Denis Jeandel

Temporal stability of Jeffery–Hamel flow

In this study of the temporal stability of Jeffery–Hamel flow, the critical Reynolds number based on the volume flux, R c , and that based on the axial velocity, Re c , are computed. It is found that both critical Reynolds numbers decrease very rapidly when the half-angle of the channel, α, increases, such that the quantity α R c remains very nearly constant and α Re c is a nearly linear function of α. For a short channel there can be more than one value of the critical Reynolds number. A fully nonlinear analysis, for Re close to the critical value, indicates that the loss of stability is supercritical. The resulting asymmetric oscillatory solutions show staggered arrays of vortices positioned along the channel.

Numerical study of coupled electromagnetic and aerothermodynamic phenomena in a circuit breaker electric arc

Two-dimensional simulations of electric arcs in air in a low-voltage circuit breaker have been performed. For this purpose, a compressible hydrodynamic code taking into account the properties of the arc plasma and the electric, magnetic and radiative phenomena has been developed. A whole evolution of the arc from its ignition to its stagnation at the end of the chamber after displacement has been simulated. The analysis of the results shows the flow compression by the pressure waves and the influence of the magnetic forces on the shape and displacement of the arc. It has been established that the viscosity has little influence on the evolution.

Validation of a k-ε model based on `experimental results in a thermally stable stratified turbulent boundary layer

Abstract A 2D ( k - e ) turbulence model was developed for use with dilatable flows at high Reynolds numbers. A new approach relative to the modelling of the density-velocity correlation term is proposed, and a relation concerning the Prandtl turbulent number was used taking into account both the wall and gravity effects. This model was validated by experimental results obtained at the E.C.L. Fluid Mechanics and Acoustics laboratory on a stable thermally stratified turbulent boundary layer developing at a quickly cooled smooth boundary surface.

An Efficient Quasi-Linear Finite Element Method for Solving the Incompressible Navier-Stokes Equations at Large Reynolds Numbers

This paper describes a numerical method for solving the time dependant Navier Stokes equations for incompressible viscous fluid flows. The method results from a three step implicit scheme for the time discretization and from a finite element approximation for the space discretization. The typical fractional step method leads to an uncoupling between the non linearity and incompressibility and the convective terms appear in a linearized semi-implicit form. The discretization avoids the use of Least Squares methods to treat the non linearity, it has shown excellent convergence properties which improve as the Reynolds number increases. Conjugate gradients algorithms are especially developed for solving the resulting linear systems including unsymmetrical matrices. For convection dominated flows, a balancing dissipation technique is introduced in order to stabilize the oscillatory nature of the solution.