When two spherical particles submerged in a viscous fluid are subjected to an oscillatory flow, they align themselves perpendicular to the direction of the flow leaving a small gap between them. The formation of this compact structure is attributed to a nonzero residual flow known as steady streaming. We have performed direct numerical simulations of a fully resolved, oscillating flow in which the pair of particles is modeled using an immersed boundary method. Our simulations show that the particles oscillate both parallel and perpendicular to the oscillating flow in elongated figure-8 trajectories. In absence of bottom friction, the mean gap between the particles depends only on the normalized Stokes boundary layer thickness δ∗, and on the normalized, streamwise excursion length of the particles relative to the fluid Ar∗ (equivalent to the Keulegan-Carpenter number). For Ar∗≲1, viscous effects dominate and the mean particle separation only depends on δ∗. For larger Ar∗ values, advection becomes important and the gap widens. Overall, the normalized mean gap between the particles scales as L∗≈3.0δ∗1.5+0.03Ar∗3, which also agrees well with previous experimental results. The two regimes are also observed in the magnitude of the oscillations of the gap perpendicular to the flow, which increases in the viscous regime and decreases in the advective regime. When bottom friction is considered, particle rotation increases and the gap widens. Our results stress the importance of simulating the particle motion with all its degrees of freedom to accurately model the system and reproduce experimental results. The insights of the particle pairs provide an important step towards understanding denser and more complex systems.

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The alignment of a pair of spherical particles perpendicular to a horizontally oscillating flow is attributed to a non-zero residual flow, known as steady streaming. This phenomenon is the basis of complex patterns in denser systems, such as particle chains and the initial stages of rolling-grain ripples. Previous studies on such self-organization processes used two distinct systems: an oscillating box filled with viscous fluid and an oscillating channel flow, where the fluid oscillates relative to the bottom boundary. In this paper, we show that particle pair dynamics in these two systems are fundamentally different, due to the presence of a Stokes boundary layer above the bottom in the oscillating channel flow. The results are obtained from direct numerical simulations in which the dynamics of a pair of particles are simulated using an immersed boundary method. The oscillating box and the oscillating channel flow are only equivalent in a limited region of the parameter space, where both the normalized Stokes boundary layer thickness and the normalized relative particle excursion length are small. Overall, the particle dynamics in the oscillating channel flow, compared to the oscillating box, are governed by an additional dimensionless parameter, that is, the particle–fluid density ratio.@en

Abstract: We discuss the application of synthetic aperture particle image velocimetry for measuring the flow around human swimmers using small bubbles as tracer. We quantify the two-dimensional projection of the velocity field in planes perpendicular to the viewing direction of an array of six cameras. With help of simulations, modelled after the experiment, we address questions about depth selectivity and occlusion in dense bubble fields. Using vortex rings in the swimming pool, we provide a proof of principle of the method. It is further illustrated by the vorticity field produced by a human swimmer. Graphic abstract: [Figure not available: see fulltext.].

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The present study concerns Lagrangian transport and (chaotic) advection in three-dimensional (3D) flows in cavities under steady and laminar conditions. The main goal is to investigate topological equivalences between flow classes driven by different forcing; streamline patterns and their response to nonlinear effects are examined. To this end, we consider two prototypical systems that are important in both natural and industrial applications: a buoyancy-driven flow (differentially heated configuration with two vertical isothermal walls) and a lid-driven flow governed by the Grashof (Gr) and the Reynolds (Re) numbers, respectively. Symmetries imply fundamental similarities between the streamline topologies of these flows. Moreover, nonlinearities induced by fluid inertia and buoyancy (increasing Gr) in the buoyancy-driven flow vs fluid inertia (increasing Re) and single- or double-wall motion in the lid-driven flow cause similar bifurcations of the Lagrangian flow topology. These analogies imply that Lagrangian transport is governed by universal mechanisms, and differences are restricted to the manner in which these phenomena are triggered. Experimental validation of key aspects of the Lagrangian dynamics is carried out by particle image velocimetry and 3D particle-tracking velocimetry.

