# Latest papers in fluid mechanics

### Impact of an initial random magnetic field on the evolution of two-dimensional shearless mixing layers

Author(s): Mahzad Chitsaz and Mani Fathali

The impact of an initial random magnetic field on the temporal evolution of a two-dimensional incompressible turbulent shearless mixing layer is investigated using direct numerical simulation. Different intensities of the initial random magnetic field are imposed with uniform probability distributio...

[Phys. Rev. E 100, 043106] Published Mon Oct 14, 2019

### Narrow escape problem for Brownian particles in a microsphere with internal circulation

Author(s): C. A. Klettner

This paper considers the narrow escape problem of a Brownian particle within a two-dimensional domain with two escape windows and an internal circulation modeled by the flow within a Hill's vortex. To account for the spatially inhomogeneous flow within the domain, a Lagrangian study is undertaken us...

[Phys. Rev. E 100, 043107] Published Mon Oct 14, 2019

### Laser induced cavitation: Plasma generation and breakdown shockwave

Laser induced cavitation is one of the effective techniques to generate controlled cavitation bubbles, both for basic study and for applications in different fields of engineering and medicine. Unfortunately, control of bubble formation and symmetry is hardly achieved due to a series of concurrent causes. In particular, the need to focus the laser beam at the bubble formation spot leads, in general, to a conical region proximal to the light source where conditions are met for plasma breakdown. A finite sized region then exists where the electric field may fluctuate depending on several disturbing agents, leading to possible plasma fragmentation and plasma intensity variation. Such irregularities may induce asymmetry in the successive bubble dynamics, a mostly undesired effect if reproducible conditions are sought for. In the present paper, the structure of the breakdown plasma and the ensuing bubble dynamics are analyzed by means of high speed imaging and intensity measurements of the shockwave system launched at breakdown. It is found that the parameters of the system can be tuned to optimize repeatability and sphericity. In particular, symmetric rebound dynamics is achieved almost deterministically when a pointlike plasma is generated at the breakdown threshold energy. Spherical symmetry is also favored by a large focusing angle combined with a relatively large pulse energy, a process which, however, retains a significant level of stochasticity. Outside these special conditions, the elongated and often fragmented conical plasma shape is found to be correlated with anisotropic and multiple breakdown shockwave emission.

### Separation of particle-laden gravity currents down a slope in linearly stratified environments

Particle-laden gravity currents down a slope in stratified fluid are important processes in lake, estuary, and ocean environments. By conducting direct numerical simulations, this study investigates the detailed dynamic features of lock-exchange particle-laden gravity currents down a slope in linearly stratified environments. The front velocity, separation depth, water entrainment ratio, and energy budget are quantitatively analyzed. This evolutionary process can be divided into three stages, i.e., the acceleration stage, deceleration stage, and separation stage, if the relative stratification parameter is larger than unity. At the acceleration stage, as the collapse of the dense fluid leads to fast entrainment of ambient water into the current, the entrainment ratios have large values, while the settling velocity and the ambient stratification are shown to have less impact on both the entrainment ratios and the front velocity. At the deceleration stage, a larger slope angle, a weaker ambient stratification, and a smaller settling velocity bring a greater front velocity. At the separation stage, the head of the current leaves the slope and intrudes into the environment; meanwhile, the dense fluid at the body of the current also intrudes into the ambient water because the density contrast has largely been reduced due to water entrainment, particle settling, and the density increase in the ambient fluid. A predictive model is developed to determine the separation depth by considering the presence of particles. The fingerlike horizontal intrusions enhance the entrainment effect between the current and the ambient water. A stronger ambient stratification suppresses the conversion of the potential energy to the kinetic energy, while a larger settling velocity accelerates the conversion of the kinetic energy to the dissipated energy.

### Electrified cone formation in perfectly conducting viscous liquids: Self-similar growth irrespective of Reynolds number

Above a critical field strength, the free surface of an electrified, perfectly conducting viscous liquid, such as a liquid metal, is known to develop an accelerating protrusion resembling a cusp with a conic tip. Field self-enhancement from tip sharpening is reported to generate divergent power law growth in finite time of the forces acting in that region. Previous studies have established that tip sharpening proceeds via a self-similar process in two distinguished limits—the Stokes regime and the inviscid regime. Using finite element simulations to track the shape and forces acting at the tip of an electrified protrusion in a perfectly conducting Newtonian liquid, we demonstrate that the conic tip always undergoes self-similar growth irrespective of the Reynolds number. The blowup exponents at the conic apex for all terms in the Navier-Stokes equation and the normal stress boundary condition at the moving interface reveal the dominant forces at play as the Reynolds number increases. Rescaling of the tip shape by the power law representing the divergence in capillary stress at the apex yields an excellent collapse onto a universal cone shape with an interior half-angle dependent on the Maxwell stress. The rapid acceleration of the liquid interface also generates a thin interfacial boundary layer characterized by a significant rate of strain. Additional details of the modeled flow, applicable to cone growth in systems such as liquid metal ion sources, help dispel prevailing misconceptions that dynamic cones resemble conventional Taylor cones or that viscous stresses at a finite Reynolds number can be neglected.

