# Latest papers in fluid mechanics

### Finite obstacle effect on the aerodynamic performance of a hovering wing

The finite obstacle effect on the aerodynamic performance of a normal hovering wing is studied using the immersed boundary method. Phenomena of a two-dimensional wing hovering above, under, or on the side of a circular obstacle are presented. Parameters including obstacle size, distance, location, and flapping angle are investigated to study how the aerodynamic force and flow field are affected. The diameter of the obstacle ranges from 0.5c to 12c and the distance between the centroid of the wing and obstacle surface from 0.5c to 6c (c is the wing chord length). Previous observations of ground effects including force enhancement, reduction, and recovery occur similarly when the wing hovers above the obstacle of diameter greater than 2c. However, finite obstacles affect the aerodynamic performance differently when the size shrinks to a critical value. Force drops when the wing moves close and rises when moving away, opposite to the ground effect. As flapping angle amplitude increases, the force change tends to be consistent for different-sized obstacles. The top or side effect shows a different influence on the force change. Force monotonically increases as the distance decreases when the wing hovers under the obstacle. The side effect places a less important factor on the aerodynamic performance. All force changes under such circumstance are less than 13% referring to nonobstacle result. The gap between the leading or trailing edge of the wing and obstacle surface plays a significant role in the leading and trailing edge vortices generating, shedding, and pairing, which greatly affects the force change.

### Revisiting the clap-and-fling mechanism in small wasp Encarsia formosa using quantitative measurements of the wing motion

The ideal clap-and-fling mechanism is described as: clap, the leading edges of the wings touch and then the wings rotate around the leading edge, closing the gap between the wings and producing a vertical force; fling, the wings rotate around the trailing edge or “fling open,” generating a vertical force (the drag required to clap or fling the wings can be 6–10 times larger than the vertical force). Here, we revisit the mechanism from the perspective of wing motion and force production, based on our measured quantitative data and flow computations, and suggest certain modifications to its description: In the clap, the wings rotate to a large angle of attack before they are close to each other and they move close to each other with the wing surface almost vertical, and then they move vertically upwards; i.e., the ideal clap motion is far from the real one. The fling is like the ideal one, except that there is a separation (approximately 0.2 chord length) between the wings. During the clap, there is no large vertical force like that in the ideal clap; however, the clapped wings can reduce the downward frictional drag in their upward motion. During the fling, a large vertical force is produced, like that in the ideal fling, but the drag required to fling the wings is no longer 6–10 times larger than the vertical force and it is even a little smaller than the vertical force.

### Erratum: “Direct molecular simulation of internal energy relaxation and dissociation in oxygen” [Phys. Fluids 31, 076107 (2019)]

### Bifurcation and instability of annular Poiseuille flow in the presence of stable thermal stratification: Dependence on curvature parameter

The bifurcation and instability of nonisothermal annular Poiseuille flow (NAPF) of air as well as water is studied. We have emphasized the impact of a gap between cylinders in terms of curvature parameter (C) for axisymmetric as well as nonaxisymmetric disturbances. The results from the linear stability analysis reveal that the first azimuthal mode acts as a least stable mode of the NAPF of air for relatively small values of C. In this situation, even though for some values of C, the NAPF has supercritical bifurcation, but the same flow may experience subcritical bifurcation under zero azimuthal mode. It has also been observed that for relatively larger values of the Reynolds number (Re) and lower values of C, the NAPF under axisymmetric disturbance always exhibits subcritical bifurcation. However, for small values of Re, the NAPF exhibits only supercritical bifurcation. The finite amplitude analysis predicts only supercritical bifurcation of NAPF of water. The influence of nonlinear interaction of different harmonics on the amplitude profile as well as kinetic energy spectrum is investigated. The amplitude profile possesses a jump in the vicinity of a point where the type of bifurcation is changed. In the subcritical regime, the induced shear production due to modification of the gradient production acts as a main destabilizing factor balanced by the gradient production of kinetic energy.

### Toy model for vortex-ring-assisted particle drag in superfluid counterflow

Author(s): L. Moriconi

The interpretation of data obtained from particle image and tracking velocimetry in the study of superfluid flows has been so far a challenging task. Tracking particles (as solid hydrogen or deuterium) are attracted to the cores of quantized vortices, so that their dynamics can be strongly affected ...

