# Latest papers in fluid mechanics

### Development of closure relations for the motion of Taylor bubbles in vertical and inclined annular pipes using high-fidelity numerical modeling

This study analyses the flow of Taylor bubbles through vertical and inclined annular pipes using high-fidelity numerical modeling. A recently developed phase-field lattice Boltzmann method is employed for the investigation. This approach resolves the two-phase flow behavior by coupling the conservative Allen–Cahn equation to the Navier–Stokes hydrodynamics. This paper makes contributions in three fundamental areas relating to the flow of Taylor bubbles. First, the model is used to determine the relationship between the dimensionless parameters (Eötvös and Morton numbers) and the bubble rise velocity (Froude number). There currently exists no surrogate model for the rise of a Taylor bubble in an annular pipe that accounts for fluid properties. Instead, relations generally include the diameter of the outer and inner pipes only. This study covered Eötvös numbers between 10 and 700 and Morton numbers between 10−6 and 100. As such, the proposed correlation is applicable to concentric annular pipes within this range of parameters. An assessment of the correlation to parameters outside of this range was made; however, this was not the primary scope for the investigation. Following this, the effect of pipe inclination was introduced with the impact on rise velocity measured. A correlation between the inclination angle and the rise velocity was proposed and its performance quantified against the limited experimental data available. Finally, the high-fidelity numerical results were analyzed to provide key insights into the physical mechanisms associated with annular Taylor bubbles and the shape they form. To extend this work, future studies on the effect of pipe eccentricity, diameter ratios, and pipe fittings (e.g., elbows and risers) on the flow of Taylor bubbles will be conducted.

### Effects of magnetization relaxation in ferrofluid film flows under a uniform magnetic field

We analyze the magnetization relaxation effects of a ferrofluid film flow governed by the ferrohydrodynamics encompassing the Fokker–Planck magnetization equation in a Couette–Poiseuille configuration subject to an applied uniform stationary magnetic field perpendicular to the boundaries. A solver based on OpenFOAM is programmed to find solutions numerically for the velocity, spin velocity, and magnetization in ferrofluid films under the combined pressure gradient, boundary flow, and magnetic field forcing. The solver is validated by comparison with the classical Couette–Poiseuille flows and the analytic solutions of the magnetization relaxation problem when the product of flow vorticity and relaxation time is much smaller than unit, [math]. We compare the effects of magnetization relaxation obtained from the phenomenological magnetization equation with those from the equation derived microscopically. The results obtained from the former equation are not suitable for the description of ferrofluid film flows. Due to the magnetization relaxation effects, a misalignment between the local magnetization and the local magnetic field is observed. The net effects are that the flow is hampered by magnetic fields and it manifests as diminished slopes of vorticity profiles and reduced volumetric flow rates. The magnetization relaxation effects also slow down the spin velocity of particles or change their direction, which leads to an enhanced effective viscosity. The total tangential stress exerted on the moving boundary is higher than that of the classical Couette–Poiseuille flow owing to the addition of a magnetic stress. The magnetization relaxation effect is more significant in cases of ferrofluids with higher relaxation times.

### Electro-drop bouncing in low-gravity

We investigate the dynamics of spontaneous jumps of water drops from electrically charged nonwetting dielectric substrates during sudden step reductions in the gravity level. In the free-fall environment of a drop tower, the dynamics of drops subject to external electric fields are dominated by the Coulombic force instead of gravity. These forces lead to a drop bouncing behavior similar to well-known terrestrial phenomena though occurring for much larger drops (∼0.5 ml). We provide a one-dimensional model for the phenomenon, its scaling, and asymptotic estimates for drop time-of-flight in two regimes: at short-times close to the substrate when drop inertia balances the Coulombic force due to net free charge and image charges in the dielectric substrate, and at long-times far from the substrate when drop inertia balances free charge Coulombic force and drag. In both regimes, the dimensionless electrostatic Euler number [math], which is a ratio of inertia to electrostatic force, appears as a key parameter.

