Real-time control of wall-bounded turbulence

Abstract

The work presented in this dissertation focuses on the developed and implementation of real-time control techniques for turbulent wall-bounded flows, with the aim of achieving skin-friction drag reduction. After an initial control system was developed that utilized instantaneous wall-shear stress fluctuations, wall-pressure fluctuations were subsequently used as the input quantity to the real-time flow control systems considered in this dissertation. Furthermore, the control algorithm complexity was escalated from a relatively simple feedforward opposition control logic to an adaptive control strategy. The research presented in this dissertation is fully experimental in nature. Experimental activities were conducted in two main facilities. The bulk of testing was performed in the W-Tunnel at Delft University of Technology: an open-return wind tunnel, where a modular test section was integrated to perform experiments on zero-pressure–gradient turbulent boundary layer flows. A subset of measurements were conducted at the Center for International Cooperation in Long-Pipe Experiments (CICLoPE) at Bologna University, in Italy. Here, simultaneous measurements were conducted of velocity fluctuations in the logarithmic region and wall-pressure.

A stochastic spectral correlation analysis between wall-pressure fluctuations and velocity fluctuations in the logarithmic of a turbulent pipe flow reveal Reynolds-number– independence of the wall-pressure linear coherence spectrum. This is a first-of-its-kind result, hinting at the feasibility of scaling an input sensing strategy based on wall-pressure fluctuations from a low-Reynolds-number environment to operational engineering conditions.

An initial controller based on wall-shear stress fluctuations was developed to target drag-producing large-scale structures in the logarithmic region. The flow response was measured in terms of both the statistical (and spectral) response of the TBL flow to realtime control and in terms of the effect the control has not only on the friction coefficient, but also on the integral measures. This analysis revealed three main findings: (1) an attenuation of energy at streamwise wavelengths characteristic of large-scale motions, (2) a decrease in skin-friction and (3) an attenuation of the statistical integral measures of skin-friction (i.e. bulk production and FIK terms).

A similar control architecture was also implemented that employed wall-pressure (and wall-pressure–squared) as the input quantity. It was found that the wall-pressure–squared term improves the accuracy of an estimator enabling the prediction of off-the-wall velocity fluctuations from a wall-based position. Furthermore, its inclusion is essential, given that the linear term does not retain sufficient coherence over the relatively large streamwise extent separating input and actuation locations.

The final controller that was developed in the context of this dissertation is an adaptive one, relying on the Filtered-X Least Means Squares (Fx-LMS) algorithm. This strategy does not rely on a-priori system identification, as was the case for the previous two control strategies mentioned above. Instead, it automatically identifies the coefficients of the transfer functions relating input to output in the controller. For this study, this algorithm was deployed both to a flow case that was strongly modulated by cylinder vortex shedding and to a fully broadband turbulent boundary layer flow. In the former case, the controller readily identified the shedding frequency as the control target. For the latter, the controller converges to a situation where the large-scales were targeted and their intensity successfully attenuated.