- Email: [email protected]
Fluid dynamics in multiphase distillation processes in packed towers
Computers and Chemical Engineering 29 (2005) 1433–1437
Fluid dynamics in multiphase distillation processes in packed towers Andreas Hoffmann ∗ , Ilja Ausner, Jens-Uwe Repke, G¨unter Wozny TU Berlin, Institute of Process and Plant Technology, TU Berlin, Sekr. KWT 9, Strasse des 17. Juni 135, 10623 Berlin, Germany Available online 9 April 2005
Abstract In order to design packed columns for multiphase operation it is necessary to include reliable data on the flow behavior in the model. Since experiments inside packings are very difficult to perform, computational fluid dynamics (CFD) simulations are considered to be a sensible approach as numerical experiments. To obtain reliable results validation is inevitable. We present the validation of two- and three-phase film flow under transient conditions. This application is not abundant in literature. Numerical results are compared with data from own experiments. The usability of a VOF-like code for such applications is shown. © 2005 Elsevier Ltd. All rights reserved. Keywords: Multiphase flow; Flow behavior; Film break-up; CFD; Validation
1. Introduction During the last decades packed columns have become popular due to their increase in efficiency and capacity. While these benefits are widely used for distillations with only one liquid phase packed towers are still avoided for processes with more liquid phases. This is mainly related to the fact that the liquid flow behavior changes dramatically with the appearance of a second phase and with that the tower efficiency. Designing packed columns for three-phase distillation requires a reasonable model (Repke, Villain, & Wozny, 2003). While various models exist for two-phase distillation (e.g. Brunazzi & Paglianti, 1997; Iliuta & Larachi, 2001; Rocha, Bravo, & Fair, 1993) yet only a few works focus on multiphase operations (e.g. Repke, 2002). One of the main problems is the prediction of the flow behavior inside the column. Most models for the two-phase distillation are based on either film or rivulet flow inside the packed columns. In case of three-phase operation it would be more appropriate to assume film flow for one phase and rivulets or droplets for the other (see Fig. 1). Since it is almost impossible to look into the packings simulations with computational fluid dynamics (CFD) will be used to minimize the experimental effort to describe and analyze the influence of various parameters. For these cases no ∗
Corresponding author. E-mail address: [email protected] (A. Hoffmann).
0098-1354/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2005.02.004
validation of the CFD codes has been done until now. We present the validation of a volume of fluid (VOF) method for two- and three-phase film flows under transient conditions where one of the phases is air. With validated methods it is possible to develop a model for the effective interfacial area which considers the flow behavior inside packings which is necessary to design packed towers.
2. Simulations The main goal is to develop a model for the interfacial area between all phases in a multiphase operated packed column. Recent models only consider parameters from binary equations i.e. obtained for two-phase flow. In three-phase film flow it is not possible to just calculate with two of the phases since the flow behavior and with that the mass transfer strongly changes under the influence of a second liquid phase (Repke & Wozny, 2002). Depending on the liquid flow rate it is probable that one of the two liquid phases forms a film and the other phase runs down as droplets or rivulets. Therefore, it is necessary that the CFD method is able to predict surface break-up, droplet and rivulet formation properly. CFD calculations are carried out with the commercial code CFX 5.6, ANSYS Inc., which uses an Euler–Euler algorithm for multiphase calculations with free surfaces. Like the VOF method (Hirt & Nichols, 1981) it uses averaged phase frac-
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A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
Nomenclature a A b Re p V˙ w x z
specific area area width of the plate Reynolds number pressure volume flow rate velocity coordinate in flow direction coordinate in width direction
Greek symbols α inclination angle Γ liquid load ν kinematic viscosity δ film thickness θ contact angle Subscripts and superscripts C critical plate total plate s surface T toluene W water wetted wetted area on plate average
Fig. 2. Model geometry and boundary conditions.
