The onset of oscillatory Marangoni convection in a two-layer system of conducting fluid in the presence of a uniform magnetic field

A combination of numerical and analytical techniques is used to analyse the effect of magnetic field and encapsulated layer on the onset of oscillatory Marangoni instability in a two layer system. Oscillatory Marangoni instability is possible for a deformed free surface only when the system is heated from above. It is observed that the existence of a second layer has a positive effect on Marangoni overstability with magnetic field whereas it has an opposite effect without magnetic field.

Thermal instability in a three-dimensional rigid container with prescribed heat flux at lower boundary

The Bénard–Marangoni convection is studied in a three-dimensional container with thermally insulated lateral walls and prescribed heat flux at lower boundary. The upper surface of the incompressible, viscous fluid is assumed to be flat with temperature dependent surface tension. A Galerkin–Tau method with odd and even trial functions satisfying all the essential boundary conditions except the natural boundary conditions at the free surface has been used to solve the problem. The critical Marangoni and Rayleigh numbers are determined for the onset of steady convection as a function of aspect ratios x0 and y0 for the cases of Bénard–Marangoni, pure Marangoni and pure Bénard convections. It is observed that critical parameters are decreasing with an increase in aspect ratios. The flow structures corresponding to the values of the critical parameters are presented in all the cases. It is observed that the critical parameters are higher for case with heat flux prescribed than those corresponding to the case with prescribed temperature. The critical Marangoni number for pure Marangoni convection is higher than critical Rayleigh number corresponding to pure Bénard convection for a given aspect ratio whereas the reverse was observed for two-dimensional infinite layer.

Steady compressible flow of cohesionless granular materials through a wedge-shaped bunker

A continuum model based on the critical-state theory of soil mechanics is used to generate stress, density, and velocity profiles, and to compute discharge rates for the flow of granular material in a mass flow bunker. The bin–hopper transition region is idealized as a shock across which all the variables change discontinuously. Comparison with the work of Michalowski (1987) shows that his experimentally determined rupture layer lies between his prediction and that of the present theory. However, it resembles the former more closely. The conventional condition involving a traction-free surface at the hopper exit is abandoned in favour of an exit shock below which the material falls vertically with zero frictional stress. The basic equations, which are not classifiable under any of the standard types, require excessive computational time. This problem is alleviated by the introduction of the Mohr–Coulomb approximation (MCA). The stress, density, and velocity profiles obtained by integration of the MCA converge to asymptotic fields on moving down the hopper. Expressions for these fields are derived by a perturbation method. Computational difficulties are encountered for bunkers with wall angles θw [gt-or-equal, slanted] 15° these are overcome by altering the initial conditions. Predicted discharge rates lie significantly below the measured values of Nguyen et al. (1980), ranging from 38% at θw = 15° to 59% at θw = 32°. The poor prediction appears to be largely due to the exit condition used here. Paradoxically, incompressible discharge rates lie closer to the measured values. An approximate semi-analytical expression for the discharge rate is obtained, which predicts values within 9% of the exact (numerical) ones in the compressible case, and 11% in the incompressible case. The approximate analysis also suggests that inclusion of density variation decreases the discharge rate. This is borne out by the exact (numerical) results – for the parameter values investigated, the compressible discharge rate is about 10% lower than the incompressible value. A preliminary comparison of the predicted density profiles with the measurements of Fickie et al. (1989) shows that the material within the hopper dilates more strongly than predicted. Surprisingly, just below the exit slot, there is good agreement between theory and experiment.

Exciting forces due to interaction of water waves with a submerged sphere in an ice-covered two-layer fluid of finite depth

Scattering of water waves by a sphere in a two-layer fluid, where the upper layer has an ice-cover modelled as an elastic plate of very small thickness, while the lower one has a rigid horizontal bottom surface, is investigated within the framework of linearized water wave theory. The effects of surface tension at the surface of separation is neglected. There exist two modes of time-harmonic waves - the one with lower wave number propagating along the ice-cover and the one with higher wave number along the interface. Method of multipole expansions is used to find the particular solution for the problem of wave scattering by a submerged sphere placed in either of the layers. The exciting forces for vertical and horizontal directions are derived and plotted against different values of the wave number for different submersion depths of the sphere and flexural rigidity of the ice-cover. When the flexural rigidity and the density of the ice-cover are taken to be zero, the numerical results for the exciting forces for the problem with free surface are recovered as particular cases. (C) 2011 Elsevier Ltd. All rights reserved.

