Volume 27, Issue 8, August 2015
Index of content:
- Interfacial Flows
27(2015); http://dx.doi.org/10.1063/1.4927538View Description Hide Description
Liquid-infused patterned surfaces offer a promising new platform for generating omniphobic surface coatings. However, the liquid infused in these surfaces is susceptible to shear-driven dewetting. Recent work [Wexler et al., “Shear-driven failure of liquid-infused surfaces,” Phys. Rev. Lett. 114, 168301 (2015)] has shown how the substrate pattern in these surfaces can be designed to exploit capillary forces in order to retain infused lubricants against the action of an immiscible shear flow. In this study, we explore the behavior of the infused lubricant when external shear causes the lubricant to overflow finite or “dead-end” surface features, resulting in either temporary or permanent lubricant loss. Microfluidic experiments illustrate how both geometry and chemical Marangoni stresses within liquid-infused surfaces generate an overflow cascade in which the lubricant escapes from the substrate and forms droplets on the surface, after which the droplets depin and are washed away by the external shear flow, allowing the overflow to repeat. General guidelines are developed to estimate the onset of the different stages of the cascade with the aim of providing additional robustness criteria for the design of future liquid-infused surfaces.
- Particulate, Multiphase, and Granular Flows
Four-way coupled simulations of small particles in turbulent channel flow: The effects of particle shape and Stokes number27(2015); http://dx.doi.org/10.1063/1.4927277View Description Hide Description
This paper investigates the effects of particle shape and Stokes number on the behaviour of non-spherical particles in turbulent channel flow. Although there are a number of studies concerning spherical particles in turbulent flows, most important applications occurring in process, energy, and pharmaceutical industries deal with non-spherical particles. The computation employs a unique and novel four-way coupling with the Lagrangian point-particle approach. The fluid phase at low Reynolds number (Re τ = 150) is modelled by direct numerical simulation, while particles are tracked individually. Inter-particle and particle-wall collisions are also taken into account. To explore the effects of particles on the flow turbulence, the statistics of the fluid flow such as the fluid velocity, the terms in the turbulence kinetic energy equation, the slip velocity between the two phases and velocity correlations are analysed considering ellipsoidal particles with different inertia and aspect ratio. The results of the simulations show that the turbulence is considerably attenuated, even in the very dilute regime. The reduction of the turbulence intensity is predominant near the turbulence kinetic energy peak in the near wall region, where particles preferentially accumulate. Moreover, the elongated shape of ellipsoids strengthens the turbulence attenuation. In simulations with ellipsoidal particles, the fluid-particle interactions strongly depend on the orientation of the ellipsoids. In the near wall region, ellipsoids tend to align predominantly within the streamwise (x) and wall-normal (y) planes and perpendicular to the span-wise direction, whereas no preferential orientation in the central region of the channel is observed. Important conclusions from this work include the effective viscosity of the flow is not affected, the direct dissipation by the particles is negligible, and the primary mechanism by which the particles affect the flow is by altering the turbulence structure around the turbulence kinetic energy peak.
- Instability and Transition
27(2015); http://dx.doi.org/10.1063/1.4927697View Description Hide Description
Motivated by recent investigations of toroidal tissue clusters that are observed to climb conical obstacles after self-assembly [Nurse et al., “A model of force generation in a three-dimensional toroidal cluster of cells,” J. Appl. Mech. 79, 051013 (2012)], we study a related problem of the determination of the equilibrium and stability of axisymmetric drops on a conical substrate in the presence of gravity. A variational principle is used to characterize equilibrium shapes that minimize surface energy and gravitational potential energy subject to a volume constraint, and the resulting Euler equation is solved numerically using an angle/arclength formulation. The resulting equilibria satisfy a Laplace-Young boundary condition that specifies the contact angle at the three-phase trijunction. The vertical position of the equilibrium drops on the cone is found to vary significantly with the dimensionless Bond number that represents the ratio of gravitational and capillary forces; a global force balance is used to examine the conditions that affect the drop positions. In particular, depending on the contact angle and the cone half-angle, we find that the vertical position of the drop can either increase (“the drop climbs the cone”) or decrease due to a nominal increase in the gravitational force. Most of the equilibria correspond to upward-facing cones and are analogous to sessile drops resting on a planar surface; however, we also find equilibria that correspond to downward facing cones that are instead analogous to pendant drops suspended vertically from a planar surface. The linear stability of the drops is determined by solving the eigenvalue problem associated with the second variation of the energy functional. The drops with positive Bond number are generally found to be unstable to non-axisymmetric perturbations that promote a tilting of the drop. Additional points of marginal stability are found that correspond to limit points of the axisymmetric base state. Drops that are far from the tip are subject to azimuthal instabilities with higher mode numbers that are analogous to the Rayleigh instability of a cylindrical interface. We have also found a range of completely stable solutions that correspond to small contact angles and cone half-angles.
