# Latest papers in fluid mechanics

### Molecular-scale friction at a water–graphene interface and its relationship with slip behavior

Understanding molecular-scale friction at a liquid–solid interface in a nanofluidic system is essential, as friction affects slip behavior and flow properties at the nanoscale. In this research, we compute the molecular-scale friction at a water–graphene interface, combined with theoretical analysis and Molecular Dynamics (MD) simulation. A solid–solid friction model is modified, regarding a new method to calculate the work done by the substrate. The reliability of the computations is validated by MD results. It is manifested that liquid–solid friction, solid–solid friction, and viscous friction within liquids have similar mechanisms in terms of energy barriers. Moreover, we analyze the relationship between the slip behavior and the friction process and obtain a theoretical foundation between the slip velocity and the friction force based on a classic molecular kinetic theory. This foundation indicates a hyperbolic-like relation between the friction force and the slip velocity for a single water molecule, which is almost linear under realistic experimental conditions. This foundation provides a new way to determine the boundary condition for water flow between graphene sheets.

### Modeling deformable capsules in viscous flow using immersed boundary method

This paper presents an immersed boundary method (IBM) for deformable capsules in incompressible viscous flow. Unlike the conventional IBM, the present method utilizes an unstructured mesh coupled with the moving least squares method, which improves the performance for applications involving a complex geometry. We validate our method through independent studies on oscillation and deformation of spherical capsules in viscous flow. Our simulations on a deformable capsule flowing in an elbow channel show that the capsule capillary number affects its shape and deformation area significantly. The maximum deformation area is found to be linearly proportional to the capillary number. In addition, our simulation on soft capsule sorting using a pinched flow fractionation microfluidic device shows that smaller capsules tend to migrate toward the pinched wall region before streaming out in the expansion region. The result is that smaller capsules drift closer to the center plane of the device and can be efficiently separated from the larger ones using branching. For capsule sorting applications using T-junction, we found that the fate of a capsule depends on the relative position of its center of mass and the dividing streamline. Larger capsules are diverted from the main stream toward the side outlet, leading to effective size fractionation.

### On the receptivity of surface plasma actuation in high-speed boundary layers

Significant amounts of work have been conducted in the area of plasma flow control, while the receptivity of plasma actuation in high-speed boundary layers has not had much attention over the last two decades. In the present study, the receptivity of a Mach 4.5 flat-plate boundary layer to plasma heating actuation produced by pulsed-DC surface dielectric barrier discharge (SDBD) has been studied by direct numerical simulation (DNS) and stability analysis. With the help of multimode decomposition technology, the amplitude of normal modes can be obtained. The results show that both fast and slow modes can be excited by plasma actuation, and the receptivity maximum is observed near the lower neutral branch. Because the pulsed-DC SDBD actuation is typical periodic pulse signals, when the total power remains constant, the Fourier components with multiples of actuation frequency have the same energy, regardless of the waveform, period, and width of the actuation signal. Such characteristics benefit the robustness of the pulsed-DC SDBD actuator. A theoretical prediction method by combining the receptivity model and linear parabolized stability equations is considered in the present study, and good agreement with the DNS results is achieved.

### N-symmetric interaction of N hetons. I. Analysis of the case N = 2

We examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-layer quasi-geostrophic model. We consider the special case of N-fold symmetry in which the original system of 4N ordinary differential equations reduces to just two equations for the so-called “equivalent” heton. We perform a qualitative analysis to classify the possible types of vortex motions for the case N = 2. We identify the regions of the parameter space corresponding to unbounded motion and to different types of bounded, or localized, motions. We focus on the properties of localized, in particular periodic, motion. We identify classes of absolute and relative “choreographies” first introduced by Simó [“New families of solutions to the N-body problems,” in Proceedings of the European 3rd Congress of Mathematics, Progress in Mathematics Vol. 201, edited by C. Casacuberta, R. M. Miró-Roig, J. Verdera, and S. Xambó-Descamps (Birkhäuser, Basel, Barcelona, 2000), pp. 101–115]. We also study the forms of vortex trajectories occurring for unbounded motion, which are of practical interest due to the associated transport of heat and mass over large distances.