### Statistical theory of helical turbulence

A statistical theory for homogeneous helical turbulence is developed under the condition of strong symmetry. The latter describes reflectional symmetry in planes through and normal to the helical unit vector eξ, which can be achieved by demanding that the mean velocity is zero. The two-point velocity correlation, the pressure–velocity correlation, and the two-point triple correlation are expressed by scalar functions in the helical unit vector system. By introducing the continuity equation for the correlations, the number of unknown functions can be reduced to such an extent that ultimately, a single scalar transport equation remains. Furthermore, a two-point Poisson equation is derived to express the pressure–velocity correlation in terms of the triple correlation. From the two-point version of the transport equation, the single-point limit is derived. Using the single-point equation, it can be shown that all velocity components are generally non-zero. Therefore, it is concluded that the phenomenon of vortex stretching is present in the helical coordinate system. Finally, the theory of axisymmetric turbulence is derived as a limiting case of helical turbulence to show consistency with former work.

### Scale locality of helicity cascade in physical space

Scale locality is a key concept in turbulent cascade theory and is also associated with reflection symmetry. Vortex stretching is proven to participate in the helicity cascade process while destroying the conservative characteristic of enstrophy transfer in three-dimensional flows. Numerical evidence indicates that a turbulent structure with scale L will also largely transfer its helicity to structures with scales of around 0.3L. However, the scale locality of the helicity cascade is slightly weaker than that of the energy cascade in physical space. The weaker scale locality suggests that more scales should be involved for turbulent modeling of helical turbulence.

### An experimental study on the spatiotemporal evolution of sand waves/ripples in turbulent boundary layer airflow

An experimental study was conducted to investigate the spatiotemporal evolution of sand waves/ripples submerged in a turbulent boundary layer airflow. While a digital image projection technique was applied to achieve temporally resolved measurements of the dynamically evolving sand surface morphology, a combined particle tracking/imaging velocimetry technique was also used to reveal the two-phase (i.e., air–sediment) flow field during the dynamic sand wave/ripple evolution process. It was found that the sand bed surface would evolve from initial random three-dimensional (3D) sand wavelets to two-dimensional (2D) sand waves and further into well-organized sequences of 3D chevron-shaped sand ripples that are separated by longitudinal streaks, when exposed to the turbulent boundary layer airflow. A discrepancy of the local sand wave propagation at different transverse locations was revealed based on the wavelet analysis of the time-series of the sand bed height variation, which was suggested to contribute to the formation of the 3D chevron-shaped sand ripples. It was also found that the evolving sand waves/ripples could dramatically affect the near-bed two-phase (i.e., air–sediment) flow structures as indicated by the dramatically disturbed air–sediment flow structures. By correlating the sand surface profiles and the near-surface sand particle velocity patterns, a complete description of the dynamic sand bedform evolution was revealed with five dominant phases being defined: (I) initial strengthening phase, (II) transition phase, (III) ripple-modulated re-strengthening phase, (IV) stabilizing phase, and (V) longitudinal phase.

### Optimal perturbations and transition energy thresholds in boundary layer shear flows

Author(s): Chris Vavaliaris, Miguel Beneitez, and Dan S. Henningson

Adjoint-based optimization is performed in a Blasius boundary layer flow, leading to the computation of the subcritical transition critical energy threshold and associated minimal seed. Simulation results demonstrate the physical characteristics and key energy growth mechanisms of the perturbations. Phase-space representation of the minimal seed’s evolution leads to the identification of a persistent attracting region.

[Phys. Rev. Fluids 5, 062401(R)] Published Tue Jun 16, 2020

### Conical shear-driven parametric instability of steady flow in precessing spheroids

Author(s): Yasufumi Horimoto, Atsushi Katayama, and Susumu Goto

The flow instability in a precessing spheroid is a fundamental subject of fluid mechanics and is also important in geophysics because Earth is precessing. There are at least three instabilities: elliptical, shearing, and conical shear. Theory predicts the dominance of the latter in a regime that depends on the spin rate and container’s ellipticity. Laboratory experiments that perfectly support the theory are presented.

