# Latest papers in fluid mechanics

### Multiplicity of solution for natural convective heat transfer and entropy generation in a semi-elliptical enclosure

The problem of steady natural convection in a bottom-heated semi-elliptical enclosure has been investigated numerically for a wide range of geometric and flow configurations using the finite volume method. The results are presented for varying Rayleigh numbers, Ra, in the range 1 × 102 ≤ Ra ≤ 5 × 104 and different values of aspect ratio, A = 1, 0.75, 0.5, and 0.25, where the aspect ratio, A, is defined as the ratio of lengths of the semi-minor axis to the semi-major axis of the semi-elliptical enclosure. It has been found that the steady-state solution appears in the form of single or multiple pairs of counter-rotating convection cells depending on the values of physical parameters. For A = 1, 0.75, and 0.5, as the value of Rayleigh number exceeds a critical value, natural convective flow inside the semi-elliptical enclosure exhibits multiple steady solutions with varying pairs of counter-rotating convection cells; however, such multiplicity of steady solutions could not be found for the cases of A = 0.25. The parametric variations of heat transfer and entropy generation rates are studied in detail. It is observed that the average Nusselt number associated with the natural convection in the semi-elliptical cavity is governed by several parameters: aspect ratio, Rayleigh number, number of convection cells, and intensity of convective motion inside the convection cells. The entropy generation due to viscous dissipation is found to be negligible as compared to the entropy generation due to conduction.

### Thermocapillary instability in a viscoelastic liquid layer under an imposed oblique temperature gradient

The linear stability analysis of a viscoelastic (Oldroyd-B) liquid layer subjected to an oblique temperature gradient (OTG) is investigated numerically. For the case of low liquid elasticity, the analysis shows a strong stabilizing effect of the horizontal component (HTG) of the OTG on the two elastic modes emerging due to the presence of the vertical component (VTG) of the OTG. However, if the liquid elasticity is sufficiently large, the HTG fails to stabilize the upstream elastic mode. The liquid elasticity stabilizes the Newtonian interaction mode arising out of the interaction between the HTG and the VTG. The thermocapillary flow introduced by the HTG leads to the development of a new elastic mode absent in the case of a Newtonian liquid layer. The present paper thus shows that the elasticity of the liquid plays a major role in the competition between various instability modes to determine the dominant mode of instability.

### Diffusiophoresis of a highly charged soft particle in electrolyte solutions induced by diffusion potential

Diffusiophoresis of a single soft particle in an electrolyte solution with induced diffusion potential is investigated theoretically in this study. A pseudo-spectral method based on Chebyshev polynomials is adopted to solve the resultant governing electrokinetic equations. Parameters of electrokinetic interest are examined extensively to explore their respective effect upon the particle motion, such as the fixed charge density and the permeability of the outer porous layer, the surface potential and size of the inner rigid core, and the electrolyte strength and magnitude of the induced diffusion potential in the solution. The nonlinear effects pertinent to highly charged particles, such as the double layer polarization effect and the counterion condensation effect, are scrutinized, in particular. Here, nonlinear effects refer to the effects that can only be properly revealed by accurately solving the complete nonlinear Poisson–Boltzmann equation governing the electric potential instead of the simplified linear Helmholtz equation under the Debye–Hückel approximation, valid for lowly charged particles only. We found, among other things, that characteristic local extrema in mobility profiles are mainly due to these two effects. Moreover, a soft particle moves fastest in dilute electrolyte solutions, in general. The smaller the soft particle is, the faster it moves under otherwise identical structural and electrokinetic conditions, provided that the particle radius is smaller than the Debye length, the characteristic thickness of the double layer. The shape of the double layer polarization takes an undulating multilayer form at large electrolyte strength. The results provided here are useful in practical applications such as drug delivery as well as microfluidic and nanofluidic operations.

