An improved free surface modeling for incompressible SPH

In Incompressible Smooth Particle Hydrodynamics (ISPH), a pressure Poisson equation (PPE) is solved to obtain a divergence free velocity field. When free surfaces are simulated using this method a Dirichlet boundary condition for pressure at the free surface has to be applied. In existing ISPH methods this is achieved by identifying free surface particles using heuristically chosen threshold of a parameter such as kernel sum, density or divergence of the position, and explicitly setting their pressure values. This often leads to clumping of particles near the free surface and spraying off of surface particles during splashes. Moreover, surface pressure gradients in flows where surface tension is important are not captured well using this approach. We propose a more accurate semi-analytical approach to impose Dirichlet boundary conditions on the free surface. We show the efficacy of the proposed algorithm by using test cases of elongation of a droplet and dam break. We perform two dimensional simulations of water entry and validate the proposed algorithm with experimental results. Further, a three dimensional simulation of droplet splash is shown to compare well with the Volume-of-Fluid simulations. (C) 2014 Elsevier Ltd. All rights reserved.

Cross polarization in laser beams

Polarization properties of Gaussian laser beams are analyzed in a manner consistent with the Maxwell equations, and expressions are developed for all components of the electric and magnetic field vectors in the beam. It is shown that the transverse nature of the free electromagnetic field demands a nonzero transverse cross-polarization component in addition to the well-known component of the field vectors along the beam axis. The strength of these components in relation to the strength of the principal polarization component is established. It is further shown that the integrated strengths of these components over a transverse plane are invariants of the propagation process. It is suggested that cross- polarization measurement using a null detector can serve as a new method for accurate determination of the center of Gaussian laser beams.

Volume conservation issues in incompressible smoothed particle hydrodynamics

A divergence-free velocity field is usually sought in numerical simulations of incompressible fluids. We show that the particle methods that compute a divergence-free velocity field to achieve incompressibility suffer from a volume conservation issue when a finite time-step position update scheme is used. Further, we propose a deformation gradient based approach to arrive at a velocity field that reduces the volume conservation issues in free surface flows and maintains density uniformity in internal flows while retaining the simplicity of first order time updates. (C) 2015 Elsevier Inc. All rights reserved.

Flow And Heat-Transfer Over An Upstream Moving Wall With A Magnetic-Field And A Parallel Free Stream

The flow and heat transfer over an upstream moving non-isothermal wall with a parallel free stream have been considered. The magnetic field has been applied in the free stream parallel to the wall and the effect of induced magnetic field has been included in the analysis. The boundary layer equations governing the steady incompressible electrically conducting fluid flow have been solved numerically using a shooting method. This problem is interesting because a solution exists only when the ratio of the wall velocity does not exceed a certain critical value and this critical value depends on the magnetic field and magnetic Prandtl number. Also dual solutions exist for a certain range of wall velocity.

Nonaxisymmetric unsteady motion over a rotating disk in the presence of free convection and magnetic field

The nonaxisymmetric unsteady motion produced by a buoyancy-induced cross-flow of an electrically conducting fluid over an infinite rotating disk in a vertical plane and in the presence of an applied magnetic field normal to the disk has been studied. Both constant wall and constant heat flux conditions have been considered. It has been found that if the angular velocity of the disk and the applied magnetic field squared vary inversely as a linear function of time (i.e. as (1??t*)?1, the governing Navier-Stokes equation and the energy equation admit a locally self-similar solution. The resulting set of ordinary differential equations has been solved using a shooting method with a generalized Newton's correction procedure for guessed boundary conditions. It is observed that in a certain region near the disk the buoyancy induced cross-flow dominates the primary von Karman flow. The shear stresses induced by the cross-flow are found to be more than these of the primary flow and they increase with magnetic parameter or the parameter ? characterizing the unsteadiness. The velocity profiles in the x- and y-directions for the primary flow at any two values of the unsteady parameter ? cross each other towards the edge of the boundary layer. The heat transfer increases with the Prandtl number but reduces with the magnetic parameter.

Unsteady free convection flow under the influence of a magnetic field

The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, and x-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer and x-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer and x-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction and x-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.

