Effects of power-law entrainment on bubble fragmentation cascades

Gaylo, Declan B.; Hendrickson, Kelli; Yue, Dick K. P.

doi:10.1017/jfm.2021.333

Cited by 8 publications

(16 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that our simulations stop at the end of the active breaking period, and as such do not describe the late-time plume evolution and steepening of the bubble size distribution, which evolves due to both degassing and further breakup, as discussed by Deane & Stokes (2002), Deike et al. (2016) and Gaylo, Hendrickson & Yue (2021). For , where the numerical resolution is sufficient to allow for a discussion of the sub-Hinze scale bubbles, we observe a scaling compatible with the experimental data set from Deane & Stokes (2002), .…”

Section: Air Entrainment and Bubble Statisticsmentioning

confidence: 94%

“…For all cases, within this range, the size distributions have developed a shape that is clearly less steep than the super-Hinze results, close to the r −3/2 scaling, but the transition between the two regimes is not as sharp as observed in the experimental data. Note that our simulations stop at the end of the active breaking period, and as such do not describe the late-time plume evolution and steepening of the bubble size distribution, which evolves due to both degassing and further breakup, as discussed by Deane & Stokes (2002), Deike et al (2016) and Gaylo, Hendrickson & Yue (2021). For Bo = 200, where the numerical resolution is sufficient to allow for a discussion of the sub-Hinze scale bubbles, we observe a scaling compatible with the experimental data set from Deane & Stokes (2002), N(r/r H ) ∝ (r/r H ) −3/2 .…”

Section: Bubble Size Distribution Over the Active Breaking Time: Comp...mentioning

confidence: 98%

See 1 more Smart Citation

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

2022

View full text Add to dashboard Cite

We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number (Re, wave inertia relative to viscous effects) and Bond number (Bo, wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo, and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value $Re_\lambda \sim 100$ , consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. (J. Fluid Mech., vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale, $r_H$ . We confirm two regimes in the bubble size distribution, $N(r/r_H)\propto (r/r_H)^{-10/3}$ for $r>r_H$ , and $\propto (r/r_H)^{-3/2}$ for $r<r_H$ . Bubbles are resolved up to one order of magnitude below $r_H$ , and we observe a good collapse of the numerical data compared to laboratory breaking waves (Deane & Stokes, Nature, vol. 418 (6900), 2002, pp. 839–844). We resolve droplet statistics at high Bo in good agreement with recent experiments (Erinin et al., Geophys. Res. Lett., vol. 46 (14), 2019, pp. 8244–8251), with a distribution shape close to $N_d(r_d)\propto r_d^{-2}$ . The evolution of the droplet statistics appears controlled by the details of the impact process and subsequent splash-up. We discuss velocity distributions for the droplets, finding ejection velocities up to four times the phase speed of the wave, which are produced during the most intense splashing events of the breaking process.

show abstract

Section: Air Entrainment and Bubble Statisticsmentioning

confidence: 94%

Section: Bubble Size Distribution Over the Active Breaking Time: Comp...mentioning

confidence: 98%

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

2022

View full text Add to dashboard Cite

show abstract

“…The fragmentation model proposed in Garrett et al (2000), which leads to a -10/3 power-law scaling for the bubble size spectrum, embodies an average air supply rate or a source volume due to the entrainment process during wave breaking. The recent work of Gaylo et al (2021) defines an entrainment size distribution of bubble sources which reproduces the same -10/3 scaling for the equilibrium bulk bubble size spectra (for super-Hinze scale bubbles) via fragmentation cascading, in the weak volume injection regime. In our current study, using the CCL algorithm mentioned in the preceding section, we are able to identify the spanwise air cylinders or cavities entrained by the breaking wave during initial stages, and treat them to be the primary source volumes which undergo breakup to generate bubbles.…”

Section: Bubble Size Spectrummentioning

confidence: 80%

High-Fidelity Simulation and Novel Data Analysis of the Bubble Creation and Sound Generation Processes in Breaking Waves