### Sloshing suppression with active controlled baffles through deep reinforcement learning–expert demonstrations–behavior cloning process

This paper presents an effective paradigm to make full use of both Deep Reinforcement Learning (DRL) and expert knowledge to find an optimal control strategy. The paradigm consists of three parts: DRL, expert demonstrations, and behavior cloning. It is the first time that the proposed paradigm is used for suppressing tank sloshing with two active controlled horizontal baffles. Meanwhile, a self-developed computational fluid dynamics (CFD) solver is used to simulate the environment of tank sloshing. For direct DRL, both the proximal policy optimization agent and the twin delayed deep deterministic policy gradient agent are tested for performing learning. The strategies obtained by different algorithms may not be uniform even for the same environment. Then, we derive a simplified parametric control policy informed from direct DRL. Finally, DRL with behavior cloning is used to optimize the simplified parametric control policy. After training, the agent can actively control the baffles and reduce sloshing by ∼81.48%. The Fourier analysis of the surface elevations pinpoints that the aim of the control strategy obtained by DRL with behavior cloning is to disperse the wave energy and change the sloshing frequency of the tank through fast oscillation of baffles. This provides an idea to suppress sloshing, similar to forcing waves to disassemble ahead of time. The experience and insights gained from this study indicate that the future development direction of DRL + CFD is how to couple DRL, expert demonstrations, and behavior cloning.

### Propulsion performance of tandem flapping foils with chordwise prescribed deflection from linear potential theory

Author(s): J. Alaminos-Quesada and R. Fernandez-Feria

Analytical expressions are obtained for the propulsion and the wake structure of tandem flapping foils with chordwise deflection, explaining the propulsive performance improvement in relation to single foils or rigid-foil counterparts for certain combinations of frequency, spacing, and phase shift. The findings are of interest for the design of small aerial or aquatic vehicles using tandem propulsors.

[Phys. Rev. Fluids 6, 013102] Published Fri Jan 22, 2021

### Fluid dynamics and efficiency of colonial swimming via multijet propulsion at intermediate Reynolds numbers

Author(s): Houshuo Jiang, John H. Costello, and Sean P. Colin

Colonial physonect siphonophores swim via laterally distributed multijet propulsion. Here, computational fluid dynamics is employed to investigate the underlying fluid mechanics and adaptive values of this unique way of propulsion. It is found that colonial swimming achieves energetic benefits for jetting individuals within the colony because they require significantly lower per-module power than that required by a lone jet module swimming at the same speed.

[Phys. Rev. Fluids 6, 013103] Published Fri Jan 22, 2021

### Interaction between dual spherical particles during settling in fluid

Settling of solid particles in the fluid is one of the most basic forms of sediment transport. However, due to the complex particle–particle and particle–fluid interactions, the mechanism of settling is not yet fully understood. This study focuses on characterizing the dynamics of dual particles settling side by side. Both settling experiments and simulations are conducted with different initial spacings between particles and Reynolds numbers (Re). The range of Re is from 30 to 300, which corresponds to the transition zone between the Stokes and the Newton regime. Particle tracking velocimetry and particle image velocimetry are used in the experiments to determine particles’ trajectories and velocity fields around particles. A new electromagnetic release device is manufactured, which ensures accurate control of the initial condition. Together with the experiments, settling processes of particles are simulated based on discrete element–lattice Boltzmann method to investigate detailed flow structures. The results show that no attraction exists between particles when released simultaneously side by side. The repulsion between the two particles is a result of the asymmetry between the inside and outside vortices, and this repulsion will vanish when the initial spacing exceeds 5 particle diameters. Depending on the repulsion between particles, the settling process can be divided into three stages. The results also demonstrate that the initial spacing of the particles and Re are the two key parameters in the determination of the final settling velocity and separation distance. Their influence can be separated into two phase regimes depending on a critical Re (≈60), which is consistent with the one for the appearance of the Karman vortex street. In regime I (Re < 60), the settling process is dominated by viscous effects, and the effect of vortex interaction starts to take dominance in regime II (Re > 60). Overall, small initial spacing and large Re lead to strong repulsion between particles.

