# Latest papers in fluid mechanics

### Aerodynamic forces and vortical structures of a flapping wing at very low Reynolds numbers

Reynolds number (Re) for miniature insects is in the range of 80–10. Here, we study how the aerodynamic forces change in this Re range when the flapping mode commonly used by larger insects is employed and explore the physical reasons for the change. We find that at Re below ∼70, the lift decreases and the drag increases rapidly with decreasing Re. This can be explained as follows. In this Re range, the viscous effect becomes very large. Much of the clockwise (CW) vorticity in the leading-edge vortex is diffused to be far above the wing and moves backward relative to the wing, and some of the counterclockwise (CCW) vorticity in the boundary layer at the lower surface of the wing is diffused to be more forward, and the boundary layer becomes thicker. This results in less CW vorticity moving with the wing and less CCW vorticity moving backward of the wing, causing a reduction in the time rate of change in the vertical component of the total first moment of vorticity, i.e., the reduction in the lift. The above changes in vorticity distributions also increase the vertical distance between the CW vorticity and the CCW vorticity, causing an increase in the time rate of change in the horizontal component of the total first moment of vorticity, i.e., the increase in the drag. These results show that if miniature insects flap their wings as the larger ones do, the aerodynamic forces required for flight cannot be produced and new flapping mode must be used.

### Dynamics of droplet and liquid layer penetration in three-dimensional porous media: A lattice Boltzmann study

Liquid penetration analyses for porous media are of great importance in a wide range of industrial applications including, but not limited to, water infiltration in complex soil, hydrocarbon recovery, and liquid seepage through sediments. Depicting the details of two-phase flow in porous media is challenging due to the complex fluid-solid interaction in porous structure. In the present work, we use the three-dimensional multiphase lattice Boltzmann model with a large density ratio to investigate the droplet and liquid layer penetration in complex porous media. It is found that lower porosity leads to larger interactions at the liquid-solid interface and causes stronger drag force acting on the droplet. Both hydrophobic and hydrophilic substrates tend to facilitate droplet migration from the outside to the inside of the porous media. Decreasing the interfacial tension enhances liquid deformation and results in more liquid breakup. Due to the large total momentum dissipation, an increased viscosity ratio causes a reduction of the penetration rate. Even with identical porosity, the pores in parallel to the gravitational force, compared with the perpendicular structure, make the drag force relatively smaller, leading to a faster penetration and stretching interfaces. Overall, this work not only demonstrates the capacity of the multiphase lattice Boltzmann method but also sheds some light on the mechanism of droplet and liquid layer penetration through the porous media.

### Numerical study of species separation in rarefied gas mixture flow through micronozzles using DSMC

This work investigates the species separation in the rarefied flow of the argon-helium mixture through convergent-divergent micronozzles. Imposing a molecular mass ratio in the order of 10, the flow of this mixture can lead to the formation of serious nonhomogeneous phenomena such as the species separation. This study is performed in the ranges of 2.0–4.0 for the geometrical expansion ratio, 200–400 K for the wall temperature, and 0.003–1.454 for the inlet Knudsen number. The effects of these parameters are examined on the separative performances of micronozzle. The direct simulation Monte Carlo method is selected as the solution method because it can provide reliable solutions in the current rarefied flow regime study. The current study reveals two important separative effects in the mixture flow through micronozzles. The first effect is the lateral species separation, which results in the enrichment of heavier species near the centerline. The second effect is the streamwise separation, which leads to the enrichment of one species, mostly the lighter one, as the mixture passes through the micronozzle. The current results show that increasing the expansion ratio will enhance the lateral separation monotonically. However, there are specific wall temperature and Knudsen values, which can result in optimum lateral separative effects. In addition, it is observed that the expansion ratio has little effect on the streamwise separation. However, increasing either the wall temperature or the Knudsen number will enhance the streamwise separation, albeit with a limiting value at very high Knudsen numbers.

### Analysis of the early stages of liquid-water-drop explosion by numerical simulation

Author(s): Thomas Paula, Stefan Adami, and Nikolaus A. Adams

A level-set-based conservative interface-interaction method is extended for phase transition and cavity formation to study the shock-driven explosion of liquid-water microdrops numerically. Comparison with experimental results shows good agreement for the initial stages of the drop dynamics.

