# Latest papers in fluid mechanics

### Regularized extended-hydrodynamic equations for a rarefied granular gas and the plane shock waves

Author(s): M. H. Lakshminarayana Reddy and Meheboob Alam

Motions of grains such as in dust storms, sand dunes, snow avalanches, Saturn’s rings, and others are categorized as “granular” flows. We have used the Maxwell-Boltzmann kinetic theory to analyze rapid granular flows with an analogy between the motion of macroscopic grains and the random motion of atoms in molecular gases, with a crucial difference that the grains collide inelastically. The inelasticity is responsible for many peculiar behaviors of granular gases as we demonstrate by considering shock-wave propagation in granular gases with higher-order hydrodynamic equations.

[Phys. Rev. Fluids 5, 044302] Published Mon Apr 06, 2020

### Investigation of flow past a cylinder embedded on curved and flat surfaces

Author(s): Pankaj Jagad, Mamdouh S. Mohamed, and Ravi Samtaney

A discrete exterior calculus investigation of flow past a stationary cylinder of circular, triangular, or square cross section embedded on a spherical or cylindrical surface shows insignificant effect of the embedding surface curvature. The contributing parameters, such as the magnitude of the Gaussian curvature term relative to the magnitude of the viscous term around the cylinder and the effect of the geometrical constraint, are insignificant. Is the dynamics of the flow past bluff bodies universal?

[Phys. Rev. Fluids 5, 044701] Published Mon Apr 06, 2020

### Segregation models for density-bidisperse granular flows

Author(s): Yifei Duan, Paul B. Umbanhowar, Julio M. Ottino, and Richard M. Lueptow

A kinetic-theory-based model of granular flow which predicts the depth-varying segregation velocities of rising and sinking particles in density-bidisperse mixtures is presented. The segregation velocity results from a balance between the buoyant force, due to particle density and concentration, and the interspecies drag force from kinetic theory, which depends on interparticle friction and local flow conditions.

[Phys. Rev. Fluids 5, 044301] Published Fri Apr 03, 2020

### Reduced-order modeling of dynamic stall using neuro-fuzzy inference system and orthogonal functions

To consider stall flutter in the design procedure of a blade, accurate models of flow loading are needed. This paper first presents a numerical simulation of an airfoil undergoing a deep dynamic stall employing a computational fluid dynamics code. Overset and polyhedral grid techniques are adopted to accurately simulate the flow field at high angles of attack. Having validated the simulation, the occurrence of stall flutter over a pitching airfoil with an increase in amplitude and frequency of oscillations is examined. The results express that the amplitude of the lift and pitching moment depends on the amplitude of the forced oscillation and there are higher harmonics of the pitching moment compared to the forced oscillation frequency content, both indicating the nonlinearity of aerodynamic lift and pitching moment. Subsequently, a nonlinear reduced model of the dynamic stall is derived using a fuzzy inference system (FIS) and the adaptive network-based FIS (ANFIS). Due to the unsatisfactory results of modeling, especially at post-stall angles of attack, the Gram–Schmidt orthogonalization technique is used to construct a more complex structure of the input variables. The new higher-order input variables have been re-employed by FIS and ANFIS. The results show that excellent modeling is achieved by ANFIS between the new structure of the inputs and the corresponding aerodynamic coefficients using only 10% of input–output data. Having found an appropriate relation, the proposed reduced-order model could properly predict the aerodynamic response of the pitching airfoil at two reduced frequencies.