Anomalous Stress Profile in a Sheared Granular Column

We present measurements of the stress as a function of vertical position in a column of granular material sheared in a cylindrical Couette device. All three components of the stress tensor on the outer cylinder were measured as a function of distance from the free surface at shear rates low enough that the material was in the dense, slow flow regime. We find that the stress profile differs fundamentally from that of fluids, from the predictions of plasticity theories, and from intuitive expectation. We argue that the anomalous stress profile is due to an anisotropic fabric caused by the combined action of gravity and shear.

On the dynamic contact angle in simulation of impinging droplets with sharp interface methods

Effects of dynamic contact angle models on the flow dynamics of an impinging droplet in sharp interface simulations are presented in this article. In the considered finite element scheme, the free surface is tracked using the arbitrary Lagrangian-Eulerian approach. The contact angle is incorporated into the model by replacing the curvature with the Laplace-Beltrami operator and integration by parts. Further, the Navier-slip with friction boundary condition is used to avoid stress singularities at the contact line. Our study demonstrates that the contact angle models have almost no influence on the flow dynamics of the non-wetting droplets. In computations of the wetting and partially wetting droplets, different contact angle models induce different flow dynamics, especially during recoiling. It is shown that a large value for the slip number has to be used in computations of the wetting and partially wetting droplets in order to reduce the effects of the contact angle models. Among all models, the equilibrium model is simple and easy to implement. Further, the equilibrium model also incorporates the contact angle hysteresis. Thus, the equilibrium contact angle model is preferred in sharp interface numerical schemes.

Interaction between a notch and cylindrical voids in aluminum single crystals: Experimental observations and numerical simulations

A combined 3D finite element simulation and experimental study of interaction between a notch and cylindrical voids ahead of it in single edge notch (tension) aluminum single crystal specimens is undertaken in this work. Two lattice orientations are considered in which the notch front is parallel to the crystallographic 10 (1) over bar] direction. The flat surface of the notch coincides with the (010) plane in one orientation and with the (1 (1) over bar1) plane in the other. Three equally spaced cylindrical voids are placed directly ahead of the notch tip. The predicted load-displacement curves, slip traces, lattice rotation and void growth from the finite element analysis are found to be in good agreement with the experimental observations for both the orientations. Finite element results show considerable through-thickness variation in both hydrostatic stress and equivalent plastic slip which, however, depends additionally on the lattice orientation. The through-thickness variation in the above quantities affects the void growth rate and causes it to differ from the center-plane to the free surface of the specimen. (c) 2012 Elsevier Ltd. All rights reserved.

Studies on rheocasting using cooling slope

In the present work, a cooling channel is employed to produce semi-solid A356 alloy slurry. To understand the transport process involved, a 3D non-isothermal, multiphase volume averaging model has been developed for simulation of the semi-solid slurry generation process in the cooling channel. For simulation purpose, the three phases considered are the parent melt, the nearly spherical grains and air as separated but highly coupled interpenetrating continua. The conservation equations of mass, momentum, energy and species have been solved for each phase and the thermal and mechanical interactions (drag force) among the phases have been considered using appropriate model. The superheated liquid alloy is poured at the top of the cooling slope/channel, where specified velocity inlet boundary condition is used in the model, and allowed to flow along gravity through the channel. The melt loses its superheat and becomes semisolid up to the end of cooling channel due to the evolving -Al grains with decreasing temperature. The air phase forms a definable air/liquid melt interface, i.e. free surface, due its low density. The results obtained from the present model includes volume fractions of three different phases considered, grain evolution, grain growth rate, size and distribution of solid grains. The effect of key process variables such as pouring temperature, slope angle of the cooling channel and cooling channel wall temperature on temperature distribution, velocity distribution, grain formation and volume fraction of different phases are also studied. The results obtained from the simulations are validated by microstructure study using SEM and quantitative image analysis of the semi-solid slurry microstructure obtained from the experimental set-up.

