Structure Optimization of a Rotating Zigzag Bed via Computational

Article pubs.acs.org/IECR

Structure Optimization of a Rotating Zigzag Bed via Computational Fluid Dynamics Simulation Yongli Sun,†,‡ Yu Zhang,† Luhong Zhang,*,† Bin Jiang,†,‡ and Zongxian Zhao† †

School of Chemical Engineering and Technology and ‡National Engineering Research Center for Distillation Technology, Tianjin University, Tianjin 300072, People’s Republic of China S Supporting Information *

ABSTRACT: 3D physical and computational fluid dynamics models have been developed to describe the rotating zigzag bed (RZB). The pressure distribution in a RZB was investigated first. It was found that the simulations agreed well with experiments, so the reliability of the models was proved. The simulations suggest that the pressure drop decreases with the rotating bed thickness (H, the height between the rotating and stationary disks) within certain limits, particularly under a high gas flow rate. Also, the dead zones in the flow field are obviously reduced when we enlarge the rotor in the radial dimension. The optimal rotating bed thickness of 96 mm obtained by the principle of equal area was verified in the simulations. So, the principle can be used in the structural design of a RZB.

1. INTRODUCTION High-gravity technology (HIGEE) was developed in the late 1970s.1 The core of HIGEE is to intensify mass transfer by using a centrifugal force field instead of a gravitational field.2,3 As one of the earliest and classical HIGEEs, the rotating packed bed (RPB) has numerous attractive advantages compared with traditional columns, such as a great reduction in the equipment volume due to its intensified mass transfer of gas and liquid, strong antiinterference capability, short liquid residence time, and reduced tendency to flooding.1,4 So, it has been extensively applied in the fields of absorption,5,6 distillation,7−10 stripping,11 ozone oxidation,12,13 biosorption,14 sulfonation,15 nanomaterial preparation,16,17 polymer devolatilization,18 etc. Meanwhile, a lot of variants of HIGEE have appeared, such as a rotating bed with wave disk plate19 and split packing,20,21 a multistaged spraying rotating bed,22 a helical rotating absorber,23 etc. Rotating zigzag bed (RZB) is a novel type of HIGEE with unique structure.24 The rotor of the RZB is quite different from the packing rotor of the RPB.9,25 It coaxially combines rotational and stationary disks, on which two series of alternating concentric circular metal sheets are installed, respectively. The one set on the stationary disk is called a stationary baffle and fixed to the casing. The other set is called a rotational baffle and driven by a motor through a vertical shaft. The new developed rotational baffles usually have its upper parts perforated. The clearance between the rotational and stationary baffles, the upper clearance between the stationary disk and rotational baffles, and the lower clearance between the rotational disk and stationary baffles provide the zigzag channel for gas and liquid flows. The gas is introduced into the casing by the centrifugal blower and then flows radially inward from the outside periphery to the eye of the rotor in a spiral way under a pressure difference. The gas is discharged through the gas outlet with high swirl flow when it emerges from the rotor center. The liquid is pumped into the rotor from the liquid inlet at the eye of the upper disk. The centrifugal force makes the liquid flow radially outward with repeated dispersion−agglomeration recycles. The liquid flows © XXXX American Chemical Society

countercurrently to the gas in general, making an intensified process of mass transfer. Compared with the conventional RPB, the RZB is characterized by the following advantages: (1) Intermediate feeds can be easily introduced by installing an inlet at the upper disk because it is stationary. Thus, we can perform a continuous distillation duty by only one unit of the RZB. By comparison, we have to utilize two units of the RPB for continuous distillation because of the incapability of installing an intermediate inlet at the rotating packing rotor. (2) It is very easy and convenient to coaxially install multiple rotors in one casing; thus, a significant increase of the theoretical plate number in a single unit can be achieved. However, this efficient design makes a more complicated structure because of the liquid collector and dynamic liquid seals between rotors. (3) The upper disk of the rotor is stationary, so the upper dynamic seal used in the RPB can be removed or replaced by a static seal. Thus, the structure of the device can be greatly simplified, and the cost of manufacture and maintenance is also reduced. (4) There is no need for an initial liquid distributor because the liquid is self-distributing over the zigs and zags, resulting in a simplified structure and reduced cost. (5) The residence time of the liquid phase in the RZB is longer than that in the RPB because of the zigzag channel formed by the rotational and stationary baffles, leading to an increase of the mass-transfer capacity. Many new-type RZBs have been developed by researchers since its first application in continuous distillation of ethanol recycling in 2004,26,27 such as a RZB with multiple rotors,28,29 a RZB with rotational baffles perforated and shuttered,30 a multistage countercurrent rotating packed bed (MSCC-RPB),31 etc. Received: March 6, 2014 Revised: July 9, 2014 Accepted: August 15, 2014

