# Latest papers in fluid mechanics

### Theory of acoustic trapping of microparticles in capillary tubes

Author(s): Jacob S. Bach and Henrik Bruus

We present a semianalytical theory for the acoustic fields and particle-trapping forces in a viscous fluid inside a capillary tube with arbitrary cross section and ultrasound actuation at the walls. We find that the acoustic fields vary axially on a length scale proportional to the square root of th...

[Phys. Rev. E 101, 023107] Published Thu Feb 20, 2020

### On-off switching of vortex shedding and vortex-induced vibration in crossflow past a circular cylinder by locking or releasing a rotational nonlinear energy sink

Author(s): Antoine B. Blanchard and Arne J. Pearlstein

Numerical simulations in two dimensions of the flow past a cylinder restrained by an elastic support find that the vortex-induced vibration can be suppressed using a nonlinear energy sink consisting of a rotating mass inside the cylinder.

[Phys. Rev. Fluids 5, 023902] Published Thu Feb 20, 2020

### Nonlinear delayed feedback model for incompressible open cavity flow

Author(s): F. Tuerke, F. Lusseyran, D. Sciamarella, L. Pastur, and G. Artana

A model based on hydrodynamic feedback mechanisms that is able to correctly reproduce power spectra commonly found in open cavity flows is presented. Using a delay differential equation, it takes into account time lags from the reflection of instability waves and the recirculation region inside the cavity.

[Phys. Rev. Fluids 5, 024401] Published Thu Feb 20, 2020

### Radial deformation and disintegration of an electrified liquid jet

Droplets stretched by electric stresses emit jets from their pointed tips. We observed in the experiment a new tip-streaming phenomenon by applying a radial electric field to a liquid jet. Droplets in the jet are stretched in the radial direction and develop into a disk-like shape. The growth of non-axisymmetric harmonics leads to the formation of tens of Taylor cones evenly distributed at the equator of a droplet. At the tip of each cone, a tiny secondary jet is emitted, which breaks up into progeny droplets orders of magnitude smaller than the parent ones. This tip-streaming pattern may provide a new spraying route to the generation of micro- and nanosized droplets.

### Dynamics of a circular cylinder with an attached splitter plate in laminar flow: A transition from vortex-induced vibration to galloping

Flow-induced vibration (FIV) of a circular cylinder with an attached splitter plate in a laminar flow with Re = 100 is studied numerically. First, the mechanical model along with mathematical formulations is proposed to describe the fluid-structure interaction (FSI) between the elastically supported cylinder–plate body and the surrounding flow. Subsequently, an FSI solution procedure is developed based on the characteristic-based split finite element method, and its accuracy and stability are validated using vortex-induced vibrations (VIVs) of a plain circular cylinder with benchmark solutions. Finally, using FSI simulations, effects of the plate length (L), reduced velocity, mass ratio and damping coefficient on the dynamic response, fluid load, and flow pattern of the cylinder–plate assembly are investigated in detail. As the plate length increases from L/D = 0–1.5 (D is the cylinder diameter), three FIV modes are observed successively: VIV, coupled VIV and galloping, and separated VIV and galloping, along with three vortex modes in the wake: 2S (two separated vortices in one cycle), P+S (a vortex pair and a separated vortex in one cycle), and 2P (two vortex pairs in one cycle). Moreover, it is found that the lift components generated from the splitter plate and the cylinder behave, respectively, as the driving force and the suppressing force of galloping, and the transition from VIV to galloping can be taken as a result of the competition between them. The cylinder–plate model presented could be taken as a benchmark model demonstrating the VIV-galloping interaction and applied to the design of novel FSI-based energy harvesters.

