Liquid Distribution and Local Hydrodynamics of Winpak: A Multiscale

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Liquid distribution and local hydrodynamics of Winpak: A multi-scale method Wenzhe Qi, Kai Guo, Chunjiang Liu, Hui Liu, and Botan Liu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.7b04194 • Publication Date (Web): 01 Dec 2017 Downloaded from http://pubs.acs.org on December 3, 2017

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Industrial & Engineering Chemistry Research

Liquid distribution and local hydrodynamics of Winpak: A multi-scale method

Wenzhe Qi1, Kai Guo1,*, Chunjiang Liu1,*, Hui Liu1, Botan Liu2 1 School of Chemical Engineering and Technology and State Key Laboratory of Chemical Engineering, Tianjin University, Tianjin 300072, China 2 College of Chemical Engineering and Materials Science, Tianjin University of Science and Technology, Tianjin 300457, China

AUTHOR INFORMATION Corresponding Author * [email protected] (K. Guo) * [email protected] (C.J. Liu)

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Abstract A multi-scale method for a novel structured packing, Winpak, was developed to study liquid distribution and local hydrodynamics. The method combines a unit network model with computational fluid dynamics (CFD) method. The unit network model was used to predict the liquid distribution at macro-scale by defining ten distribution coefficients. The distribution coefficients were obtained based on micro-scale behavior of liquid distribution which was simulated in six representative elementary units by CFD method. The VOF model was used to capture the interface between the gas phase and the liquid film. Through simulation results, three flow patterns were observed. In addition, the relatively large liquid holdup and wetting area of Winpak were elucidated. The average film thickness in REUs was also investigated. Furthermore, the liquid distribution obtained from the macro-scale model indicates that the windows could mitigate the tendency of liquid flowing toward the sidewall. Keywords: multi-scale; liquid distribution; CFD; unit network model; Winpak

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1. Introduction Structured packing has been reputed as a vital internal component for many decades in the gas-liquid separation processes, such as distillation and absorption1, for its high mass transfer efficiency at relatively low energy consumption2. The primary flow pattern of the liquid phase inside the packing is film flow, which could improve gas-liquid contact. However, the liquid phase in a packed column, especially an industrial one, is far from an ideally uniform film flow. Generally, liquid film can only wet part of a packing surface with a different film thickness for the effects of packing structure, operation conditions, and physical properties, such as the contact angle and the surface tension of the liquid phase. The resulting liquid distribution and wetting condition could determine the gas-liquid mass transfer efficiency to a certain extent3. Therefore, in-depth knowledge of the liquid distribution on a packing surface is very helpful for the advancement of modeling and design processes4. Experiments could be used to obtain the empirical correlation of effective wetting area or liquid hold up with respect to operational conditions from the global perspective2,5-13. However, the experimental method is generally black–box oriented; therefore, it is not helpful for deep insight into flow patterns within the packing. Additionally, the application of the empirical methods was gradually limited, since the measured data were generally case-dependent14-16. The inconsistency of different empirical correlations causes selection difficulty for engineers to accurately design a column. By contrast, mechanical models, such as the unit network model, could provide fair predictions of liquid distribution by defining possible directions of liquid flow17-20. However, the obtained distribution was a global description because the required distribution coefficients were generally obtained based on large-packing-domain experiments. The computational fluid dynamic (CFD) method provides a viable way to visualize the flow pattern within structured packing21. The work by Hodson22 might be one of the first CFD studies on flow patterns inside structured packing with the use of a CFD package PHOENICS. Indeed, it is difficult to simulate a whole packed column or even an integral packing layer under limited computing power in light of the considerable difference between its characteristic length and global dimension23. 3



