Volume 26, Issue 4, April 2014
Index of content:
 LETTERS


Vortexinduced drag and the role of aspect ratio in undulatory swimmers
View Description Hide DescriptionDuring cruising, the thrust produced by a selfpropelled swimmer is balanced by a global drag force. For a given object shape, this drag can involve skin friction or form drag, both being welldocumented mechanisms. However, for swimmers whose shape is changing in time, the question of drag is not yet clearly established. We address this problem by investigating experimentally the swimming dynamics of undulating thin flexible foils. Measurements of the propulsive performance together with full recording of the elastic wave kinematics are used to discuss the general problem of drag in undulatory swimming. We show that a major part of the total drag comes from the trailing longitudinal vortices that rollup on the lateral edges of the foils. This result gives a comparative advantage to swimming foils of larger span thus bringing new insight to the role of aspect ratio for undulatory swimmers.

On the extension of the eddy viscosity model to compressible flows
View Description Hide DescriptionIn the paper the authors examine the extension of the eddy viscosity modeling approach to compressible large eddy simulation. On the basis of formal algebraic relations among the generalized central moments and the filtered Favre terms, a new compressible eddy viscosity formulation is derived.

Viscosity of liquid ^{4}He and quantum of circulation: Are they related?
View Description Hide DescriptionIn the vicinity of the superfluid transition in liquid ^{4}He, we explore the relation between two apparently unrelated physical quantities—the kinematic viscosity, ν, in the normal state and the quantum of circulation, κ, in the superfluid state. The model developed here leads to the simple relationship ν ≈ κ/6, and links the classical and quantum flow properties of liquid ^{4}He. We critically examine available data relevant to this relation and find that the prediction holds well at the saturated vapor pressure. Additionally, we predict the kinematic viscosity for liquid ^{4}He along the λline at negative pressures.

 ARTICLES


Micro and Nanofluid Mechanics

Role of solution conductivity in reaction induced charge autoelectrophoresis
View Description Hide DescriptionCatalytic bimetallic Janus particles swim by a bipolar electrochemical propulsion mechanism that results from electroosmotic fluid slip around the particle surface. The flow is driven by electrical body forces which are generated from a coupling of a reactioninduced electric field and net charge in the diffuse layer surrounding the particle. This paper presents simulations, scaling, and physical descriptions of the experimentally observed trend that the swimming speed decays rapidly with increasing solution conductivity. The simulations solve the full PoissonNernstPlanckStokes equations with multiple ionic species, a cylindrical particle in an infinite fluid, and nonlinear ButlerVolmer boundary conditions to represent the electrochemical surface reactions. The speed of bimetallic particles is reduced in highconductivity solutions because of reductions in the induced electric field in the diffuse layer near the rod, the total reaction rate, and the magnitude of the rod zeta potential. This work suggests that the autoelectrophoretic mechanism is inherently susceptible to speed reductions in higher ionic strength solutions.

Stability of bubbly liquids and its connection to the process of cavitation inception
View Description Hide DescriptionThis paper presents a potential energy approach for the investigation of the stability of bubbly liquids. Using the system's free energy variations with respect to the void fraction as a stability criterion for the whole system, we consider that sudden bubble expansion occurs only when the bubble cluster expansion is energetically favorable. The results obtained provide new insight into the behavior of prenucleated liquids when the inception point is reached as well as a simple method to estimate the energy exchanges between a bubble cluster and its environment when the kinetic energy is negligible compared to the elastic energy stored during tension and compression processes. In addition to the radius of the initial nuclei, the concentration and polydispersity are shown to exert an important influence on the response of the system after inception.

Interfacial Flows

Interfacial stress balances in structured continua and free surface flows in ferrofluids
View Description Hide DescriptionInterfacial linear and internal angular momentum balances are obtained for a structured continuum and for the special case of a ferrofluid, a suspension of magnetic nanoparticles in a Newtonian fluid. The interfacial balance equations account for the effects of surface tension and surface tension gradient, magnetic surface excess forces, antisymmetric stresses, and couple stresses in driving interfacial flows in ferrofluids. Application of the interfacial balance equations is illustrated by obtaining analytical expressions for the translational and spin velocity profiles in a thin film of ferrofluid on an infinite flat plate when a rotating magnetic field is applied with axis of rotation parallel to the ferrofluid/air interface. The cases of zero and nonzero spin viscosity are considered for small applied magnetic field amplitude. Expressions for the maximum translational velocity, slope of the translational velocity profile at the ferrofluid/air interface, and volumetric flow rate are obtained and their use to test the relevance of spin viscosity and couple stresses in the flow situation under consideration is discussed.

