Finite-size Bubbles Research Articles

Interpolation methods for two-way coupled Euler-Lagrange simulation of finite-size bubbles

Dispersed multiphase flow can be simulated by the Euler-Lagrange approach where the continuous phase is described on the Euler grid and the dispersed phase is treated as Lagrange points. The point-mass Euler-Lagrange method requires the bubble or particle size to be much smaller than the cell size when the interphase coupling is considered. Otherwise, numerical instabilities may arise. However, the point-mass prerequisite is hard to achieve, for example, if very fine grids are used to resolve turbulence in LES. Therefore, interpolation methods between the Euler and the Lagrange phase for finite-size bubbles which are bigger than or of the same size as numerical cells are discussed in this work. The spatially distributed coupling method is used for the Lagrange-to-Euler coupling. For the Euler-to-Lagrange coupling, a new approach is proposed and validated in different cases. Finally, a combination of coupling approaches is employed in a square bubble column reactor.

Corrective interface tracking approach to simulate finite-size bubbly flows

This work reports on the development and application of a new approach, corrective interface tracking, to simulate finite size bubbles. Finite-size bubbles, which are by definition bigger than the grid cell size but not well resolved, are not capable of being modeled with any standard two-phase flow approaches, such as interface tracking (IT), Euler-Euler (EE), or Lagrangian particle tracking (LPT). This poses a problem when simulating bubbly flows with different bubble sizes on the same computational grid. The Finite-size Lagrangian particle tracking (FSL) approach (Badreddine et al., 2015), aimed at simulating finite-size bubbly flows by inheriting features of IT and LPT approaches, simulated a single bubble with good accuracy. However, deficiencies with the FSL approach led to a newly developed approach based on interface tracking with the addition of a correcting force. The correcting force, derived from modeling the hydrodynamic forces on a bubble, attempts to correct for errors introduced when a coarse grid is used and the flow and pressure fields around the bubble are under-resolved. Therefore, as a finer grid is used the correcting force decreases. The corrective interface tracking approach is validated against a single bubble rising in stagnant and linear flow, and then results are compared to FSL and to finely resolved IT simulations.

Interaction between a large buoyant bubble and turbulence

The free rise of isolated, deformable, finite-size bubbles in otherwise homogeneous isotropic turbulence is investigated by direct numerical simulation. The Navier-Stokes equations are solved in both phases subject to the pertinent velocity and stress conditions at the deformable gas-liquid interface. The bubble rise velocity is found to be drastically reduced by turbulence, as is widely known for microbubbles. The probability distribution functions of the horizontal bubble acceleration component are well fitted by a log-normal distribution. The distributions of the vertical components are negatively skewed, a property related to the fact that bubbles experience on average stronger decelerations than accelerations. An assessment of the correlations of bubble acceleration with properties of the surrounding flow is used to define estimates of the liquid velocity and vorticity entering in liquid acceleration and lift forces. Finally, fast rising bubbles are found to preferentially sample downflow regions of the flow, whereas those subjected to a higher turbulence level have an increased residence time in swirling regions, some features similar to those of small bubbles.

Budget analysis of the turbulent kinetic energy for bubbly flow in a vertical channel

This paper analyses the turbulent kinetic energy budget for bubble swarms in a turbulent channel flow configuration with realistic density difference. The data employed result from Euler–Lagrange Direct Numerical Simulations of vertical turbulent channel flow laden with finite-size bubbles and enable the individual evaluation of each term of the budget equation. Two monodisperse swarms are addressed with the same bubble diameter but with different total void fraction. For the parameter range investigated bubbles enhance the liquid turbulence, and this is quantified in the terms of the budget. The turbulence enhancement is generated by the interfacial term which is balanced by the dissipation term in the core region. In the near-wall region, also the production term and the transport term contribute to the budget in a significant manner. Furthermore, the local turbulence modification induced by the bubbles is investigated by means of the transport equation of the local instantaneous kinetic energy and its contributions. Finally, existing closures for the modelling of the interfacial term are assessed and an improvement of these closures is proposed. The data provided may constitute a reference for model development in the framework of Euler–Euler approaches to bubbly flows.

