# Latest papers in fluid mechanics

### A lubricant-infused slip surface for drag reduction

Seaweed and fish have slippery outer surfaces because of the secretion of a layer of mucus. The hydrodynamics over a three-dimensional lubricant-infused slip surface that mimics the mucus layers of seaweed and fish was numerically explored. The morphological features of the lubricant-infused surface were designed to mimic such biological mucus storage systems. The lubricant was assumed to fill the cavity and to be supplemented without limit from the bottom surface of the cavity. The slip motion at the interface between the lubricant and water was simulated by using the volume of fluid method. Simulations were performed for two cavity open area fractions, 40% and 60%, and for three lid thicknesses, 0.01D, 0.03D, and 0.06D, where D is the width of the cavity (D = 400 μm). The simulation was conducted by employing realistic material properties. The contact angle of the lubricant in deionized water was directly measured (θeq = 25.9°). This slippery lubricant layer contributes to drag reduction by lessening the velocity gradient of the surrounding fluid. The hydrodynamics of the slip surface was examined by scrutinizing the effects of varying the open area and the lid thickness on the slip velocity and length, the dispersion area, and the lubricant consumption. The maximum slip velocity and length were obtained in the center of the contact interface, which forms a paraboloid. The effects of varying the cavity open area fraction on the maximum slip velocity and length are significant. The lid thickness affects both the lubricant dispersion pattern and the height to which the lubricant builds up. The lubricant consumption for a cavity open area fraction of 60% is larger than that for 40%. The cavity with an open area fraction of 60% and a lid thickness of 0.06D provides the best drag reduction of the cavities we simulated.

### From turbulence to landscapes: Logarithmic mean profiles in bounded complex systems

Author(s): Milad Hooshyar, Sara Bonetti, Arvind Singh, Efi Foufoula-Georgiou, and Amilcare Porporato

We show that similarly to the logarithmic mean-velocity profile in wall-bounded turbulence, the landscape topography presents an intermediate region with a logarithmic mean-elevation profile. Such profiles are present in complex topographies with channel branching and fractal river networks resultin...

[Phys. Rev. E 102, 033107] Published Mon Sep 14, 2020

### Nonspherical modes nondegeneracy of a tethered bubble

Author(s): Maxime Fauconnier, Jean-Christophe Béra, and Claude Inserra

When excited at sufficiently high acoustic pressures, a wall-attached bubble may exhibit asymmetric nonspherical modes. These vibration modes can be decomposed over the set of spherical harmonics Ynm(θ,ϕ) for a degree n and order m. We experimentally capture the time-resolved dynamics of asymmetric ...

[Phys. Rev. E 102, 033108] Published Mon Sep 14, 2020

### Diffusion enhancement in a levitated droplet via oscillatory deformation

Author(s): Yuki Koyano, Hiroyuki Kitahata, Koji Hasegawa, Satoshi Matsumoto, Katsuhiro Nishinari, Tadashi Watanabe, Akiko Kaneko, and Yutaka Abe

Recent experimental results indicate that mixing is enhanced by a reciprocal flow induced inside a levitated droplet with an oscillatory deformation [T. Watanabe *et al.*, Sci. Rep. **8**, 10221 (2018)]. Generally, reciprocal flow cannot convect the solutes in time average, and agitation cannot take place...

[Phys. Rev. E 102, 033109] Published Mon Sep 14, 2020

### Mean-flow data assimilation based on minimal correction of turbulence models: Application to turbulent high Reynolds number backward-facing step

Author(s): Lucas Franceschini, Denis Sipp, and Olivier Marquet

We perform mean-flow reconstruction through variational data assimilation using Reynolds-Averaged Navier-Stokes equations closed by the Spalart-Allmaras model in a high Reynolds number Backward-Facing Step configuration. Two correction terms are used: a force term in the momentum equations and a scalar term in the turbulence model. We show that the force term perfectly reconstructs the target data but only for dense measurements, while the scalar solution is slightly less accurate, but independent of the number of measurements. An observability Gramian analysis shows that the scalar term is much less flexible than the force term.

