Experimental and numerical studies of void fraction distribution in rectangular bubble columns

Nuclear Engineering and Design 237 (2007) 399–408

Experimental and numerical studies of void fraction distribution in rectangular bubble columns Eckhard Krepper a,∗ , Brahma Nanda Reddy Vanga c , Alexandr Zaruba a , Horst-Michael Prasser b , Martin A. Lopez de Bertodano c b

a Forschungszentrum Rossendorf e.V., P.O. Box 510 119, 01314 Dresden, Germany Eidgen¨ossische Technische Hochschule Z¨urich, Department of Mechanical and Process Engineering, ETH-Zentrum, CH-8092 Z¨urich, Switzerland c Purdue University, School of Nuclear Engineering, 400 Central Drive, West Lafayette, IN 47907-2017, USA

Received 31 May 2006; accepted 5 July 2006

Abstract Bubbly flow is encountered in a wide variety of industrial applications ranging from flows in nuclear reactors to process flows in chemical reactors. The presence of a second phase, recirculating flow, instabilities of the gas plume and turbulence, complicate the hydrodynamics of bubble column reactors. This paper describes experimental and numerical results obtained in a rectangular bubble column 0.1 m wide and 0.02 m in depth. The bubble column was operated in the dispersed bubbly flow regime with gas superficial velocities up to 0.02 m/s. Images obtained from a high speed camera were used to observe the general flow pattern and have been processed to calculate bubble velocities, bubble turbulence parameters and bubble size distributions. Gas disengagement technique was used to obtain the volume averaged gas fraction over a range of superficial gas velocities. A wire mesh sensor was applied, to measure the local volume fraction at two different height positions. Numerical calculations were performed with an Eulerian–Eulerian two-fluid model approach using the commercial code CFX. The paper details the effect of various two-fluid model interfacial momentum transfer terms on the numerical results. The inclusion of a lift force was found to be necessary to obtain a global circulation pattern and local void distribution that was consistent with the experimental measurements. The nature of the drag force formulation was found to have significant effect on the quantitative volume averaged void fraction predictions. © 2006 Elsevier B.V. All rights reserved.

1. Introduction Bubble columns are multiphase reactors where the dispersed phase (gas) is introduced into a stationary or flowing liquid/slurry (continuous phase). The dispersed phase, owing to restricted degrees of freedom near the wall, preferentially flows at the center of the column. This leads to an uneven distribution of void fraction and thereby density across the lateral crosssection of the column. This uneven void distribution sets up a global circulation pattern that is primarily density driven. The gas phase carries the liquid along with it as it rises in the center of the column and forces the liquid to reverse flow direction

∗

Corresponding author. E-mail addresses: [email protected] (E. Krepper), [email protected] (H.-M. Prasser), [email protected] (M.A. Lopez de Bertodano). 0029-5493/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2006.07.009

near the walls of the column, setting up circulation cells. Bubble columns have extensively been studied owing to the increased use of these multiphase reactors in the chemical, metallurgical and pharmaceutical industries. Simplicity of use, lack of moving parts, cost effective technology, less maintenance and larger interfacial areas have led to the widespread use of these reactors for various commercial purposes (Shah et al., 1982). Bubble columns are also widely used in the petrochemical industry for coal liquefaction (Tarmy and Coulaloglou, 1992) and in the biotechnology industry as fermentors (Siegel and Robinson, 1992). Despite extensive research, the local physics (turbulence and interfacial transfer) and scale up of bubble columns are not well understood. Several experimental (Chen and Fan, 1992; Kumar, 1997), numerical (Sokolichin and Eigenberger, 1999; Deonij, 1997) and visualization (Chen et al., 1989; Tzeng et al., 1997) studies have been conducted on bubble columns. However, models developed using data from experiments over a limited range of flow conditions and geometries were found incapable of