However, the simulation of a representative elementary unit (REU) or a simplified inclined plate supplies a solution to reducing calculation complexity. The dry pressure drop, for example, was usually simulated in one or several REUs24-29 by differentiating the total pressure drop into several contributions. Fair results could be obtained with acceptable computing costs. In addition, systematic studies made by Sebastia-Saze et al. focused on the fluid behavior and mass transfer in the 3D elements of a commercial packing30-33. The key point in mimicking the liquid distribution inside an REU is determining how to capture the interface between the gas phase and the liquid film on the packing sheets. Published studies have substantiated the VOF method as reliable in simulating the detailed flow behavior of a gas-liquid system34-35. Szulczewska et al.36 and Gu et al.37 both used the VOF approach to investigate the liquid film flow on corrugated plates by 2D CFD simulations. Chen et al.38 applied a two-equation model proposed by Liu39 for the closure of turbulent mass transfer equation simulating the hydrodynamics and mass transfer behavior in the REU of Mellapak 350Y based on the VOF method. Quan et al.40 used the VOF method to study falling liquid film on a heated vertical plate. The research done by Raynal et al. studied the thickness of liquid film, holdup, and mass transfer between phases with the use of the VOF model, as well41-44. More recently, Dong et al.45 also used the VOF model to locate the gas-liquid interface, aiming for the determination of the mass transfer coefficient in structured packing. Essentially, a main purpose of simulating the micro-scale flow behavior, REU-based simulation for example, is to supply useful information to a larger scale (macro-scale) study. The way to build the connection between micro-scale and macro-scale, terminologically called a multi-scale method, is needed. Raynal et al.46 developed a multi-scale method to describe hydrodynamic behavior by taking the packed column as a porous media. The multi-scale method needed parameters, such as pressure drop coefficients, liquid holdup, and the velocity at gas-liquid interface, which were derived from smaller-scale simulations. Li et al.47 modified the above method to predict the hydrodynamics of a self-developed structured packing. For liquid 4


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distribution on packing sheets, recently, a multi-scale method combining the CFD method and the unit network model was developed by our group48. By creating CFD simulations in a micro-scale REU, liquid flow directions inside the packing were determined by stream split fraction, and local hydrodynamics were obtained. By inputting the stream split fraction into a unit network model, liquid distribution inside Mellapak 350X without perforations was obtained at a macro-scale. The stream split fraction is dependent on the flow rate in each unit, meaning that the distribution could reflect the local behavior of liquid flow, rather than a global description. Afterwards, to describe the liquid flowing to the back side through the openings, a new split coefficient was added to a modified multi-scale method. Next, the liquid distribution inside Mellapak 250Y with perforations was successfully predicted49. Therefore, the proposed method supplies a technically feasible solution to obtain hydrodynamics inside structured packing from a micro-scale (mm-scale) to a macro-scale (m-scale), which is difficult to detect by experimental methods. Winpak50 is a novel structured packing invented by our research group based on a multibaffled plate51. Experiments have been set up to procure empirical correlations for hydrodynamic behavior at pilot scale52-54. The CFD method has also been used in single-phase simulations for optimizing pack structure in order to reduce dry pressure drop29,55. Nevertheless, deep insight into the liquid distribution and the two-phase flow pattern inside the novel packing is still deficient. Therefore, based on previous research by our group, a novel multi-scale method was developed and applied to investigate the liquid distribution and local hydrodynamics within a 350Y-type Winpak. Six REUs were established at first to represent the geometry of the Winpak. A two-phase flow CFD simulation in these REUs could obtain local hydrodynamics and distribution coefficients of liquid flow. By inputting coefficients into a novel unit network model, the liquid distribution at the macro-scale could be predicted.

