Article pubs.acs.org/IECR
Investigation of Falling Liquid Film Flow on Novel Structured Packing Bo Sun,† Ming Zhu,‡ Bo Tan Liu,† Chun Jiang Liu,*,† and Xi Gang Yuan† †
State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China State Key Laboratory of Materials-Oriented Chemical Engineering, Nanjing University of Technology, Nanjing 210009, China
‡
ABSTRACT: Structured packings are widely used in many separation processes. In this paper, the liquid film flow behavior as well as mass transfer efficiency on the novel and the traditional structured packings is investigated after being simplified into multibaffled and inclined plate, respectively. The novel structured packing has a number of openings punched through the ridges on the inner and outer sides of the packing surface, and this structure corresponds to a certain flow pattern that influences mass transfer processes other than the traditional ones. The CFD method and VOF model are applied to investigate the vapor−liquid two-phase flow behavior and mass transfer process. Isopropanol desorption on the two kinds of plates is studied experimentally and numerically, and the experimental and simulation results are in good agreement. A significantly higher mass transfer efficiency of the multibaffled plate is observed, and the simulation results indicate successfully that the higher mass transfer efficiency on the novel structured packing results from the increased renewal rate and disturbance of liquid film flow. structured packings. Raynal et al.8 regarded that the flow path of gas−liquid flow within the structured packing bed can be simplified into a 2D zigzag channel. Gu et al.9 and Hoffmann et al.10 developed the inclined plate on the basis of the structured packing geometry. Furthermore, Nikou et al.11 established a 3D CFD model and made a calculation of the liquid film flow on Gempak 2A and SulzerBX structured packings. Chen et al.12 modeled the exact packing surface geometry and simulated the gas−liquid flow and mass transfer on the structured packing sheet three-dimensionally. Furthermore, Petre et al.13,14 abstracted five types of representative units (REU) from the large amount of repetitive structures of Montz B1-250.45+B1V, calculated the pressure drop of the REUs, and the pressure loss coefficient in each particular REU and the total bed pressure drop were obtained. The aim of this paper is to reveal the mass transfer process influenced by the structure of the novel packing based on the same simplification method described in the literature mentioned above. Figure 1 gives the structures and the liquid film flow conditions on the traditional and novel packings. For the novel structured packing shown in Figure 1b and c, a number of openings are punched through the ridges on the inner and outer sides of the packing surface to form diversion trenches having the corrugated inclination angle in the same direction. Liquid film flowing on one side of the packing surface can be directed to the other side through the openings, and a higher wetting area can therefore be obtained compared with the traditional packing. So far, the hydrodynamic behavior of this novel structured packing has been experimentally investigated by Li et al.15 with
1. INTRODUCTION During the last decades, structured packing made an inroad and growing number of industrial applications due to its high capacity and performance at subambient and near-atmospheric pressures.1,2 Thanks to an effective development, new generation structured packings have been developed and applied to replace the conventional packings allowing a significant capacity increase. For example, Sulzer, Koch-Glitsch, and Montz offer these packings in specific area sizes matching the specific needs of various industrial applications.1 For the structured packing, the liquid flow mechanism is in the form of a falling film flow, and the flow patterns of a falling liquid film on a structured packing surface affect mass transfer efficiencies. There has been a large amount of work developing novel high efficiency structured packings by improving the liquid film flow on the packing structures.3−5 Experimental study has always been a traditional way by which higher mass transfer efficiency of packing structure can be judged. However, it is not convenient or accurate in revealing the micro liquid film flow behavior and the relationship between the flow pattern and mass transfer efficiency. Recently, computational fluid dynamics (CFD) associated with the volume of fluid (VOF) approach, which was developed by Hirt6 for tracking the interface between two or more non-interpenetrated phases, has been extensively reported in the literature. By establishing a proper model describing the physical phenomena correctly, the CFD method can be an efficient numerical tool to obtain a better understanding of the complex flow patterns and mass transfer processes on structured packings. The applications of the VOF approach on the liquid film flow on the structured packings have been reported in many literatures in the past decade. Szulczewska et al.7 first simplified the structured packing into two-dimensional (2D) flat and corrugated plates to describe the vapor−liquid hydrodynamics on Mellapak 250Y. After that, a number of scholars used this simplification strategy to simulate the transport phenomena on different kinds of © 2013 American Chemical Society
Received: Revised: Accepted: Published: 4950
August 24, 2012 February 3, 2013 March 8, 2013 March 8, 2013 dx.doi.org/10.1021/ie302272s | Ind. Eng. Chem. Res. 2013, 52, 4950−4956
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50 mm wide. In addition, the alternating boards are angled inward and outward. Figure 3 shows a schematic diagram of the experimental system. The gas inlet is at the bottom and the gas, i.e., air, in the
Figure 1. Flow conditions on the surface of packing with (a) traditional structure and (b) novel structure. (c) Detail of the novel structured packing.