Thinliquidfilm flow on a topographically patterned rotating cylinder
View Description Hide DescriptionThe flow of thin liquid films on rotating surfaces is directly relevant to the coating of discrete objects. To begin understanding how surface topography influences such flows, we consider a model problem in which a thin liquid film flows over a rotating cylinder patterned with a sinusoidal surface topography. Lubrication theory is applied to develop a partial differential equation that governs the film thickness as a function of time and the angular coordinate. Static situations are considered first in order to determine the parameter regime in which the lubrication approximation is expected to be valid. When gravitational forces are relatively weak, cylinder rotation leads to the formation of droplets connected by very thin films. The number of droplets is equal to the pattern frequency at low and high rotation rates, with the droplets located at the pattern troughs at low rotation rates and the pattern crests at high rotation rates. When gravitational forces become significant, the film thickness never reaches a steady state, in contrast to the case of an unpatterned cylinder. The results of this work clearly establish that the flow of thin liquid films on rotating surfaces can be very sensitive to the presence of surface topography.

Jet orientation of a collapsing bubble near a solid wall with an attached air bubble
View Description Hide DescriptionThe interaction between a cavitation bubble and a nonoscillating air bubble attached to a horizontal polyvinyl chloride plate submerged in deionized water is investigated using a lowvoltage sparkdischarge setup. The attached air bubble is approximately hemispherical in shape, and its proximity to a sparkinduced oscillating bubble (represented by the dimensionless standoff distance H ^{′}) determines whether or not a jet is formed in the oscillating bubble during its collapse. When the oscillating bubble is created close to the plate, it jets towards or away from the plate. The ratio of oscillating bubble oscillation time and the wallattached bubble oscillation time (T ^{′}) is found to be an important parameter for determining the jet direction. This is validated with numerical simulations using an axialsymmetrical boundary element model. Our study highlights prospects in reducing cavitation damage with a stationary bubble, and in utilizing a cavitation collapse jet by controlling the jet's direction.

Jet impingement and the hydraulic jump on horizontal surfaces with anisotropic slip
View Description Hide DescriptionThis paper presents an analysis that describes the dynamics of laminar liquid jet impingement on horizontal surfaces with anisotropic slip. Due to slip at the surface and the anisotropy of its magnitude, the overall behavior departs notably from classical results. For the scenario considered the slip length varies as a function of the azimuthal coordinate and describes superhydrophobic surfaces micropatterned with alternating ribs and cavities. The thin film dynamics are modeled by a radial momentum analysis for a given jet Reynolds number and specified slip length and the influence of slip on the entire flow field is significant. In an average sense the thin film dynamics exhibit similarities to behavior that exists for a surface with isotropic slip. However, there are also important deviations that are a direct result of the azimuthally varying slip and these become more pronounced at higher Reynolds numbers and at greater slip lengths. The analysis also allows determination of the azimuthally varying radial location of the hydraulic jump that forms due to an imposed downstream depth. Departure from the no slip case and from the scenario of isotropic slip is characterized over a range of jet Reynolds numbers and realistic slip length values. The results show that for all cases the hydraulic jump is elliptical, with eccentricity increasing as the Reynolds number or slip length increases, or as the downstream depth decreases. The radial location of the hydraulic jump is greatest in the direction of greatest slip (parallel to the microribs), while it is a minimum in the direction transverse to the rib/cavity structures. The model results for the hydraulic jump radial position are compared to experimental measurements with good agreement.

Viscous and NonNewtonian Flows

Comparison of direct simulation Monte Carlo chemistry and vibrational models applied to oxygen shock measurements
View Description Hide DescriptionValidation of three direct simulation Monte Carlo chemistry models—total collision energy, Quantum Kinetic, and Kuznetsov state specific (KSS)—is conducted through the comparison of calculated vibrational temperatures of molecular oxygen with measured values inside a normal shock wave. First, the 2D geometry and numerical approach used to simulate the shock experiments is verified. Next, two different vibrational relaxation models are validated by comparison with data for the M = 9.3 case where dissociation is small in the nonequilibrium region of the shock and with newly obtained thermal rates. Finally, the three chemistry model results are compared for M = 9.3 and 13.4 in the region where the vibrational temperature is greatly different from the rotational and translational temperature, and thus nonequilibrium dissociation is important. It is shown that the peak vibrational temperature is very sensitive to the initial nonequilibrium rate of reaction in the chemistry model and that the vibrationally favored KSS model is much closer to the measured peak, but the postpeak behavior indicates that some details of the model still need improvement.

Particulate, Multiphase, and Granular Flows

Lift forces in granular media
View Description Hide DescriptionThe paper presents an experimental and numerical study of the forces experienced by a cylinder moving horizontally in a granular medium under gravity. Despite the symmetry of the object, a strong lift force is measured. Whereas the drag force increases linearly with depth, the lift force is shown to saturate at depths much greater than the cylinder diameter, and to scale like the buoyancy with a large amplification factor of order 20. The origin of this high lift force is discussed based on the stress distribution measured in discrete numerical simulations. The lift force comes from the gravitational pressure gradient, which breaks the up/down symmetry and strongly modifies the flow around the obstacle compared to the case without pressure gradient.