[Phys. Rev. Fluids 4, 044003] Published Mon Apr 15, 2019

### Pressure field generated in porous medium by air jet injected through the surface

Efficient detection of hidden volatile substances in soil requires understanding the mechanisms governing their retention or transport through porous medium. In order to increase the mass transfer rate of the hidden volatile substances, it was suggested in this work to apply forced-convection (filtration) in addition to diffusion by using a gas jet impingement vertically onto the soil (a granular bed; sand). Pressure distribution in the granular bed is studied analytically using the methods from the theory of functions of complex variables. The filtration/granular bed interaction involves the soil permeability, grain size, and jet pressure and impinging velocity. Soil failure due to the filtration-imposed forces is formulated as the Mohr-Coulomb criterion, which involves the angle of internal friction and the cohesion of grains. A comprehensive experimental investigation of the filtration pressure distribution and the jet-driven erosion of granular material is presented here. The experiments were conducted by combining a special pressure-measurement technique allowing for a simultaneous accurate detection of the crater onset and the subsequent evolution of the granular bed. The theoretical predictions are compared to the measured pressure field in the granular bed.

### Theoretical study of acoustic radiation force and torque on a pair of polymer cylindrical particles in two Airy beams fields

In this work, we describe the acoustic radiation force (ARF) and torque acting on a pair of cylindrical particles induced by two Airy beams. The finite series expansion method and the addition theorem of the cylindrical Bessel function are used to analyze the acoustic scattered field by a pair of cylindrical particles in an effective incident acoustic field. The mathematical expressions for the ARF and the torque functions in multiple acoustic scattering by a pair of cylindrical particles are obtained. The influences of the phase difference, the beam distance, and the beam amplitude on the ARFs and torques are taken into consideration. The numerical examples illustrate that greater negative or positive forces on the two cylindrical particles emerge by adjusting the phase difference, the distance, or the amplitudes of the two Airy beams, which make it easier to separate the particles. The values of the torques will also increase or change between the positive and the negative, which increase the particles’ rotation velocity or change the particles’ rotation direction. This work will be conducive to the development of acoustic tweezers for polymer drugs separation (or cells separation) in medical domain.

### Surface configurations and wave patterns of thermocapillary convection onboard the SJ10 satellite

A fluid experiment was conducted on China’s SJ10 satellite to assess the instability of thermocapillary convection under microgravity. Oscillations of thermocapillary convection in an annular pool were investigated when the difference in temperature exceeded a certain threshold. Dynamics and transitions of the wave pattern were observed using an infrared camera. This work is concerned with the effect of the surface configuration on the wave patterns. There are 3 types of surface configurations that depend on the volume ratio: Vr < 0.77 (zone 1), 0.77 < Vr < 1 (zone 2), and Vr > 1 (zone 3). An irregular local wave occurs at Vr < 0.65, and a regular azimuthal wave occurs at Vr > 0.65. We observed the regular wave with the wavenumber m = 3 in zone 1 and zone 3 and the competition between m = 3 and m = 4 in zone 2. The nonlinear dynamics of traveling waves, standing waves, and counterpropagating waves were studied. The standing wave appears near the onset and transitions to the traveling wave. With a similar mechanism, counterpropagating waves with m = 3 and m = 4 occur in some cases at the onset. Additionally, counterpropagating waves also act as a transitional mode when the traveling wave transitions from m = 4 to m = 3. The traveling wave is very stable, but it develops into standing waves or Benjamin-Feir instability under highly supercritical conditions.

