ALBERT

Description: The classical gravitational instability of a layer of denser fluid overlying a layer of less dense fluid, commonly known as the Rayleigh-Taylor instability, has been studied for well over a hundred years. In this article, we present the results of numerical simulations of a variant of this instability in which a plug of dense fluid is released from rest in a thin channel between two flat, vertical walls, causing a downward acceleration of the entire fluid column and formation of boundary layers near the walls. The plug of dense fluid undergoes distinctly different evolution near the walls and in the fluid interior. The instability in the interior, which we label the “hammerhead” instability based on its shape, is robust over a range of physical parameters, but disappears below a threshold Schmidt number. Fluid near the wall is slowed, and thin tendrils that link the near wall fluid to the main body of the fluid plug form, and in some cases undergo their own instability. We characterize the fully three-dimensionalized state, finding that while bulk measures of kinetic energy three-dimensionalization do not discriminate between low and high Schmidt number cases, the geometric distributions of the dynamical parameters Q and R from the turbulence literature are profoundly different in the high Schmidt number case. Finally, we consider the role of shear in situations in which the two plates are not exactly vertical, demonstrating that shear diminishes the importance of three-dimensionalization, while the hammerhead instability remains relevant.

Description: Flow past two cylinders of different diameters in close proximity is simulated numerically for a constant diameter ratio of 0.45, a gap ratio of 0.0625, and a Reynolds number of 1000 (defined using the diameter of the main cylinder). The effect of the position angle α of the small cylinder relative to the large one on force coefficients and wake flow patterns are studied. Depending on the position angle α of the small cylinder, four wake flow modes are identified: the upstream interference mode for α = 0°, 22.5°, and 45°, the intermittent attached gap flow mode for α = 67.5° and 90°, the attached gap flow mode for α = 112.5° and 135°, and the wake interference mode for α = 157.5° and 180°. The RMS lift coefficients of both cylinders are reduced significantly compared with that of a single cylinder, regardless of the position angle of the small cylinder. Although the variation trends of the mean drag and lift coefficients with the position angle of the small cylinder obtained from the two-dimensional (2D) and three-dimensional (3D) simulations are similar, the 2D simulations overestimate the mean drag coefficient, the RMS drag and lift coefficients compared with those obtained from the 3D simulations.

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.

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.

Description: The energy spectrum contains information not only on the intensity but also on the scale dependence of the turbulent fluctuations; the spectrum is commonly used to describe the dynamics of homogeneous isotropic turbulence. On the other hand, one-point statistical quantities such as the turbulent kinetic energy are mainly treated for inhomogeneous turbulence. Although the energy spectrum must be useful in describing the scale dependence of inhomogeneous turbulence, the Fourier transform cannot be performed in general cases. In this work, instead of the energy spectrum in the wavenumber space, the energy density in the scale space was introduced on the basis of the two-point velocity correlation in the physical space. The transport equation for the energy density was derived for inhomogeneous turbulence. Direct numerical simulation (DNS) data of homogeneous isotropic turbulence were first used to evaluate the energy transfer in the scale space. The energy density equation was compared with the energy spectrum equation to assess the role of the energy density. DNS data of turbulent channel flow were also used to evaluate the energy density equation for inhomogeneous turbulence. The energy transport in the physical and scale spaces was examined in different regions of channel flow. It was shown that the transport equation for the energy density adequately describes the energy transfer in the scale space. The energy flux from the large to the small scales was observed for both turbulent flows in a similar manner to the conventional energy cascade in the wavenumber space.

Description: The variable hard sphere and related models have proven to be accurate and computationally convenient replacements for the inverse power law model of classical kinetic theory in direct simulation Monte Carlo calculations. We attempt to provide theoretical support for this remarkable success by comparing the relaxation rates in the linearized Boltzmann equation for the Maxwellian collision model with those of its variable hard sphere surrogate. The comparison demonstrates that the linearized collision operator with variable hard sphere interactions can accurately approximate the linearized collision operator with Maxwellian inverse power law interactions under well-defined and broadly applicable conditions. Extensions of the analysis to the general inverse power law model and to more realistic intermolecular potentials are briefly discussed.

Description: We present an investigation of the stability of liquid metal flow under the influence of an imposed magnetic field by means of a laboratory experiment as well as a linear stability analysis of the setup using the finite element method. The experimental device ZUrich Cylindrical CHannel INstability Investigation is a modified cylindrical annulus with electrically driven flow of liquid GaInSn operating at Hartmann and Reynolds numbers up to M = 2022 and Re = 2.6 ⋅ 10 5 , respectively. The magnetic field gives rise to a free shear layer at the prominent inner electrode. We identify several flow regimes characterized by the nature of the instabilities. Above a critical current I c = O ( 0 . 1 A ) , the steady flow is destabilized by a Kelvin-Helmholtz mechanism at the free shear layer. The instability consists of counterrotating vortices traveling with the mean flow. For low forcing, the vortices are restricted to the free shear layer. Their azimuthal wave number m grows with M and decreases with Re . At Re / M ≈ 25, the instability becomes container-filling and energetically significant. It enhances the radial momentum transport which manifests itself in a broadening of the free shear layer width δ S . We propose that this transition may be related to an unstable Hartmann layer. At R e / M 2 = O ( 1 ) , an abrupt change is observed in the mean azimuthal velocity 〈 u ϕ ¯ 〉 and the friction factor F , which we interpret as the transition between an inertialess and an inertial regime.

Description: The immiscible displacement of one viscous liquid by another in a capillary tube is experimentally and numerically analyzed in the low inertia regime with negligible buoyancy effects. The dimensionless numbers that govern the problem are the capillary number Ca and the viscosity ratio of the displaced to the displacing fluids N μ . In general, there are two output quantities of interest. One is associated to the relation between the front velocity, U b , and the mean velocity of the displaced fluid, U ̄ 2 . The other is the layer thickness of the displaced fluid that remains attached to the wall. We compute these quantities as mass fractions in order to make them able to be compared. In this connection, the efficiency mass fraction, m e , is defined as the complement of the mass fraction of the displaced fluid that leaves the tube while the displacing fluid crosses its length. The geometric mass fraction, m g , is defined as the fraction of the volume of the layer that remains attached to the wall. Because in gas–liquid displacement, these two quantities coincide, it is not uncommon in the literature to use m g as a measure of the displacement efficiency for liquid–liquid displacements. However, as is shown in the present paper, these two quantities have opposite tendencies when we increase the viscosity of the displacing fluid, making this distinction a crucial aspect of the problem. Results from a Galerkin finite element approach are also presented in order to make a comparison. Experimental and numerical results show that while the displacement efficiency decreases, the geometrical fraction increases when the viscosity ratio decreases. This fact leads to different decisions depending on the quantity to be optimized. The quantitative agreement between the numerical and experimental results was not completely achieved, especially for intermediate values of Ca . The reasons for that are still under investigation. The experiments conducted were able to achieve a wide range of Ca . We show that in the range 1 〈 N μ 〈 2, wavy shape instabilities appear at the interface and that increasing capillary number the amplitude of those waves increases. A deeper investigation on the operation window where these instabilities occur is in order.

Description: We employ a barotropic two-phase/two-fluid model to study the primary break-up of cavitating liquid jets emanating from a rectangular nozzle, which resembles a high aspect-ratio slot flow. All components (i.e., gas, liquid, and vapor) are represented by a homogeneous mixture approach. The cavitating fluid model is based on a thermodynamic-equilibrium assumption. Compressibility of all phases enables full resolution of collapse-induced pressure wave dynamics. The thermodynamic model is embedded into an implicit large-eddy simulation (LES) environment. The considered configuration follows the general setup of a reference experiment and is a generic reproduction of a scaled-up fuel injector or control valve as found in an automotive engine. Due to the experimental conditions, it operates, however, at significantly lower pressures. LES results are compared to the experimental reference for validation. Three different operating points are studied, which differ in terms of the development of cavitation regions and the jet break-up characteristics. Observed differences between experimental and numerical data in some of the investigated cases can be caused by uncertainties in meeting nominal parameters by the experiment. The investigation reveals that three main mechanisms promote primary jet break-up: collapse-induced turbulent fluctuations near the outlet, entrainment of free gas into the nozzle, and collapse events inside the jet near the liquid-gas interface.

Description: The Kavli Institute of Theoretical Physics (KITP) program held at UC Santa Barbara in the fall of 2013 addressed the dynamics of dispersed particulate flows in the environment. By focusing on the prototypes of aeolian transport and turbidity currents, it aimed to establish the current state of our understanding of such two-phase flows, to identify key open questions, and to develop collaborative research strategies for addressing these questions. Here, we provide a brief summary of the program outcome.

Description: Generating stable cavity without droplets splatter is commonly required when process of a gas-jet penetrating into a liquid sheet is implemented in various industrial applications. In this study, experiments were carried out to investigate the cavity stability under different penetrating parameters, including different nozzle diameters, liquid sheet thicknesses, gas flow rates, and jet heights. When keeping other parameters fixed but moving the nozzle close to the liquid sheet surface, it was found that the cavity was frequently disturbed by the wall-jet and became unstable accompanied with droplets splatter at too low jet heights. Images of the cavities were captured by high speed video camera to study cavity performances, including its size, surface morphology, and droplets splatter. It was further found that violent surface waves were commonly generated by the strong wall-jet disturbance at low jet heights and droplets splatter was caused as long as Rayleigh instability happened due to higher frequency oscillation of the surface wave. Critical jet heights causing cavity stability transition were studied for different penetrating conditions, which were further expressed by a local modified Froude number as a normalized formulation. Curve fitting illustrating the conditions to generate stable penetrating cavities was given at last to provide guides for the jet controls in industry.

Description: Modelling the turbulent stress tensor is a main task for both large eddy simulations and methods based on Reynolds averaged Navier-Stokes equations. The turbulent stress is known as the subgrid-scale stress in the former and the Reynolds stress in the latter. In this paper, we examine the observation that the stress tensor tends to evolve towards a rod-like axisymmetric configuration. This observation has been well documented for the subgrid-scale stress. However, for the Reynolds stress, the available data are still too limited to draw a definite conclusion. In the first part of the paper, we show that the tendency is also universal for the Reynolds stress by direct numerical simulations of decaying anisotropic turbulence. To show the universality, it is crucial to examine the decaying process from initial turbulent fields with a wide range of levels of anisotropy. Such initial fields are generated by a novel synthetic turbulence model based on the so-called constrained multi-turnover Lagrangian map. In the second part, we use the direct numerical simulation data to study the dynamical mechanisms of the evolution towards the rod-like structures. Among others, the analyses show that the nonlinear self-interaction term is the driving force of the process, and that the pressure tends to enhance the disk-like axisymmetric structure but overall tends to reduce the anisotropy of the stress tensor. The results shed light on the subtle difference between the pressure and the nonlinear self-interaction terms.

