One-equation sub-grid scale (SGS) modelling for Euler–Euler large eddy simulation (EELES) of dispersed bubbly flow (original) (raw)
Related papers
International Journal of Heat and Mass Transfer, 2020
The Eulerian-Eulerian Large-eddy simulations (LES) of gas-liquid two-phase flow in a cylindrical bubble column reactor have been conducted. When considering the turbulent eddy viscosity in LES, apart from the well-accepted contributions from shear turbulence and bubble induced turbulence (BIT), the effect of the interaction between entrained bubbles and eddies with a similar turbulence length scale to the sub-grid scale (SGS) cannot be neglected. With the consideration of the bubble response to the eddies on the induced sub-grid stresses, a modified SGS model, which incorporates the Stokes number, St, was proposed. The results of LES clearly indicate that the use of the modified SGS model can effectively capture the transient bubbly flow in the cylindrical bubble column. The power turbulent kinetic energy spectrum obtained in LES indicates that a slope similar to Komogorov-5/3 scaling law and the-3 scaling law can still be identified for a critical frequency f=10.70 Hz.
Large eddy simulation of a bubble column using dynamic sub-grid scale model
Chemical Engineering Journal, 2008
Euler-Euler simulations of the gas-liquid flow in a square cross-sectioned bubble column with LES (two sub-grid scale models) and the k-ε model are presented. The sub-grid scale modeling is based on the Smagorinsky kernel in both its original form and the dynamic procedure of Germano. The attempt has been made to assess the performance of these two sub-grid scale models. The Smagorinsky model with model constant C s = 0.12 performs quite well, and gives results almost identical to those given by the dynamic procedure of Germano. The SGS models are modified to account for bubble induced turbulence (Sato model) and it is observed that it does not change the results much. Predictions are also compared with the available experimental data. All the non-drag forces (turbulent dispersion force (only for RANS), virtual mass force, lift force) and drag force were incorporated in the model. An extended k-ε turbulence model has been used with extra source terms introduced to account for the interaction between the bubbles and the liquid. Though both LES models showed agreement in predictions, the Germano model still can be used to have estimates of C s value which are not known a priori. Moreover, if objective is to understand the steady and time averaged features, RANS can also perform well.
Euler–Euler large eddy simulations for dispersed turbulent bubbly flows
In this paper we present detailed Euler-Euler Large Eddy Simulations (LES) of dispersed bubbly flow in a rectangular bubble column. The motivation of this study is to investigate the potential of this approach for the prediction of bubbly flows, in terms of mean quantities. The physical models describing the momentum exchange between the phases including drag, lift and wall force were chosen according to previous experiences of the authors. Experimental data, Euler-Lagrange LES and unsteady Euler-Euler Reynolds-Averaged Navier-Stokes results are used for comparison. It is found that the present model combination provides good agreement with experimental data for the mean flow and liquid velocity fluctuations. The energy spectrum obtained from the resolved velocity of the Euler-Euler LES is presented as well.
Euler-Euler large eddy simulations of the gas–liquid flow in a cylindrical bubble column
Nuclear Engineering and Design, 2020
In this work Euler-Euler Large Eddy Simulations (LES) of dispersed turbulent gas-liquid flows in a cylindrical bubble column are presented. Besides, predictions are compared with experimental data from Vial et al. 2000 using laser Doppler velocimetry (LDV). Two test cases are considered where vortical-spiral and turbulent flow regimes occur. The sub-grid scale (SGS) modelling is based on the Smagorinsky kernel with model constant = 0.08 and the one-equation model for SGS kinetic energy. The emphasis of this work is to analyse the performance of the one-equation SGS model for the prediction of bubbly flow in a three-dimensional high aspect ratio bubble column (⁄) of 20 and the investigation of the influence of the superficial gas velocity using the OpenFOAM package. The model is compared with the Smagorinsky SGS model and the mixture − model in terms of the axial liquid velocity, the gas holdup and liquid velocity fluctuations. The bubble induced turbulence and various interfacial forces including the drag, lift, virtual mass and turbulent dispersion where incorporated in the current model. Overall, the predictions of the liquid velocities are in good agreement with experimental measurement using the one-equation SGS model and the Smagorinsky model which improve the mixture − model in the core and near-wall regions. However, small discrepancies in the gas holdup are observed in the bubble plume region and the mixture − model performs much better. The numerical simulations confirm that the energy spectra of the resolved liquid velocities in churn-turbulent regime follows the classical-5/3 law for low frequency regions and close to-3 for high frequencies. More details of the instantaneous local flow structure have been obtained by the Euler-Euler LES model including large-scale structures and vortices developed in the bubble plume edge.
Comparison of turbulence models for bubble column reactors
Chemical Engineering Science, 2017
h i g h l i g h t s CFD simulations of a bubble column are done by using k-e model, RSM and LES models. Modeling approach is developed for conservation equations of k, e and RSM. True k-e model and true RSM are compared against the std. k-e model and RSM as well as against LES model. The severity of modeling assumptions and their validity for two-phase flow is discussed in great details.
