# Latest papers in fluid mechanics

### Preferential concentration by mechanically driven turbulence in the two-fluid formalism

Author(s): Sara Nasab and Pascale Garaud

Direct Numerical Simulations are employed to investigate preferential concentration of heavy inertial particles in a system in which turbulence is mechanically-driven. Using the two-fluid equations, we study this process and the resulting particle concentration enhancement for particles with St≲O(0.01). The results are similar to those found in previous work, where we established scaling laws to predict maximum and typical particle concentration enhancements in the context of the particle-driven convective instability.

[Phys. Rev. Fluids 6, 104303] Published Fri Oct 08, 2021

### Granular avalanches of entangled rigid particles

Author(s): Damien P. Huet, Maziyar Jalaal, Rick van Beek, Devaraj van der Meer, and Anthony Wachs

We explore the behavior of granular avalanches of nonconvex cross-shaped particles as a step forward in the modeling of entangled granular media. We conduct experiments and simulations of a dam break setup and report several flow regimes such as the top-driven collapse and the intermittent regime, in which the granular column sometimes remains stable and the flow outcome is determined by the random initial microstructure.

[Phys. Rev. Fluids 6, 104304] Published Fri Oct 08, 2021

### Nonequilibrium turbulent dissipation in buoyant axisymmetric plume

Author(s): Sunita and G. C. Layek

This paper established the existence of non-Kolmogorov turbulence in free shear flows. The authors propose a set of dissipation laws and link them with the spreading rates as well as the entrainment coefficient, which varies with the rise of the plume in contrast to the Kolmogorov case. The work also show how the parameters of two stretching transformations determine both Kolmogorov and non-Kolmogorov turbulence.

[Phys. Rev. Fluids 6, 104602] Published Fri Oct 08, 2021

### Hydrodynamics of a floating barge adjacent to fixed structure in transient wave fronts

Physical experiments are carried out in the wave flume to investigate the effects of transient wave fronts acting on multiple floating bodies. Two identical barges are considered with one being allowed to sway freely and the other fixed. A time-frequency analysis method based on the improved empirical mode decomposition and the Hilbert–Huang transform is developed to help analyze the localized characteristics of non-stationary wave fronts and the corresponding barge responses. A series of problems of particular concern are investigated systematically, and rich results and discussions are provided. Transient wave fronts behaving in a chirp waveform are observed. Two types of wave peaks with respect to transversal waves are recognized in the gap between two barges, whose occurrence locations are derived mathematically. The barge motion is found to be composed of the mean trend and oscillatory components, where the trend component is largely determined by the mooring system, and the oscillatory component is more relevant to the wave property. In shorter incident waves, the motion of weather-side barge can evidently amplify the wave amplitude between two barges. Both amplitudes of the barge motion and maximum wave elevation in the gap generally increase with the reduction in the gap width. Physical understandings revealed in this study are significant to help guarantee the operation safety of offshore side-by-side floating structures in practice.

### Droplet impact dynamics on single-pillar superhydrophobic surfaces

While ridged, spherical, or cone superhydrophobic surfaces have been extensively utilized to explore the droplet impact dynamics and the possibility of reducing contact time, superhydrophobic surfaces with a single small pillar have received less attention. Here, we report the rebound and splashing phenomena of impact droplets on various single-pillar superhydrophobic surfaces with the pillars having smaller or equal sizes compared to the droplets. Our results indicate that the single-pillar superhydrophobic surfaces inhibit the droplet splashing compared to the flat ones, and the rebound droplets on the former sequentially exhibit three morphologies of top, bottom, and breakup rebounds with the increasing of Weber number, while those on the latter only show the (bottom) rebound. The pillar significantly enlarges the droplet spreading factor but hardly changes the droplet width. Both the relations between the maximum spreading and width factors and the Weber number on all surfaces approximately follow a classical 1/4-power law. Reduction in the contact time is observed for the rebound droplets on the single-pillar superhydrophobic surfaces, dependent on the rebound morphology. Specially, the breakup rebound nearly shortens the contact time by more than 50% with a larger pillar-to-droplet diameter ratio yielding a greater reduction. We provide scaling analyses to demonstrate that this remarkable reduction is ascribed to the decrease in the volume of each sub-droplet after breakup. Our experimental investigation and theoretical analysis provide insight into the droplet impact dynamics on single-pillar superhydrophobic surfaces.