Description: This paper describes an experimental investigation of the initial growth of flow asymmetries over a slender body of revolution at high angles of attack with natural and disturbed noses. Time-resolved particle image velocimetry was used to investigate the flow field around the body. The experimental results show that initially different amplitudes of unsteady disturbances near the tip are established owing to the tip imperfections. These unsteady disturbances experience a super-exponential growth near the tip and continue to grow exponentially due to linear instabilities. Attachment of a piece to the tip brings a larger initial difference and extends the super-exponential growth region. Thus, the disturbance amplitudes and their differences are larger for the disturbed case than for the natural case before reaching the neutral point of linear instability. The amplified disturbances lead to different instability vortex strengths in the separated shear layers, which feed continuously into the two primary concentrated vortices. As a result, the primary vortex strengths differ, which result in the initial vortex asymmetry. The experiment results demonstrate that the initial flow asymmetry arises from an asymmetric development of the boundary layer instability.

Description: Swirling vortex rings form in any turbulent flow where a swirling component is present, such as in combustion chambers or the downwash of helicopter blades. Instabilities on initially non-swirling vortex rings result in a localized swirl velocity being generated within the core. The presence of a swirl component of velocity in a vortex ring modifies the relaxation and evolution of numerical Gaussian cores in a manner that is currently unknown. The evolution of Gaussian axisymmetric vortex rings of size 0.2 〈 Λ 〈 0.5, with Gaussian swirls of magnitude 0.0 〈 W 〈 0.5, is analyzed with reference to the governing equations. A relaxation time, at which the initial Gaussian approximation has minimal influence on the subsequent evolution, has been estimated for each case. An axial vortex forms along the axis of the ring and is responsible for the growth of a shear layer that is found to form at the leading edge. The circulation based Reynolds number is set at 10 000 to encourage the growth of shear layer instabilities from within this region. Secondary vortex rings are subsequently shown to evolve from the Kelvin-Helmholtz instability for shear layers of sufficient strength and are convected around the original ring and shed from the system. It is shown that complete settling of the strain rate within the core does not occur until all sheddings have ceased. Increasing the swirl magnitude past that considered in this paper is expected to result in the original ring losing its structure before the instability can occur. The evolution is found to be qualitatively similar to that of a piston generated axisymmetric vortex ring with swirl, with both cases eventually reaching a similar quasi-steady state.

Description: A sufficient condition for instability of full compressible inviscid streamwise vortices has been derived using asymptotic analysis with large wavenumbers. Based on the nature of instability, the obtained growth rate is described using an entropy instability term, a spiral instability term, a helicity instability term, and an acoustic instability term. The entropy instability term correlates with compressibility. The spiral instability term is reasonably expressed by the axial and azimuthal velocities and their wavenumbers. The helicity instability term depends on the helicity profiles. In particular, the unstable condition for wake-type flows is satisfied when they possess a negative helicity in the profiles. The acoustic instability term depends on the local speed of sound. Linear and nonlinear numerical simulations are used to validate the instability conditions. The effect of the helicity instability is shown to be significantly strong by the simulations.

Description: Direct numerical simulations with an immersed boundary-lattice Boltzmann method are used to investigate the effects of particle rotation on flows past random arrays of mono-disperse spheres at moderate particle Reynolds numbers. This study is an extension of a previous study of the authors [Q. Zhou and L.-S. Fan, “Direct numerical simulation of low-Reynolds-number flow past arrays of rotating spheres,” J. Fluid Mech. 765 , 396–423 (2015)] that explored the effects of particle rotation at low particle Reynolds numbers. The results of this study indicate that as the particle Reynolds number increases, the normalized Magnus lift force decreases rapidly when the particle Reynolds number is in the range lower than 50. For the particle Reynolds number greater than 50, the normalized Magnus lift force approaches a constant value that is invariant with solid volume fractions. The proportional dependence of the Magnus lift force on the rotational Reynolds number (based on the angular velocity and the diameter of the spheres) observed at low particle Reynolds numbers does not change in the present study, making the Magnus lift force another possible factor that can significantly affect the overall dynamics of fluid-particle flows other than the drag force. Moreover, it is found that both the normalized drag force and the normalized torque increase with the increase of the particle Reynolds number and the solid volume fraction. Finally, correlations for the drag force, the Magnus lift force, and the torque in random arrays of rotating spheres at arbitrary solids volume fractions, rotational Reynolds numbers, and particle Reynolds numbers are formulated.

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 , λ ci , 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.

Description: The surface impact and collisions of particle-laden nanodrops are studied using molecular dynamics computer simulations. The drops are composed of Lennard-Jones dimers and the particles are rigid spherical sections of a cubic lattice, with radii about 11 nm and 0.6 nm, respectively. Uniform suspensions of 21% and 42% particle concentrations and particle-coated drops are studied, and their behavior is compared to that of pure fluid drops of the same size. The relative velocities studied span the transition to splashing, and both wetting/miscible and non-wetting/immiscible cases are considered. Impacts normal to the surface and head-on collisions are studied and compared. In surface impact, the behavior of low-density suspensions and liquid marble drops is qualitatively similar to that of pure liquid, while the concentrated drops are solid-like on impact. Collisions produce a splash only at velocities significantly higher than in impact, but the resulting drop morphology shows a similar dependence on solid concentration as in impact. In all cases, the collision or impact produces a strong local enhancement in the kinetic energy density and temperature but not in the particle or potential energy densities. Mixing of the two colliding species is not enhanced by collisions, unless the velocity is so high as to cause drop disintegration.

Description: The flow development over a dual step cylinder is investigated numerically at a Reynolds number ( Re D ) of 150 for a range of aspect ratios, 0.2 ≤ L / D ≤ 5, and diameter ratios, 1.1 ≤ D / d ≤ 4. The results reveal the following four distinct types of wake topology downstream of the larger diameter cylinder: (i) shedding of hairpin vortices, (ii) transient asymmetric shedding, (iii) primarily spanwise shedding, and (iv) no vortex shedding. Dominant vortex interactions are reconstructed for each regime. These interactions, involving half-loop vortex connections, vortex merging, and direct vortex connections are shown to occur periodically as the large and small cylinder structures undergo vortex dislocations. Topological schematics are introduced to relate the characteristic frequencies to the periodic vortex interactions. The observed types of wake topology are shown to produce distinctly different mean and fluctuating forces on the dual step cylinder. For lower aspect and diameter ratios ( L / D ∼ 1 and D / d ∼ 1.5), a reduction in fluctuating lift of up to 80% can be achieved on the base cylinder with a minor reduction in mean drag (∼5%). The results indicate that similar performance improvements can be sustained by attaching multiple larger diameter cylinders to the base cylinder. The changes in the fluid forcing are shown to be related to the secondary flow produced by the downwash at the stepwise discontinuities. This process also involves the production of streamwise vorticity at the steps, which is shown to be associated with the deformation of the main spanwise vortical structures.

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 E k ∝   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.

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.

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.

Description: We study the flow of two immiscible, Newtonian fluids in a periodically constricted tube driven by a constant pressure gradient. Our volume-of-fluid algorithm is used to solve the governing equations. First, the code is validated by comparing its predictions to previously reported results for stratified and pulsing flow. Then, it is used to capture accurately all the significant topological changes that take place. Initially, the fluids have a core-annular arrangement, which is found to either remain the same or change to a different arrangement depending on the fluid properties, the pressure driving the flow, or the flow geometry. The flow-patterns that appear are the core-annular, segmented, churn, spray, and segregated flow. The predicted scalings near pinching of the core fluid concur with similarity predictions and earlier numerical results [I. Cohen et al. , “Two fluid drop snap-off problem: Experiments and theory,” Phys. Rev. Lett. 83 , 1147–1150 (1999)]. Flow-pattern maps are constructed in terms of the Reynolds and Weber numbers. Our result provides deeper insights into the mechanism of the pattern transitions and is in agreement with previous studies on core-annular flow [Ch. Kouris and J. Tsamopoulos, “Core-annular flow in a periodically constricted circular tube, I. Steady state, linear stability and energy analysis,” J. Fluid Mech. 432 , 31–68 (2001) and Ch. Kouris et al. , “Comparison of spectral and finite element methods applied to the study of interfacial instabilities of the core-annular flow in an undulating tube,” Int. J. Numer. Methods Fluids 39 (1), 41–73 (2002)], segmented flow [E. Lac and J. D. Sherwood, “Motion of a drop along the centreline of a capillary in a pressure-driven flow,” J. Fluid Mech. 640 , 27–54 (2009)], and churn flow [R. Y. Bai et al. , “Lubricated pipelining—Stability of core annular-flow. 5. Experiments and comparison with theory,” J. Fluid Mech. 240 , 97–132 (1992)].

Description: This work addresses the question of the stability of stratified, spatially periodic shear flows at low Péclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is often very small. Furthermore, it can be studied using a reduced set of “low-Péclet-number equations” proposed by Lignières [“The small-Péclet-number approximation in stellar radiative zones,” Astron. Astrophys. 348 , 933–939 (1999)]. Through a linear stability analysis, we first determine the conditions for instability to infinitesimal perturbations. We formally extend Squire’s theorem to the low-Péclet-number equations, which shows that the first unstable mode is always two-dimensional. We then perform an energy stability analysis of the low-Péclet-number equations and prove that for a given value of the Reynolds number, above a critical strength of the stratification, any smooth periodic shear flow is stable to perturbations of arbitrary amplitude. In that parameter regime, the flow can only be laminar and turbulent mixing does not take place. Finding that the conditions for linear and energy stability are different, we thus identify a region in parameter space where finite-amplitude instabilities could exist. Using direct numerical simulations, we indeed find that the system is subject to such finite-amplitude instabilities. We determine numerically how far into the linearly stable region of parameter space turbulence can be sustained.