[Phys. Rev. E 100, 043102] Published Thu Oct 03, 2019

### X-ray radiography of viscous resuspension

We use X-ray imaging to study viscous resuspension. In a Taylor-Couette geometry, we shear an initially settled layer of spherical glass particles immersed in a Newtonian fluid and measure the local volume fraction profiles. In this configuration, the steady-state profiles are simply related to the normal viscosity defined in the framework of the suspension balance model. These experiments allow us to examine this fundamental quantity over a wide range of volume fractions, in particular, in the semidilute regime where experimental data are sorely lacking. Our measurements strongly suggest that the particle stress is quadratic with respect to the volume fraction in the dilute limit. Strikingly, they also reveal a nonlinear dependence on the Shields number, in contrast with previous theoretical and experimental results. This likely points to shear-thinning particle stresses and to a non-Coulomb or velocity-weakening friction between the particles, as also evidenced from shear reversal experiments.

### Modeling the interplay between the shear layer and leading edge suction during dynamic stall

The dynamic stall development on a pitching airfoil at Re = 106 was investigated by time-resolved surface pressure and velocity field measurements. Two stages were identified in the dynamic stall development based on the shear layer evolution. In the first stage, the flow detaches from the trailing edge and the separation point moves gradually upstream. The second stage is characterized by the roll up of the shear layer into a large scale dynamic stall vortex. The two-stage dynamic stall development was independently confirmed by global velocity field and local surface pressure measurements around the leading edge. The leading edge pressure signals were combined into a single leading edge suction parameter. We developed an improved model of the leading edge suction parameter based on thin airfoil theory that links the evolution of the leading edge suction and the shear layer growth during stall development. The shear layer development leads to a change in the effective camber and the effective angle of attack. By taking into account this twofold influence, the model accurately predicts the value and timing of the maximum leading edge suction on a pitching airfoil. The evolution of the experimentally obtained leading edge suction was further analyzed for various sinusoidal motions revealing an increase in the critical value of the leading edge suction parameter with increasing pitch unsteadiness. The characteristic dynamic stall delay decreases with increasing unsteadiness, and the dynamic stall onset is best assessed by critical values of the circulation and the shear layer height which are motion independent.

### Pore-scale velocities in three-dimensional porous materials with trapped immiscible fluid

Author(s): Gaël Raymond Guédon, Fabio Inzoli, Monica Riva, and Alberto Guadagnini

We study and document the influence of wetting and nonwetting trapped immiscible fluid on the probability distribution of pore-scale velocities of the flowing fluid phase. We focus on drainage and imbibition processes within a three-dimensional microcomputed tomographic image of a real rock sample. ...

[Phys. Rev. E 100, 043101] Published Wed Oct 02, 2019

### Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities

Performing accurate large eddy simulations in compressible, turbulent magnetohydrodynamics (MHDs) is more challenging than in nonmagnetized fluids due to the complex interplay between kinetic, magnetic, and internal energy at different scales. Here, we extend the subgrid-scale gradient model, so far used in the momentum and induction equations, to also account for the unresolved scales in the energy evolution equation of a compressible ideal MHD fluid with a generic equation of state. We assess the model by considering box simulations of the turbulence triggered across a shear layer by the Kelvin-Helmholtz instability, testing cases where the small-scale dynamics cannot be fully captured by the resolution considered, such that the efficiency of the simulated dynamo effect depends on the resolution employed. This lack of numerical convergence is actually a currently common issue in several astrophysical problems, where the integral and fastest-growing-instability scales are too far apart to be fully covered numerically. We perform a priori and a posteriori tests of the extended gradient model. In the former, we find that, for many different initial conditions and resolutions, the gradient model outperforms other commonly used models in terms of correlation with the residuals coming from the filtering of a high-resolution run. In the second test, we show how a low-resolution run with the gradient model is able to quantitatively reproduce the evolution of the magnetic energy (the integrated value and the spectral distribution) coming from higher-resolution runs. This extension is the first step toward the implementation in relativistic MHDs.