### Leapfrogging criteria for a line vortex pair external to a circular cylinder

The interaction of two line vortices of differing strengths in the presence of a circular cylinder is considered. Explicit criteria are derived, a function of vortex strengths (including strengths of opposite signs) and the cylinder radius, which separate different behaviors of the system. If the initial position of the vortices satisfies these criteria, they will undergo a periodic leapfrogging motion as they rotate around the cylinder; otherwise, the vortices still interact weakly with one another except without leapfrogging. This is in contrast to the planar wall case where if no periodic leapfrogging occurs, the vortices move apart and do not interact with each other. Numerical results for initial vortex positions which do and do not satisfy these criteria are presented to demonstrate the different motions available, as well as the robustness of the criteria.

### A simplified discrete unified gas kinetic scheme for incompressible flow

The discrete unified gas kinetic scheme (DUGKS) is a new finite volume (FV) scheme for continuum and rarefied flows, which combines the benefits of both the lattice Boltzmann method and UGKS. By the reconstruction of the gas distribution function using particle velocity characteristic lines, the flux contains more detailed information of fluid flow and more concrete physical nature. In this work, a simplified DUGKS is proposed with the reconstruction stage on a whole time step instead of a half time step in the original DUGKS. Using the temporal/spatial integral Boltzmann Bhatnagar–Gross–Krook equation, the auxiliary distribution function with the inclusion of the collision effect is adopted. The macroscopic and mesoscopic fluxes of the cell on the next time step are predicted by the reconstruction of the auxiliary distribution function at interfaces along particle velocity characteristic lines. According to the conservation law, the macroscopic variables of the cell on the next time step can be updated through its flux, which is a moment of the predicted mesoscopic flux at cell interfaces. The equilibrium distribution function on the next time step can also be updated. The gas distribution function is updated by the FV scheme through its predicted mesoscopic flux in a time step. Compared with the original DUGKS, the computational process of the proposed method is more concise because of the omission of half time step flux calculation. The numerical time step is only limited by the Courant–Friedrichs–Lewy condition, and a relatively good stability has been preserved. Several test cases, including the Couette flow, lid-driven cavity flow, laminar flows over a flat plate, a circular cylinder, and an airfoil, and microcavity flow cases, are conducted to validate the present scheme. The observed numerical simulation results reasonably agree with the reported results.

### Multi-temperature vibrational energy relaxation rates in CO2

Rates of vibrational energy relaxation in carbon dioxide are studied in the framework of the three-temperature kinetic-theory approach. Vibrational–translational transitions in the bending mode and inter-mode exchange of vibrational quanta are considered. In the zero-order approximation of the generalized Chapman–Enskog method, the energy relaxation rates in the coupled symmetric–bending and asymmetric modes are expressed in terms of thermodynamic forces similar to chemical reaction affinities, and a compact representation for the vibrational energy production rates is proposed. Linearized theory is developed, and analytical ratios of linearized relaxation rates to those defined by the original Landau–Teller (LT) theory are obtained. The relaxation rates are calculated using the Schwartz–Slawsky–Herzfeld (SSH) and forced harmonic oscillator models for the vibrational energy transition probabilities in the temperature range 200 K–10 000 K. For inter-mode exchanges, using the SSH theory yields significantly underpredicted relaxation rates. The ranges of applicability for the LT formula and linearized theory are estimated; the original LT formula for inter-mode vibrational energy exchanges is not capable of accounting for the excitation of both vibrational modes; linearized models yield better results. Possible steps for improving the numerically efficient LT model are proposed.

