Direct Numerical Simulation of Turbulent Flows Laden with Droplets or Bubbles

Elghobashi, S.

doi:10.1146/annurev-fluid-010518-040401

Cited by 214 publications

(139 citation statements)

References 94 publications

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“…However, in smaller, finite systems (as prevalent in turbulence resolving droplet laden simulations (Elghobashi 2019)), this can be an important consideration, as the "steady state" can have its own interesting dynamics. These considerations of delayed temporal dynamics may also be relevant to developing more realistic breakup and coalescence kernels which currently correlate state-space variables instantaneously (Sajjadi et al 2013), which we have not explored given the limits of the current work.…”

Section: Discussionmentioning

confidence: 99%

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Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

Mukherjee

Safdari²,

Shardt³

et al. 2019

J. Fluid Mech.

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We perform direct numerical simulations (DNSs) of emulsions in homogeneous, isotropic turbulence using a pseudopotential lattice-Boltzmann (PP-LB) method. Improving on previous literature by minimizing droplet dissolution and spurious currents, we show that the PP-LB technique is capable of long, stable simulations in certain parameter regions. Varying the dispersed phase volume fraction φ, we demonstrate that droplet breakup extracts kinetic energy from the larger scales while injecting energy into the smaller scales, increasingly with higher φ, with the Hinze scale dividing the two effects. Droplet size (d) distribution was found to follow the d −10/3 scaling (Deane & Stokes 2002). We show the need to maintain a separation of the turbulence forcing scale and domain size to prevent the formation of large connected regions of the dispersed phase. For the first time, we show that turbulent emulsions evolve into a quasi-equilibrium cycle of alternating coalescence and breakup dominated processes. Studying the system in its state-space comprising kinetic energy E k , enstrophy ω 2 and the droplet number density N d , we find that their dynamics resemble limit-cycles with a time delay. Extreme values in the evolution of E k manifest in the evolution of ω 2 and N d with a delay of ∼ 0.3T and ∼ 0.9T respectively (with T the large eddy timescale). Lastly, we also show that flow topology of turbulence in an emulsion is significantly more different than singlephase turbulence than previously thought. In particular, vortex compression and axial straining mechanisms become dominant in the droplet phase, a consequence of the elastic behaviour of droplet interfaces.

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Section: Discussionmentioning

confidence: 99%

“…We try to maintain such a separation of scales in the study, except that we have ζ > η. Lastly, having η > d would mean sub-Kolmogorov droplets. These droplets can also deform and breakup due to the action of viscous stresses instead of inertial stresses (Elghobashi 2019).…”

Section: Length Scalesmentioning

confidence: 99%

Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

Mukherjee

Safdari²,

Shardt³

et al. 2019

J. Fluid Mech.

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“…Interface-resolved simulations of two-fluid flows are often divided into two 15 categories according to the interface representation [3]: (1) Interface-tracking (or front-tracking) methods explicitly define a mesh with Lagrangian markers, attached to and moving with the interface; (2) interface-capturing methods define the interface in a higher dimension by solving a transport equation for an auxiliary scalar field. Front-tracking methods [4] allow in general for a more accurate 20 interface representation, at the cost of more complex implementations, specially when it comes to handling surface topology changes.…”

Section: Introductionmentioning

confidence: 99%

A volume-of-fluid method for interface-resolved simulations of phase-changing two-fluid flows

Scapin

Costa

Brandt

2020

Journal of Computational Physics

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We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an algebraic VoF method for the interface representation, and extended with the transport equations of thermal energy and vaporized liquid mass for the single-component evaporating liquid in an inert gas. The conservation of vaporizing liquid and computation of the interfacial mass flux are performed with the aid of a reconstructed signed-distance field, which enables the use of well-established methods for phase change solvers based on level-set methods.The interface velocity is computed with a novel approach that ensures accurate mass conservation, by constructing a divergence-free extension of the liquid velocity field onto the entire domain. The resulting approach does not depend on the type of interface reconstruction (i.e. can be employed in both algebraic and geometrical VoF methods). We extensively verified and validated the overall method against several benchmark cases, and demonstrated its excellent mass conservation and good overall performance for simulating evaporating two-fluid flows in two and three dimensions. mechanisms drives phase change: (1) large temperatures, when phase change is triggered by a prescribed interface saturation temperature -boiling, and (2) 30 species concentration gradients near the interface, with phase change induced by a prescribed non-uniform interface concentration -evaporation. Front-tracking (FT) methods have been used to study boiling flows, with application to film boiling; see e.g. [9], [10] and [11]. Recent studies have extended this framework to evaporating two-fluid flows in two dimensions [12], 35 also in presence of chemical reactions [13]. Despite the successes of FT methods for phase change, highly scalable parallel implementations are challenging and remain scarce [14]. Such a feature is crucial for simulating e.g. turbulent gasliquid flows, which may require massive simulations with O(10 8 − 10 9 ) Eulerian grid cells [15]. 40As regards interface-capturing methods, the first study of interface-resolved simulations of phase change two-fluid flows used a level-set method, applied to film boiling [16]. Several studies have followed, aiming to incorporate interphasecoupling jump conditions with the so-called ghost-fluid method, which provides a sharp representation of the jump at the discrete level. These methods have 45 been employed for boiling [17,18,19], evaporation [20] and the combination of the two [21]. Despite the proven successes of the level-set methods for phase change problems, these are not mass-preserving by construction. Machineprecision mass conservation is desirable for numerical simulations of several systems, e.g. in multiphase turbulent flows, where the flow statistics should be 50 collected over periods of time long enough that mass loss becomes significant.Recent studies have dealt with this problem of lev...

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“…This is in contrast to a natural forcing mechanism that produces turbulent kinetic energy from finite Reynolds stresses interacting with a mean velocity gradient. While forcing homogeneous isotropic turbulence may be appropriate for studying the droplet size distributions, it has been argued that artificial forcing is inappropriate for studying two-way coupling effects (Elghobashi 2019). Therefore, for studying the turbulent kinetic energy budget, either decaying isotropic turbulence or turbulent shear flow might be preferable.…”

Section: Introductionmentioning

confidence: 99%

Droplets in homogeneous shear turbulence

Rosti

Jain

et al. 2019

J. Fluid Mech.

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We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady state conditions exhibit reduced Taylor microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small-scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplets size distribution which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering breakup in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear. † Email address for correspondence: merosti@mech.kth.se arXiv:1902.05259v2 [physics.flu-dyn]

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Direct Numerical Simulation of Turbulent Flows Laden with Droplets or Bubbles

Cited by 214 publications

References 94 publications

Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

Droplet–turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions

A volume-of-fluid method for interface-resolved simulations of phase-changing two-fluid flows

Droplets in homogeneous shear turbulence

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