[Phys. Rev. Fluids 5, 094603] Published Mon Sep 14, 2020

### Chemically reacting transverse plume

Author(s): P. Ranjan, K. Perez, T. Alvarado, B. Potter, and R. E. Breidenthal

A simple model of the transverse plume predicts that at a certain freestream speed, the entrainment rate is a maximum and the flame length is a minimum. This presumably corresponds to the most intense combustion in a compact wildfire. The model is in accord with laboratory experiments of a chemically reacting plume.

[Phys. Rev. Fluids 5, 094701] Published Mon Sep 14, 2020

### Understanding pulsed jet impingement cooling by instantaneous heat flux matching at solid-liquid interfaces

Author(s): Khan Md. Rabbi, Jake Carter, and Shawn A. Putnam

Introducing flow pulsation into a water-jet cooling system allows for flow-field control for more efficient heat removal. Here, transient thermal mapping is used to quantify how a pulsed water jet in a falling-film geometry can enhance the overall cooling performance. It is found that the influence of the jet-pulsation frequency on the maximum cooling performance can be predicted by heat flux matching at the solid-liquid interface, while the optimum pulsation frequency is dictated by the thermofluid instabilities that occur in the falling film.

[Phys. Rev. Fluids 5, 094003] Published Fri Sep 11, 2020

### Particle-induced miscible fingering: Continuum limit

Author(s): Rui Luo, Yun Chen, and Sungyon Lee

Oil is injected into a mixture of the same oil and noncolloidal particles inside a Hele-Shaw cell to investigate the connection between miscible fingering and the interfacial structure that develops inside the thin gap. By tuning the channel confinement relative to the particle size, it is demonstrated that shear-induced diffusion of particles can be enhanced and the interfacial shape caused to become more rounded, which results in changes in fingering morphologies. The results of the study suggest a potential use of the wall confinement to control hydrodynamic instabilities uniquely in suspensions.

[Phys. Rev. Fluids 5, 094301] Published Fri Sep 11, 2020

### Generating a tide-like flow in a cylindrical vessel by electromagnetic forcing

We show and compare the numerical and experimental results on the electromagnetic generation of a tide-like flow structure in a cylindrical vessel, which is filled with the eutectic liquid metal alloy GaInSn. Fields of various strengths and frequencies are applied to drive liquid metal flows. The impact of the field variations on amplitude and structure of the flow is investigated. The results represent the basis for a future Rayleigh–Bénard experiment, in which a modulated tide-like flow perturbation is expected to synchronize the typical sloshing mode of the large-scale circulation and the helicity oscillation connected with it. A similar entrainment mechanism might play a role in the synchronization of stellar dynamos by tidal forces.

### Adaptive control of transonic buffet flows over an airfoil

Flow state can be changed by multiple disturbances and uncertain factors in a complex flow environment, which calls for great interest to adjust the control law automatically to adapt to the changing flow environment. Model-based control can obtain predetermined control effects, but its adaptive ability is limited due to the modeling accuracy and unmodeled dynamics of the reduced-order model. To overcome these limitations, the data-driven adaptive control of transonic buffet flow based on the radial basis function neural network (RBF-NN) is carried out in this work. The actuator is the trailing edge flap, and the feedback signal is the lift coefficient. The historical input and output are used in the RBF-NN adaptive control to calculate the current control input from the neural network. When the flow state changes, the parameters of the neural network are adjusted by an adaptive mechanism to make the system work in an optimal or a near-optimal state automatically. Results show that buffet loads can be suppressed completely by RBF-NN control, even if the freestream Mach number and the angle of attack change continuously [from (M, α) = (0.7, 5.5°) to (M, α) = (0.8, 1.5°)]. The control strategy proposed in this work only needs the historical response data of the flow field, and it shows little dependence on the low-order linear model of the system. Therefore, it can be applied to the unstable flow control, in which the low-order model of the flow is difficult to construct and automatically adapt to the changing flow environment.

