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

Abstract

This work deals with the closed-loop control of streaky structures induced by free-stream turbulence (FST) in a zero-pressure gradient, transitional boundary layer, by means of localized sensors and actuators. A linear quadratic gaussian regulator is considered along with a system identification technique to build reduced-order models for control. Three actuators are developed with different spatial supports, corresponding to a baseline shape with only vertical forcing, and to two other shapes obtained by different optimization procedures. A computationally efficient method is derived to obtain an actuator which aims to induce the exact structures which are inside the boundary layer, given in terms of their first spectral proper orthogonal decomposition (SPOD) mode, and an actuator that maximizes the energy of induced downstream structures. Two free-stream turbulence levels were evaluated, corresponding to 3.0% and 3.5%, and closed-loop control is applied in large-eddy simulations of transitional boundary layers. All three actuators lead to significant delays in the transition to turbulence and were shown to be robust to mild variations in the free-stream turbulence levels. Differences are understood in terms of the SPOD of actuation and FST-induced fields along with the causality of the control scheme when a cancellation of disturbances is considered. The actuator optimized to generate the leading downstream SPOD mode, representing the streaks in the open-loop flow, leads to the highest transition delay, which can be understood due to its capability of closely cancelling structures in the boundary layer. However, it is shown that even with the actuator located downstream of the input measurement it may become impossible to cancel incoming disturbances in a causal way, depending on the wall-normal position of the output and on the actuator considered, which limits sensor and actuator placement capable of good closed-loop performance.

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

“…Moreover, reconstructions of flow fluctuations from a limited number of sensors are also possible using the resolvent operator (Towne et al 2020), which opens possibilities for closed-loop control of turbulent flows. As the lift-up effect studied here is also the basis of bypass transition in boundary layers (Andersson, Berggren & Henningson 1999;Brandt 2014), extension of control methods used in bypass transition (Sasaki et al 2019) is a promising direction for the control of wall-bounded turbulence.…”

The colour of forcing statistics in resolvent analyses of turbulent channel flows

“…In fact, the low-rank characteristic of the forcing reduces the number of unknown parameters to identify, which reduces the complexity of the identification problem and increases the accuracy of the estimation (Hjalmarsson & Mårtensson 2007). Moreover, the found low-rank approximation of the forcing can be helpful to the control community for the design or placement of a counteracting forcing as actuator, following ideas similar to Sasaki et al (2020).…”

“…Moreover, the found low-rank approximation of the forcing can be helpful to the control community for the design or placement of a counteracting forcing as actuator, following ideas similar to Sasaki et al. (2020).…”

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

“…Finally, it can be concluded that the performance of the best LQG result is better than those of the best IFFC thanks to the possibility of increasing the estimation accuracy through the estimation weights, which allows to slightly compensate for the reverse causality between the wall shear-stress measurements and the dynamics of the streaks. Moreover, it appears that the limitation caused by the structure of the plant, including the location of sensors and actuators and their shapes, is more critical than the choice of control technique, and thus is the key design challenge (as further discussed in the parallel work Sasaki et al (2019)).…”

“…This is efficient to excite or cancel streaks A realizable data-driven approach to delay bypass transition 883 A33-11 due to the lift-up effect. A detailed analysis on the effect of the actuator shape is presented in Sasaki et al (2019), which is the parallel work to the present one. The outputs are computed as…”