# Latest papers in fluid mechanics

### 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.

### A study on mixing performance of dean flows through spiral micro-channel under various effects

This paper reports a parametric study on mixing performance of dean flows in spiral micro-channels using the finite element method. Many important parameters such as the Reynolds number (Re), Peclet number (Pe), flow rate ratio between two species flows (α), and ratio of diffusion coefficient (β) were examined for enhancing mixing efficiency (ηmix). The numerical results matched well with those predicted by the theoretical model. In addition, mixing efficiency of dean flows in the spiral micro-channel generally increased with increasing Re, particularly at low Pe. This is in contrast to results obtained for straight micro-channels with the same channel length. Mixing efficiency (ηmix) was affected significantly by the Pe number ranging from 103 to 4 × 104, and it increases with a decrease in Pe. In addition, ηmix varied remarkably with α, and the worst point, at which the ηmix decreases by 50%, occurs when α is around 2.0. Otherwise, ηmix is shown to be influenced slightly by β. Furthermore, a new generalized correlation was proposed for predicting the pressure drop throughout a spiral micro-channel effectively. These results provide good suggestions for optimizing mixing efficiency of dean flows in spiral micro-channels, which can be used for further biological and chemical analyses.

### A comprehensive numerical analysis of cross-flow vortex-induced vibrations for top tension risers under different flows

In this paper, the cross-flow vortex-induced vibration (VIV) response of a top tension riser under different flow fields are comprehensively studied using a numerical simulation model based on time domain analysis. A semi-empirical time-domain analysis model that considers the fluid-structure interaction problem in the riser vibration process is proposed and verified by comparison with the previous experimental results. The influence of the flow velocity, the spanwise length of the flow field, and other factors on the VIV amplitude and frequency characteristics of the riser is analyzed in detail. The results show that the VIV response of the riser exhibits obvious multi-modal characteristics, which are accompanied by modal transition, lock-in vibration, synchronous vibration, etc., and the region where the lock-in or synchronous vibration occurs is exactly the region where the crest of the amplitude curve locates. Besides, the VIV intensity of the riser in the stepped flow and uniform flow fields show a tendency of fluctuating increase with the increase of the flow velocity and spanwise length of the flow field, while the VIV intensity of the riser in shear flow is positively correlated with the flow velocity and spanwise length of the flow field. The present study may provide a reference for the prediction of VIV of marine riser in the complex current environment.

### General power-law temporal scaling for unequal-size microbubble coalescence

Author(s): Rou Chen, Huidan (Whitney) Yu, Jianhuan Zeng, and Likun Zhu

We systematically study the effects of liquid viscosity, liquid density, and surface tension on global microbubble coalescence using lattice Boltzmann simulation. The liquid-gas system is characterized by Ohnesorge number Oh≡ηh/ρhσrF with ηh,ρh,σ, and rF being viscosity and density of liquid, surfac...

[Phys. Rev. E 101, 023106] Published Mon Feb 10, 2020

### Multiscale approach to model steady meniscus evaporation in a wetting fluid

Author(s): Kishan Bellur, Ezequiel F. Médici, Chang Kyoung Choi, James C. Hermanson, and Jeffrey S. Allen

Evaporation flux in the thin transition film close to the wall is up to 100 times greater than at the center of a wetting meniscus. Despite higher evaporation flux, the thin film accounts for a relatively small part of the total evaporation from the liquid-vapor interface. The thin-film contribution is directly proportional to the solid wall thermal conductivity and inversely proportional to vapor pressure and Bond number.

[Phys. Rev. Fluids 5, 024001] Published Mon Feb 10, 2020

### Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Author(s): Jean-Baptiste Salmon and Frédéric Doumenc

The impact of buoyancy on the solute mass transport in an evaporating liquid mixture confined in a horizontal slit is studied theoretically. Solvent evaporation at one end of the slit induces solute concentration gradients, which, in turn, drive free convection, thus dispersing solutes in a steadily increasing length scale along the slit.

[Phys. Rev. Fluids 5, 024201] Published Mon Feb 10, 2020

### Fluctuations of Lyapunov exponents in homogeneous and isotropic turbulence

Author(s): Richard D. J. G. Ho, Andres Armua, and Arjun Berera

Using measurements of error growth and finite-time Lyapunov exponents, the amount of chaos in a turbulent system is calculated by direct numerical simulation. The statistical distributions of the chaos are dependent on the Reynolds number and the scale, with implications for the measurement of time-averaged properties.

[Phys. Rev. Fluids 5, 024602] Published Mon Feb 10, 2020

### Defects of Bénard cell on a propagating front

Bénard-Marangoni convection can be used to self-organize hexagonal convective cells, but defects easily emerge in the hexagonal pattern, which hinders its application in industry. The dynamics of front propagation and defect generation are studied in this paper. We focus especially on the onset process of a local disturbance of a hexagonal pattern, named the “nucleus.” The front propagation of the nucleus has been researched through numerical simulations of a model equation and experiments. In the numerical simulations, a single nucleus can evolve into a perfect hexagon pattern under critical or subcritical conditions, and a random disturbance can generate multiple nuclei which evolve into grain boundaries. In addition, under supercritical conditions, defects also emerge as a single nucleus grows. The instability of front propagation is considered to be the mechanism for the generation of irregular patterns. The curvature effect makes the protrusion of the front have a larger velocity in supercriticality, which results in a wavy front, and defects are generated in the concave portion of the front. Also, because of the curvature effect, the front of an irregular pattern has a larger velocity than that of the regular pattern since the protrusion of the front in the irregular pattern increases the average velocity. Experiments have also been carried out by using an infrared camera to analyze front propagation. The results are qualitatively in agreement with the results of numerical simulations. Through the study of defect generation in front propagation, we put forward a method for generating a hexagon pattern which greatly reduces the number of defects.

### Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow

Hydrodynamic behavior of two-dimensional tandem-arranged flapping flexible foils in uniform flow is investigated numerically by an immersed boundary-lattice Boltzmann method. The leading edge of the leading foil is forced to undergo both heave and pitch motions, while the leading edge of the trailing foil is forced to undergo heave motion only. Of particular interests are the effects of stream-wise gap distance Gx (Gx/c = 0.25–1.75, where c denotes the length of the foil) and the phase difference Φ between the heave motions of the foils (Φ/π = −1.00 to 1.00) on the hydrodynamic characteristics of the foils, such as the propulsive force, the propulsive efficiency, the passive deformation, and the flow field around the foils. For the leading foil, because of the existence of the trailing foil and the resulting gap flow between the foils, the propulsive performance is noticeably influenced by Φ at small Gx/c values and such an influence is weakened with increasing Gx/c. For the trailing foil, the propulsive performance is primarily affected by Φ, and the physics behind such a strong effect is that Φ dictates the manner by which the vortices shed from the leading foil interact with the trailing foil. In contrast, the interaction of the vortices shed from the leading foil with the trailing foil is not significantly affected by Gx/c because the trailing foil experiences similar vortices shed from the leading foil, regardless of Gx/c. With different Gx/c and Φ/π values, three distinct deformation states of the foils, namely, the symmetric periodic state, the asymmetric periodic state, and the irregular state, are identified and are mapped out in the (Φ/π, Gx/c) space. Good correlation between the deformation state of the foils and the propulsive performance of the trailing foil has been observed.