An operator-splitting finite element method for the efficient parallel solution of multidimensional population balance systems

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space and internal property variables. In addition, the operator splitting allows to decouple the equations for temperature, solute partial density and particle size distribution. Further, a nodal point based parallel finite element algorithm for multi-dimensional population balance systems is presented. The method is applied to study a crystallization process assuming, for simplicity, a size independent growth rate and neglecting agglomeration and breakage of particles. Simulations for different wall temperatures are performed to show the effect of cooling on the crystal growth. Although the method is described in detail only for the case of d=2 space and s=1 internal property variables it has the potential to be extendable to d+s variables, d=2, 3 and s >= 1. (C) 2011 Elsevier Ltd. All rights reserved.

New nine-node Lagrangian quadrilateral plate element based on Mindlin-Reissner theory using IFM

This paper presents a new nine-node Lagrangian quadrilateral plate bending element (MQP9) using the Integrated Force Method (IFM) for the analysis of thin and moderately thick plate bending problems. Three degrees of freedom: transverse displacement w and two rotations theta(x) and theta(y) are considered at each node of the element. The Mindlin-Reissner theory has been employed in the formulation which accounts the effect of shear deformation. Many standard plate bending benchmark problems have been analyzed using the new element MQP9 for various grid sizes via Integrated Force Method to estimate defections and bending moments. These results of the new element MQP9 are compared with those of similar displacement-based plate bending elements available in the literature. The results are also compared with exact solutions. It is observed that the presented new element MQP9 is free from shear locking and produced, in general, excellent results in all plate bending benchmark problems considered.

Modeling of seepage flow through layered solis

A two-dimensional finite difference model, which solves mixed type of Richards' equation, whose non-linearity is dealt with modified Picard's iteration and strongly implicit procedure to solve the resulting equations, is presented. Modeling of seepage flow through heterogeneous soils, which is common in the field is addressed in the present study. The present model can be applied to both unsaturated and saturated soils and can handle very dry initial condition and steep wetting fronts. The model is validated by comparing experimental results reported in the literature. Newness of this two dimensional model is its application on layered soils with transient seepage face development, which has not been reported in the literature. Application of the two dimensional model for studying unconfined drainage due to sudden drop of water table at seepage face in layered soils is demonstrated. In the present work different sizes of rectangular flow domain with different types of layering are chosen. Sensitivity of seepage height due to problem dimension of layered system is studied. The effect of aspect ratio on seepage face development in case of the flow through layered soil media is demonstrated. The model is also applied to random heterogeneous soils in which the randomness of the model parameters is generated using the turning band technique. The results are discussed in terms of phreatic surface and seepage height development and also flux across the seepage face. Such accurate modeling of seepage face development and quantification of flux moving across the seepage face becomes important while modeling transport problems in variably saturated media.

Low temperature synthesis of layered NaxCoO2 and KxCoO2 from NaOH/KOH fluxes and their ion exchange properties

We report a low temperature synthesis of layered Na0×20CoO2 and K0×44CoO2 phases from NaOH and KOH fluxes at 400°C. These layered oxides are employed to prepare hexagonal HCoO2, LixCoO2 and Delafossite AgCoO2 phases by ion exchange method. The resulting oxides were characterised by powder X-ray diffraction, X-ray photoelectron spectroscopy, SEM and EDX analysis. Final compositions of all these oxides are obtained from chemical analysis of elements present. Na0×20CoO2 oxide exhibits insulating to metal like behaviour, whereas AgCoO2 is semiconducting.

Flow from T-spout ladles

The ladle constitutes a crucial element in the pouring system for developing process consistency and quality in the manufacture of castings. Flow of molten metal from T-spout ladles, with the spout projecting at an angle from the shell of the ladle, was investigated by simulation, modeling and analysis. This was followed by experimental validation for water flow in translucent models, and verification in a cast iron foundry. Key parameters in the design of a ladle (for its geometry) have been identified as the ladle size, spout diameter and its angle. Velocity and flow rate from a T-spout ladle are governed by and increase with increase in angle of tilt apart from the aforementioned design parameters. Cross section and profile of the issuing jet displaying a stable twisting pattern, during its free-fall of model fluid water and molten metal iron, are notable aspects in the design of the ladle, particularly the spout exit.