2. Multi-Scale Method 2.1 Packing geometry and the definition of units The 3D geometry of the 350Y-type Winpak is shown in Fig. 1, and its dimensions are 5



listed in Tab. S1. Winpak could be recognized as the deformation of general corrugated structured packing. The main distinction of Winpak is that there are several diversion windows regularly arranged on the ridges of the packing sheets that guide liquid from one side to another. [Figure 1] The corresponding 2D sketch is shown in Fig. 2. This figure could also be used to explain the unit network model, which will be introduced in detail in Section 2.4. The junctions of two solid lines are the nodes of two packing sheets. The dashed line represents the back side of each packing sheet. There are windows on the dashed lines and the solid lines. The former can guide liquid from the inner side to the back side of the packing sheet, and the latter leads liquid to flow from the back side to the interior. The rhombus encompassed by four solid lines is deemed as an interior unit (blue in Fig. 2), and the triangles (green in Fig. 2) composed of solid lines are the inlet, outlet, and sidewall unit. [Figure 2]

2.2 Procedure of the multi-scale method The procedure of the multi-scale method is shown as Fig. 3. First, in view of the Winpak geometry, several REUs were built to describe all possibilities of liquid distribution. Second, at the micro-scale, local liquid flow behavior within the REUs could be simulated by the CFD method. Distribution coefficients could be calculated based on the simulation results representing the proportion of liquid flowing to different directions. Next, a novel unit network model was used as the link between local flow behavior at micro-scale and macro-scale liquid distribution. The model parameters of the unit network model, namely, the distribution coefficients, were determined by local flow behavior simulated by the CFD method at the micro-scale. Using the distribution coefficients, the flow rate in every unit could be calculated as long as the flow behaviors in adjacent units were given. Finally, the liquid distribution could be obtained through calculating the flow rates in every unit from the top down according to the unit distribution shown as Fig. 2. It should be noted that the initial 6


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conditions shown in Fig. 3 input to the CFD model would have effects on the micro-scale flow behavior. The resulting variation of distribution coefficients, as the model parameters of the unit network model, would change the liquid distribution at macro-scale. Therefore, a variety of common operation conditions were considered in the CFD simulations. Besides, this multi-scale can be applied to different systems by adjusting the physical properties input as initial condition in the VOF model. [Figure 3]

2.3 Micro-scale strategy—REUs and the CFD model Representative elementary units As seen in Fig. 2, the window arrangement still has certain periodicity, but it is difficult to define a single REU to represent the whole packing. Only the upper three units affect the liquid flow in each interior unit, while only an upper sidewall unit and an upper interior unit have an impact on the liquid flow in each sidewall unit. Therefore, four adjacent interior units should be considered for interior REUs, while each sidewall REUs should contain three units, including two sidewall units and one interior unit. The representative units were established based on following assumptions. (1) The initial liquid distribution (inlet condition) is only on the top of the inner side of an REU, since the back side can be deemed as part of another interior unit. (2) The effects of the inlet and the outlet of the packing layer are ignored for simplification. (3) The effect of the windows on the edge of an interior unit is ignored as liquid mainly flows on the ridges. Following these assumptions, three interior REUs and three sidewall REUs are built as shown in Fig. 4, including the following. (1) The 1st interior REU (corresponding to the 1st REU colored in red shown in Fig. 2) depicted as Fig. 4a is built for studying the liquid flowing through the window. (2) The 2nd interior REU (corresponding to the 2nd REU colored in red shown in Fig. 2) shown in Fig. 4b is for studying the effect of windows on liquid flowing 7



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downward across the node. (3) The 3rd interior REU shown in Fig. 4c is constructed for the interior units with negligible windows only on the edges of units according to the aforementioned third assumption. Note that this REU could also be used to represent the corresponding general packing. All REUs are composed of two opposite packing sheets. Each sidewall REU corresponds to half of an interior REU. Because of the counter-current flow of liquid and gas phases, two liquid inlets are defined at the top of an interior REU and two gas inlets are defined at the bottom. Correspondingly, only one liquid inlet and one gas inlet are used on each sidewall REU. [Figure 4]

CFD model Because two-phase flow occurs inside the REUs, the VOF method was used to track and locate the interphase. This method solves one single set of momentum conservation equations shared by the multi-phase fluids with the calculation of volume fraction of each phase in all cells within the entire domain. The interphase is captured based on the volume fraction of one phase. For this problem, the volume fraction equation is written as 1    q q      q q uq   Sq    q  t 

