Latest papers in fluid mechanics

Physics of Fluids, Volume 32, Issue 7, July 2020.
This paper investigates droplets that evaporate and cluster in shear turbulence with direct numerical simulations. The flows are statistically stationary and homogeneous, which reduces the physical complexity and simplifies the statistical analysis. The mass loadings are about 0.1, the Stokes numbers are about 1, and the Taylor-scale Reynolds numbers are about 60. The simulations show that the clusters are anisotropic and inclined toward the flow direction on large scales, but isotropic on small scales. When the mass loading increases, the clusters contain more droplets, but their size remains unchanged, and the droplets in clusters experience higher vapor mass fractions. When the Stokes number increases, the clusters contain fewer droplets and become larger, and the droplets in clusters experience lower vapor mass fractions. When the Reynolds number increases, the clusters contain more, smaller droplets and become smaller, and the inclination angles of the clusters change.

Physics of Fluids, Volume 32, Issue 7, July 2020.
We study the effect of turbulence on a sedimenting layer of particles by means of direct numerical simulations. A Lagrangian model in which particles are considered as tracers with an additional downward settling velocity is integrated together with an isotropic homogeneous turbulent flow. We study the spatial distribution of particles when they are collected on a plane at non-asymptotic times. We relate the resulting coarse-grained particle density to the history of the stretching rate along the particle trajectory and the projection of the density onto the accumulation plane and analyze the deviation from homogeneity in terms of the Reynolds number and the settling velocity. We identify two regimes that arise during the early and well-mixed stages of advection. In the former regime, more inhomogeneity in the particle distribution is introduced for decreasing settling velocity or increasing Reynolds number, while the tendencies are opposite in the latter regime. A resonant-like crossover is found between these two regimes where inhomogeneity is maximal.

Physics of Fluids, Volume 32, Issue 7, July 2020.
Traveling ionospheric disturbances (TIDs) and atmospheric gravity waves (AGWs) generated by the Joule heating produced from intensified auroral electrojet and/or intense particle precipitation in the auroral and subauroral regions during geomagnetic storms and which propagate downward toward the lower (neutral) atmosphere are numerically simulated using a simple two-dimensional mathematical model for internal gravity waves propagating in the lower atmosphere. An explicit expression for the Joule heating is obtained, and the characteristics of the simulated TIDs/AGWs (e.g., buoyancy frequency, wavenumbers, cutoff wavelength, speed, structures) are also examined and compared with the results obtained from observations. As may be seen in the observations, small-scale TIDs/AGWs with wavelengths shorter than 100 km, medium-scale TIDs/AGWs with wavelengths of several hundred kilometers, and large-scale TIDs/AGWs with wavelengths longer than 1000 km generated by the Joule heating were modeled and numerically simulated. For example, observations have revealed that the Joule heating can generate TID/AGW pairs. The developed numerical model was used to simulate medium-scale TID/AGW wave packet pairs, and the results (wavelength, speed, structure) are in agreement with SuperDARN observations reported by Sofko and Huang, 2000. TIDs/AGWs with shorter horizontal wavelengths are more trapped than those with longer wavelengths (medium- and large-scale TIDs/AGWs). Their cutoff horizontal wavelength was approximated using the linear stability theory of AGWs. The approximated cutoff horizontal wavelength suggests that not all simulated small-scale disturbances with horizontal wavelengths shorter than 100 km are traveling as may be seen in the observations.

Physics of Fluids, Volume 32, Issue 7, July 2020.
The flow past a circular cylinder in the transitional regime at Re = 2000 has been thoroughly investigated via well resolved direct numerical simulation with a spectral element code. Spanwise periodic boundary conditions of at least Lz ≥ 2.5D are required to properly reproduce first and second order turbulent statistics in the cylinder wake. A Kelvin–Helmholtz instability can already be detected at this relatively low Reynolds number at the flapping shear layers issued from either side of the cylinder. The instability, with a frequency fKH ≃ 0.84 that is in excellent agreement with published experimental results, arises only occasionally and the associated spanwise vortices are subject to spanwise localization. We show that while Kármán vortices remain predominantly two-dimensional, streamwise vortical structures appearing along the braids connecting consecutive vortices are mainly responsible for rendering the flow three-dimensional. These structures may appear in isolation or in vortex pairs and have a typical spanwise wavelength of around λz ≃ 0.20–0.28 at a location at (x, y) = (3, 0.5), as measured via Hilbert transform along probe arrays with spanwise orientation. In line with experimental and numerical results at higher Re = 3900, the size of the structures drops in the very near-wake to a minimum at x ≃ 2.5 and then steadily grows to asymptotically attain a finite maximum for x ≳ 20. A time-evolution-based stability analysis of the underlying two-dimensional vortex shedding flow, which happens to be chaotic, shows that the fastest growing perturbations in the linear regime have a spanwise periodicity λz ≃ 0.3 and are located in the very near-wake, right within the braid that connects the last forming Kármán vortex with the previous one, thus hinting at a close relation with the fully developed vortical structures observed in full-fledged three-dimensional computations.

