Discharge of a silo through a lateral orifice: Role of the bottom inclination versus friction.

In this work we propose to identify the relative role of the inclination of gravitational acceleration and friction on the discharge flow rate of a granular media from a rectangular silo by varying the silo geometry thanks to an inclined bottom which ends up at a lateral outlet. The study is motivated by a nuclear safety problem: a fuel rod (modeled by an elongated silo) accidentally releases fuel fragments (modeled by grains). We performed experiments where we independently measured the mass flow rate and the velocity profiles, together with discrete particle simulations and continuum simulations with a frictional rheology described by a µ(I) constitutive law and taking into account the wall friction. We study monolayer flows and three-dimensional flows, and we propose an analytical model that predicts the discharge flow rate of particles from a rectangular silo with an inclined bottom according to its outlet aspect ratio and the bottom inclination angle.

A one-dimensional arterial network model for bypass graft assessment.

We propose an arterial network model based on one-dimensional hemodynamic equations to study the behavior of different vascular surgical bypass grafts in the case of an arterial occlusive pathology: a stenosis of the Right Iliac artery. We investigate the performances of three different bypass grafts (Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree of obstruction of the stenosis. Numerical simulations show that all bypass grafts are efficient since we retrieve in each case the healthy hemodynamics downstream of the stenosed region while ensuring at the same time a global healthy circulation. We analyze in detail the behavior of the Axillo-Femoral bypass graft by performing hundreds of simulations where we vary the values of its Young's modulus [0.1-50 MPa] and radius [0.01-5 cm]. Our analysis shows that Young's modulus and radius of commercial bypass grafts are optimal in terms of hemodynamic considerations. Our numerical findings prove that this model approach can be used to optimize or plan patient-specific surgeries, to numerically assess the viability of bypass grafts and to perform parametric analysis and error propagation evaluations by running extensive simulations.

Modeling the receptivity of an air jet to transverse acoustic disturbance with application to musical instruments.

A simple analytical model for the interaction between a plane jet issued from a flue and a transverse acoustic disturbance is developed in this paper. The model is inspired by direct flow simulation results confronted to experimental data. The interaction is expected to take place in the vicinity of the separation points of the jet. The influence of the detailed geometry of the channel end on the jet receptivity is discussed, and more specifically the chamfer geometries found in flute-like musical instruments. The simplified model explains quite well the difference between the jet response of a flue with square edges compared to a chamfered flue exit. The effect of rounded, lip-like flue exit is not well captured by the model.

Continuum simulation of the discharge of the granular silo: a validation test for the µ(I) visco-plastic flow law.

Using a continuum Navier-Stokes solver with the µ(I) flow law implemented to model the viscous behavior, and the discrete Contact Dynamics algorithm, the discharge of granular silos is simulated in two dimensions from the early stages of the discharge until complete release of the material. In both cases, the Beverloo scaling is recovered. We first do not attempt a quantitative comparison, but focus on the qualitative behavior of velocity and pressure at different locations in the flow. A good agreement for the velocity is obtained in the regions of rapid flows, while areas of slow creep are not entirely captured by the continuum model. The pressure field shows a general good agreement, while bulk deformations are found to be similar in both approaches. The influence of the parameters of the µ(I) flow law is systematically investigated, showing the importance of the dependence on the inertial number I to achieve quantitative agreement between continuum and discrete discharge. However, potential problems involving the systems size, the configuration and "non-local" effects, are suggested. Yet the general ability of the continuum model to reproduce qualitatively the granular behavior is found to be very encouraging.

In vitro validation of some flow assumptions for the prediction of the pressure distribution during obstructive sleep apnoea.

An adequate description of the pressure distribution exerted by the fluid flow on pharyngeal walls is a first requirement to enhance the understanding, modelling and, consequently, the prediction of airway collapse during obstructive sleep apnoea. From a fluid mechanical point of view, several flow assumptions can be formulated to reduce the governing flow equations. The relevance of some major flow assumptions and the accuracy of the resulting flow description with respect to obstructive sleep apnoea was investigated on a rigid geometrical replica of the pharynx. Special attention was given to the influence of geometrical asymmetry and to the position of the flow separation point. An in vitro experimental and theoretical study of steady pharyngeal fluid flow is presented for different constriction heights and upstream pressures. Pressure and velocity distributions along a rigid in vitro replica of the oro-pharyngeal cavity were compared with different flow predictions based on various assumptions. Fluid flow models were tested for volume flow rates ranging from 5 to 120 1 min(-1) and for minimum apertures between 1.45 and 3.00 mm. Two-dimensional flow models were required and predicted experimental results with an accuracy of 15%. Flow theories classically used in the case of a Starling resistor provided poor agreement.

Stationary shear flows of dense granular materials: a tentative continuum modelling.

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent qualitative agreement with most of the experimental or numerical results concerning free-surface shear flows as well as confined shear flows.

Influence of collision on the flow through in-vitro rigid models of the vocal folds.

Measurements of pressure in oscillating rigid replicas of vocal folds are presented. The pressure upstream of the replica is used as input to various theoretical approximations to predict the pressure within the glottis. As the vocal folds collide the classical quasisteady boundary layer theory fails. It appears however that for physiologically reasonable shapes of the replicas, viscous effects are more important than the influence of the flow unsteadiness due to the wall movement. A simple model based on a quasisteady Bernoulli equation corrected for viscous effect, combined with a simple boundary layer separation model does globally predict the observed pressure behavior.

Maximal wall shear stress in arterial stenoses: application to the internal carotid arteries.

Maximal wall shear stress (MWSS) in the convergent part of a stenosis is calculated by the interactive boundary-layer theory. A dimensional analysis of the problem shows that MWSS depends only on a few measurable parameters. A simple relationship between MWSS and these parameters is obtained, validated, and used to calculate the magnitude of MWSS in a carotid stenosis, as a function of the patency of the circle of Willis and the stenotic pattern. This demonstrates the huge effect of collateral pathways. Elevated MWSS are observed even in moderate stenoses, provided they are associated with a contralateral occlusion, a large anterior, and narrow posterior communicating arteries, suggesting a potential risk of embolus release in this configuration.