Present Numerical Technique Research Articles

Subdivision elements for large deformation of liquid capsules enclosed by thin shells

This paper presents a numerical method for studying the large deformation of a liquid capsule enclosed by a thin shell in a simple shear flow. An implicit immersed boundary method is employed for calculating the hydrodynamics and fluid–structure interaction effects. A thin-shell model for computing the forces acting on the shell middle surface during the deformation is described within the framework of the Kirchhoff–Love theory of thin shells. This thin-shell model takes full account of finite-deformation kinematics which allows thickness stretching as well as large deflections and bending strains. The interpolation of the reference and deformed surfaces of the shell is accomplished through the use of Loop's subdivision surfaces. The resulting limit surface is C 1-continuous which significantly improves the ability of the method in simulating capsules enclosed by hyperelastic thin shells with different physical properties. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical, oblate spheroidal and biconcave capsules in the shear flow. In addition, different types of motion such as tank-treading, tumbling and transition from tumbling to tank-treading have been studied over a range of shear rates and viscosity ratios.

Large deformation of liquid capsules enclosed by thin shells immersed in the fluid

The deformation of a liquid capsule enclosed by a thin shell in a simple shear flow is studied numerically using an implicit immersed boundary method. We present a thin-shell model for computing the forces acting on the shell middle surface during the deformation within the framework of the Kirchhoff-Love theory of thin shells. This thin-shell model takes full account of finite-deformation kinematics which allows thickness stretching as well as large deflections and bending strains. For hyperelastic materials, the plane-stress assumption is used to compute the hydrostatic pressure and the incompressibility condition yields the thickness strain component and the corresponding change in the thickness. The stresses developing over the cross-section of the shell are integrated over the thickness to yield the stress and moment resultants which are then used to compute the forces acting on the shell middle surface. The immersed boundary method is employed for calculating the hydrodynamics and fluid-structure interaction effects. The location of the thin shell is updated implicitly using the Newton-Krylov method. The present numerical technique has been validated by several examples including an inflation of a spherical shell and deformations of spherical and oblate spheroidal capsules in the shear flow.

The coolest path problem

We introduce the coolest path problem, which is a mixture of two well-known problems from distinct mathematical fields. One of them is the shortest path problem from combinatorial optimization. The other is the heat conduction problem from the field of partial differential equations. Together, they make up a control problem, where some geometrical object traverses a digraph in an optimal way, with constraints on intermediate or the final state. We discuss some properties of the problem and present numerical solution techniques. We demonstrate that the problem can be formulated as a linear mixed-integer program. Numerical solutions can thus be achieved within one hour for instances with up to 70 nodes in the graph.

Present numerical technique for vehicle vibration and acoustic problem

Present numerical technique for vehicle vibration and acoustic problem

A new method for solution of viscous shock-layer equations

A new method is presented that considerably improves the computational efficiency of the viscous shock-layer technique. This approach can solve both subsonic and supersonic regions of the shock layer without a starting solution for the shock shape, and the global iterations are limited only to the nose region. In the nose region, the shock shape is specified from an algebraic expression and corrected through global passes through that region. The shock shape is computed as part of the solution beyond the nose region and requires only a single global pass. Under the high Reynolds number (at low altitudes), the Cebeci—Smith (CS) turbulent model has been analysed with the present numerical technique for application to long slender bodies. The surface-slip and the currently corrected shock-slip boundary conditions are employed to account for the low-density effects. The method of solution is a spatial-marching, implicit, finite-difference technique, which includes coupling of the normal momentum and continuity equations and uses a simple relation instead of Vigneron pressure condition in the subsonic nose region for instability. Comparisons are made with available experiment data and other solutions. The comparisons demonstrated that accurate solutions are obtained.

Finite volume meshless local Petrov–Galerkin method in elastodynamic problems

A finite volume meshless local Petrov–Galerkin (FVMLPG) method is presented for elastodynamic problems. It is derived from the local weak form of the equilibrium equations by using the finite volume (FV) and the meshless local Petrov–Galerkin (MLPG) concepts. By incorporating the moving least squares (MLS) approximations for trial functions, the local weak form is discretized, and is integrated over the local subdomain for the transient structural analysis. The present numerical technique imposes a correction to the accelerations, to enforce the kinematic boundary conditions in the MLS approximation, while using an explicit time-integration algorithm. Numerical examples for solving the transient response of the elastic structures are included. The results demonstrate the efficiency and accuracy of the present method for solving the elastodynamic problems.

