Study on bubble-induced turbulence in pipes and containers with Reynolds-stress models (original) (raw)
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Bubble induced turbulence model improved by direct numerical simulation of bubbly flow
Chemical Engineering Journal, 2018
Direct numerical simulations (DNS) provide a description of turbulent flow fields at every point in space and time. Since every statistical quantity can be computed, this data should be useful for the development of closure models. In this paper, models for bubbly turbulent flows, in a two-fluid framework, are investigated using DNS data. A
A two-equation turbulence model of turbulent bubbly flows
International Journal of Multiphase Flow, 2001
A two-¯uid model of turbulent, adiabatic bubbly¯ow was implemented in the computational¯uid dynamics (CFD) CFX4.2 program and validated. Turbulence in the dispersed (bubble) phase was neglected. Liquid turbulence was modeled through a two-phase extension of the single-phase standard k±e model. Conservation equations of turbulent scales contain single-phase and interfacial terms. A closure for the interfacial turbulence terms was proposed based on the assumption of low-bubble inertia and neglecting surface tension. The interfacial turbulence terms account for additional pseudoturbulence in liquid created by bubble-induced mixing. The proposed turbulence model contained the single empirical constant in the modeled dissipation rate balance. The model was implemented in the CFX4.2 commercial CFD solver. Comparing numerical predictions to the experimental data the value of the model constant was estimated. Model predictions were compared to other bubbly¯ows to prove the universality of the model constant. The comparison showed that the constant has a certain generality. A new, two-phase logarithmic wall law was also implemented and validated. The derivation of the new law was based on an assumption of the additional eddy diusivity due to the bubble-induced stirring in the boundary layer. An improved wall friction prediction was achieved with the new wall law over conventional single-phase law. The improvement was especially noticeable for the low-liquid¯ow rates when bubble-induced pseudoturbulence plays a signi®cant role. The ability of the model to account for bubble size eect was also studied. Ó
Modelling hydrodynamics and turbulence in a bubble column using the Euler-Lagrange procedure
2002
This paper describes an extension and validation of the Euler/Lagrange approach for time-dependent calculations of the flow evolving in a bubble column. The continuous phase velocity is obtained by solving the two-dimensional axisymmetric Reynolds-averaged Navier-Stokes equations augmented by the k-e turbulence model. The coupling between the phases is considered through momentum source terms and source terms in the k-and e-equations, which include the effect of wake-generated turbulence by means of consistent Lagrangian-like terms. Bubble motion is calculated by solving the equations of motion taking into account drag force, liquid inertia, added mass, buoyancy and gravity, and the transverse lift force. In order to identify the relative importance of the different physical phenomena involved in the model, the radial variation of the corresponding constitutive terms that appear in the transport equations of the liquid variables is analyzed in an instantaneous as well as in the time-averaged configuration. As a conclusion, the bubble source terms are directly responsible for the production of fluctuating kinetic energy and dissipation rate in the liquid, which means that their modelling determines the topology of the liquid flow in the bubble column. For validation the numerical results are quantitatively compared with detailed measurements utilizing phase-Doppler anemometry.
Baseline Model for the Simulation of Bubbly Flows
Chemical Engineering & Technology, 2015
The bubble size is a key parameter appearing in closure relations for the Euler-Euler two-fluid model. The bubble size distribution is established as a result of bubble coalescence and breakup processes. These processes are very complex, and therefore, a two-step procedure is adopted for model validation where, in a first step, measured values are substituted for the bubble size distribution. In this way, the uncertainties of the less developed modeling for bubble coalescence and breakup are bypassed and a validation of the other parts of the overall model becomes possible. In a second step, the previously qualified models for bubble forces and bubble-induced turbulence are used without any change and the validity of the models for bubble coalescence and breakup can be assessed.
Journal of Applied Fluid Mechanics, 2021
This paper presents a comparative assessment of low Reynolds number k- models against standard k- model in an Eulerian framework. Three different low-Re number k- models: Launder-Sharma (LS), Yang-Shih (YS) and AbeKondoh-Nagano (AKN) have been used for the description of bubble plume behaviour in stratified water. The contribution of the gas phase movement into the liquid phase turbulence has been achieved by using the Dispersed with Bubble Induced Turbulence approach (DIS+BIT).The results reveal that the oscillation frequency of gas-liquid flow are correctly reproduced by standard k- and LS models. In fact, we found for standard K- and LS a clear dominant peak at a frequency equal to 0.1 Hz. On the other hand, YS and AKN models have predicted chaotic oscillations. The oscillation amplitude of the bubble plume predicted from LS model seems to be in good agreement with the PIV measurements of Besbes et al. (2015). However, for the standard K- model the oscillation amplitude is low. The air-water interface shows that the bubble plume mixing with the stratified water is predicted to be stronger compared to standard k- model.