Finite size Lagrangian particle tracking approach to simulate dispersed bubbly flows

A new method has been developed for the numerical simulation of finite size dispersed bubbly flows. Finite size bubbles are bigger than the numerical grid cell size, meaning that Lagrangian particle tracking (LPT) cannot be used, but they are yet too small to be accurately resolved by interface tracking (IT) methods. The need for such an approach arises mostly if large eddy simulation (LES) paradigm is used to resolve turbulence since it requires fine grids, and bubbles could easily cover several grid cells. The proposed method inherits features of IT and LPT, and features two-way coupling. The governing equations for the continuous phase are solved on Eulerian static grid. Bubbles are assumed to have a spherical shape, and a color function is used to monitor bubbles’ position and to update the physical properties in every grid cell same way as one does in IT. However, the color function is not updated by solving an advection equation, but is rather re-initialized at every time step by the new bubbles’ position calculated by solving Newton’s second law of motion for each bubble. A new method to calculate the undisturbed liquid velocity required to model the hydrodynamic forces is also proposed in this paper. Two methods are proposed to impose the two-way coupling (i.e. bubbles feedback on the fluid). The first approach considers the bubbles as spherical rigid particles, and bubbles’ velocities are imposed to the computational cells that lie inside the bubbles. In the second approach, a correction force is added inside each bubble to model the filtered scales due to usage of coarse grid resolution per bubble. The method is validated against terminal velocity of an air bubble rising in stagnant water to test the buoyancy and drag forces and its lateral motion in linear shear flow to check the lift force. The results are compared with simulations done with IT Constrained Interpolation Profile (CIP) method to verify the accuracy of the two-way coupling.

Energy spectra and bubble velocity distributions in pseudo-turbulence: Numerical simulations vs. experiments

Direct numerical simulations (DNS) are performed to study the behavior of a swarm of rising air bubbles in water, employing the front tracking method, which allows to handle finite-size bubbles. The swarms consist of monodisperse deformable 4 mm bubbles with a gas fraction of 5% and 15%. This paper focuses on the comparison of the liquid energy spectra and bubble velocity probability density functions (PDFs) with experimental data obtained by phase-sensitive constant-temperature anemometry (CTA) and three-dimensional particle tracking velocimetry (PTV), respectively. The numerical simulations confirm that the spectra of the velocity fluctuations driven by the rising bubbles follow a power law with slope close to −3, supporting the idea that the dissipation of the bubble wake is the origin of this spectral scaling, as previously proposed by Lance and Bataille. The computed PDFs of the bubble velocity show non-Gaussian features, as is also observed in the experiments. The agreement with experimental measurements is especially good in the peak region, whereas the tails of the experimental PDFs show more intermittency in comparison to the numerical results. This can be explained by the lack of large-scale flow structures in the simulations, and by the large difference in measurement time.

Распространение волн сжатия в пузырьковых зонах конечных размеров

Распространение волн сжатия в пузырьковых зонах конечных размеров

Распространение волн давления в пузырьковых зонах конечных размеров

Распространение волн давления в пузырьковых зонах конечных размеров

Modulation of homogeneous turbulence seeded with finite size bubbles or particles

The dynamics of homogeneous, isotropic turbulence seeded with finite sized particles or bubbles is investigated in a series of numerical simulations, using the force-coupling method for the particle phase and low wavenumber forcing of the flow to sustain the turbulence. Results are given on the modulation of the turbulence due to massless bubbles, neutrally buoyant particles and inertial particles of specific density 1.4 at volumetric concentrations of 6%. Buoyancy forces due to gravity are excluded to emphasize finite size and inertial effects for the bubbles or particles and their interactions with the turbulence. Besides observing the classical entrapment of bubbles and the expulsion of inertial particles by vortex structures, we analyze the Lagrangian statistics for the velocity and acceleration of the dispersed phase. The turbulent fluctuations are damped at mid-range wavenumbers by the bubbles or particles while the smallscale kinetic energy is significantly enhanced. Unexpectedly, the modulation of turbulence depends only slightly on the dispersion characteristics (bubble entrapment in vortices or inertial sweeping of the solid particles) but is closely related to the stresslet component (finite size effect) of the flow disturbances. The pivoting wavenumber characterizing the transition from damped to enhanced energy content is shown to vary with the size of the bubbles or particles. The spectrum for the energy transfer by the particle phase is examined and the possibility of representing this, at large scales, through an additional effective viscosity is discussed.