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dx.doi.org/10.1021/ie500961c | Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Industrial & Engineering Chemistry Research

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Figure 1. 3D physical model of the RZB: 1, gas inlet; 2, stationary baffles; 3, gas outlet; 4, liquid inlet; 5, rotational baffles; 6, casing; 7, liquid outlet; 8, rotational shaft; 9, rotaional disk.

Figure 2. Partial schematic diagram of the RZB: 1, ring surface for mass transfer; 2, cylindrical surface for fluid flow; 3, ring surface for fluid flow; 4, cylindrical surface for mass transfer.

2. MODEL 2.1. Physical Model and Computational Grid. The physical model of the RZB was simplified in this paper, as shown in Figure 1. For better analysis of the structure of the RZB rotor, its space is divided into four zones, as shown in Figure 2. Zones 1 and 3 are the ring surfaces between the rotational and stationary baffles, while zones 2 and 4 are the cylindrical surfaces between rotational baffles and the stationary disk. It is worth noting that mass transfer is mainly in zones 1 and 4. Zones 2 and 3 act as the flow channels for the fluid, so we should pay more attention to these to reduce fluid resistance. Thus, the principle of equal area was proposed and can be described as S2 = S3 (1)

The pressure drop of gas across HIGEE is one of the most important characteristics. Most researchers predicted a pressure drop by establishing mathematical models20,32,33 and empirical equations.8,34,35 Like our brief review of past literature,32,34−37 the pressure drop across HIGEE is usually divided into three parts according to the structure: casing, rotor, and gas outlet pressure drop, and the second part is the main component of the overall pressure drop. Moreover, mass transfer is also dramatically influenced by the distribution of the flow field in the RZB. Therefore, how to reduce the pressure drop and improve the distribution of the flow field is the primary issue that we should be concerned with before the structure design of the RZB. At present, researches9,22,25,30,38−40 of HIGEE equipment on the hydrodynamics and mass-transfer performance are mainly focused on experiments. However, the inner flow field in the RZB is very complicated. It is not easy to conduct deeper research conveniently and accurately by current experimental methods. Computational fluid dynamics (CFD) simulation technology has obvious advantages in dealing with this problem. It could not only predict the hydrodynamics of the RZB accurately but also save time and cost. Thus, it offers great convenience for structure optimization of the RZB.

To be more specific 2πR i(H − HR ) = π (R i 2 − ri 2)

(2)

The main structure parameters of the RZB are shown in Table 1. Five values of rotating bed thicknesses were simulated in this paper: 87, 90, 93, 96, and 100 mm. ICEM CFD 14.0 was used to build the 3D physical model and generate mesh in the computational domain. The whole computational domain can be divided into two parts: rotational and stationary domains. The B



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Momentum equation:

Table 1. Main Structure Parameters of the RZB

⎡ ∂Uj ⎞⎤ ∂ ∂ ∂P′ ∂ ⎢ ⎛⎜ ∂Ui ⎟⎥ + SM (ρUi) + (ρUU ) = − + μ + i j ∂t ∂xj ∂xj ∂xj ⎢⎣ eff ⎜⎝ ∂xj ∂xi ⎟⎠⎥⎦

diameter, mm component name

simulation

experiment

height, mm

rotating baffle 1 stationary baffle 1 rotating baffle 2 stationary baffle 2 rotating baffle 3 stationary baffle 3 rotating baffle 4 stationary baffle 4 casing gas inlet gas outlet liquid inlet liquid outlet