Physics of Fluids, Volume 32, Issue 7, July 2020.
The influence of a diametral acoustic mode on the flow dynamics was numerically investigated for an axisymmetric cavity system with vortex-excited acoustic resonances occurring at high Reynolds numbers and low Mach numbers. The zonal large eddy simulation (ZLES) was conducted to simulate the flow-acoustic coupling fields by the first three diametral acoustic modes at their maximum resonance intensities, respectively. First, the ZLES-simulated acoustic pressure pulsations were well validated by a preliminary acoustic modal analysis and acoustic pressure measurements in the literature. Subsequently, the acoustic-driven cavity flow dynamics were comprehensively demonstrated in terms of the time-averaged flow quantities, shear layer quantities, and high-order turbulence quantities. The results demonstrated that the shear layer momentum thickness, velocity fluctuations, and Reynolds shear stresses were remarkably intensified by the strong resonances with the first and second diametral acoustic modes. Simultaneously, large-scale helical vortex tubes were formed within the cavity, yielding an intensified flow three-dimensionality. Thereafter, the dominant flow modes behind the acoustic-driven cavity flow dynamics were extracted using the data-driven proper orthogonal decomposition from the highly noisy ZLES database. It was found that the first diametral acoustic mode significantly enhanced the dominant positions of the vertical flow-oscillation mode, yielding a large-scale flapping behavior of the mainstream flow, while the second diametral acoustic mode would modulate the cavities to synchronously absorb/release the flow streaks, resulting in the alternating expansion and compression behaviors of the mainstream flow.

Physics of Fluids, Volume 32, Issue 7, July 2020.
We present a study of the effects of external magnetic fields on the dynamics of ferrofluid droplets in suspension and its impacts on the rheology of dilute magnetic emulsions. Our analysis considers a single two-dimensional droplet of a superparamagnetic ferrofluid in an immiscible, non-magnetizable liquid. The two-phase system is confined in a channel between parallel plates and undergoes a simple shear flow under the influence of a uniform external magnetic field. We present a theoretical formulation for the stress tensor of dilute suspensions of ferrofluid droplets in which the stresslet accounts for a magnetic field-induced traction across the droplet surface. Remarkably, the stresslet is no longer symmetric in the presence of external magnetic fields. The complex configuration of the droplet leads to a misalignment between the bulk magnetization and the external magnetic field. As a result, internal torques appear in the magnetic emulsion even when both liquid phases are symmetric fluids. We also present a comprehensive investigation of the configuration and magnetization of the suspended ferrofluid droplet as a function of the intensity and direction of the external field. Then, the stresslet is used to explore how external magnetic fields affect the rheology of dilute magnetic emulsions in terms of the shear viscosity, rotational viscosity, and first normal stress difference. Our predictions show that external magnetic fields can be effectively adjusted to control the dynamics at the droplet level and the rheology of magnetic emulsions.

Physics of Fluids, Volume 32, Issue 7, July 2020.
A numerical investigation is undertaken on the effect of small-scale surface roughness on the local absolute and global stability of the flow due to a rotating disk. Surface roughness is modeled via the imposition of the partial-slip wall boundary condition, with radial and concentric anisotropic roughnesses and isotropic roughness considered. The effect of the partial-slip parameters on the neutral characteristics for absolute instability is presented, while the azimuthal mode numbers required for global linear instability to occur are determined for the genuine inhomogeneous base flow. Predictions for the threshold values for the azimuthal mode numbers needed for globally unstable behavior are also computed by coupling solutions of the Ginzburg–Landau equation with the local linear stability properties obtained using the homogeneous flow approximation. These are found to be in excellent agreement with the exact values realized from the numerical simulations. In general, surface roughness is demonstrated to stabilize the absolute instability and the global linear instabilities.

Physics of Fluids, Volume 32, Issue 7, July 2020.
Conditions for three-wave resonance between surface gravity waves on uniform current in deep water are found. The resonances occur because waves propagating downstream are elongated (relative to their still water form), whereas waves propagating upstream are contracted. Under certain conditions, the elongation and contraction is to such an extent that the difference between the wavenumbers closes resonance with a third wave. In contrast, the existing literature assumes there is no deep water gravity wave triad resonance on uniform current. Rather, the lowest order nonlinear resonance is assumed to be a four-wave interaction. In this sense, the results represent a new class of resonances. Moreover, since triads are of a lower order than four-wave interactions, the effects of the new triad resonances will be, by definition, an order of magnitude greater (in wave slope ka) than the strongest known resonances for the assumed conditions. Thus, the results represent a new and important mechanism of wave growth and energy exchange between surface gravity waves.