### Modeling of turbulent mixing with an improved K–L model

Turbulent mixing, induced by Rayleigh–Taylor (RT), Richtmyer–Meshkov (RM), and Kelvin–Helmholtz (KH) instabilities, broadly occurs in both natural phenomena, such as supernova explosions, and engineering applications, such as inertial confinement fusion (ICF). These three instabilities usually simultaneously exist and are highly coupled to drive and affect turbulent mixing, which raises a great challenge for turbulence modeling. In this study, an improved version of the K–L model is proposed. The modifications include that: (i) the deviatoric shear stress is considered to describe the KH instability; (ii) the concept of characteristic acceleration is introduced to better distinguish RT and RM instabilities; and (iii) an enthalpy diffusion is directly derived from the internal energy equation to model the turbulent diffusion term. Then, a unified set of model coefficients is systematically derived based on the self-similar analysis and physical observations. This model is validated by canonical RT, RM, and KH mixings and further investigated for more complex cases, including the RM mixing with multiple reshocks, the two-dimensional RT mixing called “tilted-rig,” and the simple spherical implosion, a much simplified version of an ICF implosion. Good agreement with the corresponding experimental and numerical data is achieved, revealing the ability of the present model to describe combined buoyancy, shock, and shear effects, which will contribute to a further application in real problems.

### Analysis of the effect of intermittency in a high-pressure turbine blade

High-pressure turbine blades are subject to large thermomechanical loads that may threaten their mechanical integrity. The prediction of the heat transfer on the blade surface, crucial to ensure its durability, thus requires an accurate description of the flow physics around the blade to be reliable. In an effort to better qualify the use of computational fluid dynamics in this design context as well as the need for an improved understanding of the flow physics, this paper investigates a transonic highly loaded linear turbine blade cascade that has been found difficult to predict in the literature using large-eddy simulations. Indeed, the configuration results in shocks and acoustic waves on the suction side of the blade, features that are commonly encountered in high-pressure turbines. Turbulent spots are observed on the suction-side boundary layer with an inlet turbulence intensity of 6%. The turbulent spots are shown to have a complex and highly unsteady effect on the shock/boundary-layer interaction, disrupting flow detachment and creating laminar spots downstream of the shock. To address these transient flow phenomena, conditional averages based on the intermittency level are introduced to show that accurate heat transfer predictions require an accurate prediction of the rate of turbulent-spot production. The analysis then focuses on the effect of intermittency on the turbulent kinetic energy exchanges in the near-wall region as the turbulent kinetic energy balance must be addressed in Reynolds-averaged Navier–Stokes models.

### Two-dimensional numerical study of gap resonance coupling with motions of floating body moored close to a bottom-mounted wall

The piston mode fluid resonance in the narrow gap between a moored floating body and a bottom-mounted vertical wall is numerically investigated based on a two-dimensional potential flow model and viscous numerical simulations. This study focuses on understanding the effect of mooring stiffness on the coupling dynamics of the gap resonance and the sway or heave motion of the floating body in regular waves. Numerical studies show that the resonant wave amplitude in the gap is reduced by the sway and heave motions. The reduction is highly dependent on the mooring stiffness. Two resonant frequencies are confirmed, and both increase with the mooring stiffness. Different modes of motions are identified in terms of the phase difference between the oscillatory motions of the gap flow and the floating body. Higher harmonic components of responses are found for the specific mooring stiffness. The performance of potential flow models in predicting resonant responses is revisited based on the understanding that the overall damping effect consists of two parts: (1) radiation damping and (2) viscous dissipation. It is confirmed that a potential model is also able to produce reasonable predictions as radiation damping plays a dominant role, for example, at the second resonant frequencies of coupling the gap resonance with the sway motion. Otherwise, as viscous dissipation dominates radiation damping, noticeable over-predictions by a potential model occur as recognized before, for example, the present results at the second peak response of gap resonance with the heave motion. The relative viscous dissipation is quantified with the reflection coefficient of viscous numerical results, while the radiation damping is quantified based on a specially designed radiation potential model with inputs of viscous numerical solutions.