[Phys. Rev. Fluids 5, 063901] Published Tue Jun 16, 2020

### Chaos and information in two-dimensional turbulence

Author(s): Daniel Clark, Lukas Tarra, and Arjun Berera

Using fully resolved direct numerical simulations of two-dimensional homogeneous and isotropic turbulence, the Kolmogorov-Sinai entropy and attractor dimension are measured across a wide range of Reynolds numbers. In contrast with the three-dimensional case, these quantities are dependent on the system size and forcing length scale, providing further evidence of nonuniversality in two-dimensional turbulence.

[Phys. Rev. Fluids 5, 064608] Published Tue Jun 16, 2020

### Hysteretic wave drag in shallow water

Author(s): G. P. Benham, R. Bendimerad, M. Benzaquen, and C. Clanet

When a boat is pushed at constant force from deep water to shallow water, the drag changes in such a way that two possible states emerge, corresponding to a slow speed and a fast speed. A study of the dynamical behavior in such a transition, including possible hysteresis routes, with reference to real applications such as rowing sports is presented

[Phys. Rev. Fluids 5, 064803] Published Tue Jun 16, 2020

### On respiratory droplets and face masks

Face mask filters—textile, surgical, or respiratory—are widely used in an effort to limit the spread of airborne viral infections. Our understanding of the droplet dynamics around a face mask filter, including the droplet containment and leakage from and passing through the cover, is incomplete. We present a fluid dynamics study of the transmission of respiratory droplets through and around a face mask filter. By employing multiphase computational fluid dynamics in a fully coupled Eulerian–Lagrangian framework, we investigate the droplet dynamics induced by a mild coughing incident and examine the fluid dynamics phenomena affecting the mask efficiency. The model takes into account turbulent dispersion forces, droplet phase-change, evaporation, and breakup in addition to the droplet–droplet and droplet–air interactions. The model mimics real events by using data, which closely resemble cough experiments. The study shows that the criteria employed for assessing the face mask performance must be modified to take into account the penetration dynamics of airborne droplet transmission, the fluid dynamics leakage around the filter, and reduction of efficiency during cough cycles. A new criterion for calculating more accurately the mask efficiency by taking into account the penetration dynamics is proposed. We show that the use of masks will reduce the airborne droplet transmission and will also protect the wearer from the droplets expelled from other subjects. However, many droplets still spread around and away from the cover, cumulatively, during cough cycles. Therefore, the use of a mask does not provide complete protection, and social distancing remains important during a pandemic. The implications of the reduced mask efficiency and respiratory droplet transmission away from the mask are even more critical for healthcare workers. The results of this study provide evidence of droplet transmission prevention by face masks, which can guide their use and further improvement.

### Can a toilet promote virus transmission? From a fluid dynamics perspective

Currently, a novel coronavirus named “SARS-CoV-2” is spreading rapidly across the world, causing a public health crisis, economic losses, and panic. Fecal–oral transmission is a common transmission route for many viruses, including SARS-CoV-2. Blocking the path of fecal–oral transmission, which occurs commonly in toilet usage, is of fundamental importance in suppressing the spread of viruses. However, to date, efforts at improving sanitary safety in toilet use have been insufficient. It is clear from daily experience that flushing a toilet generates strong turbulence within the bowl. Will this flushing-induced turbulent flow expel aerosol particles containing viruses out of the bowl? This paper adopts computational fluid dynamics to explore and visualize the characteristics of fluid flow during toilet flushing and the influence of flushing on the spread of virus aerosol particles. The volume-of-fluid (VOF) model is used to simulate two common flushing processes (single-inlet flushing and annular flushing), and the VOF–discrete phase model (DPM) method is used to model the trajectories of aerosol particles during flushing. The simulation results are alarming in that massive upward transport of virus particles is observed, with 40%–60% of particles reaching above the toilet seat, leading to large-scale virus spread. Suggestions concerning safer toilet use and recommendations for a better toilet design are also provided.

