共查询到18条相似文献,搜索用时 10 毫秒
1.
We study the generation of periodic velocity and temperature fields in a plane horizontal crucible of molten metal under the action of a horizontal temperature gradient. The geometry and the boundary conditions are similar to those encountered in the Bridgman growth process of semiconductor crystals, although the present paper is limited to two-dimensional flows. We use transient finite difference and finite element algorithms which lead to identical results. We demonstrate the oscillatory mechanism in two different geometries. 相似文献
2.
We study the transient motion of the solidification front during the growth of semiconductor crystals in the horizontal Bridgman geometry. The calculation is based on a two-dimensional flow. We use finite elements which deform with the motion of the interface. The energy equation is coupled with the isothermal constraint of the interface in an implicit transient algorithm. Several examples show the oscillatory motion of the interface caused by the periodic flow of the melt, and they reveal the importance of the growth rate on the shape of the interface. 相似文献
3.
4.
The development and application of a non-linear 3D hydrodynamic model are described. The model is based on the wave equation rearrangement of the primitive 3D shallow water equations with a general eddy viscosity formulation for the vertical shear. A Galerkin procedure is used to discretize these on simple sixnode elements: linear triangles in the horizontal with linear variations in the vertical. Resolution of surface, bottom and interfacial boundary layers is facilitated and total flexibility is preserved for specifying spatial and temporal variations in the vertical viscosity and density fields. A semi-implicit time-stepping algorithm allows the solutions for elevation and velocity to be uncoupled during each time step. The elevation solution is essentially a 2D wave equation calculation with a stationary sparse matrix representing the gravity waves. With nodal quadrature the subsequent velocity calculation is achieved by factoring only a tridiagonal diffusion matrix representing the vertical viscous terms. As a result the overall calculation scales computationally as only a 2D problem but provides the full 3D solution. Application to field-scale problems is illustrated for the English Channel/Southern Bight system and the Lake Maracaibo system. 相似文献
5.
In this paper we present a new version of the ‘modified finite element method’ (MFEM) presented by Gresho, Chan, Lee and Upson.1 The main modification of the original algorithm is the introduction of a cost-effective and memory-saving iterative solver for the discretized Poisson equation for the pressure. The vectorization of the preconditioner has been especially considered. For low Prandtl number problems we also split the advection-diffusion operator of the energy equation into explicit and implicit parts. In that sense the present approach is related to the recent implicitization of the diffusive terms introduced by Gresho and Chan2 and by Gresho.3 The algorithm is applied to the study of buoyancy-driven flow oscillations occuring in a horizontal crucible of molten metal under the action of a horizontal temperature gradient. 相似文献
6.
P. F. C. Matsoukis 《国际流体数值方法杂志》1992,14(4):379-401
Certain free surface flows exhibit in nature negligible vertical accelerations and as a result the pressure within the fluid remains hydrostatic. The method of characteristics is developed as a solution technique for the integration of the partial differential equations describing this kind of flow. The equations are integrated over the depth to provide a two-dimensional model which is then tested and validated by comparing its results with tide-induced flows occurring in a number of cases where either analytical or observational data are available for comparison. On the basis of the results of the 2D model, a finite difference 3D model is developed which provides the values of the unknown velocities u, v and w along the three axes x, y and z. This combined 2D–3D model is verified by applying it in cases of wind-induced flow inside closed or open basins for which the classical Ekman solution may be used as a testing means. 相似文献
7.
Laminar natural convection has been studied in a laterally heated vertical cylindrical enclosure with a free insulated surface
and a centrally located constant temperature wall at the top. These conditions are a simplification of the conditions existing
in a Czochralski crystal pulling system. The laminar, axisymmetric flow of a Newtonian, constant physical properties fluid
under Boussinesq’s approximation has been considered. Governing equations in primitive variable form are solved numerically
by control volume method. SIMPLE algorithm due to Patankar has been used for the numerical simulation. The effects of the
constant wall heat flux boundary condition at the side wall have been investigated whereas the bottom wall is considered to
be insulated. Streamlines and isotherms are presented for various Rayleigh numbers and Prandtl numbers. Heat flux vectors
through the melt are plotted for selected cases. The axial velocity and temperature variations at different horizontal sections
of the crucible have been presented graphically to explain the transport processes inside the crucible. It has been observed
that in case of low Pr and high Ra, flow separation occurs at the vertical wall of the crucible which leads to an oscillatory flow as Ra increases. The investigation has been extended to the oscillatory regime of flow in the zone of supercritical Rayleigh numbers
and some unsteady results are also presented. Finally a heat transfer correlation has been developed for steady-state case. 相似文献
8.
