Volume 28, Issue 7, July 2016

Large eddy simulation and particle image velocimetry measurements have been performed to evaluate the characteristics of a turbulent impinging jet with large nozzle heighttodiameter ratio (H/D = 20). The Reynolds number considered is approximately 28 000 based on the jet exit velocity and nozzle diameter. Mean normalized centerline velocity in both the free jet and impingement regions and pressure distribution over the plate obtained from simulations and experiments show good agreement. The ringlike vortices generated due to the KelvinHelmholtz instabilities at the exit of the nozzle merge, break down and transform into large scale structures while traveling towards the impingement plate. A Strouhal number of 0.63 was found for the vortices generated at the exit of the nozzle. However, this parameter is reduced along the centerline towards the impingement zone. A characteristic frequency was also determined for the large scale structures impinging on the plate. The expansion, growth, tilt, and threedimensionality of the impinging structures cause dislocation of the impinging flow from the centerline, which is significantly larger when compared with flows having small H/D ratios. Contrary to the behavior of impinging jets with small standoff distance, due to the loss of coherence, the large scale structures do not result in significant secondary vortices in the wall jet region and consequently less fluctuations were observed for wall shear stress.
 LETTERS


Pinchoff of axisymmetric vortex pairs in the limit of vanishing vortex line curvature
View Description Hide DescriptionPinchoff of axisymmetric vortex pairs generated by flow between concentric cylinders with radial separation ΔR was studied numerically and compared with planar vortex dipole behavior. The axisymmetric case approaches planar vortex dipole behavior in the limit of vanishing ΔR. The flow was simulated at a jet Reynolds number of 1000 (based on ΔR and the jet velocity), jet pulse lengthtogap ratio () in the range 10–20, and gaptoouter radius ratio () in the range 0.010.1. Contrary to investigations of strictly planar flows, vortex pinchoff was observed for all gap sizes investigated. This difference was attributed to the less constrained geometry considered, suggesting that even very small amounts of vortex line curvature and/or vortex stretching may disrupt the absence of pinchoff observed in strictly planar vortex dipoles.
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 ARTICLES

 Biofluid Mechanics

Threedimensional wake topology and propulsive performance of lowaspectratio pitchingrolling plates
View Description Hide DescriptionThe wake topology and propulsive performance of lowaspectratio plates undergoing a pitchingrolling motion in a uniform stream were numerically investigated by an inhouse immersedboundarymethodbased incompressible NavierStokes equation solver. A detailed analysis of the vortical structures indicated that the pitchingrolling plate produced doubleloop vortices with alternating signs from its trailing edge every half period. These vortices then shed and further evolved into interconnected “doubleC”shaped vortex rings, which eventually formed a bifurcating wake pattern in the downstream. As the wake convected downstream, there was a slight deflection in the spanwise direction to the plate tip, and the contained vortex ring size gradually increased. In addition, the analysis of the propulsive performance indicated that the shedding process of the doubleloop vortices led to two peaks in the lift and thrust force production per half cycle. The observation of the double peaks in the force production is in agreement with previous flapping wing studies. Simulations were also used to examine the variations in the wake structures and propulsive performance of the plates over a range of major parameters. The aforementioned vortex structures were found to be quite robust over a range of Strouhal numbers, Reynolds numbers, and plate aspect ratios.

Investigation of full and partial ground effects on a flapping foil hovering above a finitesized platform
View Description Hide DescriptionThe full and partial ground effects on the lift generation of a flapping airfoil in normal hovering mode are investigated numerically using the discrete vortex method in two dimensions. To achieve full ground effect, the airfoil of chord c is made to hover above the center of a finitesized platform of length 10c. We have observed the forceenhancement, forcereduction, and forcerecovery regimes at low, medium, and high ground clearances in line with the existing literature. This paper puts special focus on partial ground effect when the airfoil is hovering near the edge of the platform. Liftmodifying mechanisms not previously observed under full ground effect have been discovered. When stroke reversal occurs near the edge of the platform, a relatively stationary strong vortex may form above the platform edge. This strong vortex can either increase or decrease the instantaneous lift force on the airfoil depending on the position of the airfoil relative to the platform edge. Also, the platform edge may lead to the formation of an additional vortex pair which increases the instantaneous lift force as the airfoil sweeps past the edge under suitable conditions. Lastly, the platform edge can lead to the formation of a reverse von Kármán vortex street that extends well below the stroke plane under suitable geometric arrangements.

