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41.
We consider the problem of laminar mixed convection flow between parallel, vertical and uniformly heated plates where the governing dimensionless parameters are the Prandtl, Rayleigh and Reynolds numbers. Using the method based on the centre manifold theorem which was derived from the general theory of dynamical systems, we reduce a three-dimensional simplified model of ordinary differential amplitude equations emanating from the original Navier-Stokes system of the problem in the vicinity of a trivial stationary solution. We have found that when the forcing parameter, the Rayleigh number, increases beyond the critical value Ras, the stationary solution is a pitchfork bifurcation point of the system. 相似文献
42.
43.
In squeeze flow rheometry, the main problem is the boundary condition between the squeezed material and the plates. Therefore, the crucial assumption is to know the location and the shape of the sample part where wall slip may or may not occur. This question is investigated from experimental results. For this, squeeze flow experiments are carried out to visualize the flow pattern at the walls. Influence of boundary conditions is particularly studied using different plate surface condition. As a result, with wall slipping conditions, we propose a flow modelling divided into two zones: a circular central zone of the sample sticks on the plates and, beyond that zone, the sample slips at the plates with friction. 相似文献
44.
Gérard L. Vignoles Pierre Charrier Christophe Preux Bruno Dubroca 《Transport in Porous Media》2008,75(3):295-317
Viscous flow, effusion, and thermal transpiration are the main gas transport modalities for a rarefied gas in a macro-porous
medium. They have been well quantified only in the case of simple geometries. This paper presents a numerical method based
on the homogenization of kinetic equations producing effective transport properties (permeability, Knudsen diffusivity, thermal
transpiration ratio) in any porous medium sample, as described, e.g. by a digitized 3D image. The homogenization procedure—neglecting
the effect of gas density gradients on heat transfer through the solid—leads to closure problems in for the obtention of effective properties; they are then simplified using a Galerkin method based on a 21-element basis set.
The kinetic equations are then discretized in space with a finite- volume scheme. The method is validated against experimental data in the case of a closed test tube.
It shows to be coherent with past approaches of thermal transpiration. Then, it is applied to several 3D images of increasing
complexity. Another validation is brought by comparison with other distinct numerical approaches for the evaluation of the
Darcian permeability tensor and of the Knudsen diffusion tensor. Results show that thermal transpiration has to be described
by an effective transport tensor which is distinct from the other tensors. 相似文献
45.
Christophe Felder Constantin Oltean Mikhail Panfilov Michel Buès 《Comptes Rendus Mecanique》2004,332(3):223-229
The investigation of non-reactive miscible solute dispersion in a vertical Hele–Shaw cell is considered. An asymptotic method is used to extend Taylor model to the case of the fluid density, the dynamic viscosity and the molecular diffusion coefficient are solute concentration-dependent. It is demonstrated that the averaged variables over the gap are governed by a convection–dispersion equation in which the dispersion tensor is concentration-dependent. To cite this article: C. Felder et al., C. R. Mecanique 332 (2004). 相似文献
46.
Christophe Hazard 《Comptes Rendus Mecanique》2002,330(1):57-68
This paper sums up some recent studies related to the numerical solution of boundary value problems deriving from Maxwell's equations. These studies bring to light the theoretical origins of the ‘corner paradox’ pointed out by numerical experiments for years: In a domain surrounded by a perfect conductor, a ‘nodal’ discretization can approximate the electromagnetic field only if the domain has no reentrant corners or edges. The explanation lies in a mathematical curiosity: two different interpretations of the same variational equation, which are both well-posed and lead either to the physical or a spurious solution! Two strategies which were recently proposed to remedy this flaw of nodal elements are described. To cite this article: C. Hazard, C. R. Mecanique 330 (2002) 57–68 相似文献
47.
Non-linear systems are here tackled in a manner directly inherited from linear ones, that is, by using proper normal modes of motion. These are defined in terms of invariant manifolds in the system's phase space, on which the uncoupled system dynamics can be studied. Two different methodologies which were previously developed to derive the non-linear normal modes of continuous systems — one based on a purely continuous approach, and one based on a discretized approach to which the theory developed for discrete systems can be applied-are simultaneously applied to the same study case-an Euler-Bernoulli beam constrained by a non-linear spring-and compared as regards accuracy and reliability. Numerical simulations of pure non-linear modal motions are performed using these approaches, and compared to simulations of equations obtained by a classical projection onto the linear modes. The invariance properties of the non-linear normal modes are demonstrated, and it is also found that, for a pure non-linear modal motion, the invariant manifold approach achieves the same accuracy as that obtained using several linear normal modes, but with significantly reduced computational cost. This is mainly due to the possibility of obtaining high-order accuracy in the dynamics by solving only one non-linear ordinary differential equation. 相似文献
48.
This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists
in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered
that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that
the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force
required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point
between both sticking and slipping zones are finally determined. 相似文献
49.
Christophe?BrunEmail author Rainer?Friedrich Carlos?B.?da Silva 《Theoretical and Computational Fluid Dynamics》2006,20(1):1-21
A new subgrid scale (SGS) modelling concept for large-eddy simulation (LES) of incompressible flow is proposed based on the
three-dimensional spatial velocity increment δ u
i
. The new model is inspired by the structure function formulation developed by Métais and Lesieur [39] and applied in the context of the scale similarity type formulation. First, the similarity between the SGS stress tensor τ
ij
and the velocity increment tensor Q
ij
= δ u
i
δ u
j
is analyzed analytically and numerically using a priori tests of fully developed pipe flow at Re
τ = 180. Both forward and backward energy transfers between resolved and unresolved scales of the flow are well predicted with
a SGS model based on Q
ij
. Secondly, a posteriori tests are performed for two families of turbulent shear flows. LES of fully developed pipe flow up to Re
τ = 520 and LES of round turbulent jet at Re
D
= 25000 carried out with a dynamic version of the model provide promising results that confirm the power of this approach
for wall-bounded and free shear flows. 相似文献
50.
The present paper reports an experimental investigation on atomizing liquid flows produced by simplified cavity nozzles. The Weber number being kept low, the sprays produced by these injectors depend on the liquid flow characteristics only, and more precisely, on the non-axial kinetic energy and of the turbulent kinetic energy at the nozzle exit. The investigation reported here concentrates on the characterization of liquid flows during atomization by measuring the spatial variation of the local interface length and of the local interface fractal dimension. Both parameters were found representative of the physics of atomization process: they depend on the characteristics of the flow issuing from the nozzle and they are related to the subsequent drop size distribution. The local interface length is representative of the amount of liquid–gas interface surface area, and is a function of both the non-axial and the turbulent kinetic energies at the nozzle exit. The fractal dimension is representative of the tortuosity of the liquid–gas interface and, as expected, is mainly related to the turbulent kinetic energy at the nozzle exit. As far as the drop size distribution is concerned, it is found that the local interface length at the instant of break-up determines a representative drop diameter of some kind, whereas the fractal dimension at the same instant controls the dispersion of the distribution. 相似文献