# Latest papers in fluid mechanics

### Effect of porosity on separated vortex rings of dandelion seeds

Research on unstable airflow in nature has long been an important subject in work on aerodynamics, and most principles of flight have been found in nature. The design of an aircraft requires considering not only the lift required to balance gravity but also the stability of the state of balance during the cruise. Dandelion seeds happen to have a similar flow stability during flight. These seeds have a pore-like disk structure such that when air flows through them, a separated vortex ring is generated above them. Dandelions stabilize the airflow by changing the tip structure of the fluff. This study uses computational fluid dynamics to replace the fluff structure of dandelion seeds with a rigid porous disk structure and numerically simulates the resulting flow model to examine the flight of dandelion seeds. The results show that when the porosity of the disk structure exceeds a threshold, an axisymmetric and stable separated vortex ring is generated. A comparison of the simulation with observations from a wind tunnel experiment showed that the two yielded similar results, which confirms the principle of the model of flight of dandelion seeds. The authors then explore the condition for the separation of the vortex ring and conclude that the change in porosity affects the characteristics of the vortex ring.

### The deflection angle between a wind-forced surface current and the overlying wind in an ocean with vertically varying eddy viscosity

The angle between the wind stress that overlies the ocean and the resulting current at the ocean surface is calculated for a two-layer ocean with uniform eddy viscosity in the lower layer and for several assumed eddy viscosity profiles in the upper layer. The calculation of the deflection angle is greatly simplified by transforming the linear, second-order, vertical structure equation to its associated nonlinear, first-order, Riccati equation. The transformation to a Riccati equation can be used as an alternate numerical scheme, but its main advantage is that it yields analytic expressions for several eddy viscosity profiles.

### Turbulent wake suppression of circular cylinder flow by two small counter-rotating rods

In this paper, we employ the high-fidelity spectral/hp method to investigate the control of wake turbulence behind a circular cylinder by direct numerical simulations. The preliminary results at Re = 500 show that, for rod rotation rate α > 3, the cylinder wake is stabilized and the flow achieves a steady state. To further explore the efficiency of this control at the early turbulent regime, we further increase the Reynolds number to 3900. Compared to the bare cylinder, the drag coefficient is measured to reduce by 25.1% for α = 2. This drag reduction is expected to result from the pressure recovery effects of rotating rods. The statistical analysis, in terms of contours of Reynolds stresses and turbulence kinetic energy, and the turbulent wake visualization are then performed in order to show the alteration of turbulent flow. Furthermore, by applying Bernoulli equation to a streamline encircling the control rod, we show that the mechanism of pressure recovery is still viscous in the turbulent regime of Re = 3900. However, it is expected that the inertial effect sets out to play a significant role farther away from the main cylinder.

### Modeling interaction between a Taylor bubble and small bubble in a rectangular column

The slip of a small bubble (SB) from the annular film of the slug/Taylor bubble (TB) is often encountered in the chemical reactors and has intrigued many researchers. A combined experimental and numerical study has been performed to investigate the interaction of the SB and the slug bubble in a rectangular column with viscous fluids. The interaction behavior of the SB depends upon its diameter, deq, and thermo-physical properties of the fluid. The SB sprints away from the slug bubble at low Morton numbers, [math] (sprint-away regime). On the other hand, SB interacts with TB due to its lower terminal velocity at higher Mo (bubble slip regime). The SB behaves independently ahead of the TB nose but accelerates linearly into its annular film. A regime map has been proposed to differentiate between the bubble slip and the sprint-away regime. The entrapped film between TB and SB is continuously fed from the annular film and avoids the coalescence. An ad hoc pressure jump model has been proposed to explain the repulsion of SB in the annular film. Furthermore, a modified lubrication theory based model predicted the stability of the entrapped film due to interfacial velocities and curvature.