(1)

where q = L, G. When αL = 1, the cell is entirely filled with the liquid phase, while αL = 0 the cell is totally occupied by the gas phase. The relationship between volume fractions for each phase satisfies the following equation:

 L  G  1

(2)

The physical properties that appear in the conservation equations are determined as volume-fraction-weighted averages over each phase. The average density and viscosity, for example, are given as follows:

   L L  G G 8


(3)

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   L L  G G

(4)

The momentum conservation equation is

  u      uu   P      u  uT    g  F t

(5)

where Fσ stands for surface tension. It is interpreted as a continuous volume force according to the continuum surface model (CFS) proposed by Brackbill et al.56, which is defined as F   ij

 i  i 0.5  i   j 

(6)

where σ is the surface tension coefficient, and κ is the free surface curvature defined as

 =  n 

1 n

 n      n     n     n 

(7)

where n  n n , n   i . The unit surface normal at the live cell adjacent to the wall is replaced by the following equation:

n  nw cos  w  tw sin  w

(8)

where nw and t w are the unit vectors normal and tangential to the wall, respectively. The contact angle γw is the angle between the wall and the tangent to the interphase at the wall. To close the Navier-stokes equation for complex flow behavior inside REUs, the RNG k-ε turbulent model was used according to Refs. 48-49. The model equations are given as follows:

   k     kui    k      k eff   Gk   t xi xi  xi         ui     t xi xi

    2 *    C G  C   k eff  1 k 2 xi  k k 

where 9


(9)

(10)


C2*  C2 

C 3 1   0  1   3

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(11)

and   Sk  . η0, β, C1ε, and C2ε are constants as 4.38, 0.012, 1.42 and 1.68, respectively. Unstructured cells were built in the same way as Ref. 49. With the consideration of the structural complexity owing to the windows, refined cells were generated with approximately 600,000 cells for interior REUs and approximately 240,000 cells for the sidewall REUs. Water-air at 20 ℃ was treated as the simulation system. Physical properties are listed in Tab. S2. Simulations reach the convergence criteria when the residues are less than 10-5, and the mass balance between the inlet and the outlet is achieved. Through simulations in REUs, local hydrodynamics and distribution coefficients, which represent the ratios of liquid flowing to different directions, could be obtained.

2.4 Macro-scale strategy—unit network model The macro-scale strategy is based on a unit network model. As shown in Fig. 2, a packing layer of Winpak is composed of multi-row units from top to bottom. Units at different locations constitute the REUs, including both the interior and sidewall REUs. In an REU, when liquid flows out of an upper unit, it will flow towards lower units along various directions in different ratios. These ratios are defined as distribution coefficients, which can be calculated based on micro-scale flow behavior obtained by CFD method. Ten distribution coefficients are defined representing the liquid flow directions inside Winpak. If the flow rate and all distribution coefficients of liquid flows in all adjacent upper units are known, the liquid flow in a lower unit could be calculated. (1) For each interior REU, the liquid distribution can be broken down into four parts, including flowing along the channel (f), transverse flow (h), flowing downward across the nodes (g for the 1st & 3rd REUs and g’ for the 2nd REU), and flowing through the window to the back side of the packing sheet (b). It is assumed that b 10