### Instabilities and turbulence in a forced turbulent convex wall jet

The outer part of a turbulent wall jet streaming over a convex surface satisfies the centrifugal instability criterion. This gives rise to streamwise vortices that convect and grow with the wall jet. These vortices are highly unsteady, which causes the turbulence characteristics of a convex wall jet to be much stronger than that of a plane wall jet. Particle image velocimetry based investigations have been carried out in this work to understand the source of this unsteadiness. A cylinder with steady spanwise heterogeneities at the nozzle lip has been used to restrict the unsteadiness of the naturally occurring streamwise vortices such that ensemble averaging techniques can be applied. The analysis reveals that the turbulent stresses are spanwise periodic; radial and azimuthal fluctuations are highest in the upwash regions, and spanwise fluctuations are highest in the downwash regions between the counter-rotating vortices. The spanwise wavelength of the vortices increases by merging, but the merging process does not restore the spanwise uniformity of the Reynolds stresses. A Proper Orthogonal Decomposition (POD) analysis in the cross-stream plane suggests the existence of instabilities that extract energy from the mean flow to sustain these fluctuations. Secondary flows produced by steadier streamwise vortices generate inflection points in the spanwise and radial directions that trigger such secondary instabilities. POD analysis in the streamwise plane reveals the presence of a traveling wave that gives rise to the spanwise meandering of the vortices. The local Strouhal number of this traveling wave, defined using the local spanwise wavelength and jet maximum velocity, is a constant value of 1. Instability waves with similar characteristics have also been observed in other centrifugally unstable flows.

### A non-linear turbulence model of supercritical fluid considering local non-equilibrium of Reynolds stress transport

For supercritical fluid turbulence, the traditional Reynolds-averaged Navier–Stokes models cannot yield satisfying predictions under the heat transfer deterioration condition due to the modifications of the buoyancy on turbulence. Direct numerical simulation results reveal that in the buoyancy flow, the linear Reynolds stress constitutive equation in the eddy viscosity model (EVM) is invalidated, and the pressure fluctuation contributes to Reynolds stress transport. A new modeling approach for the EVM of supercritical flow is investigated in two aspects: (i) the analytical solution of the pressure strain term in the Reynolds stress transport equation is obtained by solving the Poisson equation of the pressure fluctuation of supercritical flow, and then, the models of the slow term and rapid term are proposed and (ii) a non-linear constitutive equation between the Reynolds stress and the mean strain rate is proposed. Combining these two points, the modified expressions for the eddy viscosity and turbulent Prandtl number are finally developed. We find that the accuracy of the prediction by the new model on supercritical fluid heat transfer and turbulence statistics in vertical flow and horizontal flow can be significantly improved.

### Numerical simulation of the dynamic stall of a freely rotating hydrofoil

Vortex shedding of freely rotating hydrofoils and the fluctuations in hydrodynamic loads are typical problems in marine engineering. Hence, the hydrodynamic mechanism should be investigated in detail. In this study, the Reynolds-averaged Navier–Stokes method is used to analyze the unsteady flow characteristics of a two-dimensional freely rotating hydrofoil in uniform flow at different Reynolds numbers. The accuracy of the numerical simulation method is verified through convergence analysis of the simulation results. According to the mechanical characteristics and flow field distributions, the effects of three Reynolds numbers from 5 × 104 to 1.2 × 106 and five rotation centers from 0.2c to 0.4c on the dynamic stall of the hydrofoil are analyzed. The results show that the rotation center considerably influences the dynamic stall characteristics of the hydrofoil. As the rotation center approaches 0.4c, the amplitudes of the drag and lift coefficients and the rotation angle of the hydrofoil clearly increase by at least 206%, 10.5%, and 185%, respectively, along with the vortex shedding frequency, which also leads to the increase in the Strouhal number by at least 17.3%. Furthermore, the recovery of the drag and lift coefficients is delayed, resulting in an evident hysteresis effect. Simultaneously, this dynamic stall results in the decrease in the velocity distribution amplitude in the wake field and the increase in the pressure difference between the upper and lower surfaces. The continuous shedding of strong vortices from the trailing edge also leads to more complicated flow field characteristics.