Numerical modeling of the non-isothermal liquid droplet impact on a hot solid substrate

The heat transfer from a solid phase to an impinging non-isothermal liquid droplet is studied numerically. A new approach based on an arbitrary Lagrangian-Eulerian (ALE) finite element method for solving the incompressible Navier Stokes equations in the liquid and the energy equation within the solid and the liquid is presented. The novelty of the method consists in using the ALE-formulation also in the solid phase to guarantee matching grids along the liquid solid interface. Moreover, a new technique is developed to compute the heat flux without differentiating the numerical solution. The free surface and the liquid solid interface of the droplet are represented by a moving mesh which can handle jumps in the material parameter and a temperature dependent surface tension. Further, the application of the Laplace-Beltrami operator technique for the curvature approximation allows a natural inclusion of the contact angle. Numerical simulation for varying Reynold, Weber, Peclet and Biot numbers are performed to demonstrate the capabilities of the new approach. (C) 2014 Elsevier Ltd. All rights reserved.

Flux Transport Dynamos: From Kinematics to Dynamics

Over the past several decades, Flux-Transport Dynamo (FTD) models have emerged as a popular paradigm for explaining the cyclic nature of solar magnetic activity. Their defining characteristic is the key role played by the mean meridional circulation in transporting magnetic flux and thereby regulating the cycle period. Most FTD models also incorporate the so-called Babcock-Leighton (BL) mechanism in which the mean poloidal field is produced by the emergence and subsequent dispersal of bipolar active regions. This feature is well grounded in solar observations and provides a means for assimilating observed surface flows and fields into the models in order to forecast future solar activity, to identify model biases, and to clarify the underlying physical processes. Furthermore, interpreting historical sunspot records within the context of FTD models can potentially provide insight into why cycle features such as amplitude and duration vary and what causes extreme events such as Grand Minima. Though they are generally robust in a modeling sense and make good contact with observed cycle features, FTD models rely on input physics that is only partially constrained by observation and that neglects the subtleties of convective transport, convective field generation, and nonlinear feedbacks. Here we review the formulation and application of FTD models and assess our current understanding of the input physics based largely on complementary 3D MHD simulations of solar convection, dynamo action, and flux emergence.

Fracture behavior of magnesium alloys - Role of tensile twinning

In this work, Mode-I fracture experiments are conducted using notched compact tension specimens machined from a rolled AZ31 Mg alloy plate having near-basal texture with load applied along rolling direction (RD) and transverse direction (TD). Moderately high notched fracture toughness of J(C) similar to 46 N/mm is obtained in both RD and TD specimens. Fracture surface shows crack tunneling at specimen mid-thickness and extensive shear lips near the free surface. Dimples are observed from SEM fractographs suggesting ductile fracture. EBSD analysis shows profuse tensile twinning in the ligament ahead of the notch. It is shown that tensile twinning plays a dual role in enhancing the toughness in the notched fracture specimens with reduced triaxiality. It provides significant dissipation in the background plastic zone and imparts hardening to the material surrounding the fracture process zone via operation of several mechanisms which retards micro-void growth and coalescence. (C) 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

EFFECT OF PLUME DYNAMICS FOR HEAT TRANSFER ENHANCEMENT AT SOLID-LIQUID INTERFACE

The present paper analyzes the effects of plumes for heat transfer enhancement at solid-liquid interface taking both smooth and grooved surfaces. The experimental setup consists of a tank of dimensions 265 x 265 x 300 (height) containing water. The bottom surface was heated and free surface of the water was left open to the ambient. In the experiments, the bottom plate had either a smooth surface or a grooved surface. We used 90 V-grooved rough surfaces with two groove heights, 10mm and 3mm. The experiment was done with water layer depths of 90mm and 140mm, corresponding to values of aspect ratio(AR) equal to 2.9 and 1.8 respectively. Thymol blue, a pH sensitive dye, was used to visualize the flow near the heated plate. The measured heat transfer coefficients over the grooved surfaces were higher compared that over the smooth surface. The enhanced heat transport in the rough cavities cannot be ascribed to the increase in the contact area, rather it must be the local dynamics of the thermal boundary layer that changes the heat transport over the rough surface.