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Nomenclature AP particle cross-section in flow direction CD drag coefficient CL lift coefficient CW , CW1 , CW2 , CW3 wall force coefficients dB bubble diameter dH horizontal bubble dimension Eod modified E¨otv¨os number FDISP turbulence dispersion force FDRAG drag force FLIFT lift force FWALL wall force g gravity constant JG superficial gas velocity n normal vector nP particle number density Pr Prandtl number VG gas velocity VL liquid velocity VG − VL Vrel Vterm terminal rising velocity Greek letters α gas volume fraction μL laminar viscosity bubble induced component of viscosity μS μT turbulence viscosity ρL liquid density σ surface tension

predicting hydrodynamic parameters in industrial scale units. Apart from the complex hydrodynamic and interfacial interactions, lack of an experimental database over a wide range of process parameters has further impeded modeling of bubble column reactors. An ideal, complete experimental database, would include information on bubble column geometry, specifications of flow conditions (superficial gas/liquid velocities and type of spargers used) and regimes, velocity distributions of the dispersed and continuous phases, shear distribution in the continuous phase, pressure drop data, void fraction and bubble size distributions measured at several axial locations, over a wide range of parameters (bubble column geometries and gas/liquid flow rates). The key to improvements in understanding flow phenomena in bubble columns lies in the realistic description of two-phase flow. The choice of detailed experimentation coupled with two-fluid model numerical simulations are a right step in this direction. However, the use of the two-fluid model does not offset the disadvantages of using an extended form of the Navier–Stokes equations if the interfacial transfer terms and Reynolds stresses are not accurately modeled. Accurate modeling of the interfacial transfer terms and turbulent stresses are in turn dependent on the availability of a detailed experimental database that can be used to benchmark the numerical calculations.

The gas plume hydrodynamics in a 3D bubble column are further complicated by the swirling motion of the plume. A 2D rectangular bubble column with a large width to depth ratio restricts the degrees of motion of the plume, preventing it from swirling. This makes the study of the hydrodynamics of rectangular bubble columns simpler. The motion of the plume is also influenced by the aspect ratio (height of water column to width ratio), superficial gas velocity, nature of gas injection (sparger design) and viscosity of the liquid in the bubble column. This paper presents the experimental and numerical results obtained in a rectangular bubble column. 2. The experiment 2.1. Experimental test facility The experimental test facility consists of three rectangular channels 20 cm2 in cross-section (0.10 m wide and 0.02 m in depth) bolted together at the flanges. The test section made of transparent plexiglass, facilitates visualization. The division of the test section into three sections with flanges allows mounting the wire-mesh sensor at two different axial height locations at a distance from the gas injection of 0.08 and 0.63 m. The wire mesh sensor is placed in the cross-section by bolting it to two flanged rectangular channels. A schematic of the test section along with the relevant dimensions is shown in Fig. 1. The test section is initially filled with water up to a specified height. Gas is introduced into this stationary pool of water through a sparger in the bottom of the test section. The sparger is a porous stone fitted into the bottom flange having a dimension of 0.02 m wide, 0.01 m in depth and 0.01 m height. Gas flow rate through the test section is measured using an MKS 1700 series Laminar Mass Flow Meter which determines the mass flow rate by measuring the power required to maintain a pre-established temperature along a laminar flow sensor tube. The flow meter has accuracy better than 1% of the full-scale value of 5 standard liters per minute. A RedLake MotionPro high-speed video camera with frame rates of up to 10 kHz was used to record images of the flow field, which were subsequently processed to estimate bubble velocities. The camera consists of an advanced CMOS sensor with 1280 × 1024 active pixels. The image frames recorded were stored as a series of 256 gray-scale bitmap images with a spatial resolution of 512 × 512 pixels. A scale was recorded as a part of the flow image to calibrate the image pixel size. The camera was focused to capture the entire width of the test section. The illumination system consisted of two halogen lamps of 1 kW nominal power placed on either side of the column and a diffuse white screen placed behind the rectangular channel. Such a configuration produces a uniform diffuse trans-illumination of the bubble column. The wire-mesh sensor data was recorded at a frequency of 2500 Hz for a time period of 60 s.The superficial gas flow rate, JG is varied in the range 2–20 mm/s. The superficial velocity, JG , is calculated from the measured volume flow rates using: JG =

