirred tank.35,36,42 The MRF model is used for steady simulations, and the resultant velocity and turbulence fields are obtained. After the flow is fully established, the sliding mesh is activated for unsteady simulations because the evolution of the tracer concentrations is transient and requires time-dependent computations. The detailed process is shown as follows. Step 1: In the steady simulations, the MRF model is adopted to solve the momentum equations. The velocity and turbulence fields are obtained until the flow field convergence is characterized by total, normalized residuals of 1 × 10−6. Besides, three tracer injection points and three conductivity probes are also set as indicators of convergence. The velocity at the indicators is monitored to determine the convergence. Step 2: Define a sphere at the tracer injection point and make sure the volume of the sphere is the same as the volume of the injected tracer. The initial mass fraction of the tracer included in the sphere is set as 1.0. In addition, three conductivity probes at different heights are also defined to monitor the tracer concentration.

Figure 3. Geometry of the impellers. (a) Impeller A; (b) Impeller B; (c) Impeller C; (d) Impeller D.

shown in Figure 2, panel b. Figure 3 shows the geometry of the different impellers. The impeller regions (30 mm < r < 100 mm) are defined as rotating zones. The wall regions (100 mm < r < 105 mm) are defined as stationary zones. Different mesh sizes are tested in order to make the solution mesh independent. The results are shown in Figure 4. The wall function is used to handle the wall regions. The turbulence region wall functions require y+ > 30, but large y+ is also not suitable; therefore, the areas near the impellers, baffles, and walls are further refined to keep y+ < 300. Table 2 shows the statistical data of y+ in the wall regions. A

Figure 4. Grid independence test. C



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Table 2. Statistical Data of y+ in the Wall Regions y+

grid number

percentage (%)

y+

grid number

percentage (%)

0−34 68−103 137−171 206−240 274−300

0 172 248 14 796 27 811 47 064

0 27.02 2.32 4.36 7.38

34−68 103−137 171−206 240−274 >300

225 415 35 800 9174 105 076 0

35.36 5.62 1.44 16.49 0

nonideal flow will be further analyzed through the CFD simulations. 4.2. Analysis of the Flow Field. 4.2.1. Evolution of the Tracer Concentration. To better understand the diffusion of the tracer in the LDPE autoclave reactor, the evolution of the tracer concentration in the center plane of the reactor was plotted in Figure 9. In Figure 9, panel a, when the tracer was injected at the injection point L1 (the top of the reactor), the downward diffusion rate near the reactor wall was faster than that in the region near the shaft. In Figure 9, panel b, when the tracer was injected at the injection point L2 (the middle of the reactor), the tracer stayed for a long time above the bearing, which indicates that there was a segregation of the concentration in the reactor due to the presence of the bearing and Impeller B. Similarly, it was found that the downward diffusion rate near the reactor wall was faster than that near the shaft, but the upward diffusion rate near the reactor wall was slower than that near the shaft. In Figure 9, panel c, when the tracer was injected at the injection point L3 (the bottom of the reactor), it was observed that the upward diffusion rate near the reactor wall was slower than that near the shaft. From the discussion above, it can be concluded that the downward diffusion is stronger near the reactor wall, but near the shaft, the upward diffusion is stronger in the LDPE autoclave reactor. This observation can be explained by the analysis of the velocity distribution (section 4.2.2). 4.2.2. Velocity Distribution. Figure 10 shows the velocity distribution in the center plane of the LDPE autoclave reactor. It was observed that the fluid near the wall possessed a high velocity, while that near the shaft had a lower velocity. Combined with Figure 11, the high velocity zones near the wall form the downward flows, but the low velocity zones near the shaft form the upward flows. This explains why the downward diffusion is stronger near the reactor wall, but the upward diffusion is stronger near the shaft in the LDPE autoclave reactor (section 4.2.1). It was also observed that the flow fields formed by the four kinds of impellers are different.45−48 In Figure 11, panel a, Impeller A and Impeller B form two flows near the wall: upward and downward. Impeller A and Impeller B are similar to a straight blade turbine. The fluid at the center can be absorbed along the axial direction and then discharged along the radial direction. The radial flow can be divided into two axial flows. One axial flow goes back into the previous reaction zone. The other one goes into the next reaction zone and provides the power for the axial flow downward. Impeller A and Impeller B improve the dispersion of the initiator, because the initiator injection points are near Impeller A and Impeller B. Impeller C is similar to an anchor impeller. It is at the bottom of the tank and forms a circulation flow as shown in Figure 11, panel c, which reduces the dead zone and benefits the extrusion flow of viscous polymer. In Figure 11, panels a−c, Impeller D is an oblique impeller with two blades and forms the upward flow near the shaft and the downward flow near the wall. Two adjacent

three-dimensional grid of the different impellers is shown in Figure 5.