Description: The Richtmyer-Meshkov instability (RMI) is investigated using the Direct Simulation Monte Carlo (DSMC) method of molecular gas dynamics. Due to the inherent statistical noise and the significant computational requirements, DSMC is hardly ever applied to hydrodynamic flows. Here, DSMC RMI simulations are performed to quantify the shock-driven growth of a single-mode perturbation on the interface between two atmospheric-pressure monatomic gases prior to re-shocking as a function of the Atwood and Mach numbers. The DSMC results qualitatively reproduce all features of the RMI and are in reasonable quantitative agreement with existing theoretical and empirical models. Consistent with previous work in this field, the DSMC simulations indicate that RMI growth follows a universal behavior.

Description: The increase of the thrust/weight ratio of aircraft engines is extremely restricted by different 3-D flow loss mechanisms. One of them is the corner separation that can form at the junction between a blade suction side and a hub or shroud. In this paper, in order to further investigate the turbulent characteristics of corner separation, large-eddy simulation (LES) is conducted on a compressor cascade configuration using NACA65 blade profiles (chord based Reynolds number: 3.82 × 10 5 ), in comparison with the previous obtained experimental data. Using the shear-improved Smagorinsky model as subgrid-scale model, the LES gives a good description of the mean aerodynamics of the corner separation, especially for the blade surface static pressure coefficient and the total pressure losses. The turbulent dynamics is then analyzed in detail, in consideration of the turbulent structures, the one-point velocity spectra, and the turbulence anisotropy. Within the recirculation region, the energy appears to concentrate around the largest turbulent eddies, with fairly isotropic characteristics. Concerning the dynamics, an aperiodic shedding of hairpin vortices seems to induce an unsteadiness of the separation envelope.

Description: An experimental investigation is conducted on the vortices induced by twin synthetic jets (SJs) in line with a laminar boundary layer flow over a flat plate. The twin SJs operating at four different phase differences, i.e., Δ ϕ = 0°, 90°, 180°, and 270°, are visualized using a stereoscopic color dye visualization system and measured using a two-dimensional particle image velocimetry (PIV) system. It is found that depending on the phase difference of twin SJs, three types of vortex structures are produced. At Δ ϕ = 90°, the two hairpin vortices interact in a very constructive way in terms of the vortex size, strength, and celerity, forming one combined vortex . At Δ ϕ = 270°, the two individual hairpin vortices do not have much interaction, forming two completely separated hairpin vortices that behave like doubling the frequency of the single SJ case. At Δ ϕ = 0° and 180°, the two hairpin vortices produced by the twin SJ actuators are close enough, with the head of one hairpin vortex coupled with the legs of the other, forming partially interacting vortex structures . Quantitative analysis of the twin SJs is conducted, including the time histories of vortex circulation in the mid-span plane as well as a selected spanwise-wall-normal plane, and the influence of the twin SJs on the boundary layer flow filed. In addition, dynamic mode decomposition analysis of the PIV data is conducted to extract representative coherent structures. Through this study, a better understanding in the vortex dynamics associated with the interaction of in-line twin SJs in laminar boundary layers is achieved, which provides useful information for future SJ-array applications.

Description: We consider a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. Its dynamics are governed by a coupled system of the steady Maxwell’s, the Navier-Stokes, and the continuity equations. The magnetization of the film is a function of the magnetic field and may be prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure and velocity fields inside the film. In addition, we investigate the problem in the limit of a large magnetic permeability. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape via use of the kinematic condition. The resultant one-dimensional equations are solved numerically using spectral methods. The magnetic effects give rise to a non-local contribution. We conduct a parametric study of both the linear and nonlinear stabilities of the system in order to evaluate the effects of the magnetic field. Through a linear stability analysis, we verify that the Maxwell’s pressure generated from a normally applied magnetic field is destabilizing and can be used to control the size and shape of lobes and collars on the free surface. We also find that in the case of a falling drop, the magnetic field causes an increase in the velocity and capillary ridge of the drop.

Description: In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52 , 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26 , 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self-similar solutions to the model and demonstrate that these types of solutions can model vortex kinks that gradually smooth and radiate Kelvin waves as time increases. Such solutions qualitatively agree with what one might expect from post-reconnection events.

Description: The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results. The study shows that previously proposed models underpredict the variance of frictional temperature fluctuations by a factor proportional to the square of the Taylor-scale Reynolds number.

Description: Direct numerical simulations of bubbly multiphase flows are used to find closure terms for a simple model of the average flow, using Neural Networks (NNs). The flow considered consists of several nearly spherical bubbles rising in a periodic domain where the initial vertical velocity and the average bubble density are homogeneous in two directions but non-uniform in one of the horizontal directions. After an initial transient motion the average void fraction and vertical velocity become approximately uniform. The NN is trained on a dataset from one simulation and then used to simulate the evolution of other initial conditions. Overall, the resulting model predicts the evolution of the various initial conditions reasonably well.

Description: A numerical simulation of the turbulent flow between coaxial permeable cylinders is performed for the case of the rotating inner cylinder and superimposed radial flow through the annular domain. Both forced inflow and outflow are considered in a wide range of the rotation rate and throughflow intensity. Two configurations of the rotating cylinder are examined with an entire permeable porous surface and with lengthwise porous slots. The stable rotational fluid motion is shown to be concentrated within a boundary layer close to the inner cylinder surface at strong enough imposed radial inflow. Under such conditions, the centrifugal stability boundary is independent on the gap width. Flow stabilization due to the forced inflow is possible at any rotation rate considered for both the configurations of the inner rotating cylinder. The stabilization by the forced outflow is feasible only in the case of the entire permeable rotating cylinder. But there are always large-scale vortices in the gap under conditions of the forced outflow through the slotted rotating cylinder except for the relatively low rotation rate. Transition to turbulence in the boundary layer at the inner rotating cylinder may occur before the centrifugal instability onset at large enough inflow intensity. The boundary layer thickness and turbulence intensity are influenced by the inflow rate and differ between the cases of the entire permeable cylinder and the slotted one.

Description: The friction factor for a fully developed pipe flow is examined at high Reynolds numbers up to Re D = 1.8 × 10 7 with high accuracy using the high Reynolds number actual flow facility “Hi-Reff” at AIST, NMIJ. The precise measurement of the friction factor is achieved by the highly accurate measurement of the flow rate, and the measurement uncertainty is estimated to be approximately 0.9% with a coverage factor of k = 2. The result examined here is obviously different from the Prandtl equation and the experimental results from the superpipe at Princeton University. The deviation of the present result from the Prandtl equation in the lower Reynolds number region is approximately 2.5% and −3% at the higher Reynolds number. For Re D 〈 2.0 × 10 5 , the present friction factor obtained here agrees very well with the results at the superpipe, but a deviation is observed for Re D 〉 2.0 × 10 5 , and it increases with the Reynolds number and reaches −6% at Re D = 1.0 × 10 7 . The Kármán constant estimated by the measured friction factor is 0.385. Using inner scale variables estimated by the present friction factor, the velocity profile measured by laser Doppler velocimetry in the same measurement configuration for the friction factor is normalized in order to observe the consistency of the Kármán constants between both the measurements. The Kármán constant estimated by the measured velocity profiles for Re D 〉 3.0 × 10 5 is 0.382.

Description: Two-dimensional, oblique detonations induced by a wedge are simulated using the reactive Euler equations with a detailed chemical reaction model. The focus of this study is on the oblique shock-to-detonation transition in a stoichiometric hydrogen-air mixture. A combustible, gas mixture at low pressure and high temperature, corresponding to the realistic, inflow conditions applied in oblique detonation wave engines, is presented in this study. At practical flight conditions, the present numerical results illustrate that oblique detonation initiation is achieved through a smooth transition from a curved shock, which differs from the abrupt transition depicted in the previous studies. The formation mechanism of this smooth transition is discussed and a quantitative analysis is carried out by defining a characteristic length for the initiation process. The dependence of the initiation length on different parameters including the wedge angle, flight Mach number, and inflow Mach number is discussed. Despite the hypothetical nature of the simulation configuration, the present numerical study uses parameters we deem relevant to practical conditions and provides important observations for which future investigations can benefit from in reaching toward a rigorous theory of the formation and self-sustenance of oblique detonation waves.

Description: Spreading of an initially spherical liquid drop over a textured surface is analyzed by solving an integral form of the governing equations. The mathematical model extends Navier-Stokes equations by including surface tension at the gas-liquid boundary and a force distribution at the three phase contact line. While interfacial tension scales with drop curvature, the motion of the contact line depends on the departure of instantaneous contact angle from its equilibrium value. The numerical solution is obtained by discretizing the spreading drop into disk elements. The Bond number range considered is 0.01–1. Results obtained for sessile drops are in conformity with limiting cases reported in the literature [J. C. Bird et al. , “Short-time dynamics of partial wetting,” Phys. Rev. Lett. 100 , 234501 (2008)]. They further reveal multiple time scales that are reported in experiments [K. G. Winkels et al. , “Initial spreading of low-viscosity drops on partially wetting surfaces,” Phys. Rev. E 85 , 055301 (2012) and A. Eddi et al. , “Short time dynamics of viscous drop spreading,” Phys. Fluids 25 , 013102 (2013)]. Spreading of water and glycerin drops over fully and partially wetting surfaces is studied in terms of excess pressure, wall shear stress, and the dimensions of the footprint. Contact line motion is seen to be correctly captured in the simulations. Water drops show oscillations during spreading while glycerin spreads uniformly over the surface.

Description: We demonstrate how the self-sustained oscillation of a confined jet in a thin cavity can be quantitatively described by a zero-dimensional model of the delay differential equation type with two a priori predicted model constants. This model describes the three phases in self-sustained oscillations: (i) pressure driven growth of the oscillation, (ii) amplitude limitation by geometry, and (iii) delayed destruction of the recirculation zone. The two parameters of the model are the growth rate of the jet angle by a pressure imbalance and the delay time for the destruction of this pressure imbalance. We present closed relations for both model constants as a function of the jet Reynolds number Re , the inlet velocity v in , the cavity width W , and the cavity width over inlet diameter W / d and we demonstrate that these model constants do not depend on other geometric ratios. The model and the obtained model constants have been successfully validated against three dimensional large eddy simulations, and planar particle image velocimetry measurements, for 1600 〈 Re ≤ 7100 and 20 ≤ W / d 〈 50. The presented model inherently contains the transition to a non-oscillating mode for decreasing Reynolds numbers or increasing W / d -ratios and allows for the quantitative prediction of the corresponding critical Reynolds number and critical W / d .