### Visualizing droplet dispersal for face shields and masks with exhalation valves

Several places across the world are experiencing a steep surge in COVID-19 infections. Face masks have become increasingly accepted as one of the most effective means for combating the spread of the disease when used in combination with social-distancing and frequent hand-washing. However, there is an increasing trend of people substituting regular cloth or surgical masks with clear plastic face shields and with masks equipped with exhalation valves. One of the factors driving this increased adoption is improved comfort compared to regular masks. However, there is a possibility that widespread public use of these alternatives to regular masks could have an adverse effect on mitigation efforts. To help increase public awareness regarding the effectiveness of these alternative options, we use qualitative visualizations to examine the performance of face shields and exhalation valves in impeding the spread of aerosol-sized droplets. The visualizations indicate that although face shields block the initial forward motion of the jet, the expelled droplets can move around the visor with relative ease and spread out over a large area depending on light ambient disturbances. Visualizations for a mask equipped with an exhalation port indicate that a large number of droplets pass through the exhale valve unfiltered, which significantly reduces its effectiveness as a means of source control. Our observations suggest that to minimize the community spread of COVID-19, it may be preferable to use high quality cloth or surgical masks that are of a plain design, instead of face shields and masks equipped with exhale valves.

### Rupture process of liquid bridges: The effects of thermal fluctuations

Author(s): Jiayi Zhao, Nan Zhou, Kaixuan Zhang, Shuo Chen, Yang Liu, and Yuxiang Wang

Rupture of a liquid bridge is a complex dynamic process, which has attracted much attention over several decades. We numerically investigated the effects of the thermal fluctuations on the rupture process of liquid bridges by using a particle-based method know as many-body dissipative particle dynam...

[Phys. Rev. E 102, 023116] Published Mon Aug 31, 2020

### Waves and instabilities of viscoelastic fluid film flowing down an inclined wavy bottom

Author(s): Sanghasri Mukhopadhyay and Asim Mukhopadhyay

Evolution of waves and hydrodynamic instabilities of a thin viscoelastic fluid film flowing down an inclined wavy bottom of moderate steepness have been analyzed analytically and numerically. The classical long-wave expansion method has been used to formulate a nonlinear evolution equation for the d...

[Phys. Rev. E 102, 023117] Published Mon Aug 31, 2020

### Resolvent analysis of an airfoil laminar separation bubble at $\text{Re}=500\phantom{\rule{0.16em}{0ex}}000$

Author(s): Chi-An Yeh, Stuart I. Benton, Kunihiko Taira, and Daniel J. Garmann

The perturbation dynamics over an airfoil laminar separation bubble (LSB) is examined via resolvent analysis. The computational burden of singular value decomposition (SVD) is relieved through the randomized method, and the local energy amplification mechanisms of the LSB are extracted from the global resolvent operator with the discounting approach. With the applications of input and output windows, it is shown that the Kelvin-Helmholtz instability dominates the energy amplification over the LSB, and the optimal momentum-based forcing aligns with the tangential direction of the surface.

[Phys. Rev. Fluids 5, 083906] Published Mon Aug 31, 2020

### Migration, trapping, and venting of gas in a soft granular material

Author(s): Sungyon Lee, Jeremy Lee, Robin Le Mestre, Feng Xu, and Christopher W. MacMinn

Gas migration through a soft, liquid-saturated granular material involves a strong coupling between the motion of the gas and the deformation of the material. This process is central to many natural and industrial systems, such as the generation and venting of gases from lake beds and waste ponds. Using high-resolution experiments and a simple mechanistic model, grain-scale fluid and solid mechanics are linked with macroscopic migration, trapping, and venting. The largest amount of trapping and the largest venting events are found to occur at intermediate confining stress.

[Phys. Rev. Fluids 5, 084307] Published Mon Aug 31, 2020

### Lift enhancement strategy and mechanism for a plunging airfoil based on vortex control

A new flow control strategy based on leading-edge vortex (LEV) manipulation is proposed to improve the aerodynamic performance of a plunging airfoil. It has been found that the low pressure region produced by the LEV contributes to the high lift during dynamic stall, while the growth of the secondary vortex would weaken the LEV and result in a decrease in lift. Accordingly, the vortex control hypothesis is that we change the evolution of the secondary vortex and LEV, thus achieving a higher lift coefficient with a longer duration. The suction actuator is placed at different positions on the upper surface of the airfoil to test the control hypothesis. When the suction actuator is near the leading edge, the LEV detaches from the shear layer earlier and it can only enhance the lift slightly while not delay stall time. When the suction actuator is near the middle region, it could inhibit the growth of the secondary vortex and, thus, reduce its strength greatly. Therefore, the LEV circulation could continue to increase. As a result, the suction control could increase the lift coefficient and also prolong the high-lift duration. When the suction actuator is near the trailing edge, an increase in lift could also be achieved by an increase in the negative pressure over the upper surface as well as the LEV circulation. Thus, we present and validate the lift enhancement strategy for an unsteady airfoil based on vortex control.

