Christophe Airiau

Sensitivity analysis using adjoint parabolized stability equations for compressible flows

An input/output framework is used to analyze the sensitivity of two- and three-dimensional disturbances in a compressible boundary layer for changes in wall and momentum forcing. The sensitivity is defined as the gradient of the kinetic disturbance energy at a given downstream position with respect to the forcing. The gradients are derived using the parabolized stability equations (PSE) and their adjoint (APSE). The adjoint equations are derived in a consistent way for a quasi-two-dimensional compressible flow in an orthogonal curvilinear coordinate system. The input/output framework provides a basis for optimal control studies. Analysis of two-dimensional boundary layers for Mach numbers between 0 and 1.2 show that wall and momentum forcing close to branch I of the neutral stability curve give the maximum magnitude of the gradient. Forcing at the wall gives the largest magnitude using the wall normal velocity component. In case of incompressible flow, the two-dimensional disturbances are the most sensitive ones to wall inhomogeneity. For compressible flow, the three-dimensional disturbances are the most sensitive ones. Further, it is shown that momentum forcing is most effectively done in the vicinity of the critical layer.

A methodology for optimal laminar flow control: Application to the damping of Tollmien–Schlichting waves in a boundary layer

A methodology for determining the optimal steady suction distribution for the delay of transition in a boundary layer is presented. The flow state is obtained from the coupled system of boundary layer equations and parabolized stability equations (PSE), to account for the spatially developing nature of the flow. The wall suction is defined by an optimal control procedure based on the iterative solution of the equations for the state and the dual state; the latter is available from the adjoint boundary layer equations and the adjoint PSE. The technique is applied to the control of two-dimensional Tollmien–Schlichting (TS) waves. Results show that the onset of the instability can be significantly postponed and/or the growth rate considerably reduced by applying an appropriate suction through the whole wall length, in a wide frequency band. Control over panels of finite length completes the study and brings useful, preliminary information on the practicality of the approach in view of implementation. Finally...

Optimal control of Tollmien–Schlichting waves in a developing boundary layer

Optimal control theory is used to determine the wall transpiration (unsteady blowing/suction) with zero net mass flux capable of attenuating Tollmien–Schlichting waves in a spatially developing boundary layer. The flow state is determined from the parabolized stability equations, in a linear setting. An appropriate cost functional is introduced and minimized iteratively by the numerical solution of the equations for the state and the dual state, coupled via transfer and optimality conditions. Central to the control is the determination of the wall Green’s function expressing the receptivity of the flow to wall inhomogeneities. The optimal wall velocity is obtained in few iterations and a reduction of several orders of magnitude in output disturbance energy is demonstrated, as compared to the uncontrolled case, for control laws operating both over the whole wall length and over a finite strip. Finally, white noise disturbances are applied to the optimal wall velocities already determined, to assess the inf...

On the amplification of small disturbances in a channel flow with a normal magnetic field

Optimal perturbations are investigated in a magnetohydrodynamic flow bounded by perfectly insulating or conducting walls. The parallel channel flow submitted to uniform, normal magnetic field is taken as an example. The stability equations (linearized Navier–Stokes and Maxwell equations) are solved simultaneously, because of the natural existence of a coupling between them. Exponential instability is studied first to set ideas and to fix some reference magnetic Prandtl and magnetic Reynolds numbers. Then, optimal perturbations are searched for by employing the approach first proposed by Butler and Farrell [Phys. Fluids A 4, 1637 (1992)]. The shape of the optimally perturbed velocity is poorly affected by the magnetic field; however, the magnetic field is found to stabilize both exponential instability and algebraically growing perturbations. The critical Reynolds numbers in the presence of magnetic fields can be very large and it is thus possible to find very significant transient growth in subcritical co...