Figure 5. (a) Grid of Impeller A; (b) grid of Impeller B; (c) grid of Impeller C; (d) grid of Impeller D.

4. RESULTS AND DISCUSSION 4.1. Mixing Time. The influence on the mixing time of the tracer injection points (L1, L2, L3), impeller speeds (300, 500, 700 rpm), and conductivity probe positions (M1, M2, M3) is investigated. The experimental and computed transient dimensionless tracer concentration values are compared in Figures 6−8. The solid lines represent the experimental data and the dashed lines represent the simulated results. Different colors of the lines correspond to the different conductivity probe positions. The agreement between the experiments and CFD simulations is quite good; however, local deviations are also observed because some of the internal structures in the actual reactor, such as bearings, are complicated but have been presented as simple structures in the simulations. Therefore, the actual flow field cannot be predicted accurately, which leads to the local deviations of the simulations. The experimental and simulated mixing times, θ95, are shown in Table 3. The mixing time is apparently related to the tracer injection points and conductivity probe positions.43,44 When the speed of the impeller increases, the mixing time decreases, and better homogenization can be reached in the stirred tank. From the table, it can be observed that the mixing time varies at different conductivity probe positions under the same experimental conditions. This is mainly due to the nonideal flow in the reactor. The LDPE autoclave reactor with multiple impellers is far from the ideal reactor model.24,25 In addition, the comparisons between experimental and simulated results validate the feasibility of CFD simulations for the LDPE autoclave reactor. Consequently, in the following section, the D



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Figure 6. Experimental and simulated dimensionless tracer concentration versus time for the tracer injection point L1. Solid lines, experimental data; dashed lines, simulated results.


the radial distribution of the mass flux was studied. The upward direction is assumed as the positive direction. The infinitesimal rings (dr = 5 mm) are truncated along the radial direction, and the mass flux through the infinitesimal rings are calculated. Figure

Impeller Ds form a small circulation, which is equal to a CSTR. It promotes exchange and back-mixing in the radial direction. 4.2.3. Distribution of Mass Flux. To verify that there are two different directions of axial flows in the LDPE autoclave reactor, E



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Table 3. Experimental and Simulated Mixing Time, θ95, for Tracer Injection Points (L1, L2, L3), Conductivity Probes (M1, M2, M3), and Impeller Speeds (300, 500, 700 rpm) tracer injection point

L1

L2

L3

impeller speed (rpm)

conductivity probe

M1

M2

M3

M1

M2

M3

M1

M2

M3

300

experimental θ95 (s) simulated θ95 (s) error (%) experimental θ95 (s) simulated θ95 (s) error (%) experimental θ95 (s) simulated θ95 (s) error (%)

159.2 154.9 2.7 127.7 135.7 6.3 83.4 115.9 38.9

119.5 116.4 2.6 82.3 101.4 23.2 69.4 93.4 34.6

183.1 165.6 9.6 147.5 133.7 9.4 107.6 122.7 14.0

24.2 24.8 2.5 21.2 23.3 9.9 9.2 20.3 121

28.9 31.7 9.7 22.1 28.8 30.3 10.6 28.5 169

60.4 54.1 10.4 44.1 40.7 7.7 40.1 29.1 27.4

175.2 152.9 12.7 141.9 130.5 8.1 96.1 122.2 27.1

107.9 104.1 3.5 97.7 89.1 8.8 64.8 88.1 40

167.4 146.2 12.6 124.2 129.4 4.2 83.7 113.8 35.9

500

700

12 is the radial distribution of mass flux at the height of L/H = 0.7. The x-axis is the radial distance from the shaft to the reactor wall, and the y-axis is the mass flux. The mass flux near the reactor wall is negative, which means that the axial flow is downward. The mass flux near the shaft is positive, which means that the axial flow is upward. The absolute value of the mass flux decreases at first and then increases along the radial direction from the shaft to the reactor wall. The absolute value of the mass flux near the shaft decreases along the radial direction. This means that the upward axial flow decreases, and the radial flow increases. At the center,