### A kinetic Fokker–Planck approach to model hard-sphere gas mixtures

Since its first introduction, it has always been a subject of research to find models for a meaningful approximation of the highly accurate but complex Boltzmann equation. In the kinetic Fokker–Planck (FP) approach, a FP operator in velocity space is employed to approximate the collision integral of the Boltzmann equation. Instead of directly solving the resulting FP equation, a Monte Carlo technique is used to model an associated random process. This approach leads to an efficient stochastic solution algorithm. In recent years, the FP ansatz has become increasingly popular. Nevertheless, the modeling of gas mixtures in the context of kinetic FP has so far only been addressed in a very few papers. This article introduces a kinetic FP model that is capable of describing gas mixtures with particles interacting according to the hard-sphere collision model. The model is constructed to reproduce Grad’s 13 moment equations on a Navier–Stokes level of accuracy for gas mixtures with an arbitrary number of constituents. A stochastic simulation algorithm is derived that ensures a correct evolution of the species diffusion velocities and the species temperatures for a homogeneous gas, regardless of the applied time step size. It is shown that the proposed model is capable of correctly predicting shear stresses, heat fluxes, and diffusion velocities for different test cases, employing a He–Ar mixture.

### On the spreading of non-canonical thermals from direct numerical simulations

We present results from direct numerical simulations on laminar and turbulent non-canonical thermals with an initial rectangular density distribution at a Reynolds number of Re = 500 and Re = 5000, respectively. We find the non-canonical shape to induce strong azimuthal variations in the thermal for both the laminar and turbulent cases. These include noticeable differences in downward and horizontal propagation speeds as well as differences in the strength of the vortex tube. These differences persist over a significant period of time and help generate a cross-flow component that is otherwise not present in canonical cases. The cross-flow component is in the opposite direction to that observed in gravity currents with the same initial density distribution. This is counterintuitive seeing that both flows are solely driven by buoyancy. By extracting the three-dimensional streamlines, we find the descending vortex tube to force the dense fluid to follow a helical path.

### Experimental investigation of unstart dynamics driven by subsonic spillage in a hypersonic scramjet intake at Mach 6

Understanding start–unstart behavior of intakes in hypersonic Mach numbers is essential for seamless operation of scramjet engines. We consider a high compression ratio intake (CR = 40) at a Mach number of M = 6 in this work. Start–unstart characteristics are studied in a hypersonic wind tunnel at a flight realistic Reynolds number (Re = 8.7 × 106/m, M = 6). A flap provided at the rear end of the isolator simulates the effect of backpressure for throttling ratios in the range of 0–0.69. Experiments are conducted in two modes: (a) with the flap fixed at a particular throttling ratio and (b) the flap moved to a particular throttling ratio after the started flow has been established. Unsteady pressure measurements and time-resolved Schlieren visualization are undertaken. Modal analysis of pressure (using fast Fourier transform) and Schlieren images (using dynamic mode decomposition) are carried out. The intake shows started behavior for throttling ratios up to 0.31 and a dual behavior, where it remains started in dynamic flap runs but unstarted in fixed flap runs for throttling ratios of 0.35 and 0.42. The intake exhibits a staged evolution to a large amplitude oscillatory unstart for throttling ratios of 0.55 and 0.69, with frequencies of 950 Hz and 1100 Hz, respectively. For the first time, a staged evolution (5 stages) to a subsonic spillage oscillatory unstart of a hypersonic intake is detailed using corroborative evidence from both time-resolved Schlieren and pressure measurements. A precursor to the final large amplitude oscillatory unstart is identified, and the flow mechanism for sustained oscillations is explained.

### Effects of favorable pressure gradient on turbulence structures and statistics of a flat-plate supersonic turbulent boundary layer

A Mach 2.9 flat-plate supersonic turbulent boundary layer subject to a moderate favorable pressure gradient (FPG) induced by external expansion waves is investigated through direct numerical simulation and compared with a zero pressure gradient (ZPG) boundary layer. It is found that under FPG, the logarithmic region in the van Driest transformed velocity profile is lifted above the log law, while the wake region deviates below its ZPG counterpart. The near-wall streaks are elongated in the streamwise direction with wider spanwise spacing, which leads to an attenuated meandering effect compared to the ZPG case. Although small-scale motions in the outer layer are evidently suppressed, they survive mostly in the inner layer. On the other hand, large-scale motions tend to correlate further with the lifted fluid from upstream due to bulk dilatation. However, their relative locations within the boundary layer remain unchanged. Different responses of turbulence structures in the inner and the outer layer to FPG show that this two-layer feature within the boundary layer is mainly associated with the bulk dilatation rather than the wall curvatures. The profiles of turbulent kinetic energy (TKE) and turbulent Mach number also show a two-layer behavior, where the reduction in turbulence in the outer layer is more prominent than in the inner. Positive convection occurs from the buffer to the outer layer according to the TKE budget analysis, which compensates the production and resists the decrease in the turbulence level.

