Modelling of the Bubble Size Distribution in an Aerated Stirred Tank: Theoretical and Numerical Comparison of Different Breakup Models

2014 ◽  
Vol 35 (3) ◽  
pp. 331-348 ◽  
Author(s):  
Zbyněk Kálal ◽  
Milan Jahoda ◽  
Ivan Fořt
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Water System ◽  
Secondary Phase ◽  
Bubble Size Distribution ◽  
Stirred Tank ◽  
Numerical Comparison ◽  
Size Distributions ◽  
Rushton Turbine ◽  
Breakup Model

Abstract The main topic of this study is the mathematical modelling of bubble size distributions in an aerated stirred tank using the population balance method. The air-water system consisted of a fully baffled vessel with a diameter of 0.29 m, which was equipped with a six-bladed Rushton turbine. The secondary phase was introduced through a ring sparger situated under the impeller. Calculations were performed with the CFD software CFX 14.5. The turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the MUSIG method with 24 bubble size groups. For the bubble size distribution modelling, the breakup model by Luo and Svendsen (1996) typically has been used in the past. However, this breakup model was thoroughly reviewed and its practical applicability was questioned. Therefore, three different breakup models by Martínez-Bazán et al. (1999a, b), Lehr et al. (2002) and Alopaeus et al. (2002) were implemented in the CFD solver and applied to the system. The resulting Sauter mean diameters and local bubble size distributions were compared with experimental data.

scholarly journals CFD Prediction of Gas-Liquid Flow in an Aerated Stirred Vessel Using the Population Balance Model

2014 ◽  
Vol 35 (1) ◽  
pp. 55-73 ◽  
Author(s):  
Zbyněk Kálal ◽  
Milan Jahoda ◽  
Ivan Fořt
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Water System ◽  
Population Balance ◽  
Bubble Size Distribution ◽  
Balance Model ◽  
Stirred Vessel ◽  
Rushton Turbine ◽  
Size Groups ◽  
Gas Liquid Flow

Abstract The main topic of this study is the experimental measurement and mathematical modelling of global gas hold-up and bubble size distribution in an aerated stirred vessel using the population balance method. The air-water system consisted of a mixing tank of diameter T = 0.29 m, which was equipped with a six-bladed Rushton turbine. Calculations were performed with CFD software CFX 14.5. Turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the homogeneous MUSIG method with 24 bubble size groups. To achieve a better prediction of the turbulent quantities, simulations were performed with much finer meshes than those that have been adopted so far for bubble size distribution modelling. Several different drag coefficient correlations were implemented in the solver, and their influence on the results was studied. Turbulent drag correction to reduce the bubble slip velocity proved to be essential to achieve agreement of the simulated gas distribution with experiments. To model the disintegration of bubbles, the widely adopted breakup model by Luo & Svendsen was used. However, its applicability was questioned.

CFD Simulation of Gas Dispersion in a Stirred Tank of Dual Rushton Turbines

2017 ◽  
Vol 15 (4) ◽  
Author(s):  
Xinju Li ◽  
Xiaoping Guan ◽  
Rongtao Zhou ◽  
Ning Yang ◽  
Mingyan Liu
Keyword(s):  
Flow Field ◽  
Size Distribution ◽  
Liquid Flow ◽  
Bubble Size ◽  
Great Influence ◽  
Gas Holdup ◽  
Bubble Size Distribution ◽  
Stirred Tank ◽  
Treatment Methods ◽  
Gas Dispersion

Abstract3D Eulerian-Eulerian model was applied to simulate the gas-liquid two-phase flow in a stirred tank of dual Rushton turbines using computational fluid dynamics (CFD). The effects of two different bubble treatment methods (constant bubble sizevs. population balance model, PBM) and two different coalescence models (Luo modelvs. Zaichik model) on the prediction of liquid flow field, local gas holdup or bubble size distribution were studied. The results indicate that there is less difference between the predictions of liquid flow field and gas holdup using the above models, and the use of PBM did not show any advantage over the constant bubble size model under lower gas holdup. However, bubble treatment methods have great influence on the local gas holdup under larger gas flow rate. All the models could reasonably predict the gas holdup distribution in the tank operated at a low aeration rate except the region far from the shaft. Different coalescence models have great influence on the prediction of bubble size distribution (BSD). Both the Luo model and Zaichik model could qualitatively estimate the BSD, showing the turning points near the impellers along the height, but the quantitative agreement with experiments is not achieved. The former over-predicts the BSD and the latter under-predicts, showing that the existing PBM models need to be further developed to incorporate more physics.

An Optical Method for Determining Bubble Size Distributions—Part I:Theory

1988 ◽  
Vol 110 (3) ◽  
pp. 325-331 ◽  
Author(s):  
P. R. Meernik ◽  
M. C. Yuen
Keyword(s):  
Statistical Analysis ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubbly Flow ◽  
Bubble Size Distribution ◽  
Phase Flow ◽  
Size Distributions ◽  
Optical Technique ◽  
Narrow Beam ◽  
Two Phase

A new optical technique is developed to determine the size distribution of bubbles in a two-phase flow. Implementation involves passing a narrow beam of light through the bubbly flow and monitoring the transmitted light intensity. The basic units of data are the rate at which each bubble blocks off the beam and the duration of blockage. Adding the hypothesis that the distance of closest approach between a bubble’s center and the beam axis is randomly distributed, a statistical analysis yields the bubble size distribution.

