Hydrodynamic Dispersion and Lamb Surfaces in Darcy Flow

Transport in Porous Media - Transport processes such as the dispersion and mixing of solutes are governed by the interplay of advection and diffusion, where advection acts to organise fluid...     

A parallel finite element sliding mesh technique for the simulation of viscous flows in agitated tanks

A parallel sliding mesh algorithm for the finite element simulation of viscous fluid flows in agitated tanks is presented. Lagrange multipliers are used at the sliding interfaces to enforce the continuity between the fixed and moving subdomains. The novelty of the method consists of the coupled solution of the resulting velocity–pressure‐Lagrange multipliers system of equations by an ILU(0)‐QMR solver. A penalty parameter is introduced for both the interface and the incompressibility constraints to avoid pivoting problems in the ILU(0) algorithm. To handle the convective term, both the Newton–Raphson scheme and the semi‐implicit linearization are tested. A penalty parameter is introduced for both the interface and the incompressibility constraints to avoid the failure of the ILU(0) algorithm due to the lack of pivoting. Furthermore, this approach is versatile enough so that it allows partitioning of sliding and fixed subdomains if parallelization is required. Although the sliding mesh technique is fairly common in CFD, the main advantage of the proposed approach is its low computational cost due to the inexpensive and parallelizable calculations that involve preconditioned sparse iterative solvers. The method is validated for Couette and coaxial stirred tanks. Copyright © 2011 John Wiley & Sons, Ltd.     

New silver tellurite glasses

The glass forming ranges in the TeO₂-AgO_0.5 and TeO₂-AgO_0.5-AgI systems have been assessed for two cooling rates; results based on heat capacity and electrical conductivity measurements as well as derived from infrared spectroscopy are presented. The ternary glasses are excellent conductors due to the presence of Ag⁺ ions mainly supplied by AgI. The decrease in C _P with increasing AgI-content suggests the presence of AgI microdomains which are finely distributed and do not contribute to the configurational heat capacity change. Fast motion of Ag⁺ ions (low activation energy) occurs in the glassy matrix which shows slow structural relaxation (high activation barrier).This research is performed within the frame of a P.I.R.M.A.T. action of the CNRS.     

Non-linear viscoelastic behavior of fumed silica suspensions

Suspensions of fumed silica exhibit a wide range of rheological properties depending on the nature and magnitude of the interparticle forces. In a non-polar fluid, the particles interact through hydrogen bonding and can form a three-dimensional network. The microstructure formation is responsible for the non-linear viscoelastic behavior of fumed silica suspensions, even at very small strain. These non-linear rheological properties have been studied in small amplitude oscillatory experiments as a function of particle size, surface treatment of particles, suspending medium polarity and solids concentration. The non-linear viscoelastic behavior is characterized by a non-sinusoidal waveform of the signal response. For suspensions in a non-polar fluid, both the elastic and the loss moduli are shown to be sensitive to the strain amplitude: the elastic modulus is decreasing with increasing strain whereas the loss moduli is initially increasing with strain. We have chosen to examine the dissipated energy which is clearly related to the breakup of the suspension structure. A comparison of model predictions and the experimental data shows the limitations of these models, recently proposed in the literature to describe the behavior of colloidal suspensions. Received: 9 March 1998 Accepted: 17 November 1998     

A two‐phase flow interface capturing finite element method

A new interface capturing algorithm is proposed for the finite element simulation of two‐phase flows. It relies on the solution of an advection equation for the interface between the two phases by a streamline upwind Petrov–Galerkin (SUPG) scheme combined with an adaptive mesh refinement procedure and a filtering technique. This method is illustrated in the case of a Rayleigh–Taylor two‐phase flow problem governed by the Stokes equations. Copyright © 2006 John Wiley & Sons, Ltd.     

An iterative implementation of the Uzawa algorithm for 3-D fluid flow problems

A new iterative algorithm for the solution of the three-dimensional Navier–Stokes equations by the finite element method is presented. This algorithm is based on a combination of the Uzawa and the Arrow–Hurwicz algorithms and uses a preconditioning technique to enhance convergence. Numerical tests are presented for the cubic cavity problem with two elements, namely the linear brick Q₁?P₀ and the enriched linear brick Q₁⁺ ? P₁. It is shown that the proposed methodology is optimal with the enriched element and that the CPU time varies as NEQ^1·44, where NEQ is the number of equations.     

An application of Curie’s principle to elastoplastic dynamics

This paper deals with the stability and the dynamics of a harmonically excited elastic–perfectly plastic unsymmetrical oscillator. Stability of the periodic orbits is analytically investigated with a perturbation approach. The occurrence of ratcheting effect is discussed for this system, and is related to the loss of symmetry of the periodic orbit in the phase space. Curie’s principle of symmetry is numerically verified for the symmetrical system with positive damping. Therefore, the observation of ratcheting phenomenon is necessarily associated to a breaking of symmetry in the constitutive behaviour, or in the forcing term. However, the generalized version of Curie’s principle has to be considered when a negative damping is introduced.     

Overspeed burst of elastoviscoplastic rotating disks: Part II – Burst of a superalloy turbine disk

Burst of a turbo-engine disk in case of overspeed is investigated both from experimental and computational point of view. Two twin disks made of the same nickel based superalloy are tested. For the first one (B-disk), rotation rate in increased till burst. The second one (S-disk) is kept safe by stopping rotation just before burst, and unloading it to measure residual deformations. The material model parameters are deduced either from simple tension tests, or using an inverse method on the S-disk test. Two corresponding finite element simulations of the B-disk are then performed, using either an arc-length control method to overcome the limit point, or dynamic simulations. In both cases, the numerical burst rotation rate, associated with the loss of stability of the structure, is found to be in good agreement with the experimental result.     

On the distribution of multiples of real numbers

We introduce new series (of the variable ??) that enable to measure the irregularity of distribution of the sequence of fractional parts {n??}. A detailed analysis of the convergence and divergence of these series is done, depending mainly on the convergents of ??. As a by product, we obtain new Fourier series of square integrable functions that converge almost everywhere but at no rational number.