QG ACS

(1)

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Fig. 2. Experimental flow conditions indicated on the Lin et al. (1996) flow regime map for rectangular bubble columns.

where hfinal is the height of the liquid column after the column has been aerated and hinitial is the stationary height of the liquid column before aeration. The swell in liquid height is noted after a steady liquid level is established and an average value from three measurements is used in the calculation of the volume averaged gas fraction. 2.2. The wire-mesh sensor

Fig. 1. Dimensions and geometry of the experimental test facility.

where QG is the measured volume flow rate of the gas and ACS is the cross-sectional area of the test section. The column operates in the dispersed bubble bubbly regime, characterized by the absence of bubble coalescence or breakup, for superficial gas velocities less than 10 mm/s. The experimental flow conditions are indicated on the rectangular bubble column flow regime map of Lin et al. (1996) in Fig. 2. The gas plume breaks up into bubbles of the order of 3–5 mm in size. Volume averaged void fraction is measured using the gas disengagement technique, wherein the swell in the liquid level is noted after introducing gas into the test section. This test is repeated for various superficial gas velocities and the volume average void fraction, αv , in each of the tests can be calculated using: αv =

hfinal − hinitial hfinal

(2)

The working principle of a wire-mesh sensor (Fig. 3) is based on measurement of the instantaneous conductivity of the twophase mixture in a measurement volume (determined by the pitch of the wire mesh and the separation between the transmitter and receiver planes) surrounding the points of intersection (crossing points that would be obtained if the transmitter and receiver wires were projected onto one plane) between all pairs of adjacent parallel wires in the receiver plane for every transmitter electrode that has been activated. Function and construction of wire-mesh sensors are described in Prasser et al. (1998). Information obtained from the two electrode planes is used for the numerical construction of the two-dimensional void fraction distribution. Two plane grids of wires are placed intrusively in the flow, separated by an axial distance. The angle between the wires of the transmitter and receiver planes is 90◦ . The wires of the transmitter plane are supplied with pulses of driving voltage. The excitation of a transmitter electrode results in the appearance of electric current at a receiver electrode, if the area around the respective crossing point is filled with a conducting phase (water). The magnitude of the current is proportional to the volume of liquid present in the measurement volume. This detection is performed for all crossing points of wires of the two planes using multiplex circuits (Fig. 4). The wire-mesh sensor used in the actual bubble column consists of three planes (two transmitter planes and one receiver plane) of wire grids with 8 × 32 wires (8 wires parallel to the width, i.e. along the depth of the test section and 16 wires par-

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Fig. 3. Wire-mesh sensor geometry.

allel to the depth, i.e. along the width in two axially separated planes) each made of stainless steel and 0.125 mm in diameter. Each one transmitter plane and the receiver plane act as an independent sensor. Correlating the signals of the two sensors, informations about the bubble velocities are available. The wires are equally distributed in the cross-section of the test section. The grid has a spacing of 3.03 mm along the width and 2.22 mm along the depth. The axial distance between two planes of wires is 2.4 mm. A maximum sampling frequency of 10,000 Hz can be achieved using this system. A limitation on memory size of the data acquisition system components restricts the amount of information that can be continuously obtained to 17 s with a measuring frequency of 10,000 Hz. The data evaluation started from the transformation of the instantaneously measured electrical signals ε into local instan-

taneous gas fractions. At each measuring location the instantaneous conductivity signal is related to the signal characteristic for plain water. The result is a matrix of local instantaneous volumetric gas fractions εi,j,k , where k is the number of the current measurement and i, j are the indexes of to the location in the sensor plane. From this data, cross-section averaged gas fractions as well as radial gas fraction profiles can be calculated (Prasser et al., 2002). The accuracy of the gas fraction measurement is discussed in Prasser et al. (2005). Local gas velocities are calculated by estimating the bubble time of flight between two wire-mesh sensors axially separated by a distance of 2.4 mm. Bubble velocity is estimated by cross-correlating the signals obtained from the downstream and upstream sensors. The cross-correlation aims at finding the same bubble in both wire-mesh planes and estimating the

Fig. 4. Simplified schematic of the wire-mesh sensor.