Parametric numerical study and optimization of mass transfer and bubble size distribution in a gas-liquid stirred tank bioreactor equipped with Rushton turbine using computational fluid dynamics

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sanaz Salehi ◽  
Amir Heydarinasab ◽  
Farshid Pajoum Shariati ◽  
Ali Taghvaie Nakhjiri ◽  
Kourosh Abdollahi
Keyword(s):  
Fluid Dynamics ◽  
Mass Transfer ◽  
Computational Fluid Dynamics ◽  
Transfer Coefficient ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubble Size Distribution ◽  
Stirred Tank ◽  
Operating Parameters ◽  
Stirred Tank Bioreactor

Abstract Designing and optimizing a bioreactor can be an especially challenging process. Computational modelling is an effective tool to investigate the effects of various operating parameters on bioreactor performance and identify the optimum ones. In this work, a computational fluid dynamics-population balance model (CFD-PBM) was developed to elucidate the effect of different geometrical and operating parameters on the hydrodynamics and mass transfer coefficient of a batch stirred tank bioreactor. The validated model was projected to predict the effect of different parameters including the gas flow rate, the impeller off-bottom clearance, the number of agitator blades, and rotational speed of the impeller on the velocity profiles, air volume fraction, bubble size distribution, and the local gas mass transfer coefficient (K l a) in the bioreactor. Air bubble breakup and coalescence phenomena were considered in all simulations. Factorial experimental design approach was employed to statistically investigate the impacts of the aforementioned operating and geometrical parameters on K l a and bubble size distribution in the bioreactor in order to determine the most significant parameters. This can give an essential insight into the most impactful factors when it comes to designing and scaling up a bioreactor.

scholarly journals Measurement of Bubble Size, Gas holdup and Interfacial Area in Bubble Columns using Image Processing Techniques

2019 ◽  
Vol 9 (1) ◽  
pp. 4475-4479
Keyword(s):  
Image Processing ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubble Column ◽  
Rectangular Cross Section ◽  
Bubble Diameter ◽  
Water System ◽  
Interfacial Area ◽  
Gas Holdup ◽  
Bubble Size Distribution

Bubble sizes in bubble column affect transfer processes. Therefore, it’s important to calculate bubble size and interfacial area. Bubble size distribution (BSD) in a bubble column of rectangular cross section with dimensions 0.2m x 0.02m was measured using photographic method (400 fps) for air-water system. Gas holdup, Sauter-mean bubble diameter, aspect ratio and specific interfacial area were estimated from BSD. Effect of superficial gas velocity and static bed height on these parameters was investigated. The bubble size distribution exhibited mono-modal distribution showing the presence of non-uniform homogeneous bubbling regime. The frames of video were analysed using image processing steps to obtain major and minor axis of elliptical bubbles. Values of d32, , and ai were estimated from the data. The value of d32 increased with increasing Ug but is independent of Hs. The values of d32 were somewhat higher than the values reported by other investigators. The value of ai increases with increasing Ug and with decreasing Hs. Present values of compared well with the data reported in literature.

Closure Laws for the Transport Equation of Interfacial Area in Dispersed Flow

2002 ◽  
Author(s):  
X. Rioua ◽  
J. Fabrea ◽  
C. Colin
Keyword(s):  
Transport Equation ◽  
Size Distribution ◽  
Bubble Size ◽  
Interfacial Area ◽  
Bubble Size Distribution ◽  
Bubble Coalescence ◽  
Size Distributions ◽  
Mean Diameter ◽  
The Mean ◽  
Two Fluid

Derivation of a transport equation for the interfacial area concentration. In two-phase flows, the interfacial area is a key parameter since it mainly controls the momentum heat and mass transfers between the phases. An equation of transport of interfacial area may be very useful, especially for the two-fluid models. Such an equation should be able to predict the transition between the flow regimes. With this aim in view, we shall focus our attention on pipe flow. Besides in a first step, our study will be limited to dispersed flows. Different models are used to predict the evolution of bubble sizes. Some models use a population balance that provides a detailed description of the bubble size distributions, but they require as many equations as diameter ranges (Coulaloglou & Tavlarides1). Some others use only one equation for the transport of the mean interfacial area (Hibiki & Ishii2). In that case the bubble size distribution is treated as it would be monodispersed, its mean diameter being equal to the Sauter diameter. An intermediate approach was proposed by Kamp et al.3, in which polydispersed size distributions can be taken into account. It is the starting point of the present study in which: • The choice of an interfacial velocity is discussed. • The sink and source terms due to bubble coalescence, break-up or phase change are established. The model of Kamp et al. consists of transport equations of the various moments of the density probability function P(d) of the bubble diameter. In many experimental situations, P(d) is well predicted by a log-normal law (with two characteristic parameters d00 the central diameter of the distribution and a width parameter): The different moments of order ? of P(d) may be calculated: Sγ=n∫P(d)dγd(d)(1) where n is the bubble number density, S1/n, the mean diameter and S2/?, the interfacial area. A transport equation can be written for each moment: ∂Sγ∂t+∇·(uGSγ)=φγ(2) The lhs of (2) is an advection term by the gas velocity uG and the rhs is a source or sink term due to bubble coalescence, break-up or mass transfer. Since the bubble size distribution is characterised by the two parameters d00 and σˆ, only two transport equations (for S1 and S2) have to be solved to calculate the space-time evolution of the bubble size distribution. These two equations are still too cumbersome for a two-fluid model. Under some hypotheses (σˆ ∼ constant), they are lead to a single equation for the interfacial area. In its dimensionless form the interfacial area ai+ (ai+ = π S2 D, where D is the pipe diameter) reads: d/dt+(ai+)=f(RG,Re,We,ai+)(3) where RG is the gas fraction, Re is the Reynolds number of the mixture, We the Weber number of the mixture and t+ a dimensionless time.

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