Experimental and numerical studies of the ... - Science Direct

Chemical Engineering Science 54 (1999) 4913}4920

Experimental and numerical studies of the hydrodynamics in a bubble column S. Lain, D. BroK der, M. Sommerfeld* Fachbereich Ingenieurwissenschaften, Martin-Luther-Universita( t Halle-Wittenberg, D-06099 Halle (Saale), Germany

Abstract The hydrodynamics in a bubble column of 140 mm diameter and a height of 650 mm was analysed using a phase-Doppler anemometer (PDA). In order to allow the application of PDA, the bubble column was aerated with relatively "ne bubbles with a size spectrum between about 0.3 and 1.5 mm. The gas hold-up was varied in the range between 0.5 and 3%. The measurement of the liquid velocities in the bubble swarm was done by adding #uorescing seed particles. Moreover, the Euler/Lagrange approach was extended to allow time-dependent calculations of the #ow evolving in a bubble column based on the Reynolds-averaged Navier}Stokes equations together with the k}e turbulence model which was extended to account for turbulence modi"cation by the bubbles. The coupling between the phases was considered through momentum source terms and source terms in the k- and e-equation which also include the e!ect of wake-generated turbulence. The bubble motion was calculated by solving an equation of motion taking into account drag force, added mass, buoyancy and gravity, and the transverse lift force. In order to identify the relative importance of the di!erent physical phenomena involved in the model, a detailed parametric study was performed and the numerical results were compared with the measurements for validation. 1999 Elsevier Science Ltd. All rights reserved. Keywords: Bubble column; Hydrodynamics; Turbulence; Phase-Doppler anemometer; Numerical calculations; Euler/Lagrange approach; Waketurbulence

1. Introduction Bubbly #ows are found in a number of technical and industrial processes, such as sewage water puri"cation, #otation devices, and bubble column reactors. The latter "nd applications as gas}liquid contactors in chemical and biochemical processes. The hydrodynamics in bubble columns is determined by the bubble rise and hence bubble size distribution and gas hold-up. Moreover, turbulence will be induced by the bubble rise due to the evolution of large-scale #ow structures, shear produced in the vicinity of the bubble, oscillations of the bubbles, and the wakes of the bubbles. Especially mass transfer in bubble columns will be largely a!ected by this small-scale turbulence generated on the scale of the bubble. Although attempts have been undertaken for many years to theoretically describe the #ow structure in bubble columns, in order to predict industrial processes, there is a lack of detailed physical understanding and

* Corresponding author.

predictive tools for design and optimisation of bubble columns. In recent years, computational #uid dynamics (CFD) has become an attractive tool for supporting process design and optimisation and hence commercial CFD tools are increasingly used by industry. For the numerical computation of two-phase #ows two approaches are mainly applied, namely the Euler/Euler and the Euler/Lagrange approach. The "rst method considers both phases as interacting continua, while in the second method the discrete nature of the dispersed phase is taken into account by tracking a large number of individual bubbles through the #ow "eld. Recently, numerical methods have been developed which consider the unsteady nature of the #ow in bubble columns based on both the Euler/Euler (Sokolichin & Eigenberger, 1994) and the Euler/Lagrange approach (Lapin & LuK bbert, 1994; Murai & Matsumoto, 1995). A comparison of the performance of both approaches for the prediction of bubbly #ows was recently conducted by Sokolichin, Eigenberger, Lapin and LuK bbert (1997). In all these calculations however, turbulence of the continuous phase was not considered, rather an e!ective viscosity was used in order to match calculated results with measurements.

0009-2509/99/$ - see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 2 1 2 - 2

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S. Lain et al. / Chemical Engineering Science 54 (1999) 4913}4920

Moreover, in some cases the bubble motion was calculated in a rather crude fashion, by assuming a "xed slip velocity and adding some "ctitious di!usion component for simulating turbulent dispersion (Lapin & LuK bbert, 1994). The present study concerns the extension of an Euler/Lagrange approach to allow time-dependent calculations of bubbly #ows including the modelling of turbulence and the consideration of an equation of motion to calculate the bubble motion. The numerical calculations are validated based on detailed experiments.

cross-section of the aerator which is 100 mm in diameter. The gas #ow rate is varied by increasing the supply pressure. As a result of the stronger bulging of the membrane at higher pressures also the bubble size is slightly increasing with gas #ow rate. Measurements were performed up to a gas hold-up of about 3% and the established bubble size spectrum was in the range between 0.3 and 1.5 mm. In order to reduce bubble coalescence propanol was added to the tap water at a volume concentration of 0.004%. A summary of the experimental conditions is given in Table 1.