### Modeling realistic multiphase flows using a non-orthogonal multiple-relaxation-time lattice Boltzmann method

In this paper, we develop a three-dimensional multiple-relaxation-time lattice Boltzmann method (MRT-LBM) based on a set of non-orthogonal basis vectors. Compared with the classical MRT-LBM based on a set of orthogonal basis vectors, the present non-orthogonal MRT-LBM simplifies the transformation between the discrete velocity space and the moment space and exhibits better portability across different lattices. The proposed method is then extended to multiphase flows at large density ratio with tunable surface tension, and its numerical stability and accuracy are well demonstrated by some benchmark cases. Using the proposed method, a practical case of a fuel droplet impacting on a dry surface at high Reynolds and Weber numbers is simulated and the evolution of the spreading film diameter agrees well with the experimental data. Furthermore, another realistic case of a droplet impacting on a super-hydrophobic wall with a cylindrical obstacle is reproduced, which confirms the experimental finding of Liu et al. [“Symmetry breaking in drop bouncing on curved surfaces,” Nat. Commun. 6, 10034 (2015)] that the contact time is minimized when the cylinder radius is comparable with the droplet radius.

### Effects of shear intensity and aspect ratio on three-dimensional wake characteristics of flow past surface mounted circular cylinder

Three-dimensional numerical computations have been carried out for flow past a surface mounted finite height circular cylinder using Open Source Field Operation and Manipulation. Flow field characteristics have been investigated for fixed Reynolds number equal to 300 and varying aspect ratios (AR being the ratio of height to diameter of the cylinder) from 1 to 5. The effect of nonuniform flow (linear shear) with shear intensity (K) ranging from 0 to 0.3 on flow field characteristics has been examined using iso-Q surfaces and streamline plots. Three different flow regimes are reported based on the values of AR and K: steady flow, symmetric mode, and antisymmetric mode of vortex shedding. The formation of critical points (impingement point, source, and spiral node) has been explained using the time-averaged flow field in the longitudinal plane of symmetry. Surface flow topology has been presented with the help of limiting streamlines on the surface of the cylinder. Variation in mean drag coefficient with a change in K has also been reported. Unsteady periodic and aperiodic wake flows have been characterized using the Hilbert spectra of the transverse velocity signal at a point in the wake. The extent of nonlinear interaction in the wake and its influence on frequency distribution have been analyzed using marginal spectra and quantified in terms of degree of stationarity.

### Diffusiophoretic and diffusioosmotic velocities for mixtures of valence-asymmetric electrolytes

Author(s): Ankur Gupta, Bhargav Rallabandi, and Howard A. Stone

The diffusioosmotic slip velocity due to an applied concentration gradient of the ions in the bulk is predicted for a mixture of valence-asymmetric electrolytes at arbitrary zeta potentials in the limit of a thin double layer.

[Phys. Rev. Fluids 4, 043702] Published Fri Apr 12, 2019

### The characteristics of unsteady cavitation around a sphere

The unsteady cavitation typically includes three processes: the growth of cavitation, the instability and shedding of cavitation, and the collapse of cloud cavitation and the regeneration of attached cavitation. In this paper, the unsteady features of the cavitating flow past a sphere are investigated. A detached eddy simulation turbulence model and a transport equation cavitation model are used to model the cavitating flow. The numerical results give the unsteady process of cavitation at different cavitation numbers (0.36 < σ < 1.0), which cover the cavitation state from inception to supercavitation. When the cavitation number 0.8 < σ < 1.0, the flow instability belongs to the single frequency mode; when the cavitation number σ < 0.8, the flow instability becomes the dual-frequency mode. We analyzed the Strouhal (St) number based on the length of the cavitation and found that the St numbers are stable around 0.5 and 0.2 in the dual-frequency mode. In this mode, the high frequency corresponds to the frequency of the large-scale cavity shedding caused by repeated re-entrant jets. The low frequency, caused by the combination of wake flow and cavitation, is close to the natural frequency of the sphere. In addition, the cavity leading edge position and cavity morphology are analyzed in details. Some of the numerical results are compared with existing experimental data.