MHD flow over a moving plate in a rotating fluid with magnetic field, Hall currents and free stream velocity

The non-similar boundary layer flow of a viscous incompressible electrically conducting fluid over a moving surface in a rotating fluid, in the presence of a magnetic field, Hall currents and the free stream velocity has been studied. The parabolic partial differential equations governing the flow are solved numerically using an implicit finite-difference scheme. The Coriolis force induces overshoot in the velocity profile of the primary flow and the magnetic field reduces/removes the velocity overshoot. The local skin friction coefficient for the primary flow increases with the magnetic field, but the skin friction coefficient for the secondary flow reduces it. Also the local skin friction coefficients for the primary and secondary flows are reduced due to the Hall currents. The effects of the magnetic field, Hall currents and the wall velocity, on the skin friction coefficients for the primary and secondary flows increase with the Coriolis force. The wall velocity strongly affects the flow field. When the wall velocity is equal to the free stream velocity, the skin friction coefficients for the primary and secondary flows vanish, but this does not imply separation. (C) 2002 Published by Elsevier Science Ltd.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Lead-free piezoelectric system (Na0.5Bi0.5)TiO3-BaTiO3: Equilibrium structures and irreversible structural transformations driven by electric field and mechanical impact

The structure-property correlation in the lead-free piezoelectric (1 - x)(Na0.5Bi0.5)TiO3-(x)BaTiO3 has been systematically investigated in detail as a function of composition (0 < x <= 0.11), temperature, electric field, and mechanical impact by Raman scattering, ferroelectric, piezoelectric measurement, x-ray, and neutron powder diffraction methods. Although x-ray diffraction study revealed three distinct composition ranges characterizing different structural features in the equilibrium state at room temperature: (i) monoclinic (Cc) + rhombohedral (R3c) for the precritical compositions, 0 <= x <= 0.05, (ii) cubiclike for 0.06 <= x <= 0.0675, and (iii) morphotropic phase boundary (MPB) like for 0.07 <= x < 0.10, Raman and neutron powder diffraction studies revealed identical symmetry for the cubiclike and the MPB compositions. The cubiclike structure undergoes irreversible phase separation by electric poling as well as by pure mechanical impact. This cubiclike phase exhibits relaxor ferroelectricity in its equilibrium state. The short coherence length (similar to 50A degrees) of the out-of-phase octahedral tilts does not allow the normal ferroelectric state to develop below the dipolar freezing temperature, forcing the system to remain in a dipolar glass state at room temperature. Electric poling helps the dipolar glass state to transform to a normal ferroelectric state with a concomitant enhancement in the correlation length of the out-of-phase octahedral tilt.

Enhanced electric field tunable magnetic properties of lead-free Na0.5Bi0.5TiO3-MnFe2O4 multiferroic composites

Strong magnetoelectric (ME) interaction was exhibited at both dc and microwave frequencies in a lead-free multiferroic particulate composites of Na0.5Bi0.5TiO3 (NBT) and MnFe2O4 (MFO) multiferroic, which were prepared by sol-gel route. The room temperature permeability measurements were carried out in the frequency range of 1 MHz-1 GHz. A systematic study of structural, magnetic and ME properties were undertaken. The room temperature ferromagnetic resonance (FMR) was studied. Strong ME coupling is demonstrated in 70NBT-30MFO composite by an electrostatically tunable FMR field shift up to 428 Oe (at E = 4 kV/cm), which increases to a large value of 640 Oe at E = 8 kV/cm. Furthermore, these lead-free multiferroic composites exhibiting electrostatically induced magnetic resonance field at microwave frequencies provide great opportunities for electric field tunable microwave devices.

Metastable monoclinic and orthorhombic phases and electric field induced irreversible phase transformation at room temperature in the lead-free classical ferroelectric BaTiO3

For decades it has been a well-known fact that among the few ferroelectric compounds in the perovskite family, namely, BaTiO3, KNbO3, PbTiO3, and Na1/2Bi1/2TiO3, the dielectric and piezoelectric properties of BaTiO3 are considerably higher than the others in polycrystalline form at room temperature. Further, similar to ferroelectric alloys exhibiting morphotropic phase boundary, single crystals of BaTiO3 exhibit anomalously large piezoelectric response when poled away from the direction of spontaneous polarization at room temperature. These anomalous features in BaTiO3 remained unexplained so far from the structural standpoint. In this work, we have used high-resolution synchrotron x-ray powder diffraction, atomic resolution aberration-corrected transmission electron microscopy, in conjunction with a powder poling technique, to reveal that at 300 K (i) the equilibrium state of BaTiO3 is characterized by coexistence of metastable monoclinic Pm and orthorhombic (Amm2) phases along with the tetragonal phase, and (ii) strong electric field switches the polarization direction from the 001] direction towards the 101] direction. These results suggest that BaTiO3 at room temperature is within an instability regime, and that this instability is the fundamental factor responsible for the anomalous dielectric and piezoelectric properties of BaTiO3 as compared to the other homologous ferroelectric perovskite compounds at room temperature. Pure BaTiO3 at room temperature is therefore more akin to lead-based ferroelectric alloys close to the morphotropic phase boundary where polarization rotation and field induced ferroelectric-ferroelectric phase transformations play a fundamental role in influencing the dielectric and piezoelectric behavior.