Particle mobility between two planar elastic membranes: Brownian motion and membrane deformation
View Description Hide DescriptionWe study the motion of a solid particle immersed in a Newtonian fluid and confined between two parallel elastic membranes possessing shear and bending rigidity. The hydrodynamic mobility depends on the frequency of the particle motion due to the elastic energy stored in the membrane. Unlike the singlemembrane case, a coupling between shearing and bending exists. The commonly used approximation of superposing two singlemembrane contributions is found to give reasonable results only for motions in the parallel direction, but not in the perpendicular direction. We also compute analytically the membrane deformation resulting from the motion of the particle, showing that the presence of the second membrane reduces deformation. Using the fluctuationdissipation theorem we compute the Brownian motion of the particle, finding a longlasting subdiffusive regime at intermediate time scales. We finally assess the accuracy of the employed pointparticle approximation via boundaryintegral simulations for a truly extended particle. They are found to be in excellent agreement with the analytical predictions.

Transport of helical gyrotactic swimmers in channels
View Description Hide DescriptionWe develop a mechanistic model that describes the transport of gyrotactic cells with propulsive force and propulsive torque that are not parallel. In sufficiently weak shear this yields helical swimming trajectories, whereas in stronger shear cells can attain a stable equilibrium orientation. We obtain the stable equilibrium solution for cell orientation as a function of the shear strength and determine the feasibility region for equilibrium solutions. We compute numerically the trajectories of cells in two dimensional vertical channel flow where the shear is nonuniform. Depending on the parameter values, we show that helical swimmers may display classical gyrotactic focussing towards the centre of the channel or can display a new phenomenon of focussing away from the centre of the channel. This result can be explained by consideration of the equilibrium solution for cell orientation. In this study we consider only dilute suspensions where there is no feedback from cell swimming on the hydrodynamics, and both cellwall and cellcell interactions are neglected.

On the acoustic signature of tandem airfoils: The sound of an elastic airfoil in the wake of a vortex generator
View Description Hide DescriptionThe acoustic signature of an acoustically compact tandem airfoil setup in uniform highReynolds number flow is investigated. The upstream airfoil is considered rigid and is actuated at its leading edge with smallamplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortexstreet excitation of the upstream airfoil. The nonlinear nearfield description is obtained via potential thinairfoil theory. It is then applied as a source term into the PowellHowe acoustic analogy to yield the farfield dipole radiation of the system. To assess the effect of downstreamairfoil elasticity, results are compared with counterpart calculations for a nonelastic setup, where the downstream airfoil is rigid and stationary. Depending on the separation distance between airfoils, airfoilmotion and airfoilwake dynamics shift between inphase (synchronized) and counterphase behaviors. Consequently, downstream airfoil elasticity may act to amplify or suppress sound through the direct contribution of elasticairfoil motion to the total signal. Resonancetype motion of the elastic airfoil is found when the upstream airfoil is actuated at the least stable eigenfrequency of the downstream structure. This, again, results in system sound amplification or suppression, depending on the separation distance between airfoils. With increasing actuation frequency, the acoustic signal becomes dominated by the direct contribution of the upstream airfoil motion, whereas the relative contribution of the elastic airfoil to the total signature turns negligible.
 Micro and Nanofluid Mechanics

A Brownian dynamics study on ferrofluid colloidal dispersions using an iterative constraint method to satisfy Maxwell’s equations
View Description Hide DescriptionFerrofluids are often favored for their ability to be remotely positioned via external magnetic fields. The behavior of particles in ferromagnetic clusters under uniformly applied magnetic fields has been computationally simulated using the Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. However, few methods have been established that effectively handle the basic principles of magnetic materials, namely, Maxwell’s equations. An iterative constraint method was developed to satisfy Maxwell’s equations when a uniform magnetic field is imposed on ferrofluids in a heterogeneous Brownian dynamics simulation that examines the impact of ferromagnetic clusters in a mesoscale particle collection. This was accomplished by allowing a particulate system in a simple shear flow to advance by a time step under a uniformly applied magnetic field, then adjusting the ferroparticles via an iterative constraint method applied over subvolume length scales until Maxwell’s equations were satisfied. The resultant ferrofluid model with constraints demonstrates that the magnetoviscosity contribution is not as substantial when compared to homogeneous simulations that assume the material’s magnetism is a direct response to the external magnetic field. This was detected across varying intensities of particleparticle interaction, Brownian motion, and shear flow. Ferroparticle aggregation was still extensively present but less so than typically observed.