Φ537 Φ491 Φ456 Φ410 Φ369 Φ322 Φ268 Φ220 Φ724 Φ50 Φ33.4/Φ152 Φ33.4 Φ50

Φ482 Φ459 Φ422 Φ396 Φ353 Φ322 Φ268 Φ221 Φ724 Φ50 Φ33.4/Φ152 Φ33.4 Φ50

74 76 74 76 74 76 74 76 150

(4)

where SM is the sum of the body forces,and μeff is the effective viscosity defined by μeff = μ + μt (5) The turbulent viscosity μt is computed by combining k and ε as follows: μt = Cμρ

k2 ε

P′ is a modified pressure, defined by P′ = P +

∂Uk 2 2 ρk + μeff 3 3 ∂xk

(7) 41

rotational domain contains the field that encompasses the rotational baffles and rotational disk. The stationary domain contains all of the other regions, as shown in Figure 3. Unstructured tetrahedral meshes were adopted because of the complexity of the inner structure of the RZB. Also, the meshes near rotational and stationary baffles were refined. The suitable grid number we got by a grid independence test is nearly 5,000,000. Taking the rotating bed thickness as 96 mm, for example, the minimum volume of the grid is 2.27 × 10−10 m3, the maximum volume is 8.54 × 10−7 m3, and the total number of cells is 4,935,036, as shown in Figure 4. 2.2. Mathematical Models and Boundary Conditions. A single-phase fluid flow in the RZB was simulated based on the physical model, and the steady-state assumption is acceptable. There is no energy exchange, so only the mass conservation and momentum equations were solved in the model.

The renormalization group (RNG) k−ε model is based on renormalization group analysis of the Navier−Stokes equations. The transport equations for turbulence generation and dissipation are the same as those for the standard k−ε model, but the model constants are different, and the constant Cε1 is replaced by the function Cε1RNG. The transport equation for turbulence is defined by ∂(ρk) ∂ + (ρUk j ) ∂t ∂xj =

μ ⎞ ∂k ⎤ ∂ ⎡⎢⎛ ⎥ + Pk − ρε + Pkb ⎜μ + t ⎟ ∂xj ⎢⎣⎝ σk ⎠ ∂xj ⎥⎦

(8)

where Pkb and Pεb represent the influence of the buoyancy forces and Pk is the turbulence production due to viscous forces. They are modeled using

Conservation equation: ∂ρ ∂ + (ρUj) = 0 ∂t ∂xj

(6)

⎛ ∂U ⎞ ∂Uj ⎞ ∂Ui ∂Uk 2 ∂Uk ⎛ ⎟⎟ − + ρk ⎟ Pk = μt ⎜⎜ i + ⎜3μt ∂xi ⎠ ∂xj ∂xk 3 ∂xk ⎝ ⎠ ⎝ ∂xj

(3)

(9)

Figure 3. Division for the rotating and stationary zones of the RZB by the method of a frozen rotor. C



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Figure 4. Mesh generation (XZ and XY planes) of the RZB.

Pk b = −

μt

gi

ρ

∂ρ ∂xi

(10)

Pε b = max(0, Pk b)

(11)

The transport equation for turbulence dissipation becomes ∂(ρε) ∂ + (ρUjε) ∂t ∂xj =

μt ⎞ ∂ε ⎤ ∂ ⎡⎢⎛ ⎥ + ε (Cε1RNGPk − Cε2RNGρε ⎜μ + ⎟ ∂xj ⎢⎣⎝ σεRNG ⎠ ∂xj ⎥⎦ k + Cε1RNGPε b)

(12)

where Cε1RNG = 1.42 − fη

(

η 1− fη =

η 4.38

(13) Figure 5. Comparison of pressure distributions between simulation and experimental results.

)

1 + βRNGη3

(15)

used. The interfaces between the rotational and stationary domains were managed by the method of a frozen rotor.42 That is, the frame of reference or pitch is changed, but the relative orientation of the components across the interface is fixed. All other surfaces were defined as a no-slip adiabatic wall. The highresolution advection scheme was accepted for the hydrodynamics equations and the first-order upwind for the turbulence equations. The physical time scale was set as 1.12 × 10−3 s to cater to the convergence of simulation.

A commercial package, ANSYS CFX 14.0, was used for solving the equations above. The medium is air at 25 °C. Three rotor speeds, 670, 850, and 1033 rpm, were simulated. The velocity gas inlet and opening boundary conditions for the gas outlet were

3. RESULTS AND DISCUSSION For every physical model developed in this paper, the default target root-mean-square residual value 1.0 × 10−4, which is sufficient for engineering application, was achieved. Meanwhile,

η=

(14)

Pk ρCμRNGε

The model constants have the following default values: Cμ = 0.09;

Cε2RNG = 1.68;

βRNG = 0.012;

CμRNG = 0.085;

σεRNG = 0.7179;

σk = 1.0

D



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Figure 6. Pressure contours (XY plane) at different rotating bed thicknesses.