### Numerical study of wake and aerodynamic forces on two tandem circular cylinders at Re = 103

Three-dimensional large eddy simulations were carried out to investigate the flow around two tandem circular cylinders at a subcritical Reynolds number of Re = 103. The cylinder center-to-center spacing ratio L/D is varied from 1.25 to 6, where D is the cylinder diameter. In order to enhance the understanding of flow physics around two circular cylinders, particular attention is devoted to fluctuating forces, shear-layer reattachment, flow separation, wake recirculation, Strouhal number (St), and phase lag (ϕ) between the fluctuating lift of the two cylinders. The flow structure around the cylinders is highly sensitive to L/D. A change in L/D thus leads to overshoot flow (L/D ≤ 1.25), reattachment flow (1.5 ≤ L/D ≤ 3.5), and coshedding flow (L/D ≥ 4). The boundaries are characterized by drastic changes in the flow structure and a discontinuous drop/rise in St and forces. The St drops at the boundary between overshoot and reattachment flow regimes and jumps at the boundary between reattachment and coshedding flow regimes, while fluctuating forces and ϕ both jump at both boundaries. The flow separation on the downstream cylinder is much delayed (122°–128°) in the reattachment flow regime compared to that on the single cylinder (95°) or upstream cylinder (92°–95.5°). The fluctuating pressure on the entire surface of either cylinder is low for the overshoot flow because the two cylinders are enclosed by the upstream-cylinder-generated shear layers having the longest wake recirculation. The ϕ is almost zero in the overshoot flow. With increasing L/D, ϕ linearly increases in the reattachment and coshedding regimes with different gradients, larger in the latter regime than in the former, by nearly twice.

### Passive feedback control of transonic buffet flow

The activated structural degree of freedom often causes undesirable large-amplitude structural vibrations in unstable flows, such as the frequency lock-in phenomenon in the transonic buffet flow. The underlying mechanism is the instability characteristic of the system that becomes more complex, namely, further instability on the structural mode because of the effect of fluid-structure interaction. In this paper, we study the feasibility of improving the stability of the transonic buffet flow by activating the structural degree of freedom based on numerical simulations and a low-dimensional model. Results reveal that the activated structural degree of freedom can stabilize the buffet flow, eliminating the source of the oscillatory flow. The essence of this strategy is to efficiently utilize the coupling effect between the structural mode and the fluid mode to improve the stability of the fluid mode by properly decreasing the stability margin of the structural mode. From another perspective, this approach is a new passive-feedback flow control strategy, which does not change the shape of the subject compared with the classical passive control and which does not need extra actuation and power compared with the active control.

### Bubble interactions and bursting behaviors near a free surface

The strong bubble interactions and bursting behaviors near a free surface are studied numerically with a compressible two-phase flow solver. The interface is captured by the volume of fluid method. We investigate the effects of the dimensionless distance between the bubble and the free surface γf (scaled by the maximum bubble radius) ranging from 0.25 to 1.5. For the nonbursting cases, the essential evolution of the toroidal bubble is well captured, including the splitting, coalescence, and recollapse. Generally, a relatively thin spike is generated at the free surface during the first cycle of the bubble. Subsequently, a wider secondary spike at the base of the first spike is formed during the second bubble cycle, which leads to the formation of the crown-shaped spike. When γf is sufficiently small, the bubble bursts at the free surface and an opening cavity is generated. The pressure inside the cavity and the atmospheric pressure are not balanced immediately, and the pressure difference lasts for a while, causing the inward gas flow and the final closure of the cavity. The gas flow is found to play a vital role in the bubble bursting behaviors, which has not been well understood. By comparing with previous studies, three distinct bursting patterns are identified and discussed.

### A three-dimensional smoothed particle hydrodynamics dispersion simulation of polydispersed sediment on the seafloor using a message passing interface algorithm

Technical activities on seafloor for harvesting polymetallic nodules result in a displacement of a large amount of sediment, which is convected away from the site by the underlying currents and turbulent diffusion, with a possible impact on the benthic communities living in the neighborhood. To better understand the dispersion mechanism of the resuspended sediment, a smoothed particle hydrodynamics technique augmented by a message passing interface parallel algorithm to address the intensive demand on the three-dimensional simulations is developed. Our numerical results show that the resuspended sediment would occupy a downstream area extending to about 5 km, for a nominal current speed of 5 cm/s. The evolution of the sediment plume occurs mainly along the current direction, while the turbulent diffusion disperses the sediment laterally. Coarse sediment particles are found to return to the seafloor fairly quickly after being resuspended, while fine particles are more persistent in the suspended state and travel much further downstream. In 900 tons of sediment resuspended for 18 h, 318 tons have returned to the bottom at the end of the simulation period. The majority of the deposited sediment is composed of coarse sediment particles (d > 60 μm), and almost half of the deposited sediment is distributed within the harvesting region. The sediment deposition rate reaches up to 48% of the resuspension rate and is still rising after 18 h. The horizontal turbulent diffusivity, which is supposed to be weak at the ocean bottom, does not have any obvious influence on the dispersion of the resuspended sediment; it only slightly reduces the deposition rate.