### Stabilized motion of a freely falling bristled disk

Several tiny insects have peculiar porous wings composed of many bristles and perform an interesting passive flight known as parachuting. Despite numerous studies on the freefall of objects such as disks, the aerodynamic principles of the effects of a bristled configuration on the parachuting motion under external disturbances remain unexplored. Here, we experimentally investigate freely falling bristled disks over a wide range of Reynolds numbers by changing the number of bristles and the initial orientation angle and compare their kinematics with those of a full circular disk with no bristles. Given the same diameter and moment of inertia, bristled disks with a smaller area have a steady-state flow field similar to that of a circular disk by virtue of the presence of a fully formed virtual fluid barrier at low-Reynolds numbers. However, in the initial transient phase after release, the bristled disks show different damped oscillatory motions from a circular disk. Regardless of their initial orientation angle, the lateral and angular deviations of the bristled disks are smaller than those of the circular disk, producing a more stable freefall. This trend is also observed even for higher Reynolds numbers, where the bristled wings are known to be ineffective from the perspective of aerodynamic performance. By considering the vorticity fields around the disk, we suggest two vortex-related mechanisms that account for the stable falling of the bristled disk, namely, the formation of more symmetric vortex structures and the location of vortex cores closer to the disk center.

### Magnetic field based actuation and amalgamation of ferrofluid droplets on hydrophobic surface: An experimental and numerical study

This article presents a detailed experimental analysis along with numerical simulations to provide the information about shape evolutions and mechanism of actuation and amalgamation of the ferrofluid droplets deposited on a hydrophobic surface by moving a permanent magnet. To validate the numerical methods used in this article, a benchmark phenomenon of a sessile droplet spreading under the effect of a non-uniform magnetic field is first simulated, and the results are compared with available experimental observations. To further ensure the accuracy of experimental and numerical techniques and to understand the wetting properties and spreading behavior of non-stationary ferrofluid droplets, a prototype demonstration of the merging droplets on a hydrophobic solid surface in the presence of a permanent magnet is designed. It is observed that for hydrophobic surfaces, the merging droplets entrap an air bubble at the time of first contact. Moreover, the physics behind the transient variations of droplet morphology and the effect of the state-of-the-art parameters on droplet actuation are also discussed. The force evaluation, energy variations, velocity contours, and velocity vectors of the moving droplet are provided to understand the internal behavior of droplet mobility. Experiments are performed several times with different speeds of moving a magnet to find the critical velocity when the droplet fails to follow the magnet motion. While doing so, we encounter an anomalous phenomenon of thread formation and daughter droplet generation at the receding end of the sliding droplet. A phase diagram is also provided in the end, which describes different regions of the sliding phenomenon.

### Pipe flow with large particles and their impact on the transition to turbulence

Author(s): Martin Leskovec, Fredrik Lundell, and Fredrik Innings

Large particles disturb a flow more than small particles. Using Magnetic Resonance Imaging (MRI) and pressure drop measurements we find that large spherical and cubic particles in pipe flow promote subcritical turbulent-like flow disturbances (as seen in the radial mean velocity and rms profiles at Re=700). These disturbances lead to significant changes in the laminar-turbulent transition at low particle concentrations (<5% per volume). We suggest these observations can be explained by the relative magnitude of (i) particle interactions, (ii) flow disturbances introduced by the particles and (iii) viscous dissipation in the system.

[Phys. Rev. Fluids 5, 112301(R)] Published Mon Nov 16, 2020

### Heat transfer scaling in natural convection with shear due to rotation

Author(s): R. Vishnu and A. Sameen

Axial vortices are ubiquitous in nature and in engineering, and the breakdown of these vortices can have far-reaching consequences. In the presence of a temperature gradient, topological behavior dramatically changes depending on the various flow parameters. Quantities such as heat transport, scalar mixing, and turbulent correlations are influenced immensely by the interplay between rotation and convection.

