Microsoft Word - 66iervolino.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 65, 2018 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Eliseo Ranzi, Mario Costa Copyright © 2018, AIDIC Servizi S.r.l. ISBN 978-88-95608-62-4; ISSN 2283-9216 Numerical Simulation of Mass Transfer of Slug Flow in Microchannel Ying Li*, Huanran Lv Institute of Environmental and Chemical Engineering, Dalian Jiaotong University, Dalian 116028, China liying630@sina.com Computational fluid dynamics (CFD) is used to investigate mass transfer characteristics of gas-liquid two- phase slug flow in microchannel. Simulation results illustrates liquid volumetric mass transfer coefficient kLa is proportional to the square root of diffusion coefficient D and gas bubble velocity uB, and inversely proportional to the length of slug unit cell. Moreover, kLa shows a similar tendency to Higbie penetration model, but has a large deviation. In this paper, an improved expressions including two contributions of the caps and liquid film is presented based on Higbie penetration model. The effect of Fo on mass transfer of liquid film contribution is discussed. The predicted kLa with the new correlation agree well with the simulated kLa, the average relative error is within 20%. The control variables which determine slug flow mass transfer in microchannel such as gas bubble velocity uB、 liquid film thicknessδF、liquid film length LF and unit cell length LUC can be deduced from superficial gas velocity uG 、 superficial liquid velocity uL and liquid physical properties. Thus, the developed correlation not only reflects the characteristics of mass transfer process, but also has simplicity and practicality as empirical correlations. 1. Introduction Microreactor has wide application in gas liquid absorption (Ye et al., 2013) and reaction (Zhao et al., 2013) due to its high efficient mass transfer characteristic. Slug flow in microchannle is an ideal flow pattern to intensify gas liquid mass transfer (Haase et al., 2016; Khramtsov et al., 2016). Slug flow is characterized by the presence of elongated gas bubbles with lengths greater than the capillary diameter, which rise along the capillary separated from each other by liquid slugs. The gas bubbles occupy most of capillary cross section, separated from the channel wall by a thin liquid film. This flow arrangement has been reported to yield superior mass-transfer performance. Liquid side mass transfer coefficient correlation kLa of slug flow in capillaries was presented in eq.(1). It illustrated that kLa relies on the length and speed of liquid slug (Berčrč and Pintar, 1997). kLa of slug flow contains two parts of gas cap and liquid film shown in Eq.(2) and can be calculated through Higbie penetration theory such as Eq.(3) (Van baten and Krishna, 2004). A new colourimetric technique and calculation method were developed to determine the liquid side mass transfer coefficients around the slug bubbles (Dietrich et al., 2013). When residence time was defined as the length of gas bubble divided by gas liquid relative velocity, liquid side mass transfer coefficient was to penetration theory (Haghnegahdar et al., 2016). The contribution of liquid film to mass transfer coefficient was reduced when the residence time was long enough (Abolhasani et al., 2015). A new correlation Eq(4) was developed combined penetration theory and empirical representations (Yue et al., 2009). ( ) ( )( ) 57.0 19.1 1 111.0 UCG LG L L uu ak ε− + = (1) FLFCLCL akakak += (2) H G UCG B UCH B L dL Du Ld Du ak ε εππ 42422 ⋅+⋅= (3) 325 DOI: 10.3303/CET1865055 Please cite this article as: Li Y., Lv H., 2018, Numerical simulation of mass transfer of slug flow in microchannel, Chemical Engineering Transactions, 65, 325-330 DOI: 10.3303/CET1865055 3.05.0 2       +       + = SB B SB B H L LL L LL Du d ak (4) Eq.(3) reflected the mass transfer characteristic of slug flow in microchannel. But the calculation of kLa needed information such as bubble length and velocity and was not convenient for practical application. Many researchers put forward empirical correlations like Eq.(5) (Sobieszuk et al., 2011) and (6) (Yue et al., 2007). 