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time displacement in the signals obtained from the two sensors as a result of the bubble passing through them. With known axial distance between the sensors and the time displacement between the corresponding signals from the two sensors, velocity can be estimated. Further details of the velocity estimation are detailed in Prasser (1999). The velocity estimation based on cross-correlation technique is accurate enough for the estimation of individual bubble velocities and the calculation of gas volume flow rate through the sensor. Further work needs to be done before the dispersed phase time averaged velocity profiles can be estimated using this method. Bubble size distributions were extracted from the measuring data using the algorithm described by Prasser et al. (2001). First step is an identification of bubbles. A bubble is defined as a region of connected gas-containing elements in gas fraction data εi,j,k that is completely surrounded by elements containing the liquid phase. Each element of such a region obtains a common number that is unique for the detected bubble, a so-called bubble identificator. Local instantaneous gas fractions adopt intermediate values between 100% (gas) and 0% (liquid), when the corresponding control volume formed by a pair of crossing wires contains both gas and liquid in the same time. After the bubble identification, the volume of the bubble is obtained by integrating the local gas fraction over elements owning the given bubble number. The sum of gas fractions is multiplied by the extension of the control volume Vbub , which is the product of the lateral electrode pitch in x and y directions and the sampling period divided by the bubble velocity. The corresponding bubble size diameter db then can be calculated according to  db =

3

6Vbub π

(3)

The measured bubble size distributions presented in Fig. 5 show that at gas superficial velocities smaller than 10 mm/s bubbles smaller than 5 mm are found.

Fig. 5. Bubble size distributions measured by the wire-mesh sensor.

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3. Simulations using the CFD code CFX 3.1. Introduction and problem definition The hydrodynamics of bubble plumes in a channel with a rectangular cross-section (0.1 m in width and 0.02 m in depth) and for a superficial gas velocities up to 0.02 m/s were studied numerically using the CFD code CFX from ANSYS. The turbulence in flows that have engineering relevance spans a wide spectrum of length and time scales. The largest scales of motion are responsible for most of the momentum and energy transport and are strongly dependent on the flow geometry, while the eddy motions in the inertial sub-range depend only on the dissipation rate and are more universal in their behavior compared to that of the larger eddies. In the past therefore several authors modeled the flow using the large eddy simulation (LES). Previous published work in two-fluid model LES includes that of Deen et al. (2001), Milelli (2002) and Lakehal et al. (2002). Deen et al. (2001) simulated the hydrodynamics to a bubble plume in a test section with a square cross-section of 15 cm × 15 cm, a height of 45 cm and a superficial gas velocity of 4.9 mm/s. Milelli (2002) studied the motion of a bubble plume in a cylindrical test section 50 cm in diameter, 40 cm in height and for a maximum superficial gas velocity of 6.11 mm/s. Lakehal et al. (2002) studied turbulent bubbly shear flows in a vertical square channel 30 cm wide, 4 cm in depth and 60 cm in height. The void fractions involved in the study were lower than 2%. LES as currently practiced is limited to small particles and low void fractions, and there remains a need for new techniques that will be less restricted in range of available parameters. Borchers et al. (1999) and Sokolichin and Eigenberger (1999) investigated the application of the standard k-␧ turbulence model to the dynamic simulation of a bubble column having a width of 0.5 m, a depth of 0.08 m and a height of 2.0 m. Modeling the column fully in 3D they found good qualitative and acceptable quantitative agreement to the experiments. To limit the numerical effort and to simulate gas superficial velocities up to 0.02 m/s in the present case was modeled as an unsteady Reynolds averaged Navier Stokes problem. The two fluid Eulerian–Eulerian time averaged model (Ishii and Mishima, 1984) was applied. Two sets of governing equations, continuity and momentum equations are solved for either phase and their interactions are modeled using interface transfer terms for interfacial heat, mass and momentum exchange. In the actual case the flow is assumed to be adiabatic and only the momentum exchange has to be considered. For the liquid a turbulence shear stress (SST) model according to Menter (1994) was applied. The SST model switches between the standard k-␧ (for the flow away from walls) and the k-␻ turbulence model (for the vicinity of walls) using a blending function, excluding the user influence modeling the near wall conditions. Modeling the influence of the gas bubbles on the liquid turbulence the Sato’s eddy viscosity model for bubble-induced turbulence was applied (Sato et al., 1981). The liquid viscosity μ is modeled consistent of the laminar component μL , the turbulence viscosity caused by the