[Phys. Rev. Fluids 5, 113504] Published Mon Nov 16, 2020

### Energetics of a bouncing drop: Coefficient of restitution, bubble entrapment, and escape

Drops bouncing on an ultra-smooth solid surface can either make contact with the surface or be supported on a thin cushion of gas. If the surface is superhydrophobic, either complete or partial rebound usually occurs. Recent experiments have shed light on the lubrication effect of the underlying gas layer at the onset of impact. Using axisymmetric direct numerical simulations, we shed light on the energetics of a drop bouncing from a solid surface. A complete energy budget of the drop and the surrounding gas during one complete bouncing cycle reveals a complex interplay between various energies that occur during impact. Using a parametric study, we calculate the coefficient of restitution as a function of Reynolds and Weber numbers, and the results are in good agreement with the reported experiments. Our simulations reveal that the Weber number, not the Reynolds number, has a stronger effect on energy losses as the former affects the shape of the drop during impact. At higher Weber and Reynolds numbers, a tiny gas bubble gets trapped inside the drop during impact. We show that a large amount of dissipation occurs during the bubble entrapment and escape process. Finally, analysis of the flow field in the underlying gas layer reveals that maximum dissipation occurs in this layer, and a simple scaling law is derived for dissipation that occurs during impact.

### Efficient modeling of three-dimensional convection–diffusion problems in stationary flows

A large number of transport processes in physics, chemistry, and engineering are described by a convection–diffusion equation. This equation is notoriously difficult to solve due to the presence of convection-related first-order gradient differential operators. We describe a new and efficient numerical method for solving the convection–diffusion equation for laminar flows within channels of arbitrary cross section. It is based on reducing the convection–diffusion equation to a set of pure diffusion equations with a complex-valued potential for which fast and numerically stable solvers are readily available. Additionally, we use an eigenvector projection method that allows us to compute snapshots of full concentration distributions over millions of finite elements within a few seconds using a conventional state-of-the-art desktop computer. Our results will be important for all applications where diffusion and convection are both important for correctly describing material transport.

### Direct numerical simulations of turbulent periodic-hill flows with mass-conserving lattice Boltzmann method

The multi-relaxation time lattice Boltzmann method is used to perform direct numerical simulations of laminar and turbulent pressure-driven flows within a channel with hill-shape periodic constriction for the first time. The simulations are conducted on a graphics processing unit cluster with two-dimensional domain decomposition to accelerate the computation. The hill-shape boundary is represented using the interpolated bounce back scheme. However, the scheme generates mass leakage across the boundary, which is more pronounced in the turbulent flow regime, and this may produce diverging solutions for turbulent flows. The mass leakage due to the local mass imbalance along the curved boundary is solved by modifying the distribution functions locally or globally, and both predict similar velocity distributions. Since the global correction method is more computing time-consuming, the local correction method is adopted. The present numerical implementation’s capability is first validated by performing direct numerical simulations of turbulent channel flow at Reτ = 180, and the current predicted results agree well with the benchmark solutions. Direct numerical simulations are further conducted for the turbulent flow over the periodic hill at Reh = 2800. Both the mean velocity and turbulent stress compare favorably with the benchmark solutions. The present simulation also correctly predicts the turbulence splatting effect near the windward hill. Both phenomena are in good accordance with the benchmark solutions.

### Genesis, evolution, and apocalypse of Loop Current rings

We carry out assessments of the life cycle of Loop Current vortices, so-called rings, in the Gulf of Mexico by applying three objective (i.e., observer-independent) coherent Lagrangian vortex detection methods on velocities derived from satellite altimetry measurements of the sea-surface height (SSH). The methods reveal material vortices with boundaries that withstand stretching or diffusion or whose fluid elements rotate evenly. This involved a technology advance that enables framing vortex genesis and apocalypse robustly and with precision in a truly parameter-free fashion. We find that the stretching- and diffusion-withstanding assessments produce consistent results, which show large discrepancies with Eulerian assessments that identify vortices with regions instantaneously filled with streamlines of the SSH field. The even-rotation assessment, which is vorticity-based, is found to be quite unstable, suggesting life expectancies much shorter than those produced by all other assessments.