contact angle is limited to the measuring error range (Stein, 1999). Turbulence is not taken into account since the range of the Reynolds-number Re indicates laminar or pseudo laminar flow (Re < 350). The model uses a specified velocity profile at the inlet, a wall boundary (no slip, defined contact angles) as the plate, and a pressure outlet (gauge pressure of p = 0) at the outlet. The geometry sides are either implemented as symmetry boundaries or as walls and the upper boundary can be modeled as an opening (inlet and outlet with zero-gaugepressure) or as a wall with free slip (Fig. 2). The Reynoldsnumber is defined with the average film velocity and the film thickness: Re =
¯ wδ ν
tions in the finite volume cells. The surface tension is implemented using the method of Brackbill, Kothe, and Zemach (1992). In case of strong interaction between the phases it is sufficient to reduce the model to one velocity field for all phases. The contact angles used are derived from static measurements. It is assumed that the influence of the dynamics on the
Γ =
Fig. 1. Possible flow behaviors on a sheet in a packed column where liquid 1 forms a film or rivulets, liquid 2 flows as rivulets or droplets and the vapor flows countercurrent to the liquids. Entrainments of the three phases in each other are also possible.
To get reliable results for model development, it is necessary to validate the CFD code. To our knowledge, this has not been done yet for this application which has various difficulties. Two-phase film flow with free surfaces has already been considered in literature but mostly two-dimensional closed films. Three-dimensional (3D) effects like film break-up and rivulet or droplet flow remain to be investigated. Three-phase film flow with different interfaces is more complex to simulate. Interaction and surface tension between all phase pairs have to be considered. Two and three dimensional cases are simulated with one and two liquid phases (Fig. 3). The main interest lies in the correct prediction of the critical liquid load for the surface break-up and the resulting shadow (or wetted wall) area (example result in Fig. 3a). For the model development it is necessary to calculate the interfacial areas between the fluids. We assume that it is sufficient to define the interface at a specific phase fraction.
(1)
This corresponds to the liquid load Γ over Eq. (2): V˙ ¯ = Re · ν = wδ b
(2)
A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
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Fig. 3. Simulation: (a) momentary result with one liquid phase (water) at a liquid load of Γ = 1.0 cm2 /s or Re = 112; (b) momentary result with two liquid phases (toluene: light grey; water: dark grey) at ReW = 250 and ReT = 220.
3. Experiments The experimental setup is shown in Fig. 4. A particle tracking velocimetry (PTV) method is applied to measure film flow velocities and the wetted wall area can be determined by optical means. Depending on the present fluids the PTV method uses particles, droplets and waves as tracers to measure the surface velocities. As particles Isospheres SG-300-B of Omega Minerals Germany GmbH (mean diameter of 110–130 m and density in the range of 0.65–0.75 g/ccm) are added to the liquid. The tracers are exposed with a stroboscope with a fre-
quency of 250 Hz. With a CCD-camera with a frequency of 60 images/s this results into a double exposure per image. To get the shadow area the pictures taken with the CCDcamera are analyzed with an image analysis software. Dyes are used to increase the contrast. The applicability of fluorescent dyes to measure the film thickness additionally is examined. The feed tubes shown in Fig. 4 can be replaced by an overflowing weir. This setup better resembles the Nusselt inlet boundary condition of the CFD simulations but is not applicable for two liquid phases.
4. Validation For validation the simulation results are compared with the data obtained from our experiments and the well known Nusselt solution. Parameters for the validation are e.g. the critical fluid load at which the single liquid phase first breaks up, film velocities and the wetted wall area. It is not sufficient to consider only one of these parameters. In Fig. 5 the specific shadow area a, obtained from simulations and experiments, is shown. It is assumed that the shadow area corresponds to the wetted wall area. a=
Fig. 4. Experimental setup for the case of two immiscible liquid phases.
Awetted Aplate
(3)
It can be seen that the shadow area is underestimated or, to put it the other way, that the curve is shifted right about Re
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A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
Fig. 5. Comparison of experimental data with numerical results for water flow on an inclined steel plate with an inclination of 60◦ ; the simulation curve (a) was obtained with a contact angle of θ = 80◦ the simulation curve (b) with a contact angle of θ = 70◦ .
