Marc Medale

Determination of the critical Shields number for particle erosion in laminar flow

We present reproducible experimental measurements for the onset of grain motion in laminar flow and find a constant critical Shields number for particle erosion, i.e., θc=0.12±0.03, over a large range of small particle Reynolds number: 1.5×10−5⩽Rep⩽0.76. Comparison with previous studies found in the literature is provided.We present reproducible experimental measurements for the onset of grain motion in laminar flow and find a constant critical Shields number for particle erosion, i.e., θc=0.12±0.03, over a large range of small particle Reynolds number: 1.5×10−5⩽Rep⩽0.76. Comparison with previous studies found in the literature is provided.

A three-dimensional numerical model for dense granular flows based on the µ(I) rheology

This paper presents a three-dimensional implementation of the so-called µ ( I ) rheology to accurately and efficiently compute steady-state dense granular flows. The tricky pressure dependent visco-plastic behaviour within an incompressible flow solver has been overcome using a regularisation technique along with a complete derivation of the incremental formulation associated with the Newton-Raphson algorithm. The computational accuracy and efficiency of the proposed numerical model have been assessed on two representative problems that have an analytical solution. Then, two application examples dealing with actual lab experiments have also been considered: the first one concerns a granular flow on a heap and the second one deals with the granular flow around a cylinder. In both configurations the obtained computational results are in good agreement with available experimental data.

A parallel computer implementation of the Asymptotic Numerical Method to study thermal convection instabilities

We have developed a numerical model to efficiently compute steady-state combined buoyancy and thermocapillary convection solutions. It features a parallel computer implementation of an Asymptotic Numerical Method to perform steady-state path-following and locate bifurcation points in problems involving large size algebraic systems, up to few million degrees of freedom. The model has been first validated on a problem for which a reference solution exists and then is used to analyse the influence of the container size and shape on Rayleigh-Benard-Marangoni convection and its related cellular pattern.

Power series analysis as a major breakthrough to improve the efficiency of Asymptotic Numerical Method in the vicinity of bifurcations

This paper presents the outcome of power series analysis in the framework of the Asymptotic Numerical Method. We theoretically demonstrate and numerically evidence that the emergence of geometric power series in the vicinity of simple bifurcation points is a generic behavior. So we propose to use this hallmark as a bifurcation indicator to locate and compute very efficiently any simple bifurcation point. Finally, a power series that recovers an optimal step length is build in the neighborhood of bifurcation points. The reliability and robustness of this powerful approach is then demonstrated on two application examples from structural mechanics and hydrodynamics.

Local mesh adaptation technique for front tracking problems

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented : the broken dam problem and the Rayleigh-Taylor instability

The Osmotic Migration of Cells in a Solute Gradient

The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.

NUMERICAL SIMULATION OF BE´NARD-MARANGONI CONVECTION IN SMALL ASPECT RATIO CONTAINERS

This study investigates, by means of numerical simulation, coupled gravity and capillarity-driven thermoconvection of a fluid layer heated from below (Be´nard-Marangoni convection), close to the threshold and in small aspect ratio containers. First, we present a broad validation of the numerical model we have developed onto widely recognized results available from experimental, theoretical, and numerical fields. Furthermore, we report the numerical results we have obtained in analyzing the dependence on the convective cell pattern of the container shape. In the smallest aspect ratio range only a few cells can develop, so the convective patterns mainly depend on the aspect ratio and the shape of the container, but no major transient evolution can be observed. On the other hand, larger aspect ratio containers allow a comparatively large number of cells to develop. The shape of the container plays a significant part in the transient stage until the stationary pattern is attained, in which hexagonal cells prevail at the core surrounded by a row of predominantly pentagonal cells.

NUMERICAL SIMULATION OF INCOMPRESSIBLE FLOWS WITH MOVING INTERFACES

A numerical model has been developed for the 2D simulation of free surface flows or, more generally speaking, moving interface ones. The bulk fluids on both sides of the interface are taken into account in simulating the incompressible laminar flow state. In the case of heat transfer the whole system, i.e. walls as well as possible obstacles, is considered. This model is based on finite element analysis with an Eulerian approach and an unstructured fixed mesh. A special technique to localize the interface allows its temporal evolution through this mesh. Several numerical examples are presented to demonstrate the capabilities of the model.

Benchmark solution for a three-dimensional mixed convection flow - Part 1: reference solutions

A solution to a benchmark problem for a three-dimensional mixed-convection flow in a horizontal rectangular channel heated from below and cooled from above (Poiseuille-Rayleigh-Bénard flow) is proposed. This flow is a steady thermoconvective longitudinal roll flow in a large-aspect-ratio channel at moderate Reynolds and Rayleigh numbers (Re = 50, Ra = 5,000) and Prandtl number Pr = 0.7. The model is based on the Navier-Stokes equations with Boussinesq approximation. We propose reference solutions resulting from computations on large grids, Richardson extrapolation (RE), and cubic spline interpolations. The solutions obtained with one finite-difference, one finite-volume, and two finite-element codes are in good agreement, and reference values for the flow and thermal fields and for the heat and momentum fluxes are given with four to five significant digits.

Numerical investigation of thermocapillary flow around a bubble

The thermocapillary flow induced by a gas bubble in a Newtonian liquid layer subjected to a stable temperature stratification is investigated. This flow is analyzed for a special configuration when the surface tension and buoyant forces oppose one another. The driving mechanism is the surface tension gradient related to the Marangoni number whereas the stabilizing effects are the viscous and buoyant forces related to the Prandtl and the Rayleigh numbers. In a previous work, this flow has been investigated experimentally for a few combinations of these three parameters. In order to make a more systematic study of the influence of these parameters, numerical simulations are used as a decisive tool. Indeed, it allows the contribution of the different mechanisms to be evaluated. To validate the finite element model, developed for this purpose, the numerical results are first compared to experimental ones. Then, the influence of these three dimensionless parameters on the flow pattern and the magnitude of the ...