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only affects the flow rate inside a unit rather than the flow direction and it exists only when the window is located on the flow direction (the 1st REU), so f + h + g = 1 (or f + h + g’ = 1); (2) Descending liquid flowing across the nodes is evenly divided into two streams. Each stream flows along the left-inclining or right-inclining channels; (3) Liquid flowing along the wall can partly reflect to the interior unit (rs for the 1st, rss for the 2nd, and r for the 3rd sidewall REU, respectively); (4) Due to wall effects, the transverse flow in the sidewall REU (hs) and the proportion of flowing through the window (bs) are different from that of the interior REU. Fig. 5 depicts the principle of liquid distribution via taking the 1st interior and sidewall REUs for explanation. Series numbers represent different streams flowing along certain directions. In addition, streams colored black represent the liquid flow in the inner side of the REU. Correspondingly, blue streams stand for liquid flows through the window to the back side of the packing sheets. The flow rates of each stream could be calculated based on the distribution coefficients if the flow rate of liquid that flows out of the unit A is known. For example, stream 5 in the 1st interior REU shown in Fig. 5a could be calculated based on the liquid flowing along the left-inclining channel and the distribution coefficients b and f. A detailed explanation and calculation of each stream is listed in Tab. S3 and Tab. S4 for the 1st interior REU and the 1st sidewall REU, respectively. According to the tables, the flow rates of liquid flowing out from unit D to each direction could be calculated on the basis of the adjacent units. It should be noted that for the sidewall REU shown in Fig. 4a, the liquid can flow along the left-inclining channel to unit A from an adjacent interior unit. Due to wall effects, part of the liquid flows transversely to unit D (LA*(1-bs)*hs), and the other part (LA*(1-bs)*(1-hs)) is merged into SWL (stream 1) flowing downward along the wall. Distribution in other REUs can be calculated in a similar manner, which is omitted here. In order to obtain the liquid distribution inside a packing layer, the first step is to determine the feeding condition on the top. After the feeding condition is given, the 11



flow rate of liquid flowing to a certain direction in each unit in the second row could be calculated based on distribution coefficients. Then, similarly, the liquid flow in each unit could be calculated sequentially from top to bottom. The total flow rate in the bottom unit is the sum of the liquid flowing to all directions in the unit. Finally, the liquid distribution of a packing layer is determined. [Figure 5]

3. Results and Discussion 3.1 Flow characteristics within Winpak Fig. 6 shows the water flow behavior within different REUs of Winpak. For the 1st interior REU shown in Fig. 6a, the windows divide the liquid film into two streams. One part flows continuously along the channel bypassing the window, and the other flows through the window to the back side of the packing sheet, which could enlarge the wetting area. In addition, the surface renewal also increases because of the liquid clinging to the packing surface, recognized as the viscous layer, becomes the gas-liquid contact surface after passing through the windows. For the other two REUs shown in Figs. 6b-c, all liquid inclines to flow along the channel, which might be because water cannot perfectly wet the packing surface (contact angle ≠ 0°). In addition, a more obvious disturbance of the liquid film, even the formation of small droplets, is observed in the 1st REU due to the rupture of the film by the window increasing its instability. The flow behavior within the corresponding sidewall REUs is shown in Figs. 6d-f. There is a common feature: part of liquid in the inner side flowing along the sidewall would reflect to the interior unit. However, distinctions still exist. For the 1st sidewall REU shown in Fig. 6d, part of the liquid would flow to the back side because of the existence of a small part of the window, which explains why the parameter bs is needed. Correspondingly, the window at the node in the 2nd sidewall REU, shown as Fig. 6e, enlarges the space for descending liquid along the sidewall, which leads to the reduction of liquid reflecting to the interior unit. [Figure 6] 12