2. Experimental facility

3. Phase-doppler anemometer

A schematics of the entire experimental facility is shown in Fig. 1. The bubble column used in the experimental investigations has a diameter of 140 mm and a height of 650 mm (i.e. water level in the column). The aerator is build by using a porous membrane with a pore size of 0.7 lm. In order to "x the membrane it is mounted between two perforated plates, which are screwed on top of a small stagnation chamber. The aerator is connected via a #ow meter to a pressurised air supply system. Once the aerator is pressurised the membrane bulges and small bubbles are produced at the holes of the perforated plate so that a homogeneous aeration is established over the

A two-component "bre optics PDA (Dantec, FiberPDA) was used to measure bubble size and velocities, and also the continuous-phase velocities. In order to reduce refraction e!ects of the laser beams at the curved wall of the bubble column, it is placed in a square vessel which is also "lled with tab water. The transmitting and receiving optics modules were mounted on a computercontrolled 3-d traversing system (Fig. 1). This allowed fully automated measurements of cross-sectional pro"les at di!erent heights above the aerator. The pro"les were measured in the direction of the optical axis of the transmitting optics. As a result, the optical path length of the laser beams in the water changes when scanning a pro"le. This results in a shift of the measurement volume away from the geometric beam crossing location. In order to compensate for this e!ect, the receiving optics was automatically moved in the horizontal direction in order to ensure that the optical axis always intersects with the centre of the measurement volume. The optical path length of the scattered light remains constant since the bubble column is placed in a square vessel. The receiving optics is mounted at a scattering angle of 703, where re#ection by the bubbles is the dominant scattering mechanism and a linear phase-size relation is obtained (BroK der & Sommerfeld, 1998). The selected optical con"guration of the PDA-system allowed for a sizing range up to 2 mm (BroK der & Sommerfeld, 1998). For allowing the measurement of the liquid-phase velocities, #uorescing tracer particles with a nominal size of 8.3 lm are added. These particles are excited by the green

Fig. 1. Schematics of the test facility with bubble column and PDASystem.

Table 1 Flow conditions and measured cross-sectional averages (z"480 mm) of bubble number mean diameter and bubble Reynolds number based on average slip velocity Air #ow rate (l/h)

Super"cial gas velocity (cm/s)

Gas hold-up (%)

Bubble number mean diameter (lm)

Bubble Reynolds number (dimensionless)

80 160 320

0.14 0.29 0.58

0.68 1.24 2.92

750 850 900

143 187 180


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laser light at a wave length of 514.5 nm. The radiated light emission has a wave length of 585 nm. Hence, the Doppler signals from bubbles and tracer particles can be separated using a narrow band optical "lter around a wave length of 575 nm. When this "lter is inserted into the optical system the scattered light from the bubbles is blocked and only Doppler signals from the #uorescing tracer particles are received. Therefore, the measurements of the liquid phase velocities and bubble phase properties is done sequentially, once with the optical "lter and once without.

4. Experimental results The measurement of the bubble-phase properties and the continuous-phase velocities was performed at four cross-sections above the aerator (i.e. at 30, 100, 300, and 480 mm). Results of these measurements for di!erent gas hold-up have been published previously (BroK der & Sommerfeld, 1998) and will be presented here only in comparison with the numerical calculations. However, one phenomenon which is quite important for the calculations will be discussed. The experimental data revealed that the bubble rise and slip velocity which was obtained from the di!erence of the mean velocity of the entire bubble size spectrum and the mean velocity of the tracer particles, are considerably larger than the terminal velocity of single bubbles in contaminated water (Clift, Grace & Weber 1978). This e!ect is illustrated in Fig. 2 showing the size distributions of the bubbles measured in the core region of the bubble column 480 mm above the aerator and the size}velocity correlations for di!erent gas holdups. It is obvious, that the bubble size distributions have a peak around 800 lm and a long tail up to about 1800 lm. With increasing air #ow rate a second maximum appears in the size distribution around 1300 lm. The "rst reason for this e!ect is connected with the increase of the aeration pressure in order to increase the gas #ow rate. Secondly, there might be still some coalescence whereby also larger bubbles are produced. The measured correlations between bubble size and rise velocity are compared with the terminal velocity of single bubbles in Fig. 2(b). As expected, the measured rise velocity increases with size up to a value of 1000 lm and approaches a limiting value of about 0.3 m/s, which is close to the maximum rise velocity of single bubbles (Clift et al., 1978). With further increasing size the rise velocity again decreases slightly up to a value of 0.25 m/s which corresponds to the behaviour of single bubbles. For the larger bubbles the rise velocity is independent of the volume fraction. However, for bubble sizes up to about 1200 lm the measured rise velocity in the bubble swarm is considerably larger than the terminal velocity of single bubbles. It is supposed that this observation is the result of hydrodynamic interactions between bubbles and the

Fig. 2. Bubble number size distribution (a) and bubble size}velocity correlation (b) in the core of the bubble column 480 mm above the aerator for di!erent gas hold-ups.

turbulence induced by the bubbles whereby the drag coe$cient is reduced. A drastic increase of the measured rise velocity with gas hold-up is found for the smaller bubbles up to a diameter of 900 lm. This indicates that the liquid #ow is driven by the large bubbles and hence the smaller bubbles are dragged by the larger ones due to the hydrodynamic interaction. In order to further analyse this e!ect detailed experiments by particle tracking velocimetry are presently conducted which allow to study the bubble behaviour and liquid #ow structure in the bubble swarm.

5. Basic equations and numerical approach The time-dependent calculations of the #ow pattern evolving in the bubble column were performed using the Euler/Lagrange approach. The #uid #ow was calculated based on the Euler approach by solving the Reynoldsaveraged conservation equations in a time-dependent way. The resulting conservation equations are closed using the well-known k}e turbulence model (Launder

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Table 2 Summary of terms in the general equation, e!ective viscosity, and constants of the turbulence model

1

S ( !

S (. 0

C !

;

* *; *p C H ! #og V *x *x *x H

S 3.

k#k R