05.012.1Re1.0 ScSh = (5) 5.0937.0213.0 ReRe084.0 LLGHL ScadSh = (6) It is difficult to measure liquid side mass transfer coefficient in the narrow microchannel. Numerical simulation is used to investigate the mass transfer performance of gas liquid two phase flow in microchannels. Combined with the influence of the flow parameters of slug flow on the liquid side mass transfer coefficient in the simulated results and the correlation formula based on the two contributions derived from the Higbie permeation model, an improved correlation formula is proposed to predict the liquid side mass transfer coefficient of slug flow in microchannel. 2. Numerical simulation 2.1 Mathematical model In microchannel, each gas bubble and liquid slug with the same size constitute one unit cells shown in Figure 1(a). One of the unit cells was intercepted in this study and periodic boundary condition was set at the inlet and outlet in Figure 1(b). (a) (b) Figure 1(a) Schematic representation of slug flow Figure 1(b) Mathematical model of the unit cell in microchannel The volume averaged mass and momentum conservation equations in the Eulerian framework were given by ( ) 0=⋅∇+ ∂ ∂ v t ρ ρ (7) ( ) Fgpvv t v  ++⋅∇+−∇=⋅∇+ ∂ ∂ ρτρρ (8) The boundary condition was periodic in the vertical direction (u1 =u2; p1 =p2). Simulations were performed in a reference system in which the bubble was stationary and the wall moved up with the bubble rise velocity uB. At the outside wall, the boundary condition was set to uz=-uB, ur=0, where r and z were the radial and axial coordinates. At the axis of symmetry, we had duz/dr = 0. The simulations were carried out using axi-symmetric 2D grids using cylindrical coordinates. Mass transfer equation was, ( ) 0=∇−⋅∇+ ∂ ∂ LLL L CDCv t C (9) Here, CL was the concentration of solute in the liquid phase and D was the diffusion coefficient. At the top and bottom, the periodic boundary conditions were used, CL,1 = CL,2. Through the outside wall, dCL/dr =0. Symmetry conditions applied to the center axis, dCL=dr=0. At the bubble surface, the concentration was specified as CL,s = 1. 326 First, the computational domain of Figure 1(b) was divided into grids. For this irregular area, unstructured mesh was adopted and fined on the surface of bubbles. PISO algorithm was used to solve velocity pressure coupling to ensure computation accuracy while accelerating convergence. In order to prevent numerical diffusion, the QUICK format was used to discrete time convection terms. The whole simulation process was carried out in two steps. First, the steady state simulation was used to solve the mass and momentum conservation equation, and the convergence velocity field was used for the next step of mass transfer simulation. Mass transfer was performed by unsteady state. The time step was 0.0001, and the iteration was 15000 steps. The liquid side mass transfer coefficient kLa was calculated from: ( ) ( )         + − −− = 2 / 12 12 ,, , 12,, tLtL sL tLtL L CC C ttCC ak   = domain i domain tLi tL vol Cvol C ,, (10) = t LL adtkt ak 0 1 τ (11) 2.2 Numerical simulation The values of kLa calculated at each time step using Eq. (11) were shown in Figure 2. After about 1 s kLa reached a quasi-steady state value. And the simulated kLa values were independent of the number of grids in Figure 3. Figure 2 Effect of calculation time on liquid volumetric mass transfer coefficient Figure 3 Effect of number of grid on outlet mass fraction of solution absorption 0 3 6 9 12 15 18 21 24 27 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1 1,1 k L a/ s- 1 Time/s 0 2 4 6 8 10 12 14 0 10000 20000 30000 40000 50000 60000 70000 80000 O ul et m as s fr ac tio n *1 04 Number of grid 327 3. Results and discussion According to the analysis of the experimental data, the basic flow parameters of slug flow in the microchannel were as follows: bubble velocity uB=0.6m/s, liquid film thickness δF=13μm, liquid film length LF=2mm and slug unit length LUC=6mm. When the size of the slug bubble is larger than the channel characteristic size dH=300μm, the internal circulation is produced inside the bubble under the shear action between the bubble and the continuous liquid film or the channel wall, which reduces the thickness of the bubble boundary layer and the diffusion distance, increases the contact time and the interface area of gas and liquid, and eventually leads to the intensifying of mass transfer process. The simulated results fitted well