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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18
Bertrand Braunschweig and Xavier Joulia (Editors)
© 2008 Elsevier B.V./Ltd. All rights reserved.
Three Dimensional Multiphase Computations for
the Characterizing the Counter-Current Flow
Behavior
Y. Xu, a.b J. Yuan,a S. Paschke, b J-U. Repke, b G. Wozny b
a
Shanghai JiaoTong University, Dongchuan Road 800, Shanghai, 200240, China
TU Berlin, Department of process dynamics and operation, Strasse des 17. Juni 135KWT9, 10623 Berlin, Germany
b
Abstract
A three-dimension two-phase counter-current CFD model is developed for predicting
the local hydrodynamics of falling film flow in structured packing. The transient model,
which is based on volume of fluid (VOF) method, not only considers gravity and
surface tension, but also takes drag force into account. The simulation results show that
the presence of counter-current vapor flow tends to increase the fluctuation of film flow,
to increase the film thickness, and to change the velocity profile of the liquid phase,
which are in accordance with the experience and experiment data.
Keywords: CFD, counter-current flow, drag force, pressure drop
1. Introduction
During the last decades packed columns have been widely used in many industrial
processes such as distillation and absorption. This is due to higher separation
efficiencies with a higher capacity and a lower pressure drop compared to tray columns
in most applications. However, for the reason there is inadequate knowledge of
phenomena inside the structured packed columns, the design of packed columns still
mainly depends on empirical or semi-empirical methods. It has been known that the
liquid flow pattern in packed columns is an important factor affecting the separation
efficiencies of packed columns. Furthermore, the flow behavior of the liquid phase such
as film, rivulet or droplet flow taking place only in a few inches inside the packing are
governed by liquid and vapor loads as well as by system parameters like the contact
angle [5]. The lack of understanding for the intricate local-flow behavior is the main
problem to estimate or improve the separation efficiencies of packed columns.
Therefore, a deeper knowledge of the fluid dynamic behavior on the packing surface is
required urgently.
Usually, it is not possible to carry out observations inside the packed columns,
simulations with computational fluid dynamic (CFD) methods make it possible to
describe the flow performance concerning on intricate multiphase flow. Especially in
the recent years, more and more researchers have been interested in adopting CFD to
investigate the phenomena appeared in packed columns. A rivulet flow on an inclined
plate in three-dimension to study the spreading of liquid phase without counter-current
vapor phase has been investigated in [1]. Two-dimension two-phase counter-current
flows in a plate-type and corrugate plates structured packing are investigated in [3-4].
However, in distillation and absorption processes, the vapor phase is almost in countercurrent flow to the liquid phase. It has been demonstrated that the interaction between
two phases is the key to successfully describe the flow behavior. Furthermore, the flow
behavior in packing is not really symmetrical and the effective wetted area estimated by
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Yuanyuan Xu et al.
two-dimensional computations is unreliable [3]. Therefore, a three-dimension countercurrent model has to be applied in order to describe correctly the complex flow behavior.
In this paper, a three-dimensional two-phase transient CFD model considering the
counter-current drag force is developed to investigate the local film performance such as
the film thickness and the liquid velocity profile. To confirm the trustiness of CFD
model, simulation results in the case of a single liquid phase are compared with
experiment data. Furthermore, in order to show the influence of counter-current vapor
phase on the liquid phase, CFD simulations are carried out on the same plate of a single
liquid phase and compared with the data of that.
2. Models and Simulation
The local-flow of liquid phase and vapor phase can be regarded as a two-phase countercurrent free-surface flow, where each phase is treated as a continuous fluid and interacts
with the other phase. For the description of this free-surface flow, a VOF model with
geometric reconstruction scheme which is a limiting case of Eulerian-Eulerian
multiphase flow is considered here. The VOF model can capture the interface between
the two phases by solving a single set of momentum equations and tracking the volume
fraction of each of the fluids throughout the domain.
2.1. Model Equations
The CFD conservation equations of momentum for two-phase flow are:


 



 
( v )    ( v v )  P     v  v T  g  F
t
(1)
The interaction between the vapor and liquid phases is attributed
to the momentum

source term, F . According to the character of film flow, F is denoted by surface
tension source term for single-phase flow, whereas in the case of counter-current vapor
flow, it stands for surface tension source term and drag force source term.
The surface tension is taken into account by using the continuous surface force model
(CSF) proposed by [2], where a characteristic function is adopted to implement the
surface tension as volume force instead of surface force into the momentum source
term.
As maintained in [10], the drag force between counter-current two phases results in a
friction pressure drop. The frictional pressure drop along flow direction can be
expressed as a function of friction factor fi, vapor density ρg, hydraulic diameter of
channel for vapor phase dhg and velocity differences between vapor velocity ug and
interfacial velocity ui, which can be written as an expression below
p f
z

1 f i  g u g  ui u g  ui
2
dh g
(2)
Where, fi adopted here is developed by [9]. The friction factor fi, which depends on
channel geometry, the material properties and the Bond number, can be expressed by
f i  0.079 Re G0.25 (1  115  ) ; N  3.95 /(1.8  3.0 / Bo )
N
(3)
Where, δ* and Bo are the dimensionless ratios of film thickness δ and channel hydraulic
diameter dh, respectively, to the Laplace length [σ/(ρl - ρg )g cosα]1/2. Equation (2) is the
drag force momentum source term.