### Impingement and freezing of a supercooled large droplet on an ice surface

In the present study, we carried out an experimental investigation of the impinging and freezing processes of a supercooled large water droplet on an ice surface. One high speed camera was used to measure the dynamic motions of the water droplet while two charge coupled device (CCD) cameras were adopted to obtain the images of the freezing process and the freezing morphologies, respectively. The effects of the water droplet temperature and the ice surface temperature on the impact and freezing processes of the water droplet were carefully evaluated. The results showed that the subcooling degree of the water droplet had an apparent influence not only on the spreading process but on the freezing morphology as well. When the subcooling temperature of the water droplet was high (e.g., Tw = –3.0 °C), a triangle cross-section profile formed. However, once the subcooling temperature of the water droplet was relatively low (e.g., Tw = –9.0 °C), the final ice morphology consisted of two parts: one part was a cone-like bead in the center while the other part was an ice ring at the periphery. Moreover, at the same water droplet temperature, raising the ice surface temperature led to an increase in the maximum spreading factor.

### Spanwise organization of upstream traveling waves in transonic buffet

This experimental study has the objective of providing new insight into the role of upstream traveling waves (UTWs) in the transonic buffet phenomenon, using the background-oriented schlieren (BOS) technique and corroborating the results with particle image velocimetry. The experiments were carried out on the supercritical OAT15A airfoil under transonic conditions, at a Mach number of 0.7, an angle of attack of 3.5°, and a chord-based Reynolds number of [math]. The specific scope of the investigation is the characterization of the spanwise organization of the buffet phenomenon; therefore, the measurements consider a streamwise–spanwise-oriented field of view on the suction side of the airfoil. A particular topic of interest is the propagation and orientation of upstream traveling pressure waves (UTWs) that occur in transonic buffet. The experimental setup used allowed to confirm the two-dimensionality of the velocity field and of the shockwave, but revealed that the UTWs propagate at a non-zero orientation. Processing of the BOS images with two different procedures (normal and differential), has furthermore allowed to extract the frequency and propagation velocity of the UTWs, which have been confirmed to behave as acoustic waves, traveling at the speed of sound relative to the flow. A further analysis has given hints that the strength of the UTWs is modulated during the buffet cycle and, therefore, in support of the feedback-mechanism description of transonic buffet.

### Propulsive efficiency and efficacy of a pumping sail

This study presents a framework to analyze the propulsive performance of a sail under oscillatory pumping motion, which should be modified from the analysis framework for conventional flapping wings. A new set of metrics, including the propulsive efficiency ηs and efficacy [math], which depend not only on the aerodynamic coefficient but also on kinematic conditions of the sailing vehicle, are proposed to characterize the propulsive performance of sail pumping. The necessity of the proposed metrics is illustrated by studying the propulsive performance of a two-dimensional airfoil under different heaving and kinematic conditions through computational fluid dynamic simulations. It was found that the sail pumping typically improves the propulsive performance by lift enhancement instead of drag reduction. Thus, the formation of leading-edge vortices may not be detrimental to the propulsive efficiency of a pumping sail, contrary to that for flapping wings. A propulsive efficiency greater than unity is achievable under certain sailing conditions because a sailing vehicle can extract energy from the wind.

### Experimental insights on the water entry of hydrophobic sphere

This article reports experimental insights into the physics of water entry of hydrophobic spheres. In the set of experiments, parameters such as sphere density, diameter, and impact velocity are varied. The trajectory of the sphere after impact, the dynamics of trapped air-cavity, including the cavity formation, and the retraction analysis are given. Furthermore, analysis of the Worthington-jet, the cavity ripple, and early bubble shedding after the air-cavity detachment is carried out. At the location of cavity closure, radial expansion and contraction behavior are reported for the case of the shallow seal (near the air–water interface), while for the deep seal, only one such behavior is observed. Further, five cavity shapes are recorded based on the cavity retraction behavior (i.e., shallow, deep seal), namely, conical shape, slender-cone shape, telescopic shape, spearhead shape, and the thick spearhead shape. The radial dynamics and radial surface energy analysis are reported at various locations on these cavity shapes to find that the thick spearhead cavities hold the most cross-sectional surface energy. The slender-cone shaped cavity generates the fastest Worthington-jet, followed by the telescopic shaped cavities. The thick spearhead shaped cavities are reported to have the longest intact Worthington-jets, followed by the spearhead shaped cavities. Finally, a new regime map is presented for single ripple and multiple ripple behaviors at the time of retraction in the wake of descending spheres. A bubble shedding behavior has also been characterized as the most frequent bubble shedding for shallow seal and associated longer bubble length compared to the other cases.