with the experimental results of Yue et al. (2009) in Figure 4. The kLa values were higher one to two orders than traditional gas liquid contactors. Otherwise, the simulated results had large deviation from the results of Dietrich et al. (2013) which overestimated the contribution of liquid film to mass transfer because of the suppose of complete mix between liquid slug and liquid film. Figure 4 Comparison between the simulated kLa values and predictions of other research According to simulated results in Figure 5(a),(b) and (c), liquid side mass transfer coefficient was proportional to square root of diffusion coefficient D and square root of bubble velocity uB, inversely proportional to slug unit length LUC. These tendencies were completely consistent with the predictions of penetration theory. Liquid side mass transfer coefficient increased with the thinning of liquid film in Figure 5(d), which was not expressed in Eq.(3). (a) (b) 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Pr ed ic te d k L a/ s- 1 Simulated kLa/s-1 Yue et al.2009 Dietrich et al.2013 -20% 20% 0 0,5 1 1,5 2 2,5 3 0 2 4 6 k L a/ s- 1 D1/2×105/m⋅s-1/2 0 0,5 1 1,5 2 2,5 3 0 0,5 1 1,5 k L a/ s- 1 uB1/2/m⋅s-1/2 328 (c) (d) Figure (5) Dependence of the liquid side mass transfer coefficient on (a) diffusion coefficient D, (b) bubble velocity uB, (c) slug unit length LUC and (d) liquid film thickness δF According to the original penetration theory represented by Eq.(3), the model assumed the presence of a well- mixed liquid phase within the liquid slugs and short contact times at the gas−liquid interface (Fo ≪ 1).The contributions of bubble caps and liquid film to liquid side mass transfer coefficient were changeable at different conditions. The correlation in Eq.(3) can be simplified based on the practical application. When Fo ( 2 FB B u DL Fo δ = ) was larger than 1, liquid film was saturated. Thus liquid side mass transfer coefficient was controlled only by liquid slug such as Abolhasani et al.( 2015) and the second term in Eq. (3) can be ignored. The contribution of liquid film to mass transfer was effective when Fo was between 0.0075-0.074 (Ren et al., 2012). In this study, liquid film was not saturated and Fo was between 0.01 and 0.1. The contribution of liquid film to mass transfer can be regressed as function of Fo. An improved correlation based on penetration theory was presented in this paper shown in Eq. (12). Liquid side mass transfer coefficient was inversely proportional the exponential function of Fo through fitting simulated results. The improved correlation can better predict liquid side mass transfer coefficient with a relative error below 20% in Figure 6. )( 42422 Fof L L dL Du Ld Du ak UC F HF B UCH B L ⋅⋅⋅+⋅= ππ FoeFof −= 3.0)( (12) Figure 6 Comparison between the simulated kLa values and predictions of improve correlation Eq.(12) 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 0 0,1 0,2 0,3 0,4 k L a/ s- 1 1/LUC/mm-1 0 0,5 1 1,5 2 2,5 3 0 5 10 15 20 k L a/ s- 1 Liquid film thickness δF/μm 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Im pr ov ed p re di ct ed k L a/ s- 1 Simulated kLa/s-1 -20% 20% 329 4. Conclusions In this paper, the numerical simulation method was used to calculate the liquid side mass transfer coefficient of the gas liquid two phase flow in microchannel. Simulation results were in good agreement with the experimental results of Yue et al.(2009). According to the simulation results, the relationship between the mass transfer coefficient kLa and the diffusion coefficient D, the bubble velocity uB and the length of sluf unit length LUC was consistent with the prediction trend of Higbie penetration theory model. Combined with the effect of liquid film thickness on the liquid side mass transfer coefficient, an improved correlation of the two parts of kLa based on the penetration model was proposed. The relative error between prediction results of the new correlation and the simulation results was within 20%. Acknowledgments The authors gratefully acknowledge the financial support provided for this work by the New Century Excellent Talents in University of Liaoning Province (Grant no. LJQ2015019) and Natural Science Foundation of Liaoning Province (Grant no. 2015020220). 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