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turbulence of the liquid phase μT : k2 with Cμ = 0.09 ε and a bubble induced component:

This coefficient depends on the modified E¨otv¨os number given by

μT = Cμ ρL

(4)

μS = CS ρL αdB |VL − VG | with CS = 0.6

(5)

The phenomenon of an aerated bubble column is clearly a transient process. In the present case it was modeled as an unsteady Reynolds averaged Navier Stokes problem. 3.2. Modeling of momentum transfer 3.2.1. Drag force The drag force between bubbles and the liquid are calculated according to nP ρL Ap (6) CD |Vrel |Vrel 2 with the particle number density n, the liquid density ρL , the particle cross-section in flow direction Ap and the difference velocity between particles and liquid Vrel . The drag coefficient CD was calculated according to Grace et al. (1976):   4 ρL − ρG dB g CD = (7) 2 3 ρL Vterm FDRAG =

Besides the drag forces, representing the flow resistance in flow direction, the so-called non-drag forces acting perpendicular to the flow direction have to be modeled to simulate the correct flow structure. Namely the lift force, the turbulent dispersion and the wall force were considered. In the following expressions the forces for the gaseous dispersed phase are given. 3.2.2. Lift force The lift force considers the interaction of the bubble with the shear field of the liquid and was first introduced by Zun (1980). Related on the unit volume it can be calculated as F LIFT = −CL ρL (VG − VL )rot VL

g(ρL − ρG )dH2 (10) σ Here dH is the maximum horizontal dimension of the bubble. It is calculated using an empirical correlation for the aspect ratio by the following equation (Wellek et al., 1966): 3 (11) dH = db 1 + 0.163Eo0.757 Eod =

(8)

The classical lift force, which has a positive coefficient CL , acts in the direction of decreasing liquid velocity. In case of co-current upwards pipe flow this is the direction towards the pipe wall. DNS simulations (Ervin and Tryggvason, 1997) and experimental investigations (Tomiyama et al., 1995) showed that for bubbles with large deformations a force occurs, which can be modeled with the same approach as the classical lift force, but with a negative sign of the lift force coefficient. Tomiyama did investigations on single bubbles and conducted the following correlation for the coefficient of the lift force from these experiments: ⎧ ⎪ ⎨ min[0.288 tanh(0.121Re), f (Eod )] for Eod < 4 for 4 < Eod < 10 , CL = f (Eod ) ⎪ ⎩ −0.27 for Eod > 10 with f (Eod ) = 0.00105Eo3d − 0.0159Eo2d − 0.0204Eod + 0.474 (9)

For the water–air system at normal conditions CL changes its sign at an db = 5.8 mm. This result was confirmed by investigations of the cross-sectional gas volume fraction distribution on vertical upward air/water flow (Lucas et al., 2005a). 3.2.3. Turbulent dispersion force The turbulent dispersion force is the result of the turbulent fluctuations of liquid velocity. Gosman et al. (1992) derived a turbulent dispersion force as F DISP = −

3CD νt,l ρL Vrel grad α 4db Pr

(12)