Gao¹,

Deane²,

Basak³

et al. 2022

Preprint

View full text Add to dashboard Cite

Recent increases in computing power have enabled the numerical simulation of many complex flow problems that are of practical and strategic interest for naval applications. A noticeable area of advancement is the computation of turbulent, two-phase flows resulting from wave breaking and other multiphase flow processes such as cavitation that can generate underwater sound and entrain bubbles in ship wakes, among other effects. Although advanced flow solvers are sophisticated and are capable of simulating high Reynolds number flows on large numbers of grid points, challenges in data analysis remain. Specifically, there is a critical need to transform highly resolved flow fields described on fine grids at discrete time steps into physically resolved features for which the flow dynamics can be understood and utilized in naval applications. This paper presents our recent efforts in this field. In previous works, we developed a novel algorithm to track bubbles in breaking wave simulations and to interpret their dynamical behavior over time (Gao et al., 2021a). We also discovered a new physical mechanism driving bubble production within breaking wave crests (Gao et al., 2021b) and developed a model to relate bubble behaviors to underwater sound generation (Gao et al., 2021c). In this work, we applied our bubble tracking algorithm to the breaking waves simulations and investigated the bubble trajectories, bubble creation mechanisms, and bubble acoustics based on our previous works.

show abstract

“…When modelling the bubble-size distribution, the equilibrium solution () may be available, such as for PBE with only a fragmentation source term (Garrett et al. 2000) or fragmentation with power-law entrainment, where the size distribution of the bubbles injected by entrainment follows a power law (Gaylo, Hendrickson & Yue 2021). The time, , it takes to reach these equilibrium solutions is of interest: if is much less than the time scale over which the flow is transient, we expect an equilibrium fragmentation cascade (generally ) to be obtained.…”

Section: Three Fundamental Time Scales Of Fragmentationmentioning

confidence: 99%

“…Gaylo et al. (2021) provide an expression for which allows for arbitrary and , but its derivation is specific to power-law entrainment. For general fragmentation cascades, is characterised by the time it takes for the volume of the largest bubble to reach the Hinze scale (Deike et al.…”

Section: Three Fundamental Time Scales Of Fragmentationmentioning

confidence: 99%

Fundamental time scales of bubble fragmentation in homogeneous isotropic turbulence

2023

Self Cite

View full text Add to dashboard Cite

We investigate the fundamental time scales that characterise the statistics of fragmentation under homogeneous isotropic turbulence for air–water bubbly flows at moderate to large bubble Weber numbers, $We$ . We elucidate three time scales: $\tau _r$ , the characteristic age of bubbles when their subsequent statistics become stationary; $\tau _\ell$ , the expected lifetime of a bubble before further fragmentation; and $\tau _c$ , the expected time for the air within a bubble to reach the Hinze scale, radius $a_H$ , through the fragmentation cascade. The time scale $\tau _\ell$ is important to the population balance equation (PBE), $\tau _r$ is critical to evaluating the applicability of the PBE no-hysteresis assumption, and $\tau _c$ provides the characteristic time for fragmentation cascades to equilibrate. By identifying a non-dimensionalised average speed $\bar {s}$ at which air moves through the cascade, we derive $\tau _c=C_\tau \varepsilon ^{-1/3} a^{2/3} (1-(a_{max}/a_H)^{-2/3})$ , where $C_\tau =1/\bar {s}$ and $a_{max}$ is the largest bubble radius in the cascade. While $\bar {s}$ is a function of PBE fragmentation statistics, which depend on the measurement interval $T$ , $\bar {s}$ itself is independent of $T$ for $\tau _r \ll T \ll \tau _c$ . We verify the $T$ -independence of $\bar {s}$ and its direct relationship to $\tau _c$ using Monte Carlo simulations. We perform direct numerical simulations (DNS) at moderate to large bubble Weber numbers, $We$ , to measure fragmentation statistics over a range of $T$ . We establish that non-stationary effects decay exponentially with $T$ , independent of $We$ , and provide $\tau _r=C_{r} \varepsilon ^{-1/3} a^{2/3}$ with $C_{r}\approx 0.11$ . This gives $\tau _r\ll \tau _\ell$ , validating the PBE no-hysteresis assumption. From DNS, we measure $\bar {s}$ and find that for large Weber numbers ( $We>30$ ), $C_{\tau }\approx 9$ . In addition to providing $\tau _c$ , this obtains a new constraint on fragmentation models for PBE.

show abstract

Effects of power-law entrainment on bubble fragmentation cascades

Abstract: Abstract

Cited by 8 publications

References 24 publications

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production

High-Fidelity Simulation and Novel Data Analysis of the Bubble Creation and Sound Generation Processes in Breaking Waves

Fundamental time scales of bubble fragmentation in homogeneous isotropic turbulence

Contact Info

Product

Resources

About