Session J02: Focus Session: Turbulence Modeling in Bubble- and Particle-Laden Multiphase Flows

Particles and fibres in homogeneous isotropic turbulence

We investigate how spheres and fibers of finite size can modify a homogeneous, isotropic turbulent flow. A decrease in the micro-scale Reynolds number characterizes the bulk effect that is produced by both spheres and fibers. A spectrum examination of the flows reveals how fundamentally different the multiscale effects of the two suspensions are. For spheres, the flow is altered at scales comparable to its diameter, while at smaller scales there is little change in the flow, and the canonical turbulent energy cascade is recovered. For fibers, modulation spans a much greater range of length-scales, from its length to its thickness, and a new turbulent kinetic energy scaling is found.   

On the turbophoresis of small inertial particles and implications for particle-laden wall-modeled large-eddy simulations

In a turbulent shear flows, gradients in turbulence intensity drive a net migration of small, heavy inertial particles toward regions of lower turbulence intensity. This phenomenon, known as turbophoresis, causes particles to preferentially accumulate in the near-wall region of wall-bounded turbulent flows. Simulating high Reynolds number wall-bounded flows requires an approach that does not resolve near-wall dynamics, such as wall-modeled large-eddy simulations (WMLES). At first glance, WMLES may seem ill-suited for accurately simulating turbophoresis, given that coherent structures in the viscous and buffer layers are completely unresolved. In this talk, I will examine the role of near-wall coherent structures on particle transport and demonstrate effect of Stokes number on WMLES of particle-laden flows. The biased sampling of low-speed streaks is very important for low and moderate Stokes numbers (based on wall friction units) but may be neglected for higher Stokes numbers. This means that accurate prediction of particle concentration profiles with WMLES is significantly easier at higher Stokes numbers. At low Stokes numbers, models for the fluid velocity seen by the particles must account for the complex spatio-temporal coherence of near-wall fluctuations.   

Physics Informed Stochastic Model for the Residence of Solid Particles in Turbulent Rayleigh-Benard Flow

The Pi Chamber, located at Michigan Technological University, generates moist turbulent Rayleigh-

Benard flow in order to generate steady-state cloud conditions. We take inspiration from this setup in

order to create a particle-laden, convectively-driven turbulent environment. The use of direct numerical

simulation (DNS) coupled with Lagrangian particles allows us to track individual droplet trajectories and

record Lagrangian statistics throughout their lifetimes. In particular, we are interested in developing a

meaningful framework to describe the behavior of solid, isothermal particles. This conceptual stochastic

model takes advantage of the repeated trips particles take between the top and bottom boundaries, driven

by the convective cells naturally occurring in Rayleigh-Benard turbulence. By describing the time required

to complete one of these trips, as well as the likelihood of falling out to the bottom boundary after each

trip, we can create a conceptual picture for particle behavior. We investigate varying Stokes numbers and

settling velocities in order to shed light on the independent roles that gravity and inertia play in governing

particle behavior.   

Direct numerical simulations of bubble-mediated gas transfer and dissolution in the quiescent and turbulent flow

Mass transfer of gases at the ocean-atmosphere interface is significantly enhanced by air entrainment by breaking waves. The bubbles formed are subjected to highly turbulent flow are critical to the mass transfer of gases as the molecular diffusivity of atmospheric gases is very low (Sc ≈ 600). We develop a numerical method for gas transfer in two-phase flows, including volume change effects. We investigate the bubble rising in quiescent flow and suspended in homogeneous and isotropic turbulent (HIT) flow. We show the dissolution of a single component bubble rising in quiescent flow can be described by the classic Levich formula (Levich, 1962). We show that for the bubble suspended in homogeneous and isotropic turbulent (HIT) flow, the mass transfer coefficient k_L is governed by the smallest scales in the flow, the Kolmogorov η and Batchelor η_B microscales, and is independent from the bubble size. We present a model for mass transfer coefficient as a function of Reynolds and Schmidt numbers and is verified in the range of 50 < Pe < 5 x 10⁴.

    

Effect of Size Distribution on Turbulence Induced by Inertial Particles

The mechanisms of multiphase turbulence remain unclear, despite the efforts yielding light upon its singular nature. Multiphase flows defy the postulates of classic Richardson-Kolmogorov turbulence and exhibit peculiar features, the most well-known of which is the -3 spectral slope. Of particular interest are multiphase dispersed flows, where particles (the term ‘particle’ herein is used in a wide sense) disrupt the natural evolution of vortex shedding within the fluid matrix whereas the production of turbulent kinetic energy at the particles’ scale might be significant.