Analysis of homogeneous/nonhomogeneous nanofluid models accounting for nanofluidsurface interactions
View Description Hide DescriptionThis article reports an unbiased analysis for the water based rod shaped alumina nanoparticles by considering both the homogeneous and nonhomogeneous nanofluid models over the coupled nanofluidsurface interface. The mechanics of the surface are found for both the homogeneous and nonhomogeneous models, which were ignored in previous studies. The viscosity and thermal conductivity data are implemented from the international nanofluid property benchmark exercise. All the simulations are being done by using the experimentally verified results. By considering the homogeneous and nonhomogeneous models, the precise movement of the alumina nanoparticles over the surface has been observed by solving the corresponding system of differential equations. For the nonhomogeneous model, a uniform temperature and nanofluid volume fraction are assumed at the surface, and the flux of the alumina nanoparticle is taken as zero. The assumption of zero nanoparticle flux at the surface makes the nonhomogeneous model physically more realistic. The differences of all profiles for both the homogeneous and nonhomogeneous models are insignificant, and this is due to small deviations in the values of the Brownian motion and thermophoresis parameters.

General slip regime permeability model for gas flow through porous media
View Description Hide DescriptionA theoretical effective gas permeability model was developed for rarefied gas flow in porous media, which holds over the entire slip regime with the permeability derived as a function of the Knudsen number. This general slip regime model (GSR model) is derived from the porescale NavierStokes equations subject to the firstorder wall slip boundary condition using the volumeaveraging method. The local closure problem for the volumeaveraged equations is studied analytically and numerically using a periodic sphere array geometry. The GSR model includes a rational fraction function of the Knudsen number which leads to a limit effective permeability as the Knudsen number increases. The mechanism for this behavior is the viscous fluid inner friction caused by convergingdiverging flow channels in porous media. A linearization of the GSR model leads to the Klinkenberg equation for slightly rarefied gas flows. Finite element simulations show that the Klinkenberg model overestimates the effective permeability by as much as 33% when a flow approaches the transition regime. The GSR model reduces to the unified permeability model [F. Civan, “Effective correlation of apparent gas permeability in tight porous media,” Transp. Porous Media 82, 375 (2010)] for the flow in the slip regime and clarifies the physical significance of the empirical parameter b in the unified model.
 Interfacial Flows

Physical understanding of gasliquid annular flow and its transition to dispersed droplets
View Description Hide DescriptionTransformation from annular to droplet flow is investigated for cocurrent, upward gasliquid flow through a cylindrical tube using grid based volume of fluid framework. Three transitional routes, namely, orificing, rolling, and undercutting are observed for flow transformation at different range of relative velocities between the fluids. Physics behind these three exclusive phenomena is described using circulation patterns of gaseous phase in the vicinity of a liquid film which subsequently sheds drop leading towards transition. Orifice amplitude is found to grow exponentially towards the core whereas it propagates in axial direction in a parabolic path. Efforts have been made to fit the sinusoidal profile of wave structure with the numerical interface contour at early stages of orificing. Domination of gas inertia over liquid flow has been studied in detail at the later stages to understand the asymmetric shape of orifice, leading towards lamella formation and droplet generation. Away from comparative velocities, circulations in the dominant phase dislodge the drop by forming either a ligament (rolling) or a bag (undercut) like protrusion in liquid. Study of velocity patterns in the plane of droplet dislodge reveals the underlying physics behind the disintegration and its dynamics at the later stages. Using numerical phase distributions, rejoining of dislodged droplet with liquid film as postrolling consequences has been also proposed. A flow pattern map showing the transitional boundaries based on the physical mechanism is constructed for airwater combination.

Free films of a partially wetting liquid under the influence of a propagating MHz surface acoustic wave
View Description Hide DescriptionWe use both theory and experiment to study the response of thin and free films of a partially wetting liquid to a MHz vibration, propagating in the solid substrate in the form of a Rayleigh surface acoustic wave (SAW). We generalise the previous theory for the response of a thin fully wetting liquid film to a SAW by including the presence of a small but finite three phase contact angle between the liquid and the solid. The SAW in the solid invokes a convective drift of mass in the liquid and leaks sound waves. The dynamics of a film that is too thin to support the accumulation of the sound wave leakage is governed by a balance between the drift and capillary stress alone. We use theory to demonstrate that a partially wetting liquid film, supporting a weak capillary stress, will spread along the path of the SAW. A partially wetting film, supporting an appreciable capillary stress, will however undergo a concurrent dynamic wetting and dewetting at the front and the rear, respectively, such that the film will displace, rather than spread, along the path of the SAW. The result of the theory for a weak capillary stress is in agreement with the previous experimental and theoretical studies on the response of thin silicon oil films to a propagating SAW. No corresponding previous results exist for the case of an appreciable capillary stress. We thus complement the large capillary limit of our theory by undertaking an experimental procedure where we explore the response of films of water and a surfactant solutions to a MHz SAW, which is found to be in qualitative agreement with the theory at this limit.
 Viscous and NonNewtonian Flows

