Mattias Chevalier

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 ...

State estimation in wall-bounded flow systems. Part 2. Turbulent flows

(Received 16 November 2004 and in revised form 18 July 2005) This work extends the estimator developed in Part 1 of this study to the problem of estimating a turbulent channel flow at Reτ = 100 based on a history of noisy measurements on the wall. The key advancement enabling this work is the development and implementation of an efficient technique to extract, from direct numerical simulations, the relevant statistics of an appropriately defined ‘external forcing’ term on the Navier–Stokes equation linearized about the mean turbulent flow profile. This forcing term is designed to account for the unmodelled (nonlinear) terms during the computation of the (linear) Kalman filter feedback gains in Fourier space. Upon inverse transform of the resulting feedback gains computed on an array of wavenumber pairs to physical space, we obtain, as in Part 1, effective and well-resolved feedback convolution kernels for the estimation problem. It is demonstrated that, by applying the feedback so determined, satisfactory correlation between the actual and estimated flow is obtained in the near-wall region. As anticipated, extended Kalman filters (with the nonlinearity of the actual system reintroduced into the estimator model after the feedback gains are determined) outperform standard (linear) Kalman filters on the full system.

Optimal secondary energy growth in a plane channel flow

The optimal growth of perturbations to transiently growing streaks is studied in Poiseuille flow. Basic flows are generated by direct numerical simulation giving “primary” optimal spanwise periodic vortices of finite amplitude as the initial condition. They evolve into finite amplitude primary transiently growing streaks. Linear “secondary” optimal energy growth supported by these primary flows are computed using an adjoint technique which takes into full account the unsteadiness of the basic flows. Qualitative differences between primary and secondary optimal growths are found only when the primary streaks are locally unstable. For locally stable primary streaks, the secondary optimal growth has the same scalings with Reynolds number R as the primary optimal growth and the maximum growth is attained by streamwise uniform vortices, suggesting that the primary and secondary optimal growth are based on the same physical mechanisms. When the primary streaks are locally unstable the secondary optimal growth o...

Linear compensator control of a pointsource induced perturbation in a Falkner–Skan–Cooke boundary layer

We focus on the problem of controlling pointsource induced perturbations on an infinite swept wing using linear control theory. Based on wall measurements in a spatial simulation of localized disturbances in Falkner–Skan–Cooke boundary layers, an extended Kalman filter is used to estimate the full three-dimensional wave packet. The estimated field is in turn used to calculate a feedback control which changes the growth of the disturbance into decay. This is the first time that optimal control and estimation concepts are successfully applied to construct a dynamic output feedback compensator which is used to control disturbances in spatially developing boundary layers.

Optimal feedback control applied to boundary layer flow

Linear feedback control has been applied to channel and boundary-layer flows using blowing and suction control. In channel flows the transition threshold is increased for three different perturbation types and a turbulent flow at Re τ = 100 is relaminarized using full state information control. In a spatially developing Falkner–Skan–Cooke boundary-layer flow a full-state information controller is shown to change exponential growth in perturbation energy to exponential decay. In a similar configuration, the full-state information controller is combined with an estimator to reduce the requirement of full-state information to only measurements of different flow quantities at wall. The combined controller and estimator is referred to as a compensator and is shown to work well for a pointsource induced wave-packet. This is a review article based on several publications. However, here we have also included selected animations that illustrate the characteristics of the control in more detail. An important observation from the animations is that the control acts and reduces the disturbance level in a short amount of time. Also, the transient of the convergence in the estimator forcing is relatively fast. Overall these studies show that both the controller and estimator is quite insensitive to the specific conditions they were constructed for.

Stability of a jet in crossflow

We have produced a fluid dynamics video with data from Direct Numerical Simulation (DNS) of a jet in crossflow at several low values of the velocity inflow ratio R. We show that, as the velocity ratio R increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behavior, before finally exhibiting asymmetric chaotic motion. We also perform a stability analysis just above the first bifurcation, where R is the bifurcation parameter. Using the overlap of the direct and the adjoint eigenmodes, we confirm that the first instability arises in the shear layer downstream of the jet orifice on the boundary of the backflow region just behind the jet.

A Gradient-based Optimization Method for Natural Laminar Flow Design

A Gradient-based Optimization Method for Natural Laminar Flow Design : OPTLAM Project Final Report

LINEAR FEEDBACK CONTROL OF TRANSITION IN SHEAR FLOWS

This work focuses on the application of linear feedback control to transition to turbulence in shear flows. The controller uses wall-mounted sensor information to estimate the flow disturbances and uses wall actuators to prevent transition to turbulence. The flow disturbances are induced by external sources of perturbations described by means of a stochastic volume forcing. We show that improved performance can be achieved if the proper destabilisation mechanisms are targeted.

FEEDBACK CONTROL IN SPATIALLY GROWING BOUNDARY LAYERS

Linear feedback control has been applied to transitional boundary layer flows. Information from wall-mounted sensors is used to estimate the flow state. The estimated state is then used to compute the optimal feedback control which is applied as blowing and suction with zero net mass-flux through the wall. The performance of the controller is tested in direct numerical simulations of a spatially growing Falkner-Skan- Cooke boundary layer where an inflectional instability is triggered. The extension to spatial boundary layer flows is an important step towards real applications.