the result of higher pressure drop and liquid holdup. However, the flow features of liquid film on this novel packing surface and the relationship between the mass transfer process and the flow behavior are still unknown. Due to the complexity of the packing structure, it is necessary to establish simplified physical and CFD models based on the flow characteristics on the practical structured packing. Then, the isopropanol desorption process on the simplified models is studied numerically and experimentally to obtain the effect of falling film flow patterns on the mass transfer process.
Figure 3. Schematic diagram of the experimental setup (1, air compressor; 2 and 3, solution storage tanks; 4, centrifugal pump; 5, temperature controller; 6, rotor flow meter; 7, gas−liquid contactor).
present case flows upwardly. The gas phase flows upward to contact the liquid film counter-currently and is released to the atmosphere. The liquid phase is pumped from a receiving tank into a head tank on the upper left side of the system. Liquid from this tank passes an overflow wire and flows down along the plate. When the liquid film flows across the junction of two baffles, the flow direction is changed. The discharged liquid is collected by a tank below the system. The vapor phase is fed into the system by an air compressor from both sides of the multibaffled mesh plates. Thus, gas is in contact with the liquid phase from both sides. For the inclined mesh plate, there is only one gas inlet because the plate is wetted by the liquid film only on one side. The liquid phase is a diluted aqueous solution of isopropanol, which flows onto the plate from the liquid inlet at the top. The isopropanol was provided by Kewei Chemical Co. Inc. and had a declared purity of 99.7%. The physical properties of the vapor and liquid phases are listed in Table 1. The plate exterior, in
2. SIMPLIFIED PHYSICAL MODELS AND EXPERIMENTAL PROCEDURE On the basis of the simplification strategy put forward by Szulczewska et al.,7 the traditional structured packing can be simplified into an inclined plate, and the structure is shown in Figure 2a. The liquid film flows directly down along the plate,
Table 1. Physical Properties of Vapor and Liquid Phases
Figure 2. (a) Inclined plate, (b) multibaffled plate.