Electric field induced short range to long range structural ordering and its influence on the Eu+3 photoluminescence in the lead-free ferroelectric Na1/2Bi1/2TiO3

Eu+3 was incorporated into the lattice of a lead-free ferroelectric Na1/2Bi1/2TiO3 (NBT) as per the nominal formula Na0.5Bi0.5-xEuxTiO3. This system was investigated with regard to the Eu+3 photoluminescence (PL) and structural behaviour as a function of composition and electric field. Electric field was found to irreversibly change the features in the PL spectra and also in the x-ray diffraction patterns below the critical composition x = 0.025. Detailed analysis revealed that below the critical composition, electric field irreversibly suppresses the structural heterogeneity inherent of the host matrix NBT and brings about a long range ferroelectric state with rhombohedral (R3c) distortion. It is shown that the structural disorder on the nano-scale opens a new channel for radiative transition which manifests as a new emission line branching off from the main D-5(0)-> F-7(0) line along with a concomitant change in the relative intensity of the other crystal field induced Stark lines with different J values. The study suggests that Eu+3 luminescence can be used to probe the relative degree of field induced structural ordering in relaxor ferroelectrics and also in high performance piezoelectric alloys where electric field couples very strongly with the lattice and structural degrees of freedom. (C) 2015 AIP Publishing LLC.

Relaxor ferroelectricity and electric-field-driven structural transformation in the giant lead-free piezoelectric (Ba,Ca)(Ti, Zr)O-3

There is great interest in lead-free (Ba0.85Ca0.15)(Ti0.90Zr0.10)O-3 (15/10BCTZ) because of its exceptionally large piezoelectric response Liu and Ren, Phys. Rev. Lett. 103, 257602 (2009)]. In this paper, we have analyzed the nature of: (i) crystallographic phase coexistence at room temperature, (ii) temperature-and field-induced phase transformation to throw light on the atomistic mechanisms associated with the large piezoelectric response of this system. A detailed temperature-dependent dielectric and lattice thermal expansion study proved that the system exhibits a weak dielectric relaxation, characteristic of a relaxor ferroelectric material on the verge of exhibiting a normal ferroelectric-paraelectric transformation. Careful structural analysis revealed that a ferroelectric state at room temperature is composed of three phase coexistences, tetragonal (P4mm)+ orthorhombic (Amm2) + rhombohedral (R3m). We also demonstrate that the giant piezoresponse is associated with a significant fraction of the tetragonal phase transforming to rhombohedral. It is argued that the polar nanoregions associated with relaxor ferroelectricity amplify the piezoresponse by providing an additional degree of intrinsic structural inhomogeneity to the system.

Electric field and temperature dependence of the local structural disorder in the lead-free ferroelectric Na0.5Bi0.5TiO3: An EXAFS study

The complex nature of the structural disorder in the lead-free ferroelectric Na1/2Bi1/2TiO3 has a profound impact on the perceived global structure and polar properties. In this paper, we have investigated the effect of electric field and temperature on the local structure around theBi and Ti atoms using extended x-ray absorption fine structure. Detailed analysis revealed that poling brings about a noticeable change in the bond distances associated with the Bi-coordination sphere, whereas the Ti coordination remains unaffected. We also observed discontinuity in the Bi-O bond lengths across the depolarization temperature of the poled specimen. These results establish that the disappearance of the monoclinic-like (Cc) global distortion, along with the drastic suppression of the short-ranged in-phase octahedral tilt after poling B. N. Rao et al., Phys. Rev. B 88, 224103 (2013)] is a result of the readjustment of theA-O bonds by the electric field, so as to be in conformity with the rhombohedral R3c structure.