### Magnetic field-induced self-assembly of multiple nonmagnetic bubbles inside ferrofluid

In this work, a comprehensive numerical study of the magnetic field-induced dynamic self-assembly process of multiple bubbles inside the ferrofluid is presented. For multiple bubbles inside the ferrofluid, the magnetic attraction force between bubbles is usually greater and lasts longer than the magnetic repulsion force, resulting in self-assembly movement. This process can be influenced by a number of factors, such as surface tension, inertia force, and initial position, and their specific mechanisms have not been fully understood. Particularly, what roles the magnetic field strength, the surface tension coefficient, and the initial position play are our major interest. Results show that higher magnetic field strength is unfavorable for improving self-assembly efficiency as it leads to stronger magnetic interactions, including attraction and repulsion. In contrast, an increase in the surface tension coefficient can enhance the effect of attraction and weaken the effect of repulsion. Further analysis of the influence of the initial position shows that the magnetic repulsive force can be enhanced by increasing the horizontal gap, which causes a reversing motion along the magnetic field direction. However, an increase in the vertical gap has a nonlinear effect on the efficiency of the self-assembly process, and there is a critical distance below which the self-assembly process could be accelerated with the increase in the vertical gap.

### Rivulet flow over and through a permeable membrane

Author(s): Abdulwahed S. Alshaikhi, Stephen K. Wilson, and Brian R. Duffy

Motivated by small-scale natural and industrial processes involving flow over and/or through a layer of a porous medium, a mathematical model for the steady gravity-driven flow of a slowly varying and thin rivulet of fluid over and through an even thinner permeable membrane is formulated and analyzed. The three-dimensional shape of the free surface of a rivulet with either fixed semi-width or fixed contact angle is determined, and it is shown how the length, base area and volume of the rivulet on the permeable part of the membrane depend on the physical properties of the system.

[Phys. Rev. Fluids 6, 104003] Published Thu Oct 07, 2021

### Coherent structures associated with interscale energy transfer in turbulent channel flows

Author(s): Hongping Wang, Zixuan Yang, Ting Wu, and Shizhao Wang

The flow fields of direct numerical simulation of turbulent channel flow are decomposed into large scales and small scales based on the interscale energy transfer spectra. The former is characterized by streaks and quasi-streamwise vortices even in the outer layer, and the latter is characterized by hairpin-like vortical structures that are similar to the original flow fields. We further investigated the coherent structures associated with the real-space energy transfer. The formation of small-scale hairpin-like vortices is related to the large-scale shear layer.

[Phys. Rev. Fluids 6, 104601] Published Thu Oct 07, 2021

### Revisiting the “pearl string” in draining soap bubble film first witnessed by Sir James Dewar some 100 years ago: A note of analyses for the phenomena with related findings

The flow patterns of “pearl string” in draining bubble film as first witnessed by Sir James Dewar some 100 years ago were successfully reproduced by using chemically stable aqueous alkylbenzenesulfonate instead of alkylcarboylate used by Dewar as a soap. The concentration of aqueous surfactant used is as high as 5% by weight. The close-up pictures were taken by both still and video cameras at the magnification of around 10× with time for the draining flat bubble film prepared in vertically held rectangular frame made of a thin glass rod. The flow pattern of “threaded white beads” was found to appear at the shear boundary of black and gray flowing films. The successive and periodical deposition of tiny white particles to form “threaded pearls” is explained as the result of repeated nucleation of liquid crystalline phase as triggered by the stick-slip frictional sliding of black film at the boundary of the isotropic gray film and the subsequent growth of particles by isothermal condensation. The frequency of oscillational shear was found to be around 10 Hz for the shear velocity of 3 cm/s, which was approximated from the increased rate of black film area and the interval of beads in video images. The phenomena were explained as the deposition of liquid crystalline phase in the isotropic gray film the nucleation of which is triggered by the stick-slip frictional sliding motion of black film at the border of gray film. The whole process occurs in the course of gravity-induced syneresis of aqueous soap film.