∼50. The mesh is sufficiently fine, i.e. if we change the mesh size near the plate boundary from a thickness of 0.1–0.05 mm we get a solution close to the previous one. The contact angle has a critical impact on the flow behavior. Although of only minor influence on the wetted area at low Reynolds numbers it is essential to determine the correct contact angle in order to predict the critical liquid load. In Fig. 5 simulation curve (a) makes use of a contact angle of 80◦ which is the value found in literature for water–air on steel. Curve (b) gives the results for a contact angle of 70◦ which is the value measured on the plate used in the experiments. In cases where the liquid forms a stable laminar film, the solution gained by simulation meets the Nusselt solution for laminar film flow. Film thickness and velocities are predicted accurately. This can be seen in Fig. 6 where the film thickness δ is plotted along the flow direction x. With an inlet height greater than the Nusselt film thickness, the thickness decreases along the plate approaching the analytical solution. The velocities result from mass conservation and therefore meet the analytical value too. Furthermore the film thickness shows a characteristic profile over the plate width (Fig. 7). At the plate support the liquid
Fig. 6. Calculated film thickness in flow direction at Re = 220 in comparison to the analytical Nusselt solution.
Fig. 7. Calculated film thickness profile over plate width and measured intensity of emitted light of a fluorescent dye.
forms a meniscus and smaller film thickness in its vicinity. Along with the numerical solution Fig. 7 shows the result from a fluorescence measurement. This method is based on the linear proportionality of the film thickness to the emitted light intensity for liquid films with δ < 1.5 mm (Vlachogiannis & Bontozoglou, 2002). The plot shows a good agreement between the measured and simulated profile. Where the film breaks up and forms rivulets, the numerical results are to be compared with experimental data. Since the liquid accelerates along the plate it is necessary to compare the velocity profiles in flow direction (Fig. 8). The different simulation profiles are obtained by different methods to read the velocity. The triangles give the maximum surface velocities within a specific range in flow direction while the crosses show the surface velocities obtained by averaging the surface velocity within the same range. As shown here exemplarily for one specific liquid load, the numerical solution meets the measured velocity profile when we consider the maximum surface velocities. The averaged surface velocities are lower than the measured values but show a comparable flow development. The differing behavior at the end of the plate, where the simulated velocities still accelerate and the measured ones seem to reach a constant value, can be explained by the fact that in the experiments the liquid dams up at the
Fig. 8. Measured (with standard deviation) and calculated profiles of averaged and maximum surface velocity along the plate for a liquid load of Re = 110; the simulation uses a contact angle of 70◦ .
A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
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Experimental investigations inside the packings are very difficult to perform. Here computational fluid dynamics provide an alternative to the experiments. The available models have to be validated for such flow behaviors as found in this application. It is shown that a VOF-like code is capable of describing film break-up and rivulet flow. These types of flow behavior require three-dimensional calculations and are strongly influenced by the geometry. Although threephase flows remain to be validated with quantitative values, qualitative comparison shows good agreement of simulations with experiments. Experiments are carried out to gain more validation data. A next step is to investigate complex geometries.
Acknowledgement
Fig. 9. Qualitative comparison between simulated (left) and experimental (right) two-liquid flow (water–toluene); in the simulation the water phase is colored dark-grey and the toluene phase white.
lower edge of the plate. Additionally the standard deviation of the measurements is shown. The simulation results are very sensitive to the model geometry. Two-dimensional simulations are not capable of describing some flow effects correctly, like the droplet and rivulet. Even three-dimensional simulations with symmetry boundaries at the sides give no satisfactory results, e.g. the critical load is strongly overpredicted (ReC = 350 in comparison to 200. In case of three-phase flow it was not possible to gain two-dimensional solutions, whereas 3D simulations show the expected effect of water film break-up. Fig. 9 compares a simulated with a corresponding measured two liquid flow. A test system of water and toluene is used to investigate the various flow behaviors. Here again the good agreement between simulation and experiment can be observed. The simulation has a different geometry than the experimental setup. The width is set to 2 cm in order to reduce the computational time. Thus, the simulated flow cannot be the same as in the experiments but is sufficient to compare the qualitative flow behavior. The different flow behavior at the beginning of the plate results from the different inlet conditions. In the simulation a film flow inlet was chosen to demonstrate the spontaneous break-up of the water phase which than flows down as rivulets and droplets on top of the toluene film. The same is observed during the experiments.
5. Conclusion Designing packed columns requires information on the local flow behavior in particular for multiphase operation.