### Capillary flow of sodium and zinc ionomers

The capillary flow properties of several commercial ionomers (sodium and zinc) were studied to assess their processability in terms of instabilities such as wall slip and melt fracture. Using capillary dies of various diameters and lengths to control capillary extrusion pressure, it was found that the viscosity of these polymers exhibits a relatively small dependence on pressure, more importantly at relatively smaller pressures. Using capillaries of various diameters at fixed length-to-diameter ratios, it was also found that the no-slip boundary condition is a valid assumption for these polymers due to the strong ionic associations and strong interactions with the capillary wall. All ionomers were found to exhibit gross melt fracture (no sharkskin), a phenomenon more dominantly observed at lower temperatures. The occurrence of gross melt fracture and the absence of surface (sharkskin) melt fracture is a characteristic of extensional strain-hardening polymers, noting that all ionomers examined exhibit this phenomenon. The critical shear stress for the onset of gross melt fracture was found to depend on the lifetime of associations, τS ([math], where ZE is the number of entanglements and ZS is the number of associations), independent of temperature, molecular weight, and type of ion (zinc or sodium).

### Numerical study of the Richtmyer–Meshkov instability of a three-dimensional minimum-surface featured SF6/air interface

The Richtmyer–Meshkov instability of a three-dimensional (3D) minimum-surface featured SF6/air interface subjected to a planar weak incident shock is numerically studied. The focus is placed on presenting more intuitive details of the complex shock-interface interactions. In the present work, 3D Euler equations are solved. The fifth-order weighted essentially non-oscillatory scheme and the level-set method combined with the real ghost fluid method are adopted. The gas interface morphologies are precisely reproduced according to the previous experimental images, the wave systems in 3D space are illustrated, and the velocity distribution in a characteristic plane is depicted. Based on which, the unknown lagging structure in the previous experiment can be reasonably explained. It is actually the soap fog driven by the flow field. The baroclinic vorticity generation and the perturbation amplitude growth histories are measured. The present numerical study well confirms the 3D curvature effect and supports the extended 3D theoretical model for the heavy/light interface scenario.

### Numerical study of fluid flow and heat transfer characteristics of an oscillating porous circular cylinder in crossflow

In this paper, numerical simulation of fluid flow and heat transfer characteristics of a porous cylinder subjected to a transverse oscillation in subcritical crossflow are studied for the first time. As such, the effects of Darcy number, 10−6 ≤ Da ≤ 10−2, reduced frequency, 0.2688 ≤ f* ≤ 1.075, dimensionless amplitude, A/d = 0.5 and 1, and Reynolds number, 5 ≤ Re ≤ 40, on the problem are investigated. It is revealed by the results that for an oscillating porous cylinder even at the subcritical Reynolds number of 40, the vortex shedding surprisingly develops behind the cylinder for cases with Da ≤ 10−4, f* = 1.075, and A/d = 1. Furthermore, it is shown that this subcritical vortex shedding always happens at the lock-in situation. The oscillation of the cylinder is shown to always increase the lift and drag coefficients compared to the stationary cylinder. According to the results, interestingly, the average drag coefficient increases with increasing Darcy number at intermediate Darcy numbers (10−4 ≤ Da ≤ 10−3). It is concluded that two mechanisms boost the heat transfer rate, namely, the vortex shedding, which is the case for the low Darcy zone at the highest frequency and amplitude of the oscillation, and the flow penetration, which is of more importance to the high Darcy zone. In conclusion, the maximum increase in the average Nusselt number is achieved at the highest values of the frequency and amplitude, which provide 18%, 28%, 51%, and 81% heat transfer enhancement compared to the stationary cylinder for Da = 10−6, 10−4, 10−3, and 10−2, respectively.