Figure 7. Relationship between the dry bed pressure drop and rotating bed thickness at different gas flow rates.

Figure 8. Relationship between the pressure drop and square of the gas flow rate at different rotating bed thicknesses.

the gas flows of the inlet and outlet have reached equilibrium. Therefore, the simulation could be deemed to have converged. 3.1. Model Validation. In this study, a 3D physical model in conformity with experiment40 was developed to simulate the hydrodynamics of the RZB. The total pressure and static pressure distribution of simulation and experiment40 were compared to get the following conclusions, as shown in Figure 5. (1) The total pressure distribution obtained in simulation is basically consistent with that of experiment. The maximum and minimum relative errors are 4.3% and 2.9%, respectively; the average relative error is 3.6%. (2) The trend of the static pressure distribution in simulation is nearly the same as that with experiment. However, the value of the static pressure in simulation is slightly larger than that in experiment. The maximum difference appears at the third investigated point,

which is near the rotating baffle. This is mainly because the upper part of the rotational baffles in experiment is perforated with Φ1.5 mm holes, where the gas could pass through, leading to a lower growth of the static pressure. The maximum and minimum relative errors are 21.4% and 9.3%, respectively; the average relative error is 13.0%. The comparisons above suggest that the 3D physical and mathematical models of the RZB correctly reflect the real process. The errors of calculations are all within allowance, so we can analyze quantitatively to provide a theoretical basis for structure optimization of the RZB. 3.2. Pressure Drop. The rotor pressure drop accounts for the largest proportion of the overall pressure drop. Hence, the hydrodynamics of different rotating bed thicknesses was simulated to achieve the optimal structure of the RZB rotor. E



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zone 2 is equal to that of zone 3. Thus, the principle of equal area is satisfied at this point. If we continue to increase the rotating bed thickness, the zigzag channel will be damaged and the pressure drop will remain unchanged, or even increase a little. Therefore, the optimal rotating bed thickness is 96 mm in this paper. In Figure 8, the effects of the gas flow rate on the pressure drop at different rotating bed thicknesses are shown. Despite the same results as those revealed in Figure 7, we still get some new points. Obviously, when the gas flow rate increases, the gaps of the pressure drop at different rotating bed thicknesses will get wider. For example, the difference between rotating bed thicknesses of 87 and 90 mm increases to 1 kPa when the gas flow rate is 0.2 m3/s. So, the structure design of the RZB rotor is especially important under high gas flow rate. H = 104 mm in Figure 8 is the rotating bed thickness in experiment; other radial sizes of the rotor can be found in Table 1. We can see that the pressure drop of H = 104 mm at various gas flow rates is almost equal to that of H = 93 mm. They are both higher than that of H = 96 and 100 mm. This suggests that the rotor that is optimized according to the principle of equal area is superior to that in experiment with respect to the pressure drop. In Figure 9, the pressure drop is investigated versus rotating bed thickness at different rotor speeds. The trend of the pressure drop with the rotating bed thickness is nearly the same at different rotor speeds. The curves both achieve the minimum value when H = 96 mm. So, it was demonstrated again that the optimal rotating bed thickness is 96 mm in this paper. Moreover, obviously the pressure drop increases with the rotor speed because that causes an increase of the centrifugal pressure drop. 3.3. Flow Field. Figure 10 reveals that the gas phase flows along a zigzag path in the rotor. The gas spirals upward and downward through the channel between the rotational and stationary baffles. We can see that the gas flow is a 3D flow consisting of radial, tangential, and axial velocities. In the eye of the rotor, the gas is discharged through the gas outlet with high swirl flow.

Figure 9. Relationship between the dry bed pressure drop and rotating bed thickness at different rotor speeds.

Figure 6 shows the pressure distribution contour of different rotating bed thicknesses. The red circle lines represent rotational baffles, and the black circle lines represent stationary baffles. As is indicated, the pressure field of the RZB is symmetrically distributed. The pressure decreases radially inward to the eye of the rotor. The pressure changes severely near the rotational and stationary baffles. It also reveals that the pressure gradient decreases with the rotating bed thickness. Figure 7 illustrates the relationship between the pressure drop and rotating bed thickness at different gas flow rates. It is evident that the pressure drop increases with the gas flow rate. The tendency of pressure drop with rotating bed thickness is basically the same at different gas flow rates. That is, the pressure drop decreases with rotating bed thickness at first. This is because when the rotating bed thickness increases, zone 2 in Figure 2 will be enlarged and result in reduced resistance of the gas phase. When the rotating bed thickness comes to 96 mm, the area of

Figure 10. Gas velocity vectors (XZ plane) in the rotor. F



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Figure 11. Velocity contours (XZ plane) at different rotating bed thicknesses.