The turbulent Prandtl number (or Schmidt number) has an order of magnitude of 1 and is given by Pr =

νleff νg

(13)

Similar expressions were obtained from Drew (2001), Carrica et al. (1999) and Burns et al. (2004). They base on Favre averaged drag models. As shown by Moraga et al. (2003) this turbulent dispersion force formulation correspond to a diffusion term in the mass balance equation with D∗ =

νleff Pr

(14)

3.2.4. Wall force In experiments investigating a vertical upward gas liquid flow a pushing away of the gas bubbles from the wall is observed. As the consequence the maximum gas volume fraction is found not at the wall but at a certain distance. In terms of bubble forces this phenomenon is expressed by a wall force. The wall force can be considered according to F WALL = −CW αρL |(VG − VL ) − ((VG − VL )nr n r )|2 n r with CW



CW1 CW2 = max 0, + db y



according to Antal et al. (1991) respective:   db 1 1 CW = CW3 − 2 y2 (D − y)2 with CW3 =



(15)

exp(−0.933Eo + 0.179) for 1 ≤ Eo ≤ 5 0.007Eo + 0.04 for 5 ≤ Eo ≤ 33

(16)

(17)

(18)

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according to Tomiyama (1998) with n as the normal vector to the wall, db as the bubble size diameter, wrel as the velocity difference between the phases and α as the gas volume fraction. The force is dependent on the distance to the wall y. Antal et al. (1991) proposes an inverse proportionality to y, whereas Tomiyama (1998) proposes an inverse quadratic proportionality to y. For the usage of the Tomiyama correlation in a CFD code only the first term in the bracket of equation has to be implemented, since the second term is considered automatically. 3.3. Definition of the CFD problem The rectangular bubble column was simulated using a regular hexagonal grid having a cell size of 5 mm. A second order advective discretisation scheme was applied. Grid refinement studies have proved the adequate spatial resolution (see Section 4.2). The time step of the transient problem was set to 0.005 s. A second order backward Euler time discretisation scheme was set. Also here time step refinement studies proved the adequate time step (see Section 4.2). The gas inlet at the bottom was simulated by an inlet having the size of the sparger. The outlet was defined by an opening boundary condition, let out only gas. At the beginning the bubble column was filled only with water and the hydrostatic pressure was set.

Fig. 7. Measured and calculated final gas volume fraction.

tion is reached after about 10 s of problem time. In Fig. 7 the measured and calculated final gas volume fractions are presented for different superficial gas velocities. The good agreement of the measured and calculated values shows the adequate simulation of the phase drag. 4.2. Study of the mesh size and the time step

4. Results 4.1. Average gas fraction The measurement of the gas bubble size distribution (see Fig. 5) shows, that with increasing gas superficial velocity JG the average bubble size and the width of the bubble size distribution increase. Nevertheless for JG less than 10 mm/s the maximum found bubble size is smaller than the critical diameter of 5.8 mm. So for this case a monodispersed approach assuming an average bubble size of dB = 3 mm is justified. Fig. 6 shows the time dependent average gas volume fractions for different superficial gas velocities. Starting from a column filled only with water a constant final average gas volume frac-

Milelli (2002) and Lakehal et al. (2002) investigated the grid resolution necessary for a correct large eddy simulation. They derived a criterion that the mesh size has to be larger than 1.5 times the bubble size. In the actual experiments a bubble size of 3 mm was found. Therefore, a mesh size of 5 mm seems to be correct. On the other hand the actual flat geometry is then resolved by only four nodes in depth. To prove the correct mesh size and the time step a parameter study according to the Best Practise Guidelines (Menter, 2002) was performed. Additional to the reference grid a grid (A) with doubled node number in the depth, a grid (B) with additional doubled node number in the width and grid (C) with doubled node numbers in all three directions were investigated. For the case of the air superficial velocity JG = 0.01 m/s the final holdup was calculated. The results are presented in Table 1. The table shows the almost independence of the final gas holdup on the selected mesh. Furthermore, for the specification of the spatial resolution it has to be kept in mind, that a grid size resolution smaller than the bubble size would not be meaningful according to the applied model approach. To investigate the influence of the selected constant time step in the transients, additional calculations halving and doubling Table 1 Influence of the mesh size on the gas holdup for the case JG = 0.01 m/s

Fig. 6. Time dependent average gas volume fraction for JG = 6–10 mm/s.

