# Latest papers in fluid mechanics

### Optimal spanwise-periodic control for recirculation length in a backward-facing step flow

Author(s): E. Yim, I. Shukla, F. Gallaire, and E. Boujo

Spanwise-harmonic control in a separated flow can modify the mean length of the recirculation region. A second-order sensitivity analysis is used to compute small-amplitude spanwise-harmonic wall controls (blowing/suction or deformation) that most efficiently increase or decrease the mean recirculation length in the flow past a backward-facing step.

[Phys. Rev. Fluids 5, 083901] Published Tue Aug 04, 2020

### Viscous free-surface flows past cylinders

Author(s): Edward M. Hinton, Andrew J. Hogg, and Herbert E. Huppert

Free-surface flows of viscous liquid down an inclined plane and past cylinders of various cross-sections are studied theoretically and experimentally. For relatively wide cylinders, a pond of nearly stationary fluid forms upstream of the cylinder, and a dry region without fluid occurs downstream of it. The flow structure in the pond region depends on the cylinder cross-section and curvature at the upstream stagnation point. The theory is used to deduce simplified asymptotic expressions of the force on the cylinders. The work is relevant to volcanic lava flow deflection by barriers.

[Phys. Rev. Fluids 5, 084101] Published Tue Aug 04, 2020

### Spectra and scaling in chemically reacting compressible isotropic turbulence

Author(s): Jian Teng, Jianchun Wang, Hui Li, and Shiyi Chen

Spectra and statistics in chemically reacting compressible homogeneous isotropic turbulence is studied using numerical simulations. Reaction heat release significantly enhances the spectra of velocity and thermodynamic variables over a wide range of length scales. For exothermal reactions, acoustic mode dominates over the dynamics of compressible velocity and pressure from weak to highly compressible turbulence, and the ratio of compressible to solenoidal kinetic energy and the ratio of compressible to solenoidal dissipation appear to be independent of turbulent Mach number.

[Phys. Rev. Fluids 5, 084601] Published Tue Aug 04, 2020

### Sedimentation of a suspension of paramagnetic particles in an external magnetic field

Author(s): Jérémy Vessaire, Nicolas Plihon, Romain Volk, and Mickaël Bourgoin

We investigate the sedimentation of initially packed paramagnetic particles in the presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle-induced magnetic interactions are sign...

[Phys. Rev. E 102, 023101] Published Mon Aug 03, 2020

### Effect of a product on spontaneous droplet motion driven by a chemical reaction of surfactant

Author(s): Takahiro Tanabe, Takuto Ogasawara, and Nobuhiko J. Suematsu

We focus on the self-propelled motion of an oil droplet within an aqueous phase or an aqueous droplet within an oil phase, which originates from an interfacial chemical reaction of surfactant. The droplet motion has been explained by mathematical models, which require the assumption that the chemica...

[Phys. Rev. E 102, 023102] Published Mon Aug 03, 2020

### Effective aspect ratio of helices in shear flow

Author(s): Brian Rost, Justin T. Stimatze, David A. Egolf, and Jeffrey S. Urbach

We report the results of simulations of rigid colloidal helices suspended in a shear flow, using dissipative particle dynamics for a coarse-grained representation of the suspending fluid, as well as deterministic trajectories of non-Brownian helices calculated from the resistance tensor derived unde...

[Phys. Rev. E 102, 023103] Published Mon Aug 03, 2020

### Frozen patterns of impacted droplets: From conical tips to toroidal shapes

Author(s): Man Hu, Feng Wang, Qian Tao, Li Chen, Shmuel M. Rubinstein, and Daosheng Deng

Experiments find different forms of droplets that freeze on impacting a cold surface, including conical tipped (ICT), spherical caped (SCP), single torus (STS) and double torus (DTS).

[Phys. Rev. Fluids 5, 081601(R)] Published Mon Aug 03, 2020

### Pressure scrambling effects and the quantification of turbulent scalar flux model uncertainties

Author(s): Zengrong Hao and Catherine Gorlé

The epistemic uncertainty in turbulent scalar flux modeling directly affects the accuracy of scalar transport simulations. Two classical phenomenological theories on the pressure scrambling effect in scalar flux dynamics—return-to-isotropy and isotropization-of-production—are revisited from the perspective of uncertainty quantification (UQ). A prototype scalar flux model UQ method is thus formulated, providing a physical ground for the future data-driven UQ practice.