### Dynamics of a viscoelastic liquid filament connected to two mobile droplets

A filament of liquid is usually unstable and breaks up into small droplets, while a filament of polymer solution is known to be quite stable against such instability, and they form a stable configuration of a filament connecting two spherical droplets. If the droplets are fixed in space, the liquid flows from the filament region to the droplet region to reduce the surface energy and the filament gets thinner. If the whole liquid is placed in another viscous fluid, the droplets approach each other and the filament can get thicker. Here, we study the dynamics of such a system. We derive time evolution equations for the radius and the length of the filament taking into account the fluid flux from the filament to the droplets and the motion of the droplets. We will show that (a) if the centers of the droplets are fixed, the filament thins following the classical prediction of Entov and Hinch and (b) if the droplets are mobile (subject to the Stokes drag in the viscous medium), the thinning of the filament is suppressed and, under certain conditions, the filament thickens. This theory explains the phenomena observed by Yang and Xu [“Coalescence of two viscoelastic droplets connected by a string,” Phys. Fluids 20, 043101 (2008)] in a four-roller mill device.

### Jet breakup in superfluid and normal liquid $^{4}\mathrm{He}$

Author(s): N. B. Speirs, K. R. Langley, P. Taborek, and S. T. Thoroddsen

The breakup of jets of superfluid and normal liquid 4He is studied between 1.2 K and the liquid-vapor critical point at 5.2 K. Both gas and liquid properties vary widely over this small temperature range, creating a unique parameter space with variations of several orders of magnitude for the Ohnesorge number, Reynolds number, and gas-liquid density ratio. The five breakup regimes seen previously, and transitions between them, are described in detail and shown pictorially. New criteria are proposed for the Rayleigh to 1st wind, 1st wind to sinuous, and sinuous to 2nd wind transitions.

[Phys. Rev. Fluids 5, 044001] Published Thu Apr 02, 2020

### Dynamics of liquid nanothreads: Fluctuation-driven instability and rupture

Author(s): Chengxi Zhao, Duncan A. Lockerby, and James E. Sprittles

The influence of thermal fluctuations on the dynamics of nanoscale liquid threads is investigated using both molecular dynamics (MD) and a stochastic lubrication equation (SLE) derived from fluctuating hydrodynamics. These methods recover a range of breakup profiles, including the ‘double cone’, and we quantify their occurrence statistics. The SLE is about 5000 times faster than MD and permits access to a broader range of parameters. We use it to probe the final stages of rupture and compare to proposed similarity solutions, showing its usefulness for investigating nanoscale interfacial flows.

[Phys. Rev. Fluids 5, 044201] Published Thu Apr 02, 2020

### Hairpin vortex structures in a supersonic, separated, longitudinal cylinder wake

The near-wake flow structure behind a blunt-based cylinder aligned with a Mach 2.49 freestream is studied experimentally using tomographic particle image velocimetry (TPIV), which acquires three-component velocity measurements throughout a volumetric region. TPIV measurements were acquired in three different volumetric regions throughout this flow, including two regions in the separated shear layer and one in the high-speed portion of the trailing wake, with a large ensemble of measurement volumes (approximately 2500) acquired in each region. The quality of these data is validated using point-by-point comparisons to previous experimental data with known uncertainty estimates. Hairpin vortex structures were observed to exist commonly throughout this flow field (in both subsonic and supersonic regions), and they induced strong turbulent fluctuations aligned with a consistent direction. Inverted hairpin vortex structures were also observed to commonly exist in this flow, inducing strong turbulent fluctuations in a direction opposite to that of the upright hairpins, but their presence was limited to subsonic flow regions. These coherent structures are demonstrated to be significant drivers of kinematic Reynolds shear stress and turbulent kinetic energy throughout this flow. A planar turbulent quadrant analysis was used to provide a measure of the spatial dependencies of these structures within the flow, and a linear stochastic estimation was used to provide robust statistical evidence of their frequent existence in various subregions. Upright hairpins were demonstrated to statistically grow with streamwise progression, and the strength of their induced velocity fluctuations increased in the presence of the adverse pressure gradient associated with flow field reattachment.