Reference A B C

Nodes (W × D × H)

Cell number

Final gas holdup

20 × 4 × 200 20 × 8 × 200 40 × 8 × 200 40 × 8 × 400

16000 32000 64000 128000

0.0426 0.0408 0.0405 0.0405

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Table 2 Influence of the time step on the gas holdup for the case JG = 0.01 m/s Time step

Final holdup

0.005 s (reference case) 0.0025 s 0.01 s

0.0426 0.0416 0.0427

the time step were performed. The calculated final gas holdup for the case of the air superficial velocity JG = 0.01 m/s is shown in Table 2. Also here the almost independence of the final gas holdup indicate the correct selection of the time step. 4.3. Flow characteristics 4.3.1. Flow visualization A careful observation of the gas flow in the column shows that oscillating plumes are seen in a small region right above the gas injection point. The plume like structure disappears (approximately after an axial distance of 1.5–5 times the width of the column, depending of the superficial gas velocity) beyond a certain height and the bubbles are found to rise in a string like motion. Fig. 8 shows the picture preferably in the near injection region up to a height of about 0.3 m. The numerical setup according to Section 3 yields the similar qualitative behavior. Fig. 9 shows a snapshot of the gas distribution in the column after a problem time of 30 s. Oscillations are found only near the gas injection. In the upper region the bubbles rise almost equally distributed. The right side shows a schematic view of the flow pattern in the lower and upper zone of the bubble column. To find a numerical value to compare the calculated and measured lateral gas distribution in the column, the time averaged volume fraction profiles at a height of y = 0.63 m in the upper

Fig. 9. Snapshot of the calculated gas volume fraction distribution after a problem time of 30 s for JG = 10 mm/s (left side) and found regions of different behavior (right side).

region and at y = 0.08 m in the near injection region were calculated. The averaging is performed over a time period, when the average gas fraction has reached already the final value. The experimental values are determined by time averaging of the local gas fractions measured by the wire-mesh sensor. Fig. 10 shows the measured and calculated lateral gas distribution. Both in the measurements and in the calculations with good agreement maxima near the right and left wall are found. 4.3.2. Role of the non-drag forces To investigate the influence of the non-drag forces a calculation without consideration of these forces was performed. Fig. 11 left side shows a snapshot of the gas fraction distribution after 30 s of problem time. The transient solution shows an oscillat-

Fig. 8. Long plume oscillations at a superficial gas velocity JG = 4 mm/s.

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Fig. 10. Time averaged spatial gas volume fraction distribution at a height of y = 0.63 m (upper region of the column).

ing meandering behavior of the gas volume fraction in the whole column. Based on this solution the values of the different components of non-drag forces were calculated. Fig. 11 right side shows a snapshot. A small value means here, that activating this component will not change the solution. The distribution of the value for the lift force FLIFT shows the largest contributions, where in the gas fraction distribution the largest gradients of the gas volume fraction is found. That means that the lift force has an equalizing dumping effect of the flow behavior. Lucas et al. (2005b) performed a linear stability analysis and could show the damping effect of the lift force. The turbulent dispersion force yields considerable values only near the gas injection. The wall force yields considerable contributions only near the wall and causes the wall peak found in the lateral distribution (Fig. 10).

407

Fig. 12. Time averaged spatial gas volume fraction distribution at a height of y = 0.08 m (gas injection region of the column).