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The liquid flow behavior would change by adjusting operational conditions, namely, the gas capacity represented by F-factor (𝐹 = 𝑢√𝜌 ) and the liquid flow rate. Generally, the increase of gas/liquid flux would intensify the interaction between the two phases further enhancing the disturbance of the liquid film. With the increase of the disturbance, the liquid flow patterns would experience three typical flow patterns: film flow, film-droplets flow, and chaotic flow as shown in Fig. 7. First, stable liquid film forms under the modest conditions. Then, the increasing disturbance would make part of the liquid film disperse to droplets to form the film-droplet flow. In this flow region, the size of dispersed droplets gradually increases with the increase of the gas/liquid flux. When the disturbance increases to an extent, the liquid film is finally ruptured to form chaotic flow. The irregular flow behavior of chaotic flow results in considerable liquid back mixing, which corresponds to the characteristic of the flooding phenomenon. [Figure 7] The distinct structures of the three REUs would result in the difference of interphase interactions. The consequent distinctions between the flow patterns are shown in Fig. 8. For the 1st REU, the increasing gas/liquid flux enables liquid to experience the aforementioned change of flow behavior. This phenomenon might be observed because the windows in the 1st REU split the film, which would exacerbate the instability of liquid flow, making the liquid more susceptible to the gas disturbance. In contrast, only the film flow appears in both the 2nd and the 3rd REUs because relatively moderate operational conditions have little impact on stable liquid film. Even though the gas flow may be more disturbed by the window in the 2nd REU, the flow behavior within it is still a stable film flow, which is the same as that of 3rd REU. Note that the chaotic flow only exits above the flooding line57. This behavior means that the flow behavior within the 1st REU could represent the appearance of flooding phenomenon. [Figure 8] 13



3.2 Distribution coefficients The distribution coefficients could be obtained by monitoring the liquid flows out of different outlets of the REUs. The transverse flow and the flow downward across the nodes do not exist under almost all operation conditions. This behavior was also revealed by Zhang et al. that water tends to flow along the packing channel58. Therefore, in Tab. 1, the corresponding distribution coefficients, f, h, hs, g, g’, are constants. It might be because of the effects of the contact angle and the relatively high channel height of the packing. Additionally, the fine surface texture on the metal sheet, which is neglected for simplification as in many numerical simulation studies, might be another reason. The variations of the rest of the distribution coefficients with respect to operational conditions are shown in Fig. 9, which means that simulations are related to initial conditions. Fig. 9a shows that b increases with increasing liquid flux since the liquid flows toward the windows more quickly. Almost all liquid flows to the back side through the window when liquid flux increases to 80 m3/ (m2·h). For a lower liquid flux, the increase of gas flux may make the liquid film shrink leading more liquid to flow through the window. However, overall, the gas flux has little effect on b, except for the lower liquid flux. Opposite to b, increasing liquid flux would reduce bs shown in Fig. 9b, as the liquid inclines to flow to the sidewall rather than flow through just a little part of the window. Similarly, the gas flux effect is not obvious except for the lower liquid flux. The most significant difference is the ratio of liquid reflecting the interior unit in different REUs. For the 1st and the 3rd REUs, almost all liquid reflects to the interior unit (r → 1, rs → 1). This is especially true with respect to the large gas flux as shown in Fig. 9c. It is because the counter-current gas phase constraints descending liquid along the wall and enforce the liquid to flow along the channel. Oppositely, rss is considerably affected by liquid flux shown as Fig. 9d. Since the window in the 2nd REU increases the space for the liquid flowing downward, less liquid would reflect to the interior unit (rss < 0.6). However, the increase of liquid flux could reduce the effects of the window, leading rss to increase to 1 approximately. 14


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[Figure 9] [Table 1]

3.3 Local hydrodynamics Liquid holdup and effective wetting area are two important hydrodynamic parameters for structured packing. The former was obtained according to the average fluid density inside the REUs, and the latter was quantified by a given phase volume fraction, which represents the gas-liquid interface. Water flowing through the window to the back side lowers the internal fluid between two packing sheets, so that the true values of both liquid holdup and the wetting area would be underestimated if only the liquid on the inner side of the 1st REU is considered. Therefore, the settlement is adding the liquid holdup or wetting area of both the inner side and back side to characterize the whole REU given as Eq. 12-13. h  hin  hout

ae  ae   ae       ap  ap   ap  in out

(12)

