Modelling of Bubbly Flow Using CFD-PBM Solver in OpenFOAM: Study of Local Population Balance Models and Extended Quadrature Method of Moments Applications

Askari, Ehsan; Proulx, Pierre; Passalacqua, Alberto

doi:10.3390/chemengineering2010008

Cited by 14 publications

(7 citation statements)

References 56 publications

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“…Often, Eulerian-Eulerian models include a gas generation term as a boundary condition and information about the bubble sizes can be obtain through the implementation of a nucleation rate in a Population Balance Model (PBM) [9]. Examples of the use of these models can be found in the context of electrochemical reactions, where gasses are produced on electrodes.…”

Section: Introductionmentioning

confidence: 99%

Euler–Lagrange Modeling of Bubbles Formation in Supersaturated Water

et al. 2018

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Phase transition, and more specifically bubble formation, plays an important role in many industrial applications, where bubbles are formed as a consequence of reaction such as in electrolytic processes or fermentation. Predictive tools, such as numerical models, are thus required to study, design or optimize these processes. This paper aims at providing a meso-scale modelling description of gas–liquid bubbly flows including heterogeneous bubble nucleation using a Discrete Bubble Model (DBM), which tracks each bubble individually and which has been extended to include phase transition. The model is able to initialize gas pockets (as spherical bubbles) representing randomly generated conical nucleation sites, which can host, grow and detach a bubble. To demonstrate its capabilities, the model was used to study the formation of bubbles on a surface as a result of supersaturation. A higher supersaturation results in a faster rate of nucleation, which means more bubbles in the column. A clear depletion effect could be observed during the initial growth of the bubbles, due to insufficient mixing.

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Section: Introductionmentioning

confidence: 99%

Euler–Lagrange Modeling of Bubbles Formation in Supersaturated Water

et al. 2018

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“…For the CFD‐PBM model, the Sauter diameter computed by the PBM is used as the bubble diameter for the gas phase while a constant value is given to the liquid phase. The Sauter diameter defined in the OpenFOAM solver is given as (Askari et al, 2019)

d_{s} = \frac{\sum_{i} f_{i}}{\sum_{i} \frac{f_{i}}{d_{i}}}

where

f_{i}

is the normalized volume fraction of gas bubble class i with bubble size of

d_{i}

. Further discussion is provided in Section 4.3, which deals with the PBM.…”

Section: Governing Equationsmentioning

confidence: 99%

Effects of flow velocity and bubble size distribution on oxygen mass transfer in bubble column reactors—A critical evaluation of the computational fluid dynamics‐population balance model

Khalil

Rosso

DeGroot

2021

Water Environment Research

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Computational fluid dynamics (CFD) is used to simulate a bubble column reactor operating in the bubbly (homogenous) regime. The Euler–Euler two‐fluid model, integrated with the population balance model (PBM), is adopted to compute the flow and bubble size distribution (BSD). The CFD‐PBM model is validated against published experimental data for BSD, global gas holdup, and oxygen mass transfer coefficient. The sensitivity of the model with respect to the specification of boundary conditions and the bubble coalescence/breakup models is assessed. The coalescence model of Prince and Blanch (1990) provides the best results, whereas the output is shown to be insensitive to the breakup model. The CFD‐PBM study demonstrates the importance of considering the BSD in order to correctly model mass transfer. Results show that the constant bubble size assumption results in a large error in the oxygen mass transfer coefficient, while giving acceptable results for gas holdup. Practitioner points Constant bubble size (CBS) and population balance model (PBM) are compared for a bubble column reactor. Both PBM and CBS can predict gas holdup; however, PBM can correctly predict gas–liquid mass transfer whereas CBS cannot. Best practices for selecting coalescence, breakup, and drag models are determined.

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“…It can be assumed either as a constant mean value or in the form of a distribution function. Also, a polydisperse model can be utilised, which applies local distribution functions known as the method of classes (CM) or the method of moments (MOM) [46,47]. The Sauter mean diameter (SMD) using the Rosin-Rammler [48] distribution function within the range of 20-50 is adopted in the present case study.…”

Section: Bubble Shape and Sizementioning

confidence: 99%