Thermophoretic Deposition in a Cylindrical Tube: Computations and Comparison with Experiments

Thermophoresis causes particle deposition on nuclear reactor components from gas/vapor streams, both during normal and accident conditions, and it is of interest to develop good computational tools for estimation of such deposition. This paper describes a numerical technique to solve the coupled equations of energy and particle continuity. The numerical technique was verified by comparing the solution of the Graetz energy transport problem obtained by using the present numerical technique with the series solution. Thermophoretic deposition efficiency obtained from the present numerical technique agrees with the analytical solution for short tubes. Deposition efficiencies for the case RePr = 1 and Pr K = 1 are in good agreement with the published theoretical expressions for thermophoretic deposition efficiency. Also, the results from the numerical solution for thermophoretic deposition efficiency compare well with some experimental data published in the literature. Dependence of deposition efficiency η on thermophoretic coefficient K was studied, and it was observed that the dependence is more linear for smaller thermal gradients than for the larger gradients. Further, the computational fluid dynamics program FLUENT® 6.3 was also used to explore calculations of the thermophoretic deposition efficiencies for some cases, and it was noted that results are sensitive to mesh size and that very fine mesh near the surface was needed for accurate results. The results computed are in good agreement with our numerical calculations and experimental data.

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.

Creeping motion of a sphere along the axis of a closed axisymmetric container

The creeping flow around a sphere settling along the axis of a closed axisymmetric container is obtained both theoretically and experimentally. The numerical technique for solving the Stokes equations uses the classical Sampson expansion; the boundary conditions on the sphere are satisfied exactly and those on the container walls are applied in the sense of least squares. This is an extension to the axisymmetric case of the technique for solving various two-dimensional flow problems. Two types of axisymmetric container are considered here as examples: circular cylinders closed by planes at both ends, and cones closed by a base plane. Calculated streamlines patterns show various sets of eddies, depending upon the geometry and the sphere position. Results are in agreement with earlier Stokes flow calculations of eddies in corners and in closed containers. Experiments use laser interferometry to measure the vertical displacement of a steel bead a few millimetres in diameter settling in a container filled with a very viscous silicone oil. The Reynolds number based on the sphere radius is typically of the order of 10−5. The accuracy on the vertical displacement is 50nm. Experiments show that the motion towards the apex of a cone is much slower than that towards a plane; the bead takes hours to reach the micrometre size roughness asperities on a conical wall, as compared with minutes to reach those on a plane wall. The numerical results for the drag force are in excellent agreement with experiments both for the cylindrical and the conical containers. With standard computer accuracy, the present numerical technique applies when the gap between the sphere and the nearby wall is larger than about one radius. For a sphere in the vicinity of any plane horizontal wall, these results also match with a previous analytical solution. That solution is in excellent agreement with our experimental results at small distances from the wall (typically less than a diameter, depending on the sphere size).

Wave propagation and dynamic analysis of smoothly graded heterogeneous continua using graded finite elements

The dynamic behavior of smoothly graded heterogeneous materials is investigated using the finite element method. The global variation of material properties (e.g., Young’s modulus, Poisson’s ratio and mass density) is treated at the element level using a generalized isoparametric formulation. Three classes of examples are presented to illustrate this approach and to investigate the influence of material inhomogeneity on the characteristics of wave propagation pattern and stress redistribution. First, a cantilever beam example is presented for verification purposes. Emphasis is placed on the comparison of numerical results with analytical ones, as well as modal analysis for beams with different material gradation profiles. Second, wave propagation patterns are explored for a fixed-free slender bar considering homogeneous, bi-material, tri-layered and smoothly graded materials (steel/alumina), which also provide further verification of the numerical procedures. Comparison of stress histories in these samples indicates that the smooth transition of material gradation considerably alleviates the stress discontinuity in the bi-material system (with sharp interface). Third, a three-point-bending epoxy/glass graded beam specimen is investigated for validation purposes. The beam is graded along the height direction. Stress evolution history at a location of interest is analyzed in detail, which not only reveals the dependence of stress evolution on material gradation direction, but also provides information predictive of potential material failure time for graded beams with different material gradation profiles. Jointly, these three classes of examples provide proper verification and validation for the present numerical techniques.