### Tip vortices formation and evolution of rotating wings at low Reynolds numbers

The wake structures generated by rotating wings are studied numerically to investigate the complex vortex formation and evolution in both near-wake and far-wake regions. Flat rectangular wings with finite aspect ratios (AR = 1–8) that rotate from rest at an angle of attack ranging from 15° to 90° in a low Reynolds number regime (200–1600) are considered. Simulations were carried out using an in-house immersed-boundary-method-based incompressible flow solver. A detailed analysis of the vortex formation showed that the general wake pattern near the wingtip shifted from a single vortex loop to a pair of counter-rotating vortex loops with the enhancement of the leading-edge vortex (LEV) strength. Specifically, a stronger LEV due to the high angles of attack or high aspect ratios can induce an enhanced counter-pair trailing-edge vortex (TEV). As the TEV intensifies, a secondary tip vortex will be generated at the bottom corner of the wingtip, regardless of the wing geometry. This forms a pair of counter-rotating vortex loops around the wingtip. This type of wingtip vortex formation and evolution are found to be universal for the range of angle of attack and aspect ratio investigated. In addition to the vortex formation, surface pressure distribution and aerodynamic performance are also discussed. The findings from this work could help advance the fundamental understanding in the vortex dynamics of finite-aspect ratio rotating wings at a high angle of attack (>15°).

### Hydrodynamics of flow over two-dimensional dunes

The turbulence characteristics in flow over and within the interface of two-dimensional dunes are investigated experimentally. Besides the spatial flow and turbulence quantities, their double-averaged profiles are also analyzed. The flow over dunes is recognized to be a wake-interference flow, where the decelerated flow at the immediate downstream of the crest causes the kolk-boil effect. The flow reattachment can be explained from the perspective of the Coandă effect. The inner boundary layer edge follows the locus of the inflection points of velocity profiles having a velocity defect. The Reynolds shear stress profiles attain their respective peaks along this locus. In addition, the dispersive shear stress initiates from the edge of the form-induced sublayer being negative, indicating a spatially decelerated flow. The third-order correlations reveal that an inrush of rapidly moving fluid streaks coupled with a downward-downstream Reynolds stress diffusion prevails within the interfacial sublayer, while an arrival of slowly moving fluid streaks coupled with an upward-upstream stress diffusion governs the flow zone above the crest. The turbulent kinetic energy (TKE) flux results corroborate the similar findings. Concerning the TKE budget, the dispersive kinetic energy diffusion is found to be substantial within the roughness sublayer. The budget terms exhibit their respective peaks near the crest. The production rate is greater than the dissipation rate. However, the TKE diffusion and pressure energy diffusion rates are negative in the interfacial sublayer. The bursting analysis endorses that the sweeps and ejections govern within the interfacial sublayer and the flow zone above the crest, respectively.

### Model-based estimation of vortex shedding in unsteady cylinder wakes

Author(s): Jiwen Gong, Jason P. Monty, and Simon J. Illingworth

Two model-based estimation methods are proposed to estimate the time-resolved cylinder wake based on a single sensor measurement. The two methods are compared at Re = 100 in simulations and at Re = 1036 in experiments. Results show that estimation can be improved when the nonlinear trigonometric relations between harmonics of the vortex shedding frequency are considered. A physical interpretation of the results is also given.

[Phys. Rev. Fluids 5, 023901] Published Thu Feb 13, 2020

### Friction scaling laws for transport in active turbulence

Author(s): Sanjay C. P. and Ashwin Joy

A continuum model is used to study the transport of light particles in a dense bacterial suspension. Universal scaling laws are provided for the diffusion coefficient, mean vortex size, and relaxation time as a function of fluid friction. The findings should apply to transport phenomena in generic active systems such as dense bacterial suspensions, microtubule networks, or even artificial swimmers, to name a few.

