### Motivation and philosophy

Fluid flow manipulation and control is ubiquitous and has become a crucial tool for enhancing aircraft maneuver capabilities, reducing fuel consumption, mitigating aeroacoustic noise or preventing buffeting, to name just a few examples. Beyond aeronautics, flow control is also of interest for ground commercial vehicles to reduce the drag, hence the fuel consumption, at cruise speed. This is further motivated by ever more stringent CO2 emission restrictions whose major reduction is achieved by a decrease in the fuel consumption. Other environmentally motivated examples include the reduction of the noise emitted by open cavities in high speed flows, as encountered between two cars of a high-speed train or in the landing gear system of commercial aircraft.

Adaption, or control, of a complex system is hence of very wide applicability in everyday life and a leap towards its generalization would make a large impact given the expected improvement in performance and robustness of the design.

### Presentation of the team

The team has developed an expertise in all aspects of flow control, covering plasma actuators, wind tunnel experiments, sophisticated visualization techniques (time- and space-resolved PIV, Laser Doppler Anemometry), numerical simulations and methodological developments. Different control strategies have also been considered, ranging from a time-delayed control to stabilize unstable periodic orbits, experimental open loop control of the shear layer of an open cavity flow, reduction of the skin friction of a simulated turbulent flow over a flat plate using a neural network, reduction of the recirculation bubble at the back of a Ahmed body in LES simulations, etc.

### Scope and research activities

The FLOCON group is interested in a wide range of flow control aspects, from theoretical developments to experimental demonstrators and numerical simulations; from open- to closed-loop, for both laminar and turbulent flows, separated or not.

In many applications, the most efficient control strategy generally consists in stabilizing a natural solution of the deterministic flow equations (e.g. the Navier-Stokes equations), although such solutions may be unstable without external action and therefore never observed in usual conditions. When successful, the cost of the control is actually evanescent to zero in ideal conditions, while it remains of the order of the noise amplitude in real environments. As an example, stabilizing the steady laminar solution of the cylinder wake is well-known to be the most efficient way to significantly reduce drag and torques on the rigid body.

However, such strategies are most often demanding, because an a priori knowledge of the system phase space, which is of infinite dimension, would be welcome prior any modeling attempts be pursued. Input-output strategies, much simpler to implement in experimental configurations, are however a possible way to overcome the difficulty of identifying a simple though efficient reduced model. In our group, we explore(d) several strategies for input-output-based feedback control.

#### The cavity flow

A challenging flow configuration is provided by open cavity flows, in which energetic self-sustained oscillations may develop as the result of a global instability, resulting from a Hopf bifurcation beyond a critical value of the Reynolds number. Physically, the cavity flow oscillations result from the feedback loop formed by impinging shear-layer vortices and the instantaneous feedback through the pressure field. In many applications, such oscillations are a powerful source of noise, and are adversely interacting with the solid structure, resulting in a premature fatigue of materials. In such non-linearly driven dynamics, the suppression of the oscillations and restoration of the steady base-flow are the foreseen goal.

*Cavity flow: snapshot from the experimental facility.*

In the phase portrait of the system, the steady base-flow reduces to an (unstable) fixed point, and the control scheme is here aimed at stabilizing the fixed point, while starting from the limit cycle associated with the unsteady regime. In this view, a time-delayed feedback control, based on an input signal designed from the time-delayed output signal, sounds natural. The command must deal with several delays included in the loop (delays from the flow dynamics and from the processing line), and mainly involves two parameters, the time delay and the output-input gain. Direct numerical oscillations of the cavity flow not only proved such a law to be highly efficient in suppressing the self-sustained oscillations of the flow, but also demonstrated the command to be evanescent once the goal is reached, while being rather simple to implement experimentally.

See Rizi et al, *International Journal of Flow Control* **6** (2015) pp 171-187.

Experimentally, a test-section has been implemented for the control of self-sustained oscillations in open cavity flows. The command is applied to the flow, at the leading wall, through a DBD plasma actuator, while the output signal can be provided by a set of pressure sensors placed at the trailing wall of the cavity. The closed loop line is based on a D-Space system, programmed under Simulink.

The experimental facility was also used to learn the flow response to periodic forcing. Preliminary results show that beyond a critical forcing amplitude, when the forcing frequency is not too far from the natural dominant frequency of the shear layer, the shear layer oscillations lock on the forcing frequency. The locking onset depends on the forcing frequency, as expected for the non-linear locking of two oscillators. At frequencies smaller than about half the natural frequency, the shear layer locks on harmonics of the forcing frequency, indicating that the shear layer transfers energy from low frequencies to higher most amplified frequencies. At frequencies larger than about twice the natural frequency, no locking is observed anymore. Deeper insights on non-linear modes coupling and design of a control loop are expected from this preliminary study.

See C. Douay, PhD Thesis (2014).