Article pubs.acs.org/IECR
Hydrodynamics of Layered Wire Gauze Packing Jicai Huang,†,‡ Mei Li,†,‡ Zhaohu Sun,† Maoqiong Gong,*,† and Jianfeng Wu† †
Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100039, China
‡
ABSTRACT: The hydrodynamics of layered wire gauze packing is studied. An experimental setup is established to measure the pressure drop of the packing. By some rational simplification, a 3D model is built to investigate the liquid film flow behavior in the packing, with which the influences of gas load and liquid spray density on liquid holdup and wetting area are analyzed in detail. Simulated results show that the liquid tends to accumulate at the intersection where the film is thicker. Based on the simulated results of liquid holdup and part of experimental data, a pressure drop correlation is proposed which can well predict experimental pressure drop of other operation conditions. The average relative errors are less than 10% in the study range. To study the pressure drop contribution of each term, a 3D single phase model is built. The results show that the concentrated losses caused by changes in the flow directions are the main factor to the pressure drop. irregular flow channels in it. The previous simulations on the packings13,14 were highly dependent on the empirical or semiempirical correlations such as pressure drop, liquid holdup, and wetting area correlations for which it made little sense to carry out CFD simulations on the random packing column. To reduce or avoid experimental tests, it is necessary to build a rational and simplified model of random packing that can be used to predict the performance of the packing. Since the use of structured packings requires high capital investment, a kind of layered wire gauze packing with high specific area is studied here. Because of the simple production process, the packing will reduce the capital investment. Therefore, the hydrodynamics of the packing is studied to investigate the performance. Although the flow channels in the packing are irregular, to reduce the experimental work and understand flow field, a simplified model is built which considers the representative units of the packing and the wire diameter. Few researches have reported the CFD simulation of multiphase flow in the wire gauze packing, and it is attempted in this work. By the rational simplification, two-phases flow in the packing is modeled, with which, liquid holdup and wetting area are analyzed. Combined with several groups of experimental data on dry and wet pressure drop, a pressure drop correlation is proposed that can well predict the pressure drop in the packing. Besides, a 3D single phase model is built to study the pressure drop contribution of each term. The results show that the concentrated losses are the main factor to the pressure drop.
1. INTRODUCTION Gas purification by absorption constitutes an important aspect in industrial application such as an amine-based CO2 capture process.1 The capture process usually deals with a huge volume of gas with low CO2 partial pressure, which calls for high capacity, high efficiency, and low pressure-drop gas−liquid contacting internals.2 Because of their geometric characteristics, high specific area ranging from 250 to 750 m2/m3, and high void fraction around 90%, structured packings appear to meet the requirements.3,4 However, one drawback of using structure packings is their high cost per unit volume which leads to high capital investment compared to that for the use of dumped packing.5 Therefore, to obtain packings with good performance or reduce the capital investment, many kinds of packings have been developed. For a long time the performance of a prototype was mainly based on numerous experiments which are expensive and time-consuming.6 With the developments of CFD theory and computer technology, many studies have been devoted to hydrodynamics of structured packings, to develop models for pressure drop, liquid holdup, and contact area which are further used in mass transfer models. Because of the complexity of the structured packing geometry and the limited CPU resources of computers, it is impossible to run a simulation at column scale. Petre et al.7 and Larachi et al.8 proposed a method based on mesoscale three-dimensional calculations in the representative elementary units (REU) of packings. The obtained results in REU were further used for dry pressure drop calculation at the scale of an entire packing. The approach reduces the calculation resources significantly. However, since the method does not correspond to an entire packing directly, the simulated results deviate from the experiments in some extent. To address the problem, the following models9,10 considered the entire representative geometry of packings directly and represented the experimental dry pressure drop well. Based on the entire models, multiphase flow and mass transfer in the structured packing were studied.11,12 Although CFD simulation is also available to the random packing column, it is impossible to consider the detailed structure in the column which results from the © 2015 American Chemical Society
2. EXPERIMENT The experimental setup is shown in Figure 1. The column is made of transparent Plexiglas, with an internal diameter of 0.19 m and height of packing of 0.58 m. The packing is stainless wove gauze with square aperture of 2.25 mm and wire diameter Received: Revised: Accepted: Published: 4871
November 29, 2014 March 23, 2015 April 17, 2015 April 17, 2015 DOI: 10.1021/ie504689s Ind. Eng. Chem. Res. 2015, 54, 4871−4878
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multiphase flow on Mellapak 250Y. Gu et al.16 and Hoffmann et al.17 developed the inclined plate on the basis of structured packing. Recently, Sun et al.18 applied the multibaffled and inclined plates to simplify novel and traditional structured packing, based on which the multiphase flow and mass transfer were studied. With reference to the method mentioned above, some rational simplification is also made in the model. For the layered wire gauze packing, it is hard to make sure that all the square apertures of two adjacent layers are vertically aligned. Therefore, the packing seems to possess irregular flow channels and some rational simplification should be made before modeling. It is assumed that the apertures of two adjacent layers mainly have the two arrangements shown in Figure 3. Because of the existence of surface tension, liquid will
Figure 1. Schematic diagram of experimental setup.