### Unsteady behavior of wall-detached flow inside a steam turbine control valve

Wall-detached flow inside an ultra-supercritical steam turbine control valve was comprehensively investigated with detached-eddy simulation, proper orthogonal decomposition (POD), and flow reconstruction. The dependency of the wall-detached flow on the control valve’s opening ratio and pressure ratio was established first. Scattered wall-detached-flow, merged wall-detached-flow, and intersected wall-detached-flow were then identified by distinguishing the detachment scale of the wall-detached jet. Subsequently, flow analysis was conducted in terms of the statistical flow quantities, i.e., velocity fluctuation, turbulent kinetic energy, pressure loss, and pressure fluctuation. The statistical results demonstrated that the merged wall-detached-flow facilitated the most intensive velocity and pressure fluctuations inside the steam turbine control valve. The intersected wall-detached-flow encountered significant shock-wave reflections along the downstream pipe. By conducting POD analysis and flow reconstruction on the instantaneous flow snapshots, the dominant vortex structures and energetic pressure fluctuation modes were extracted to illustrate the wall-detached flow’s unsteady behavior. The results showed that the instabilities of the scattered wall-detached-flow were primarily represented by the horizontal flapping motion of the wall-detached jet. However, for the merged wall-detached-flow, both the vertical out-phase oscillation and the horizontal flapping motion of the wall-detached jet intensified, yielding essential axial pressure fluctuation modes. As for the intersected wall-detached-flow, due to the complex wave reflections and propagations, essential regions with velocity discontinuities and diagonal crosslines with intensive pressure fluctuations formed inside the valve pipe. These findings are of great practical significance for the operation and optimization of steam turbine control valves in thermal power plants.

### Formation and turbulent breakdown of large-scale vortical structures behind an obstacle in a channel at moderate Reynolds numbers

This paper deals with experimental investigation and direct numerical simulation of three-dimensional separated laminar and transitional flows behind a semicircular spanwise rib on a bottom wall of a rectangular channel at Reynolds numbers of up to 480. Particular emphasis is given to the formation mechanism of quasiperiodic large-scale vortex clouds in the mixing layer behind the rib. Vortical structures near the channel axis are formed due to pairing of spiral vortices emerging close to the vertical walls when the corner boundary layers impact on the rib. The effect of the Reynolds number and normalized channel size on the spiraling motion, generation, and shedding of large-scale vortex clouds has been estimated.

### Beyond the Langevin horn: Transducer arrays for the acoustic levitation of liquid drops

The acoustic levitation of liquid drops has been a key phenomenon for more than 40 years, driven partly by the ability to mimic a microgravity environment. It has seen more than 700 research articles published in this time and has seen a recent resurgence in the past 5 years, thanks to low cost developments. As well as investigating the basic physics of levitated drops, acoustic levitation has been touted for container free delivery of samples to a variety of measurements systems, most notably in various spectroscopy techniques including Raman and Fourier transform infrared in addition to numerous X-ray techniques. For 30 years, the workhorse of the acoustic levitation apparatus was a stack comprising a piezoelectric transducer coupled to a horn shaped radiative element often referred to as the Langevin horn. Decades of effort have been dedicated to such devices, paired with a matching and opposing device or a reflector, but they have a significant dependence on temperature and require precision alignment. The last decade has seen a significant shift away from these in favor of arrays of digitally driven, inexpensive transducers, giving a new dynamic to the topic which we review herein.