Three Dimensional Multiphase Computations for the Characterizing the Countercurrent Flow Behavior
3
Figure 1: Experiment setup for single-phase flow (left); Geometry, mesh and boundary conditions
adopted in simulations in FLUENT 6.3 (right).
2.2. Geometry, Mesh and Boundary Conditions
To investigate fundamental details, the packing is substituted and simplified by a small,
flat and smooth plate, shown in Figure 1. The flow behavior of a single liquid phase on
the same plate which resembles the experimental setup [5-6] of a 60mm*10mm*50mm
stainless steel plate held by steel supports on the left and on the right hand side has been
investigated in detail. Simulations are implemented in the commercial CFD software,
FLUENT 6.3, ANSYS Inc. To acquire the phenomena happened between the liquid
phase and the gas phase, the mesh has to be very fine especially around the interface.
On the other hand, considering the effect of wall adhesion at fluid interfaces in contact
with wall boundaries, the mesh should also be refined in the direction of plate as well as
the side walls. Geometry, mesh and boundary conditions adopted in simulations are
shown in Figure 1, where left column displays boundary conditions in the case of single
liquid phase and the other side presents that in counter-current case. On the other hand,
in the case of counter-current flow, the drag force source term is taken into account by
equation (2) and implemented together with the two pressure-inlet boundaries into
FLUENT by User Defined Functions (UDF).
3. Results and Discussion
First simulations with this developed three-dimension CFD model are carried out for the
system water-air on the inclined stainless steel plate under the condition of T=25ºC and
the inclination angle for plate is fixed to 60°. Since the Re-number of the liquid phase
are lower than 300 (ReL=ρlwδ/μl) and the vapor flow velocities expressed by F-factor are
far from that trigger flooding, the simulations are made in laminar or quasi laminar
region. Simulations begin with a closed film given by the highest Reynolds number and
are carried out by decreasing liquid flow rates, which correspond well with [6]. When
the liquid phase comes to a quasi stable state, the vapor phase is counter-currently
induced to the liquid phase according to the F-factor. The effects of vapor phase on
liquid phase are investigated by increasing gradually the F-factor.
As an important parameter for mass and heat transfer in packed columns, specific
wetted area, a, is defined as the ratio of the wetted plate area to the geometrical plate
area. Figure 2 shows the comparison of specific wetted area between experimental data
and simulation results. A free surface model in software CFX was adopted to
investigate the specific wetted area in the literature [5], where the author concluded that
the contact angle had a critical effect on specific wetted area and that simulation results
were underestimated comparing with experiment data. Here a static contact angle
(θ=70°) is applied for both simulation cases and a developed inlet boundary condition
based on Nusselt theory is applied in VOF model in FLUENT. As shown in Figure 2,
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specif wetted area
1
0.8
0.6
0.4
0.2
Experiment Data [5]
Simulation (a) [5]
Simulation (b)
Exp2.
0
0
50
100
150
200
ReL
Figure 2: Comparison of experimental data with simulation results for water flow on an inclined
stainless steel plate without counter-current vapor phase, (θ=70º); simulation (a): Free surface
model in CFX [5]; simulation (b): VOF model with developed boundaries we defined in
FLUENT.
Figure 3: Local morphological descriptions for the water flow on a smooth plate in the case of a
single liquid phase in FLUENT (Left: ReL =168, a=1; Middle: ReL =112, a=0.5; Right: ReL = 56,
a=0.197)
simulation results from VOF model with the developed boundary are in good agreement
with experiment data, which also demonstrates that CFD simulation results are
especially sensitive to boundary conditions. On the other hand, Figure 2 also illustrates
that the critical Reynolds number where the specific area falls below 1, can be
accurately predicted by simulation.
To show further the change of specific wetted area on the plate, a qualitative
comparison in simulations is shown in Figure 3. Morphological descriptions which
highly depend on the liquid flow rate can be seen in Figure 3. At a higher Re-number
(ReL =168), water flow forms a closed stable film so that the specific wetted area on the
plate is 1. With a decrease of Re-number (ReL =112), the film breaks up and a rivulet
flow appears which gives a reduction of the specific wetted area. At a lower Re-number
(ReL =56), the liquid flow rate is less than a certain level to support rivulet flow,
consequently droplets appear on the plate. This type of flow behavior (film breakup,
rivulet and droplet) represents highly three dimensional effects and therefore can not be
correctly predicted by 2D simulation. In addition, Figure 3 illuminates indirectly that
VOF model is capable of predicting complex free surface behavior like film breakup
and rivulet or droplet flow.