The authors would like to thank the Deutsche Forschungsgemeinschaft (German Research Foundation) for the financial support.
References Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modelling surface tension. Journal of Computational Physics, 100, 335–354. Brunazzi, E., & Paglianti, A. (1997). Liquid-film mass-transfer coefficient in a column equipped with structured packings. Industrial and Engineering Chemistry Research, 36, 3792–3799. Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39, 201–225. Iliuta, I., & Larachi, F. (2001). Mechanistic model for structured-packingcontaining columns: irrigated pressure drop, liquid holdup, and packing fractional wetted area. Industrial and Engineering Chemistry Research, 40, 5140–5146. Repke, J. -U. (2002). Experimentelle und theoretische Analyse der Dreiphasenrektifikation in Packungs- und Bodenkolonnen. FortschrittBericht VDI, Reihe 3, Nr. 751 VDI-Verlag D¨usseldorf 2002. ISBN 3-18-375103-8. Repke, J.-U., & Wozny, G. (2002). Experimental investigations of threephase distillation in a packed column. Chemical Engineering and Technology, 25(No. 5), 513–519. Repke, J. -U., Villain, O., & Wozny, G. (2003). A nonequilibrium model for three-phase distillation in packed a column: modelling and experiments. Computer-Aided Chemical Engineering (Vol. 14), Elsevier, 881-886, ESCAPE-13, Lappeenranta, Finnland, 1.-4.6.2003. Rocha, J. A., Bravo, J. L., & Fair, J. R. (1993). Distillation columns containing structured packings: A comprehensive model for their performance. 1. Hydraulic models. Industrial and Engineering Chemistry Research, 32, 641–651. Stein, W. A. (1999). Benetzung und Zwickelfl¨ussigkeit bei zwei nebeneinander liegenden Zylindern. Forschung im Ingenieurwesen, 64, 329–343. Vlachogiannis, M., & Bontozoglou, V. (2002). Experiments on laminar film flow along a periodic wall. Journal of Fluid Mechanics, 457, 133–156.
Fluid dynamics in multiphase distillation processes in packed towers Andreas Hoffmann ∗ , Ilja Ausner, Jens-Uwe Repke, G¨unter Wozny TU Berlin, Institute of Process and Plant Technology, TU Berlin, Sekr. KWT 9, Strasse des 17. Juni 135, 10623 Berlin, Germany Available online 9 April 2005
Abstract In order to design packed columns for multiphase operation it is necessary to include reliable data on the flow behavior in the model. Since experiments inside packings are very difficult to perform, computational fluid dynamics (CFD) simulations are considered to be a sensible approach as numerical experiments. To obtain reliable results validation is inevitable. We present the validation of two- and three-phase film flow under transient conditions. This application is not abundant in literature. Numerical results are compared with data from own experiments. The usability of a VOF-like code for such applications is shown. © 2005 Elsevier Ltd. All rights reserved. Keywords: Multiphase flow; Flow behavior; Film break-up; CFD; Validation
1. Introduction During the last decades packed columns have become popular due to their increase in efficiency and capacity. While these benefits are widely used for distillations with only one liquid phase packed towers are still avoided for processes with more liquid phases. This is mainly related to the fact that the liquid flow behavior changes dramatically with the appearance of a second phase and with that the tower efficiency. Designing packed columns for three-phase distillation requires a reasonable model (Repke, Villain, & Wozny, 2003). While various models exist for two-phase distillation (e.g. Brunazzi & Paglianti, 1997; Iliuta & Larachi, 2001; Rocha, Bravo, & Fair, 1993) yet only a few works focus on multiphase operations (e.g. Repke, 2002). One of the main problems is the prediction of the flow behavior inside the column. Most models for the two-phase distillation are based on either film or rivulet flow inside the packed columns. In case of three-phase operation it would be more appropriate to assume film flow for one phase and rivulets or droplets for the other (see Fig. 1). Since it is almost impossible to look into the packings simulations with computational fluid dynamics (CFD) will be used to minimize the experimental effort to describe and analyze the influence of various parameters. For these cases no ∗
Corresponding author. E-mail address: [email protected] (A. Hoffmann).