### Unsteady dynamics of wedge-induced oblique detonations under periodic inflows

Two-dimensional, wedge-induced oblique detonation waves (ODWs) subject to periodic inflow are simulated using the reactive Euler equations with a two-step induction–reaction kinetic model. The focus of this work is how the periodic unsteadiness of a sinusoidal density disturbance with varying frequency and amplitude influences an initially established ODW structure. Three fundamental ODW structures with different transition types and inflow Mach numbers are disturbed, resulting in two types of triple-point formations: the main triple point (MTP) and the train of triple points (TTP). The TTP features multi-triple points arising almost simultaneously and traveling together, which has never been observed before. A parametric study and frequency analysis reveal that the MTP derives from forced destabilization, while the TTP derives from the combined effect of surface instability and inflow disturbance. Furthermore, a new phenomenon of MTP degeneration is observed for a proper inflow Mach number and disturbance amplitude. Finally, the oscillation amplitudes of unsteady ODWs are analyzed with respect to the Mach number and inflow disturbance, demonstrating the effects of transition type on surface unsteadiness.

### Mixed convection between rotating sphere and concentric cubical enclosure

This paper presents numerical investigations of the mix convection between a rotating inner sphere and a concentric cubical enclosure, using the recently developed immersed boundary-simplified lattice Boltzmann method. The validity of the method has been established through benchmark tests, and a grid independence study is also carried out to ensure the accuracy of the conveyed results. Various factors that may influence the mixed convection system, such as the rotational direction, Rayleigh number, and rotational Reynolds number, are considered in the present study. Three representative rotational axes, namely, the vertical, the horizontal, and the diagonal axes, are selected. The Rayleigh number spans from 104 to 106, which covers the transition range from a conduction-dominated system to a convection-dominated one. Moreover, the rotational Reynolds number varies from 0 to 300. Distinct flow patterns, global heat transfer behavior, and the heat transfer rates on cubic walls are studied to reveal the characteristics of this problem. It is found that the rotationality of the inner sphere would increase the global heat transfer rate of the system and the rotating motion would stimulate heat transfer in the radial direction of the rotational axis while suppressing the thermal expansion in the axial direction.

### Editorial: The 2020 François Naftali Frenkiel Award for Fluid Mechanics

Author(s): John Kim and Gary Leal

[Phys. Rev. Fluids 6, 010001] Published Thu Jan 21, 2021

### A primitive variable discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes

A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier–Stokes equations is performed. An existing DEC method [M. S. Mohamed, A. N. Hirani, and R. Samtaney, “Discrete exterior calculus discretization of incompressible Navier–Stokes equations over surface simplicial meshes,” J. Comput. Phys. 312, 175–191 (2016)] is modified to this end and is extended to include the energy-preserving time integration and the Coriolis force to enhance its applicability to investigate the late-time behavior of flows on rotating surfaces, i.e., that of the planetary flows. The simulation experiments show second order accuracy of the scheme for the structured-triangular meshes and first order accuracy for the otherwise unstructured meshes. The method exhibits a second order kinetic energy relative error convergence rate with mesh size for inviscid flows. The test case of flow on a rotating sphere demonstrates that the method preserves the stationary state and conserves the inviscid invariants over an extended period of time.

### Tear-film breakup: The role of membrane-associated mucin polymers

Author(s): Anjishnu Choudhury, Mohar Dey, Harish N. Dixit, and James J. Feng

Mucin polymers in the tear film protect the corneal surface from pathogens and modulate the tear-film flow characteristics. Recent studies have suggested a relationship between the loss of membrane-associated mucins and premature rupture of the tear film in various eye diseases. This work aims to el...

[Phys. Rev. E 103, 013108] Published Wed Jan 20, 2021

### Hydrodynamic interactions between swimming microorganisms in a linearly density stratified fluid

Author(s): Rishabh V. More and Arezoo M. Ardekani

Oceans and lakes sustain intense biological activity due to the motion of marine organisms, which has significant ecological and environmental impacts. The motion of individual organisms and their interactions with each other play a significant role in the collective motion of swimming organisms. Ho...