Eulerian-Eulerian Large-Eddy Simulations in Bubble-Columns
2015
In this paper the Eulerian-Eulerian two-fluid model implemented in STAR-CCM+ is used to predict the turbulent mixing of a bubble-column flow. Calculations are performed using the Reynolds-averaged Navier-Stokes equations (RANS) and typical two-point turbulence closure models, as well as by means of large-eddy filtering techniques (LES), based on the Smalgorinsky subgrid-scale method (SGS). The bubble and fluid phases are coupled by integrating momentum exchange terms due to drag, lift and virtual-mass forces, while turbulent dispersion effects are also accounted. Validation of the multiphase Eulerian model is performed against available Laser Doppler Anemometry measurements (LDA), reported in the experimental work of Deen et al. (Chem Eng Sci 56: 6341–6349, 2001 [1]).
Fluid dynamic modelling of bubble column reactors
2014
Numerical simulations of rectangular shape bubble column reactors (BCR) are validated starting from preliminary simulations aimed at identifying proper simulation parameters for a given system and resulting up to the numerical simulation with mass transfer and chemical reactions. The transient, three dimensional simulations are carried out using FLUENT software and the results obtained for a system with low gas flow rate (48 L/h) indicated that we need enough fine mesh grid and appropriate closure of interfacial forces to predict reliably plume oscillation period, liquid axial velocity and gas holdup profiles. In case of high flow rate (260 L/h), we compared the results for the effect of different interfacial closure forces and change in inlet boundary condition for gas volume fraction. There is no change in hydrodynamic results when there is change in gas volume fraction at inlet boundary condition. The effect of virtual mass interfacial force on the simulation results is also negl...
Reactive LES-Euler/Lagrange modelling of bubble columns considering effects of bubble dynamics
Chemical Engineering Journal, 2021
Bubble columns are complex multiphase reactors producing large contact areas for mass transfer and subsequent chemical reactions. For allowing a deeper insight into this complexity and providing strategies for process optimisation, CFD (computational fluid dynamics) has become a standard tool. However, accurate models are needed to reproduce correctly such dynamic systems. Numerical computations of reactive bubble columns are conducted based on a LES-Euler/Lagrange approach. For extending this approach beyond the point-mass assumption for the dispersed elements, a bubble oscillation model based on stochastic generation of eccentricity and motion angle is proposed. The effects of bubble dynamics are modelled in the interfacial forces accounting for instantaneous eccentricity. A dynamic Sherwood number is used to consider bubble dynamics in the mass transfer. The influence of chemical reactions in species consumption within the liquid phase was modelled through the enhancement factor. Large Eddy Simulation (LES) was used for calculating the fluid flow with momentum source terms for bubbles and modelling sub-grid-scale (SGS) turbulence in the continuous phase through a transport equation for the turbulent kinetic energy. The effect of sub-grid-scale (SGS) turbulence on bubble motion, and also SGS turbulence modification by bubbles (BIT) is considered, introducing an extra source term in a k SGS equation. This source term automatically accounts for turbulence dissipation as well as enhancement (i.e. BIT). Numerical simulations of the chemisorption process for CO 2 bubbles rising in highly concentrated NaOH solutions were compared with data presented in the literature. A very good agreement was only found when applying the full bubble dynamics model.
Large eddy simulation of the Gas–Liquid flow in a square cross-sectioned bubble column
Chemical Engineering Science, 2001
In this work the use of large eddy simulations (LES) in numerical simulations of the gas-liquid flow in bubble columns is studied. The Euler-Euler approach is used to describe the equations of motion of the two-phase flow. It is found that, when the drag, lift and virtual mass forces are used, the transient behaviour that was observed in experiments can be captured. Good quantitative agreement with experimental data is obtained both for the mean velocities and the fluctuating velocities. The LES shows better agreement with the experimental data than simulations using the k-epsilon model.
Multiscale Simulation of Bubbly Flows
Large eddy simulation coupled with a Lagrangian bubble tracker is used to investigate the dynamics of a liquid containing microbubbles in a turbulent, horizontal channel flow. Such flows are relevant in a number of engineering and environmental applications, including bubble columns, gas-liquid reactors, fluidised beds and fluid transfer in pipelines. Sub-grid scale stresses are parameterised using a dynamic model, with the microbubbles assumed to be spherical and non-deformable, and subject to drag, lift, gravity, buoyancy, added mass and pressure gradient forces. The bubbles are also momentum-coupled with the carrier fluid. A channel flow of water at a shear Reynolds number, í µí± í µí±í µí¼ = 150, and bubble diameter, í µí± = 80 í µí¼í µí±, is considered. Results are consistent with those from previous direct numerical simulations, and demonstrate bubble migration towards the upper channel wall with time due to buoyancy effects, and the associated impact on the flow velocity and bubble concentration distribution.