# Latest papers in fluid mechanics

### Risk assessment of COVID infection by respiratory droplets from cough for various ventilation scenarios inside an elevator: An OpenFOAM-based computational fluid dynamics analysis

Respiratory droplets—which may contain disease spreading virus—exhaled during speaking, coughing, or sneezing are one of the significant causes for the spread of the ongoing COVID-19 pandemic. The droplet dispersion depends on the surrounding air velocity, ambient temperature, and relative humidity. In a confined space like an elevator, the risk of transmission becomes higher when there is an infected person inside the elevator with other individuals. In this work, a numerical investigation is carried out in a three-dimensional domain resembling an elevator using OpenFoam. Three different modes of air ventilation, viz., quiescent, axial exhaust draft, and exhaust fan, have been considered to investigate the effect of ventilation on droplet transmission for two different climatic conditions (30 [math], 50% relative humidity and 10 [math], 90% relative humidity). The risk assessment is quantified using a risk factor based on the time-averaged droplet count present near the passenger's hand to head region (risky height zone). The risk factor drops from 40% in a quiescent scenario to 0% in an exhaust fan ventilation condition in a hot dry environment. In general, cold humid conditions are safer than hot dry conditions as the droplets settle down quickly below the risky height zone owing to their larger masses maintained by negligible evaporation. However, an exhaust fan renders the domain in a hot dry ambience completely safe (risk factor, 0%) in 5.5 s whereas it takes 7.48 s for a cold humid ambience.

### Numerical study of droplet thermocapillary migration behavior on wettability-confined tracks using a three-dimensional color-gradient lattice Boltzmann model

Thermocapillary migration describes the phenomenon whereby liquid droplets move from warm to cold regions on a nonuniformly heated hydrophilic surface. Surface modifications can be applied to manipulate this migration process. In the present study, a three-dimensional color-gradient lattice Boltzmann model is used to investigate the droplet migration behavior on a series of wettability-confined tracks subject to a uniform temperature gradient. The model is validated by simulating the thermocapillary-driven flow with two superimposed planar fluids in a heated microchannel and the capillary penetration of a wetting fluid in a capillary tube. An in-depth study of the wettability-confined tracks confirms the capacity to manipulate the droplet migration process, that is, the wettability-confined tracks can accelerate thermocapillary migration compared with a smooth surface. The effects of changes in the viscosity ratio and interfacial tension are investigated, and it is found that a lower viscosity ratio and larger interfacial tension cause the droplet to migrate faster. Moreover, a systematic study of the track vertex angle is conducted, and the mechanism through which this parameter influences the droplet migration is analyzed. Then the effect of the track wettability on droplet migration is explored and analyzed. Finally, a serial wettability-confined track is designed to realize long-distance droplet migration, and the narrow side width of the connection region is found to play a key role in determining whether the droplets can migrate over long distances. The results provide some guidance for designing tracks that enable precise droplet migration control.

### Study on characteristics of fragment size distribution generated via droplet breakup by high-speed gas flow

In a design of scramjet engine using liquid hydrocarbon fuels, predictions of the fragment size distribution generated by liquid droplet breakup in high-speed gas flow are useful. However, the characteristics of fragment size distribution may be unclear, especially in high-velocity flows. In this study, the diameter of fragments formed by the disintegration of water droplets in a high-speed gas flow behind the shock wave was measured. The fragment diameters of several μm to several tens of μm moving at high speeds were clearly captured via high resolution visualization using a microscope and pulse laser with a flash time of 20 ns as a backlight. The parameters used to measure the fragment diameter from the captured images were determined from calibration experiments using a device that can change the working distance; thus, highly reliable particle size measurements were conducted. From the experimental results, the time variation in the volume probability density distribution of fragments size, Sauter mean diameter (SMD), and mass median diameter (MMD) were calculated. As a result, it was clarified that the volume probability density was successfully described by a root-normal distribution for high Weber number, for which catastrophic breakup should occur according to conventional classification. It was also observed that SMD and MMD increase with time, and the ratio of MMD to SMD was found to be 1.2, except at the initial stage. In this study, the characteristics of size distribution of the fragments generated by liquid droplet breakup in high-velocity flows, which was unclear, has been clarified.

### Anisotropic diffusion of ellipsoidal tracers in microswimmer suspensions

Author(s): Henrik Nordanger, Alexander Morozov, and Joakim Stenhammar

Tracers immersed in suspensions of microswimmers such as bacteria or algae display several phenomena unseen in equilibrium systems, including strongly enhanced diffusivity relative to the Brownian value. Previous theoretical studies have focussed on spherical tracers undergoing isotropic diffusion. Here, we present a computational model of ellipsoidal tracer particles undergoing anisotropic diffusion due to a collection of microswimmers. Our results show that the anisotropic translational diffusion due to microswimmers is qualitatively different from the corresponding equilibrium case, and occurs only for microswimmer concentrations where correlations are significant.

