Abdelhak Ambari

Flow around a confined rotating cylinder at small Reynolds number

A numerical finite-volume technique to solve the two-dimensional Navier-Stokes equations is applied to the rotation of a rigid circular cylinder between parallel plane walls. In this confined situation, the torque exerted on the cylinder is a function of both the distance between the two walls and the position between them. In the absence of experimental results for this problem, we propose here new data of the torque in a wide range of confinements and we study the influence of the eccentricity of the cylinder. When the cylinder rotates close to a wall, there is also a fall of pressure that is likely to create cavitation in the fluid, in accordance with experimental results. Finally, a force parallel to the plane parallel boundaries is numerically obtained, whereas it is theoretically found to be equal to zero in the presence of a single wall. This phenomenon is studied in detail and an explanation is proposed here. The same results could be obtained for the torque experienced by a cylinder translating p...

Catalyst surface at a fractal of cost: a quest for optimal catalyst loading

Abstract Intuition tells us that any decrease in the catalytically active surface area should result in an equivalent decrease in the reaction yield and efficiency. Our findings counter this by showing that the active surface and hence the catalyst loading can be reduced drastically in the diffusion-limited heterogeneous reaction systems, while the conversion rate remains essentially unchanged by using fractals for spatial distribution of the catalyst load. The results of this study provide an unusual circumstance for optimal design of chemically active surfaces and can be used to drastically reduce cost of heterogeneous chemical and biological reactors, sensors, and electrodes of fuel cells. The proposed approach can be exploited to its fullest extent in chemical microsystems by utilizing the latest advances in our abilities to manipulate matter on the micro/nano scale.

Kinematics of a symmetrically confined cylindrical particle in a “Stokes-type” regime

To contribute to the study of the influence of the hydrodynamic interactions governing the dynamics of solid particles such as fibers in nondilute regimes, we consider in this work a cylindrical particle confined between two parallel walls at low Reynolds numbers. The particle moves with its axis always parallel to both walls. Our numerical results, derived with a projection method and a finite-volume approach, turn out to be very accurate and enable us to solve different problems using the matrix resistance technique. The first problem considers the consequences of these interactions on the settling velocity of a particle. In such confined situations, the hydrodynamic interactions are expressed by a backflow leading to a decrease of the settling velocity when the confinement increases with an asymptotical behavior varying like e5∕2, where e stands for the gap between the plane walls and the cylinder. The second problem consists in the accurate determination of the actual velocity of a neutrally buoyant p...

Stability diagram and effect of initial density stratification for a two-layer system in a supercritical fluid

A numerical study of the stability in a two-layer system filled with a single pure supercritical fluid subjected to an initial temperature difference is performed. The very large compressibility and the very low heat diffusivity of near-critical fluids lead to a Rayleigh-Taylor-like gravitational instability of the heat diffusion layer. This instability is similar to the one of two miscible fluids where molecular species diffusion coefficient is replaced by the heat diffusion coefficient. Our numerical results are consistent with respect to the dispersion relation derived by Duff et al. [Phys. Fluids 5, 417 (1962)] for a system of two incompressible miscible fluids (argon-bromine mixture falling into helium or air). It has also been shown that when the thickness of the lower layer becomes smaller than the heat diffusion length based on the maximum growth rate, the system is stable [Phys. Fluids 17, 054102 (2005)]. A linear stability diagram has been established as a function of three parameters: the thick...

Reliability of a Hydrodynamic Journal Bearing

Journal fluid bearings are widely used in industry due to their static and dynamic behavior and their very low coefficient of friction. The technical requirements to improve the new technologies design are increasingly focused on the indicators of dependability of systems and machines. Then, it is necessary to develop a methodology to study the reliability of bearings in order to improve and to evaluate their design quality. Few works are referenced in literature concerning the estimation of the reliability of fluid journal bearings. This paper deals with a methodology to study the failure probability of a hydrodynamic journal bearing. An analytical approach is proposed to calculate static characteristics in using the Reynolds equation. The commonly methods used in structural reliability such as FORM (First Order Reliability Method), SORM (Second Order Reliability Method) and Monte Carlo are developed to estimate the failure probability. The function of performance bounding two domains (domain of safety and domain of failure) is estimated for several geometrical configurations of a hydrodynamic journal bearing (long journal bearings with the hypotheses of Sommerfeld, Gümbel and Reynolds, and a short journal bearing with the hypothesis of Gümbel).

Levitating spherical particle in a slightly tapered tube at low Reynolds numbers: Application to the low-flow rate rotameters

In this study, a theoretical framework is developed to predict the equilibrium conditions of a non-neutrally buoyant sphere placed in a vertical conical tube as encountered in liquid rotameters. The analysis presented herein is applicable for a sphere heavier than the surrounding fluid, situated on the axis of a slightly tapered tube. The sphere is subject to the laminar flow conditions with the Reynolds numbers ranging between the Stokes type regimes up to values corresponding to slightly inertial regimes. In this work, we assume that the aperture angle of the tube is small and that the drag force is mainly due to the dissipation located in the gap between the tube and the sphere. Under these conditions, it is possible to consider the tube as locally cylindrical and we can use the results previously obtained for the correction factor of the Stokes force on a sphere subject to a Poiseuille flow in a tube of constant cross-section. We obtain an equation relating the flow rate to the vertical position of the sphere in the tube and the validity of this analysis is demonstrated by applying it to a commercially available rotameter. The present study provides a simple but sound theoretical method to calibrate such flowmeters.

Drag Force and Heat Transfer Corrections for a Confined Circular Cylinder in Uniform and Poiseuille Flow

The modifications to the drag force and to the heat transfer on an infinite circular cylinder induced by the presence of two bounding walls are numerically investigated in the case where the cylinder is located midway between two parallel planes in uniform motion and in Poiseuille flow. At very low Reynolds and Peclet numbers, we show that the solutions are of the “Stokes type” and we give new expressions of the drag force and of the heat flux corrections, valid for a very wide range of confinements extending from a weak interaction to the lubrication regime.Copyright