and there is only one side of the plate that can be wetted by liquid film. However, for the novel structured packing, multibaffled plate geometry is established to describe the changed flow direction, splashed and the transformed surface of liquid film when the liquid film flows through the openings. The structure of the multibaffled plate is shown in Figure 2b. Both plates shown in Figure 2 are made of sintering of 316L mesh stainless net packing and 200 mm long. Since the angle between the ridge on the opening and the ridge on the inner side of the packing is 75°, the same gradient angle is applied in the two plates. The multibaffled plate shown in Figure 2b consists of five mesh baffles, each of which is 40 mm long and
applied system
density (kg/m3)
viscosity (kg/(m·s))
surface tension (N/m)
temperature (K)
water isopropanol air
998.3 795.5 1.2
1.004 × 10−3 2.31 × 10−3 1.81 × 10−5
0.072 0.021
293 293 293
which desorption of isopropanol occurs, is made of polymethyl methacrylate. The flow rates of both the liquid and gas phases were controlled by a rotor flow meter. All the experiments were conducted under atmospheric pressure and at a temperature of 20 ± 0.5 °C maintained by a PID controller. The liquid phase was sampled at the inlet and outlet of the contactor, and the concentration was analyzed by a gas chromatograph (HP4890) with a Porapak-Q packed column. The temperatures of the oven, injector, and detector in the chromatograph were 423, 453, and 453 K, respectively. 4951
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3. THEORETICAL AND NUMERICAL METHODOLOGIES 3.1. CFD Model. Figure 4 shows the CFD geometrical dimensions used in the simulation. The mass transfer efficiency
surface tension as a body force in the momentum equation according to the method proposed by Brackbill et al.17 This technique interprets the surface tension forces as continuous volume forces, and it is defined as
FVOL = σij
ρκi∇αi 0.5(ρi + ρj )
(7)
where σ is the surface tension coefficient and κ is the free surface curvature, which is defined as κ = ∇·n ̑ =
⎤ 1 ⎡⎜⎛ n ⎟⎞ ⎢⎝ ·∇⎠|n| − (∇·n)⎥ ⎦ |n| ⎣ |n|
(8)
where n̑ is the divergence of the unit normal, and n̑ = n/|n|, n = ∇αq. The unit surface normal at the live cell next to the wall is replaced by the following equation: n ̑ = n ̑w cos θ + m̑ w sin θ
(9)
where n̑w and m̑ w are the unit vectors normal to and tangential to the wall, respectively. The contact angle θ is the angle between the wall and the tangent to the interface at the wall. The drag force source term between the vapor and liquid phases can be described as18 Figure 4. Physical geometries of (a) inclined plate and (b) multibaffled plate. Dimensions are in millimeters.
FLG = 0.5
ρfLG |uL⃗ − uG⃗ |(uL⃗ − uG⃗ )
where the friction coefficient f LG is defined as was measured for liquid phase Reynolds numbers and inlet isopropanol concentrations within the ranges of 40−110 and 100−700 mol/m3, respectively. 3.2. Governing Equations. The basic model equations are written as follows. The continuity and volume fraction equation is ∂ρ + ∇·(ρu ⃗) = 0 ∂t
∂αq ∂t
+ u ⃗ ·∇αq = 0
fLG =
fSC =
(2)
∂ (ρu ⃗) + ∇·(ρuu⃗ ⃗) ∂t (3)
The momentum equation depends on the phase volume fraction because the physical properties in the momentum equation are calculated as volume-fraction-weighted averages over each phase. The average density ρ and viscosity μ are given by eqs 4 and 5. ρ = αLρL + (1 − αL)ρG
(4)
μ = αLμL + (1 − αL)μG
(5)
⎡ ⎛ ρ ⎞1/3 δ ⎤ fSC ⎢ ⎥ 1 + 24⎜⎜ L ⎟⎟ ⎥ 10 ⎢⎣ d ρ ⎝ G⎠ ⎦
(11)
16 ReG
(12)
FMa = 0.5
(∂σ /∂C) ·(∂C /∂X ) ∂σ /∂X = 0.5 δ δ
(13)
In the isopropanol desorption experiment, (∂σ/∂C) can be considered constant,22 so eq 13 above can be simplified to FMa = 0.5
A ·(∂C /∂X ) δ
(14)
where A = −0.018. The mass transport equation is
The source term F of the momentum equation in our research arises from the surface tension (FVOF), drag force (FLG), and Marangoni effect (FMa).