Direct numerical simulations of bubble-laden turbulent flows using the two-fluid formulation
Physics of Fluids, 1998
Direct numerical simulations ͑DNS͒ of bubble-laden isotropic decaying turbulence are performed using the two-fluid approach ͑TF͒ instead of the Eulerian-Lagrangian approach ͑EL͒. The motivation for the study is that EL requires considerable computational resources, especially for the case of two-way coupling, where the instantaneous trajectories of a large number of individual bubbles need to be computed. The TF formulation is developed by spatially averaging the instantaneous equations of the carrier flow and bubble phase over a scale of the order of the Kolmogorov length scale, which, in our case, is much larger than the bubble diameter. On that scale, the bubbles are treated as a continuum ͑without molecular diffusivity͒ characterized by the bubble phase velocity field and concentration ͑volume fraction͒. The bubble concentration, C, is assumed small enough (Cр10 Ϫ3) to neglect the bubble-bubble interactions. As a test case, direct simulation of a bubble-laden Taylor-Green vortex with one-way coupling is performed with a bubble response time of the order of the flow time scale ͑inverse of the mean vorticity͒. This simple flow allows a direct examination of the effects of the preferential accumulation of bubbles in the high-enstrophy regions of the flow on the accuracy of the two-fluid formulation. The temporal development of the maximum bubble concentration obtained from DNS agrees well with the analytical solution. DNS of the bubble-laden decaying turbulence are also performed for both cases of one-way and two-way coupling. Here, the bubble diameter and response time are much smaller than the Kolmogorov length and time scales, respectively. In this case, as expected, the effects of the preferential accumulation of the bubbles are not pronounced. The results also show that the bubble-laden flow is analogous to a stratified flow with an effective density ϭ(1ϪC) f. Thus, due to the two-way interaction between the bubbles and carrier flow, the turbulence decay is enhanced with stable stratification, and reduced with unstable stratification.
The effect of bubbles on developed turbulence
Journal of Fluid Mechanics, 2005
Hot-film anemometry measurements are performed in a fully developed turbulent bubbly flow. For the bubble detection in the signal, both a threshold method and a new pattern recognition algorithm are employed. The measurements are carried out with gas fractions up to 3 % and a mean water velocity of 0.20 m s −1 , corresponding to a Reynolds number of about 9 × 10 4 . The typical bubble radius is 1-2 mm, corresponding to 10-20 Kolmogorov length scales. In this regime, a 'bubblance' parameter b which compares the kinetic energy originating from the rising bubbles with that of the turbulence fluctuations is smaller than 1. Probability distribution functions, structure functions (with and without the extended self-similarity (ESS) method), and spectra of the water velocity time series are calculated. Both our results for the turbulent energy spectra and the second-order structure functions show qualitative agreement with numerical results by Massitelli, Lohse & Toschi (Phys. Fluids, vol. 15 (2003), p. L5), i.e. a more pronounced energy enhancement on small scales than on large scales owing to the presence of bubbles, leading to a less steep slope in the spectrum as compared to the Kolmogorov −5/3 law. These results are robust, i.e. do not depend on details of the bubble detection scheme.
Bubble Induced Turbulence in Bubble Plumes
In bubbly flow, bubbles and the surrounding fluid interact through both force and turbulence coupling. The effects of flow turbulence on bubble trajectory are reflected in turbulent dispersion. Bubbles will introduce extra turbulence into the fluid through wake effects (so-called pseudo turbulence). The single phase k-epsilon model does not incorporate the bubble-induced turbulence [1]. This study aimed to develop and implement a model to account for these effects. The gas-stirred-ladle experiments of [10] and [1] were employed for validation. The model framework combines a volume of fluid (VOF) and discrete phase model (DPM). VOF is used to capture the fountain shape formed by the bubble plume reaching the surface, while DPM is a parcel-based Lagrangian approach to track bubbles.
Direct Numerical Simulations of Bubbly Flows
Fluid Mechanics and Its Applications
Direct numerical simulations (DNS) of multi-fluid and multiphase flows have progressed enormously over the last decade or two. It is, in particular, now possible to simulate the evolution of hundreds of bubbles in laminar and turbulent flows for a long enough time so that meaningful statistical quantities can be collected. For bubbly flow in vertical channels DNS have provided considerable new insight into the structure of the flow and how it can be modeled. The flow structure depends sensitively on the sign of the lift force on the bubbles. For nearly spherical bubbles in both upflow and downflow the lateral migration of bubbles results in a core region where the weight of the mixture exactly balances the imposed pressure gradient. For upflow bubbles accumulate at the wall but for downflow the region next to the wall is free of bubbles. The results lead to a very simple model of the void fraction distribution and, for downflow the velocity and the flow rate can be predicted relatively accurately. Deformable bubbles result in a very different flow structure, with no bubbles accumulating at the wall. Simulations of the transient motion show that it takes a long time for the flow to reach a steady state and that the evolution is complex, with bubbles moving in and out of the wall-layer. The availability of DNS results calls for more intense efforts to use the data for developing closure terms for models of the average and large-scale flows, as well as the development of efficient and accurate methods for more complex flows, such as those undergoing topology changes and involving additional physical effects like surfactants and heat and mass transfer.
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.