Kinematic flow patterns in slow deformation of a dense granular material

The kinematic flow pattern in slow deformation of a model dense granular medium is studied at high resolution using in situ imaging, coupled with particle tracking. The deformation configuration is indentation by a flat punch under macroscopic plane-strain conditions. Using a general analysis method, velocity gradients and deformation fields are obtained from the disordered grain arrangement, enabling flow characteristics to be quantified. The key observations are the formation of a stagnation zone, as in dilute granular flow past obstacles; occurrence of vortices in the flow immediately underneath the punch; and formation of distinct shear bands adjoining the stagnation zone. The transient and steady state stagnation zone geometry, as well as the strength of the vortices and strain rates in the shear bands, are obtained from the experimental data. All of these results are well-reproduced in exact-scale non-smooth contact dynamics simulations. Full 3D numerical particle positions from the simulations allow extraction of flow features that are extremely difficult to obtain from experiments. Three examples of these, namely material free surface evolution, deformation of a grain column below the punch and resolution of velocities inside the primary shear band, are highlighted. The variety of flow features observed in this model problem also illustrates the difficulty involved in formulating a complete micromechanical analytical description of the deformation.

Simulations of impinging droplets with surfactant-dependent dynamic contact angle

An arbitrary Lagrangian-Eulerian (ALE) finite element scheme for computations of soluble surfactant droplet impingement on a horizontal surface is presented. The numerical scheme solves the time-dependent Navier-Stokes equations for the fluid flow, scalar convection-diffusion equation for the surfactant transport in the bulk phase, and simultaneously, surface evolution equations for the surfactants on the free surface and on the liquid-solid interface. The effects of surfactants on the flow dynamics are included into the model through the surface tension and surfactant-dependent dynamic contact angle. In particular, the dynamic contact angle (theta(d)) of the droplet is defined as a function of the surfactant concentration at the contact line and the equilibrium contact angle (theta(0)(e)) of the clean surface using the nonlinear equation of state for surface tension. Further, the surface forces are included into the model as surface divergence of the surface stress tensor that allows to incorporate the Marangoni effects without calculating the surface gradient of the surfactant concentration on the free surface. In addition to a mesh convergence study and validation of the numerical results with experiments, the effects of adsorption and desorption surfactant coefficients on the flow dynamics in wetting, partially wetting and non-wetting droplets are studied in detail. It is observed that the effects of surfactants are more in wetting droplets than in the non-wetting droplets. Further, the presence of surfactants at the contact line reduces the equilibrium contact angle further when theta(0)(e) is less than 90 degrees, and increases it further when theta(0)(e) is greater than 90 degrees. Nevertheless, the presence of surfactants has no effect on the contact angle when theta(0)(e) = 90 degrees. The numerical study clearly demonstrates that the surfactant-dependent contact angle has to be considered, in addition to the Marangoni effect, in order to study the flow dynamics and the equilibrium states of surfactant droplet impingement accurately. The proposed numerical scheme guarantees the conservation of fluid mass and of the surfactant mass accurately. (C) 2015 Elsevier Inc. All rights reserved.

Investigation of Annealing Induced Yttria Segregation in Sputtered Yttria-Stabilized Zirconia Thin Films

8mol% yttria-stabilized zirconia (8YSZ) is an extensively studied solid electrolyte. But there is no consistency in the reported ionic conductivity values of 8YSZ thin films. Interfacial segregation in YSZ thin films can affect its ionic conductivity by locally altering the surface chemistry. This article presents the effects of annealing temperature and film thickness on free surface yttria segregation behavior in 8YSZ thin film by Angle Resolved XPS and its influence on the ionic conductivity of sputtered 8YSZ thin films. Surface yttria concentration of about 32, 20, and 9mol% have been found in 40nm 8YSZ films annealed at 1273, 1173, and 1073K, respectively. Yttria segregation is found to increase with increase in annealing temperature and film thickness. Ionic conductivities of 0.23, 0.16, and 0.08Scm(-1) are observed at 923K for 40nm 8YSZ films annealed at 1073, 1173, and 1273K, respectively. The decrease in conductivity with increase in annealing temperature is attributed to the increased yttria segregation with annealing. Neither segregation nor film thickness is found to affect the activation energy of oxygen ion conduction. Target purity is found to play a key role in determining free surface yttria segregation in 8YSZ thin films.