[Phys. Rev. Fluids 7, 013103] Published Mon Jan 24, 2022

### Unsteady and lineal translation of a sphere through a viscoelastic fluid

Author(s): Mary A. Joens and James W. Swan

Unsteady translation of a sphere in a viscoelastic fluid is studied analytically. General, fully invertible relationships between an imposed time-dependent velocity and the resultant force are described in terms of a Volterra series expansion. These results are used to analyze particle motion in fluids described by the Johnson-Segalman and Giesekus models and to define a general framework for analyzing weakly nonlinear microrheology measurements.

[Phys. Rev. Fluids 7, 013301] Published Mon Jan 24, 2022

### Sinking dynamics and splitting of a granular droplet

Author(s): Jens P. Metzger, Christopher P. McLaren, Sebastian Pinzello, Nicholas A. Conzelmann, Christopher M. Boyce, and Christoph R. Müller

A granular droplet that is composed of smaller and denser particles in a bed of larger and lighter particles is found to sink and split when subjected to a combination of vibration and fluidizing gas flow. Despite visual similarities with fluid-like instabilities, the observed phenomenon is a result of the particulate character of granular matter. Combining experiments and numerical simulations, we show that the droplet of high-density particles causes the formation of an immobilized zone that obstructs the downwards motion of the droplet and causes the droplet to spread and ultimately to split. We further investigate the conditions required for droplet splitting.

[Phys. Rev. Fluids 7, 014309] Published Mon Jan 24, 2022

### LES wall modeling for heat transfer at high speeds

Author(s): Peng E. S. Chen, Yu Lv, Haosen H. A. Xu, Yipeng Shi, and Xiang I. A. Yang

Temperature transformation does not collapse data, but the resulting wall model accurately predicts temperatures in high-speed boundary layer flows. Here we explain why this is so. The insights gained lead to a new turbulent Prandtl number formulation and more accurate wall models.

[Phys. Rev. Fluids 7, 014608] Published Mon Jan 24, 2022

### Directional characteristics of spatially evolving young waves under steady wind

Author(s): Krishanu Kumar, Santosh Kumar Singh, and Lev Shemer

A novel nonintrusive optical wave gauge is developed to simultaneously measure three components of the wave field. The synchronous single point measurement of temporal variation of surface elevation and its orthogonal slope components allowed us to estimate directional spectra. Unlike in field experiments, where the directional wave spreading is affected also by variation in the wind direction, in a laboratory facility the wind is unidirectional thus allowing characterization of directional spreading as an intrinsic property of wind waves.

[Phys. Rev. Fluids 7, 014801] Published Mon Jan 24, 2022

### Space-time-resolved measurements of the effect of pinned contact line on the dispersion relation of water waves

Author(s): E. Monsalve, A. Maurel, V. Pagneux, and P. Petitjeans

Surface wave dynamics in small scale configurations can be substantially modified by edge constraints, in particular a pinned contact line, when the force it exerts is non-negligible with respect to gravity and surface tension. This work develops a hybrid approach, which combines a theoretical model with a complete space-time resolved measurement of the surface deformation and static menisci, allowing an accurate estimation of the contribution of a pinned contact line to shift the dispersion relation towards faster phase velocities.

[Phys. Rev. Fluids 7, 014802] Published Mon Jan 24, 2022

### Role of edge effects and fluid depth in azimuthal Faraday waves

Author(s): P. Wilson, X. Shao, J. R. Saylor, and J. B. Bostwick

Faraday waves are created in experiment with spatial structure that conforms to the cylindrical container geometry and is defined by the mode number pair (n,ℓ). The shape of the instability tongue in the frequency-acceleration space depends upon the edge conditions, filling depth, and liquid properties.

[Phys. Rev. Fluids 7, 014803] Published Mon Jan 24, 2022

### Nonlinear interaction among second mode resonance waves in high-speed boundary layers using the method of multiple scales