 

This work investigates the effect of particle size on the turbulence signature produced by a swarm of spherical inertial particles falling subjected to their own weight within an initially quiescent fluid. To this effect, Direct Numerical Simulations are performed using an in-house Finite-Differences Navier-Stokes solver. Monodispersed and polydispersed distributions of different characteristic sizes will be compared to determine the effect of size on the turbulent kinetic energy production and the energy transfer among scales. Special attention is paid to the comparison of the spectral energy distribution across the different scales, wake-to-wake interaction and the probability density functions of second-order statistics.   

Direct-numerical simulation of droplet breakup in homogeneous isotropic turbulence

We investigate the break-up of an immiscible liquid droplet in homogeneous isotropic turbulence of a continuous liquid. We perform direct-numerical simulations with the Basilisk software (Popinet, 2022), following the approach developed for bubble break-up in Riviere et al 2021 and leveraging an adaptive mesh resolution. A spherical droplet of diameter is placed in fully developed HIT for fixed Taylor-scale Reynolds number and followed until break-up. The Taylor-scale Reynolds number is varied from 40 to 150. A systematic investigation varying the Weber number (comparing inertial and surface tension effects, from 1 to 20), Ohnesorge number (comparing viscous and surface tension effects, from 0.1 to 10) and viscosity ratio (from 0.01 to 200) is carried out. We discuss the map of break-up existence, break-up time/frequency, mode of break-up and child size distribution as a function of the controlling non-dimensional number.

 

Popinet, Stephane & collaborators 2013–2022 Basilisk. http://basilisk.fr.

A. Riviere, W. Mostert, S. Perrard and L. Deike (2021). Sub-Hinze scale bubble production in turbulent bubble break-up. Journal of Fluid Mechanics. 917, A40.

    

Author not Attending

We experimentally explore the surfactant effect on bubble-induced turbulence (BIT) at different scales. To this end, high-resolution Particle Shadow Velocimetry measurements are carried out in a bubble column in which the flow is generated by a homogeneous distributed bubble swarm rising in water for two different bubble diameters (3 mm & 4 mm) and moderate gas volume fractions. To contaminate the flow, different amounts of 1-Pentanol were added to the bubble column, leading to different bubble shapes and surface boundary conditions. Concerning the surfactant effect on the flow kinetic energy at different scales, the velocity structure functions are found to be influenced differently in the vertical and horizontal directions of the flow. Furthermore, we considered the issue of modeling BIT with respect of surfactant effect. The experimental results reveal that with increasing concentration of surfactants, the generated BIT increases as well, although the bubbles rise slower. We show that this phenomenon has not be considered so far in the standard BIT modeling using the ansatz with a source term, reading C_IF_D·u_r added to the transport equation of turbulent kinetic energy. Here, C_I, F_D and u_r are a coefficient, drag and slip velocity, respectively.   

Dynamics of floating two-dimensional bubbles rafts

Turbulent liquid jets impacting a liquid surface can entrain air and push bubbles underneath the liquid. The entrained air eventually rises to the free surface and may either form a collective "raft" of bubbles, or remain as isolated islands of bubbles. The stability and structure of these bubble rafts are determined by the turbulence and the surface tension of the air-water interface. Here we explore the statistical behavior of 2D bubbles rafts formed by an impinging jet, and the gravity-capillary waves emanating from the intermittent coalescence and bursting of the bubbles. We characterise the raft in terms of it's average radius, the radial distribution function, and the trajectories of the individual bubbles using particle tracking methods. We observe swarm-like collective dynamics for this passive particle-laden system, wherein cheerios-like capillary forces clump the bubbles together, while the turbulence and the background advective flow field pull the bubble raft apart. Simultaneously, we reconstruct the gravity-capillary waves generated on the free surface and the share insights into the audio spectrum.   