(13)

where h stands for liquid holdup, ae and ap are for wetting area and the specific area of the packing, respectively. The subscripts “in” and “out” are for inner side and back side, respectively. For the other two REUs, only the inner side of Winpak needs to be considered. Figs. 10 and 11 show the common feature that raising the liquid flux would increase both the liquid holdup and the wetting area of all REUs. Specifically, compared with the 2nd and 3rd REUs, the 1st REU considerably increases both the liquid holdup and the wetting area by at least 34.6% and 71%, respectively. It is because the viscous resistance increases as the liquid film is split by the window into two parts, which increases the contact area with the packing sheets. In addition, it also explains why Winpak has a relatively large liquid holdup and excellent mass transfer performance. In addition, increasing the gas flux would affect the two parameters for the instability of splitting films in the 1st REU, especially when the flow behavior reaches the 15



chaotic region. By contrast, the liquid holdups/wetting areas of the 2nd and the 3rd REUs are almost the same. In addition, the values of these two parameters are almost constant under the same liquid flux since the effect of the gas flow could be neglected before the flooding point in line with classical theory. [Figures 10&11]

The average thickness of the liquid film is often connected with liquid holdup based on the specific area ap. However, the simulation results show the wetting area is much smaller than the specific area, which means that using ae to calculate the average film thickness is more reasonable. Fig. 12 compares the average film thickness based on both ae and ap in different REUs. From Figs. 12a-c, the film thickness based on ap has the same tendency as the liquid holdup, because its value is only affected by the holdup. Conversely, a much larger film thickness can be obtained when the wetting area is considered. Its tendency is also changed, even with a converse trend, because except for the holdup, the wetting area increases with gas flux. Fig. 12d shows that the liquid flows in the 2nd and the 3rd REUs have roughly the same film thickness, while the much smaller film thickness occurs in the 1st REU. This difference is because the 1st REU represents the unique feature of Winpak structure, namely, the occurrence of the distribution coefficient b, which leads the liquid film to be divided to two films by the window. The resulting increase in wetting area is larger than the rise in the liquid holdup. Considering Fig. 9a and Fig. 12a at the same time, a larger b caused by the increasing liquid flux always corresponds to a larger film thickness. But the effect of gas flux is different. Even though a larger gas flux would increase b at a low liquid flux, the film thickness only changes slightly. Therefore, the liquid flux has similar effects on the distribution coefficient b and the average film thickness. [Figure 12]

3.4 Liquid distribution in two pieces of packing sheets of Winpak The liquid distribution from the macro-scale model could be obtained based on the distribution coefficients determined by the micro-scale flow behavior. Taking two 16


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pieces of packing sheets as an example, Fig. 13 compares the liquid distribution at the bottom of a packing layer with 110 mm height and 220 mm width between Winpak and the general packing (presented by the 3rd REU). Two feeding ways, a uniform feeding and a central-point feeding, are employed. The comparison results indicate fewer wall flows occur within Winpak and more liquid accumulates in the center of the packing under the uniform feeding condition. This result is due to fact that the windows increase the possibility of flowing along the packing channels at both the inner and the back sides and lessen liquid flows to the sidewall. By contrast, the liquid inclines to flow toward the sidewall for the general packing, which is in accordance with the published work48. For the central-point feeding condition, the liquid is fed in the middle of the packing at the top. The liquid distinctly inclines to flow to the sidewall for the general packing, while this kind of tendency is mitigated in Winpak because the window would change the direction of liquid flows along the channel to the lower back-side unit. [Figure 13]

4. Conclusions A multi-scale method is developed to predict the liquid distribution and local hydrodynamics of Winpak. The combination of the CFD method and the unit network model enables the visualization of the liquid flow inside the structured packing to be created. The conclusions can be drawn as follows:  Six REUs for the micro-scale model and ten distribution coefficients for the macro-scale unit network model were defined to describe the flow behavior within the complex geometric structure of Winpak. Theoretically, the liquid distribution of all systems could be predicted because the corresponding distribution coefficients can be accurately determined by CFD method. In addition, the multi-scale method could be extended to study the mass transfer process inside structured packings.  The windows have significant effects on liquid distribution and the flow pattern within Winpak. First, the windows lead to more uniform liquid distribution and mitigate the tendency of liquid flowing toward the sidewall. Second, the liquid 17



flowing through the windows to the back side of the packing sheets results in the increase of liquid holdup and wetting area more than 34.6% and 71%, respectively. The liquid flow further leads to a decrease in film thickness. Furthermore, three flow patterns on the packing sheets were observed, in which the appearance of the chaotic flow formed in the 1st REU indicates the occurrence of a flooding phenomenon. Therefore, the structural optimization of the 1st REU of Winpak can be considered as a feasible way to amplify the operation range of a large-scale column.