Nonlinear interaction among resonance waves prior to transition has been observed in earlier numerical and experimental studies. However, these earlier studies were performed for incompressible or compressible flow with a wave triad composed of either Tollmien–Schlichting mode or oblique and planner first modes or crossflow mode. In the case of high-speed flow, the significance of first mode waves becomes lesser, or in most cases, it is not responsible for instability, and second mode waves mostly dominate the flow. The nonlinear interaction among resonance waves in a high-speed boundary layer where a wave triad is composed of second mode waves is presented. The nonlinear interaction formulation is performed using the method of multiple scales. The nonparallel effect has been taken into account by considering the mean flow to be slightly nonparallel. A detuning parameter is used for the wavenumbers, whereas frequencies are assumed to be perfectly tuned, satisfying the resonance condition. Based on the eigenfunctions' distribution normal to the wall, it is observed that the temperature disturbance is more dominant than the other disturbances. With an increase in Mach number, the disturbances shift toward the boundary layer edge. A significant increase in amplification factor due to wave interaction has been observed. The maximum amplification factor for the second mode wave due to wave interaction has increased by around 20% of its non-interaction value. Although the non-interaction amplification factor for the difference mode is much smaller than the other modes, its interaction amplification factor has increased more significantly. The amplification factor for the difference mode has increased almost by 60% due to wave interaction.

### Numerical simulation of flow over flapping wings in tandem: Wingspan effects

We report direct numerical simulations of a pair of wings in horizontal tandem configuration to analyze the effect of their aspect ratio on the flow and the aerodynamic performance of the system. The wings are immersed in a uniform free stream at the Reynolds number Re = 1000, and they undergo heaving and pitching oscillation with the Strouhal number St = 0.7. The aspect ratios of forewing and hindwing vary between 2 and 4. The aerodynamic performance of the system is dictated by the interaction between the trailing edge vortex (TEV) shed by the forewing and the induced leading-edge vortex formed on the hindwing. The aerodynamic performance of the forewing is similar to that of an isolated wing irrespective of the aspect ratio of the hindwing, with a small modulating effect produced by the forewing–hindwing interactions. On the other hand, the aerodynamic performance of the hindwing is clearly affected by the interaction with the forewing's TEV. Tandem configurations with a larger aspect ratio on the forewing than on the hindwing result in a quasi-two-dimensional flow structure on the latter. This yields an 8% increase in the time-averaged thrust coefficient of the hindwing, with no change in its propulsive efficiency.

### Spatial and temporal evolution of three-dimensional thermovibrational convection in a cubic cavity with various thermal boundary conditions

Thermovibrational flow in a differentially heated cubic cavity with vibrations applied in a direction parallel to the imposed temperature gradient is investigated by solving numerically the governing equations for mass, momentum, and energy in their original nonlinear form. A parametric analysis is conducted through the stepwise examination of the following degrees of freedom: magnitude of the Rayleigh number and the thermal behavior of the sidewalls. A complete characterization of the emerging time-varying convective structures is attempted in terms of spatial symmetries broken or retained, related temporal evolution, and global parameters, such as the Nusselt number. It is shown that the intrinsically three-dimensional nature of the problem and its sensitivity to the thermal boundary conditions can have a remarkable influence on the multiplicity of emerging solutions and the system temporal response.

### Carriers of Sargassum and mechanism for coastal inundation in the Caribbean Sea

We identify effective carriers of Sargassum in the Caribbean Sea and describe a mechanism for coastal choking. Revealed from satellite altimetry, the carriers of Sargassum are mesoscale eddies (vortices of 50-km radius or larger) with coherent material (i.e., fluid) boundaries. These are observer-independent—unlike eddy boundaries identified with instantaneously closed streamlines of the altimetric sea-surface height field—and furthermore harbor finite-time attractors for networks of elastically connected finite-size buoyant or “inertial” particles dragged by ocean currents and winds, a mathematical abstraction of Sargassum rafts. The mechanism of coastal inundation, identified using a minimal model of surface-intensified Caribbean Sea eddies, is thermal instability in the presence of bottom topography.

### Directional strengthening and weakening in hydrodynamically sheared granular beds

Author(s): Marios Galanis, Mark D. Shattuck, Corey S. O'Hern, and Nicholas T. Ouellette

When a shear flow delivers sufficient stress to a granular bed, bed particles will start to erode. It has long been known that the critical stress required to initiate sediment transport depends on the shear history of the bed, and that beds tend to strengthen in response to weak flow. We find here that this strengthening effect is highly directional, in that beds only become stronger against flows oriented in the same direction as the conditioning flow. In fact, we find that conditioned beds are actually significantly weaker against flows oriented in other directions, with significant implications for predictions of sediment transport.

[Phys. Rev. Fluids 7, 013802] Published Fri Jan 21, 2022

### Three-phase Leidenfrost effect

Author(s): Mojtaba Edalatpour, Daniel T. Cusumano, Saurabh Nath, and Jonathan B. Boreyko

We replace the classical two-phase Leidenfrost effect with a three-phase system: ice and its meltwater levitating on water vapor. The critical Leidenfrost temperature, which is about 150 °C for water droplets on smooth aluminum, increased to about 550 °C for ice disks. This results in an order of magnitude increase in heat flux from 150–550 °C, suggesting that ice quenching may be a superior alternative to spray quenching for firefighting, metallurgy, and preventing pressure buildup in nuclear reactors.

