# Latest papers in fluid mechanics

### Asymptotic reductions of the diffuse-interface model with applications to contact lines in fluids

Author(s): E. S. Benilov

All existing theories of contact lines in fluids assume isothermality. However, an analysis shows that this assumption does not hold for a number of common liquids including water. The variations of temperature are caused by production/consumption of heat on a microscopic scale near the liquid-gas interface due to the effects of compressibility and viscosity.

[Phys. Rev. Fluids 5, 084003] Published Wed Aug 05, 2020

### Variance-reduction kinetic simulation of low-speed rarefied gas flow through long microchannels of annular cross sections

In micro/nano-devices, the low-speed transport of mass, momentum, and energy through long-ducts is frequently encountered, thereby necessitating scientific investigations. Here, long-ducts of various annular cross sections conducting low-speed gas flows under the influence of a small pressure gradient are considered, in order to understand how the mass flow rate is affected by rarefaction, variations in the radius ratio, and eccentricity of annular geometries. The Boltzmann model equation is treated by a low-variance formulation and simulated by a stochastic kinetic particle-based approach, which addresses the deviation of the molecular distribution function from equilibrium to reduce computational cost significantly. An efficient parallel solver has also been developed and utilized in this research, which is validated against the reported results in the literature. The efficient kinetic particle treatment provides a powerful simulation tool to reveal multi-scale flow physics, which is essential to develop and optimize micro/nano-fluidic devices.

### Investigation of the drag reduction performance of bionic flexible coating

The drag is a crucial factor in reducing the speed of movement and increasing unnecessary energy loss. In this work, inspired by dolphins, five bionic flexible coatings with drag reduction performance were designed and manufactured. First and foremost, the mixed solution, composed of the polydimethylsiloxane and ethyl acetate, was sprayed on aluminum disks with a spray gun, and the bionic flexible coatings were obtained by heating the aluminum disks sprayed with the mixed solution. Afterward, the mechanical properties and surface characteristics of the flexible coatings were characterized. The experimental results for the flexible coatings of drag reduction performance were obtained by using the drag force device. Above all, the parametric study focusing on the flexible coating of the mechanical properties affects the station of flow, which is performed to analyze the impact on drag reduction. Selecting the aluminum disk without any coating as a reference, numerical simulation methods were introduced to explore the drag reduction mechanism of the bionic flexible coating. The results evidence that the drag reduction ratio is 21.6% at the rotation velocity 50 rpm. Under the action of frictional resistance, the coating of elastic deformation caused by the viscoelasticity of the coating like the dolphin skin results in a decrease in frictional resistance of the wall.

### Harnessing flow-induced vibration of a D-section cylinder for convective heat transfer augmentation in laminar channel flow

Flow-induced vibration (FIV) of a D-section cylinder is computationally studied and utilized to augment convective heat transfer in a heated laminar channel flow. An in-house fluid–structure interaction (FSI) solver, based on a sharp-interface immersed boundary method, is employed to solve the flow and thermal fields. In conjunction, a spring–mass system is utilized to solve for the rigid structural dynamics. Using numerical simulations, we highlight that the oscillations of a D-section cylinder are driven by vortex-induced vibration and galloping. It is observed that as the cylinder vibrates, vortices are shed from the apex of the cylinder due to the separating shear layers. These vortices, categorized using shedding patterns, interact with the heated channel walls. This interaction results in disruption of the thermal boundary layer (TBL), thus leading to heat transfer augmentation. The enhancement in thermal performance has been quantified using time and space-averaged Nusselt numbers at the channel walls. It is observed that the oscillation amplitude of the D-section cylinder and the extent of vortex–TBL interaction are crucial for determining heat transfer augmentation. Both symmetric and asymmetric thermal augmentation at the top and bottom channel walls have been reported. Finally, to assess the effectiveness of heat transfer augmentation, the D-section cylinder FIV is compared to other FSI systems operating under similar conditions.

