Closed-loop control of turbulent shear flows using reduced-order models – TUCOROM

The employed methods comprise feature extraction of the raw flow data, dynamic reduced-order modelling, coupling strategies for spatially distributed ROM, local linear embedding (LLE) for the manifolds and closure methods for the Galerkin methods.

We have advanced on control-oriented reduced-order modelling with respect to data analysis, modelling subgrid turbulence, to coupling strategies, to closures of dynamical systems. For details, see the report.

In the coming period (until T18), we expect the dedicated wind-tunnel for closed-looped control of the mixing-layer and other control plants to be in place. Moreover, the theoretical work makes good progress thanks to the IFFC visitor program.

One Springer book was finished, 5 Journal articles were accepted or have appeared. See report for details.

This proposal addresses a pressing need for the industrial flow control applications: the development of active control methods adapted to broadband turbulence dynamics with limited number of actuators and sensors. We propose to develop a strategy based on dynamic least-order models and target robust and real-time controllers. Control shall be tested in experimental demonstrators. In this project, we focus on shear flows of industrial interest accessible to reduced-order modeling and closed-loop control.

Turbulence control can often not directly suppress instabilities via linear control but relies on an exploitation of nonlinear mechanisms of the turbulence cascade. Mathematically, the effect of a single frequency on broadband dynamics constitutes a major challenge, both to modeling and control design. In principle, optimal control based on Navier-Stokes discretizations (white-box models) could provide control strategies. In practice, the large computational load prevents online capability in the foreseeable future. On the empirical side, currently identified black-box models can only predict the effect actuation and sensing at one discrete frequency, i.e. have to discard the enabling turbulence nonlinearities.

We pursue semi-empirical reduced-order models (ROM) as a gray-box compromise between too expensive white-box and too inaccurate black-box models. Starting point is a reduced-order Galerkin method based on the proper orthogonal decomposition (POD) with associated control design. Our efforts will address current challenges of ROM-based control of turbulent shear flows specifically related to broad-band dynamics and to convection effects. One key enabler is a novel stochastic frequency-band model for the normal cascade and Reynolds stress effects, inspired by turbulence theory. Another key enabler are domain decomposition techniques for the inverse cascade and convection effects, adopting CFD methods.

Three benchmark demonstrators are chosen among the configurations studied intensively in the Institute Pprime: coherent structure manipulation of a turbulent mixing layer, noise reduction of a turbulent jet and lift increase of an airfoil at high angle of attack.

This research program will synergize expertises from Pprime on the experimental approaches and numerical modelling and from the author on reduced-order modelling for turbulence control including his network of international collaborators. These collaborations with the leading experts of modeling and flow control shall be continued and strengthened in the proposed international visitor program. This program constitutes a key point of our proposal. This form of collaboration is essential to find solutions to the inherently interdisciplinary turbulence control challenges.

This program shall help to establish a leading-edge research group in closed-loop turbulence control targeting real-world industrial applications. Thus, internationally and interdisciplinary visible demonstrators for closed-loop turbulence control shall be established.