Induced currents on vibrating perfect surfaces under the illumination of electromagnetic waves: One-dimensional simulation

One-dimensional numerical results of the induced currents on traveling and/or vibrating perfect conductor surfaces are presented in this report. The computational data are obtained using the method of characteristics with the application of the characteristic variable boundary conditions and the relativistic boundary conditions. The perfect plane may travel at a constant speed and/or vibrate sinusoidally or in zigzag with a constant frequency and a constant amplitude. The Doppler effects on both magnitude and frequency of induced currents were investigated by comparing computational results with the theoretical double-Doppler shift values. Good agreements were found. It is also found that when conductor travels and vibrates simultaneously, modulation on the magnitude of induced current is dependent on the combined instantaneous velocity while that on frequency is on the translational velocity. The scattering of electromagnetic waves from perfectly conducting objects in motion has been attracting significant attentions of many researchers since the 60s. This arouse from the need of knowledge for such as target identification. Kleinman and Mack (1), Cooper (2), and Harfoush et al. (3) developed analytical expressions for the electromagnetic wave scattering by either moving or vibrating bodies with the following conclusions. Object undergoing translational motion results in double-Doppler shifts in the reflected fields. An oscillating perfect electric conductor changes both phase and magnitude of the scattered fields. Though theoretical studies are available, the objective of the present effort is to develop an accurate numerical approach for electromagnetic scattering problems. The validation of the present numerical technique is carried out by the comparison of computational results with analytical values. Among variety of computational methods that provide numerical approximations to the solutions of the scattering of electromagnetic waves, the method of moment (MoM) and the finite-difference time-domain (FDTD) technique are the two most popular approaches. The method of characteristics is a recently developed numerical solver for like purpose. Whitfield and Janus applied the method of characteristics to solve fluid dynamic problems in the early 80s (4). By incorporating the explicit centered finite-difference scheme into the method of characteristics, Shang directly approximates the time-domain Maxwell curl equations (5) in the early 90s. In reference (6), the method of characteristics was formulated as an implicit numerical solver and found to have good agreement with the FDTD method. In contrast to the FDTD method where fields are allocated at node points, in the method of characteristics all field variables

Optimal design of preform geometry and tribological conditions in can forming

PurposeTo present numerical techniques and results of finite element based optimisation of material forming process for production of shaped food and beverage cans.Design/methodology/approachThe objectives were achieved by combining finite element system ELFEN with optimisation shell INVERSE. These computer systems were applied to optimisation of preform design, optimisation of tribological conditions between can body and individual segments of the tooling system as well as to optimisation of kinematics of the tooling segments.FindingsNumerical analyses show that preform design offers the highest optimisation potential. For preform shape optimisation a very efficient algorithm has been developed which enables effective minimisation of the objective function.Originality/valueThe paper identifies three main technological possibilities to optimise production process for shaped cans and quantifies the effects of each option. It also identifies the most efficient optimisation techniques to improve the investigated process.

2909 マイクロ流路内での生体高分子輸送過程の解析(OS-29B,OS-29 生体高分子の動力学シミュレーション)

We numerically investigate migration of biological polymers through a microchannel with periodically spaced electrodes. The numerical model is based on Brownian dynamics simulation of bead-spring chain. Electric potential inside the channel is determined by solving the linearized Poisson-Boltzrnann equation using the boundary element method. In this study, we mainly discuss mobility of biological polymers which would depend on the chain length of the model and on voltage of the electrodes. The present numerical technique would provide useful suggestions for future researches and basic design tools for practical μ-TAS devises.

Numerical method for calculating the apparent eddy current conductivity loss on randomly rough surfaces

Because of their frequency-dependent penetration depth, eddy current measurements are capable of mapping the near-surface depth profile of the electrical conductivity. This technique is used to nondestructively characterize the subsurface residual stress and cold work distributions in shot-peened metal components. Unfortunately, the spurious surface roughness produced by the shot peening process causes an apparent loss of eddy current conductivity, thereby decreasing the accuracy of the measurements, especially in thermally relaxed specimens where the primary material effects are significantly reduced. In this paper, a numerical method is introduced based on the Rayleigh approximation for calculating the apparent eddy current conductivity loss exhibited by 1D randomly rough surfaces. The relevant boundary conditions are satisfied using the so-called point-by-point technique, and the results are first compared to the previously developed Rayleigh–Fourier technique for a 1D sinusoidal corrugation. Pseudorandom surface profiles of different autocorrelation functions are considered. It is found that the Gaussian model lends itself the best to numerical simulations, but it significantly underestimates the apparent eddy current conductivity loss expected on real shot-peened surfaces, which exhibit essentially exponential correlation function. It is also demonstrated that the Lorentzian model is numerically less stable, but physically closer to the exponential one. The latter could not be simulated reliably by the present numerical technique because of its slowly decaying high-frequency spectral components.