### Rayleigh–Taylor instability at spherical interfaces between viscous fluids: The fluid/fluid interface

Through the computation of the most-unstable modes, we perform a systematic analysis of the linear Rayleigh–Taylor instability at a spherical interface separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration over the entire parameter space. Using the growth rate as the dependent variable, the parameter space is spanned by the spherical harmonic degree n and three dimensionless variables: the Atwood number A, the viscosity ratio s, and the dimensionless variable [math], where aR, ρ2, and μ2 are the local radial acceleration at the interface and the density and viscosity of the denser overlying fluid, respectively. To understand the effect of the various parameters on the instability behavior and to identify similarities and differences between the planar and spherical configurations, we compare the most-unstable growth rates [math] (planar) and [math] (spherical) under homologous driving conditions. For all A, when s ≪ 1, the planar configuration is more unstable than the spherical ([math]) within the interval 0 < B < ∞. However, as s increases to [math], there is a region for small values of B where [math], whereas for larger values of B, [math] once again. When s ∼ 2, the maximum of [math] for the n = 1 mode is greater than [math] for any other mode (n ≥ 2). For [math], [math] for all A within 0 < B < ∞. We find that the instability behavior between the planar and spherical systems departs from each other for s ≳ 2 and diverges considerably for s ≫ 1. In the limit when s → ∞, the planar configuration reduces to the trivial solution [math] for all B and A, whereas [math] has a non-zero limiting value for the n = 1 mode but vanishes for all the other modes (n ≥ 2). We derive an equation for [math] in this limit and obtain closed form solutions for the maximum of [math] and the value of B at which this occurs. Finally, we compare the most-unstable growth rates between the exact dispersion relation and three different approximations to highlight their strengths and weaknesses.

### Effects of symmetry on magnetohydrodynamic mixed convection flow in a vertical duct

Magnetohydrodynamic convection in a downward flow of liquid metal in a vertical duct is investigated experimentally and numerically. It is known from earlier studies that in a certain range of parameters, the flow exhibits high-amplitude pulsations of temperature in the form of isolated bursts or quasi-regular fluctuations. This study extends the analysis while focusing on the effects of symmetry introduced by two-sided rather than one-sided wall heating. It is found that the temperature pulsations are robust physical phenomena appearing for both types of heating and various inlet conditions. At the same time, the properties, typical amplitude, and range of existence in the parametric space are very different at the symmetric and asymmetric heating. The obtained data show good agreement between computations and experiments and allow us to explain the physical mechanisms causing the pulsation behavior.

### Direct numerical simulations of nanoparticle formation in premixed and non-premixed flame–vortex interactions

Direct numerical simulations (DNSs) of nanoparticle formation in reactive flows are challenging, and only greatly simplified DNS test-cases are possible, which help clarify the turbulence–particle–dynamics interaction and guide the necessary modeling efforts. As a basis for such studies, a new DNS database is introduced, which resolves the smallest relevant scales of the nanoparticle concentration field to obtain insights into the statistics of nanoparticle formation in reactive flows. Formation and evolution of iron oxide nanoparticles in premixed and non-premixed flames wrapped-up by a vortex have been investigated using the sectional model and direct chemistry. The DNSs capture the “engulfing” and local dilution of the particle fields. Different zones of high particle number concentration have been found in every flame, and it was shown that the thickness of these zones decreases with increasing Schmidt number, which confirms that in simulations of nanoparticle-forming turbulent reacting flows, the grid resolution has to be very fine to resolve the characteristic scale for high sections. The contributions to the change in particle concentration due to diffusion, coagulation, and nucleation have been analyzed in detail, and dominant contributions across the particle number concentration layers and across the flames have been identified. This analysis has also been carried out in terms of flat, concave, and convex iso-surface geometries, induced by the flame–vortex interaction and characterized by the curvature of the particle number concentration fields and also by the flame curvature. The results demonstrate that the flame curvature effects cannot be ignored in modeling strategies. The probability density functions for the particle number concentrations have been analyzed and quantified in terms of Shannon information entropy, which illustrates the effect of fast diffusion (and entropy production) of the smaller particles and slow diffusion (and entropy production) of the largest particles with high Schmidt numbers. In addition, the unclosed filtered or averaged agglomeration term was evaluated as a basis for future modeling efforts, showing that agglomeration rates will be underestimated by orders of magnitude unless suitable models are developed.