F = FVOF + FLG + FMa
19
Variations in the temperature or concentration can produce the Marangoni effect, and the concentration-driven Marangoni effect in particular essentially determines the mass transfer behavior.20 For a highly positive surface tension system, such as the isoproponal/water system, the Marangoni effect is significant. However, when the surface tension is slightly positive or negative, the Marangoni effect is marginal, and its effect on mass transfer can be neglected. The results without21 and with22 the consideration of the Marangoni effect source term for the isopropanol/water system in the CFD model indicated the importance of it, and the source term is defined as
(1)
where q = L, G. The momentum transport equation is
= −∇P + ∇·[μ(∇u ⃗ + u ⃗ T)] + ρg ⃗ + F ⃗
(10)
δ
∂ (αqρq wq) + ∇(αqρq wqu ⃗) = ∇(Dq ∇(αqρq wq)) + SLG ∂t
(6)
(15)
In thin film flow, the effect of surface tension can be significant.16 The FLUENT software includes the effects of
In eq 15, mass transfer through the vapor−liquid interface can be involved in the source term of the species SLG. On the 4952
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basis of the double-film theory and the equilibrium condition at the interface, SLG can be defined as22
Table 2. Boundary Conditions
SLG = kLαeMA C LT(xA − xAI ) = k GαeMA CGT(yAI − yA )
liquid liquid vapor vapor wall
(16)
where αe is the effective interfacial area per unit volume and is defined as ae = |∇αG| = |∇αL|19
(17)
βxAI 1 + (β − 1)xAI
velocity
volume fraction
mass fraction
uL,x = 0, uL,y = uL,in pressure outlet uG,x = 0, uG,y = uG,in pressure outlet no slip
αL = 1, αG = 0
wL = wL,in
αL = 0, αG = 1
wG = 0
applied in the liquid flow and gas−liquid interface regions according to the experimental liquid phase flow rate. The grid strategy is illustrated in detail in Figure 5. In Figure 5a, quadrilateral-shaped grids are applied in the film flow and
For equilibrium between vapor and liquid phases, yAI =
inlet outlet inlet outlet
(18)
where the relative volatility β equals 1.2. Substituting eq 16 into eq 18 gives m1SLG 2 + m2SLG + m3 = 0
(19)
where β−1 kLk GC LTCGT(αeMA )2
m1 =
(β − 1)yA − β
m2 =
kLαeMA C LT
−
(β − 1)xA + 1 kLαeMA C LT
m3 = βxA − [(β − 1)xA + 1]yA
(20)
Figure 5. (a) Quadrilateral mesh in the film flow and interface transition region. (b) Triangular mesh in the film flow and interface transition region.
(21) (22)
interface regions, whereas, in Figure 5b, unstructured triangular grids are used. In the vapor phase region, triangular grids are applied in both strategies, and a finer mesh is created near the gas−liquid interface region. Figure 6 shows the effect of the mesh shape and number on the simulation results under the same liquid and vapor
The source term can be calculated from SLG =
−m2 +
m2 2 − 4m1m3 2m1
(23)
In addition, the penetration theory is applied to determine the mass transfer coefficients23 as follows kG = 2
DG πt
(24)
kL = 2
DL πt
(25)
Further, the contact times t of different phases are defined, respectively, as tL = tG =
l uL,surf
(26)
l uG,surf
(27)
where usurf is the surface velocity of the liquid or vapor phase. 3.3. Boundary and Initial Conditions. The physical geometries of the two types of plates shown in Figure 2 consist of a liquid inlet and outlet and a gas inlet and outlet. The boundary conditions of the calculation model are given in Table 2. Initially, the calculation domain is completely filled with vapor phase, and the isopropanol concentration in the vapor phase is 0. 3.4. Grid Strategy. Because the structure of the multibaffled plate is complicated, as depicted in Figure 2b, it is difficult to generate a grid directly to represent the complex model precisely. Therefore, two types of grid strategies are
Figure 6. Effect of mesh number and strategy on the difference in isopropanol concentration (ReL = 89, ReG = 378, Cin = 392 mol/m3).
