Olivier Vauquelin

The history force on a small particle in a linearly stratified fluid

The hydrodynamic force experienced by a small spherical particle undergoing an arbitrary time-dependent motion in a density-stratified fluid is investigated theoretically. The study is carried out under the Oberbeck-Boussinesq approximation, and in the limit of small Reynolds and small Peclet numbers. The force acting on the particle is obtained by using matched asymptotic expansions in which the small parameter is given by a/l, where a is the particle radius and l is the stratification length defined by Ardekani & Stocker (2010), which depends on the Brunt-Vaisala frequency, on the fluid kinematic viscosity and on the thermal or the concentration diffusivity (depending on the case considered). The matching procedure used here, which is based on series expansions of generalized functions, slightly differs from that generally used in similar problems. In addition to the classical Stokes drag, it is found the particle experiences a memory force given by two convolution products, one of which involves, as usual, the particle acceleration and the other one, the particle velocity. Owing to the stratification, the transient behaviour of this memory force, in response to an abrupt motion, consists of an initial fast decrease followed by a damped oscillation with an angular-frequency corresponding to the BruntVaisala frequency. The perturbation force eventually tends to a constant which provides us with correction terms that should be added to the Stokes drag to accurately predict the settling time of a particle in a diffusive stratified-fluid.

On the modelling of steady turbulent fountains

The paper deals with steady-state turbulent fountains in a homogeneous surrounding. A set of mono-dimensional conservation equations is first derived from the Navier–Stokes equations. In contrast with equations used for plumes or rising fountains, these equations reveal additional terms in order to account for the effect of the (annular) down-flow on the fountain up-flow. Large-eddy simulations are then performed and used to determine, from radial profiles, the values of the constants (associated with these additional terms) to be fitted in the model. With these constants, analytical solutions of the model for steady-state fountain are proposed and compared with previous experiments.

Effect of vertical density stratification on the buoyancy-induced flow at a doorway opening

This study deals with the process of smoke filling in a compartment and the exhaust of smoke through a doorway located in a side of the enclosure. This configuration is a typical scenario of smoke propagation during a fire event in a compartment. This study focuses on the vertical temperature stratification in the smoke layer and its consequences on buoyancy flow induced at the doorway. From two theoretical approaches, considering or not considering the vertical temperature stratification in the smoke layer, this study highlights how vertical temperature stratification may modify the doorway flow. The first approach is a well-mixed description considering constant temperature and thus no thermal stratification in the smoke layer. The second one describes the vertical density stratification with multilayer approach. The results show that the vertical stratification is the consequence of the process of air entrainment within the plume. The consideration of temperature stratification in the smoke layer changes the prediction of the flow through the doorway. A sensitivity analysis points out how two variables (the initial buoyancy flux and the dimension of the enclosure) modify this influence. The discussion improves the understanding of the stratification in an enclosure and gives new insight into the predictions of smoke propagation for fire safety applications.

An Experimental Procedure for Determining Both the Density and Flow Rate From Pressure Drop Measurements in a Cylindrical Pipe

An experimental procedure was developed for determining both the density and flow rate of a gas from measurements of pressure drops caused by an abrupt flow area contraction in a cylindrical pipe. Experiments were carried out by varying the density and flow rate of a light gas mixture of air and helium, spanning a Reynolds number range from 0.2 X10 4 to 3.4 X 104. From experimental results, a procedure was then proposed for evaluating the density from pressure change measurements in the scope of light gas extraction experiments.