### Comparison of wave–structure interaction dynamics of a submerged cylindrical point absorber with three degrees of freedom using potential flow and computational fluid dynamics models

In this paper, we compare the heave, surge, and pitch dynamics of a submerged cylindrical point absorber, simulated using potential flow and fully resolved computational fluid dynamics (CFD) models. The potential flow model is based on the time-domain Cummins equation, whereas the CFD model uses the fictitious domain Brinkman penalization technique. The submerged cylinder is tethered to the seabed using a power take-off (PTO) unit, which restrains the heave, surge, and pitch motions of the converter and absorbs energy from all three modes. It is demonstrated that the potential theory overpredicts the amplitudes of heave and surge motions, whereas it results in an insignificant pitch for a fully submerged axisymmetric converter. It also underestimates the slow drift of the buoy, which the CFD model is able to capture reliably. Furthermore, we use fully resolved CFD simulations to study the performance of a three degrees of freedom cylindrical buoy under varying PTO coefficients, mass density of the buoy, and incoming wave heights. It is demonstrated that the PTO coefficients predicted by the linear potential theory are sub-optimal for waves of moderate and high steepness. The wave absorption efficiency improves significantly when a value higher than the predicted value of the PTO damping is selected. Simulations with different mass densities of the buoy show that converters with low mass densities have an increased tension in their PTO and mooring lines. Moreover, the mass density also influences the range of resonance periods of the device. Finally, simulations with different wave heights show that at higher heights, the wave absorption efficiency of the converter decreases and a large portion of available wave power remains unabsorbed.

### Yielding of cellulose nanocrystal suspensions in the presence of electrolytes

The rheological properties and yielding behavior of 1 wt. % aqueous sulfonated cellulose nanocrystals (CNCs) in the presence of monovalent (Na+) ions have been investigated. The introduction of more than 20 mM NaCl to the system causes aggregation of neutralized CNCs and leads to the formation of self-similar clusters, which grow in size until they form a three-dimensional network. In the present work, we report a comprehensive study of nonlinear rheology and yielding behavior of CNC/salt gels in steady shear and oscillatory experiments. Two yield stresses have been determined. The first yield stress at low shear rates is attributed to the disconnected CNC clusters as a result of bond breakage. The second yield point occurs at higher shear rates, and it is related to the deformation of clusters, where individual nanorods are nearly separated and dispersed. The existence of these two yield stresses has been identified in both steady-shear scans (high to low and low to high) as well as oscillatory experiments, resulting in consistent results.

### Consequences of the close relation between Rortex and swirling strength

Direct consequences stem from the close relation between the recently proposed vortex vector (Rortex) and the swirling strength. It is shown that these vortex-identification methods share some relevant properties: (i) both provide the same and, practically, the largest vortex region, (ii) both allow an unlimited uniaxial stretching described by an axisymmetric strain rate, so the strain-rate magnitude inside a vortex may become much larger (without any limitation) than the vorticity magnitude, and (iii) both exhibit a discontinuous outcome, known as the so-called disappearing vortex problem.

### Quasi-two-dimensional foam flow through and around a permeable obstacle

Author(s): Natalia Shmakova, Thibaud Chevalier, Antti Puisto, Mikko Alava, Christophe Raufaste, and Stéphane Santucci

In a study of the evolving structure of two-dimensional liquid foams flowing through an inhomogeneous confining cell, the motion and deformation of their elementary components, the bubbles, are quantified for various confinement ratios. The flow experiments highlight the elastoplastic properties of foams, controlled by their liquid fraction, which are notably responsible for the symmetry breaking of the flow, with multipolar deformation and velocity fields around the localized inhomogeneity.

[Phys. Rev. Fluids 5, 093301] Published Thu Sep 10, 2020