of 0.3 mm, meaning that the thickness of each layer is twice the wire diameter. The specific area aP is 1000 m2/m3, and the voidage is 0.924. The stacking form and packing structure are shown in Figure 2. Air is blown to the bottom of the column
Figure 3. Arrangement of experimental packing representative units: (left) rotation alignment of square aperatures; (right) vertical alignment of square aperatures.
mainly accumulate at the intersections displayed in the shadows of Figure 3. For this reason, the intersection has considerable effect on the liquid holdup and wetting area. However, no matter the rotation or vertical alignments of square apertures, the numbers of shadows are the same and are 4 for each aperture. Therefore, for the liquid holdup and wetting area model, the stacking form of two layers is simplified as Figure 4a, meaning that the square apertures of two adjacent layers are vertically aligned. On the basis of the structure, a computational domain is built as Figure 4b, which is a quarter of the square aperture (shadow in Figure 4a) because of its symmetry. The wire diameter is 0.3 mm which is considerable compared to the flow channels, since when the inlet and outlet boundary conditions are close to the wire gauze, the convergence will be difficult. To solve the problem, the regions beyond the research one are built to ensure the convergence of simulation. It should be noted that the research region has almost the same specific area and voidage as the experimental packing. In addition, the computational domain remains the same representative unit of the packing mentioned previously. Therefore, the simplified model is appropriate to simulate the liquid holdup and wetting area of the packing. The boundary conditions are shown in Figure 4b while only liquid is fed to the packing. For the gas−liquid countercurrent flow, the gas inlet boundary condition is changed to pressure inlet. The uniform velocity and film thickness are assumed at the liquid inlet, and the thickness is given by2
Figure 2. Picture of packing used in the present study: (left) stacking form of packing in the transparent column; (right) local picture of the packing.
and water is fed into the packing surface from the distributor on the top of the packing. The pressure drop is measured by the U-tube manometer. The liquid spray density is 10 to 30 m3/ (m2·h).
3. MODEL DEVELOPMENT Hydrodynamics study of packing mainly focuses on the pressure drop, liquid holdup, and contact area. Although there are many empirical correlations available in the published literature, they are limited to the specific tested packings. Since the measurements of liquid holdup and wetting area are demanding on experimental setup and time-consuming, the two variables are modeled by CFD technology, and the liquid holdup is further used to correlate the pressure drop. 3.1. Liquid Holdup and Wetting Area. Most of CFD studies of multiphase flow on the packing included some assumption or simplification which results from the complexity of packing geometry and the limited computational resources. Szulczewska et al.15 first simplified the structured packing into two-dimensional flat and corrugated plates to model the
⎛ 3μ q ⎞1/3 L L ⎟⎟ δ = ⎜⎜ ρ ⎝ Lg ⎠
(1)
where qL is the liquid flow rate per unit of wetted perimeter length, μL is the liquid viscosity, ρL is the liquid density, and g is the acceleration of gravity. Then, the liquid inlet velocity is 4872
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Figure 4. Computational domain and corresponding boundary conditions for the 3D-VOF calculations.