### The role of the free surface on interfacial solitary waves

We investigated theoretically and experimentally internal solitary waves (ISWs) in a two-layer fluid system with a top free surface. Laboratory experiments are performed by lock-release, under Boussinesq and non-Boussinesq conditions. Experimental results are compared with those obtained by the analytical solution of the Korteweg–de Vries (KdV) weakly nonlinear equation and by the strongly nonlinear Miyata-Choi-Camassa (MCC) model. We analyze the initial conditions which allow to find soliton solutions for both rigid-lid (-RL) and free-surface (-FS) boundary conditions. For the MCC-FS model, we employ a new mathematical procedure to derive the ISW-induced free surface displacement. The density structure strongly affects the elevation of the free surface predicted by the MCC-FS model. The free surface maximum displacement increases mostly with the density difference, assuming non-negligible values also for smaller interfacial amplitudes. Larger displacements occur for thinner upper layer thickness. The MCC-FS model gives the best prediction in terms of both internal waves geometric/kinematic features and surface displacements. The existence of a free surface allows the ISW to transfer part of its energy to the free surface: the wave celerity assumes lower values with respect to ISW speed resulting from the MCC-RL model. For ISWs with a very large amplitude, this behavior tends to fade, and the MCC-RL and the MCC-FS model predict approximately the same celerity and interfacial geometric features. For small-amplitude waves also, the predictions of the KdV-RL equation are consistent with experimental results. Thus, ISWs with an intermediate amplitude should be modeled taking into account a free top surface as the boundary condition.

### Probing vortex-shedding at high frequencies in flows past confined microfluidic cylinders using high-speed microscale particle image velocimetry

Vortex-shedding from micropins has the potential to significantly enhance and intensify scalar transport in microchannels, for example by improving species mixing. However, the onset of vortex-shedding and the mixing efficiency are highly sensitive to the confinement imposed by the microchannel walls. In this work, the time dependent flow past a cylindrical pin in microchannels with different levels of confinement was studied experimentally. The onset of vortex-shedding in such flows is associated with high, kilohertz range frequencies that are difficult to resolve using conventional laser-based microscale particle image velocimetry (μPIV) techniques. Hence, in this study, a high-speed μPIV technique was implemented in order to obtain time-resolved measurements of the velocity fields downstream of the micropin to estimate the corresponding vortex-shedding frequencies and quantify the mixing in the pin wake. The vertical confinement (pin length to diameter ratio) was found to delay the onset of vortex-shedding. When vortex-shedding was present, the shedding frequency and the corresponding Strouhal numbers were found to be greater in channels with higher lateral confinement for the same Reynolds number. Finite-time Lyapunov exponent analysis was performed on the acquired velocity fields to estimate the mixing performance. The results clearly illustrated the significant enhancement in both the mixing in the wake and the mass flux across the centerline of the wake induced by vortex-shedding.

### Probing vortex-shedding at high frequencies in flows past confined microfluidic cylinders using high-speed microscale particle image velocimetry

Vortex-shedding from micropins has the potential to significantly enhance and intensify scalar transport in microchannels, for example by improving species mixing. However, the onset of vortex-shedding and the mixing efficiency are highly sensitive to the confinement imposed by the microchannel walls. In this work, the time dependent flow past a cylindrical pin in microchannels with different levels of confinement was studied experimentally. The onset of vortex-shedding in such flows is associated with high, kilohertz range frequencies that are difficult to resolve using conventional laser-based microscale particle image velocimetry (μPIV) techniques. Hence, in this study, a high-speed μPIV technique was implemented in order to obtain time-resolved measurements of the velocity fields downstream of the micropin to estimate the corresponding vortex-shedding frequencies and quantify the mixing in the pin wake. The vertical confinement (pin length to diameter ratio) was found to delay the onset of vortex-shedding. When vortex-shedding was present, the shedding frequency and the corresponding Strouhal numbers were found to be greater in channels with higher lateral confinement for the same Reynolds number. Finite-time Lyapunov exponent analysis was performed on the acquired velocity fields to estimate the mixing performance. The results clearly illustrated the significant enhancement in both the mixing in the wake and the mass flux across the centerline of the wake induced by vortex-shedding.

### Numerical analysis of electroconvection in cross-flow with unipolar charge injection

Author(s): Yifei Guan and Igor Novosselov

Electrohydrodynamic convection between parallel electrodes with unipolar injection is investigated numerically. A parameter Y, defined as the ratio of the local electric force to the viscous force, characterizes the stability of the flow system.