0098-1354/$ – see front matter © 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2005.02.004
validation of the CFD codes has been done until now. We present the validation of a volume of fluid (VOF) method for two- and three-phase film flows under transient conditions where one of the phases is air. With validated methods it is possible to develop a model for the effective interfacial area which considers the flow behavior inside packings which is necessary to design packed towers.
2. Simulations The main goal is to develop a model for the interfacial area between all phases in a multiphase operated packed column. Recent models only consider parameters from binary equations i.e. obtained for two-phase flow. In three-phase film flow it is not possible to just calculate with two of the phases since the flow behavior and with that the mass transfer strongly changes under the influence of a second liquid phase (Repke & Wozny, 2002). Depending on the liquid flow rate it is probable that one of the two liquid phases forms a film and the other phase runs down as droplets or rivulets. Therefore, it is necessary that the CFD method is able to predict surface break-up, droplet and rivulet formation properly. CFD calculations are carried out with the commercial code CFX 5.6, ANSYS Inc., which uses an Euler–Euler algorithm for multiphase calculations with free surfaces. Like the VOF method (Hirt & Nichols, 1981) it uses averaged phase frac-
1434
A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
Nomenclature a A b Re p V˙ w x z
specific area area width of the plate Reynolds number pressure volume flow rate velocity coordinate in flow direction coordinate in width direction
Greek symbols α inclination angle Γ liquid load ν kinematic viscosity δ film thickness θ contact angle Subscripts and superscripts C critical plate total plate s surface T toluene W water wetted wetted area on plate average
Fig. 2. Model geometry and boundary conditions.
contact angle is limited to the measuring error range (Stein, 1999). Turbulence is not taken into account since the range of the Reynolds-number Re indicates laminar or pseudo laminar flow (Re < 350). The model uses a specified velocity profile at the inlet, a wall boundary (no slip, defined contact angles) as the plate, and a pressure outlet (gauge pressure of p = 0) at the outlet. The geometry sides are either implemented as symmetry boundaries or as walls and the upper boundary can be modeled as an opening (inlet and outlet with zero-gaugepressure) or as a wall with free slip (Fig. 2). The Reynoldsnumber is defined with the average film velocity and the film thickness: Re =
¯ wδ ν
tions in the finite volume cells. The surface tension is implemented using the method of Brackbill, Kothe, and Zemach (1992). In case of strong interaction between the phases it is sufficient to reduce the model to one velocity field for all phases. The contact angles used are derived from static measurements. It is assumed that the influence of the dynamics on the
Γ =
Fig. 1. Possible flow behaviors on a sheet in a packed column where liquid 1 forms a film or rivulets, liquid 2 flows as rivulets or droplets and the vapor flows countercurrent to the liquids. Entrainments of the three phases in each other are also possible.
To get reliable results for model development, it is necessary to validate the CFD code. To our knowledge, this has not been done yet for this application which has various difficulties. Two-phase film flow with free surfaces has already been considered in literature but mostly two-dimensional closed films. Three-dimensional (3D) effects like film break-up and rivulet or droplet flow remain to be investigated. Three-phase film flow with different interfaces is more complex to simulate. Interaction and surface tension between all phase pairs have to be considered. Two and three dimensional cases are simulated with one and two liquid phases (Fig. 3). The main interest lies in the correct prediction of the critical liquid load for the surface break-up and the resulting shadow (or wetted wall) area (example result in Fig. 3a). For the model development it is necessary to calculate the interfacial areas between the fluids. We assume that it is sufficient to define the interface at a specific phase fraction.
(1)
This corresponds to the liquid load Γ over Eq. (2): V˙ ¯ = Re · ν = wδ b
(2)
A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
1435
Fig. 3. Simulation: (a) momentary result with one liquid phase (water) at a liquid load of Γ = 1.0 cm2 /s or Re = 112; (b) momentary result with two liquid phases (toluene: light grey; water: dark grey) at ReW = 250 and ReT = 220.