Figure 12. Velocity contours and vectors (XY plane) at different rotating bed thicknesses.

As shown in Figure 11, the flow fields in the optimized rotors are basically the same, perhaps because the difference in the rotating bed thicknesses is not big enough to affect it. We can see that there are some dead zones in the rotor, and they are mainly concentrated near the first and second stationary baffles. This phenomenon is more serious at the side of the gas inlet and mainly results from the velocity maldistribution under a high gas flow rate. Going deep into the rotor, the velocity distribution of gas tends to be more uniform and symmetrical because of the

high rotor speed. Thus, the dead zones in the RZB rotor are nearly eliminated. In Figures 11 and 12, compared with the RZB used in experiment, the dead zones of the optimized RZB are obviously reduced. This might be because the rotor designed in this paper is bigger in the radial direction than that used in experiment. Then the space for gas flow in the radial direction is enlarged. This means that the radial size of the rotor has great influence on the gas flow field. Therefore, we should pay special attention to G



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Pkb, Pεb = influence of the buoyancy forces, kg/m·s3 Q = gas flow rate, m3/s r = radius of the location in the rotor, m ri = radius of the stationary baffle, m Ri = radius of the rotational baffle, m SM = momentum source, kg/m2·s2 t = time, s U = vector of velocity, m/s x = coordinate, m

the radial dimension of the RZB rotor to minimize the dead zones in it.

4. CONCLUSION (1) A 3D model was developed to predict the hydrodynamic behavior in the RZB. The pressure field of the RZB is symmetrically distributed. The pressure drop is nearly linear with the square of the gas flow rate and also increases with the rotor speed. These are both consistent with the previous experimental results. (2) The rotor pressure drop accounts for a large proportion of the total pressure drop, so we mainly concentrated on structure optimization of the RZB rotor. The rotating bed thickness has some impact on the pressure drop of RZB, and it is more obvious under high gas flow rate. The pressure drop first decreases with the rotating bed thickness; after the minimum value was achieved at the optimum point, it remains constant or even increases slightly. We can calculate the optimum point by the principle of equal area and thus provide a theoretical basis for the structural design of the RZB. (3) The effect of the rotating bed thickness on the flow-field distribution is very small. The dead zones are mainly concentrated at the side of the gas inlet, so the gas flow rate and rotor speed are the factors that heavily affect the flow-field distribution in the RZB. The dead zones of the RZB designed in this paper are obviously minimized compared with those in experiment. Therefore, the dead zones decrease with increasing radial size of the rotor within certain limits. (4) From the above, the experiment supports our theoretical work to some extent. The RZB that has been optimized according to the principle of equal area is better than that in experiment with respect to the pressure drop and flow field.

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ASSOCIATED CONTENT

S Supporting Information *

Grid independence test of the RZB model. This material is available free of charge via the Internet at http://pubs.acs.org.

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βRNG = RNG k−ε turbulence model constant ρ = density, kg/m3 σk = turbulence model constant for the k equation σεRNG = RNG k−ε turbulence model constant η = RNG k−ε turbulence model coefficient ε = turbulence dissipation rate, m2/s3 μ = molecular (dynamic) viscosity, kg/m·s μt = turbulent viscosity, kg/m·s μeff = effective viscosity, kg/m·s

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel/Fax: +86 22 27400199. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful for financial support from the National Natural Science Foundation of China (Grant 21336007). NOMENCLATURE Cε2RNG, CμRNG = RNG k−ε turbulence model constant Cε1RNG = RNG k−ε turbulence model coefficient Cμ = k−ε turbulence model constant fη = RNG k−ε turbulence model coefficient g = gravity vector, m/s2 H = rotating bed thickness, m HR = height of the rotational baffle, m HS = height of the stationary baffle, m k = turbulence kinetic energy per unit mass, m2/s2 n = rotating speed of the rotor, rpm P = static pressure, N/m2 P′ = modified pressure, N/m2 Pk = shear production of turbulence, kg/m·s3 H



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