### Fully resolved simulation of a shockwave interacting with randomly clustered particles via a ghost-cell immersed boundary method

Fully resolved direct numerical simulations are performed to investigate the interaction between a planar shockwave and 300 randomly clustered particles. The particle interfaces are captured with the ghost-cell immersed boundary method. Four cases of different shock Mach numbers up to 6.0 are investigated with a relatively high volume fraction of 14.7% of clustered particles. Results show that the reflected shocks form a planar shockwave propagating upstream, with its velocity decreasing with the increase in Mach number. In small Mach number cases, the transmitted shock remains planar and exceeds its original propagating speed. In high Mach number cases, the transmitted shock is highly curved and slowed down. The peak drag coefficients of all particles could exhibit a linear correlation with the streamwise location. The lift force coefficients could become similar to or even larger than the drag coefficients when the particles reside in post-shock regions. The peak lift force coefficients are the smallest for the first and last rows, and highest in the first half part of clusters, which is due to different mechanisms. The transverse effects of shock–cluster interaction are stronger in higher Mach number cases. This result indicates that the transverse force could not be ignored in a particle cluster with a relatively high volume fraction, especially when the Mach number is high. Fluctuating flow quantities indicate that the increase in Mach number could enhance the fluctuations in the transverse direction and reduce the streamwise mean velocity, resulting in stronger fluctuating fields compared with the mean flows.

### Investigation on boundary schemes in lattice Boltzmann simulations of boiling heat transfer involving curved surfaces

The lattice Boltzmann (LB) method has been applied to simulate boiling heat transfer in recent years. However, the existing studies are mostly focused on boiling on flat surfaces or structured surfaces with square pillars/cavities, and very few LB studies have been made regarding boiling on curved surfaces. In order to clarify the issues involved in the curved boundary implementation for boiling simulations, we numerically investigate the performances of two LB boundary schemes in simulating boiling on curved surfaces. One is the halfway bounce-back scheme, which is very popular in the LB community because of its easy implementation, and the other is a curved boundary scheme. Numerical results clearly show that the halfway bounce-back scheme leads to “artificial” nucleation sites in simulating boiling on curved surfaces because of its staircase approximation. A curved boundary scheme can overcome such a drawback, but it yields serious mass leakage. Hence, a mass-conservation correction should be enforced to the curved boundary scheme so as to eliminate the mass leakage in boiling simulations. The present study indicates that the halfway bounce-back scheme is not suitable for the LB simulations of boiling involving curved surfaces, while the curved LB boundary schemes must be combined with a mass-conservation correction when applied to simulate boiling on curved surfaces.

### Broadband cloaking of multiple truncated cylinders in water waves using the arrangement defects

Cloaking based on scattering cancellation is investigated for a surface-piercing truncated cylinder surrounded by several annularly arranged small truncated cylinders in water waves. The cloaking condition of a body in water waves corresponds to the absence of scattered waves radiating to infinity; that is, the cloaked structure appears invisible to a far-field observer. The effects of three kinds of defects of the outer cylinders on cloaking are considered: a radial location defect, a circumferential location defect, and a size defect. The higher-order boundary element method is combined with the wave interaction theory to accurately study this wave–structure interaction problem. Both the scattered wave energy of the entire structure and the wave drift force on the inner cylinder are calculated and analyzed for the different defects. The symmetry of the defect effects and the cloaking-wavenumber offset caused by a radial position defect of the entire outer cylinder array are first identified. The radial location defect is successfully adopted to control the cloaking frequencies over a wide band.

### Streamwise evolution of drag reduced turbulent boundary layer with polymer solutions

The effect of local polymer solution injection on the evolution of a flat-plate turbulent boundary layer has been investigated experimentally. Polyethylene oxide (PEO) solutions were injected through an inclined slot. The influence of polymer injection on boundary layer development downstream of the slot is assessed at three different concentrations (100 ppm, 500 ppm, and 1000 ppm) using planar velocity field and concentration measurements. A local drag reduction (DR) of up to 60% was obtained in the vicinity of the slot. A systematic change observed in the inverse of the von Kármán constant (k = 1/κ) with an increase in DR is used to define the sub-regimes of the high DR regime, and a linear relation between k and DR is shown to persist over a wide range of Reynolds numbers. The analysis of combined velocity and concentration measurements provides added insight into the associated changes in the boundary layer characteristics and the underlying flow physics.