Another important parameter is the velocity profile along film thickness. Figure 4 (left)
presents a comparison of velocity profiles in liquid film without counter-current vapor
phase between experimental data [7] and simulation results. Simulation and experiment
are both carried out with a water-glycerol mixture (xwater = 0.8) on a glass plate with 60
degree inclination. As can be seen in Figure 4 (left), simulation results and experimental
Three Dimensional Multiphase Computations for the Characterizing the Countercurrent Flow Behavior
5
0.4
0.7
0.35
ReL = 12
α = 60 º
θ = 30 º
ρl = 1137 kg/m3
μl = 8.995 mPa s
σ = 0.07104 N/m
0.5
Y [mm]
0.4
ReL = 168
α = 60 º
θ = 70 º
ρl = 997 kg/m3
μl = 0.89 mPa s
σ = 0.072 N/m
0.3
0.25
Y [mm]
0.6
0.3
0.2
ρg = 1.185 kg/m3
μg = 0.015 mPa s
0.15
0.2
Nusselt
VOF Simulation
Experiment(a)[7]
Experiment(b)[7]
0.1
0.1
0
0
5
10
15
u [cm/s]
20
Nusselt
Sim(ReG =0)
Sim(ReG =1386)
Sim(ReG =1848)
0.05
25
0
0
0.1
0.2
0.3
u [m/s]
0.4
0.5
0.6
Figure 4 Comparisons of velocity profiles in liquid film; Left: for a water-glycerol mixture on a
glass plate without counter-current vapor phase between simulation results and experiment data
[7] for ReL =12; Right: for pure water on a stainless steel plate against different ReG for ReL =168.
data have a good agreement except for small deviations close to the wall. The reason for
that is the feeder of experimental set-up. This jet flow induces turbulence in experiment
at the inlet section, which hasn’t been considered in CFD model. Additionally, owing to
the liquid viscous friction, the velocity of liquid phase is very low near the plate and
increases steadily with the distance from the plate. Nusselt analyzed falling liquid films
theoretically and concluded that the velocity profile in falling liquid films meets semiparabola profile, which can also be observed in simulation results. A slight deviation at
the interface between simulation results and Nusselt theory is due to the fact that
Nusselt theory is based on a laminar waveless film flow. Whereas waves can be found
which cause the film thickness and the velocity at the interface in simulation to be
faintly higher than that in Nusselt theory. As a conclusion from Figure 4 (left) can be
drawn that CFD simulation with VOF model can predict and analyze the liquid flow
behavior and the results from simulation are believable.
Due to the absence of experimental measurements in the case of counter-current vapor
flow, simulations with pure water and air on an inclined stainless steel plate are carried
out to investigate the effect of different vapor flow rate on liquid phase by fixing the
liquid flow rate as ReL =168. A comparison of velocity profiles against different gas
flow rates is plotted in Figure 4 (right). In the case of single liquid phase on the plate
(ReG =ρgugdhg/μg=0), the velocity profile in water film expresses a semi-parabola
distribution which meets Nusselt solution, and the location of maximum velocity
appears at the interface. When counter-current air flow comes into the domain, it tends
to reduce the amplitude of waves but increase the fluctuation of waves. At a lower air
velocity, the presence of the counter-current air flow has no obvious effect on water
velocity profiles, which exhibits a similar tendency with that in single liquid phase on
the same plate, with the exception of a slightly decreased velocity profile and a slightly
elevated film thickness at interface (ReG = 1386). This can be attributed to the drag
force caused by the different velocities between phases, which reduces the water flow at
the surface region and tends to increase the film thickness and decrease the velocity
profile. With the increase of air velocity, the drag force intensifies as well. At a higher
air velocity, a higher drag force can prevent a part of interface water flowing
downwards and a noticeable increasing of film thickness can be observed (ReG = 1848).
In addition, the higher drag force decreases further velocity at the interface so that a
change of velocity profile in water film can be found, where the maximum velocity
appears not at the interface, but at a position under the liquid surface.
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4. Conclusions
The design of packed columns requires a detailed knowledge on the local flow behavior
in structured packing under counter-current vapor flow. In this paper, a threedimensional two-phase and transient CFD model considering the local drag force is
developed. With the model, the local, time-dependent performance of liquid film flow
under the counter-current vapor phase is investigated. In order to elucidate the trustiness
of simulation results, comparisons and analyses between simulation results and
experimental data are carried out in the case of single liquid phase flow. To show the
size of interactions between the liquid phase and the vapor phase, results from the
counter-current flow are compared with data of a single liquid flow on the same plate
which resembles the experimental setup. The change in velocities and the increase of
liquid film thickness are in accordance with the experience. Furthermore, film flow and
the formations of rivulet flow and droplets flow that express a highly three-dimension
characteristic can also be found in simulations, which illustrate that CFD model can be
used to predict and analyze the complicated phenomenon appeared in packed columns.
Experiments will be carried out to gain validation data for simulations in a next step.
Acknowledgements
The authors would like to acknowledge the Deutscher Akademischer Austausch Dienst
(DAAD) and the Deutsche Forschungsgemeinschaft (DFG, WO 565 191) for the
financial support.
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