Description: In many important natural and industrial systems, gravity currents of dense fluid feed basins. Examples include lakes fed by dense rivers and auditoria supplied with cooled air by ventilation systems. As we will show, the entrainment into such buoyancy driven currents can be influenced by viscous forces. Little work, however, has examined this viscous influence and how entrainment varies with the Reynolds number, Re . Using the idea of an entrainment coefficient, E , we derive a mathematical expression for the rise of the front at the top of the dense fluid ponding in a basin, where the horizontal cross-sectional area of the basin varies linearly with depth. We compare this expression to experiments on gravity currents with source Reynolds numbers, Re s , covering the broad range 100 〈 Re s 〈 1500. The form of the observed frontal rises was well approximated by our theory. By fitting the observed frontal rises to the theoretical form with E as the free parameter, we find a linear trend for E ( Re s ) over the range 350 〈 Re s 〈 1100, which is in the transition to turbulent flow. In the experiments, the entrainment coefficient, E , varied from 4 × 10 −5 to 7 × 10 −2 . These observations show that viscous damping can be a dominant influence on gravity current entrainment in the laboratory and in geophysical flows in this transitional regime.

Description: A rich variety of flow regimes in a Newtonian fluid inside a vertical large-aspect ratio and a wide-gap Taylor-Couette system with a radial temperature gradient has been determined in experiments and in direct numerical simulations (DNSs). Compared to previous experiments and numerical studies, a wider range of temperature differences (i.e., of the Grashof number Gr ) and of the rotation rate (the Taylor number Ta ) has been covered. The combined effect of rotation and of the radial temperature gradient is the occurrence of helicoidal vortices or modulated waves at the onset. Stationary axisymmetric vortices are found for very weak temperature differences. A good agreement was found for critical states between results from experiments, linear stability analysis, and DNS. Higher instability modes have been determined for a wide range of parameters and a state diagram of observable flow regimes has been established in the plane spanned by Gr and Ta . Some higher states observed in experiments were retrieved in DNS.

Description: In this work, the influence of the initial geometry on the evolution of a fluid filament deposited on a substrate is studied, with a particular focus on the thin fluid strips of nano-scale thickness. Based on the analogy to the classical Rayleigh–Plateau (R–P) instability of a free-standing fluid jet, an estimate of the minimal distance between the final states (sessile droplets) can be obtained. However, this numerical study shows that while the prediction based on the R–P instability mechanism is highly accurate for an initial perturbation of a sinusoidal shape, it does not hold for a rectangular waveform perturbation. The numerical results are obtained by directly solving fully three-dimensional Navier–Stokes equations, based on a Volume of Fluid interface tracking method. The results show that (i) rectangular-wave perturbations can lead to the formation of patterns characterized by spatial scales that are much smaller than what is expected based on the R–P instability mechanism; (ii) the nonlinear stages of the evolution and end states are not simply related, with a given end state resulting from possibly very different types of evolution; and (iii) a variety of end state shapes may result from a simple initial geometry, including one- and two-dimensional arrays of droplets, a filament with side droplets, and a one-dimensional array of droplets with side filaments. Some features of the numerical results are related to the recent experimental study by Roberts et al . [“Directed assembly of one- and two-dimensional nanoparticle arrays from pulsed laser induced dewetting of square waveforms,” ACS Appl. Mater. Interfaces 5 , 4450 (2013)].

Description: In the present work, an optimization methodology to compute the best control parameters, χ and Δ, for the selective frequency damping method is presented. The optimization does not suppose any a priori knowledge of the flow physics, neither of the underlying numerical methods, and is especially suited for simulations requiring large quantity of grid elements and processors. It allows for obtaining an optimal convergence rate to a steady state of the damped Navier-Stokes system. This is achieved using the Dynamic Mode Decomposition, which is a snapshot-based method, to estimate the eigenvalues associated with global unstable dynamics. Validations test cases are presented for the numerical configurations of a laminar flow past a 2 D cylinder, a separated boundary-layer over a shallow bump, and a 3 D turbulent stratified-Poiseuille flow.

Description: Finite Reynolds number behaviors of the asymptotically logarithmic mean velocity profile in fully developed turbulent channel flow are investigated. The scaling patch method of Fife et al. [“Multiscaling in the presence of indeterminacy: Wall-induced turbulence,” Multiscale Model. Simul. 4 , 936 (2005)] is used to reveal invariance properties admitted by the appropriately simplified form of the mean momentum equation. These properties underlie the existence of a similarity solution to this equation over an interior inertial domain. The classical logarithmic mean velocity profile equation emerges from this similarity solution as the Reynolds number becomes large. Originally demonstrated via numerical integration, it is now shown that the solution to the governing nonlinear equation can be found by straight-forward analytical integration. The resulting solution contains both linear and logarithmic terms, but with the coefficient on the linear term decaying to zero as the Reynolds number tends to infinity. In this way, the universality of the classical logarithmic law comports with the existence of an invariant form of the mean momentum equation and is accordingly described by the present similarity solution. Existing numerical simulation data are used to elucidate Reynolds number dependent properties of the finite Reynolds number form of the similarity solution. Correspondences between these properties and those indicated by finite Reynolds number corrections to the classical overlap layer formulation for the mean velocity profile are described and discussed.

Description: Two different particle tracking velocimetry techniques are used to measure the fluid velocities close to the substrate in the vicinity of both receding and advancing contact lines. The slip velocity is found to be as much as 60% of the substrate speed near the contact line and persists as far as 10 μ m from the liquid-gas interface. The estimated slip length near the contact line singularity requires a measurement of the shear rate close the substrate which depends strongly on the spatial resolution of the measurement technique. The slip length is found to be approximately 5 μ m when flood illumination is used and approximately 500 nm when total internal reflection fluorescence illumination is used.

Description: Gas cavities trapped on structured hydrophobic surfaces play important roles in realizing functionalities such as superhydrophobicity, drag reduction, and surface cleaning. The morphology of the cavities exhibits strong dependence on system parameters which impact the performance of these surfaces. In this work, a complete theoretical analysis is presented to predict cavity morphological change under reduced liquid pressure, on a submerged hydrophobic surface patterned with cylindrical pores. Equilibrium solutions are derived for five different phases, namely, (I) pinned recession, (II) depinned recession, (III) Cassie-Baxter, (IV) expansion, and (V) coalescence; their stabilities are also analyzed. A phase map is developed outlining the different regimes with respect to the gas amount and liquid pressure. Importantly, phase (IV) exhibits a complex stability behavior that leads to two possible routes to coalescence, which lends two different mechanisms of cavitation. Accordingly, the threshold pressure for cavitation can be calculated. The theoretical model is supported by direct experimental measurements via confocal microscopy and demonstrates good quantitative accuracy. This work provides a predictive tool for the design of functional structured hydrophobic surfaces.

Description: Modulation of shock foot oscillation due to energy deposition by repetitive laser pulses in shock wave-boundary layer interaction over an axisymmetric nose-cylinder-flare model in Mach 1.92 flow was experimentally studied. From a series of 256 schlieren images, density oscillation spectra at each pixel were obtained. When laser pulses of approximately 7 mJ were deposited with a repetition frequency, f e , of 30 kHz or lower, the flare shock oscillation had a peak spectrum equivalent to the value of f e . However, with f e of 40 kHz–60 kHz, it experienced frequency modulation down to lower than 20 kHz.

Description: Large-eddy simulations have been conducted to investigate the mechanisms of separated-flow control using a dielectric barrier discharge plasma actuator at a low Reynolds number. In the present study, the mechanisms are classified according to the means of momentum injection to the boundary layer. The separated flow around the NACA 0015 airfoil at a Reynolds number of 63 000 is used as the base flow for separation control. Both normal and burst mode actuations are adopted in separation control. The burst frequency non-dimensionalized by the freestream velocity and the chord length ( F + ) is varied from 0.25 to 25, and we discuss the control mechanism through the comparison of the aerodynamic performance and controlled flow-fields in each normal and burst case. Lift and drag coefficients are significantly improved for the cases of F + = 1, 5, and 15 due to flow reattachment associated with a laminar-separation bubble. Frequency and linear stability analyses indicate that the F + = 5 and 15 cases effectively excite the natural unstable frequency at the separated shear layer, which is caused by the Kelvin-Helmholtz instability. This excitation results in earlier flow reattachment due to earlier turbulent transition. Furthermore, the Reynolds stress decomposition is conducted in order to identify the means of momentum entrainment resulted from large-scale spanwise vortical structure or small-scale turbulent vortices. For the cases with flow reattachment, the large-scale spanwise vortices, which shed from the separated shear layer through plasma actuation, significantly increase the periodic component of the Reynolds stress near the leading edge. These large-scale vortices collapse to small-scale turbulent vortices, and the turbulent component of the Reynolds stress increases around the large-scale vortices. In these cases, although the combination of momentum entrainment by both Reynolds stress components results in flow reattachment, the dominant component is identified as the turbulent component. This indicates that one of the effective control mechanisms for laminar separation is momentum entrainment by turbulent vortices through turbulent transition.

Description: We report the results of experimental and numerical studies of two-phase flow in a periodic, rectangular network of microfluidic channels. This geometry promotes the formation of anisotropic, dendrite-like structures during viscous fingering experiments. The dendrites then compete with each other for the available flow, which leads to the appearance of hierarchical growth pattern. Combining experiments and numerical simulations, we analyze different growth regimes in such a system, depending on the network geometry and fluid properties. For immiscible fluids, a high degree of screening is present which results in a power-law distribution of finger lengths. Contrastingly, for miscible fluids, strong lateral currents of displaced fluid lead to the detachment of the heads of the longest fingers from their roots, thus preventing their further growth.

Description: This work extends a one-dimensional continuum model for granular flows down inclined planes [C. H. Lee and C. J. Huang, “Kinetic-theory-based model of dense granular flows down inclined planes,” Phys. Fluids 24 , 073303 (2012)] to solve three-dimensional problems involving both static and flow states. The new model decomposes the shear stress and pressure into enduring-contact and kinetic components. One novelty of the present model is the determination of the enduring-contact component of pressure, which is a composition of a pressure depending only on the volume fraction and a pressure derived from the dilatancy law together with the equation of state from the kinetic theory. Another novelty of this study is a new numerical scheme that can avoid numerical instability caused by large volume fractions. To demonstrate its capability, the present model is applied to simulate the collapse of a granular column with various aspect ratios. The evolution of the column shape, the flow field, the final height, and the run-out predicted by the present model agree well with those provided by discrete element methods and experiments.