Reynolds numbers. As the mesh number increases, the simulation results approach the experimental data, and the result for quadrilateral-shaped grids is better than that of triangular grids. In particular, when the number of grids in the numerical region is more than 40 000, the simulation fits the experimental results very well. Thus, quadrilateral-shaped grids were applied in the film flow and interface regions, whereas, in 4953
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the vapor phase region, triangular grids were used. The total number of grid cells used in the simulation was about 300 000. 3.5. Simulation Scheme. The governing equations were solved using the commercial CFD software FLUENT to simulate the liquid film flow on the two types of plates. The species transport equation (eq 15) was solved as a user-defined scalar equation in FLUENT. A first-order upwind discretization scheme was chosen for the advection terms in the momentum equation and species transport equation. The body force weighted scheme was used for pressure interpolation, and the pressure-implicit with splitting of operators scheme was adopted for pressure−velocity coupling. The time step size was 10−4. The simulation procedure includes three main steps. First, the liquid phase is fed into the calculation domain from the liquid inlet at the top. When it reaches a quasi-stable state, the vapor phase is introduced from the gas inlet at the bottom to contact the liquid phase counter-currently, and a momentum source term is added to the equation at the same time. After the mass flow rate at the outlet boundary fluctuates around a certain value, the mass transfer equation with the mass source term is implemented in the calculation.
Figure 8. Isopropanol concentration profile in vapor phase and streamlines on the multibaffled plate (ReL = 67, ReG = 378, Cin = 400 mol/m3).
4. RESULTS AND DISCUSSION Figures 7 and 8 show the isopropanol concentration distribution and streamlines of the vapor phase on the inclined
isopropanol desorbed from the liquid film was smaller, especially in the upper part of the calculation region. Figure 9 shows the effects of the liquid phase Reynolds number on the amount of isopropanol desorption on different
Figure 7. Isopropanol concentration profile in vapor phase and streamlines on the inclined plate (ReL = 67, ReG = 378, Cin = 392 mol/ m3).
Figure 9. Isopropanol concentration at different ReL (ReG = 378, Cin = 392 mol/m3) for inclined and multibaffled plates.
simplified physical geometries. The desorption quantity of isopropanol was large for both cases at lower liquid Reynolds numbers. As the Reynolds number increased, a smaller concentration difference was reached. The reason is that the contact time for the vapor and liquid phases decreased as the liquid phase Reynolds numbers increased. For the multibaffled plate, the desorption quantity of isopropanol was 50% higher on average than that for the inclined plate. The higher mass transfer rate on the multibaffled plate can be explained by the increased disturbance of liquid film flow induced by changed flow direction in the region of two baffles. Figure 10 shows the effect of the inlet concentration of isopropanol on the desorption quantity. As the inlet concentration increased, the desorption quantity increased in both cases. A higher concentration of isopropanol in the liquid phase produced a higher mass transfer driving force between
and multibaffled plates, respectively. The isopropanol concentration was greatly enhanced in the vapor phase for falling film flow on the multibaffled plate. The flow direction of the air upward near the plates changed after the air contacted the liquid phase counter-currently at the vapor−liquid interface, and vortices appeared in the vapor phase near the liquid film. The simulation results also indicate that large velocity and concentration gradients appeared around the vortex, whereas, near the vortex center, the gas velocity and isopropanol concentration were small. Because the vortices send fresh gas directly to the plate and improve the mixing between the interface and the bulk flow of the gas phase, the mass transfer efficiency is enhanced significantly. In contrast, for the inclined plate, fewer vortices appeared, and they affected only a small area near the liquid outlet. Consequently, the quantity of 4954
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Figure 12. Streamline on (a) inclined plate and (b) multibaffled plate.
deep understanding of the mass transfer process. The streamlines of the liquid phase on the two types of plates are shown. For the multibaffled plate, the liquid flowing above falls down and splashes on the surface of the lower baffle, which partly mixed and redistributed the liquid to form film flow. In this way, the surface renewal rate is artificially increased and the mass transfer driving force between the two phases is enhanced. However, for the inclined plate, the mass transfer rate is evidently smaller without any remix and redistribution of the liquid film.