uL =
Brackbill et al.21 While there are only two phases, Fsv is defined as
ρL gδ 2 3μL
(2)
Fsv = σij
Because of the complexity of packing geometry, it is difficult to use the Eulerian multiphase model which solves the momentum equation for each phase. The model calls for a greater amount of computational resources and may lead to convergence difficulty. Therefore, the VOF method is chosen to track the gas−liquid interface, and the RNG k−ε model19 is adopted to describe turbulent flow on the packing. The basic model equations are represented as follows. For the qth phase, the volume fraction equation is ∂αq ∂t
+ ∇·(αqvq⃗ ) = 0
⎯n ) = 1 ⎡⎛⎜ n ⃗ ·∇⎞⎟|n | − (∇·n )⎤ κ = −(∇·→ ⃗ ⃗ ⎥ ⎢ e ⎦ | n ⃗ | ⎣⎝ | n ⃗ | ⎠
(3)
ne⃗ = ne⃗ ,wall cos θ + ne⃗ ,t sin θ
(8)
where ne,wall is the unit wall normal directed into the wall, and ⃗ ne,t ⃗ lies in the wall and is normal to the contact line between the interface and the wall at the point. The contact angle in the model is set to 1.446°.22 The influence of the interfacial drag force can be described by the model developed by Brunazzi and Paglianti,5 and is defined as
(4)
The material properties such as density and viscosity are averaged by the volume fraction and take on the following form:
1 FLG = − aefi ρG (VG + VL)2 2
n
∑ αqφq q=1
(7)
where ne⃗ is the unit normal to the surface, thus ne⃗ = n ⃗ /|n ⃗|. The effect of wall adhesion at the fluid interface can be estimated easily within the framework of the CSF model in terms of contact angle (θ) between the fluid and wall. The normal to the interface at a point on the wall is
∂ (ρv ⃗) + ∇·(ρvv⃗ ⃗) ∂t
φ=
(6)
where σ is the surface tension coefficient and κ is the free surface curvature and is calculated from
A single momentum equation is solved throughout the domain, and the velocity field is shared among the phases:
= −∇P + ∇·[μ(∇v ⃗ + ∇v ⃗T )] + ρg ⃗ + F ⃗
ρκ ∇αi 0.5(ρi + ρj )
(9)
where ae is the interfacial area per unit volume and can be evaluated by
(5)
The source term F in eq 4 only arises from the surface tension Fsv and gas−liquid interfacial drag force FLG. Although only a single momentum equation is solved for the VOF method, the existence of interfacial drag force will actually reduce the liquid and gas velocity at the interface for the gas−liquid countercurrent flow, and it seems necessary to consider the force in the model. Xu et al.20 and Sun and co-workers4,18 have included the influence of interfacial drag force in the VOF method by user defined functions which can well reflect the multiphase flow behavior in the packing. Therefore, the influence of interfacial drag force is also considered in this work. For thin film flow on the gauze packing, the effect of surface tension can be significant. Fluent includes the effect of surface tension as a body force in the momentum equation according to the continuum surface force (CSF) model proposed by
ae = |∇αG| = |∇αL|
(10)
VG is the effective gas velocity, and is given by
VG =
USG e − hL
(11)
where USG is the superficial gas velocity, e is the porosity of dry packing, and hL is the liquid holdup. VL is the effective liquid velocity, and can be computed from the superficial liquid velocity, USL, taking into account the liquid holdup:
VL =
USL hL
(12)
f i is the interfacial friction factor, and is given by23 4873
DOI: 10.1021/ie504689s Ind. Eng. Chem. Res. 2015, 54, 4871−4878
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Industrial & Engineering Chemistry Research fi = 0.079ReG−0.25(1 + 115δ*N ) ReG =
is to build an accurate pressure drop correlation for the packing with the aid of CFD technology. Since the simplification of apertures vertical alignment (as shown in Figure 4a) makes the gas flow path unobstructed and will underestimate the concentrated losses, the total pressure drop is correlated by part of the experimental data, combined with the simulated liquid holdup. Because the pressure drop is mainly affected by the gas velocity, voidage, and physical property, on the basis of Ergun equation,25 the correlation is defined as
(13)
dGVGρG μG
(14)
N = 3.95(1.8 + 3/D*)
(15)
where dG is the hydrodynamic diameter, and is given by 4(e − hL)/ag.24 δ* and D* are the dimensionless ratios of δ and dG to the Laplace length [σ/g/(ρL − ρG)]0.5. The turbulent kinetic energy k and dissipation rate ε equations are
D ⎛ ⎛ dP ⎞ B ⎞⎛ 1 − (e − hL) ⎞ ⎜ ⎟ ⎟ = ⎜A + ⎜ ⎟ ⎝ dz ⎠tot ⎝ ReGC ⎠⎝ e − hL ⎠
∂ ∂ ∂ ⎛⎜ ∂k ⎞⎟ (ρ k ) + (ρkvi) = + Gk + Gb − ρε αkμeff ⎜ ∂t ∂xi ∂xj ⎝ ∂xj ⎟⎠