Description: We consider evaporation of an aqueous solution near an apparent contact line separating a macroscopically dry area of a heated solid substrate and a constant-curvature meniscus far away from the substrate. Viscous flow, described by a lubrication-type model, is coupled to the interaction of electrical double layers formed near the solid-liquid and liquid-vapor interfaces. The electrostatic interaction is described using the nonlinear Poisson-Boltzmann equation and is shown to affect both normal and shear stress balances at the deformable interface. For steady configurations, we find that the apparent contact line region becomes wider and the total evaporation rate there increases as the substrate potential is increased. Motion of the apparent contact line in response to changes in the substrate temperature is also investigated. The contact line speed is found to increase when the electrostatic effects are incorporated into the model.

Description: A detailed experimental study on the evolution of charged droplet formation and jet transition from a capillary is reported. By means of high-speed microscopy, special attention has been paid to the dynamics of the liquid thread and satellite droplets in the dripping mode, and a method for calculating the surface charge on the satellite droplet is proposed. Jet transition behavior based on the electric Bond number has been visualized, droplet sizes and velocities are measured to obtain the ejection characteristic of the spray plume, and the charge and hydrodynamic relaxation are linked to give explanations for ejection dynamics with different properties. The results show that the relative length is very sensitive to the hydrodynamic relaxation time. The magnitude of the electric field strength dominates the behavior of coalescence and noncoalescence, with the charge relationship between the satellite droplet and the main droplet being clear for every noncoalescence movement. Ejection mode transitions mainly depend on the magnitude of the electric Bond number, and the meniscus dynamics is determined by the ratio of the charge relaxation time to the hydrodynamic relaxation time.

Description: This article presents the results of experimental investigations of the process of transition from two-dimensional (2D) to three-dimensional (3D) waves in liquid films falling down a vertical plate. The method of laser induced fluorescence was used to obtain instant shapes of three dimensional waves and to investigate the regularities of formation of 3D wave patterns arising due to transverse instability of 2D waves. The obtained results were compared to the results from the published literature on the modeling of 3D wave regimes of film flow. Although many details of 3D wave patterns correspond well, there are a few significant distinctions between our experiments and modeling. In particular, during 2D-3D wave transition, we observed a strong transverse redistribution of liquid leading to the formation of rivulets on the surface of isothermal liquid film, which is a phenomenon not described previously. Possible discrepancies between modeling and experiments, including applicability of boundary layer models and downstream periodic boundary conditions, are discussed. The authors hope that the results presented in the article are of interest not only for modeling of film flows but also for practical applications because at large distances from the film inlet due to 2D-3D wave transition the local flow rates can differ several times at the transverse distances of about 1 cm, which is an effect that cannot be neglected.

Description: A round liquid jet impinging on a circular disc with free edge generates a thin liquid film in the center surrounded by a thick film. For low flow rates, the thick film is bounded by a stable rim around the disc edge and flows off only from one spot at the edge. The outer Froude number remains constant for varied flow rates and disc sizes but changes with the surface tension of the fluid. The jump radius increases linearly with the flow rate, and the linear slope varies with the surface tension. Due to the stable-rim edge condition, the constant outer Froude numbers observed in our study are different from the constant value reported by Duchesne et al. [“Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection,” Europhys. Lett. 107 , 54002 (2014)]. Despite the constant outer Froude numbers being independent of the flow rate, the inner Froude number changes with the flow rate, which is due to the surface tension force at the jump location. Force analysis is conducted by taking into account the stable rim, and the derived equations provide the relationship of jump radius with the contact angle of the stable rim, disc size, and jet flow. The maximum outer Froude number and the minimum inner Froude number are theoretically analyzed. Depending on the pre-jump velocity profile and the surface tension force at the jump, the maximum outer Froude number could be larger than unity. The shape of free surface at the jump is analyzed to evaluate the theoretical assumption of steep jump.

Description: Acoustically forced oscillation of spherical gas bubbles in a viscoelastic material is studied through comparisons between experiments and linear theory. An experimental setup has been designed to visualize bubble dynamics in gelatin gels using a high-speed camera. A spherical gas bubble is created by focusing an infrared laser pulse into (gas-supersaturated) gelatin gels. The bubble radius (up to 150 μ m) under mechanical equilibrium is controlled by gradual mass transfer of gases across the bubble interface. The linearized bubble dynamics are studied from the observation of spherical bubble oscillation driven by low-intensity, planar ultrasound driven at 28 kHz. It follows from the experiment for an isolated bubble that the frequency response in its volumetric oscillation was shifted to the high frequency side and its peak was suppressed as the gelatin concentration increases. The measurement is fitted to the linearized Rayleigh–Plesset equation coupled with the Voigt constitutive equation that models the behavior of linear viscoelastic solids; the fitting yields good agreement by tuning unknown values of the viscosity and rigidity, indicating that more complex phenomena including shear thinning, stress relaxation, and retardation do not play an important role for the small-amplitude oscillations. Moreover, the cases for bubble-bubble and bubble-wall systems are studied. The observed interaction effect on the linearized dynamics can be explained as well by a set of the Rayleigh–Plesset equations coupled through acoustic radiation among these systems. This suggests that this experimental setup can be applied to validate the model of bubble dynamics with more complex configuration such as a cloud of bubbles in viscoelastic materials.

Description: The direct molecular simulation (DMS) approach is used to predict the internal energy relaxation and dissociation dynamics of high-temperature nitrogen. An ab initio potential energy surface (PES) is used to calculate the dynamics of two interacting nitrogen molecules by providing forces between the four atoms. In the near-equilibrium limit, it is shown that DMS reproduces the results obtained from well-established quasiclassical trajectory (QCT) analysis, verifying the validity of the approach. DMS is used to predict the vibrational relaxation time constant for N 2 –N 2 collisions and its temperature dependence, which are in close agreement with existing experiments and theory. Using both QCT and DMS with the same PES, we find that dissociation significantly depletes the upper vibrational energy levels. As a result, across a wide temperature range, the dissociation rate is found to be approximately 4–5 times lower compared to the rates computed using QCT with Boltzmann energy distributions. DMS calculations predict a quasi-steady-state distribution of rotational and vibrational energies in which the rate of depletion of high-energy states due to dissociation is balanced by their rate of repopulation due to collisional processes. The DMS approach simulates the evolution of internal energy distributions and their coupling to dissociation without the need to precompute rates or cross sections for all possible energy transitions. These benchmark results could be used to develop new computational fluid dynamics models for high-enthalpy flow applications.

Description: We study the onset of magnetoconvection between two infinite horizontal planes subject to a vertical magnetic field aligned with background rotation. In order to gain insight into the convection taking place in the Earth’s tangent cylinder, we target regimes of asymptotically strong rotation. The critical Rayleigh number Ra c and critical wavenumber a c are computed numerically by solving the linear stability problem in a systematic way, with either stress-free or no-slip kinematic boundary conditions. A parametric study is conducted, varying the Ekman number E (ratio of viscous to Coriolis forces) and the Elsasser number Λ (ratio of the Lorentz force to the Coriolis force). E is varied from 10 −9 to 10 −2 and Λ from 10 −3 to 1. For a wide range of thermal and magnetic Prandtl numbers, our results verify and confirm previous experimental and theoretical results showing the existence of two distinct unstable modes at low values of E –one being controlled by the magnetic field, the other being controlled by viscosity (often called the viscous mode). It is shown that oscillatory onset does not occur in the range of parameters we are interested in. Asymptotic scalings for the onset of these modes are numerically confirmed and their domain of validity is precisely quantified. We show that with no-slip boundary conditions, the asymptotic behavior is reached for E 〈 10 −6 and establish a map in the ( E , Λ) plane. We distinguish regions where convection sets in either through the magnetic mode or through the viscous mode. Our analysis gives the regime in which the transition between magnetic and viscous modes may be observed. We also show that within the asymptotic regime, the role played by the kinematic boundary conditions is minimal.

Description: The centrifugal instability of stratified two-phase flow in a curved channel is investigated in this work. The fluids are laterally stratified between cylindrical walls of infinite extent. We focus on the limiting case of small capillary numbers (relatively high surface tension), wherein interfacial deformation and associated instabilities are suppressed. The centrifugal instability, caused by unstable gradients of angular momentum, destabilizes the axisymmetric azimuthal base flow. As in single phase Dean flow, an array of vortices is formed within each fluid at the critical Reynolds number. A numerical linear stability analysis is carried out using a recombined Chebyshev Galerkin spectral method, as well as a shooting method. Across the space of physical parameters (volume fractions, density, and viscosity ratios), six critical modes corresponding to distinct secondary flows are observed. These are classified into axisymmetric stationary vortices and rotating spiral vortices (travelling waves). Each category consists of three subtypes based on the relative vortex strength in the fluids: stronger in the outer fluid, stronger in the inner fluid, and comparable strength in both fluids. The critical mode switches amongst these six types as parameters are varied. The outer fluid is found to be more unstable than the inner fluid, even if the fluids have equal physical properties. This is explained using Rayleigh’s criterion for inviscid flows. Consequently, the arrangement of fluids has a significant impact on stability. Instability and vortex motion are promoted if the fluid with a higher density, a lower viscosity, and a larger volume fraction is placed on the outer side of the channel.

Description: A vortex close to a no-slip wall gives rise to the creation of new vorticity at the wall. This vorticity may organize itself into vortices that erupt from the separated boundary layer. We study how the eruption process in terms of the streamline topology is initiated and varies in dependence of the Reynolds number Re . We show that vortex structures are created in the boundary layer for Re around 600, but that these disappear again without eruption unless Re 〉 1000. The eruption process is topologically unaltered for Re up to 5000. Using bifurcation theory, we obtain a topological phase space for the eruption process, which can account for all observed changes in the Reynolds number range we consider. The bifurcation diagram complements previously analyzes such that the classification of topological bifurcations of flows close to no-slip walls with up to three parameters is now complete.

Description: We present a simple stochastic quadrant model for calculating the transport and deposition of heavy particles in a fully developed turbulent boundary layer based on the statistics of wall-normal fluid velocity fluctuations obtained from a fully developed channel flow. Individual particles are tracked through the boundary layer via their interactions with a succession of random eddies found in each of the quadrants of the fluid Reynolds shear stress domain in a homogeneous Markov chain process. In this way, we are able to account directly for the influence of ejection and sweeping events as others have done but without resorting to the use of adjustable parameters. Deposition rate predictions for a wide range of heavy particles predicted by the model compare well with benchmark experimental measurements. In addition, deposition rates are compared with those obtained from continuous random walk models and Langevin equation based ejection and sweep models which noticeably give significantly lower deposition rates. Various statistics related to the particle near wall behavior are also presented. Finally, we consider the model limitations in using the model to calculate deposition in more complex flows where the near wall turbulence may be significantly different.