### A smoothed particle hydrodynamics (SPH) formulation of a two-phase mixture model and its application to turbulent sediment transport

A Smoothed Particle Hydrodynamics (SPH) formulation and implementation of the classical two-phase mixture model are reported, with a particular focus on the turbulent sediment transport and the sediment disturbances generated by moving equipment operating near or on the seabed. In the mixture model, the fluid-particle system is considered to be an equivalent medium whose evolution is described by a set of equations for the mixture continuity and momentum conservation, with the particle volume fraction being tracked by a transport equation. The governing equations are adapted to a Lagrangian, weakly-compressible SPH framework, the turbulence is modeled by a Reynolds-averaged Navier-Stokes approach, and adaptive boundary conditions for shear stress and turbulent quantities are implemented to account for laminar or turbulent local flow conditions. The complex rheological behavior of clay sediment/water mixtures is modeled using a volume fraction, shear rate-dependent viscosity which accounts for the existence of a yield stress. Hence, the proposed work encompasses several challenging modeling aspects: turbulence, non-Newtonian fluid behavior, sediment transport, and fluid-structure interactions. It is then illustrated on diverse cases of interest: a fluid-particle mixture column release, its subsequent turbulent transport and return to a hydrostatic equilibrium, the settling of particle clouds and two cases of particle-driven gravity currents, and their comparisons with available results. Finally, SPH simulation results for the disturbance of a bed of clay sediment/water mixture induced by a moving plate are reported and compared with experiments performed in our laboratory. The proposed SPH two-phase mixture model agrees well with the existing results considered in this study.

### Separated boundary layer transition under pressure gradient in the presence of free-stream turbulence

Large-eddy simulation (LES) has been carried out to investigate the transition process of a separated boundary layer on a flat plate. A streamwise pressure distribution is imposed to mimic the suction surface of a low-pressure turbine blade, and the free-stream turbulence intensity at the plate leading edge is 2.9%. A dynamic subgrid scale model is employed in the study, and the current LES results compare well with available experimental data and previous LES results. The transition process has been thoroughly analyzed, and streamwise streaky structures, known as the Klebanoff streaks, have been observed much further upstream of the separation. However, transition occurs in the separated shear layer and is caused by two mechanisms: streamwise streaks and the inviscid K-H instability. Analysis suggests that streamwise streaks play a dominant role in the transition process as those streaks severely disrupt and break up the K-H rolls once they are formed, leading to significant three-dimensional (3D) motions very rapidly. It is also demonstrated in the present study that the usual secondary instability stage under low free-stream turbulence intensity where coherent two-dimensional (2D) spanwise rolls get distorted gradually and eventually broken up into 3D structures has been bypassed.

### Three-dimensional rotation of paramagnetic and ferromagnetic prolate spheroids in simple shear and uniform magnetic field

We examine a time-dependent, three-dimensional rotation of magnetic ellipsoidal particles in a two-dimensional, simple shear flow and a uniform magnetic field. We consider that the particles have paramagnetic and ferromagnetic properties, and we compare their rotational dynamics due to the strengths and directions of the applied uniform magnetic field. We determine the critical magnetic field strength that can pin the particles’ rotations. Above the critical field strength, the particles’ stable steady angles were determined. In a weak magnetic regime (below the critical field strength), a paramagnetic particle’s polar angle will oscillate toward the magnetic field plane while its azimuthal angle will execute periodic rotations. A ferromagnetic particle’s rotation depends on its initial angles and the magnetic field strength and direction. Even when it is exposed to a critical magnetic field strength, its rotational dynamics will either be pinned in or out of the magnetic field plane. In a weak magnetic regime, a ferromagnetic particle will either execute out-of-plane rotations or will oscillate toward the magnetic field plane and perform periodic rotations. For both particles, we analytically determine the peaks and troughs of their oscillations and study their time-dependent rotations through analytical and numerical analyses.