3. Experiments The experimental setup is shown in Fig. 4. A particle tracking velocimetry (PTV) method is applied to measure film flow velocities and the wetted wall area can be determined by optical means. Depending on the present fluids the PTV method uses particles, droplets and waves as tracers to measure the surface velocities. As particles Isospheres SG-300-B of Omega Minerals Germany GmbH (mean diameter of 110–130 m and density in the range of 0.65–0.75 g/ccm) are added to the liquid. The tracers are exposed with a stroboscope with a fre-
quency of 250 Hz. With a CCD-camera with a frequency of 60 images/s this results into a double exposure per image. To get the shadow area the pictures taken with the CCDcamera are analyzed with an image analysis software. Dyes are used to increase the contrast. The applicability of fluorescent dyes to measure the film thickness additionally is examined. The feed tubes shown in Fig. 4 can be replaced by an overflowing weir. This setup better resembles the Nusselt inlet boundary condition of the CFD simulations but is not applicable for two liquid phases.
4. Validation For validation the simulation results are compared with the data obtained from our experiments and the well known Nusselt solution. Parameters for the validation are e.g. the critical fluid load at which the single liquid phase first breaks up, film velocities and the wetted wall area. It is not sufficient to consider only one of these parameters. In Fig. 5 the specific shadow area a, obtained from simulations and experiments, is shown. It is assumed that the shadow area corresponds to the wetted wall area. a=
Fig. 4. Experimental setup for the case of two immiscible liquid phases.
Awetted Aplate
(3)
It can be seen that the shadow area is underestimated or, to put it the other way, that the curve is shifted right about Re
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A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
Fig. 5. Comparison of experimental data with numerical results for water flow on an inclined steel plate with an inclination of 60◦ ; the simulation curve (a) was obtained with a contact angle of θ = 80◦ the simulation curve (b) with a contact angle of θ = 70◦ .
∼50. The mesh is sufficiently fine, i.e. if we change the mesh size near the plate boundary from a thickness of 0.1–0.05 mm we get a solution close to the previous one. The contact angle has a critical impact on the flow behavior. Although of only minor influence on the wetted area at low Reynolds numbers it is essential to determine the correct contact angle in order to predict the critical liquid load. In Fig. 5 simulation curve (a) makes use of a contact angle of 80◦ which is the value found in literature for water–air on steel. Curve (b) gives the results for a contact angle of 70◦ which is the value measured on the plate used in the experiments. In cases where the liquid forms a stable laminar film, the solution gained by simulation meets the Nusselt solution for laminar film flow. Film thickness and velocities are predicted accurately. This can be seen in Fig. 6 where the film thickness δ is plotted along the flow direction x. With an inlet height greater than the Nusselt film thickness, the thickness decreases along the plate approaching the analytical solution. The velocities result from mass conservation and therefore meet the analytical value too. Furthermore the film thickness shows a characteristic profile over the plate width (Fig. 7). At the plate support the liquid
Fig. 6. Calculated film thickness in flow direction at Re = 220 in comparison to the analytical Nusselt solution.
Fig. 7. Calculated film thickness profile over plate width and measured intensity of emitted light of a fluorescent dye.
forms a meniscus and smaller film thickness in its vicinity. Along with the numerical solution Fig. 7 shows the result from a fluorescence measurement. This method is based on the linear proportionality of the film thickness to the emitted light intensity for liquid films with δ < 1.5 mm (Vlachogiannis & Bontozoglou, 2002). The plot shows a good agreement between the measured and simulated profile. Where the film breaks up and forms rivulets, the numerical results are to be compared with experimental data. Since the liquid accelerates along the plate it is necessary to compare the velocity profiles in flow direction (Fig. 8). The different simulation profiles are obtained by different methods to read the velocity. The triangles give the maximum surface velocities within a specific range in flow direction while the crosses show the surface velocities obtained by averaging the surface velocity within the same range. As shown here exemplarily for one specific liquid load, the numerical solution meets the measured velocity profile when we consider the maximum surface velocities. The averaged surface velocities are lower than the measured values but show a comparable flow development. The differing behavior at the end of the plate, where the simulated velocities still accelerate and the measured ones seem to reach a constant value, can be explained by the fact that in the experiments the liquid dams up at the
Fig. 8. Measured (with standard deviation) and calculated profiles of averaged and maximum surface velocity along the plate for a liquid load of Re = 110; the simulation uses a contact angle of 70◦ .