Analytical solution for the lubrication force between two spheres in a biviscous fluid
View Description Hide DescriptionAn analytical solution for the calculation of the normal lubrication force acting between two moving spheres embedded in a shearthinning fluid represented by a biviscous model is provided. The resulting force between the suspended spheres exhibits a consistent transition between the Newtonian constantviscosity limits and it reduces to the wellknown standard Newtonian lubrication theory for viscosityratio approaching one. Effects of several physical parameters of the theory are analyzed under relevant physical conditions, i.e., for a prototypical case of two noncolloidal spheres immersed in a nonNewtonian fluid with rheology parameterized by a biviscosity model. Topological results for high/lowviscosity regions in the gap between spheres are also analyzed in detail showing a rich phenomenology. The presented model enables the extension of lubrication dynamics for suspensions interacting with nonNewtonian matrices and provides a clean theoretical framework for new numerical computations of flow of dense complex particulate systems.
 Particulate, Multiphase, and Granular Flows

Homogeneous cooling of mixtures of particle shapes
View Description Hide DescriptionIn this work, we examine theoretically the cooling dynamics of binary mixtures of spheres and rods. To this end, we introduce a generalized mean field analytical theory, which describes the free cooling behavior of the mixture. The relevant characteristic time scale for the cooling process is derived, depending on the mixture composition and the aspect ratio of the rods. We simulate mixtures of spherocylinders and spheres using a molecular dynamics algorithm implemented on graphics processing unit (GPU) architecture. We systematically study mixtures composed of spheres and rods with several aspect ratios and varying the mixture composition. A homogeneous cooling state, where the time dependence of the system’s intensive variables occurs only through a global granular temperature, is identified. We find cooling dynamics in excellent agreement with Haff’s law, when using an adequate time scale. Using the scaling properties of the homogeneous cooling dynamics, we estimated numerically the efficiency of the energy interchange between rotational and translational degrees of freedom for collisions between spheres and rods.

Breakup modes of fluid drops in confined shear flows
View Description Hide DescriptionUsing a conservative level set method we investigate the deformation behavior of isolated spherical fluid drops in a fluid channel subjected to simple shear flows, accounting the following three nondimensional parameters: (1) degree of confinement (Wc = 2a/h, where a is the drop radius and h is the channel thickness); (2) viscosity ratio between the two fluids (λ = μd/μm, where μd is the drop viscosity and μm is the matrix viscosity); and (3) capillary number (Ca). For a given Wc, a drop steadily deforms to attain a stable geometry (Taylor number and inclination of its long axis to the shear direction) when Ca < 0.3. For Ca > 0.3, the deformation behavior turns to be unsteady, leading to oscillatory variations of both its shape and orientation with progressive shear. This kind of unsteady deformation also occurs in a condition of high viscosity ratios (λ > 2). Here we present a detailed parametric analysis of the drop geometry with increasing shear as a function of Wc, Ca, and λ. Under a threshold condition, deforming drops become unstable, resulting in their breakup into smaller droplets. We recognize three principal modes of breakup: Mode I (midpoint pinching), Mode II (edge breakup), and Mode III (homogeneous breakup). Each of these modes is shown to be most effective in the specific field defined by Ca and λ. Our study also demonstrates the role of channel confinement (Wc) in controlling the transition of Mode I to III. Finally, we discuss implications of the three modes in determining characteristic drop size distributions in multiphase flows.

Investigation of drop impact on dry and wet surfaces with consideration of surrounding air
View Description Hide DescriptionNumerical simulations were conducted to investigate drop impingement and splashing on both dry and wet surfaces at impact velocities greater than 50 m/s with the consideration of the effect of surrounding air. The NavierStokes equations were solved using the variable density pressure projection method on a dynamic block structured adaptive grid. The moment of fluid method was used to reconstruct interfaces separating different phases. A dynamic contact angle model was used to define the boundary condition at the moving contact line. Simulations showed that lowering the ambient gas density can suppress dry surface splashing, which is in agreement with the experiments. A recirculation zone was observed inside the drop after contact: a larger recirculation zone was formed earlier in the higher gas density case than in the lower gas density case. Increasing gas density also enhances the creation of secondary droplets from the lamella breakup. For high speed impact on a dry surface, lowering ambient gas density attenuates splashing. However, ambient air does not significantly affect splashing on a wet surface. Simulations showed that the splashed droplets are primarily from the exiting liquid film.