Optimal and robust control of small disturbances in a channel flow with a normal magnetic field

Active closed-loop control of subcritical and supercritical instabilities amplified in a channel flow submitted to a constant normal magnetic field is investigated. Control is carried out at both the upper and lower walls by blowing and suction (velocity control) or by a perturbation of the normal magnetic field (magnetic control). Even if a velocity control is more efficient than a magnetic one, we found that magnetic control succeeds in stabilizing supercritical instabilities. Development of new actuators using magnetic field for flow control may thus be promising. Closed-loop control modifies the optimal perturbation but does not destruct the lift-up effect.

Mechanisms and Active Control of Jet-Induced Noise

Fundamental mechanisms of jet noise are investigated by means of direct numerical simulation. In the mixing layer, subharmonics of the respective vortex pairing are found to be responsible for the main part of the generated noise which is directed in downstream direction. By modifying the phase shift between introduced disturbances it is possible to diminish or enhance relevant portions of the emitted sound. Optimal control has been applied successfully to a plane mixing layer. In the far field, the mean noise level could be reduced. Depending on the measurement line, some distributed control or anti-noise is generated by the control. A more realistic configuration is achieved by adding a splitter plate representing the nozzle end. Rectangular serrations lead to a breakdown of the large coherent spanwise vortical structures and thus provide a noise reduction of 9dB.

Global stability and control of the confined turbulent flow past a thick flat plate

This article investigates the structural stability and sensitivity properties of the confined turbulent wake behind an elongated D-shaped cylinder of aspect-ratio 10 at Re = 32 000. The stability analysis is performed by linearising the incompressible Navier-Stokes equations around the numerically computed and the experimentally measured mean flows. We found that the vortex-shedding frequency is very well captured by the leading unstable global mode, especially when the additional turbulent diffusion is modelled in the stability equations by means of a frozen eddy-viscosity approach. The sensitivity maps derived from the computed and the measured mean flows are then compared, showing a good qualitative agreement. The careful inspection of their spatial structure highlights that the highest sensitivity is attained not only across the recirculation bubble but also at the body blunt-edge, where tiny pockets of maximum receptivity are found. The impact of the turbulent diffusion on the obtained results is investigated. Finally, we show how the knowledge of the unstable adjoint global mode of the linearised mean-flow dynamics can be exploited to design an active feedback control of the unsteady turbulent wake, which leads, under the adopted numerical framework, to completely suppress its low-frequency oscillation.

Powering a Commercial Datalogger by Energy Harvesting from Generated Aeroacoustic Noise

This paper reports the experimental demonstration of a wireless sensor node only powered by an aeroacoustic energy harvesting device, meant to be installed on an aircraft outside skin. New results related to the physical characterization of the energy conversion process are presented. Optimized interface electronics has been designed, which allows demonstrating aeroacoustic power generation by supplying a commercial wireless datalogger in conditions representative of an actual flight.

Broadband shock-cell noise signature identification using a wavelet-based method

Civil and military aircraft manufacturers need to respond to increasingly more restrictive standards about noise emission. In order to fulfil those requirements the mechanisms underlying the noise production need to be understood. The supersonic jets at the exit of aircraft engines are known to contain several sources of noise, namely: screech (military air-crafts), Broadband Shock–cell Associated Noise (BBSAN) and large–scale structures. The current work is focused on the study of BBSAN by means of a wavelet–based technique. The technique was applied to a pressure nearfield line array for the sake of extracting the signatures’ related to noise production mechanisms. Each ’signature’ characterized by its shape and time–scale. The signature found up to approximatively x/D = 6D has a ’wave–packet’ like shape. The same shape is obtained at farfield locations for forward angles. The Sound Pressure Level (SPL) was computed using the nearfield signatures and it is in good agreement with the SPL computed using the pressure signals. The ’wave–packet’ like shape ’signature’ is associated to BBSAN as it has the same characteristics: same SPL and forward angles directivity.

On the generation of the mean velocity profile for turbulent boundary layers with pressure gradient under equilibrium conditions.

This is the authors final draft of the paper presented at CEAS 2009 European Air and Space Conference, Manchester, 26-29 October 2009. Further information about CEAS events can be found at http://www.ceas.org/