Author(s): M. Lorite-Díez, J. I. Jiménez-González, L. Pastur, O. Cadot, and C. Martínez-Bazán

This study reveals that injecting a light fluid of density ρb in the recirculating bubble of a bluff body at Re≈6.4×104 has a greater drag reduction potential than blowing fluid of a density greater than or equal to that of the free stream ρ. It is found that the maximum drag reduction scales as (ρb...

[Phys. Rev. E 102, 011101(R)] Published Tue Jul 07, 2020

Author(s): B. Goshayeshi, G. Di Staso, F. Toschi, and H. J. H. Clercx

The focus of this research is to delineate the thermal behavior of a rarefied monatomic gas confined between horizontal hot and cold walls, physically known as rarefied Rayleigh-Bénard (RB) convection. Convection in a rarefied gas appears only for high temperature differences between the horizontal ...

[Phys. Rev. E 102, 013102] Published Tue Jul 07, 2020

Author(s): T. Watanabe, K. Tanaka, and K. Nagata

Shearing motions in isotropic turbulence are studied with a triple decomposition of velocity gradient tensor. A mean flow around the shearing motions exhibits a thin shear-layer pattern sustained by a biaxial strain. The thickness of each shear layer is well predicted by Burgers’ vortex layer. Interplay between the shear and biaxial strain causes enstrophy production and strain self-amplification.

[Phys. Rev. Fluids 5, 072601(R)] Published Tue Jul 07, 2020

Author(s): Mohammad Rezay Haghdoost, Daniel Edgington-Mitchell, Maikel Nadolski, Rupert Klein, and Kilian Oberleithner

The dynamic evolution of a highly underexpanded transient supersonic jet is investigated via high-resolution time-resolved schlieren and numerical simulations. Experimental evidence is provided for the presence of a second triple shock configuration along with a shocklet between the reflected shock and the slipstream. A model is developed and applied to the numerical simulations to reveal the mechanism leading to the formation of the second triple point.

[Phys. Rev. Fluids 5, 073401] Published Tue Jul 07, 2020

Author(s): X. I. A. Yang, Z.-H. Xia, J. Lee, Y. Lv, and J. Yuan

While it is known that the mean flow in a spanwise rotating channel follows a linear law at the pressure side with an additive constant C, the exact dependence of this additive constant on the Reynolds number and the rotation speed was not entirely clear. It is shown that this additive constant C is a logarithmic function of a rotating induced length scale. After determining the mean-flow scaling, this knowledge is used for wall modeling and for relating the skin friction and the flow rate.

[Phys. Rev. Fluids 5, 074603] Published Tue Jul 07, 2020

Physics of Fluids, Volume 32, Issue 7, July 2020.
The flow enhancement and convective heat transfer along with entropy generation analysis are studied numerically in a micro-slit with alternating hydrodynamic slip patches. The advances in molecular simulations and micro-scale experiments confirmed that the slip of fluid on the solid surfaces occurred at small scale flows and the traditional no-slip boundary conditions cannot be applicable for the flow simulation at the micro- and nano-scale. The coupled Poisson–Boltzmann–Navier–Stokes equations dealing with an external electric potential are involved for the flow enhancement and entropy generation analysis of non-Newtonian fluids in a micro-slit with periodic slips. From the finite volume simulation, it is observed that the drag force effect is very strong along the wall for the transportation and mixing of fluids. This effect is found to be minimized by imposing periodic hydrophobic slippage along the boundary. An additional pressure gradient is generated by imposing electrokinetic pumping, resulting in a higher velocity gradient in the flow direction in the presence of viscous dissipation and Joule heating effects. The results are predicted in terms of the flow enhancement factor (Ef) (which provides maximum species transport), the average heat transfer rate (Nu), and the average entropy generation due to fluid friction, heat transfer, and Joule heating effects. The advantages and disadvantages of utilizing slip conditions are discussed, which has large scale applications on drug delivery and DNA analysis and sequencing, since cell damage due to pumping will be minimized.