4.3.3. Region near the gas injection The same averaging procedure was performed in the near gas injection region, where both the observation and the calculation show oscillating gas plumes. The result for a height of 0.08 m is shown in Fig. 12. In the face of the excellent agreement for the upper region (see Fig. 10) in the near gas injection region the accordance is quite poor. Obviously the CFX two-fluid model in its present configuration is not able to resolve the turbulence structures. This could be reached by a large eddy simulation. 5. Summary The paper describes experimental and numerical investigations of a rectangular bubble column having a width of 0.1 m, a depth of 0.02 m and a height of 1.0 m. Air is injected in the center of the bottom with superficial velocities up to 20 mm/s. Besides

Fig. 11. Gas fraction distribution without consideration of the non-drag forces (left side) and based on this solution calculated value of the different components of non-drag forces (right side).

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high speed video observations, a wire-mesh sensor for the measurement of the lateral gas fraction distribution was applied. For the numerical study of the flow in the bubble column, the CFD code CFX was applied. Transient simulations based on the Euler/Euler approach and the unsteady Reynolds averaged Navier Stokes turbulence modeling were performed. Concerning the momentum exchange between gas and liquid, besides the drag forces the non-drag forces were considered. The average gas volume fraction in the bubble column dependent on the gas superficial velocity could be simulated with good accordance to the measurements. So the applied drag law was confirmed. The simulation of the transient flow pattern was found strong influenced by the modeling of the non-drag forces. Without considering the non-drag forces, the numerical simulations show a meandering oscillation of the gas volume fraction distribution in the whole column. The experiments however showed in the upper region of the column an equalized rising of the bubbles. Particularly the stabilizing effect of the lift bubble force could be proven. The unstable processes near the gas injection could not be simulated. Here an approach is necessary, which is able to resolve appropriate the turbulence structures. References Antal, S.P., Lahey, R.T., Flaherty, J.E., 1991. Analysis of phase distribution in fully developed laminar bubbly two-phase flow. Int. J. Multiphase Flow 17, 635–652. Borchers, O., Busch, C., Sokolichin, A., Eigenberger, G., 1999. Applicability of the standard k-␧ turbulence model to the dynamic simulation of bubble columns. Part II. Comparison of detailed experiments and flow simulations. Chem. Eng. Sci. 54, 5927–5935. Burns, A.D., Frank, T., Hamill, I., Shi, J.-M., 2004. The Favre averaged drag model for turbulence dispersion in Eulerian multi-phase flows. In: Proceedings of the Fifth International Conference on Multiphase Flow, ICMF’2004, Yokohama, Japan. Carrica, P.M., Drew, D.A., Lahey, R.T., 1999. A polydisperse model for bubbly two-phase flow around a surface ship. Int. J. Multiphase Flow 25, 257–305. Chen, J.J., et al., 1989. Effect of depth on circulation in bubble columns. Chem. Eng. Res. Des. 67, 203–207. Chen, R.C., Fan, L.S., 1992. Particle image velocimetry for characterizing the flow structure in three dimensional gas–liquid–solid fluidized beds. Chem. Eng. Sci. 47, 3615. Deen, N.G., Solberg, T., Hjertager, B.H., 2001. Large eddy simulation of the gas–liquid flow in a square cross-sectioned bubble column. Chem. Eng. Sci. 56, 6341–6349. Deonij, E., et al., 1997. Computational fluid dynamics applied to gas–liquid contactors. Chem. Eng. Sci. 52 (1). Drew, D.A., 2001. A turbulent dispersion model for particles or bubbles. J. Eng. Math. 41, 259–274. Ervin, E.A., Tryggvason, G., 1997. The rise of bubbles in a vertical shear flow. J. Fluid. Eng. 19, 443–449. Gosman, A.D., Lekakou, C., Politis, S., Issa, R.I., Looney, M.K., 1992. Multidimensional modeling of turbulent two-phase flow in stirred vessels. AIChE J. 38, 1946–1956. Grace, J.R., Wairegi, T., Niguyen, T.H., 1976. Shapes and velocities of simple drops and bubbles moving freely through immiscible liquids. Trans. Inst. Chem. Eng. 54, 167.

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