Description: The objective of the paper is to study the effect of wall bending resistance on the motion of an initially spherical capsule freely suspended in shear flow. We consider a capsule with a given thickness made of a three-dimensional homogeneous elastic material. A numerical method is used to model the fluid-structure interactions coupling a boundary integral method for the fluids with a shell finite element method for the capsule envelope. For a given wall material, the capsule deformability strongly decreases when the wall bending resistance increases. But, if one expresses the same results as a function of the two-dimensional mechanical properties of the mid-surface, which is how the capsule wall is modeled in the thin-shell model, the capsule deformed shape is identical to the one predicted for a capsule devoid of bending resistance. The bending rigidity is found to have a negligible influence on the overall deformation of an initially spherical capsule, which therefore depends only on the elastic stretching of the mid-surface. Still, the bending resistance of the wall must be accounted for to model the buckling phenomenon, which is observed locally at low flow strength. We show that the wrinkle wavelength is only a function of the wall bending resistance and provide the correlation law. Such results can then be used to infer values of the bending modulus and wall thickness from experiments on spherical capsules in simple shear flow.

Description: Injection of anthropogenic carbon dioxide (CO 2 ) into geological formations is a promising approach to reduce greenhouse gas emissions into the atmosphere. Predicting the amount of CO 2 that can be captured and its long-term storage stability in subsurface requires a fundamental understanding of multiphase displacement phenomena at the pore scale. In this paper, the lattice Boltzmann method is employed to simulate the immiscible displacement of a wetting fluid by a non-wetting one in two microfluidic flow cells, one with a homogeneous pore network and the other with a randomly heterogeneous pore network. We have identified three different displacement patterns, namely, stable displacement, capillary fingering, and viscous fingering, all of which are strongly dependent upon the capillary number ( Ca ), viscosity ratio ( M ), and the media heterogeneity. The non-wetting fluid saturation ( S nw ) is found to increase nearly linearly with log Ca for each constant M . Increasing M (viscosity ratio of non-wetting fluid to wetting fluid) or decreasing the media heterogeneity can enhance the stability of the displacement process, resulting in an increase in S nw . In either pore networks, the specific interfacial length is linearly proportional to S nw during drainage with equal proportionality constant for all cases excluding those revealing considerable viscous fingering. Our numerical results confirm the previous experimental finding that the steady state specific interfacial length exhibits a linear dependence on S nw for either favorable ( M ≥ 1) or unfavorable ( M 〈 1) displacement, and the slope is slightly higher for the unfavorable displacement.

Description: Turbulence modulation by inertial-range-size, neutrally buoyant particles is investigated experimentally in a von Kármán flow. Increasing the particle volume fraction Φ v , maintaining constant impellers Reynolds number attenuates the fluid turbulence. The inertial-range energy transfer rate decreases as ∝ Φ v 2 / 3 , suggesting that only particles located on a surface affect the flow. Small-scale turbulent properties, such as structure functions or acceleration distribution, are unchanged. Finally, measurements hint at the existence of a transition between two different regimes occurring when the average distance between large particles is of the order of the thickness of their boundary layers.

Description: Experiments were performed to understand the complex fluid-structure interactions that occur during aircraft internal store carriage. A cylindrical store was installed in a rectangular cavity having a length-to-depth ratio of 3.33 and a length-to-width ratio of 1. The Mach number ranged from 0.6 to 2.5 and the incoming boundary layer was turbulent. Fast-response pressure measurements provided aeroacoustic loading in the cavity, while triaxial accelerometers provided simultaneous store response. Despite occupying only 6% of the cavity volume, the store significantly altered the cavity acoustics. The store responded to the cavity flow at its natural structural frequencies, and it exhibited a directionally dependent response to cavity resonance. Specifically, cavity tones excited the store in the streamwise and wall-normal directions consistently, whereas a spanwise response was observed only occasionally. The streamwise and wall-normal responses were attributed to the longitudinal pressure waves and shear layer vortices known to occur during cavity resonance. Although the spanwise response to cavity tones was limited, broadband pressure fluctuations resulted in significant spanwise accelerations at store natural frequencies. The largest vibrations occurred when a cavity tone matched a structural natural frequency, although energy was transferred more efficiently to natural frequencies having predominantly streamwise and wall-normal motions.

Description: Bow-shock instability has been experimentally observed in a low- γ flow. To clarify its mechanism, a parametric study was conducted with three-dimensional numerical simulations for specific heat ratio γ and Mach number M . A critical boundary of the instability was found in the γ - M parametric space. The bow shock tends to be unstable with low γ and high M , and the experimental demonstration was designed based on this result. The experiments were conducted with the ballistic range of the single-stage powder gun mode using HFC-134a of γ = 1.12 at Mach 9.6. Because the deformation of the shock front was observed in a shadowgraph image, the numerical prediction was validated to some extent. The theoretical estimation of vortex formation in a curved shock wave indicates that the generated vorticity is proportional to the density ratio across the shock front and that the critical density ratio can be predicted as ∼10. A strong slipstream from the surface edge generates noticeable acoustic waves because it can be deviated by the upstream flow. The acoustic waves emitted by synchronizing the vortex formation can propagate upstream and may trigger bow-shock instability. This effect should be emphasized in terms of unstable shock formation around an edged flat body.

Description: Lag-averaged Lagrangian statistics from direct numerical simulations over a range of Reynolds numbers are analyzed to test the predictions of the Lagrangian Refined Similarity Hypothesis (LRSH). The analysis uses the Lagrangian integral time scale to scale the lag since it is the natural time scale to reveal trends and scaling with Reynolds number. Both the velocity difference and the dissipation rate probability density functions (PDFs) collapse across inertial sub-range and diffusive scales for approximately the same values of the scaled lag, and in the zero lag limit are independent of the lag and depend only on the Reynolds number. These findings are consistent with the LRSH. The velocity difference PDFs are characterized by stretched exponential tails, while the dissipation rate PDFs for small lags have a log normal core with power law tails at both large and small values of the dissipation rate. The velocity structure functions show inertial sub-range similarity scaling with Reynolds number which extends to smaller scales with increasing Reynolds number. Estimates of the scaling exponents obtained are consistent with those from previous studies. They tend to saturate at a value of about two for high order moments. Non-dimensional acceleration moments show a striking power law dependence on Reynolds number from which novel estimates of the scaling exponents have been determined. Similarity scaling is much more elusive to demonstrate in the dissipation rate moments. The data are consistent with, but do not confirm, the Oboukhov relationship connecting velocity structure functions and dissipation rate moments on inertial sub-range scales.

Description: We study a self-propelling pair of steadily counter-rotating cylinders in simulations of a two-dimensional viscous fluid. We find two strikingly, opposite directions for the motion of the pair that is characterized by its width and rotational Reynolds number. At low Reynolds numbers and large widths, the cylinder pair moves similarly to an inviscid point vortex pair, while at higher Reynolds numbers and smaller widths, the pair moves in the opposite direction through a jet-like propulsion mechanism. Increasing further the Reynolds number, or decreasing the width, gives rise to non-polarised motion governed by the shedding direction and frequency of the boundary-layer vorticity. We discuss the fundamental physical mechanisms for these two types of motion and the transitions in the corresponding phase diagram. We discuss the fluid dynamics of each regime based on streamline plots, tracer particles, and the vorticity field. The counter rotating cylinder pair serves as a prototype for self-propelled bodies and suggests possible engineering devices composed of simple components and tunable by the rotation and width of the cylinder pair.

Description: Longitudinal libration corresponds to the periodic oscillation of a body’s rotation rate and is, along with precessional and tidal forcings, a possible source of mechanically-driven turbulence in the fluid interior of satellites and planets. In this study, we present a combination of direct numerical simulations and laboratory experiments, modeling this geophysically relevant mechanical forcing. We investigate the fluid motions inside a longitudinally librating ellipsoidal container filled with an incompressible fluid. The elliptical instability, which is a triadic resonance between two inertial modes and the oscillating base flow with elliptical streamlines, is observed both numerically and experimentally. The large-scale inertial modes eventually lead to small-scale turbulence, provided that the Ekman number is small enough. We characterize this transition to turbulence as additional triadic resonances develop while also investigating the properties of the turbulent flow that displays both intermittent and sustained regimes. These turbulent flows may play an important role in the thermal and magnetic evolution of bodies subject to mechanical forcing, which is not considered in standard models of convectively driven magnetic field generation.

Description: In the present experimental work, the behavior of laminar liquid jet in its own vapor as well as supercritical fluid environment is conducted. Also the study of liquid jet injection into nitrogen (N 2 ) environment is carried out at supercritical conditions. It is expected that the injected liquid jet would undergo thermodynamic transition to the chamber condition and this would alter the behavior of the injected jet. Moreover at such conditions there is a strong dependence between thermodynamic and fluid dynamic processes. Thus the thermodynamic transition has its effect on the initial instability as well as the breakup nature of the injected liquid jet. In the present study, the interfacial disturbance wavelength, breakup characteristics, and mixing behavior are analysed for the fluoroketone liquid jet that is injected into N 2 environment as well as into its own vapor at subcritical to supercritical conditions. It is observed that at subcritical chamber conditions, the injected liquid jet exhibits classical liquid jet characteristics with Rayleigh breakup at lower Weber number and Taylor breakup at higher Weber number for both N 2 and its own environment. At supercritical chamber conditions with its own environment, the injected liquid jet undergoes sudden thermodynamic transition to chamber conditions and single phase mixing characteristics is observed. However, the supercritical chamber conditions with N 2 as ambient fluid does not have significant effect on the thermodynamic transition of the injected liquid jet.

Description: The acoustic signature of an acoustically compact tandem airfoil setup in uniform high-Reynolds number flow is investigated. The upstream airfoil is considered rigid and is actuated at its leading edge with small-amplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortex-street excitation of the upstream airfoil. The non-linear near-field description is obtained via potential thin-airfoil theory. It is then applied as a source term into the Powell-Howe acoustic analogy to yield the far-field dipole radiation of the system. To assess the effect of downstream-airfoil elasticity, results are compared with counterpart calculations for a non-elastic setup, where the downstream airfoil is rigid and stationary. Depending on the separation distance between airfoils, airfoil-motion and airfoil-wake dynamics shift between in-phase (synchronized) and counter-phase behaviors. Consequently, downstream airfoil elasticity may act to amplify or suppress sound through the direct contribution of elastic-airfoil motion to the total signal. Resonance-type 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.