The liquid holdup hL can be obtained from section 3.1. Combined with several groups of experimental data on pressure drop, the constants A, B, C, and D can be determined. After knowing the total pressure drop, the pressure drop contribution of each term is analyzed. Brunazzi and Paglianti5 suggested that the total pressure drop per unit height of column was given by the sum of the frictional, gravitational, and acceleration terms:
(16)
∂ ∂ (ρε) + (ρεvi) ∂t ∂xi ε ε2 ∂ ⎛⎜ ∂ε ⎞⎟ C G C α μ ρ = + − − Rε 1 k 2 ε ε ε k k ∂xj ⎜⎝ eff ∂xj ⎟⎠
(18)
⎛ dP ⎞ ⎛ dP ⎞ ⎛ dP ⎞ ⎛ dP ⎞ ⎜ ⎟ =⎜ ⎟ +⎜ ⎟ +⎜ ⎟ ⎝ dz ⎠tot ⎝ dz ⎠F ⎝ dz ⎠G ⎝ dz ⎠ A
(17)
where αk and αε are the inverse Prandtl numbers for k and ε, μeff is the effective viscosity, Gk represents the generation of turbulence kinetic energy due to the mean velocity gradients, Gb is the generation of turbulence kinetic energy due to buoyancy, C1ε = 1.44, C2ε = 1.68. Calculations are carried out with an unsteady method with time step size 1 × 10−5 s. The mass flow of liquid and gas at the outlet and the liquid holdup of the research region are monitored to determine when the solution is reaching steady state. However, since there is a coexistence of liquid and gas flow, the outlet mass fluxes fluctuate at a midvalue which will lead to the fluctuation of liquid holdup. Therefore, the time averaged values are considered. The cell number is about 72900 for the computation domain. The Pressure Implicit with Splitting for Operators (PISO) method is chosen for the pressure−velocity coupling which is appropriate to model unsteady flow. The Geo-Reconstruct method is used to track the gas−liquid interface which is the most accurate and is applicable for general unstructured mesh. The Body Force Weighted method is employed for pressure discretization. 3.2. Pressure Drop. Pressure drop is another key parameter of packing performance which determines the feasibility and economy of packing column. There are many factors affecting the pressure drop in the packing column, such as packing structure, operation condition, and physical properties. Because of the complexity of multiphase flow in the packing, in the past the pressure drop was primarily correlated by experimental data which called for numerous experimental works and was hard to extend to untested systems. Besides, the correlations are intricate and not accurate for some instances resulting from poor correlation formulas. With the development of CFD technology, many studies have been devoted to the structured packing and can well represent the pressure drop. However, the study of random packing still mainly depends on the numerous experiments. To reduce the time and expenditure for studying a prototype packing, it is a significant attempt to adopt CFD technology to analyze the influence factors of pressure drop and further to build an accurate pressure drop correlation. The objective of this section
(19)
The friction losses arising from the flow of gas phase through the column consist of two terms. The first considers distributed losses at the channel walls and gas−liquid interface, while the other term takes into account concentrated losses caused by changes in the flow directions: ⎛ dP ⎞ ⎛ dP ⎞ ⎛ dP ⎞ ⎜ ⎟ = ⎜ ⎟ +⎜ ⎟ ⎝ dz ⎠F ⎝ dz ⎠F,d ⎝ dz ⎠F,c
(20)
The gravitational and acceleration terms are calculated by
⎛ dP ⎞ ⎜ ⎟ = −ρ g G ⎝ dz ⎠G
(21)
⎛ dP ⎞ dVG ⎜ ⎟ = ρ U SG G ⎝ dz ⎠ A dz
(22)
where VG is calculated from eq 11, and for a column with uniform voidage at the axial direction, the acceleration term is zero. The gravitational term (eq 21) can be calculated easily. Therefore, the friction losses can be calculated by subtracting the gravitational and acceleration terms from the total pressure. To evaluate the proportion of the distributed losses in the friction losses, a simplified model (Figure 5) layered by the structure in Figure 4a is built. The model consists of 30 layers of wire gauze, and the specific area and voidage are nearly equal to the experimental packing. Therefore, it is assumed that the model can predict the distributed losses of the packing with reasonable accuracy. It should be noted that, because of the complexity of flow channels, the simplified model does not aim to model the concentrated losses caused by changes in the flow direction directly. The cell number is 1051904 which is determined by a series of grid independency studies. The RNG k−ε turbulent model is adopted. The boundary conditions for gas inlet and outlet are velocity inlet and pressure outlet. The periodic conditions are set to the surrounding faces. The surfaces of gauze are set to wall, and the shear condition is set to no-slip and zero-shear-stress, respectively. For the no-slip 4874
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Figure 5. Computational domain and corresponding boundary conditions for the 3D pressure drop calculations.