### Crystallization and jamming in narrow fluidized beds

A fluidized bed is basically a suspension of granular material by an ascending fluid in a tube, and it has a rich dynamics that includes clustering and pattern formation. When the ratio between the tube and grain diameters is small, different behaviors can be induced by high confinement effects. Some unexpected and curious behaviors that we investigate in this paper are the crystallization and jamming of grains in liquids with velocities higher than those for incipient fluidization, supposed to maintain the grains fluidized. In our experiments, performed in a vertical tube of transparent material, different grains, water velocities, resting times, and velocity decelerations were used. An analysis of the bed evolution based on image processing shows that, after a decreasing flow that reaches a velocity still higher than that for incipient fluidization, grains become organized in lattice structures of high compactness, where they are trapped though with small fluctuations. These structures are initially localized and grow along time, in a similar manner as happens in phase transitions and glass formation. After a certain time, if the liquid velocity is slightly increased, jamming occurs, with grains being completely blocked and their fluctuation disappearing. We show that different lattice structures appear depending on the grain type. Our results provide new insights into fluidization conditions, glass-like formation, and jamming.

### Optimal spanwise-periodic control for recirculation length in a backward-facing step flow

Author(s): E. Yim, I. Shukla, F. Gallaire, and E. Boujo

Spanwise-harmonic control in a separated flow can modify the mean length of the recirculation region. A second-order sensitivity analysis is used to compute small-amplitude spanwise-harmonic wall controls (blowing/suction or deformation) that most efficiently increase or decrease the mean recirculation length in the flow past a backward-facing step.

[Phys. Rev. Fluids 5, 083901] Published Tue Aug 04, 2020

### Viscous free-surface flows past cylinders

Author(s): Edward M. Hinton, Andrew J. Hogg, and Herbert E. Huppert

Free-surface flows of viscous liquid down an inclined plane and past cylinders of various cross-sections are studied theoretically and experimentally. For relatively wide cylinders, a pond of nearly stationary fluid forms upstream of the cylinder, and a dry region without fluid occurs downstream of it. The flow structure in the pond region depends on the cylinder cross-section and curvature at the upstream stagnation point. The theory is used to deduce simplified asymptotic expressions of the force on the cylinders. The work is relevant to volcanic lava flow deflection by barriers.

[Phys. Rev. Fluids 5, 084101] Published Tue Aug 04, 2020

### Spectra and scaling in chemically reacting compressible isotropic turbulence

Author(s): Jian Teng, Jianchun Wang, Hui Li, and Shiyi Chen

Spectra and statistics in chemically reacting compressible homogeneous isotropic turbulence is studied using numerical simulations. Reaction heat release significantly enhances the spectra of velocity and thermodynamic variables over a wide range of length scales. For exothermal reactions, acoustic mode dominates over the dynamics of compressible velocity and pressure from weak to highly compressible turbulence, and the ratio of compressible to solenoidal kinetic energy and the ratio of compressible to solenoidal dissipation appear to be independent of turbulent Mach number.

[Phys. Rev. Fluids 5, 084601] Published Tue Aug 04, 2020

### Numerical investigation of the bevelled effects on shock structure and screech noise in planar supersonic jets

Rectangular supersonic jets exist widely in propulsion systems of aircrafts. When they are imperfectly expanded under certain conditions, the upstream traveling waves referred to as screech tones will be produced, which may cause structural fatigue failure. In this work, high fidelity simulations are employed to investigate the bevelled effects due to the asymmetric lips of nozzles on shock structures and screech noise in planar supersonic jets. The present results are in agreement with previous experimental and numerical data for the symmetric case. For asymmetric cases, it is found that the bevelled effects will affect the shear layer transition, noise radiation, and shock cell oscillations. The level of screech noise generally decreases with increasing the length difference of two lips. The maximum 7.9 dB drop is identified, and the deflection angle of the mainstream of 9.35° is achieved when this length difference reaches the height of the nozzle. Moreover, dynamic mode decomposition (DMD) is specifically utilized to analyze shock cell oscillations. The results show that the bevelled effects suppress the most energetic DMD mode, corresponding to the dominant frequency of shock screech. The phenomenon of shock leakage is detected in the symmetric case, which is assumed to be an important screech noise source, while it seems to be weakened when the nozzle is bevelled. The longitudinal flapping motion of shock cells is substantially weakened due to the bevelled effects, which might be responsible for the suppression of shock leakage and the screech noise reduction.