- Turbulent Flows
27(2015); http://dx.doi.org/10.1063/1.4927647View Description Hide Description
This study derives and compares vortex identification methods for detecting vortices in planar velocity fields. Two-dimensional (2D) forms of the commonly used Δ, Q, λci , and λ 2 criteria are derived in detail based on the 2D counterpart of the full velocity gradient tensor. These four criteria are compared mathematically and experimentally in the case of using zero thresholds. The results show that while all methods are capable of extracting strong vortices, their efficiencies in identifying weaker vortices are not necessarily the same. The Δ and λ ci criteria impose the least requirements on the identified structures and extract the most number of vortices, and the λ 2 criterion is the most restrictive one and tends to discard the weakest vortices. However, non-zero thresholds are generally necessary for applying vortex identification criteria in real turbulent flows, and normalizing the vortex indicators with their root mean squares is needed to enable the selection of universal threshold for vortices residing at different wall-normal positions in wall turbulence. The introduction of threshold makes the four vortex identification criteria equally efficacious, and equivalent thresholds are proposed to facilitate quantitative comparison of results based on different criteria in wall turbulence.
27(2015); http://dx.doi.org/10.1063/1.4927680View Description Hide Description
We perform the systematic numerical study of high vorticity structures that develop in the 3D incompressible Euler equations from generic large-scale initial conditions. We observe that a multitude of high vorticity structures appear in the form of thin vorticity sheets (pancakes). Our analysis reveals the self-similarity of the pancakes evolution, which is governed by two different exponents e −t/T ℓ and e t/T ω describing compression in the transverse direction and the vorticity growth, respectively, with the universal ratio T ℓ/T ω ≈ 2/3. We relate development of these structures to the gradual formation of the Kolmogorov energy spectrum Ek ∝ k −5/3, which we observe in a fully inviscid system. With the spectral analysis, we demonstrate that the energy transfer to small scales is performed through the pancake structures, which accumulate in the Kolmogorov interval of scales and evolve according to the scaling law ω max ∝ ℓ−2/3 for the local vorticity maximums ω max and the transverse pancake scales ℓ.
Evaluation of machine learning algorithms for prediction of regions of high Reynolds averaged Navier Stokes uncertainty27(2015); http://dx.doi.org/10.1063/1.4927765View Description Hide Description
Reynolds Averaged Navier Stokes (RANS) models are widely used in industry to predict fluid flows, despite their acknowledged deficiencies. Not only do RANS models often produce inaccurate flow predictions, but there are very limited diagnostics available to assess RANS accuracy for a given flow configuration. If experimental or higher fidelity simulation results are not available for RANS validation, there is no reliable method to evaluate RANS accuracy. This paper explores the potential of utilizing machine learning algorithms to identify regions of high RANS uncertainty. Three different machine learning algorithms were evaluated: support vector machines, Adaboost decision trees, and random forests. The algorithms were trained on a database of canonical flow configurations for which validated direct numerical simulation or large eddy simulation results were available, and were used to classify RANS results on a point-by-point basis as having either high or low uncertainty, based on the breakdown of specific RANS modeling assumptions. Classifiers were developed for three different basic RANS eddy viscosity model assumptions: the isotropy of the eddy viscosity, the linearity of the Boussinesq hypothesis, and the non-negativity of the eddy viscosity. It is shown that these classifiers are able to generalize to flows substantially different from those on which they were trained. Feature selection techniques, model evaluation, and extrapolation detection are discussed in the context of turbulence modeling applications.