[Phys. Rev. Fluids 7, 014004] Published Fri Jan 21, 2022

### Conceptual model to quantify uncertainty in steady-RANS dissipation closure for turbulence behind bluff bodies

Author(s): Zengrong Hao and Catherine Gorlé

In turbulent bluff body flows, the presence of vortex shedding, a form of coherent structures, introduces a new characteristic scale that is distinct from the scale of background stochastic turbulence. This double-scale picture essentially invalidates the conventional single-scale modeling for the turbulence energy dissipation in steady-RANS simulations. This paper presents a conceptual model to quantify the uncertainty in the steady-RANS dissipation closure for flows past bluff bodies with vortex shedding.

[Phys. Rev. Fluids 7, 014607] Published Fri Jan 21, 2022

### Acoustic streaming in water induced by an asymmetric dielectric-barrier-discharge plasma actuator at the initiation stage

When acoustic waves with broadband frequency and high amplitude pass through a medium, it absorbs their momentum to induce a quasi-steady flow, which is commonly referred to as acoustic streaming (AS). The acoustic energy in AS is clean energy, and actuators that release acoustic energy by AS can control flow without contacting the controlled object and have considerable potential in microfluidic systems for enhancing transport and mixing. Recently, AS was observed to be induced in quiescent air by a dielectric-barrier-discharge plasma actuator. However, a normal AS flow and a tangential wall jet can be created by the plasma actuator in quiescent air. The AS flow suffers unavoidably from the induced wall jet. For example, the location of the production of the AS flow moves downstream of the upper electrode under the influence of the induced wall jet. In addition, whether the plasma actuator can generate AS in a liquid is the key to applying AS in biomedicine and remains unknown. Here, an asymmetric dielectric-barrier-discharge plasma actuator during the first sinusoidal high-voltage cycle when the induced flow field and the effect of the heating are not significant is suspended over the surface of distilled water but not in contact with the water. Importantly, AS in distilled water produced by a plasma actuator and causing depressions in the liquid surface is first observed by using the highly accurate phase-locked image-freezing schlieren technique. Based on the results, the formation process for AS in distilled water is proposed.

### A maximum entropy formalism model for the breakup of a droplet

A model for the prediction of the size and velocity distribution of daughter droplets created by the breakup of an unstable parent droplet is proposed. The basis of the model is the maximum entropy formalism, which states that the most probable joint probability density function (JPDF) for the daughter droplet population is the one that maximizes the Bayesian entropy conditional on the enforcement of a set of constraints, which are the conservation laws for the problem. The result is a closed-form expression for the JPDF. Validation against experimental and Direct Numerical Simulations data over the bag, multimode, and sheet-thinning breakup regimes is included. Predictions from the model show that the daughter droplet velocity distribution widens as the droplet size decreases. This result is due to a heightened sensitivity to drag force with lower droplet inertia and coincides with spray behavior. The velocity distribution is found to be near Gaussian. The model does not treat size and velocity as independently distributed, as generally assumed in the literature. In fact, marginal conditional densities derived from JPDF show that the distribution of size and velocity are interrelated.

### Vortex dynamics of supercritical carbon dioxide flow past a heated circular cylinder at low Reynolds numbers

The vortex dynamics in the steady regime and laminar vortex shedding regime with Reynolds number (Re) ranging from 15 to 150 are systematically investigated for supercritical carbon dioxide (SCO2) through a high-resolution numerical method in this paper. Numerical results of constant-property air are validated with the available experimental and numerical data from various angles. Excellent agreements are found between the present work and the previous studies. By comparing one vortex shedding process between SCO2 and conventional air, it is found that for SCO2 the period from the initial growth state of one vortex to its dominant state of inducing a new counter-rotating vortex on the other side of the body wake is accelerated, which contributes to the higher Strouhal frequency of SCO2 to a certain extent. By analyzing the development of lift coefficient history and the instantaneous vorticity near the onset of vortex shedding, transition from the steady separated flow to the primary wake instability for SCO2 is found between Re of 28 and 29, exactly 28.2 predicted by the intersection of the fitting curves of the base suction, much lower than the classical value (∼ 47). The wake bubble in the steady regime enlarges in size as Re increases, while in the laminar shedding regime the mean recirculation region decreases with Re. The distributions of local quantities, such as pressure coefficient, friction coefficient, and Nusselt number along the circumference, are presented to understand the development of the flow. The two dimensionality of the wake is confirmed at Re of 150 by comparing with the three-dimensional calculation. A new three-term correlation is proposed to represent the Strouhal–Reynolds number relation for SCO2 in parallel shedding mode.