[Phys. Rev. Fluids 5, 082501(R)] Published Mon Aug 03, 2020

### Investigation into the rheology of a solid sphere suspension in second-order fluid using a cell model

Author(s): Liam J. Escott and Helen J. Wilson

The rheology of suspensions of solid spheres in viscoelastic background media is analytically calculated for dilute values of solid volume fraction. A mean-field cell model is used to express the influence of the solid particles in a suspending fluid, which obeys the second-order fluid model. A semi-analytical constitutive equation is created for the whole suspension, itself a second-order fluid with modified material parameters. The resulting rheology of the whole suspension is presented in simple shear, which shows predictions for the behavior of viscometric functions past explicitly dilute concentrations.

[Phys. Rev. Fluids 5, 083301] Published Mon Aug 03, 2020

### Collective vibrations of confined levitating droplets

Author(s): S. J. Thomson, M. M. P. Couchman, and J. W. M. Bush

Experiments are performed exploring the dynamics and stability of quasi-one-dimensional lattices of self-propelled millimetric droplets bouncing on a vertically vibrating liquid bath and confined to an annular ring. Depending on the droplet spacing, instability of the lattice may take the form of either out-of-phase oscillations or a striking solitarylike wave. Our results offer a new macroscopic platform to study collective phenomena and emergent structures in the burgeoning field of active and driven matter.

[Phys. Rev. Fluids 5, 083601] Published Mon Aug 03, 2020

### Influence of gravity on the frozen wave instability in immiscible liquids

Author(s): D. Gligor, P. Salgado Sánchez, J. Porter, and V. Shevtsova

Gravity is crucial to the frozen wave instability because it both sets the threshold of applied forcing and limits the growth of unstable perturbations. Through numerical simulations of immiscible liquids in finite containers we examine the transition from a supercritical pitchfork bifurcation in ordinary gravity, which is accompanied by stable finite-amplitude waves, to a degenerate bifurcation in weightlessness, which is followed by large columnar patterns. The vibroequilibria effect plays a symmetry-breaking role in the bifurcation, selecting frozen waves with the heavier fluid displaced upward along the lateral walls.

[Phys. Rev. Fluids 5, 084001] Published Mon Aug 03, 2020

### Lévy walking droplets

Author(s): V. S. Akella, R. Rajesh, and Mahesh V. Panchagnula

Lévy walks are abnormal random walks, characterized by Lévy-stable distributed step lengths. Lévy walks occur in a wide range of phenomena such as foraging, socio-physics. etc. An octanoic acid drop performing a Lévy walk on aqueous unsaturated octanoic acid solutions is presented as an inanimate, controlled, and inexpensive model system for studying Lévy walks in a laboratory.

[Phys. Rev. Fluids 5, 084002] Published Mon Aug 03, 2020

### Liquid sloshing in an upright circular tank under periodic and transient excitations

Author(s): Hui Liang, Harrif Santo, Yanlin Shao, Yun Zhi Law, and Eng Soon Chan

Time-harmonic and periodically modulated swirling waves can be excited in an upright circular tank undergoing periodic oscillations in a single degree-of-freedom. The swirling direction is determined by the initial condition. While the time-harmonic swirling waves can reach steady state after the initial buildup, the periodically modulated swirling waves switch back and forth between planar waves and swirling waves.

[Phys. Rev. Fluids 5, 084801] Published Mon Aug 03, 2020

### Invisibility concentrator for water waves

We theoretically design and experimentally demonstrate an invisibility concentrator, consisting of several truncated cylinders, for water waves based on a scattering cancellation method. The invisibility concentrator works by controlling the scattered waves from the target device. Our simulated and experimental results verify the concentration of waves and show the effective invisibility of the designed concentrator. This approach provides the possibility of simultaneously realizing wave concentration and an invisibility cloak, which has potential applications in energy harvesting.

### Passive and active control of turbulent flows

### Flow of yield stress materials through annular abrupt expansion–contractions

We present an experimental study of the flow of yield stress materials through annular abrupt expansions–contractions, to evaluate the flow invasion into the cavity formed in the larger cross section region. Steady inertialess flows of Carbopol® aqueous dispersions were investigated. The flow pattern reveals yielded and unyielded regions, which were visualized using tracer particles, laser sheets, and a digital camera. The yield surfaces were identified in the experiments by choosing large enough exposure times that allow sufficient particle displacement in the yielded region. To estimate the amount of fluid that remains stagnant in the cavity, we defined the invasion ratio, a quantity that was determined through image processing for different combinations of the governing parameters. The influence of the cavity diameter and axial length, eccentricity, and inlet velocity on the invasion ratio was investigated. Fore-aft asymmetric yield surfaces were observed for all tests, probably due to elastic effects.