Laminar Flows

Transition in vortex breakdown modes in a coaxial isothermal unconfined swirling jet
View Description Hide DescriptionThis paper reports first observations of transition in recirculation pattern from an openbubble type axisymmetric vortex breakdown to partially open bubble mode through an intermediate, critical regime of conical sheet formation in an unconfined, coaxial isothermal swirling flow. This timemean transition is studied for two distinct flow modes which are characterized based on the modified Rossby number (Ro m ), i.e., Ro m ≤ 1 and Ro m > 1. Flow modes with Ro m ≤ 1 are observed to first undergo conetype breakdown and then to partially open bubble state as the geometric swirl number (S G ) is increased by ∼20% and ∼40%, respectively, from the baseline openbubble state. However, the flow modes with Ro m > 1 fail to undergo such sequential transition. This distinct behavior is explained based on the physical significance associated with Ro m and the swirl momentum factor (ξ). In essence, ξ represents the ratio of angular momentum distributed across the flow structure to that distributed from central axis to the edge of the vortex core. It is observed that ξ increases by ∼100% in the critical swirl number band where conical breakdown occurs as compared to its magnitude in the S G regime where open bubble state is seen. This results from the fact that flow modes with Ro m ≤ 1 are dominated by radial pressure gradient due to swirl/rotational effect when compared to radial pressure deficit arising from entrainment (due to the presence of costream). Consequently, the imparted swirl tends to penetrate easily towards the central axis causing it to spread laterally and finally undergo conical sheet breakdown. However, the flow modes with Ro m > 1 are dominated by pressure deficit due to entrainment effect. This blocks the radial inward penetration of imparted angular momentum thus preventing the lateral spread of these flow modes. As such these structures fail to undergo cone mode of vortex breakdown which is substantiated by a mere 30%–40% rise in ξ in the critical swirl number range.

Numerical simulation of fluid flow through random packs of cylinders using immersed boundary method
View Description Hide DescriptionThe macroscopic properties of twodimensional random periodic packs of monomodal and bimodal cylinders are investigated by means of numerical methods. We solve the unsteady, twodimensional NavierStokes equations on a staggered Cartesian grid and use the immersed boundary method to treat internal flow boundaries. A number of verification problems for the numerical method are presented. The effects of porosity, diameter ratio, largetototal particle ratio, and Reynolds number on the macroscopic permeability are studied. For small Reynolds numbers, we show that the permeability can be correlated to the underlying microstructure by means of a suitably defined statistical descriptor, the mean shortest Delaunay edge. With proper scaling, the results for bimodal cylinders collapse onto the data for monomodal cylinders, which can then be fitted with a universal curve. For larger Reynolds numbers we show that a modified Forchheimer equation can characterize the flow.

Instability and Transition

The Taylorvortex dynamo
View Description Hide DescriptionThe generation of a magnetic field by dynamo action in a Taylorvortex flow is investigated numerically. We first discuss how the Taylor vortices generate a spatially subharmonic dynamo, for which the axial wavelength of the magnetic field is twice the one of the flow pattern. Then, we investigate the influence of the Reynolds number and the turbulent fluctuations on the structure and the onset of the TaylorCouette dynamo. Finally, based on the subharmonic nature of this dynamo, we propose new configurations which could be relevant for laboratory experiments.

Experimental study of a buoyancydriven instability of a miscible horizontal displacement in a HeleShaw cell
View Description Hide DescriptionWhen a given fluid displaces another less viscous miscible one in a horizontal HeleShaw cell, the displacement is stable from the viscous point of view. Nevertheless, thin stripes perpendicular to the moving interface can be observed in the mixing zone between the fluids both in rectilinear and radial displacements. This instability is due to buoyancy effects within the gap of the cell which develop because of an unstable density stratification associated with the underlying concentration profile. To characterize this buoyancydriven instability and the related striped pattern, we perform a parametric experimental study of viscously stable miscible displacements in a horizontal HeleShaw cell with radial injection. We analyze the influence of the flow rate, the thickness of the gap, and the relative physical fluid properties on the development and characteristics of the instability.