### Non-Newtonian laminar flow in pipes using radius, stress, shear rate or velocity as the independent variable

The flow of a non-Newtonian fluid in a circular pipe is a classic introductory transport phenomena problem, familiar to readers of Robert Byron Bird textbooks. A characteristic of Bird's work was taking the time to explore alternative ways to describe a problem and refine the results into elegant and readable formulas. Inspired by that approach, we compare methods for pipe flow solutions that differ on the independent variable used (radius, stress, shear rate) to obtain flow rate and residence time distributions for generalized Newtonian fluids. We highlight cases where using the shear rate as the independent variable has advantages for analytical and numerical solutions. We describe a method to use velocimetry experimental data coupled with a pressure drop measurement to directly construct a curve of flow rate vs pressure drop without the need of fitting the data to any rheological models. We present a geometrical interpretation of velocity profiles as areas in the stress–shear rate plane and derive analytical solutions for a three-parameter model of soft glassy materials [Caggioni et al., “Variations of the Herschel–Bulkley exponent reflecting contributions of the viscous continuous phase to the shear rate-dependent stress of soft glassy materials,” J. Rheol. 64, 413 (2020)] and a four-parameter model for chocolate melts [H. D. Tscheuschner, “Rheologische eigenschaften von lebensmittelsystemen,” in Rheologie Der Lebensmittel, edited by D. Weipert, H. Tscheuschner, and E. Windhab (Behr's Verlag, Hamburg, 1993), pp. 101–172]. We also compare the speed of various numerical approaches for a fractional viscoelastic model [A. Jaishankar and G. H. McKinley, “A fractional K-BKZ constitutive formulation for describing the nonlinear rheology of multiscale complex fluids,” J. Rheol. 58, 1751 (2014)].

### Targeted particle delivery via vortex ring reconnection

A conceptual model for targeted particle delivery is proposed using controlled vortex ring reconnection. Entrained particles can be efficiently transported within the core of vortex rings which advect via self-induction. A pair of these particle-transporting vortex rings traveling in the streamwise direction along parallel trajectories will mutually interact, resulting in a pair of vortex reconnection events. The reconnection causes a topological change to the vortex ring which is accompanied by a rapid repulsion in a perpendicular plane to the direction of travel, effectively transporting the particles toward the desired location on the sidewalls of a ducted flow. In addition to proposing this conceptual model, we show the dominant physics of the process and the considerations for targeted delivery.

### Viscous extension of vortex methods for unsteady aerodynamics

The Kutta condition has been extensively used to determine aerodynamic loads of steady and unsteady flows over airfoils. Nevertheless, the application of this condition to unsteady flows has been controversial for decades. A viscous correction to the Kutta condition was recently developed by matching the potential flow solution with a special boundary layer theory that resolves the flow field in the immediate vicinity of the trailing edge: the triple-deck boundary layer theory. In this work, we utilize this viscous condition to extend two common numerical methods for unsteady aerodynamics to capture viscous effects on the dynamics of unsteady lift and pitching moment—we develop viscous versions of the traditional discrete vortex method and unsteady vortex lattice/panel method. The resulting aerodynamic loads obtained from the proposed numerical models are compared against higher-fidelity simulations of unsteady Reynolds-averaged Navier–Stokes equations for an airfoil undergoing step, harmonic, and complex maneuvers. The obtained results are consistently in better agreement with the unsteady Reynolds-averaged Navier–Stokes simulations in comparison to their potential flow counterpart. In conclusion, the developed numerical methods are capable of capturing (i) unsteady effects; (ii) viscous effects (e.g., viscosity-induced lag) on the dynamics of lift and moment at high frequencies and low Reynolds numbers; and (iii) wake deformation, for arbitrary time-varying motion.