### Vibrational relaxation time measurements in shock-heated oxygen and air from 2000 K to 9000 K using ultraviolet laser absorption

Vibrational relaxation times of oxygen (O2) were measured behind reflected shocks in shock-tube experiments with O2 and nitrogen (N2) collision partners. To determine relaxation times, a tunable ultraviolet laser absorption diagnostic probed time-histories involving the fourth (v″ = 4), fifth (v″ = 5), and sixth (v″ = 6) vibrational levels of the ground electronic state of O2. Taking the ratio of two absorbance time-histories involving different vibrational levels yielded vibrational temperature time-histories that were fit to isolate the relevant vibrational relaxation times. Pure O2 experiments were used to isolate the vibration–translation (VT) relaxation time of O2 with O2. Results for [math] agree with the Millikan and White correlation at temperatures below 4000 K. However, high-temperature data deviate from the Millikan and White correlation, exhibiting a reduced temperature dependence—an observation that remains consistent with previous experimental studies. Additional experiments in 10% and 21% O2 in N2 mixtures were used to isolate both the VT and vibration–vibration (VV) relaxation times of O2 with N2. The data for [math] exceed the Millikan and White correlation by 70% but show reasonable agreement with previous data below 5000 K. High-temperature results again show a reduced temperature dependence, but this study shows longer relaxation times than the previous work. The data for [math] exceed the semi-empirical relation developed by Berend et al. [“Vibration-vibration energy exchange in N2 with O2 and HCl collision partners,” J. Chem. Phys. 57, 3601–3604 (1972)] by 70% but overlap with previous measurements. Due to insensitivity of the chemical system to VV transfer at high temperatures, results for [math] were only measured below 6000 K.

### Linear stability of the flow of a second order fluid past a wedge

The linear stability analysis of Rivlin–Ericksen fluids of second order is investigated for boundary layer flows, where a semi-infinite wedge is placed symmetrically with respect to the flow direction. Second order fluids belong to a larger family of fluids called order fluids, which is one of the first classes proposed to model departures from Newtonian behavior. Second order fluids can model non-zero normal stress differences, which is an essential feature of viscoelastic fluids. The linear stability properties are studied for both signs of the elasticity number K, which characterizes the non-Newtonian response of the fluid. Stabilization is observed for the temporal and spatial evolution of two-dimensional disturbances when K > 0 in terms of increase of critical Reynolds numbers and reduction of growth rates, whereas the flow is less stable when K < 0. By extending the analysis to three-dimensional disturbances, we show that a positive elasticity number K destabilizes streamwise independent waves, while the opposite happens for K < 0. We show that, as for Newtonian fluids, the non-modal amplification of streamwise independent disturbances is the most dangerous mechanism for transient energy growth, which is enhanced when K > 0 and diminished when K < 0.

### Analysis of combustion acoustic phenomena in compression–ignition engines using large eddy simulation

As computational capabilities continue to grow, exploring the limits of computational fluid dynamics to capture complex and elusive phenomena, which are otherwise difficult to study by experimental techniques, is one of the main targets for the research community. This paper presents a detailed analysis of the physical processes that lead to combustion noise emissions in internal combustion engines. In particular, diesel combustion in a compression–ignition (CI) engine is studied in order to understand the singular behavior of the in-cylinder flow field responsible for the acoustic emissions. The main objective is, therefore, to improve the understanding of the phenomena involved in CI engine noise using large eddy simulations. Several visualization methods are employed to investigate the connection between combustion behavior and its effects on the pressure field. In addition, proper orthogonal decomposition is used to analyze the modal energy distribution among all the acoustic modes. The results show that the acoustic signature is fundamentally conditioned by the intensity of the premixed combustion rather than by the pressure oscillations generated by turbulent fluctuations in the flame surface established during the diffusion stage.

### Transport and deposition of dilute microparticles in turbulent thermal convection

We analyze the transport and deposition behavior of dilute microparticles in turbulent Rayleigh–Bénard convection. Two-dimensional direct numerical simulations were carried out for the Rayleigh number (Ra) of 108 and the Prandtl number (Pr) of 0.71 (corresponding to the working fluids of air). The Lagrangian point particle model was used to describe the motion of microparticles in the turbulence. Our results show that the suspended particles are homogeneously distributed in the turbulence for the Stokes number (St) less than 10−3, and they tend to cluster into bands for 10−3 ≲ St ≲ 10−2. At even larger St, the microparticles will quickly sediment in the convection. We also calculate the mean-square displacement (MSD) of the particle’s trajectories. At short time intervals, the MSD exhibits a ballistic regime, and it is isotropic in vertical and lateral directions; at longer time intervals, the MSD reflects a confined motion for the particles, and it is anisotropic in different directions. We further obtained a phase diagram of the particle deposition positions on the wall, and we identified three deposition states depending on the particle’s density and diameter. An interesting finding is that the dispersed particles preferred to deposit on the vertical wall where the hot plumes arise, which is verified by tilting the cell and altering the rotation direction of the large-scale circulation.