ТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИ, 2013, том 47, № 2, с. 149-157
УДК 66.011
CFD SIMULATION OF HYDRODYNAMICS OF AIR SPARGING IN A VERTICAL TUBULAR MEMBRANE
© 2013 г. M. K. Moraveji, A. Amirimehr, S. Nadery, P. Rafiee
Department of Chemical Engineering, Faculty of Engineering, Arak University, Arak 38156-8-8349, Iran
m-moraveji@araku.ac.ir Received 30.05.2011
Computational fluid dynamics (CFD) simulation of the hydrodynamics of slug flow which is generated by air sparging in a vertical tubular membrane has been investigated. The results of simulation have been reported in the form of parameters such as shape, velocity profile, surface shear stresses and gas slug (Taylor bubble) rising velocities, and evaluated with experimental data which were presented in previous articles. This study showed that CFD modeling is able to accurately simulate the shape and velocity field around the gas slugs. Also the shear stress induced by slug flow passage and rising velocity of gas slugs for high-velocity liquid and low-velocity gas fit appropriately to values in reference data. Simulation results for gas slug rising velocity showed about 0.35—9% error in the different conditions investigated in respect to experimental data.
DOI: 10.7868/S004035711302005X
INTRODUCTION
Air sparging, generating gas—liquid two-phase flow, has been introduced as an effective method for membrane fouling mitigation [1]. When gas—liquid mixtures flow upwards in a vertical tube, different flow patterns can be observed according to aeration rate and value of the liquid flow rates, channel geometry and the properties of the two fluids [2—4]. Each flow pattern is characterized by a different spatial distribution of the gas and of the liquid along the membrane [4]. For a given liquid flow rate, Fig. 1 shows four flow regimes which can be observed when the gas flow rate is increased: bubble flow, slug flow (also called Taylor flow), churn flow and annular flow [1, 3, 4].
In membrane systems using two-phase flow, the most likely flow patterns among modules to overcome concentration polarization and membrane fouling are bubble flow and slug flow due to the relatively low gas flow rates applied [1].
Ghosh and Cui [3] reported that fouling control in vertical tubular membranes depends largely on hydro-dynamic conditions induced by slug flow near to membrane surface. Figure 2 shows the direction of gas and liquid flow as well as the direction of the wall shear stress for gas—liquid slug flow in a tube. Gas slugs move faster than the liquid due to buoyancy, pushing the slower moving liquid on top towards the side. This displaced liquid flows down the side of the gas slug in the form of a thin falling film. The space between consecutive gas bubbles are made up of liquid slugs which have smaller gas bubbles dispersed within them. The liquid slugs are in turn made up of two zones (Fig. 2a): (1) an extremely turbulent wake region following the gas slugs, in which liquid coming down from the liquid film region meets the upward bulk liquid flow, and (2)
the remaining liquid slug region (which may be either turbulent or laminar), following the wake, in which liquid and dispersed gas bubbles move in an upward direction.
Also, Fig. 2b shows that the liquid flow direction and consequently the direction of the induced surface shear stresses change while gas slugs rising [3]. Ochoa et al. [5] and Rochex et al. [6] claimed that this change in surface shear stresses direction improves fouling control.
The aim of the present study is the modeling of the hydrodynamics of a slug flow in a vertical tubularm-embrane with computational fluid dynamics (CFD) tools. The simulation results are reported within some parameters such asshape of gas slug, velocity profile around slug, surface shear stress and rising velocity of gas slug.
Bubble flow
Slug flow
Churn flow
Annual flow
Fig. 1. Flow regimes for two-phase flow [3].
(a)
irh
(b)
Falling film zone
Wake zone
Liquid slug zone
Gas slug
Liquid slug
mt
-Direction of flow
—^ Direction of shear stress
Fig. 2. (a) Zones in slug flow; (b) direction of shear stress and fluid flow [6].
fp + v-(p V) = 0.
dt
(1)
I (pV ) + v • (p VV) = = -v p + v-[^(vv + vVT )] + pg + F.
(2)
The momentum equation is dependent on volume fraction of all phases due to density and viscosity properties [10—12]. Density and viscosity are defined as
p
У =
: Xakpk' X akpk
(3)
(4)
Tracking the gas—liquid interface is done by solving a continuity equation for volume fraction of gas phase:
£ ( aG ) + V -vaG = 0.
(5)
It is not necessary to solve the equation for liquid volume fraction. It can be obtained from
ag
= 1.