### Viscous fluid flow inside an oscillating cylinder and its extension to Stokes’ second problem

We present the analytical solution for the fluid motion inside a cylindrical tank whose angular velocity starts from rest and undergoes a harmonic oscillation. This problem, which has not yet been reported, is an extension to Stokes’ second problem where the fluid motion is governed by an outer moving cylindrical boundary and a zero velocity condition at the cylinder center. Different from the flow on the outside of a cylinder, the cylinder radius has a large influence on the internal fluid motion. We show that the fluid approaches solid body rotation for cylinders with outer radii similar to the characteristic viscous length scale of the flow, whereas the motion approaches that of Stokes’ original flat plate solution within very large cylinders. We detail both the transient starting condition and the quasi-steady fluid motion, which we present along with a particle image velocimetry experiment for validation. After decay of the initial startup transient, both quasi-steady analytical and experimental results predict that the oscillatory flow inside has an amplitude of velocity that decreases toward the center of the cylinder. The thickness of the Stokes layer, which is proportional to the penetration depth of the viscous wave, is altered by the size of the cylinder and/or the frequency of oscillation. We show that the penetration depth of the Stokes layer reaches its maximum thickness at intermediate cylinder sizes. The solution and results presented herein are potentially of value to describe the fluid motion in many applications where fluids are contained within cylindrical geometries.

### Effects of the fresh mixture temperature on thermoacoustic instabilities in a lean premixed swirl-stabilized combustor

This numerical study investigated the effects of the fresh mixture temperature on thermoacoustic instabilities in a lean premixed swirl-stabilized combustion chamber by utilizing high-fidelity, fully compressible large eddy simulations. At low fresh mixture temperatures, the side recirculation zone stabilized the premixed flame on the boundary of the burner rim, while the central part of the flame was detached from the burner due to the inability of the central recirculation zone to assist in flame stabilization. However, the central recirculation zone became stable enough to stabilize the central portion of the flame near the burner rim as the fresh mixture temperature increased. Moreover, the coherencies and penetration depths of the coherent structures and precessing vortex cores in the combustor increased with the fresh mixture temperature. Analyses showed that the limit cycle instabilities that occurred at low fresh mixture temperatures resulted from coupling between heat release fluctuations and the first tangential acoustic mode of the combustor. However, as the fresh mixture temperature increased, a combustor dynamics transition occurred, through which the coupling between heat release and pressure fluctuations shifted toward the mixed tangential and radial acoustical modes of the combustor. During this mode transition, limit cycle oscillations were replaced by burst oscillations. The results revealed that recirculation zones are the key features that trigger thermoacoustic instabilities at low fresh mixture temperatures, while coherent structures and precessing vortex cores are the main combustion instability drivers at high fresh mixture temperatures.

### Dynamics of moving contact line on a transversely patterned inclined surface

We study the dynamics of moving contact lines and film deposition on a chemically patterned plate withdrawn from a liquid bath obliquely. The plate is patterned with transverse stripes and characterized by alternating wettability. We assume that the inclination of the plate is small enough, so lubrication theory can be employed. The finite element method is used to solve the one-dimensional unsteady lubrication equation, and it is combined with the precursor film model and disjoining pressure to realize the moving contact line with finite contact angles. When the width of the strips is relatively large, four typical modes of contact line dynamics are observed as the withdrawal speed of the plate increases. In particular, if the withdrawal speed is smaller than the critical value of the wetting transition on the more wettable strip, the contact line would periodically move between the equilibrium positions of the more wettable and less wettable regions, which is known as a “stick-slip” motion. In accordance with the Cox–Voinov law, a quantitative analysis of the “stick-slip” motion is conducted, which predicts the critical condition of the “stick” process and the relaxation time of the “slip” process. When the stripe width is sufficiently small, the evolution of the contact line and liquid film is similar to that on an equivalent homogeneous substrate, whose contact angle can be predicted via Cassie theory.