[Phys. Rev. E 103, 013109] Published Wed Jan 20, 2021

### Rebound of large jets from superhydrophobic surfaces in low gravity

Author(s): Karl Cardin, Sheng Wang, Olivier Desjardins, and Mark Weislogel

The rebound of large water jets from a superhydrophobic substrate in the low-gravity environment of a drop tower is investigated. A regime map is constructed from drop tower test data. Scaling laws and simulations are used to identify boundaries between jet rebound regimes and to predict landing flow geometry.

[Phys. Rev. Fluids 6, 014003] Published Wed Jan 20, 2021

### Film coating by directional droplet spreading on fibers

Author(s): Tak Shing Chan, Carmen L. Lee, Christian Pedersen, Kari Dalnoki-Veress, and Andreas Carlson

Plants and insects use slender conical structures to transport and collect small droplets that are propelled along conical structures by capillary action. It is shown that these droplets can deposit a film with a thickness that depends on the fiber’s radius and the droplet size, highlighting that the coating is affected by finite size effects relevant to film deposition on fibers of any slender geometry. These self-propelled droplets have significant potential to create passively coated structures.

[Phys. Rev. Fluids 6, 014004] Published Wed Jan 20, 2021

### Molecular viscosity and diffusivity effects in transitional and shock-driven mixing flows

Author(s): F. S. Pereira, F. F. Grinstein, D. M. Israel, and R. Rauenzahn

This paper investigates the importance of molecular viscosity and diffusivity for the prediction of transitional and shock-driven mixing flows featuring high and low Reynolds and Mach number regions. Two representative problems are computed with implicit large-eddy simulations using the inviscid Eul...

[Phys. Rev. E 103, 013106] Published Tue Jan 19, 2021

### Compressibility effects in turbulent transport of the temperature field

Author(s): I. Rogachevskii and N. Kleeorin

Compressibility effects in a turbulent transport of temperature field are investigated by applying the quasilinear approach for small Péclet numbers and the spectral τ approach for large Péclet numbers. The compressibility of a fluid flow reduces the turbulent diffusivity of the mean temperature fie...

[Phys. Rev. E 103, 013107] Published Tue Jan 19, 2021

### Sound of effervescence

Author(s): Mathis Poujol, Régis Wunenburger, François Ollivier, Arnaud Antkowiak, and Juliette Pierre

An experimental study focuses on the airborne sound generated during bubble bursting at the surface of a liquid bath. It is found that the acoustic frequency drifts and increases, consistent with a Helmholtz-type resonance of the cavity being more and more opened as the thin film in the air retracts. As an extension, a simple model based on a collection of drifting Helmholtz resonators is proposed, capturing the main features of the fizzing sound of an effervescing beverage.

[Phys. Rev. Fluids 6, 013604] Published Tue Jan 19, 2021

### Theoretical framework for energy flux analysis of channels under drag control

Author(s): Xi Chen, Jie Yao, and Fazle Hussain

A new framework analyzes energy flux in turbulent channels under various controls, enabling estimations of drag reduction and net power saving, and also suggesting a perspective of composite control for future exploration.

[Phys. Rev. Fluids 6, 013902] Published Tue Jan 19, 2021

### Origin of hydrodynamic instability from noise: From laboratory flow to accretion disk

Author(s): Subham Ghosh and Banibrata Mukhopadhyay

The problem of the origin of turbulence, and hence, transport of angular momentum, in accretion flows (particularly cold flows) as well as laboratory flows like plane Couette flow, prevails due to their stability under linear perturbation. We attempt to resolve this long-standing issue with linear analysis by considering an extra stochastic force with a nonzero mean (m). We show that these flows become unstable, and the corresponding maximum growth rate (Im(β)max) increases, if the mean is increased, with other parameters fixed. Since accretion flow has a central sink a fluid parcel must take less time to become nonlinear than to cross the local analysis region, consistent with our analysis.

[Phys. Rev. Fluids 6, 013903] Published Tue Jan 19, 2021