Description: Bubble size distributions in cloud cavitation are important in cavitating flows. In this study, a numerical model was developed to study the evolution of the internal structure of cloud cavitation. The model includes (1) an evolution equation of bubble number density, which considers the bubble breakup effect and (2) the multiphase Reynolds-averaged Navier–Stokes equations with a modified cavitation model for background cavitating flows. The proposed model was validated with a flow over a projectile. Results show that the numerical model can predict the evolution of the internal structure of cloud cavitation. Comparisons of the proposed model and Singhal model were discussed. The effects of re-entrant jet and bubble number density on cavitating flows were also investigated.

Description: This paper presents two key contributions; the first concerns the development of analytical expressions for the axial and transverse acoustic radiation forces exerted on a 2D rigid elliptical cylinder placed in the field of plane progressive, quasi-standing, or standing waves with arbitrary incidence. The second emphasis is on the acoustic radiation torque per length. The rigid elliptical cylinder case is important to be considered as a first-order approximation of the behavior of a cylindrical fluid column trapped in air because of the significant acoustic impedance mismatch at the particle boundary. Based on the rigorous partial-wave series expansion method in cylindrical coordinates, non-dimensional acoustic radiation force and torque functions are derived and defined in terms of the scattering coefficients of the elliptic cylinder. A coupled system of linear equations is obtained after applying the Neumann boundary condition for an immovable surface in a non-viscous fluid and solved numerically by matrix inversion after performing a single numerical integration procedure. Computational results for the non-dimensional force components and torque, showing the transition from the progressive to the (equi-amplitude) standing wave behavior, are performed with particular emphasis on the aspect ratio a / b , where a and b are the semi-axes of the ellipse, the dimensionless size parameter, as well as the angle of incidence ranging from end-on to broadside incidence. The results show that the elliptical geometry has a direct influence on the radiation force and torque, so that the standard theory for circular cylinders (at normal incidence) leads to significant miscalculations when the cylinder cross section becomes non-circular. Moreover, the elliptical cylinder experiences, in addition to the acoustic radiation force, a radiation torque that vanishes for the circular cylinder case. The application of the formalism presented here may be extended to other 2D surfaces of arbitrary shape, such as Chebyshev cylindrical particles with a small deformation, stadiums (with oval shape), or other non-circular geometries.

Description: A new variational method is proposed to calculate the evolution of liquid film and liquid droplet moving on a solid substrate. A simple time evolution equation is obtained for the contact angle of a liquid film that starts to move on a horizontal substrate. The equation indicates the dynamical transition at the receding side and the ridge formation at the advancing side. The same method is applied for the evolution of a droplet that starts to move on an inclined solid surface, and again the characteristic shape change of the droplet is obtained by solving a simple ordinary differential system. We will show that this method has a potential application to a wide class of problems of droplets moving on a substrate.

Description: The pressure-driven Stokes flow through a plane channel with arbitrary wall separation having a continuous pattern of sinusoidally varying slippage of arbitrary wavelength and amplitude on one/both walls is modelled semi-analytically. The patterning direction is transverse to the flow. In the special situations of thin and thick channels, respectively, the predictions of the model are found to be consistent with lubrication theory and results from the literature pertaining to free shear flow. For the same pattern-averaged slip length, the hydraulic permeability relative to a channel with no-slip walls increases as the pattern wave-number, amplitude, and channel size are decreased. Unlike discontinuous wall patterns of stick-slip zones studied elsewhere in the literature, the effective slip length of a sinusoidally patterned wall in a confined flow continues to scale with both channel size and the pattern-averaged slip length even in the limit of thin channel size to pattern wavelength ratio. As a consequence, for sufficiently small channel sizes, the permeability of a channel with sinusoidal wall slip patterns will always exceed that of an otherwise similar channel with discontinuous patterns on corresponding walls. For a channel with one no-slip wall and one patterned wall, the permeability relative to that of an unpatterned reference channel of same pattern-averaged slip length exhibits non-monotonic behaviour with channel size, with a minimum appearing at intermediate channel sizes. Approximate closed-form estimates for finding the location and size of this minimum are provided in the limit of large and small pattern wavelengths. For example, if the pattern wavelength is much larger than the channel thickness, exact results from lubrication theory indicate that a worst case permeability penalty relative to the reference channel of ∼23% arises when the average slip of the patterned wall is ∼2.7 times the channel size. The results from the current study should be applicable to microfluidic flows through channels with hydrophobized/super-hydrophobic surfaces.

Description: The rotation and an axial gradient of temperature drive the meridional circulation of a fluid filling a sealed cylindrical container. This numerical study explains why the flow remains stable up to the Grashof number Gr around 10 11 ; Gr characterizes the circulation strength. The shear-layer instability, occurring in a rotating pipe for small values of the Prandtl number Pr [M. A. Herrada and V. N. Shtern, “Stability of centrifugal convection in a rotating pipe,” Phys. Fluids 27 , 064106 (2015)], is suppressed here even for the cylinder length-to-radius ratio being ten. The cold end disk enhances the fluid circulation near the sidewall and diminishes it near the axis. The inflection point in the radial profile of axial velocity shifts to the sidewall vicinity where the stable centrifugal stratification and the no-slip condition prevent the disturbance growth. The cases Pr = 0, 0.015 (mercury), 0.7 (air), and 5.8 (water) are particularly analyzed. At Pr 〉 0, the stable density stratification develops and helps to suppress the disturbances. The obtained results are of fundamental interest and might be important for the development of efficient heat exchangers.

Description: This paper investigates the effects of surface roughness on nanoflows using molecular dynamics simulations. A fractal model is employed to model wall roughness, and simulations are performed for liquid argon confined by two solid walls. It is shown that the surface roughness reduces the velocity in the proximity of the walls with the reduction being accentuated when increasing the roughness depth and wettability of the solid wall. It also makes the flow three-dimensional and anisotropic. In flows over idealized smooth surfaces, the liquid forms parallel, well-spaced layers, with a significant gap between the first layer and the solid wall. Rough walls distort the orderly distribution of fluid layers resulting in an incoherent formation of irregularly shaped fluid structures around and within the wall cavities.

Description: The second-order non-Navier-Fourier constitutive laws, expressed in a compact algebraic mathematical form, were validated for the force-driven Poiseuille gas flow by the deterministic atomic-level microscopic molecular dynamics (MD). Emphasis is placed on how completely different methods (a second-order continuum macroscopic theory based on the kinetic Boltzmann equation, the probabilistic mesoscopic direct simulation Monte Carlo, and, in particular, the deterministic microscopic MD) describe the non-classical physics, and whether the second-order non-Navier-Fourier constitutive laws derived from the continuum theory can be validated using MD solutions for the viscous stress and heat flux calculated directly from the molecular data using the statistical method. Peculiar behaviors (non-uniform tangent pressure profile and exotic instantaneous heat conduction from cold to hot [R. S. Myong, “A full analytical solution for the force-driven compressible Poiseuille gas flow based on a nonlinear coupled constitutive relation,” Phys. Fluids 23 (1), 012002 (2011)]) were re-examined using atomic-level MD results. It was shown that all three results were in strong qualitative agreement with each other, implying that the second-order non-Navier-Fourier laws are indeed physically legitimate in the transition regime. Furthermore, it was shown that the non-Navier-Fourier constitutive laws are essential for describing non-zero normal stress and tangential heat flux, while the classical and non-classical laws remain similar for shear stress and normal heat flux.

Description: An exact solution is found for laminar fluid flow along the grooves of a family of surfaces whose shape is given by the Lambert W-function. This simple solution allows for the slip length in the direction parallel to the grooves to be calculated exactly. With this analytical model, we establish the regime of validity for a previously untested perturbation theory intended for calculating the surface mobility tensor of arbitrary periodic surfaces, finding that it compares well to the exact expression for nearly all choices of parameters of the conformal map. To test this perturbation theory further, the mobility tensor is evaluated for a simple sinusoidal surface for flow both parallel and perpendicular to the grooves, finding that the perturbation theory is less accurate in the latter of these two cases.

Description: This paper investigates the bubbling behaviors induced by gas-liquid mixture permeating through porous medium (PM), which was observed in developing immersion lithography system and was found having great differences with traditional bubbling behaviors injected with only gas phase through the PM. An experimental setup was built up to investigate the bubbling characteristics affected by the mixed liquid phase. Both the flow regimes of gas-liquid mixture in micro-channel (upstream of the PM) and the bubbling flow regimes in water tank (downstream of the PM) were recorded synchronously by high-speed camera. The transitions between the flow regimes are governed by gas and liquid Weber numbers. Based on the image analysis, the characteristic parameters of bubbling region, including the diameter of bubbling area on PM surface, gas-phase volume flux, and dispersion angle of bubbles in suspending liquid, were studied under different proportions of gas and liquid flow rate. Corresponding empirical correlations were developed to describe and predict these parameters. Then, the pertinent bubble characteristics in different bubbling flow regimes were systematically investigated. Specifically, the bubble size distribution and the Sauter mean diameter affected by increasing liquid flow rate were studied, and the corresponding analysis was given based on the hydrodynamics of bubble-bubble and bubble-liquid interactions. According to dimensionless analysis, the general prediction equation of Sauter mean diameter under different operating conditions was proposed and confirmed by experimental data. The study of this paper is helpful to improve the collection performance of immersion lithography and aims to reveal the differences between the bubbling behaviors on PM caused by only gas flow and gas-liquid mixture flow, respectively, for the researches of fluid flow.

Description: We discuss the behavior of partially wetting liquids on a rotating cylinder using a model that takes into account the effects of gravity, viscosity, rotation, surface tension, and wettability. Such a system can be considered as a prototype for many other systems where the interplay of spatial heterogeneity and a lateral driving force in the proximity of a first- or second-order phase transition results in intricate behavior. So does a partially wetting drop on a rotating cylinder undergo a depinning transition as the rotation speed is increased, whereas for ideally wetting liquids, the behavior only changes quantitatively. We analyze the bifurcations that occur when the rotation speed is increased for several values of the equilibrium contact angle of the partially wetting liquids. This allows us to discuss how the entire bifurcation structure and the flow behavior it encodes change with changing wettability. We employ various numerical continuation techniques that allow us to track stable/unstable steady and time-periodic film and drop thickness profiles. We support our findings by time-dependent numerical simulations and asymptotic analyses of steady and time-periodic profiles for large rotation numbers.