### A generalized minimal residual method-based immersed boundary-lattice Boltzmann flux solver coupled with finite element method for non-linear fluid-structure interaction problems

A generalized minimal residual method (GMRES) based immersed boundary-lattice Boltzmann flux solver (IB-LBFS) coupled with the finite element method (FEM) is presented in this paper for nonlinear fluid-structure interaction (FSI) problems. This approach effectively combines LBFS for the simulation of the flow field, the total Lagrangian FEM for the evaluation of nonlinear structural deformations, and the immersed boundary method (IBM) for the exchange of information on the fluid-solid interface and implementation of boundary conditions. Both the multidirect forcing and the implicit IBM are considered to examine their effects on numerical accuracy and efficiency. Through numerical simulations on flow past a cylinder, it is shown that the implicit IBM with the GMRES for the linear equation system is more efficient and accurate, which justify the conventional misunderstanding that implicit IBM is always less efficient than explicit methods. Numerical simulations on the lid-driven cavity flow in an inclined cavity, incompressible flows of a uniformly accelerated vertical plate, and the flow induced vibrations of a beam attached behind a cylinder in a channel are also successfully carried out and the obtained results are in good agreement with the published data, which verify the reliability and flexibility of the proposed solver for simulating nonlinear FSI problems. After that, the external flows past two hyperelastic cylinder-beam structures at the Reynolds number of 40–300 are studied and three different modes of static, linear, and nonlinear deformations of the beam are obtained, demonstrating its capability of simulating flows with nonlinear FSI problems with multiple deformable objects.

### Wake adjustment and vortex-induced vibration of a circular cylinder with a C-shaped plate at a low Reynolds number of 100

The vortex-induced vibration (VIV) of a circular cylinder with a C-shaped plate arranged in its wake at a low Reynolds number of 100 is numerically investigated in this work using the direct numerical simulation. Four typical streamwise spacing ratios of 1.5, 3, 4.5, and 6 are examined in the computations that were carried out for the range of reduced velocities (Ur = 2–12). In terms of shear layer reattachment, wake interference, and vortex shedding, five flow regimes are identified, i.e., the extended-body regime, the front-face reattachment regime, the shear-layer combination regime, the one-row co-shedding regime, and the two-row co-shedding regime. The wake regime is sensitive to the spacing ratio and the reduced velocity. The switching of the flow regime occurs at the transition between the initial VIV branch and the lower VIV branch, accompanying a phase jump of 180°. Furthermore, the shift of the wake regime leads to the prominent fluctuation of the response amplitude. Among the five regimes, the two-row co-shedding regime has the maximum wake width, resulting in the maximum amplitude. In contrast, the shear layers are elongated in the extended-body regime and hence the prolongation of the vortex formation length, contributing to the suppression of VIV. The best suppression is achieved by placing the C-shaped plate behind the cylinder with a spacing of 1.5D, and the reductions in the lift force and the cross-flow amplitude reach 85.5% and 94.5%, respectively.

### Sound waves propagating in a slightly rarefied gas over a smooth solid boundary

Author(s): Masanari Hattori and Shigeru Takata

A fluid-dynamic-type system for acoustic phenomena in the slip-flow regime is obtained with an asymptotic analysis of the linearized Boltzmann equation. The system permits a comprehensive understanding of the phenomena. The occurrence of various non-Navier-Stokes effects is clarified.

[Phys. Rev. Fluids 4, 103401] Published Fri Oct 11, 2019

### Impulse-driven Richtmyer-Meshkov instability in Hall-magnetohydrodynamics

Author(s): Naijian Shen, D. I. Pullin, Vincent Wheatley, and Ravi Samtaney

With the Hall-magnetohydrodynamics model for conducting fluids we study the stability of an impulsively accelerated, perturbed density interface, separating two fluids immersed in a background magnetic field. The presence of the magnetic field is found to suppress the Richtmyer-Meshkov instability.

[Phys. Rev. Fluids 4, 103902] Published Fri Oct 11, 2019

### Edge flame propagation statistics in igniting monodisperse droplet-laden mixtures

The effects of droplet diameter, overall (i.e., liquid+gaseous phases) equivalence ratio, and turbulence intensity on the edge flame propagation statistics for localized forced ignition of uniformly dispersed n-heptane droplet-laden mixtures under homogeneous isotropic decaying turbulence have been analyzed based on direct numerical simulations data. It has been found that the edge flame structure becomes increasingly prominent for large overall equivalence ratios and droplet diameters. Although the mean edge flame speed has been found to be positive and its most probable value remains comparable to the theoretical value for laminar edge flames in purely gaseous mixtures, the mean values have been found to decrease and the probabilities of finding locally negative edge flame speeds have been found to increase with increasing turbulence intensity. The marginal probability density function and curvature and strain rate dependences of the edge flame speed have been found to be principally governed by the displacement speed of the fuel mass fraction isosurface intersecting the stoichiometric mixture fraction isosurface. The displacement speed of the stoichiometric mixture fraction isosurface has also been found to influence the local scalar gradient dependences of the edge flame speed in this configuration, especially for large droplets. The displacement speed of the fuel mass fraction isosurface Sd has been found to be principally governed by leading order contributions of the reaction and molecular diffusion components and the evaporation contribution remains weak in comparison to these leading order contributors. The local edge flame speed exhibits nonlinear curvature and strain rate dependences and its variation with the magnitudes of both fuel mass fraction and mixture fraction gradients has been found to be nonmonotonic for all cases considered here. The correlations of the edge flame speed with curvature, strain rate, and scalar gradient have been found to be qualitatively similar to the corresponding statistics reported in the existing literature for edge flames in purely gaseous mixtures. Additionally, the curvature and tangential strain rate dependences of the edge flame speed have been found to be dependent on the droplet size and overall equivalence ratio, and these dependences become weak for cases with large droplets.