### Dynamics of impact cratering on granular bed by hydrogel sphere

A lot of studies on the dynamics of a granular impact cratering by a liquid drop have been carried out. However, the results so far are controversial due to the complex impact dynamics of a liquid drop, such as deformation, splash, and penetration into the granular bed. In this study, we focused on the dynamics of the granular impact cratering by a hydrogel sphere, which deforms without splashing and penetrating. We investigated the maximal deformation time of the sphere and the lift-off time of the grains. Both the maximal deformation time and the lift-off time are similar to each other and depend on the −1/2 power of the Young’s modulus of the hydrogel sphere. This power law of the maximum deformation time is the same as an impact of a gel sphere on a flat solid surface. The angle of the ejected curtain was evaluated. The angle is larger for the impact with small deformation of the sphere than that for the impact with large deformation, and the angle is less dependent on the free-fall height. We also investigated the distributions of the ejected grains using the grains dyed by a fluorescent dye. The distribution was visualized by the fluorescent images captured before and after the impact. At the crater rim, the number of the dyed grains flying to and away are balanced. The number of the dyed grains gathered at the dimensionless distance from the crater center of 1.15, where the distance is nondimensionalized by the crater radius, is the largest. This maximum value for the number of the gathered grains is larger for the impact with small deformation than that with large deformation. This result is consistent with the dependence of the impact mode on the angle of the ejected curtain.

### Jet ejection following drop impact on micropillared hydrophilic substrates

Author(s): Anayet Ullah Siddique, Marcus Trimble, Feng Zhao, Mark M. Weislogel, and Hua Tan

The jetting phenomenon from impinging droplets on partially wetting hydrophilic substrates composed of cylindrical micropillars is studied. Impact velocity and fluid viscosity are varied to characterize the jets. It is found that the jetting phenomenon arises for certain ranges of Weber and Ohnesorge numbers. Jet speed, height, and diameter scale linearly with the Weber number. The scaling analysis indicates that the jet is produced by pure inertial focusing of radial flow due to the collapse of an air cavity formed at the center of the drop during the recoiling phase of the impact.

[Phys. Rev. Fluids 5, 063606] Published Mon Jun 15, 2020

### Data compression for turbulence databases using spatiotemporal subsampling and local resimulation

Author(s): Zhao Wu, Tamer A. Zaki, and Charles Meneveau

A data compression methodology for fluid dynamics is introduced. The simulation domain is divided into subdomains with equal size, and the simulation data is compressed by storing it only on the subdomain boundaries. When data is requested by users, a re-simulation of the Navier-Stokes equations within the subdomain is performed using the stored boundary data. The data storage scheme is carefully designed to avoid any errors during the compression-decompression process. A 40:1 lossless compression ratio is easily achieved.

[Phys. Rev. Fluids 5, 064607] Published Mon Jun 15, 2020

### Dynamic wetting and heat transfer during droplet impact on bi-phobic wettability-patterned surfaces

This paper reports the dynamic wetting behavior and heat transfer characteristics for impinging droplets on heated bi-phobic surfaces (superhydrophobic matrix with hydrophobic spots). A non-patterned superhydrophobic and a sticky hydrophobic surface acted as control wettability surfaces. As expected, differences in wetting and heat transfer dynamics were noticeable for all surfaces with the most pronounced variation during the receding phase. During spreading, inertia from the impact dominated the droplet dynamics, and heat transfer was dominated by convection at the contact line and internal flow. As contact line velocities decreased over time, evaporative cooling at the contact line gained importance, especially for the bi-phobic surfaces, where liquid remained trapped on the hydrophobic spots during receding. These satellite droplets increased the contact area and contact line length and assisted heat transfer and substrate cooling after lift-off of the main droplet. Compared with the hydrophobic surface, the contribution of the contact line heat transfer increased by 17%–27% on the bi-phobic surfaces depending on the location of impact relative to the hydrophobic spots. Nonetheless, the bi-phobic surfaces had a lower total thermal energy transfer. However, compared with the plain superhydrophobic surface, heat transfer was enhanced by 33%–46% by patterning the surface. Depending on the application, a trade-off exists between the different surfaces: the sticky hydrophobic surface provides the best cooling efficiency yet is prone to flooding, whereas the superhydrophobic surface repels the liquid but has poor cooling efficiency. The bi-phobic surfaces provide a middle path with reasonable cooling effectiveness and low flooding probability.