### Flow map of foil undergoing combined fast and slow pitching

The drag-thrust transition and wake structures of a pitching foil undergoing combinations of fast and slow pitching are systematically investigated. The foil locomotion having combinations of fast and slow pitching is made by setting a variable s defined as the fraction of the pitching time required on the upper side of the wake centerline. On the other hand, time 1-s is required for the foil to pitch on the lower side of the wake centerline. Compared to the symmetric pitching (s = 0.5) case, the time-mean thrust rapidly increases and the drag-thrust boundary advances with increasing |s − 0.5|. The Kármán vortex street slants and produces thrust when |s − 0.5| is sufficiently large, which supersedes the previous thumb rule that only reverse Kármán vortex street can produce thrust. The faster forward stroke determines the slant direction of the vortex street. The detailed wake structures produced by the pitching foil are discussed, showing how the combined pitching affects vortex dynamics, drag-thrust transition, slant direction, and wake jet. This work provides a physical basis for understanding the hydrodynamics of native swimmers which may be useful to design bio-inspired underwater robots.

### Study on the rheology of a dilute emulsion of surfactant-covered droplets using the level set and closest point methods

In this work, we study the effects of surfactant elasticity (E), coverage factor (X), and Péclet number (Pe) on the droplet shape and emulsion rheology. Our analysis considers a single two-dimensional surfactant-covered droplet in an immiscible liquid submitted to a simple shear flow. The numerical methodology combines the level set, to capture the interface, and the closest point method to solve the surfactant transport equation. We separate the dilute phase contribution to the bulk stress tensor in the capillary stress, associated with the normal stress jump, and the Marangoni stress, related to the stress tangent to the interface. Our results show that E and X affect the droplet shape more intensely than the Pe. On the other hand, Pe directly affects the emulsion's bulk viscosity. For [math], the capillary viscosity decreases with X, while the Marangoni viscosity grows with X. Such a compensation mechanism allows the increase in the bulk viscosity with X. We also present results for the first normal stress difference.

### Wall-modeled lattice Boltzmann large-eddy simulation of neutral atmospheric boundary layers

The lattice Boltzmann method (LBM) sees a growing popularity in the field of atmospheric sciences and wind energy, largely due to its excellent computational performance. Still, LBM large-eddy simulation (LES) studies of canonical atmospheric boundary layer flows remain limited. One reason for this is the early stage of development of LBM-specific wall models. In this work, we discuss LBM–LES of isothermal pressure-driven rough-wall boundary layers using a cumulant collision model. To that end, we also present a novel wall modeling approach, referred to as inverse momentum exchange method (iMEM). The iMEM enforces a wall shear stress at the off-wall grid points by adjusting the slip velocity in bounce-back boundary schemes. In contrast to other methods, the approach does not rely on the eddy viscosity, nor does it require the reconstruction of distribution functions. Initially, we investigate different aspects of the modeling of the wall shear stress, i.e., an averaging of the input velocity as well as the wall-normal distance of its sampling location. Particularly, sampling locations above the first off-wall node are found to be an effective measure to reduce the occurring log-layer mismatch. Furthermore, we analyze the turbulence statistics at different grid resolutions. The results are compared to phenomenological scaling laws, experimental, and numerical references. The analysis demonstrates a satisfactory performance of the numerical model, specifically when compared to a well-established mixed pseudo-spectral finite difference (PSFD) solver. Generally, the study underlines the suitability of the LBM and particularly the cumulant LBM for computationally efficient LES of wall-modeled boundary layer flows.

### Investigating sweep effects on the stability of leading-edge vortices over finite-aspect ratio pitch-up wings

The flow field around a finite-span flat wing in pitch motion is modeled by means of large-eddy simulation. The effect of moderate sweep angles on the stability of the leading-edge vortex (LEV) is investigated. The relative stability of LEVs on flapping profiles can be improved by moderating LEV growth through spanwise vorticity convection and vortex stretching. The LEV growth over an unswept wing and two sweep angles, namely, [math], is studied by investigating the spanwise flow. The calculated results are in good agreement with experimental data, establishing confidence in the approach. Results show that sweeping the wing profile increases not only the scale of the secondary vortices but also expedites the initiation of the vortices at lower angles of attack. For the sweep angle of [math], increasing the angle of attack is associated with annihilation of vorticity and thereby limits the vortex growth as a necessary condition for LEV stability. Analysis shows that increasing the sweep angle results in a higher circulation intensity, especially in the inner region of the wing, and significant spanwise flow is observed through the vortex core. The pattern of vorticity remains stable and attached to the surface as the angle of attack continues to grow for the swept wing, while the patterns of vorticity depart the wing surface for the unswept wing. It is suspected that sweeping the wing can control the scale of the vortex by introducing a substantial vortex stretching.