### Response to “Comment on ‘A periodic grain consolidation model of porous media’” [Phys. Fluids 31, 109101 (2019)]

### Comment on “A periodic grain consolidation model of porous media” [Phys. Fluids A 1, 38 (1989)]

In this document, we correct the friction coefficient values presented in Table III in a study by Larson and Higdon [“A periodic grain consolidation model of porous media,” Phys. Fluids A 1, 38 (1989)]. The authors addressed the problem of Stokes flow through periodic arrays of (non)overlapping spheres and determined the friction coefficients. It appears that the volume of the overlapping region of spheres was not taken into account, which affected the total solid concentration and systematically biased the corresponding friction coefficient values. We correct the sphere concentration and friction coefficients, and validate our approach with lattice-Boltzmann simulations. The suggested correction is valid in the case of overlapping spheres only, when the volume of the overlapping region is positive.

### Hydrodynamics and rheology of a vesicle doublet suspension

Author(s): Bryan Quaife, Shravan Veerapaneni, and Y.-N. Young

Effects of membrane-membrane adhesion on vesicle hydrodynamics are studied theoretically (using lubrication theory) and numerically (using time-adaptive boundary integral simulations). Novel vesicle dynamics are quantified to help design future microfluidic experiments to probe membrane adhesion.

[Phys. Rev. Fluids 4, 103601] Published Thu Oct 10, 2019

### Influence of Langmuir adsorption and viscous fingering on transport of finite size samples in porous media

Author(s): Chinar Rana, Satyajit Pramanik, Michel Martin, A. De Wit, and Manoranjan Mishra

We combine two known independent phenomena, viscous fingering dynamics in miscible fluids and nonlinear wave fronts, to investigate how these two nonlinear dynamics interact. The difference between cases with/without nonlinear adsorption of solute arise in creation/annihilation of nonlinear waves.

[Phys. Rev. Fluids 4, 104001] Published Thu Oct 10, 2019

### Inertial migration of a deformable particle in pipe flow

Author(s): Dhiya Alghalibi, Marco E. Rosti, and Luca Brandt

A study of the migration of a hyperelastic particle suspended in a Newtonian pipe flow for different Reynolds numbers and elasticity is presented. The particle deforms and undergoes a lateral displacement while traveling downstream through the pipe, finally focusing at the pipe centerline.

[Phys. Rev. Fluids 4, 104201] Published Thu Oct 10, 2019

### Dynamic Leidenfrost behaviors of different fluid drops on superheated surface: Scaling for vapor film thickness

For an impact drop on a superheated surface, the dynamic Leidenfrost temperature, TLF, depends on several parameters such as impact velocity, vapor layer thickness, and thermophysical properties of the fluids. In this letter, we derived a scaling formula for TLF using the well-known balance relation between the pressures exerted by drop impact and evaporated vapor flow. As the TLF scale intrinsically requires estimating the vapor film thickness δv, it should be scaled based on the consideration of relevant physics postulated on the impact drop and evaporated vapor. Thus, for proper scaling of δv, we considered the drop–vapor interface deformation by drop inertial and surface tension forces during initial impact of drop. Results showed that δv could be scaled with drop diameter D0 and Weber number We. For drops with low We (<10), δv scaled to ∼D0We−1/4 and ∼D0We−2/5 for drops with higher We. The explicit scale for TLF agreed well with present experimental data.

### Bi-global stability analysis in curvilinear coordinates

A method is developed to solve biglobal stability functions in curvilinear systems which avoids reshaping of the airfoil or remapping the disturbance flow fields. As well, the biglobal stability functions for calculation in a curvilinear system are derived. The instability features of the flow over a NACA (National Advisory Committee for Aeronautics) 0025 airfoil at two different angles of attack, corresponding to a flow with a separation bubble and a fully separated flow, are investigated at a chord-based Reynolds number of 100 000. The most unstable mode was found to be related to the wake instability, with a dimensionless frequency close to one. For the flow with a separation bubble, there is an instability plateau in the dimensionless frequency ranging from 2 to 5.5. After the plateau and for an increasing dimensionless frequency, the growth rate of the most unstable mode decreases. For a fully separated flow, the plateau is narrower than that for the flow with a separation bubble. After the plateau, with an increased dimensionless frequency, the growth rate of the most unstable mode decreases and then increases once again. The growth rate of the upstream shear layer instability was found to be larger than that of the downstream shear layer instability.