Figure 7. Relationship of liquid holdup and gas load.
calculated by integration of the iso-surface of volume fraction.26 Since the contact angle is small for the gauze which is beneficial to wet behavior, the interface fluctuates and the interspace between two layers can be filled by liquid; the wetting area ratios remain at relative high values and exceed 1 for low liquid spray densities, as shown in Figure 8. It should be noted that
condition, the modeled pressure drop consists of the concentrated losses of the simplified model, the gravitational term, the acceleration term, and the distributed losses, while for the zero-shear-stress condition, the model result only involves the former three terms. Therefore, the distributed losses are the difference between the two model results of no-slip and zeroshear-stress conditions. Since all of the contribution terms except for the concentrated losses have been determined, the concentrated losses can be calculated.
4. RESULTS AND DISCUSSION 4.1. Liquid Holdup and Wetting Area. In this work, the study gas range varies from 0.6 m/s to the flooding point obtained by experiment. Liquid holdup is an important parameter of packed bed which affects the bed pressure drop and mass transfer performance. In the study, the liquid holdup and wetting area are modeled by CFD technology. The liquid holdup is directly calculated by volume integral of volume fraction. With the increase of liquid spray density, the liquid holdup rises. Besides, the increase has a lower gradient for high liquid spray density, as shown in Figure 6. For the gas−liquid Figure 8. Relationship of wetting area ratio and liquid spray density.
even for sheet packing, the wetting area ratio may be higher than 1,27−29 not to mention the existence of interspace for the wire gauze packing. However, the wetting area is not always equal to the effective mass transfer area, despite that packing can be wetted at a low liquid spray density. The reasons are that the film is thin and the surface renew is slow, which result in the quick balance of mass transfer. While the superficial gas velocity is zero, the wetting ratio increases with the increment of liquid spray density. Below the flooding point, the enhancement of gas load leads to the increase of wetting area ratio which is caused by the intensive interfacial fluctuation. When the gas velocity reaches to the flooding point, the wetting area ratios tend to unity and the average increment of wetting area ratio is 11.3% for the studied liquid spray density range. The liquid film flow behavior for different spray density is shown in Figure 9. The film thickness is not uniform and is thicker at the intersection for all cases. Therefore, the analysis in section 3.1 that the intersection has significant effect on the liquid holdup is reasonable. The film thickness away from the crisscross increases with a rising spray density which is beneficial to mass transfer. However, a high liquid spray
Figure 6. Relationship of liquid holdup and liquid spray density.
countercurrent flow, the rising gas load leads to a slow increment of liquid holdup blow flooding point, as shown in Figure 7, which results from the existence of interfacial resistance and fluctuation. The wetting area is of determinant importance in the gas− liquid mass transfer. In this work, the VOF simulated results can provide the interfacial information. The wetting area is 4875
DOI: 10.1021/ie504689s Ind. Eng. Chem. Res. 2015, 54, 4871−4878
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Figure 9. Relationship of liquid distribution and liquid spray density.
displayed in Figure 10. With the increment of gas load, the pressure drop increases. The influence of liquid spray density on the pressure drop has the same trend. With a rising liquid spray density, the gas velocity leading to flood decreases. On the basis of the liquid holdup obtained in the previous simulation, part of the experimental data on dry pressure drop, and wet pressure drop of gas−liquid countercurrent flow at L = 15 m3/(m2·h), the model parameters in eq 18 can be regressed. To validate the model, the Leva model30 which has been widely used to predict the pressure drop of highly specific area gauze packing is also fitted with the same groups of experimental data mentioned above. The form of the Leva model is given by
density will no doubt lead to high pressure drop and high cost of operation. Besides, the liquid holdup on the crisscross may not be used effectively. Therefore, an appropriate liquid spray density should make a balance between the effective wetting area and the operation cost. The simulation of mass transfer phenomenon can be conducted to determine the effective wetting area in the model. To relieve the accumulation of liquid at the intersection and make it better distributed on the wire surface away from the intersection, the gauze with minor wire diameter which involves stronger capillarity and can be completely wetted at a low liquid spray density maybe a good choice. However, to ensure the stability of the square aperture, a small wire diameter usually corresponds to a small aperture which leads to a high pressure drop. 4.2. Pressure Drop. The relationship of experimental pressure drop to the gas load and liquid spray density is
⎛ dP ⎞ ⎜ ⎟ = A(USG ρG )B 10C·L ⎝ dz ⎠tot
(23)
Parameter values for the models are given in Table 1. Comparing with experimental pressure drop of dry and liquid 4876
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With the increase of gas load, the proportion decreases, and the gradient is greater for a lower gas velocity. Since most of the operations involve a relative high gas load, the proportion of distributed losses tends to a low value, and the pressure drop is nearly equal to the concentrated losses.