Turbulent Flows

Study of a stall cell using stereo particle image velocimetry
View Description Hide DescriptionThe structure of Stall Cells (SCs) on wings is analyzed on the basis of stereo particle image velocimetry measurements. All experiments regard a Reynolds number 0.87 × 10^{6} flow around a rectangular wing with endplates and an aspect ratio of 2.0. The inherently unstable stall cell is stabilized by means of a localized spanwise disturbance. Velocity, vorticity, and Reynolds stress data above the wing and in the wake are presented and discussed, also in combination with Computational Fluid Dynamics data. The present study completes and clarifies the previously suggested models regarding the SC structure. The SC emerges in between the separation and trailing edge shear layer where three different types of vortices are identified: (a) the stall cell vortices that start normal to the wing surface and continue downstream aligned with the free stream, (b) the separation line vortex, and (c) the trailing edge line vortex that both run parallel to the wing trailing edge and grow significantly at the center of the stall cell. Analysis of the Reynolds stress data reveals high anisotropy. Concentration of high streamwise shear stress values is connected to the two shear layers and high cross shear Reynolds stresses are connected to vortex stretching. High normal Reynolds stress values are observed (a) in the separation but not in the trailing edge shear layer indicating the flapping of the former and (b) along the stall cell vortices indicating their wandering motion. The eddy viscosity based Reynolds averaged NavierStokes simulations are found in good qualitative agreement with the experiments in terms of the type and position of the identified vortex structures, an agreement which is linked to the correct trend in the predicted shear Reynolds stresses distributions. Quantitative deviations of the numerical results from the measurements are attributed to the isotropic definition of the turbulence model. Therefore, use of large eddy simulation is suggested for better prediction of the flow.

Development of turbulence behind the single square grid
View Description Hide DescriptionIn this paper, direct numerical simulations are carried out to study singlesquare gridgenerated turbulence at a Reynolds number = 20 000 (based on the inlet velocity U in and the length of grid bar L 0). Different from the regular grid and the multiscale/fractal grid, here only single large square grid is placed at the center near the inlet. First, we investigate the evolutions of turbulence characteristics (e.g., mean streamwise velocity, turbulence intensity, Taylor microscale, etc.) along the centerline. The common characteristics possessed by turbulent flows generated by the single square grid and by the fractal square grid are presented. We confirm the hypothesis proposed by Mazellier and Vassilicos [“Turbulence without RichardsonKolmogorov cascade,” Phys. Fluids22, 075101 (2010)] that for the fractal square grid, the location of turbulence intensity peak along the centerline is mainly determined by largescale wake interactions. Current numerical results show that in turbulence generated by the single square grid, wake interactions occur close to the grid and cause extreme/intense events. Then, the spatial development of invariants of the velocity gradient tensor is studied. For example, the (Q W , −Q S ) maps are analyzed to show how turbulence generated by a single square grid obtains large scale vortices along the centerline.

Geometry of scaletoscale energy and enstrophy transport in twodimensional flow
View Description Hide DescriptionUsing filterspace techniques, we analyze the transport of energy and enstrophy between scales in an experimental quasitwodimensional weakly turbulent flow. By decomposing the scaletoscale energy and enstrophy fluxes into three components that consist of distinct types of triad interactions, we find that different triads are responsible for forward and inverse flux. To understand this behavior, we analyze the geometric alignment between the turbulent stresses that drive scaletoscale transfer and the largescale velocity and vorticity gradients, and show that different triad interactions have distinct alignment signatures. Our results shed light on the role played by geometric alignment in the net behavior of triad interactions in turbulence.

Analysis of the Lagrangian path structures in fluid turbulence
View Description Hide DescriptionBecause in the Lagrangian frame the time scale separation has a stronger Reynolds number dependence than the length scale case in the Eulerian frame, it is more difficult to reveal inertial range scaling laws, as predicted from dimensional arguments. The present work introduces a newly defined trajectory segment structure to tentatively understand Lagrangian statistics. When a fluid particle evolves in space, its Lagrangian trajectory encounters regions of different dynamics, which can be characterized by the magnitude of material acceleration, i.e., , in certain time span. The extrema of are considered as the representative markers along the Lagrangian trajectories. A trajectory segment is defined as the part bounded by two adjacent extrema of . The time difference and magnitude of the velocity difference at the two ends of each segment are chosen as the characteristic parameters. It shows that such structure reveals interesting turbulence physics, such as the scaling of the structure function and the quantitative description of the time scale. The corresponding explanation and analysis of flow physics are provided as well to improve the understanding of some remaining challenging issues.

Collapse of the turbulent dissipative range on Kolmogorov scales
View Description Hide DescriptionIt is pointed out that the collapse of the turbulent dissipative range on Kolmogorov scales does not require either of the two major assumptions in Kolmogorov's [“The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers,” Dokl. Akad. Nauk USSR30, 299 (1941)] similarity hypothesis, i.e., R λ, the Taylor microscale Reynolds number, is very large and local isotropy is satisfied. In particular, the Kolmogorov velocity and length scales are shown to be the appropriate normalization scales when the largescale terms in the transport equations for the secondorder statistics can be neglected. Evidence for this scaling is discussed critically on the basis of the available data. It is also shown that this scaling breaks down when R λ becomes too small, typically below 20.