Multi-phase Turbulent Rayleigh–Bénard convection with Bubbles

We report a direct numerical simulation of multiphase turbulent Rayleigh–Bénard convection to investigate the heat transfer mechanism and flow modulations. The numerical simulations are performed in a three-dimensional domain at Prandtl number Pr = 4 (water), Rayleigh number 10⁸ ≤ Ra ≤10⁹, and Weber number We = 6000. We recently found that when non-colloidal, rigid spherical particles are present in this flow, the heat transfer rate is enhanced. However, beyond a threshold particle volume fraction value, the Nusselt number exhibits a substantial drop due to the dense particle layering in the near-wall region which results in reducing the convection in that region and prevents the formation of any coherent structures within one particle diameter from the wall. In this work, by considering bubbles (as the secondary phase) inside the fluid flow, we aim to investigate the effects of deformability of the secondary phase on the heat transfer rate. For this purpose, a parametric study of the effects of bubble volume fraction (0 < α < 0.4) and the dynamic viscosity ratio (0.01 < µ_d /µ_c < 100) is performed and the results presented in details.

    

Multiscale influences of particles in high-Re wall turbulence

The two-way coupling between inertial particles and wall-bounded turbulence has been the subject of decades of theoretical, experimental, and numerical research, and has analyzed phenomena including coherent structure modulation, particle clustering, and turbophoresis. For the many studies using DNS, however, flow Reynolds numbers have been generally small (friction Reynolds numbers less than, say, 300), falling well beneath the onset of asymptotic outer scale behavior (friction Reynolds numbers around 1000). In this study, we use DNS up to friction Reynolds numbers of 5200 coupled with Lagrangian point particles to focus on particle-turbulence interaction in the context of high-Reynolds number wall turbulence. The goal is to better understand initial particle behavior in the presence of a significant range of flow scales. Multiple mechanisms of particle modulation of the turbulent flow are found, where even small particle Stokes numbers can influence outer-scale motions by modulating inner-scale motions and regeneration cycles, and in all cases, the influence of the particles is broadband, meaning that the entire range of flow scales feels the influence of particles whose size are smaller than the Kolmogorov scales.   

A new closure for PDF-based transport equations for inertial particles in turbulent boundary layers

Transport equations for inertial particles in turbulent boundary layers may be derived from an underlying phase-space, probability density function (PDF) equation. However, these equations are unclosed, and the standard closure approach is to use a quasi-Normal approximation (QNA) in which the fourth moments are approximated as behaving as if the velocities were Normally distributed. Except for particles with weak inertia, the QNA leads to large quantitative errors, and is not consistent with the asymptotic predictions of Sikovsky (Flow, Turb. and Comb. 92, 2014) for the moments of the PDF in the viscous sublayer. We derive a new closure approximation based on an asymptotic solution to the transport equations in regions where the effect of particle inertia is significant. The new closure is consistent with the asymptotic predictions of Sikovsky, but is valid even outside the viscous sublayer, and captures the strong non-Gaussianity of the particle velocities. Comparisons with DNS show that the new closure performs much better than the QNA, and while the predictions leave room for improvement, the results suggest that this new closure approach is promising.

    

Author not Attending

Turbulent multiphase flows are ubiquitous in nature and engineering applications. Examples include air bubbles in the ocean, dispersed pollutants in atmosphere, waterfall mists and bubble columns in process technology. In all these flows,there exists a complex interaction between the dispersed particle phase and the carrier phase triggering modification of the underlying turbulence. In this work, we investigate the modulation of homogeneous turbulence in buoyancy driven bubbly flows. To this end, we use Direct Numerical Simulation (DNS) to study rising bubbles in a two-fluid system (5 % volume fraction of the dispersed phase) with density and viscosity ratio of the carrier phase to the dispersed phase equal to 100. In our study, spherical bubbles are initially randomly distributed in the turbulent flow, the Volume of Fluid method is exploited to capture the complex feature of the liquid-gas interface, and the energy is injected at large scales using the Arnold-Beltrami-Childress (ABC) forcing to sustain the background turbulence. In the present work, we examine the effect of gravity on turbulence modulation in terms of global quantities, energy spectra, fluctuating velocity correlation and scale by scale (SBS) energy budgets. The results show that by increasing Galilei number (ratio of buoyancy to viscous force) larger bubbles rise faster due to the buoyancy force, resulting in anisotropic flow behavior, an increase of the energy content at small scales, and also augmentation of bubble break ups and consequently total interface area when increasing the ratio between bubble rising velocity and turbulence fluctuations.