Axisymmetric laser welding of ceramics: comparison of experimental and finite element results

In this paper, we compare experimental data for a laser spot weld on a ceramic to the solution from an adaptive finite element model of the system. Our focus is on validating the finite element model, which necessarily includes numerous simplifications. We assume an axisymmetric geometry and flow profile, with a flat free surface. Buoyancy and surface tension drive the liquid motion in the molten ceramic pool beneath the laser, which is calculated using the axisymmetric forms of the continuity, momentum and energy equations. Latent heat, temperature-dependent material properties and radiation effects are all included in the formulation. These equations are solved with standard finite element techniques utilizing mesh relocation with a movement indicator based on solution gradients. Comparision with experimental data indicates that the numerical techniques used successfully predicted the depth and diameter of the actual ceramic weld pool.     

Experimental investigation of turbulent natural convection flow in a channel

This paper presents the results of velocity measurements of natural convection in symmetrically heated vertical channel using the particle image velocimetry (PIV) system. Velocity measurements were conducted at three different sections on the horizontal plane to validate the flow two-dimensionality and at three different heights in the vertical plane to establish vertical mean velocity profiles. The results indicate a considerable influence of the Rayleigh number and aspect ratio on the mean velocity profile. The results also indicate significant diffusion rates of the vertical mean velocity component and normal Reynolds stresses towards the center of the channel.     

On the slow motion of a cluster of bubbles under the combined action of gravity and thermocapillarity

The slow migration of N spherical bubbles under combined buoyancy and thermocapillarity effects is investigated by appealing solely to $3N+1$ boundary-integral equations. In addition to the theory and the associated implementation strategy, preliminary numerical results are both presented and discussed for a few clusters involving 2, 3, 4 or 5 bubbles with a special attention paid to the case of rigid configurations. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

Drag-induced apparent mass gain in thermogravimetry

This paper shows how aerodynamic drag in thermogravimetric equipment may be corrected, and noise inherent in the data removed. Although it is entirely possible to correct drag-induced mass gain empirically, this publication is intended to allow the reader to understand the cause, correct for it, and remove noise appropriately. Apparent mass gain is described in terms of a generalised Stokes' formulation. A method is developed that enables the quantification of drag inside thermogravimetric equipment, which when combined with the Savitsky-Golay smoothing filter enables temperature-dependent apparent weight gain effects to be removed. It is necessary to account for this effect in proximate analysis and in the determination of kinetic parameters of thermal degradation.     

Comment on “Group solution of a time dependent chemical convective process” by M.M. Kassem and A.S. Rashed, Applied Mathematics and Computation, 215 (2009) 1671-1684

The mathematical model formulated by M.M. Kassem and A.S. Rashed in their article: “Group solution of a time dependent chemical convective process, Applied Mathematics and Computation, 215 (2009) 1671-1684”, through group analysis, is reformulated and interpreted correctly so that it can represent a feasible situation. A perturbation analysis that replaces their incorrect analysis is performed and proved to compare well with a finite difference solution of the problem.     

Validation of fluid–particle interaction force relationships in binary-solid suspensions

In this work several relationships governing solid–fluid dynamic interaction forces were validated against experimental data for a single particle settling in a suspension of other smaller particles. It was observed that force relationships based on Lattice-Boltzmann simulations did not perform as well as other interaction types tested. Nonetheless, it is apparent that, in the case of a suspension of different particle types, it is important that the correct choice is made as to how the contribution to the overall fluid–particle interaction force is split between buoyancy and drag. Experimental evidence clearly suggests that the “generalized” Archimedes’ principle (where the foreign particle is considered to displace the whole suspension and not just the fluid) provides the best result.     

Theoretical and numerical study of a thermal convection problem with temperature-dependent viscosity in an infinite layer

A convection problem with temperature-dependent viscosity in an infinite layer is presented. This problem has important applications in mantle convection. The existence of a stationary bifurcation is proven together with a condition to obtain the critical parameters at which the bifurcation takes place. A numerical strategy has been developed to calculate the critical bifurcation curves and the most unstable modes for a general dependence of viscosity on temperature. An exponential dependence of viscosity on temperature has been considered in the numerical calculations. Comparisons with the classic Rayleigh-Bénard problem with constant viscosity indicate that the critical temperature difference threshold decreases as the exponential rate parameter increases. The vertical velocity of the marginal mode exhibits motion concentrated in the region where viscosity is smaller.     

Buoyancy driven flow of light gases in atmosphere compared to that of hot gases

The transient formation and subsequent dispersion of the plumes of a fixed mass of lighter than air gases emerging out of open cylindrical enclosures with negligible pressure difference was investigated using 3-D and 2-D CFD models. Subsequently, the dispersion into atmosphere of a similar amount of equally buoyant hot air was also considered. The structure and dynamics of the resulting thermally driven hot air plumes were compared to the corresponding characteristics of the mass-transfer driven isothermal plumes. Some cases were investigated in which the dispersing gases were both lighter than air and at a different temperature from that of the atmosphere. The similarities and differences of these double heat-mass-transfer driven problems with the other cases were discussed. It was shown that a criterion developed previously for judging the validity of the 2-D model relative to the more complex 3-D approach for mass-transfer driven problems could be equally applied for the thermally driven or double heat and mass-transfer driven plume flow characteristics.     

Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. Part II: Weakly non-linear solutions

The buoyancy-driven instability of a monocomponent or binary fluid that is completely contained in a vertical circular cylinder is investigated, including the influence of the Soret effect for the binary mixture. The Boussinesq approximation is used, and weakly-non-linear solutions are generated via Galerkin's technique using an expansion in the eigensolutions of the associated linear stability problem. Various types of fluid mixtures and cylindrical domains are considered. Flow structure and associated heat transfer are computed and experimental observations are cited when possible.