### Ferro-advection aided evaporation kinetics of ferrofluid droplets in magnetic field ambience

The present article discusses the physics and mechanics of evaporation of pendant, aqueous ferrofluid droplets, and modulation of the same by an external magnetic field. We show experimentally and by mathematical analysis that the presence of a horizontal magnetic field augments the evaporation rates of pendant ferrofluid droplets. First, we tackle the question of improved evaporation of the colloidal droplets compared to water and propose physical mechanisms to explain the same. Experiments show that the changes in evaporation rates aided by the magnetic field cannot be explained on the basis of changes in surface tension or based on classical diffusion driven evaporation models. Probing via particle image velocimetry shows that the internal advection kinetics of such droplets plays a direct role toward the augmented evaporation rates by modulating the associated Stefan flow. Infrared thermography reveals changes in thermal gradients within the droplet and evaluating the dynamic surface tension reveals the presence of solutal gradients within the droplet, both brought about by the external field. Based on the premise, a scaling analysis of the internal magneto-thermal and magneto-solutal ferroadvection behavior is presented. The model incorporates the role of the governing Hartmann number, the magneto-thermal Prandtl number, and the magneto-solutal Schmidt number. The analysis and stability maps reveal that the magneto-solutal ferroadvection is the more dominant mechanism, and the model is able to predict the internal advection velocities with accuracy. Furthermore, another scaling model to predict the modified Stefan flow is proposed and is found to accurately predict the improved evaporation rates.

### The dispersion of spherical droplets in source–sink flows and their relevance to the COVID-19 pandemic

In this paper, we investigate the dynamics of spherical droplets in the presence of a source–sink pair flow field. The dynamics of the droplets is governed by the Maxey–Riley equation with the Basset–Boussinesq history term neglected. We find that, in the absence of gravity, there are two distinct behaviors for the droplets: small droplets cannot go further than a specific distance, which we determine analytically, from the source before getting pulled into the sink. Larger droplets can travel further from the source before getting pulled into the sink by virtue of their larger inertia, and their maximum traveled distance is determined analytically. We investigate the effects of gravity, and we find that there are three distinct droplet behaviors categorized by their relative sizes: small, intermediate-sized, and large. Counterintuitively, we find that the droplets with a minimum horizontal range are neither small nor large, but of intermediate size. Furthermore, we show that in conditions of regular human respiration, these intermediate-sized droplets range in size from a few μm to a few hundred μm. The result that such droplets have a very short range could have important implications for the interpretation of existing data on droplet dispersion.

### Pulsed-jet propulsion via shape deformation of an axisymmetric swimmer

By using an axisymmetric immersed-boundary model, we numerically investigate the thrust generation of a deformable body via pulsed jetting. We focus on a single discharging process resulting from the deflation of the body as inspired by the jetting mechanism of cephalopods, such as squids. We examine three jet velocity profiles, namely, impulsive, half-cosine, and cosine, in the relatively low Reynolds number regime. For the impulsive profile, we demonstrate via wake visualization that the leading vortex ring does not pinch off from the trailing jet although its circulation stops growing after a critical formation number (hereby, the formation number is defined as the ratio between the length and diameter of the jet plug) of 6–7. The exact value of the critical formation number depends on the jet velocity profile, suggesting that jet acceleration and viscous dissipation play significant roles in vortex ring evolution. In terms of thrust generation, our results indicate that besides the jet momentum flux, an important source of thrust generation is jet acceleration. The implication is that the jet velocity profile is a key factor in determining the propulsive performance.