### On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows

The near-wall structures and statistics of fluctuating pressure (p′) in compressible turbulent channel flows (CTCF) with isothermal walls have been investigated by direct numerical simulations. Two typical cases for high bulk Mach number Ma = 3.83 and low one Ma = 1.56 are considered. A novel type of near-wall pressure structures named “alternating positive and negative structures (APNS)” is found in the high-Ma case based on the comprehensive analysis of spectra and dynamic mode decomposition of p′. These APNS of p′ are identified to have the streamwise and spanwise length scales of (λx/h, λz/h) ≈ (0.9, 1.5), where h is the channel half-height, and prefer to inhabit the low-speed wall streaks. It is also verified via a pressure splitting method that the APNS of p′ are dominated by the compressibility effects. Based on the linear stability analysis, the APNS of p′ can be intimately related to a linear stability eigenmode of the high-Ma CTCF and are sustained by the transient growth mechanism as the disturbances of the APNS length scales. Furthermore, these APNS of p′ offer an extra mechanism to generate the near-wall p′ for the high-Ma case. Moreover, it is found that the APNS of p′ have a dominating effect on the pressure-dilatation correlation and the production of Reynolds shear stress. The present study may provide a reliable way to achieve a better understanding and modeling of compressibility effects in the wall-bounded turbulence of high Ma.

### Structures of liquid jets in supersonic crossflows in a rectangular channel with an expansion section

The structures of liquid jets in supersonic crossflows (LJISC) are characterized by using high-speed photography and shadowgraph techniques. These flow structures substantially interfere with the atomization and mixing of the jet. Experimental studies on flow and spray fields are performed under various Mach numbers, injection positions, and injection angles. The results establish that (1) the evolution process of LJISC in the expansion section can be divided into three stages, namely, aerodynamic induced liquid column fracturing, expansion wave promoted spray accelerating, and compression wave disturbed spray blending, and (2) increasing the injection angle or the incoming Mach number effectively improves the penetration depth of the jet spray and enhances the gas–liquid mixing efficiency. However, the position of injection has little effect on the penetration depth. This research provides a critical and deep understanding about the atomization process of injection in an air-breathing engine with a combustion chamber with an expansion section.

### Optimal chordwise stiffness distribution for self-propelled heaving flexible plates

The effect of non-uniform chordwise stiffness distribution on the self-propulsive performance of three-dimensional flexible plates is studied numerically. Some typical stiffness distributions, including uniform, declining, and growing distribution, are considered. First, the normalized bending stiffness [math] is derived, which can well represent the overall bending stiffness of the non-uniform plates. For different non-uniformly distributed plates with the same [math], the maximum displacement difference between the trailing and leading edges of the plate during the flapping is almost identical. There exists a common optimal [math] at which all the plates achieve their optimal performance, i.e., the highest cruising speed and efficiency. Second, we reveal what kind of non-uniform distribution could be the best at a specific [math] in terms of the propulsive performance. The force analysis indicates that a larger bending deformation in the anterior part for the growing distribution leads to a larger thrust. Hence, the large local slope along the anterior flexible plate is preferred to enhance the propulsive performance. The results obtained in this study may shed some light on a better understanding of the hydrodynamic effect on the self-propulsion of the non-uniform stiffness wings or fins of animals.

### Rough-wall turbulence in minimal flow units with rod-roughened walls

Numerical simulation of minimal flow units (MFUs) can obtain “healthy turbulence” below a certain wall-normal height by limiting the effects of large-scale motions in the outer region. By “health,” it is meant that the mean velocity profile is consistent with the full-sized flow. In the present study, MFUs with rod-roughened walls at friction Reynolds numbers of 1000, 2000, and 4000 are studied by direct numerical simulation. For all the minimal channels, the domain size in streamwise and spanwise directions and the geometric parameters of roughness elements remain unchanged under the normalization of viscous units. The spurious spanwise uniform motions (SUM), induced by the narrow width of MFU, have significant contribution to turbulent fluctuations, especially to pressure. The spurious SUM are proved to be structures traveling downstream, holding strong relationship with the domain width. A new decomposition method is proposed to eliminate the spurious SUM. The results of MFU show that the roughness functions at different Reynolds numbers agree well with each other, implying that the effect of roughness on the main flow is independent of Reynolds numbers. In the context of the same wall roughness, the turbulent fluctuations and the roughness-induced fluctuations exhibit good Reynolds number independence. Additionally, the results of premultiplied spectra of the three velocity components suggest that the MFU could represent the near-wall small-scale motions within the full-sized domain. The universal signals extracted from the full-sized channel agree well with the near-wall velocity fluctuations in the MFU for all three velocity components.