### Numerical study on reflection of an oblique detonation wave on an outward turning wall

Oblique detonation waves (ODWs) have been studied widely as the basis of detonation-based hypersonic engines, but there are few studies on ODWs in a confined space. This study simulates ODW reflection on a solid wall before an outward turning corner for a simplified combustor–nozzle flow based on a two-step kinetic model. Numerical results reveal three types of ODW structures: stable, critical, and unstable. When the reflection occurs at the turning point, the stable ODW structure remains almost the same as before reflection. When the wave reflects at the wall before the turning point, either the critical structure or the unstable structure arises, which has never been investigated before. Both structures have the same initial two-section detonation surface: but the critical one becomes stationary at a certain position, while the unstable one keeps traveling upstream. By adjusting the location of the expansion wave and degree of the turning angle, the difference of the two structures is attributed to the thermal choking appearing only in the unstable structure. The thermal choking is achieved by the merging of subsonic zones, whose dependence on the various parameters is discussed.

### Cooperative evaporation in two-dimensional droplet arrays

Author(s): Khushboo Pandey, Sandeep Hatte, Keshav Pandey, Suman Chakraborty, and Saptarshi Basu

The evaporation of a sessile drop in a gaseous environment may be critical to many practical applications. Evaporation dynamics of interacting sessile droplets is strongly influenced by the proximity of adjacent droplets. We study the effects of droplet-droplet vapor-mediated interactions on the eva...

[Phys. Rev. E 101, 043101] Published Wed Apr 01, 2020

### Scaling laws in axisymmetric magnetohydrodynamic duct flows

Author(s): A. Poyé, O. Agullo, N. Plihon, W. J. T. Bos, V. Desangles, and G. Bousselin

The features of axisymmetric magnetohydrodynamic duct flows in annular geometry, driven by current injection perpendicular to an externally applied magnetic field, is investigated numerically and analytically. Scaling laws for the velocity in the three regimes previously reported in the literature are derived for a wide range of control parameters and systematically compared to experimental data.

[Phys. Rev. Fluids 5, 043701] Published Wed Apr 01, 2020

### Agglomeration dynamics in liquid–solid particle-laden turbulent channel flows using an energy-based deterministic approach

A deterministic particle–particle agglomeration technique is applied together with direct numerical simulation and four-way coupled Lagrangian particle tracking in order to accurately simulate and investigate fully coupled agglomerating particle-laden channel flows at a shear Reynolds number, Reτ = 180. The collision outcome determination (recoil or aggregate) is based on the balance between kinetic energy dispersed in the collision and the work required to overcome the van der Waals attractive potential. The influence of particle size (dP = 202 μm, 286 μm, and 405 μm), both at a fixed volume fraction (ϕP = 10−3) and a fixed primary injected particle number (NP = 109 313), on the resulting collision and agglomeration dynamics is investigated. Attention is also focused on how collision and agglomeration rates vary throughout the wall-normal regions of the channel flow. The results demonstrate that the normalized collision rates are similar for all particle sizes at the fixed volume fraction but increase with particle size at the fixed particle number, and a preference is observed for collisions to occur close to the walls. Despite this, in all cases considered here, agglomeration events are most frequent at the center of the channel, with agglomeration efficiencies also peaking in this region. In terms of particle diameter effects, the smallest particles exhibit the greatest preference to aggregate, given that a collision has already occurred. Furthermore, whereas normalized collision and agglomeration event counts show differing diameter-dependence based on whether the number of primary particles or the volume fraction is fixed, agglomeration rates show diameter-independence and as such are based solely on particle size and local dispersive properties. Analysis of the dynamic collision properties throughout the channel confirms that agglomeration is favored within the bulk flow region due to low relative particle velocities and small collision angles at this location. The temporal evolution of important interaction properties is investigated, all of which demonstrate stability over the course of the time simulated. Particle diameter is also shown to influence the long-term population of higher-order agglomerates, with (for a given volume fraction) smaller particles aggregating faster to form larger particles. The systems studied, which resemble those present in the processing of nuclear waste, all exhibit substantial agglomeration over the time considered. This reinforces the importance of accurately modeling agglomeration dynamics in flows where electrokinetic interactions are important in order to correctly predict multiphase flow properties over long timeframes.