3D finite element modelling of a composite patch repair

Composite-patching on cracked/weak metallic aircraft structures improves structural integrity. A Boron Epoxy patch employed to repair a cracked Aluminum sheet is modeled employing 3D Finite Element Method (FEM). SIFs extracted using ''displacement extrapolation'' are used to measure the repair effectiveness. Two issues viz., patch taper and symmetry have been looked into.

A Revisit to Capture the Entire Behavior of Ultrasonic Wave Dispersion Characteristics of Single Walled Carbon Nanotubes Based on Nonlocal Elasticity Theory and Flugge Shell Model

In this paper, an ultrasonic wave propagation analysis in single-walled carbon nanotube (SWCNT) is re-studied using nonlocal elasticity theory, to capture the whole behaviour. The SWCNT is modeled using Flugge's shell theory, with the wall having axial, circumferential and radial degrees of freedom and also including small scale effects. Nonlocal governing equations for this system are derived and wave propagation analysis is also carried out. The revisited nonlocal elasticity calculation shows that the wavenumber tends to infinite at certain frequencies and the corresponding wave velocity tends to zero at those frequencies indicating localization and stationary behavior. This frequency is termed as escape frequency. This behavior is observed only for axial and radial waves in SWCNT. It has been shown that the circumferential waves will propagate dispersively at higher frequencies in nonlocality. The magnitudes of wave velocities of circumferential waves are smaller in nonlocal elasticity as compared to local elasticity. We also show that the explicit expressions of cut-off frequency depend on the nonlocal scaling parameter and the axial wavenumber. The effect of axial wavenumber on the ultrasonic wave behavior in SWCNTs is also discussed. The present results are compared with the corresponding results (for first mode) obtained from ab initio and 3-D elastodynamic continuum models. The acoustic phonon dispersion relation predicted by the present model is in good agreement with that obtained from literature. The results are new and can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

On an Integrated Transfer Matrix method for multiply connected mufflers

The commercial automotive mufflers are generally of a complicated shape with multiply connected parts and complex acoustic elements. The analysis of such complex mufflers has always been a great challenge. In this paper, an Integrated Transfer Matrix method has been developed to analyze complex mufflers. Integrated transfer matrix relates the state variables across the entire cross-section of the muffler shell, as one moves along the axis of the muffler, and can be partitioned appropriately in order to relate the state variables of different tubes constituting the cross-section. The paper presents a generalized one-dimensional (1-D) approach, using the transfer matrices of simple acoustic elements, which are available from the literature. The present approach is robust and flexible owing to its capability to construct an overall matrix of the muffler with the transfer matrices of individual acoustic elements and boundary conditions, which can then be used to evaluate the transmission loss, insertion loss, etc. Results from the present approach have been validated through comparisons with the available experimental and three-dimensional finite element method (FEM) based results. The results show good agreement with both measurements and FEM analysis up to the cut-off frequency. (C) 2011 Elsevier Ltd. All rights reserved.

Coupled Wavenumbers in an Infinite Flexible Fluid-Filled Circular Cylindrical Shell: Comparison between Different Shell Theories

Analytical expressions are found for the wavenumbers in an infinite flexible in vacuo I fluid-filled circular cylindrical shell based on different shell-theories using asymptotic methods. Donnell-Mushtari theory (the simplest shell theory) and four higher order theories, namely Love-Timoshenko, Goldenveizer-Novozhilov, Flugge and Kennard-simplified are considered. Initially, in vacuo and fluid-coupled wavenumber expressions are presented using the Donnell-Mushtari theory. Subsequently, the wavenumbers using the higher order theories are presented as perturbations on the Donnell-Mushtari wavenumbers. Similarly, expressions for the resonance frequencies in a finite shell are also presented, using each shell theory. The basic differences between the theories being what they are, the analytical expressions obtained from the five theories allow one to see how these differences propagate into the asymptotic expansions. Also, they help to quantify the difference between the theories for a wide range of parameter values such as the frequency range, circumferential order, thickness ratio of the shell, etc.

