A realizable data-driven approach to delay bypass transition with control theory

Abstract

The current work presents a realizable method to control streaky disturbances in boundary layer flows and delay transition to turbulence by means of active flow control. Numerical simulations of the nonlinear transitional regime in a Blasius boundary layer are performed where streaks are excited in the boundary layer by means of a high level of free-stream turbulence. The occurring disturbances are measured by means of localized wall-shear-stress sensors and damped out using near-wall actuators, which resemble ring plasma actuators. Each actuator is powered by a time-varying signal whose amplitude is computed by processing signals from the sensors. The processed signal is the result of two control laws: the Linear Quadratic Gaussian regulator (LQG) and the Inverse Feed-Forward Control technique (IFFC). The use of the first control method, LQG, requires a state-space representation of the system dynamics, so the flow is described by means of a linear time-invariant operator that captures only the most relevant information of the dynamics and results in a reduced order model (ROM). The ROM is computed by means of the eigensystem realization algorithm (ERA), which is based on the impulse responses of the real system. Collecting such impulse responses may be unfeasible when considering free-stream turbulence because of the high dimensionality of the input forcing needed for a precise description of such a phenomenon. Here, a new method to identify the relevant system dynamics and generate the needed impulse responses is proposed, based on additional shear-stress measurements in an upstream location. Transfer functions between such measurements and other downstream sensors are obtained and allow the derivation of the ERA system, in a data-driven approach that would be realizable in experiments. Finally, the effectiveness of the technique in delaying bypass transition is shown. The work (i) presents a systematic and straightforward way to deal with high dimensional disturbances in order to build ROMs for a feasible control technique, and (ii) shows that even when considering practical constraints such as the type and size of actuators and sensors, it is possible to achieve at least as large delay of bypass transition as that obtained in more idealized cases found in literature.

On the role of actuation for the control of streaky structures in boundary layers

“…where N β is the number of discrete transverse wavenumbers considered, provides empirically identified impulse responses which may be directly applied in the ERA method for the construction of ROMs for designing LQG. This procedure based only on the measured signal, which permits the definition of LQG controllers even for experimental implementations, was firstly introduced in Morra et al (2019) and the reader is directed for such work for further details. Application of ERA for this problem results in a system with N ERA = 387 modes, which accurately reproduces the empirically identified transfer functions.…”

“…Figure 2 presents a sample of the prediction of z(t, x 3 ) from the measurements y(t, x 3 ) for the set-up considered in this paper, and validates the procedure. For more details concerning the application of the proposed methodology for the time-domain prediction of streaky structures induced by free-stream turbulence, the reader is referred to the work of Morra et al (2019), which firstly introduced the method for this type of application.…”

“…where q(x, t) = (u(x, t), v(x, t), w(x, t)) and p(x, t) are the velocity and pressure, respectively, at each time step t and position x = (x 1 , x 2 , x 3 ), taken in the cartesian coordinates. The same flow configuration of the parallel investigation of Morra et al (2019) will be considered here. A plate of semi-infinite length lies in the x 1 x 3 plane, where no-slip conditions are enforced at x 2 = 0.…”

“…This behaviour leads to an imperfect cancellation of the incoming streak. Since a destructive interference is the physical mechanism behind flow control of convectively unstable flows (Sasaki et al 2018a;Morra et al 2019), the f x2 -only and optimal forcing actuators lead to a lower performance in terms of transition delay. It should also be noted that the identified actuator presents a peak in its spatial support which is at a higher wall-normal location than the other two (as shown in figure 8); this is probably related to the higher peak of the streak it is identifying inside the flow.…”

Spectral proper orthogonal decomposition and resolvent analysis of near-wall coherent structures in turbulent pipe flows

“…The linearized Navier-Stokes operator here involves only the molecular viscosity, as in McKeon & Sharma (2010). Even though it has been shown in some works that inclusion of an eddy viscosity improves the agreement between resolvent modes and flow statistics (Morra et al 2019;Pickering et al 2020), the present choice is motivated by a more straightforward interpretation of the forcing f as the nonlinear terms; more detailed analysis of such forcing terms are currently being carried out by our group in related works (Nogueira et al 2020). All variables here are Fourier transformed in time, streamwise and azimuthal directions.…”