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Supporting Information Dimensions of the 350Y-type Winpak (Table S1), physical properties of the gas and liquid phases (Table S2), and description of the streams in Figure 5a (Table S3) and Figure 5b (Tables S4).

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Acknowledgments The authors acknowledge the National High Technology Research and Development Program of China (863 Program No. 2015BAC04B01) and China Postdoctoral Science Foundation Funded Project (No. 2016M601263) for financial support.

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Nomenclature ae effective wetting area per unit volume, m2/m3 ap specific area, m2/m3 b proportion of liquid flows to the back side for the interior REU bs proportion of liquid flows to the back side for the sidewall REU f proportion of liquid flows along the channel F F-factor, Pa0.5 momentum source term, N/m3 F g gravitational acceleration, m/s2 g proportion of liquid mixing in the node for the 1st & 3rd REUs g' proportion of liquid mixing in the node for the 2nd REU h proportion of liquid flows transverse in the interior unit h liquid holdup, m3/m3 hs proportion of liquid flows transverse in the sidewall unit k turbulent kinetic energy, m2/s2 L spray density, m3/m2 h m window width, mm P pressure, Pa q window height, mm Q volume flow rate, m3/h r proportion of liquid reflects to the interior for the 3rd sidewall REU rs proportion of liquid reflects to the interior for the 1st sidewall REU rss proportion of liquid reflects to the interior for the 2nd side wall REU S source term velocity, m/s u Greek letters α volume fraction γw contact angle, ° δ thickness of the liquid film, mm ε turbulent dissipation rate, m2/s3 κ free surface curvature, m-1 μ dynamic viscosity, Pa·s ρ density, kg/m3 σ surface tension, N/m Subscripts G gas phase L liquid phase in inner side out back side

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Figures

Figure 1 Winpak geometry

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Figure 2 Unit network model

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Figure 3 Multi-scale method procedure

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Figure 4 Structures of three interior REUs and its corresponding sidewall REUs, (a) 1st REU, (b) 2nd REU, (c) 3rd REU

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Figure 5 Principle of liquid distribution of (a) the 1st interior REU and (b) the 1st sidewall REU

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Figure 6 Flow behavior within (a) the 1st interior REU; (b) the 2nd interior REU; (c) the 3rd interior REU; (d) the 1st sidewall REU; (e) the 2nd sidewall REU; (f) the 3rd sidewall REU

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Figure 7 Three typical flow patterns within Winpak including (a) film flow; (b) film-droplets flow; (c) chaotic flow

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Figure 8 Liquid flow patterns within different REUs under various operation conditions

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Figure 9 Variation of distribution coefficients with different operation conditions including (a): b; (b): bs; (c): r/rs; (d): rss

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Figure 10 Liquid holdup of different REUs under various operation conditions

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Figure 11 Effective wetting area of different REUs under various operation conditions

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Figure 12 Film thickness based on both ae and ap of Winpak under different operation conditions—(a) the 1st REU; (b) the 2nd REU; (c) the 3rd REU; (d) comparison among REUs at L = 60 m3/(m2·h) based on ae

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Figure 13 Comparison of liquid distribution between Winpak and the general packing as (a) uniform feeding and (b) central-point feeding.

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Table f 1

Table 1 Constants among distribution coefficients h hs g 0 0 0

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g' 0


For Table of Contents Only

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Liquid Distribution and Local Hydrodynamics of Winpak: A Multiscale

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