[Phys. Rev. Fluids 4, 103701] Published Tue Oct 01, 2019

### Fluid-structure investigation of a squid-inspired swimmer

We propose a novel underwater propulsion system inspired by the jet-propelled locomotion mechanism of squids and other cephalopods. A two-dimensional nonaxisymmetric fluid-structural interaction model is developed to illustrate the physical mechanisms involved in the propulsive performance of this design. The model includes a deformable body with a pressure chamber undergoing periodic inflation and deflation motions enabled by attached springs and a nozzle through which the chamber is refilled and discharged (to form a jet). By using an immersed-boundary algorithm, we numerically investigate the dynamics of this system in the tethered mode. The thrust generation is found to increase with the frequency of body deformation, whereas the efficiency reaches a peak at a certain frequency. Examinations of the surrounding flow field illustrate a combination of vortices shed from the body and the nozzle. The optimal efficiency is reached when the nozzle-generated vortices start to dominate the wake. Our simulations also suggest that steady-state response can only be sustained for a few cycles before the wake is disturbed by a symmetry-breaking instability, which significantly affects the propulsive performance. Special strategies are needed to achieve stable long-distance swimming.

### The atmospheric Rayleigh-Bénard problem on the f-plane

When applied to a system of sizeable vertical extent that can undergo adiabatic expansion/compression, the Rayleigh-Bénard treatment of convection between two parallel plates, kept at constant temperature, needs to be amended with the consideration of potential temperature as the conserved thermodynamic variable. The fixed-temperature boundary conditions are therefore expressed as a combination of potential temperature and pressure, and this causes the solutions to be a mixture of the odd and even modes of the classical problem. Here, solutions are presented for a rotating system, which supports both stationary and oscillatory modes. While the stationary modes are all stabilized by this mechanism, as was shown previously for a nonrotating system, the oscillatory modes can have a lower critical Rayleigh number than their traditional counterpart, when the Prandtl number is approximately between 0.2 and 1.0.

### On the selection of perturbations for thermal boundary layer control

The convective instability of the natural convection boundary layers of air (Pr = 0.7) in the laminar-to-turbulent transition regime (Ra = 8.7 × 107–1.1 × 109) is investigated by stability analysis in the framework of direct numerical simulations. To understand the spatial and temporal evolution of the convective instability of the thermal boundary layers, small-amplitude random-mode numerical perturbations are first introduced into the boundary condition of the boundary layer flow. The prescribed full spectral perturbations (i.e., white noise) are mostly damped out immediately by a limited upstream boundary layer. A low-frequency band is initially distinct in the upstream near the leading edge but decays spatially as the instability propagates downstream. In contrast, a high-frequency band emerges to finally become the most dominant frequency band in the thermal boundary layer transition regime. To obtain further insights into the nature of the established high-frequency band, single-mode perturbations of various frequencies are then introduced into the boundary layer near the leading edge. It is found that a single-mode perturbation at the peak frequency within the high-frequency band excites the maximum response of the thermal boundary layer, suggesting that the peak frequency is in fact the characteristic frequency or resonance frequency of the thermal boundary layer. The dimensionless form of the dependence of the characteristic frequency on Ra is then found to be fc = 0.07Ra2/3. The single-mode perturbation numerical experiments also revealed the propagation speed of convective instability waves, which was significantly greater than the convection speed of the thermal boundary layer. The smaller the Ra, the larger the difference between the two propagation speeds. A semi-analytical scaling of the wave propagation speed in the form csc ∼ Ra1/2y1/2Pr was derived (y denoting the streamwise location of the boundary layer), providing a predictive correlation that can be used for thermal boundary layer control.

### Relations between skin friction and other surface quantities in viscous flows

This paper presents the derivations of the exact relations between skin friction and other important dynamical and kinematical quantities on a stationary curved surface in a viscous flow by applying the standard methods of differential geometry to the governing partial differential equations in fluid mechanics. In particular, the mathematical structures of the effects of the surface curvature are explicitly expressed, which extend the previous results on a flat surface. These relations reveal that skin friction is intrinsically coupled with surface pressure, temperature, and scalar concentration through the boundary enstrophy flux, heat flux, and mass flux, respectively. As an example, the relation between skin friction and surface pressure is examined in the Oseen flow over a sphere to elucidate the significant effect of the surface curvature at a very small Reynolds number. Two other validation examples are a gravity-driven creeping liquid film flow over a wavy surface and the Falkner-Skan flow over a wedge. Furthermore, the relation is applied to a simulated turbulent channel flow to explore the local near-wall coherent structure and understand its dynamical roles in turbulence production.