Jérôme Hoepffner

State estimation in wall-bounded flow systems. Part 1. Perturbed laminar flows

In applications involving the model-based control of transitional wall-bounded flow systems, it is often desired to estimate the interior flow state based on a history of noisy measurements from ...

Linear feedback control and estimation applied to instabilities in spatially developing boundary layers

This paper presents the application of feedback control to spatially developing boundary layers. It is the natural follow-up of Hogberg & Henningson (J. Fluid Mech. vol. 470, 2002, p. 151), whe ...

Stochastic approach to the receptivity problem applied to bypass transition in boundary layers

To study the flow behavior in the presence of external disturbances of chaotic nature, a stochastic approach is pursued. In particular, transition to turbulence in boundary layers exposed to high levels of free-stream turbulence is considered. The late stages of this transition scenario, characterized by the growth and breakdown of streamwise-elongated streaks, are examined by considering the linear evolution of perturbations to a base flow consisting of the Blasius profile and the streaks. A stochastic initial condition is considered where the free-stream perturbations are described by the correlations of isotropic homogeneous turbulence. The spatial correlation of the excited flow at later times can be computed by the numerical solution of a Lyapunov equation. It is shown that free-stream turbulence has the necessary features to excite secondary energy growth, thus playing a central role in the transition to turbulence. The method proposed here can be used to examine the receptivity of other flows to external noise whose statistical properties are known or can be modeled.

Vortices catapult droplets in atomization

A droplet ejection mechanism in planar two-phase mixing layers is examined. Any disturbance on the gas-liquid interface grows into a Kelvin-Helmholtz wave, and the wave crest forms a thin liquid film that flaps as the wave grows downstream. Increasing the gas speed, it is observed that the film breaks up into droplets which are eventually thrown into the gas stream at large angles. In a flow where most of the momentum is in the horizontal direction, it is surprising to observe these large ejection angles. Our experiments and simulations show that a recirculation region grows downstream of the wave and leads to vortex shedding similar to the wake of a backward-facing step. The ejection mechanism results from the interaction between the liquid film and the vortex shedding sequence: a recirculation zone appears in the wake of the wave and a liquid film emerges from the wave crest; the recirculation region detaches into a vortex and the gas flow over the wave momentarily reattaches due to the departure of the vortex; this reattached flow pushes the liquid film down; by now, a new recirculation vortex is being created in the wake of the wave—just where the liquid film is now located; the liquid film is blown up from below by the newly formed recirculation vortex in a manner similar to a bag-breakup event; the resulting droplets are catapulted by the recirculation vortex.

The evolution of a localized nonlinear wave of the Kelvin–Helmholtz instability with gravity

At the interface between two fluids of different density and in the presence of gravity, there are well known periodic surface waves which can propagate for long distances with little attenuation, as it is for instance the case at the surface of the sea. If wind is present, these waves progressively accumulate energy as they propagate and grow to large sizes—this is the Kelvin–Helmholtz instability. On the other hand, we show in this paper that for a given wind strength, there is potential for the growth of a localized nonlinear wave. This wave can reach a size such that the hydrostatic pressure drop from top to bottom equals the stagnation pressure of the wind. This process for the disruption of the flat interface is localized and nonlinear. We study the properties of this wave using numerical simulations of the Navier–Stokes equations.

Modeling flow statistics using convex optimization

A method is proposed to estimate the covariance of disturbances to a stable linear system when its state covariance is known and a dynamic model is available. This is an issue of fundamental interest for estimation and control of fluid mechanical systems whose dynamics is described by the linearized Navier–Stokes equations. The problem is formulated in terms of a matrix norm minimisation with linear matrix inequality constraint, and solved numerically by means of alternating convex projection. The method is tested on covariance estimation in a low Reynolds number channel flow.