LES of bubble dynamics in wake flows

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.

Journal of Fluid Mechanics, 2002

Direct numerical simulations of the motion of up to 216 three-dimensional buoyant bubbles in periodic domains are presented. The full Navier-Stokes equations are solved by a parallelized finite-difference/front-tracking method that allows a deformable interface between the bubbles and the suspending fluid and the inclusion of surface tension. The governing parameters are selected such that the average rise Reynolds number is about 12-30, depending on the void fraction; deformations of the bubbles are small. Although the motion of the individual bubbles is unsteady, the simulations are carried out for a sufficient time that the average behaviour of the system is well defined. Simulations with different numbers of bubbles are used to explore the dependence of the statistical quantities on the size of the system. Examination of the microstructure of the bubbles reveals that the bubbles are dispersed approximately homogeneously through the flow field and that pairs of bubbles tend to align horizontally. The dependence of the statistical properties of the flow on the void fraction is analysed. The dispersion of the bubbles and the fluctuation characteristics, or 'pseudo-turbulence', of the liquid phase are examined in Part 2.

Journal of Fluid Mechanics, 2003

Microbubble-laden homogeneous and isotropic turbulent flow is investigated by using direct numerical simulation of the three-dimensional Navier-Stokes equations and computing the bubble trajectories with Lagrangian tracking. The bubble motion is calculated by taking into account the effect of fluid acceleration plus added mass, drag, gravity, and in particular the lift force, which had been neglected in many previous simulations. By comparing the results from simulations with and without lift, we find the effect of the lift force to be crucial: for passive bubbles, i.e. bubbles without backreaction on the flow (one-way coupling), the lift enhances the accumulation of bubbles on the downward flow side of vortices, resulting in a considerably reduced rise velocity of bubbles in turbulent flow, compared to still water. This also has consequences for the active bubble case, i.e. for bubbles with backreaction on the flow (two-way coupling): the energy spectrum of the turbulence is modified non-uniformly. Because of the combined effect of preferential bubble clustering in downflow zones and the local buoyant transfer, which reduces the vertical fluid velocity fluctuations, large-scale motions (small wavenumbers k) are suppressed. In contrast, small-scale motions (large wavenumbers k) are enhanced due to the local bubble forcing. The net effect turns out to be a reduction of the energy dissipation rate.

International Journal of Multiphase Flow, 2016

An experimental investigation is reported for the flow structures in the wake of an air bubble sliding under an inclined surface in quiescent water. Time-resolved particle image velocimetry (PIV) is used to study the wakes of sliding bubbles for a range of measurement planes, bubble diameters and surface inclination angles. Additionally, key aspects of the bubble's motion are measured simultaneously using a novel method that accounts for the motion of the bubble's interface. Thus, vortex shedding may be linked to changes in the bubble shape and path. Analysis of the measured velocity and vorticity fields reveals a wake structure consisting of a near wake that moves in close proximity to the bubble, shedding vorticity at the inversion points of the bubble path. Downstream of the bubble in the far wake, these structures evolve into asymmetrical, oppositelyoriented hairpin vortices that are generated in the near wake. These hairpin vortices bear similarities to those observed behind freely rising bubbles and near-wall bluff bodies and are found to cause significant motion of the bulk fluid. This bulk fluid motion has the potential to offer significant convective cooling of adjacent heated surfaces, such as submerged electronics components.

Physical Review Fluids

International Journal of Multiphase Flow, 2013

Prediction of the bubble size distribution in the wake of a ship is important to analyze its acoustic signature. To achieve CFD simulation of dynamic ships with moving control surfaces and rotating propellers in waves, a robust implementation is paramount. In this work a mass conserving multigroup discretization strategy of the Boltzmann transport equation for polydispersed bubbly flows is presented, as well as an analysis of available breakup and coalescence models. Modifications of the discrete equations for the fixed pivot method at the boundaries are introduced that guarantee exact bubble mass conservation. The role of the time stepping scheme in the conservation of mass and number of bubbles is discussed. Though the conservation properties of the discrete system of equations are satisfied provided they are solved exactly, in practice an iterative procedure must be used since the ODE's are non-linear. Three iterative schemes are proposed and they are analyzed in terms of robustness and efficiency. Breakup, coalescence and dissolution models are analyzed from the numerical point of view. Available models of breakup and coalescence are studied finding appropriate choices for ship applications. Other models are appropriate as well, but are more costly numerically. As appropriate for ship applications, an extension to the model of Prince and Blanch for salt water is proposed and analyzed. The final model is tested against experimental data and computations by other researchers, and convergence properties in bubble size discretization is studied. It is found that for salt water the final steady state is dependent on the initial condition since there is a range of sizes for which coalescence and breakup are both negligible.