[Phys. Rev. Fluids 5, 024302] Published Thu Feb 13, 2020

### Three-dimensional biological hydrodynamics study on various types of batoid fishlike locomotion

Author(s): Namshad Thekkethil, Atul Sharma, and Amit Agrawal

Three-dimensional (3D) fluid-structure-interaction simulations are conducted for real and hypothetical batoid-fish-like swimming, using a unified 3D kinematic model; proposed here. The combined effect of batlike flapping and fishlike undulation results in various types of 3D vortex structures that are correlated with the propulsive performance parameters and can be used for an efficient design of underwater vehicles.

[Phys. Rev. Fluids 5, 023101] Published Wed Feb 12, 2020

### Deep learning methods for super-resolution reconstruction of turbulent flows

Two deep learning (DL) models addressing the super-resolution (SR) reconstruction of turbulent flows from low-resolution coarse flow field data are developed. One is the static convolutional neural network (SCNN), and the other is the novel multiple temporal paths convolutional neural network (MTPC). The SCNN model takes instantaneous snapshots as an input, while the MTPC model takes a time series of velocity fields as an input, and it includes spatial and temporal information simultaneously. Three temporal paths are designed in the MTPC to fully capture features in different time ranges. A weight path is added to generate pixel-level weight maps of each temporal path. These models were first applied to forced isotropic turbulence. The corresponding high-resolution flow fields were reconstructed with high accuracy. The MTPC seems to be able to reproduce many important features as well, such as kinetic energy spectra and the joint probability density function of the second and third invariants of the velocity gradient tensor. As a further evaluation, the SR reconstruction of anisotropic channel flow with the DL models was performed. The SCNN and MTPC remarkably improve the spatial resolution in various wall regions and potentially grasp all the anisotropic turbulent properties. It is also shown that the MTPC supplements more under-resolved details than the SCNN. The success is attributed to the fact that the MTPC can extract extra temporal information from consecutive fluid fields. The present work may contribute to the development of the subgrid-scale model in computational fluid dynamics and enrich the application of SR technology in fluid mechanics.

### Ceiling effects on the aerodynamics of a flapping wing with advance ratio

The ceiling effect on the aerodynamics of flapping wings with an advance ratio is investigated by solving the three-dimensional incompressible Navier–Stokes equations. The aerodynamic forces and flow fields around the model wings flapping in a horizontal plane were simulated at various advance ratios, Reynolds numbers, as well as the distance between the wing and the ceiling. It is found that the ceiling could improve the aerodynamic forces at a low advance ratio and this improvement in aerodynamic forces decreases as the distance between the wings and ceiling increases, similar to the results under hovering condition. However, the flow fields show that the aerodynamic force enhancement is only caused by the increment in the relative velocity of the oncoming flow; the ceiling would no longer enlarge the angle of incidence of the oncoming flow at the range of advance ratios considered, which is different from that under hovering condition. As the advance ratio increases, the enhancement in aerodynamics from the ceiling effect decreases. This is mainly due to the degeneration of the ceiling effect at the outer part of the wing, where the effect of increasing velocity becomes rather small at a high advance ratio. The weakened “increasing velocity effect” is closely associated with the detachment of the leading-edge vortex at the outer part of the wing at a high advance ratio.

### Observation and quantification of inertial effects on the drift of floating objects at the ocean surface

We present results from an experiment designed to better understand the mechanism by which ocean currents and winds control flotsam drift. The experiment consisted of deploying in the Florida Current and subsequent satellite tracking of specially designed drifting buoys of various sizes, buoyancies, and shapes. We explain the differences in the trajectories described by the special drifters as a result of their inertia, primarily buoyancy, which constrains the ability of the drifters to adapt their velocities to instantaneous changes in the ocean current and wind that define the carrying flow field. Our explanation of the observed behavior follows from the application of a recently proposed Maxey–Riley theory for the motion of finite-sized particles floating on the ocean surface. The nature of the carrying flow and the domain of validity of the theory are clarified, and a closure proposal is made to fully determine its parameters in terms of the carrying fluid system properties and inertial particle characteristics.