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We perform direct numerical simulation of the Couette flow as a model for the stable boundary layer. The flow evolution is investigated for combinations of the (bulk) Reynolds number and the imposed surface buoyancy flux. First, we establish what the similarities and differences are between applying a fixed buoyancy difference (Dirichlet) and a fixed buoyancy flux (Neumann) as boundary conditions. Moreover, two distinct parameters were recently proposed for the turbulent-to-laminar transition: the Reynolds number based on the Obukhov length and the "shear capacity," a velocity-scale ratio based on the buoyancy flux maximum. We study how these parameters relate to each other and to the atmospheric boundary layer. The results show that in a weakly stratified equilibrium state, the flow statistics are virtually the same between the different types of boundary conditions. However, at stronger stratification and, more generally, in nonequilibrium conditions, the flow statistics do depend on the type of boundary condition imposed. In the case of Neumann boundary conditions, a clear sensitivity to the initial stratification strength is observed because of the existence of multiple equilibriums, while for Dirichlet boundary conditions, only one statistically steady turbulent equilibrium exists for a particular set of boundary conditions. As in previous studies, we find that when the imposed surface flux is larger than the maximum buoyancy flux, no turbulent steady state occurs. Analytical investigation and simulation data indicate that this maximum buoyancy flux converges for increasing Reynolds numbers, which suggests a possible extrapolation to the atmospheric case.@en

In this paper a video-based method to automatically track instantaneous velocities of a swimmer is presented. Single cameras were used to follow a marker (LED) attached to the body. The method is inspired by particle tracking techniques, traditionally used in the field of fluid dynamics, to measure local velocities of a fluid flow. During the validation experiment, a white LED was attached to the hip of a swimmer together with a speedometer. A swimmer performed four different stroke types. The velocity profiles using LED tracking were captured and showed less noise than the speedometer measurements. Only at times when the marker disappeared above the water surface due to body role in front crawl and backstroke swimming did the LED tracking fail to capture the athlete’s motion. The algorithm was tested in a 2D case with a single LED to illustrate the proof of principle, but should be suitable for implementation in a 3D analysis or multiple LED analysis.

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The evening transition is investigated in an idealized model for the nocturnal boundary layer. From earlier studies it is known that the nocturnal boundary layer may manifest itself in two distinct regimes, depending on the ambient synoptic conditions: strong-wind or overcast conditions typically lead to weakly stable, turbulent nights; clear-sky and weak-wind conditions, on the other hand, lead to very stable, weakly turbulent conditions. Previously, the dynamical behaviour near the transition between these regimes was investigated in an idealized setting, relying on Monin–Obukhov (MO) similarity to describe turbulent transport. Here, we investigate a similar set-up, using direct numerical simulation; in contrast to MO-based models, this type of simulation does not need to rely on turbulence closure assumptions. We show that previous predictions are verified, but now independent of turbulence parametrizations. Also, it appears that a regime shift to the very stable state is signaled in advance by specific changes in the dynamics of the turbulent boundary layer. Here, we show how these changes may be used to infer a quantitative estimate of the transition point from the weakly stable boundary layer to the very stable boundary layer. In addition, it is shown that the idealized, nocturnal boundary-layer system shares important similarities with generic non-linear dynamical systems that exhibit critical transitions. Therefore, the presence of other, generic early warning signals is tested as well. Indeed, indications are found that such signals are present in stably stratified turbulent flows.

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This study aims to find the typical growth rate of the temperature inversion during the onset of the stable boundary layer around sunset.The sunset transition is a very challenging period for numerical weather prediction, since neither accepted theories for the convective boundary layer nor those for the stable boundary layer appear to be applicable. To gainmore insight in this period, a systematic investigation of the temperature inversion growth rate is conducted. A statistical procedure is used to analyze almost 16 years of observations from the Cabauw observational tower, supported by observations from two additional sites (DomeCandKarlsruhe). The results show that, on average, the growth rate of the temperature inversion (normalized by the maximum inversion during the night) weakly declines with increasing wind speed. The observed growth rate is quantitatively consistent among the sites, and it appears insensitive to various other parameters. The results were also insensitive to the afternoon decay rate of the net radiation except when this decay rate was very weak. These observations are compared to numerical solutions of three models with increasing complexity: a bulk model, an idealized single-column model (SCM), and an operational-level SCM. It appears only the latter could reproduce qualitative features of the observations using a first-order closure. Moreover, replacing this closure with a prognostic TKE scheme substantially improved the quantitative performance. This suggests that idealized models assuming instantaneous equilibrium flux-profile relations may not aid in understanding this period, since history effects may qualitatively affect the dynamics.

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Three-dimensional particle tracking velocimetry (3D-PTV) is a promising technique to study the behavior of granular flows. The aim of this paper is to cross-validate 3D-PTV against independent or more established techniques, such as particle image velocimetry (PIV), electronic ultrasonic sensor measurements for bed height, and the discrete element model (DEM), for the complicating circumstance in which granular particles are flowing down a rotating chute. 3D-PTV was used to gain access to Lagrangian trajectory data of surface particles in such flows, from which independent measurements of both the surface velocity and the bed height in the chute were derived. The 3D-PTV method was based on imaging and tracking colored tracer particles that were introduced in the granular material, which are viewed from three directions. The three cameras collected consecutive frames a known time interval apart and the PTV algorithm for locating and tracking particles was used to determine particle trajectories and velocities. We found that the 3D-PTV results are in good agreement with PIV results with regard to the streamwise and spanwise surface velocity of particles in the rotating chute. The particle bed height obtained from 3D-PTV was also found to be in good agreement with data from an ultrasonic bed-height sensor. The experimental findings from PTV for the non-rotating case were used to tune the friction coefficient in our DEM simulations. The simulation method was validated by the good agreement between experimental findings and simulations at all rotation rates studied.@en