Figure 10. Isopropanol concentration at different Cin (ReL = 67, ReG = 378) for inclined and multibaffled plates.
the vapor and liquid phases, which increased the desorption quantity. Moreover, the difference in the desorption quantity between the two types of plates increased with increasing inlet concentration, indicating improved mass transfer at higher inlet concentrations of isopropanol on the multibaffled plate. For the multibaffled plate, the desorption quantity of isopropanol was still approximately 50% higher than that of the inclined plate. The isopropanol concentration distribution at different vertical positions is shown in Figure 11. Y is a dimensionless
5. CONCLUSIONS The multibaffled and inclined plate are applied as the simplified physical configurations of novel and traditional structured packing, respectively, to study the liquid film flow behavior in this paper. The results of flow pattern and mass transfer process on the two plates provide a reasonable foundation research for identifying the real condition in complex novel packing structures. The experiment and simulation on the isopropanol desorption process are carried out on the two configurations, and good agreement between the experimental and simulation results is obtained. The results indicate that the vapor−liquid mass transfer efficiency is approximately increased by 50% on the multibaffled plate. The simulation results also indicate that the higher mass transfer rate on the multibaffled plate can be attributed to two main mechanisms. First, the renewal rate of the liquid film is promoted. The liquid draining from the above falls down and splashes on the surface of the lower baffle, which makes the liquid partly mixed and redistributed as well as the position of liquid film surface transformed. Second, the disturbance is increased when the flow direction of liquid film changes at the junction of two baffles. Therefore, by the reasons mentioned above, the novel structured packing can enhance the mass transfer efficiency of falling liquid flow significantly. Meanwhile, the effect of the hydrodynamics on the mass transfer efficiency can also provide a theoretical guideline for the design of high efficiency equipment in many industrial fields.
Figure 11. Concentration distribution on four sections of the inclined and multibaffled plates (ReL = 67, ReG = 378, Cin = 392 mol/m3).
height defined as Y* = h/H, where h is the vertical distance from the measuring point to the inlet and H is the total height of the plate. The concentration distribution of the falling liquid film decreases significantly as the liquid film flows downward along the multibaffled plate, and the isopropanol concentration is smaller than that of the inclined plate. The higher isopropanol desorption rate on the multibaffled plate can be explained by the instability induced by collision of the liquid film with the plate at the junction of two baffles. Thus, the flow behavior of the falling liquid film has an important effect on the mass transfer rate. Figure 12 shows the detailed flow behavior of the falling liquid film on the two flow configurations in order to obtain a
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. 4955
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ACKNOWLEDGMENTS The authors acknowledge financial support from the National Basic Research Program of China (973 Program No. 2012CB720500).
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NOMENCLATURE C = mole fraction of isopropanol in liquid phase CGT = molar concentration of all components in vapor phase, mol/m3 CLT = molar concentration of all components in liquid phase, mol/m3 D = diffusion coefficient, m2/s d = width of flow channel, m F = momentum source term, N/m3 FLG = drag force source term, N/m3 FMa = Marangoni effect source term, N/m3 FVOF = surface tension source term, N/m3 f LG = drag force coefficient kG = mass transfer coefficient of isopropanol in vapor phase, m/s kL = mass transfer coefficient of isopropanol in liquid phase, m/s l = length of falling film in simulation region, m MA = molecular weight, kg/kmol m = surface normal n = surface tangential P = pressure, Pa Re = Reynolds number SLG = mass transfer source term, kg/(m3·s) t = contact time, s u = velocity, m/s usurf = surface velocity of liquid or vapor phase, m/s w = mass fraction X = coordinate in the direction of the film thickness, m x = mole fraction of isopropanol in liquid phase y = mole fraction of isopropanol in vapor phase
Greek Letters
ρ = density, kg/m3 α = volume fraction αe = effective interfacial area per unit volume, m2/m3 β = relative volatility θ = contact angle, deg σ = surface tension coefficient, N/m μ = viscosity, kg/(m·s) δ = liquid film thickness, m κ = free surface curvature, 1/m
Superscript
I = interfacial domain Subscripts
G = vapor phase L = liquid phase LG = vapor−liquid phase interface w = wall in = inlet
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REFERENCES
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