Physics of Fluids, Volume 32, Issue 7, July 2020.
Hydrodynamics and instabilities of a thin viscous liquid film flowing down an undulated inclined plate with linear temperature variation have been investigated. Using the long-wave expansion method, a non-linear evolution equation for the development of the free surface is derived under the assumption that the bottom undulations are of moderate steepness. A normal mode approach has been considered to take into account the linear stability of the film to investigate both the spatial and temporal instabilities, while the method of multiple scales is used to obtain the Ginzburg–Landau-type worldly equation for studying the weakly non-linear stability solutions. The numerical study has been carried out in python with a newly developed library Scikit–FDif. The entire investigation is done for a general bottom profile followed by a case study with a sinusoidal topography. The case study reveals that the Marangoni effect destabilizes the film flow throughout the domain, whereas the bottom steepness ζ gives a dual effect for the linear stability. In the “uphill” portion, an increase in ζ stabilizes the flow, and in the “downhill” portion, an increase in ζ gives a destabilizing effect. Furthermore, a weakly non-linear study shows that both supercritical and subcritical solutions are possible for the system. It is noted that the unconditional stable region decreases and all the other region increases in the “downhill” portion in comparison with the “uphill” portion for a fixed set of parameters. The stability analysis of a truncated bimodal system is investigated. The spatial uniform solution of the complex Ginzburg–Landau equation for sideband disturbances has also been discussed. Numerical simulation indicates that a different kind of finite-amplitude permanent wave exists. The amplitudes and the phase speeds of the wave are dependent on thermocapillary as well as the bottom steepness.

Physics of Fluids, Volume 32, Issue 7, July 2020.
We numerically investigate the hydrodynamics of a two-dimensional compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core–shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. The presence of the core affects both deformation and migration dynamics of the compound drop. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in the stable state pushes the compound drop toward the walls, while the revolving core in the limit-cycle state causes the compound drop to oscillate at its equilibrium position. The migration of the compound drop also affects the eccentricity of the core significantly. From the parametric study, we find that the core affects the compound drop dynamics only at intermediate sizes, and an increase in any parameter sufficiently causes a transition from the limit-cycle state to the stable state.

Physics of Fluids, Volume 32, Issue 7, July 2020.
The critical velocity of dislodgment of a permeating oil droplet in crossflow filtration is an important parameter in the analysis of the filtration of produced water systems using membrane technology. In this work, the effects of the viscosity contrast between the droplet and the surrounding fluid on the critical velocity of dislodgment are investigated. In the limit when the viscosity of the droplet approaches infinity, the gripping of the crossflow field on the droplet is maximum. When the viscosity contrast is finite, the smaller the viscosity contrast is, the smaller the gripping becomes. In order to highlight this effect, a comprehensive computational fluid dynamics study is conducted. A permeating droplet in the crossflow field is considered with the viscosity contrast ranging within two orders of magnitude. For each scenario, the critical velocity of dislodgment is determined by increasing the velocity incrementally until breakup occurs for every viscosity contrast. It is found that an increase in the viscosity contrast results in a decrease in the critical velocity of dislodgment. This represents a direct manifestation of the effect of the gripping of the droplet by the crossflow field, which increases as the viscosity contrast increases. Modification of the critical velocity of dislodgment, therefore, needs to be considered to account for this effect of viscosity contrast. The formula that was developed to estimate the critical velocity of dislodgment has been modified, and comparison with simulation gives a very good match.

Author(s): Kuldeep Singh

Fundamental investigations of how boundary slip relative to the no-slip condition for liquid flow in a set of two distinct idealized pore geometries, i.e., a diverging-converging tortuous pore, in contrast to a straight tube capillary pore, contribute to emergent Darcy flow and flow enhancement are ...

[Phys. Rev. E 102, 013101] Published Mon Jul 06, 2020

Author(s): Cara V. Neal, Atticus L. Hall-McNair, Jackson Kirkman-Brown, David J. Smith, and Meurig T. Gallagher

Sperm have evolved to perform a difficult but crucial task, swimming thousands of times their body length to the egg through highly viscous fluids. This is achieved through their beating tail, a beautiful structure consisting of sliding filaments, powered by the action of motor proteins. Scientists have spent decades studying sperm propulsion but have tended to ignore the end piece of the tail, characterizing it as a “ragged end” with no motor activity. Mathematical modeling shows that the end piece helps the sperm to perform a faster and more efficient swimming stroke.

[Phys. Rev. Fluids 5, 073101] Published Mon Jul 06, 2020

Author(s): Yoshiharu Tamaki, Yuma Fukushima, Yuichi Kuya, and Soshi Kawai

Predictability of trailing-edge stall phenomena using wall-modeled large-eddy simulations (LES) is investigated with a wall-resolved LES database. An analysis based on the momentum integral relation shows that the skin friction accumulation effect near the leading edge to the mid chord dominates boundary layer development, and thus, affects flow separation prediction near the trailing edge. The results indicate that accurate wall modeling near the leading edge to the mid chord is essential for predicting stall phenomena, but not necessarily required near and downstream of the separation.

[Phys. Rev. Fluids 5, 074602] Published Mon Jul 06, 2020