We have investigated the effect of crosslink density on shear and elongational flow properties of alkali-swellable acrylic
thickener solutions using a mixing series of the two commercial thickeners Sterocoll FD and Sterocoll D as model system. Linear
viscoelastic moduli show a smooth transition from weakly elastic to gel-like behavior. Steady shear data are very well described
by a single mode Giesekus model at all mixing ratios. Extensional flow behavior has been characterized using the CaBER technique.
Corresponding decay of filament diameter is also well fitted by the Giesekus model, except for the highest crosslink densities,
when filament deformation is highly non-uniform, but the non-linearity parameter α, which is independent of the mixing ratio, is two orders of magnitude higher in shear compared to elongational flow. Shear
relaxation times increase by orders of magnitude, but the characteristic elongational relaxation time decreases weakly, as
gel content increases. Accordingly, variation of gel content is a valuable tool to adjust the low shear viscosity in a wide
range while keeping extensional flow resistance essentially constant. 相似文献
9.
Nikola Popović Dirk Praetorius Anja Schlömerkemper 《Continuum Mechanics and Thermodynamics》2007,19(1-2):81-109
The analysis of magnetoelastic phenomena is a field of active research. Formulae for the magnetic force in macroscopic systems
have been under discussion for some time. In Popović et al. (Continum. Mech. Thermodyn. 2007), we rigorously justify several
of the available formulae in the context of rigid bodies in two and three space dimensions. In the present, second part of
our study, we investigate these formulae in a series of numerical experiments in which the magnetic force is computed in dependence
on the geometries of the bodies as well as on the distance between them. In case the two bodies are in contact, i.e., in the
limit as their distance tends to zero, we focus especially on a formula obtained in a discrete-to-continuum approximation.
The aim of our study is to help clarify the question which force formula is the correct one in the sense that it describes
nature most accurately and to suggest adequate real-life experiments for a comparison with the provided numerical data.
相似文献
10.
Randi Moe 《国际流体数值方法杂志》1993,16(11):967-988
In this paper a new type of transient multidimensional two-fluid model has been applied to simulate intermittent or slug flow problems. Three different approaches to modelling interfacial friction, including an interfacial tracking scheme, have been investigated. The numerial method is based on an implicit finite difference scheme, solved directly in two steps applying a separate equation for the pressure. 2D predictions of Taylor bubble propagation in horizontal and inclined channels have been compared with experimental data and analytical solutions. The 2D model has also been applied to investigate a number of special phenomena in slug flow, including slug initiation, bubble turning in downflow and the bubble centring process at large liquid flow rates. 相似文献
11.
Giuseppe Alì Vidar Furuholt Roberto Natalini Isabella Torcicollo 《Transport in Porous Media》2007,69(2):175-188
We present a numerical investigation of a degenerate nonlinear parabolic–elliptic system, which describes the chemical aggression
of limestones under the attack of SO2, in high permeability regime. This system has been introduced in the first part of this paper. We present a finite element
scheme for our model and its numerical stability is given under suitable CFL conditions. Numerical tests are discussed as
well as some examples of the numerical behavior of the solutions. 相似文献
12.
We present the results of some numerical experiments which were carried out in order to investigate the general characteristics of the algorithm described in Part I of this paper. 相似文献
13.