A. Hoffmann et al. / Computers and Chemical Engineering 29 (2005) 1433–1437
1437
Experimental investigations inside the packings are very difficult to perform. Here computational fluid dynamics provide an alternative to the experiments. The available models have to be validated for such flow behaviors as found in this application. It is shown that a VOF-like code is capable of describing film break-up and rivulet flow. These types of flow behavior require three-dimensional calculations and are strongly influenced by the geometry. Although threephase flows remain to be validated with quantitative values, qualitative comparison shows good agreement of simulations with experiments. Experiments are carried out to gain more validation data. A next step is to investigate complex geometries.
Acknowledgement
Fig. 9. Qualitative comparison between simulated (left) and experimental (right) two-liquid flow (water–toluene); in the simulation the water phase is colored dark-grey and the toluene phase white.
lower edge of the plate. Additionally the standard deviation of the measurements is shown. The simulation results are very sensitive to the model geometry. Two-dimensional simulations are not capable of describing some flow effects correctly, like the droplet and rivulet. Even three-dimensional simulations with symmetry boundaries at the sides give no satisfactory results, e.g. the critical load is strongly overpredicted (ReC = 350 in comparison to 200. In case of three-phase flow it was not possible to gain two-dimensional solutions, whereas 3D simulations show the expected effect of water film break-up. Fig. 9 compares a simulated with a corresponding measured two liquid flow. A test system of water and toluene is used to investigate the various flow behaviors. Here again the good agreement between simulation and experiment can be observed. The simulation has a different geometry than the experimental setup. The width is set to 2 cm in order to reduce the computational time. Thus, the simulated flow cannot be the same as in the experiments but is sufficient to compare the qualitative flow behavior. The different flow behavior at the beginning of the plate results from the different inlet conditions. In the simulation a film flow inlet was chosen to demonstrate the spontaneous break-up of the water phase which than flows down as rivulets and droplets on top of the toluene film. The same is observed during the experiments.
5. Conclusion Designing packed columns requires information on the local flow behavior in particular for multiphase operation.
The authors would like to thank the Deutsche Forschungsgemeinschaft (German Research Foundation) for the financial support.
References Brackbill, J. U., Kothe, D. B., & Zemach, C. (1992). A continuum method for modelling surface tension. Journal of Computational Physics, 100, 335–354. Brunazzi, E., & Paglianti, A. (1997). Liquid-film mass-transfer coefficient in a column equipped with structured packings. Industrial and Engineering Chemistry Research, 36, 3792–3799. Hirt, C. W., & Nichols, B. D. (1981). Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39, 201–225. Iliuta, I., & Larachi, F. (2001). Mechanistic model for structured-packingcontaining columns: irrigated pressure drop, liquid holdup, and packing fractional wetted area. Industrial and Engineering Chemistry Research, 40, 5140–5146. Repke, J. -U. (2002). Experimentelle und theoretische Analyse der Dreiphasenrektifikation in Packungs- und Bodenkolonnen. FortschrittBericht VDI, Reihe 3, Nr. 751 VDI-Verlag D¨usseldorf 2002. ISBN 3-18-375103-8. Repke, J.-U., & Wozny, G. (2002). Experimental investigations of threephase distillation in a packed column. Chemical Engineering and Technology, 25(No. 5), 513–519. Repke, J. -U., Villain, O., & Wozny, G. (2003). A nonequilibrium model for three-phase distillation in packed a column: modelling and experiments. Computer-Aided Chemical Engineering (Vol. 14), Elsevier, 881-886, ESCAPE-13, Lappeenranta, Finnland, 1.-4.6.2003. Rocha, J. A., Bravo, J. L., & Fair, J. R. (1993). Distillation columns containing structured packings: A comprehensive model for their performance. 1. Hydraulic models. Industrial and Engineering Chemistry Research, 32, 641–651. Stein, W. A. (1999). Benetzung und Zwickelfl¨ussigkeit bei zwei nebeneinander liegenden Zylindern. Forschung im Ingenieurwesen, 64, 329–343. Vlachogiannis, M., & Bontozoglou, V. (2002). Experiments on laminar film flow along a periodic wall. Journal of Fluid Mechanics, 457, 133–156.