(6)
Surface tension modeling in this simulation is based on the continuum surface force which has been introduced by Brackbill et al. [13]. After applying this model, addition of surface tension to the VOF calculations results in a source term in momentum equation.
The importance of surface tension effects is determined based on the value of two dimensionless quantities: the Reynolds number, Re, and the capillary number, Ca; or the Reynolds number, Re, and the Weber number, We. For Re < 1, the quantity of interest is the capillary number that is defined as below:
Ca =
yU a
(7)
Fig. 3. Generated geometry with fine mesh near the wall.
CFD MODELING
Here a two-phase flow modeling using volume-of-fluid (VOF) method has been applied to track traveling route of a bubble in vertical tubes in both stagnant and flowing liquids [7, 8]. VOF model is used for immiscible fluids where the interface is important. It models the flow by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain [9, 10].
Governing equations. The continuity equation can be written as follows:
For Re > 1, the quantity of interest is the Weber number that is defined as below:
We =
p LU2
(8)
A single momentum equation is solved for the entire domain and the resulting velocity field is shared among the phases:
where U is free-stream velocity. Surface tension effect can be neglected if Ca > 1 or We > 1.
Model geometry and boundary conditions. Ratkov-ich [7] focused on the investigating the hydrodynamics induced by air sparging in side commercial-scale vertical tubular membrane with a height of 2 m and a radius of 0.00495 m. Thus two-dimensional geometry of 2 m high and 0.00495 m radius has been generated with axial symmetry.It is necessary to apply a relatively fine mesh near the wall where shear stress is derived for better results (Fig. 3) [8, 9—11]. The numbers of cells in length and radius are respectively 4000 and 15.
Table 1 shows the physical properties of water and nitrogen which we used instead of electrolyte solution and nitrogen in Ratkovich's experiments [7]. Reynolds num-
pLUTBc
ber according to slug flow Rera =
Hl
for differ-
ent conditions simulated ranged from 1300 to 2800. Desired quantity to determine the importance of surface tension is Weber number. Weber Number for a
vertical tube containing a gas—liquid flow can be obtained as
Table 1. Physical properties of used material in simulation
We =
pGdUTB
(9)
where UTB is rising velocity, m/s; pG is density of gas, kg/m3; d is tube diameter, m; and a is surface tension, N/m.
In this study, the slug rising velocities were found to be between 0.13 and 0.28 m/s, which results in Weber numbers between 0.0026 and 0.0119. It is conclud-edthat surface tension can effectively influence slug flow. Surface tension of the water—nitrogen system was assumed to be 0.075 N/m.
Differencing schemes. Solving method has been based on explicit interpolation with geometric reconstruction discretization for VOF which is recommended for unsteady-state transient simulation [9, 12]. For unsteady-state behavior of slug flow (difference in size, shape and coalescence of bubbles), large eddy simulation seems to be the best point of view. This technique requires very fine mesh and large amount of calculations (even in two-dimensional state) especially when a chain of bubbles are modeled. Thus, the unsteady Reynolds-averaged Navier—Stokes equation was applied. Falling film zone and wake zone are turbulent, therefore the renormalization group (RNG) k—e turbulence model has been used [8—11]. The quadratic upstream interpolation for convective kinematics (QUICK) has been used to discretize the convection term in momentum equation which increases stability in solution, fast converging, and has accuracy of 4th order [14]. The set of nonlinear equations was linearized using a modified version of the semi-implicit method for pressure linked equations (SIMPLE) algorithm [14]. In all simulation the time step size has been set as 0.0001 s with maximum 30 iterations per time step and the total run time has been set as 10 s.
RESULTS AND DISCUSSION
Hydrodynamic properties of liquid—gas slug flow in vertical tubes are affected by tube geometry, viscous forces, interface forces, inertia forces and physical properties of fluids. In this study a chain of rising gas slugs in a vertical tubular membrane has been simulated. Water and nitrogen flows have continuously been entering from the bottom of tube and exiting from the top. In this part, the results of simulations have been presented in the form of parameters such as gas slugs' shape, velocity field around gas slugs, rising velocity and surface shear stress of gas slug.
Gas slugs' shape. Taylor bubble shape in calculation of mass, momentum and energy transfer is significantly important [1, 10, 11, 15—18]. According to the result reported in these studies, Taylor bubbles consist of a round head, cylindrical body, and an oscillatory tail.
Viscous forces, interface forces and inertia forces effects on the bubble shape are determined through three
Material Density, kg/m3 Viscosity, mPa s
Water 1016 1
Nitrogen 1.170 0.01755
Table 2. Froude number values for different conditio
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