### Formulating turbulence closures using sparse regression with embedded form invariance

Author(s): S. Beetham and J. Capecelatro

In recent years, machine-learning techniques have been leveraged to improve closures for the Reynolds-average Navier-Stokes equations. The efficacy of a sparse regression-based method that results in compact, algebraic models and ensures key physical properties such as form invariance is demonstrated. Further, success for learning accurate models from data spanning full high-fidelity sets to experimental (sparse and noisy) data is shown.

[Phys. Rev. Fluids 5, 084611] Published Fri Aug 28, 2020

### Frameworks for investigation of nonlinear dynamics: Experimental study of the turbulent jet

Analysis methods that have been developed in the field of nonlinear dynamics have provided valuable insights into the physics of turbulent flows, although their application to open flows is less well explored. The nonlinear dynamics of a turbulent jet with a low-to-moderate Reynolds number is investigated by using the single-trajectory framework and ensemble framework. We have used Lyapunov exponents to calculate the spectra of scaling indices of the attractor. First, we evaluated the frameworks on two theoretical models, one with a stationary attractor (Lorenz-63) and the other with time-varying characteristics (Lorenz-84). Theoretical studies showed that in dynamical systems with a stable attractor, both frameworks estimated the same largest Lyapunov exponent. The ensemble framework enables us to resolve the unsteady characteristics of a time-varying strange attractor. Second, we applied both frameworks to time-resolved planar velocity fields in a turbulent jet at local Reynolds numbers (Reδ) of 3000 and 5000. Time-resolved particle image velocimetry was utilized to measure streamwise and transverse velocity components. Results support the presence of a low-dimensional attractor in the reconstructed phase space with a chaotic characteristic. Despite considerable changes in the dynamics for the higher Reynolds number case, the system’s fractal dimension did not change significantly. We have used Lagrangian Coherent Structures (LCSs) to study the relationship between changes in the Lyapunov exponent with flow topological features. Results suggest that holes in the stable LCSs provide a path for the entrainment of the coflow, which is shown to be one of the main contributors to high Lyapunov exponents.

### Centrifugal filtration convection in bidisperse media

This work is concerned with thermal dispersion through a rotating fissured porous medium. In particular, linear and nonlinear analyses are made to investigate centrifugation driven thermal convection in a bidisperse porous medium. The presence of micro-pores in addition to the usual ones in a porous medium is considered, which allows the possibility of momentum exchange between the two families of pores. The linear analysis is performed through the normal modes, whereas the nonlinear one is based on a suitably defined generalized energy functional. Sharp and unconditional nonlinear L2 stability limits are obtained through the variational principles. Compound matrix method based numerical solutions of the resulting eigenvalue problems are obtained, and the usefulness of nonlinear results is established in most parts of the parameter space. It is found that an increase in momentum exchange delays convection, however, depending on the ratio of permeabilities in the two families of pores.

### Elastohydrodynamical instabilities of active filaments, arrays, and carpets analyzed using slender-body theory

Author(s): Ashok S. Sangani and Arvind Gopinath

A linear stability theory is developed to examine the conditions under which self-sustained oscillations occur in elastic filaments attached to a sphere or a wall subject to uniform force applied parallel to the axis of the filament. We shown that N equi-spaced filaments attached to a wall can undergo N different oscillation modes. The mode of first oscillation onset as the magnitude of the tangential force is increased, however, always corresponds to the mode of all filaments oscillating together in-phase. The figure shows the critical load and emergent frequency at the onset of instability for filaments oscillating in phase.

[Phys. Rev. Fluids 5, 083101] Published Thu Aug 27, 2020