Description: A steady pseudo-plane ideal flow (PIF) model is derived from the 3D Euler equations under Boussinesq approximation. The model is solved analytically to yield high-degree polynomial exact solutions. Unlike quadratic flows, the cubic and quartic solutions display reduced geometry in the form of straightline jet, circular vortex, and multipolar strain field. The high-order circular-vortex solutions are vertically aligned and even the non-aligned multipolar strain-field solutions display vertical concentricity. Such geometry reduction is explained by an analytical theorem stating that only straightline jet and circular vortex have functional solutions to the PIF model.

Description: New transport equations for chemical reaction rate and its mean value in turbulent flows have been derived and analyzed. Local perturbations of the reaction zone by turbulent eddies are shown to play a pivotal role even for weakly turbulent flows. The mean-reaction-rate transport equation is shown to involve two unclosed dominant terms and a joint closure relation for the sum of these two terms is developed. Obtained analytical results and, in particular, the closure relation are supported by processing two widely recognized sets of data obtained from earlier direct numerical simulations of statistically planar 1D premixed flames associated with both weak large-scale and intense small-scale turbulence.

Description: In this work, the interfacial instability and transition of a two-fluid flow from a stratified state to large amplitude waves or slugs is considered. By combining an asymptotic approximation of the linear Orr-Sommerfeld analysis with nonlinear resonant wave interaction theory, a novel nonlinear slug-transition criterion is derived. This criterion corresponds to a bounding condition on the upper fluid’s velocity in order to limit the amount of energy (provided by the linear instability) which is transferred to long waves through resonant wave interactions. It is proposed that such a condition can predict the formation of large-amplitude long waves and/or slugs. Quantitative comparisons of the onset of slugging are made between the prediction by the nonlinear transition criterion and the experimental measurements carried out in a horizontal square channel. Good agreement is observed. An additional heuristic model is developed which generalizes the transition criterion to flow through horizontal pipes. Comparisons are made for flows through different pipe diameters and over a wide range of fluid properties. Good agreement between the present theoretical predictions and the experimental measurements is also observed.

Description: Cavities behind a surface irregularity appear in vortices drifting downstream of it. Cavitation can occur there substantially earlier than over smooth surfaces of the same bodies. Cavitation inception and desinence behind surface irregularities have been intensively studied in the course of water tunnel experiments several decades ago, but no corresponding quantitative theoretical (numerical) analysis was reported. This numerical study is aimed at elaboration of a general approach to the prediction of cavitation desinence numbers for various irregularities over various surfaces and on determination of the major factors influencing these numbers in both computations and experiments. The developed multi-level computational method employs diverse models for flow zones of diverse scale. The viscous-inviscid interaction approach is used for the flow around irregularities submerged (or partially submerged) in the turbulent boundary layer. Combinations of the semi-empirical and asymptotic analyses are used for vortices and cavities in their cores. The computational method is validated with various known experimental data.

Description: Experiments are conducted in a linear stratified fluid with a momentum source modeled via a nozzle jet moving horizontally. The generation mechanism of the quasi-two-dimensional dipolar vortex streets is investigated and their evolution characteristics are analyzed. Observation shows that the formation of a dipolar vortex street requires a nonzero motion of the nozzle in addition to conditions of the Reynolds and Froude number ( Re , Fr ). The ( Re , Fr ) condition that the dipolar vortex streets can be generated is determined via experimental measurements. The explanation for the absence of such a vortex street can be the low energy of the jet and the strong body-effect disturbance of the solid nozzle. The dependence of the vortex street dimensionless formation time τ and the Strouhal number St on the Froude number Fr or the Reynolds number Re is analyzed. This analysis shows that τ and St appear to be independent of Re and approximately have power-law relations with Fr via data fitting. The exponents of Fr in the two power-law functions are −0.27 for τ and −0.21 for St , while the constant coefficients are 65 and 0.21.

Description: A 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 pore-scale Navier-Stokes equations subject to the first-order wall slip boundary condition using the volume-averaging method. The local closure problem for the volume-averaged 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 converging-diverging 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.

Description: Pinch-off of axisymmetric vortex pairs generated by flow between concentric cylinders with radial separation Δ R was studied numerically and compared with planar vortex dipole behavior. The axisymmetric case approaches planar vortex dipole behavior in the limit of vanishing Δ R . The flow was simulated at a jet Reynolds number of 1000 (based on Δ R and the jet velocity), jet pulse length-to-gap ratio ( L Δ R ) in the range 10–20, and gap-to-outer radius ratio ( Δ R R o ) in the range 0.01-0.1. Contrary to investigations of strictly planar flows, vortex pinch-off 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 pinch-off observed in strictly planar vortex dipoles.

Description: We study the late time flow structure of Richtmyer-Meshkov instability. Recent numerical work [F. J. Cherne et al. “On shock driven jetting of liquid from non-sinusoidal surfaces into a vacuum,” J. Appl. Phys. 118 , 185901 (2015)] has suggested a self-similar collapse of the development of this instability at late times, independent of the initial surface profile. Using the form of collapse suggested, we derive an analytic expression for the mass-velocity relation in the spikes, and a global theory for the late time flow structure. We compare these results with fluid dynamical simulation.

Description: Computer simulations are performed to study translational motion and deformation of a liquid column or jet, in a plane perpendicular to its axis, due to a transverse electric field. A front tracking/finite difference scheme is used in conjunction with the Taylor-Melcher leaky dielectric theory to solve the governing equations. The column is confined within a rectangular channel, wall-bounded in the vertical direction and periodic in the horizontal direction. It is shown that perfect dielectric columns move toward electrode wall of shorter initial distance, but the leaky dielectric columns may move toward or away from it, depending on the relative importance of the ratios (drop fluid to suspending fluid) of their electric permittivity and conductivity. Furthermore, the degree of interface deformation might increase or decrease with the initial separation distance from the shorter electrode wall due to the same factor. Scaling arguments are used to discern the correlation between the translational velocity and the initial separation distance from the electrodes.

Description: A series of three-dimensional numerical simulations on thermal-solutal capillary-buoyancy flow in an annular pool were carried out. The pool was filled with silicon-germanium melt with an initial silicon mass fraction of 1.99%. The Prandtl number and the Lewis number of the working fluid are 6.37 × 10 −3 and 2197.8, respectively. Both the radial temperature gradient and the solute concentration gradient were applied to the annular pool. The capillary ratio was assumed to be −1, which means that the solutal and thermal capillary effects were equal and opposite. Results show that the thermal-solutal capillary-buoyancy flow always occurs at this special case with the capillary ratio of −1, and even in a shallow annular pool with an aspect ratio of 0.05. With the increase of the thermal Marangoni number, four kinds of flow patterns appear orderly, including concentric rolls, petal-like, spoke, and rosebud-like patterns. These flow patterns are strongly influenced by the local interaction between the solutal and thermal capillary effects and the vertical solute concentration gradient near the outer cylinder. A small vortex driven by the dominant solutal capillary effect emerges near the inner cylinder, which is different from the flow pattern in a pure fluid. In addition, the critical thermal Marangoni number of the initial three-dimensional flow decreases with the increase of the aspect ratio of the annular pool.

Description: In this paper we apply the short-wavelength perturbation method to derive instability criteria for the three-dimensional nonlinear Pollard geophysical waves. We show that these waves are linearly unstable when the wave steepness exceeds a certain threshold.

Description: Recent advances in numerical methods coupled with the substantial enhancements in computing power and the advent of high performance computing have presented first principle, high fidelity simulation as a viable tool in the prediction and analysis of spray atomization processes. The credibility and potential impact of such simulations, however, has been hampered by the relative absence of detailed validation against experimental evidence. The numerical stability and accuracy challenges arising from the need to simulate the high liquid-gas density ratio across the sharp interfaces encountered in these flows are key reasons for this. In this work we challenge this status quo by presenting a numerical model able to deal with these challenges, employing it in simulations of liquid jet in crossflow atomization and performing extensive validation of its results against a carefully executed experiment with detailed measurements in the atomization region. We then proceed to the detailed analysis of the flow physics. The computational model employs the coupled level set and volume of fluid approach to directly capture the spatiotemporal evolution of the liquid-gas interface and the sharp-interface ghost fluid method to stably handle high liquid-air density ratio. Adaptive mesh refinement and Lagrangian droplet models are shown to be viable options for computational cost reduction. Moreover, high performance computing is leveraged to manage the computational cost. The experiment selected for validation eliminates the impact of inlet liquid and gas turbulence and focuses on the impact of the crossflow aerodynamic forces on the atomization physics. Validation is demonstrated by comparing column surface wavelengths, deformation, breakup locations, column trajectories and droplet sizes, velocities, and mass rates for a range of intermediate Weber numbers. Analysis of the physics is performed in terms of the instability and breakup characteristics and the features of downstream flow recirculation, and vortex shedding. Formation of “Λ” shape windward column waves is observed and explained by the combined upward and lateral surface motion. The existence of Rayleigh-Taylor instability as the primary mechanism for the windward column waves is verified for this case by comparing wavelengths from the simulations to those predicted by linear stability analyses. Physical arguments are employed to postulate that the type of instability manifested may be related to conditions such as the gas Weber number and the inlet turbulence level. The decreased column wavelength with increasing Weber number is found to cause enhanced surface stripping and early depletion of liquid core at higher Weber number. A peculiar “three-streak-two-membrane” liquid structure is identified at the lowest Weber number and explained as the consequence of the symmetric recirculation zones behind the jet column. It is found that the vortical flow downstream of the liquid column resembles a von Karman vortex street and that the coupling between the gas flow and droplet transport is weak for the conditions explored.

Description: Linear stability of the stratified gas-liquid and liquid-liquid plane-parallel flows in the inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict the parameter regions in which the stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in the inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of the non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of the steady state solutions are presented on the flow pattern map and are accompanied by the critical wavenumbers and the spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by the streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of two stable stratified flow configurations in a region of low flow rates in the countercurrent liquid-liquid flows. These configurations become unstable with respect to the shear mode of instability. It was revealed that in slightly upward inclined flows the lower and middle solutions for the holdup are stable in the part of the triple solution region, while the upper solution is always unstable. In the case of downward flows, in the triple solution region, none of the solutions are stable with respect to the short-wave perturbations. These flows are stable only in the single solution region at low flow rates of the heavy phase, and the long-wave perturbations are the most unstable ones.