The behavior of spherical particles flowing down a three-dimensional chute, inclined at fixed angle, is commonly simulated by a discrete element method (DEM). DEM is nowadays a standard tool for numerical studies of e.g. gas-solid fluidized beds. We have modified DEM for the simulation of rotating granular flows. In view of future extensions aimed at, for example, segregation studies of (rotating) bi- and polydisperse granular flows or mixtures of two kinds of granular particles with different densities, several validation steps are required. In a first step we compare DEM simulations with experiments of monodisperse spherical glass particles flowing through a rotating semi-cylindrical chute inclined at a fixed angle and constant flow rate. Different measurement techniques such as Particle Image Velocimetry and Particle Tracking Velocimetry are used to measure the averaged surface velocity of the particles and the bed height in the chute. We observe that the prevailing flow patterns depend strongly on the rotation rate of the chute. The streamwise and the spanwise particle velocities are influenced by the centrifugal and Coriolis forces, where with increasing rotation rate the particles are moving increasingly sideways. We find that the details of the particle feeding pattern are important only for the particle flow near the entrance of the chute, whereas after a relatively short distance the particle flow depends only on other factors such as the mass rate, inclination angle and rotation rate. Our DEM model predictions agree well with the experimental measurements for bed height and surface velocity.

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A discrete element model (DEM) is used to investigate the behavior of spherical particles flowing down a semicylindrical rotating chute. The DEM simulations are validated by comparing with particle tracking velocimetry results of spherical glass particles flowing through a smooth semicylindrical chute at different rotation rates of the chute. The DEM model predictions agree well with experimental results of surface velocity and particle bed height evolution. The validated DEM model is used to investigate the influence of chute roughness on the flow behavior of monodisperse granular particles in rotating chutes. To emulate different base roughnesses, a rough base is constructed out of a square close packing of fixed spherical particles with a diameter equal to, smaller, or larger than the flowing particles. Finally, the DEM model is used to study segregation in a binary density mixture for different degrees of roughness of the chute.@en

A discrete element model of spherical glass particles flowing down a rotating chute is validated against high quality experimental data. The simulations are performed in a corotating frame of reference, taking into account Coriolis and centrifugal forces. In view of future extensions aimed at segregation studies of polydisperse granular flows, several validation steps are required. In particular, the influence of the interstitial gas, a sensitivity study of the collision parameters, and the effect of system rotation on particle flow is investigated. Shirsath et al. have provided the benchmark laboratory measurements of bed height and surface velocities of monodisperse granular flow down an inclined rotating chute. With a proper choice of the friction coefficients, the simulations show very good agreement with our experimental results. The effect of interstitial gas on the flow behavior is found to be relatively small for 3-mm granular particles.

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In blast furnaces, particles like coke, sinter and pellets enter from a hopper and are distributed on the burden surface by a rotating chute. Such particulate flows suffer occasionally from particle segregation during transportation caused by differences in density or size. To get a more fundamental insight into these effects, we started an experimental study to investigate the effect of rotation on such particulate flows.Here, as a first step, we present an experimental study of granular flow of monodisperse 3. mm spherical glass particles flowing with a constant mass rate through a rotating smooth rectangular chute, which is inclined at a fixed angle. Experiments are performed for a sufficiently long time to study steady (but streamwise accelerating) flow. Particle image velocimetry (PIV), electronic ultrasonic height sensors, and a dynamic weighing scale are used to measure the surface velocity of the particle stream, the particle bed height and mass flow rate in the chute, respectively. The influence of rotation speed and angle of inclination of the chute is studied. We find an interesting interplay between the Coriolis force, which pushes the granular flow to the sidewall of the chute and tends to diminish the acceleration of the flow, and centrifugal forces that accelerate the flow. The velocity components display a complex dependence on the spanwise and streamwise position in the chute. The bed height in the chute is also influenced by these effects of system rotation. These measurements provide a well-defined set of observations for refining and validating computer simulations of granular flows, and point out some important limitations of physical experiments. We present preliminary three-dimensional discrete particle simulations, which show that the experimental measurements of bed height and surface particle velocity in a chute inclined at 30° can be predicted nearly quantitatively both without and with rotation of the chute.@en