Part I of this work addressed quasi-static loading of the shear compression specimen (SCS), which has been especially developed
to investigate the shear dominant response of materials at various strain rates. The stress and strain states were characterized
numerically. Approximations were presented to reduce the measured load,P, and displacement,d, into equivalent stress
and strain
. This paper addresses dynamic loading of the SCS. Several simulations were made for representative materials, whose stress-strain
behavior is assumed to be rate-independent. The results show that stress wave loading induces strong oscillations in theP-d curve. However, the
curve remains smooth in the gage section. The oscillations are about the quasistatic load values, so that with suitable filtering
of the dynamicP-d curves, the quasi-static ones are readily recovered. Consequently, the approach that was developed for quasi-static loading
of the SCS is now extended to dynamic loading situations. The average strain rate is rather constant and scales linearly with
the prescribed velocity. As the plastic modulus becomes smaller, the strain rate reaches higher values. Friction at the end
pieces of the specimen is also investigated, and shown to have a small overall influence on the determined mechanical characteristics.
This paper thereby confirms the potential of the SCS for large strain testing of materials, using a unified approach, over
a large range of strain rates in a seamless fashion. 相似文献
14.
Based on the microstructure-based constitutive model established in Part I, a detailed numerical investigation on the role
of each microstructure parameter in the kinematical and kinetic evolution of polycrystalline SMA under axisymmetrical tension
loading is performed. Some macroscopic constitutive features of stress-induced martensite transformation are discussed.
The subject supported by the Research Grant Committee (RGC) of Hong Kong SAR, the National Natural Science Foundation of China
and the Provincial Natural Science Foundation of Jiangxi Province of China 相似文献
15.
Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
16.
This paper gives the results of an application of the SWEs (shallow water equations) to a part of the Hamburg harbour area, which is a complex flow domain, using the BFG approach, outlined in Part I. The results of a grid doubling procedure generating the desired computational grid from a coarse initial mesh are also presented. A second class of problems which is addressed, demands time-dependent co-ordinate systems. The problems which are solved are the free surface problem for a moving wave which eventually breaks and for a wave which is reflected by the solid walls of a rectangular basin. 相似文献
17.
In the first part of this work (Bleyer and de Buhan, 2014), the determination of the macroscopic strength criterion of periodic thin plates has been addressed by means of the yield design homogenization theory and its associated numerical procedures. The present paper aims at using such numerically computed homogenized strength criteria in order to evaluate limit load estimates of global plate structures. The yield line method being a common kinematic approach for the yield design of plates, which enables to obtain upper bound estimates quite efficiently, it is first shown that its extension to the case of complex strength criteria as those calculated from the homogenization method, necessitates the computation of a function depending on one single parameter. A simple analytical example on a reinforced rectangular plate illustrates the simplicity of the method. The case of numerical yield line method being also rapidly mentioned, a more refined finite element-based upper bound approach is also proposed, taking dissipation through curvature as well as angular jumps into account. In this case, an approximation procedure is proposed to treat the curvature term, based upon an algorithm approximating the original macroscopic strength criterion by a convex hull of ellipsoids. Numerical examples are presented to assess the efficiency of the different methods. 相似文献
18.
This second part of the two-part study is devoted to the numerical Limit Analysis of a hollow sphere model with a Mohr–Coulomb matrix and its use for the assessment of theoretical results. Brief background and fundamental of the static and kinematic approaches in the context of numerical limit analysis are first recalled. We then present the hollow sphere model, together with its axisymmetric FEM discretization and its mechanical position. A conic programming adaptation of a previous iterative static approach, based on a piecewise linearization (PWL) of the plasticity criterion, was first realized. Unfortunately, the resulting code, no more than the PWL one, did not allow sufficiently refined meshes for loss of convergence of the conic optimizer. This problem was solved by using the projection algorithm of Ben Tal and Nemriovski (BTN) and the (interior point) linear programming code XA. For the kinematic approach, a first conic adaptation appeared also inefficient. Then, an original mixed (but fully kinematic) approach dedicated to the general Mohr–Coulomb axisymmetric problem was elaborated. The final conic mixed code appears much more robust than the classic one when using the conic code MOSEK, allowing us to take into account refined numerical meshes. After a fine validation in the case of spherical cavities and isotropic loadings (for which the exact solution is known) and comparison to previous (partial) results, numerical lower and upper bounds (a posteriori verified) of the macroscopic strength are provided. These bounds are used to assess and validate the theoretical results of the companion (part I) paper. Effects of the friction angle as well as that of the porosity are illustrated. 相似文献