### Intense sound radiation by high-speed flow: Turbulence structure, gas properties, and near-field gas dynamics

Author(s): David A. Buchta and Jonathan B. Freund

Weak near-field nonlinearities explain key features of the intense sound radiated by high-speed turbulence. The sound-field wave structure, pressure skewness, and pressure intensity are also shown to be relatively insensitive to the large-scale turbulence structure.

[Phys. Rev. Fluids 4, 044605] Published Thu Apr 11, 2019

### A new formulation for two-wave Riemann solver accurate at contact interfaces

This study proposes a new formulation for the Harten, Lax, and van Leer (HLL) type Riemann solver which is capable of solving contact discontinuities accurately but with robustness for strong shock. It is well known that the original HLL, which has incomplete wave structures, is too dissipative to capture contact discontinuities accurately. On the other side, contact-capturing approximate Riemann solvers such as HLL with Contact (HLLC) usually suffer from spurious solutions, also called carbuncle phenomenon, for strong shock. In this work, a new accurate and robust HLL-type formulation, the so-called HLL-BVD (HLL Riemann solver with boundary variation diminishing) is proposed by modifying the original HLL with the BVD algorithm. Instead of explicitly recovering the complete wave structures like the way of HLLC, the proposed method restores the missing contact with a jump-like function. The capability of solving contact discontinuities is further improved by minimizing the inherent dissipation term in HLL. Without modifying the original incomplete wave structures of HLL, the robustness for strong shock has been reserved. Thus, the proposed method is free from the shock instability problem. The accuracy and robustness of the new method are demonstrated through solving several one- and two-dimensional tests. Results indicate that the new formulation based on the two-wave HLL-type Riemann solver is not only capable of capturing contact waves more accurately than the original HLL or HLLC but, most importantly, is free form carbuncle instability for strong shock.

### Comparative study of the dynamics of laser and acoustically generated bubbles in viscoelastic media

Author(s): Chad T. Wilson, Timothy L. Hall, Eric Johnsen, Lauren Mancia, Mauro Rodriguez, Jonathan E. Lundt, Tim Colonius, David L. Henann, Christian Franck, Zhen Xu, and Jonathan R. Sukovich

Experimental observations of the growth and collapse of acoustically and laser-nucleated single bubbles in water and agarose gels of varying stiffness are presented. The maximum radii of generated bubbles decreased as the stiffness of the media increased for both nucleation modalities, but the maxim...

[Phys. Rev. E 99, 043103] Published Wed Apr 10, 2019

### Generation of high-intensity ultrasound through shock propagation in liquid jets

Author(s): Gabriel Blaj, Mengning Liang, Andrew L. Aquila, Philip R. Willmott, Jason E. Koglin, Raymond G. Sierra, Joseph S. Robinson, Sébastien Boutet, and Claudiu A. Stan

An investigation shows how single shock waves, produced in water jets by x-ray laser pulses, propagate and become ultrasonic shock trains through oblique shock reflections and cavitation. These trains are one of the loudest sounds ever made in liquid water and may damage samples studied with x-ray lasers.

[Phys. Rev. Fluids 4, 043401] Published Wed Apr 10, 2019

### Faraday instability in double-interface fluid layers

Author(s): Kevin Ward, Farzam Zoueshtiagh, and Ranga Narayanan

Three-fluid systems subjected to periodic mechanical oscillations are theoretically and experimentally examined. The addition of the third fluid can trigger both stabilizing or destabilizing effects on the interfaces, and additional codimension points are obtainable.

[Phys. Rev. Fluids 4, 043903] Published Wed Apr 10, 2019