Spectral Element Approach to Wave Propagation in Uncertain Composite Beam Structures

This paper presents a study of the wave propagation responses in composite structures in an uncertain environment. Here, the main aim of the work is to quantify the effect of uncertainty in the wave propagation responses at high frequencies. The material properties are considered uncertain and the analysis is performed using Neumann expansion blended with Monte Carlo simulation under the environment of spectral finite element method. The material randomness is included in the conventional wave propagation analysis by different distributions (namely, the normal and the Weibul distribution) and their effect on wave propagation in a composite beam is analyzed. The numerical results presented investigates the effect of material uncertainties on different parameters, namely, wavenumber and group speed, which are relevant in the wave propagation analysis. The effect of the parameters, such as fiber orientation, lay-up sequence, number of layers, and the layer thickness on the uncertain responses due to dynamic impulse load, is thoroughly analyzed. Significant changes are observed in the high frequency responses with the variation in the above parameters, even for a small coefficient of variation. High frequency impact loads are applied and a number of interesting results are presented, which brings out the true effects of uncertainty in the high frequency responses. [DOI: 10.1115/1.4003945]

Enhanced efficiency of tri-layered dye solar cells with hydrothermally synthesized titania nanotubes as light scattering outer layer

In the present study dye sensitized solar cells (DSSCs) have been fabricated with a tri-layer photo anode consisting of hydrothermally prepared titania nano tubes (TNT) having a diameter of 9-10 nm and length of several micrometers as outer layer, P25 TiO2 powder as transparent light absorbing middle layer and a compact TiO2 inner layer to improve the adhesion of different layers on a transparent conducting oxide coated substrate. In comparison to cells fabricated using TNTs or P25 alone, the tri-layer DSSCs exhibit an enhanced efficiency of 7.15% with a current density of 17.12 mA cm(-2) under AM 1.5 illumination. The enhancement is attributed to the light scattering generated by TNTs aggregates, reduction in electron transport resistance at the TiO2/dye/electrolyte interface and an improvement in electron life-time. (c) 2012 Elsevier B.V. All rights reserved.

Characterization and finite element modeling of montmorillonite/polypropylene nanocomposites

Finite element modeling can be a useful tool for predicting the behavior of composite materials and arriving at desirable filler contents for maximizing mechanical performance. In the present study, to corroborate finite element analysis results, quantitative information on the effect of reinforcing polypropylene (PP) with various proportions of nanoclay (in the range of 3-9% by weight) is obtained through experiments; in particular, attention is paid to the Young's modulus, tensile strength and failure strain. Micromechanical finite element analysis combined with Monte Carlo simulation have been carried out to establish the validity of the modeling procedure and accuracy of prediction by comparing against experimentally determined stiffness moduli of nanocomposites. In the same context, predictions of Young's modulus yielded by theoretical micromechanics-based models are compared with experimental results. Macromechanical modeling was done to capture the non-linear stress-strain behavior including failure observed in experiments as this is deemed to be a more viable tool for analyzing products made of nanocomposites including applications of dynamics. (C) 2011 Elsevier Ltd. All rights reserved.

Time and Frequency Domain Finite Element Models for Axial Wave Analysis in Hyperelastic Rods

The propagation of axial waves in hyperelastic rods is studied using both time and frequency domain finite element models. The nonlinearity is introduced using the Murnaghan strain energy function and the equations governing the dynamics of the rod are derived assuming linear kinematics. In the time domain, the standard Galerkin finite element method, spectral element method, and Taylor-Galerkin finite element method are considered. A frequency domain formulation based on the Fourier spectral method is also developed. It is found that the time domain spectral element method provides the most efficient numerical tool for the problem considered.

Arbitrary Lagrangian-Eulerian finite-element method for computation of two-phase flows with soluble surfactants

A finite-element scheme based on a coupled arbitrary Lagrangian-Eulerian and Lagrangian approach is developed for the computation of interface flows with soluble surfactants. The numerical scheme is designed to solve the time-dependent Navier-Stokes equations and an evolution equation for the surfactant concentration in the bulk phase, and simultaneously, an evolution equation for the surfactant concentration on the interface. Second-order isoparametric finite elements on moving meshes and second-order isoparametric surface finite elements are used to solve these equations. The interface-resolved moving meshes allow the accurate incorporation of surface forces, Marangoni forces and jumps in the material parameters. The lower-dimensional finite-element meshes for solving the surface evolution equation are part of the interface-resolved moving meshes. The numerical scheme is validated for problems with known analytical solutions. A number of computations to study the influence of the surfactants in 3D-axisymmetric rising bubbles have been performed. The proposed scheme shows excellent conservation of fluid mass and of the total mass of the surfactant. (C) 2012 Elsevier Inc. All rights reserved.