### Experimental investigation of internal two-phase flow structures and dynamics of quasi-stable sheet cavitation by fast synchrotron x-ray imaging

The quasi-stable sheet cavitation produced in a small Venturi channel is investigated using a fast synchrotron x-ray imaging technique aided with conventional high speed photography. The use of x rays instead of visible light solves cavitation opacity related issues, and x-ray phase contrast-based edge enhancement enables high-definition visualization of the internal two-phase morphology. The simultaneous acquisition of time-resolved velocity and void fraction fields through post-processing of the recorded x-ray images reveals, for the first time, the complex diphasic flow structures inside the sheet cavity, which is essentially divided into six characteristic parts. Distinct from the current mainstream view, the globally steady sheet cavitation is found to be characterized by a weak but constantly existing re-entrant flow that can penetrate the entire cavity. The turbulent velocity fluctuations inside the sheet cavity are also investigated. The turbulence level in the reverse flow region is observed to be as low as in the outer main flow, demonstrating the relatively steady status of the re-entrant flow. Unlike the streamwise and cross-stream fluctuations, the shear stress appears to be weakly correlated with the velocity gradient. The collapse of the vapor phase and the vaporization at the upstream cavity interface are found to be the primary causes of shear stress intensification.

### Transient compressible flow in a compliant viscoelastic tube

Motivated by problems arising in the pneumatic actuation of controllers for micro-electromechanical systems, labs-on-a-chip or biomimetic soft robots, and the study of microrheology of both gases and soft solids, we analyze the transient fluid–structure interactions (FSIs) between a viscoelastic tube conveying compressible flow at low Reynolds number. We express the density of the fluid as a linear function of the pressure, and we use the lubrication approximation to further simplify the fluid dynamics problem. On the other hand, the structural mechanics is governed by a modified Donnell shell theory accounting for Kelvin–Voigt-type linearly viscoelastic mechanical response. The fluid and structural mechanics problems are coupled through the tube’s radial deformation and the hydrodynamic pressure. For small compressibility numbers and weak coupling, the equations are solved analytically via a perturbation expansion. Three illustrative problems are analyzed. First, we obtain exact (but implicit) solutions for the pressure for steady flow conditions. Second, we solve the transient problem of impulsive pressurization of the tube’s inlet. Third, we analyze the transient response to an oscillatory inlet pressure. We show that an oscillatory inlet pressure leads to acoustic streaming in the tube, attributed to the nonlinear pressure gradient induced by the interplay of FSI and compressibility. Furthermore, we demonstrate an enhancement in the volumetric flow rate due to FSI coupling. The hydrodynamic pressure oscillations are shown to exhibit a low-pass frequency response (when averaging over the period of oscillations), while the frequency response of the tube deformation is similar to that of a bandpass filter.

### Nanoscale thin-film flows with thermal fluctuations and slip

Author(s): Yixin Zhang, James E. Sprittles, and Duncan A. Lockerby

The combined effects of thermal fluctuations and liquid-solid slip on nanoscale thin-film flows are investigated using stochastic lubrication equations (SLEs). The previous no-slip SLE for films on plates is extended to consider slip effects and a new SLE for films on fibers is derived, using a long...

[Phys. Rev. E 102, 053105] Published Fri Nov 13, 2020

### Thermoelectrohydrodynamic convection in parallel plate capacitors under dielectric heating conditions

Author(s): Harunori N. Yoshikawa, Changwoo Kang, Inoccent Mutabazi, Florian Zaussinger, Peter Haun, and Christoph Egbers

A theoretical model of thermal convection induced by dielectric heating is developed via further exploitation of the analogy between gravity-driven thermal convection and convection driven by an electrohydrodynamic effect. The model is applied to a horizontal layer of dielectric fluid to determine the conditions of convection generation by the linear stability theory. The competition between gravity and the electrohydrodynamic effect under dielectric heating gives rise to different flow patterns depending on the Rayleigh number.

[Phys. Rev. Fluids 5, 113503] Published Fri Nov 13, 2020