5. CONCLUSION To avoid the high capital investment of structured packing, the hydrodynamics of a kind of packing layered by wire gauze is studied. An experiment setup is established to measure the pressure drop of the packing. With the increment of gas load or liquid spray density, the pressure drop increases. By some rational simplification, a 3D model of the gauze packing is built to study the multiphase flow in it. With the increment of liquid spray density, the liquid holdup, wetting area, and film thickness increase. For all of the cases, the liquid film at the crisscross is thicker than other places. The reason that wetting area ratios remain at relative high values and exceed 1 for low liquid spray densities is the small contact angle of wire gauze, interfacial fluctuation, and the interspace between two adjacent layers where can be filled by liquid. With the increment of gas load, the liquid holdup increases slowly. When the gas velocity reaches to the flooding point, the wetting area ratios tend to unity and the average increment of wetting area ratio is 11.3% for the studied liquid spray density range. On the basis of the simulated results and part of the experimental results, a correlation of pressure drop is proposed which can well predict the pressure drop of other operation conditions, and the average absolute relative deviations are less than 10% in the study range. Simultaneously, a 3D single phase model is built to study the pressure drop contribution of each term. The model result shows that the concentrated losses are the main factor causing the pressure drop. The proposed model can greatly reduce the experimental work and help in understanding the flow in the packing.
Figure 10. Relationship of pressure drop and Fs factor.
Table 1. Model Parameters of eq 18 and eq 23 model
A
B
C
D
present Leva
−260.523 427.256
0.031 2.266
−1.932 0.015
0.268
spray density from 10 to 30 m3/(m2·h), the average absolute relative derivations for the present model are 5.37%, 6.96%, 6.37%, 6.03%, 6.97%, and 9.26%, respectively. For the Leva model, the values are 11.73%, 13.30%, 11.71%, 17.96%, 30.71%, and 49.39%, respectively. Therefore, the present model can better represent the pressure drop within the studied gas and liquid load. Furthermore, since the influence of gas physical properties has been included in the Reynolds number and the influence of liquid physical properties have been included in the liquid holdup simulation, the present model parameters shown in Table 1 have potential use in other systems directly. However, for the Leva model, the lack of consideration of physical properties makes it difficult to extend the parameters to other systems. To study the pressure drop contribution of each term, the dry pressure drop is analyzed. From eq 21 and eq 22, the pressure drop caused by gravitational and acceleration terms are small. In the study gas load, the proportion of friction losses is from 84% to 99% which increases with a rising gas velocity. As mentioned previously, the friction losses consist of distributed losses and concentrated losses. Figure 11 represents the relationship of proportion of distributed losses and gas load.
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[email protected]. Notes
The authors declare no competing financial interest.
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Figure 11. Proportion of distributed losses in the friction losses. 4877
NOTATION ae = interfacial area per unit volume, m2/m3 aP = specific area of packing, m2/m3 awet = wetting area, m2/m3 d = hydrodynamic diameter, m e = porosity F = source term of the momentum equation, N/m3 f i = interfacial friction factor g = gravitational acceleration, m/s2 hL = liquid holdup, m3/m3 k = turbulent kinetic energy, m2/s2 L = liquid spray density, m3/(m2·h) P = pressure, Pa qL = volume flow rate per unit of perimeter length, m3/(m·s) ReG = gas Reynolds number uL = liquid inlet velocity, m/s USG = superficial gas velocity, m/s USL = superficial liquid velocity, m/s VG = effective gas velocity, m/s VL = effective liquid velocity, m/s DOI: 10.1021/ie504689s Ind. Eng. Chem. Res. 2015, 54, 4871−4878
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Industrial & Engineering Chemistry Research Greek Letters
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α = volume fraction δ = thickness of the liquid film, m ε = turbulent dissipation rate, m2/s3 θ = contact angle, ° κ = free surface curvature, 1/m μ = dynamic viscosity, Pa·s ρ = density, kg/m3 σ = surface tension, N/m Subscripts
L = liquid phase G = gas phase
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DOI: 10.1021/ie504689s Ind. Eng. Chem. Res. 2015, 54, 4871−4878
