Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics最新文献

We investigate the filtration law in rigid porous media for steady-state slow flow of an electrically conducting, incompressible and viscous Newtonian fluid in the presence of magnetic field. The seepage law under magnetic field is obtained by upscaling the flow at the pore scale by using the method of multiple scale expansions. The macroscopic magnetic field and electric flux are also obtained. For finite Hartmann number, i.e. $\text{ε⪡Ha⪡ε}{}^{\mathrm{-1}}$ where $\text{ε}$ characterizes the separation of scale, the filtration law is shown to resemble a Darcy's law but with an additional term proportional to the electric field. The permeability tensor which strongly depends on the magnetic induction, i.e. Hartmann number, is symmetric, positive and verifies the filtration analog of the Hall effect. Mass and electric fluxes are coupled.

We consider a Stokes flow of a viscous incompressible fluid in a semi-infinite two-dimensional channel $\text{x>0}$, $\text{−1<y<1}$ with rigid walls $\text{y=±1}$ and a prescribed uniform normal velocity at the end $\text{x=0}$. Recently, Katopodes, Davis and Stone have used the biorthogonal eigenfunctions expansion to construct the solution of that syringe flow. It is an analytical solution, but details of the asymptotic behaviour of the coefficients in the complex series remain unclear. We construct the analytical solution by means of the method of superposition. This solution allows us both to analytically describe the local Goodier–Taylor scraper flow and to establish the asymptotic properties of the coefficients in the eigenfunctions expansions. Knowledge of these non-decaying coeffiicents is essential for a discussion of a pointwise convergence of the non-orthogonal complex series.

We show how Favre density-weighted filtering, used with a macro-temperature, simplifies considerably the formalism of large-eddy simulations in compressible turbulence. The method gives good results for a plane channel at Mach 0.3, and a transonic flow above a rectangular cavity. In both cases, the shedding of $\text{Λ}$-shaped coherent vortices is very well characterized thanks to positive iso-surfaces of $\text{Q}$, the velocity-gradient tensor second invariant.

In this Note we give a short review on recent developements in shape optimization. We explain how the generic non-existence of solutions can be circumvent. Either one can impose some geometric restrictions on the class of admissible domains to get existence (we then explain how to write the usual optimality conditions), or generalized designs are allowed which leads to relaxation by homogenization techniques (we thus obtain topology optimization methods).

This note presents a derivation of the appropriate inertial corrections to the Darcy law in a Hele–Shaw cell based on a perturbative method and a polynomial approximation to the velocity field. The obtained equation is optimal in the sense that every method of weighted residuals will converge to it as the number of test functions is increased. A good agreement with the study of the shear instability in a Hele–Shaw cell at low Reynolds number is found.

We determine by Fourier transform method, the effect of homogeneous initial stress in a 3D compressible elastic half-space on harmonic stresses superimposed by a surface force when the initial deformation is not finite. We then show that such an initial tension homogenizes amplitude fields to a small extent.

The model of generalized standard materials gives a convenient framework to extend Koiter's shakedown theorems into hardening plasticity. The extension of the static shakedown theorem (Melan–Koiter's theorem), proposed previously in [5], is considered here. It leads to the definition of safety coefficients in hardening plasticity by duality. Static and kinematic approaches are discussed for the models of isotropic hardening, of linear kinematic hardening (Ziegler–Prager's model) and of limited kinematic hardening. This discussion also leads to an extension of Koiter's kinematic shakedown theorem and to a second kinematic coefficient.

Two-phase flow modeling has been under constant development for the past forty years. Actually there exists a hierarchy of models which extends from the homogeneous model valid for two-phase flows where the phases are strongly coupled to the two-fluid model valid for two-phase flows where the phases are a priori weakly coupled. However the latter model has been used extensively in computer codes because of its potential in handling many different physical situations.

The two-fluid model is based on the balance equations for mass, momentum and energy, averaged in a certain sense and expressed for each phase and for the interface between the phases. The difficulty in using the two-fluid model stems from the closure relations needed to arrive at a complete set of partial differential equations describing the flow. These closure relations should supply the information lost during the averaging of the balance equations and should specify in particular the interactions of mass, momentum and energy between the phases. Another requirement for the interaction terms is that they should satisfy the interfacial balance equations. Some of these terms such as the added mass term or the lift force term do not depend on the interfacial area but some others do, such as the mass transfer term, the drag term or the heat flux term. It is then necessary to model the interfacial area in order to evaluate the corresponding fluxes. Another benefit resulting from the modeling of the interfacial area would be to replace the usual static flow pattern maps which specify the flow configuration by a dynamic follow-up of the flow pattern. All these reasons explain why so much effort has been put during the past twenty years on the modeling and measurement of the interfacial area in two-phase flows.

This article contains two parts. The first one deals with the conceptual issues and has the following objectives:

1.

to give precise definitions of the interfacial area concentrations;

2.

to explain the origin of the interfacial area concentration transport equation suggested by M. Ishii in 1975;

3.

to explain some paradoxical behaviors encountered when calculating the interfacial area concentration transport velocity.

We present an experimental and numerical study of convection driven by a central heat source in a vertical and cylindrical cavity with a higth aspect ration, filled by air and submitted to the action of non homogeneous intence magnetic field. We show how the magnetization force applying on oxygene is able to intensify, reduce, stop or even reverse the natural convection fluid flow.

We continue a previous work [1] on propagation of singularities for model problems of thin shell theory in the parabolic and hyperbolic cases. The singularities along the characteristic boundaries are considered using extensions of the solutions out of the domain, adapted to either free or fixed boundaries. The corresponding transport equations are given except for the case of a characteristic fixed boundary for a hyperbolic shell, where the phenomenon is non local, but depends on the whole domain.