### Development of a stagnation streamline model for thermochemical nonequilibrium flow

A stagnation streamline model incorporating quantum-state-resolved chemistry is proposed to study hypersonic nonequilibrium flows along the stagnation streamline. This model is developed by reducing the full Navier–Stokes equations to the stagnation streamline with proper approximations for equation closure. The thermochemical nonequilibrium is described by either the state-to-state approach for detailed analysis or conventional two-temperature models for comparison purpose. The model is validated against various data, and nearly identical results are obtained as compared with those from full field computational fluid dynamics data. In addition, the calculated distributions agree well with the measurement data of a shock tube experiment for the dissociation and vibrational relaxation of O2, including the distributions of species mole fractions and vibrational temperature of the first excited state of O2 molecules. Furthermore, the results with the state-resolved chemistry show that the flow within a shock layer exhibits a strong thermochemical nonequilibrium behavior, which is beyond the capability of commonly used two-temperature models to correctly evaluate the dissociation rate and the associated reaction energy. The present model is also employed to calculate the nonequilibrium re-entry flow along the stagnation streamline for a five-species air mixture as an example to demonstrate the model capability. It is found that both species and internal energy are in a nonequilibrium state, especially the vibrational distributions are strongly deviated from the Boltzmann distribution right behind the bow shock and near the wall surface. The results demonstrate that the proposed stagnation streamline model is very useful to understand thermochemical nonequilibrium phenomena in hypersonic flows.

### Oscillating grid generating turbulence near gas-liquid interfaces in shear-thinning dilute polymer solutions

Author(s): T. Lacassagne, S. Simoëns, M. EL Hajem, and J.-Y. Champagne

A first experimental characterization of low Reynolds number, oscillating grid generated, and near-surface turbulence in shear-thinning dilute polymer solutions is presented. Energy transfer and horizontal damping mechanisms are evidenced. The evolution of the viscous sublayer depth can be explained by both viscous and shear-thinning effects.

[Phys. Rev. Fluids 5, 033301] Published Tue Mar 31, 2020

### Differential diffusion effects on density-driven instability of reactive flows in porous media

Author(s): Timan Lei and Kai H. Luo

In diverse applications such as enhanced oil recovery and carbon sequestration, solute A in fluid 1 diffuses into fluid 2 where it reacts with solute B following A + B → C. Pore-scale simulations based on the lattice Boltzmann method reveal intricate density-driven instability and differential diffusion effects. New fingering regimes are observed under certain combinations of density ratios, diffusivity ratios, and Rayleigh number ratios among the participating fluids and species.

[Phys. Rev. Fluids 5, 033903] Published Tue Mar 31, 2020

### Equilibrium measurement method of slip length based on fluctuating hydrodynamics

Author(s): Hiroyoshi Nakano and Shin-ichi Sasa

We perform equilibrium molecular dynamics simulations for nanoscale fluids confined between two parallel walls and investigate how the autocorrelation function of force acting on one wall is related to the slip length. We demonstrate that for atomically smooth surfaces, the autocorrelation function ...

[Phys. Rev. E 101, 033109] Published Mon Mar 30, 2020

### Generalized Shields criterion for weakly cohesive granular materials

Author(s): Florian Brunier-Coulin, Pablo Cuéllar, and Pierre Philippe

The erosion onset and kinetics of weakly cohesive granular materials based on experimental data from optically adapted jet erosion tests is investigated. The scouring kinetics are examined qualitatively for samples with an intergranular cohesion induced by either liquid or solid bonds. From a quantitative perspective, the erosion onset for the case of solid bond cohesion is here described by a generalized form of the usual Shields criterion including a cohesion number defined from yield tensile values considering both the micro- and macroscales.

[Phys. Rev. Fluids 5, 034308] Published Mon Mar 30, 2020