Particle organization after viscous sedimentation in tilted containers
View Description Hide DescriptionA series of sedimentation experiments and numerical simulations have been conducted to understand the factors that control the final angle of a static sediment layer formed by quasimonodisperse particles settling in an inclined container. The set of experiments includes several combinations of fluid viscosity, container angle, and solids concentration. A comparison between the experiments and a set of twodimensional numerical simulations shows that the physical mechanism responsible for the energy dissipation in the system is the collision between the particles. The results provide new insights into the mechanism that sets the morphology of the sediment layer formed by the settling of quasimonodisperse particles onto the bottom of an inclined container. Tracking the interface between the suspension solids and the clear fluid zone reveals that the final angle adopted by the sediment layer shows strong dependencies on the initial particle concentration and the container inclination, but not the fluid viscosity. It is concluded that (1) the hindrance function plays an important role on the sediment bed angle, (2) the relation between the friction effect and the slope may be explained as a quasilinear function of the projected velocity along the container bottom, and (3) prior to the end of settling there is a significant interparticle interaction through the fluid affecting to the final bed organization. We can express the sediment bed slope as a function of two dimensionless numbers, a version of the inertial number and the particle concentration. The present experiments confirm some previous results on the role of the interstitial fluid on low Stokes number flows of particulate matter.

Origin of particle accumulation structures in liquid bridges: Particle–boundaryinteractions versus inertia
View Description Hide DescriptionThe formation of particleaccumulation structures in the flow in a cylindrical liquid bridge driven by the thermocapillary effect is studied with the aim of determining the physical mechanism which forms the structures. The flow is modeled using the incompressible Navier–Stokes and energy equations with the assumption of constant fluid properties except for surface tension, which is assumed to depend linearly on temperature. Different models for the motion of small noninteracting spherical particles at low concentration are employed, taking into account particle inertia due to density differences between fluid and particles and the restricted particle motion near the boundaries of the flow domain. Attention is focused on differences in formation time between particleaccumulation structures arising as a result of inertial effects only, particle–boundaryinteraction effects only, and a combination of the two.
 Laminar Flows

Stokesian swimming of a sphere at low Reynolds number by helical surface distortion
View Description Hide DescriptionExplicit expressions are derived for the matrices determining the mean translational and rotational swimming velocities and the mean rate of dissipation for Stokesian swimming at low Reynolds number of a distorting sphere in a viscous incompressible fluid. As an application, an efficient helical propellertype stroke is found and its properties are calculated.

Oscillating flow and separation of species in rectangular channels
View Description Hide DescriptionThe mass transfer and separation of species in a tube using oscillatory flows are strongly affected by the fluid flow profiles in the tube. It has been well established that oscillatory motion in a onedimensional flow configuration leads to a single tuning dimensionless frequency, where optimum separation may be effected. In this work, the effect on species separation by twodimensional laminar flow arising in a rectangular cross section is studied and a surprising result is that a second tuning frequency may occur at lower dimensionless oscillation frequencies. The physics reveals that this new optimum disappears when the aspect ratio is either very large or close to unity. These observations are related to the flow profiles at different aspect ratios.
 Instability and Transition

Phenomenology of a flow around a circular cylinder at subcritical and critical Reynolds numbers
View Description Hide DescriptionIn this work, the flow around a circular cylinder is investigated at Reynolds numbers ranging from 79 000 up to 238 000 by means of a combined acquisition system based on Temperature Sensitive Paint (TSP) and particle velocimetry. The proposed setup allows simultaneous and timeresolved measurement of absolute temperature and relative skin friction fields onto the cylinder surface and nearwake velocity field. Combination of timeresolved surface measurements and planar nearfield velocity data allows the investigation of the profound modifications undergone by the wall shear stress topology and its connections to the nearfield structure as the flow regime travels from the subcritical to the critical regime. Laminar boundarylayer separation, transition, and reattachment are analyzed in the light of temperature, relative skin friction maps, and Reynolds stress fields bringing about a new perspective on the relationship between boundary layer development and shear layer evolution. The fastresponding TSP employed allows high acquisition frequency and calculation of power spectral density from surface data. Correlation maps of surface and nearwake data provide insight into the relationship between boundarylayer evolution and vortex shedding. We find that as the Reynolds number approaches the critical state, the separation line oscillations feature an increasingly weaker spectrum peak compared to the nearwake velocity spectrum. In the critical regime, separation line oscillations are strongly reduced and the correlation to the local vorticity undergoes an overall decrease giving evidence of modifications in the vortex shedding mechanism.