the mass flux decreases to zero, which indicates that there is only radial flow at the center. This is consistent with the analysis above that shows that there is radial circulation similar to that encountered in the small CSTR between the two axial flows. The absolute value of the mass flux near the reactor wall increases along the radial direction, which means that the downward axial flow increases. Figure 13 is the mass flux near the reactor wall versus the reactor height. The mass flux sharply increases when the downward flow comes across the bearing and Impeller B, which F



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Figure 10. Velocity distribution in the center plane of the LDPE autoclave reactor (N = 500 rpm). (a) The center plane of LDPE autoclave reactor; (b) partial enlarged view.

Figure 9. Evolution of the tracer concentration in the center plane of the LDPE autoclave reactor (N = 500 rpm).

indicates that the reactor is divided into multiple zones due to the bearing and Impeller B. Therefore, it is supposed that the reactor is divided to two reaction zones. The downward flow formed by Impeller A comes into the first reaction zone and decreases along the flow direction because of the resistance. When it reaches Impeller B, the downward flow formed by Impeller B comes into

Figure 11. Velocity vector distribution in the center plane of the LDPE autoclave reactor (N = 500 rpm). (a) L/H = 1−0.65; (b) L/H = 0.65− 0.33; (c) L/H = 0.33−0.

G



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Figure 12. Radial distribution of mass flux at L/H = 0.7 (N = 500 rpm). Figure 14. Mass flux near the shaft versus the height of the reactor (N = 500 rpm).

Figure 13. Mass flux near the reactor wall versus the height of the reactor (N = 500 rpm).

the second reaction zone, which provides the main power for the downward flow and increases the mass flux. Another upward flow is formed by Impeller B that goes back into the first reaction zone and affects the downward flow at the end of the first reaction zone. This is why the direction of the mass flux changes from negative to positive. Similarly, at the end of the second reaction zone, the direction of the mass flux changes from positive to negative again for the circulation flow form by Impeller C. The mass flux near the shaft versus the reactor height is plotted in Figure 14. The reactor is divided into two reaction zones due to Impeller B and the bearing. It can be observed that the upward flow near the reactor shaft is formed by Impeller D. Along the flow direction, it is promoted by each Impeller D and its mass flux continues to rise. The mass flux decreases sharply in the flow field near Impeller B and the bearing, because Impeller B and the bearing act as baffles. The conclusion proves that the reactor can be divided into multiple zones. 4.3. Flow Pattern. 4.3.1. Flow Characteristics. From the discussion above, the flow pattern in the LDPE autoclave can be described by Figure 15. Figure 15, panel (a) is the threedimensional flow pattern. Obviously, there are two annular flows in two different axial directions in the reactor. The flow near the reactor wall is downward, and that near the shaft is upward. Figure 15, panel b is the two-dimensional flow pattern. The LDPE autoclave reactor can be divided into two reaction zones

Figure 15. Flow pattern in the LDPE autoclave reactor. (a) Threedimensional flow pattern; (b) two-dimensional flow pattern.

by the bearing and Impeller B. There is a big circulation pattern in each reaction zone. The circulation is formed by two axial flows: the downward flow near the reactor wall and the upward flow near the shaft, which promotes the axial back-mixing. There are many small circulations formed by two Impeller Ds, which promote the radial back-mixing between the two axial flows. The exchange between the reaction zones takes place at Impeller B. H



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The center fluids of the two reaction zones are absorbed by Impeller B. After the exchange, the fluids are discharged along the radial direction and then separated into two axial flows when they encounter the reactor wall. 4.3.2. Macromixing Model. The flow behavior in the LDPE autoclave reactor deviates significantly from the ideal flow. In the literature, a number of macromixing models have been proposed to describe the nonideal flow patterns. In Figure 16, the reactor is

internal recycle stream from each CSTR of a zone to the previous CSTR is introduced to account for the nonideal macromixing behavior of the reactor. On the basis of the CFD simulations, the more accurate flow pattern is used to describe the macromixing behavior in the LDPE autoclave reactor. As shown in Figure 16, panel c, the differences are summarized as follows: (1) The LDPE autoclave reactor can be divided into two reaction zones. (2) The big axial circulations in each reaction zone are formed by the outside annular flow and the inside annular flow. It is assumed that the annular flows are PFR models, but their flow rates are not constant and are defined as Q n , j = f (H )