Finite element solution of the Orr–Sommerfeld equation using high precision Hermite elements: plane Poiseuille flow

This paper presents a comprehensive review of the numerical techniques used during the past half century and their accuracy in hydrodynamic stability analysis of plane parallel flows. The paper also describes a finite element solution of the Orr–Sommerfeld equation using high precision Hermite elements. A stability analysis technique is performed by imposing an infinitesimal perturbation to the laminar base flow to determine the thresholds of neutral instabilities or the growth rate of the perturbation for any Reynolds and wave numbers. Validation of the present numerical technique is performed for plane Poiseuille flow. The numerical results, obtained with uniform and nonuniform meshes, show excellent agreement with the most accurate results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.

Intermodulation-borne fractional-N frequency synthesiser spurious components

Fractional-N frequency synthesisers have long been known to suffer from a set of spurious components, often referred to as ‘fractional spurs’. The authors propose an intermodulation mechanism that is responsible for the production of these components and present numerical and analytic techniques to predict their distribution. These predictions are validated against a range of simulated and measured results to determine the role of intermodulation in fractional-N frequency synthesisers. Finally, two techniques are suggested to allow at least partial mitigation of this effect.

The transverse tensile behavior of SiC-fiber/Ti–6Al–4V composites 2. Stress distribution and interface failure

The use of a cruciform specimen geometry has allowed the quantification of the applied stress where the interface debonds in single and multiple-fiber titanium-matrix composites under transverse tension. The applied debond stress, however, is not equal to the local interface stresses and is dependent on specimen geometry. In the present study, both analytical and numerical techniques were employed to determine the interface stresses for several fiber arrangements. For single-fiber tests, the specimen thickness was found to have little influence over the range modeled (250–550 μm). The presence of neighboring fibers was found to significantly alter the interfacial stress levels upon loading for a single-ply composite, but not for a multiple-ply arrangement, where only the residual stress level was influenced. The analyses were applied to experimental results to estimate the interface strength and to explain the applied debond loads measured for different fiber arrangements with the three SiC fibers studied in Part 1.

On analysis and optimization in structural acoustics ? Part I: Problem formulation and solution techniques

This paper is devoted to problems of structuralacoustic coupling with emphasis on analysis, design sensitivity analysis and optimization. The paper is divided into two parts, and it is the aim of Part I to (i) give a brief survey of recent developments in sensitivity analysis and sound emission and NVH (Noise, Vibration and Harshness) design of acoustically loaded structures, and (ii) discuss alternative objective functions and optimization formulations for structural acoustics. The aims of Part II are to (i) present consistent numerical techniques commonly used for treatment of coupled structural and acoustic dynamics, (ii) use the structural optimization tool ODESSY for solution of several coupled problems, and (iii) compare the numerical efficiency of alternative techniques and the relevance of selected objective functions.

On analysis and optimization in structural acoustics ? Part II: Exemplifications for axisymmetric structures

This two-part paper is devoted to problems of structural-acoustic coupling with emphasis on analysis, design sensitivity analysis and optimization. Part II of the paper aims to (i) present consistent numerical techniques commonly used for treatment of coupled structural and acoustic dynamics, (ii) use the structural optimization tool ODESSY for solution of several coupled problems, and (iii) compare the numerical efficiency of alternative techniques and the relevance of selected objective functions.

Three-dimensional arbitrary Lagrangian-Eulerian numerical prediction method for non-linear free surface oscillation

SUMMARY A numerical prediction method has been proposed to predict non-linear free surface oscillation in an arbitrarily-shaped three-dimensional container. The liquid motions are described with Navier‐Stokes equations rather than Laplace equations which are derived by assuming the velocity potential. The profile of a liquid surface is precisely represented with the three-dimensional curvilinear co-ordinates which are regenerated in each computational step on the basis of the arbitrary Lagrangian‐Eulerian (ALE) formulation. In the transformed space, the governing equations are discretized on a Lagrangian scheme with sufficient numerical accuracy and the boundary conditions near the liquid surface are implemented in a complete manner. In order to confirm the applicability of the present computational technique, numerical simulations are conducted for the free oscillations of viscid and inviscid liquids and for highly non-linear oscillation. In addition, non-linear sloshing motions caused by horizontal and vertical excitations and a transition from non-linear sloshing to swirling are numerically predicted in three-dimensional cylindrical containers. Conclusively, it is shown that these sloshing motions associated with high non-linearity are reasonably predicted with the present numerical technique. © 1998 John Wiley & Sons, Ltd.