Chemical Engineering Science, 2021

h i g h l i g h t s An enhanced turbulence model has been developed and validated, which is generally applicable to bubble plumes. The model accounts for the extra turbulence agitation introduced by bubble wakes. The model also considers the turbulence modulations due to bubble-induced stratification and free surface damping effects. The implications of each physical process in turbulence modelling are investigated.

2015

Two-phase bubbly flows are widely applied in engineering and environmental processes. The interaction of the dispersed phase with the continuous phase has a great effect on transfer processes between the phases. The interstitial relative velocities between the phases and the interfacial area and the shape of the dispersed phase are the key dependent parameters in the drag, heat and mass transfer between the phases. Although the physical understanding of bubbles rise in a liquid is a significant practical importance in many areas of engineering, neither the interactions between bubbles in clusters nor the bubble-induced pseudo-turbulence (i.e., the generation of velocity fluctuations by bubbles and their wakes in a laminar flow) are fully understood. The modeling of bubbly flows with the Computational Fluid Dynamics (CFD) codes requires detailed information about the full field velocity close to the bubble and its wake. Such information is not widely available. Experimental data exis...

Chemical Engineering Science, 2008

Gas-liquid bubbly flow in a flat bubble column ("Becker" case with a gas flow rate of 1.6 l/min) is studied by means of large-eddy simulation (LES) combined with Lagrangian particle tracking with two-way coupling. The unsteady two-phase flow considered is relatively dilute in a global sense, but has higher gas clustering locally. The bubble size, of the order of millimeter, is relatively large compared to the smallest liquid fluctuation scales. It is demonstrated that, in such a setting, a single-phase LES along with the point-volume treatment of the dispersed phase can serve as a viable closure model, even though its application assumptions are not fully met. For the backward momentum coupling we used a "particle-source-in-ball" (PSI-ball) concept, which in essence is a generalization of the conventional particle-source-in-cell (PSI-cell) method as well as template-function based treatment. A high prediction accuracy is achieved in an extensive comparison with classical experimental data, covering not only the mean feature of the flow and transient bubble dispersion patterns, but also the second-order statistics of the liquid which is vital in assessing a closure model and has not been enough addressed in the past RANS-based studies. ᭧

Physics of Fluids, 2007

The dynamics and dispersion of small air bubbles in isotropic turbulence are analyzed computationally. The flow field is simulated using a pseudo-spectral code, while the bubble dynamics are analyzed by integration of a Lagrangian equation of motion that accounts for buoyancy, added mass, pressure, drag, and lift forces. Probability density functions (pdfs) of bubble velocities, lift and drag forces, and of field velocities and vorticities along bubble trajectories are used to analyze bubble dynamics. Lagrangian bubble trajectories are also employed to determine dispersion characteristics, following the theoretical development of Cushman and Moroni . Consistent with available experimental data, bubble rise velocities are increasingly suppressed with increasing turbulence intensity. The analysis also reveals that the vertical bubble velocities are characterized by asymmetric pdfs that are positive or negative-skewed dependent upon the non-dimensional turbulence intensity and the Taylor length scale. The role of the lift force in moving the bubbles to the down-flow side of turbulent eddies, and consequently retarding their rise, is consistently observed in all analysis. The dispersion of 40 µm bubbles and transition to Fickian behavior is shown to be weakly affected by the turbulence level. Larger, 400 µm bubbles are shown to be more sensitive to turbulence level with transition to Fickian behavior delayed in low turbulence fields.