(7)

(3) There are n CSTR models where two annular flows exchange material and energy in each reaction zone. The number of CSTRs and the volume are determined by the number of Impeller Ds and their distribution. The first reaction zone consists of 16 CSTRs, and the second reaction zone consists of 15 CSTRs. The volume of each CSTR may be different, for example, the volume of the first CSTR in reaction zone 1, V1,1, must consider the effect of Impeller A; the volume of the last CSTR in reaction zone 1, V1,16, and the volume of the first CSTR in reaction zone 2, V2,1, must consider the effect of Impeller B; and the volume of the last CSTR in reaction zone 2, V2,15 must consider the effect of Impeller C. The axial and radial mass fluxes can be obtained by the CFD simulations.

5. CONCLUSION The macromixing characteristic in a LDPE autoclave reactor with 32 impellers was investigated by means of experimentation and CFD simulations in this paper. The simulation results are compared to the experimental data for a wide range of operating conditions. The simulated mixing curves show a fairly good agreement with the experimental results. These results validate the feasibility of CFD as a tool to study the LDPE autoclave reactor. The CFD simulated results, such as the flow field, the distribution of velocity, and the mass flux, are analyzed in detail, which provides a better understanding of the flow characteristics in the LDPE autoclave reactor. It was observed that the downward flows were formed by Impeller A and Impeller B in the high velocity zones near the reactor wall and that they decrease along the flow direction. Nevertheless, the upward flows were formed by Impeller D in the low velocity zones near the shaft and they increase along the flow direction. The LDPE autoclave reactor can be divided into two reaction zones by the bearing and Impeller B. There is a big circulation loop formed by two axial flows in each reaction zone, which promotes the axial backmixing. There are many small circulation loops formed by two Impeller Ds in each big circulation loop, which promotes the radial back-mixing. The exchange between the reaction zones takes place at Impeller B. On the basis of the analysis, the new accurate macromixing model is proposed, which provides a further understanding of multizone phenomenon and flow characteristics in industrial LDPE autoclave reactors.

Figure 16. Macromixing models in the LDPE autoclave reactor. (a) External recycle model; (b) backflow model; (c) new model.

subdivided into a number of reaction zones. Each zone is divided into a sequence of perfectly mixed vessels. Figure 16, panel (a) is the external recycle model.19−21,23,49,50 To account for the recirculation of the reaction mixture, an external recycle stream from the first CSTR of a zone to all CSTRs of the zone above is introduced. Figure 16, panel b is the backflow model.10,51,52 An I



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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-571-87951227. Fax: +86-571-87951227. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors gratefully acknowledge the support and encouragement of the National Natural Science Foundation of China (21176207, 21236007), the Specialized Research Fund for the Doctoral Program of Higher Education of China (20130101110063), Zhejiang Provincial Natural Science Foundation of China (LQ13B060002, R14B060003), and the National Basic Research Program of China (2012CB720500).

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NOMENCLATURE Ct = conductivity at any time Ct=0 = conductivity at time zero Ct=∞ = conductivity after infinite time, that is, final steady-state value Ct* = normalized conductivity Dm,i = molecular diffusivity, m2/s Dt = turbulent diffusivity, m2/s H = height of the reactor, mm Jm,i = diffusion flux of species m, kg/(m2·s) k = turbulent kinetic energy, m2/s2 L = height of the tracer injection points or conductivity probes, mm m = species m n = the number of CSTRs N = impeller speed, rpm p = pressure, Pa Q = flow rate, m3/s Sct = turbulent Schmidt number Sm = source term due to chemical reactions, kg/(m3·s) t = time, s ui = velocity in the direction i, m/s uj = velocity in the direction j, m/s V = volume of the CSTR, m3 xi = space coordinate, m xj = space coordinate, m Ym = mass fraction of species m

Greek Letters

ε = dissipation rate of turbulent kinetic energy, m2/s3 θ95 = mixing time, s μt = turbulent viscosity, kg/(m·s) ν = kinematic viscosity, m2/s ρ = density, kg/m3

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REFERENCES

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