### Novel similarities in the free-surface profiles and velocities of solitary waves traveling over a very steep beach

This study investigates experimentally similarity and Froude number similitude (FNS) in the dimensionless flow features of three solitary waves traveling on a 1:3 sloping beach. These three waves, designated as cases A, B, and C, respectively, have different heights H0 (=5.8 cm, 2.9 cm, and 1.815 cm) and still water depths h0 (=16.0 cm, 8.0 cm, and 5.0 cm), but identical ratios H0/h0 (=0.363). A high-speed particle image velocimetry system is employed to obtain the free surface profiles (FSPs) and velocity fields/profiles. These features include the free surface elevation (FSE)/FSP time series; velocity fields and profiles, positions, and propagation speeds of flow demarcation curves; times and maximum onshore distances of the maximum run-up heights (MRHs); and times and onshore distances of hydraulic jumps for cases A and B. When the swash tip of a solitary wave reaches the MRH, the contact point becomes almost immobile for a short time interval, with the contact angle changing from obtuse, via right, to acute angle. For cases A and B, the similarities in the dimensionless MRHs and times, at which the run-down motions of the wave tips start, are affirmed. These facts highlight that the swash tips and contact points are subject to complex interactions among gravity force, viscous friction, and surface tension of fluid. Case C, having the smallest length scale, is only focused on the arrival or starting time of the MRH or run-down motion and the MRH and used as a counterexample to demonstrate the absence of similarity or FNS due to the relatively prominent effects of viscous friction and surface tension.

### Energy loss and developing length during reciprocating flow in a pipe with a free-end

Direct numerical simulations of reciprocating pipe flow in a straight pipe with a free-end are presented. The range of amplitudes and frequencies studied span the laminar regime and the beginning of transition toward a conditionally turbulent flow. Two primary results are reported: the measurement of the flow development length and the loss of energy, both due to the presence of the free-end. Two regimes of flow are identified with distinct length scales. For low frequencies, the development length scales with the pipe diameter D. However, for higher frequencies, the development length scales with the Stokes layer thickness [math]. The energy loss is studied by calculating the viscous dissipation function, indicating where energy is lost, and allowing the energy lost due to the presence of the free-end to be isolated. While strong vortices are formed and convected from the exit, most of the energy they dissipate is lost within a few pipe diameters of the exit. It is shown that these trends continue even as the amplitude and frequency are increased so that the flow begins to transition from a laminar toward a turbulent state. Two modes of instability are observed in the Stokes layers near the free-end, one short wavelength mode with a wavelength set by the Stokes layer thickness and the other long wavelength mode with a wavelength set by the amplitude of the oscillatory flow. These modes are related to those observed in the fully developed oscillatory flow.

### Global characteristics of transverse jets of aviation kerosene–long-chain alcohol blends

Long-chain alcohol is a promising alternative for commercial fuels. This study aims at experimentally determining the characteristics of transverse jets using long-chain alcohol in aviation applications. The surface wavelength, breakup regime, upper trajectory of a transverse jet, and liquid column breakup point location are investigated. The column breakup and surface breakup are both observed in experiments, and in the surface breakup regime, there exist bag breakup, multimode breakup, and shear breakup. Shear breakup appears in the conditions with Weg lower than 80. An equation for predicting the upper trajectory of aviation kerosene–long chain alcohol (AKL) blends is proposed. Addition of n-butanol makes the upper trajectory lower, whereas addition of n-pentanol makes the upper trajectory higher. Two equations are proposed for predicting the horizontal and vertical positions of the liquid column breakup point, taking Weg, Oh, and q into account. Blending of n-butanol increases xb and zb, whereas the addition of n-pentanol decreases them. By introducing Kelvin–Helmholtz instability and Rayleigh–Taylor instability into the theoretical analysis, λs is showed to be related with Weg and Oh. Using the results of theoretical analysis, as well as the experimental data, a prediction equation for λs is proposed. The variation of λs caused by fuel modification is studied, the λs is shortened with the addition of long-chain alcohol, and aviation kerosene–n-pentanol blends show shorter surface wavelengths than those of aviation kerosene–n-butanol blends with the same blending ratios. This work provides a better understanding of the characteristics of AKL blends, which will be useful in expanding aviation applications of this fuel.