Proposal of control laws for turbulent skin friction reduction based on resolvent analysis

Abstract

This paper evaluates and modifies the so-called suboptimal control technique for turbulent skin friction reduction through a combination of low-order modelling and direct numerical simulation (DNS). In a previous study, Nakashima et al. (J. Fluid Mech., vol. 828, 2017, pp. 496–526) employed resolvent analysis to show that the efficacy of suboptimal control was mixed across spectral space when the streamwise wall shear stress (case ST) was used as a sensor signal, i.e. specific regions of spectral space showed drag increment. This observation suggests that drag reduction may be attained if control is applied selectively in spectral space. DNS results presented in the present study, however, do not show a significant effect on the flow with selective control. A posteriori analyses attribute this lack of efficacy to a much lower actuation amplitude in the simulations compared to model assumptions. Building on these observations, resolvent analysis is used to design and provide a preliminary assessment of modified control laws that also rely on sensing the streamwise wall shear stress. Control performance is then assessed by means of DNS. The proposed control laws generate as much as $10\,\%$ drag reduction, and these results are broadly consistent with resolvent-based predictions. The physical mechanisms leading to drag reduction are assessed via conditional sampling. It is shown that the new control laws effectively suppress the near-wall quasi-streamwise vortices. A physically intuitive explanation is proposed based on a separate evaluation of clockwise and anticlockwise vortices.

Predicting the response of turbulent channel flow to varying-phase opposition control: Resolvent analysis as a tool for flow control design

“…As a consequence, one of the questions posed at the beginning of this study can be answered in the affirmative: The results suggest that the resolvent model is indeed a suitable low-order flow model to design active flow control schemes for drag reduction in internal flows. This gives a formal foundation to recent studies which already use the resolvent model for controller design, such as [23], and provides a tool to systematically design future controllers. Since there is nothing particular about the choice of varying-phase opposition control, we expect that the resolvent model is able to approximate the DR trend of any control scheme with linear control law as long as the controlled mean velocity profile is not too drastically different from the uncontrolled one.…”

“…The resolvent model predicts that the effectiveness of opposition control in turbulent pipe flow strongly depends on the phase ∠Â d between the sensor measurement and the actuation response, but this prediction has not yet been confirmed in the full nonlinear system. The same resolvent model was subsequently used by Nakashima et al [22] to study the effect of suboptimal control in a turbulent channel flow and building on this work, Kawagoe et al [23] used resolvent analysis to design modified versions of the suboptimal control law. In this case the agreement between resolvent prediction and DNS was mixed: The study considered two modified controllers and good agreement between the model and DNS was observed for one of them, while the two predictions deviated for the other controller.…”

“…The literature results reviewed above suggest that linear models are able to capture at least aspects of the response of internal flows to control. With regard to resolvent-based models, it remains unclear to what extent the model is able to capture the response of the nonlinear system, since the available data set for comparison (compiled in [13,22,23]) is small and shows mixed agreement. Furthermore, previous resolvent-based control designs in internal flows have been limited to low Reynolds numbers and it remains to be clarified how the approach can be generalized to technologically relevant Re τ .…”

Resolvent analysis of turbulent channel flow with manipulated mean velocity profile

“…In paticular, resolvent analysis reveals which mode is amplified or suppressed in the spectral space when a specific control is applied. Based on such knowledge, Kawagoe et al (2019) proposed a modified feedback control law and confirmed its performance by DNS. Therefore, application of resolvent analysis will provide additional physical insight also for the case where the mean velocity profile is flattened similarly to Kühnen et al (2018).…”

Reduced order modeling of fluid flows using convolutional neural networks

“…The 【Review Paper】 representatives of those methods are Proper Orthogonal Decomposition (POD) (Lumley, 1967), which is essentially the same as the Principal Component Analysis (PCA), Dynamic Mode Decomposition (DMD) (Schmid, 2010), and resolvent analysis (McKeon and Sharma, 2010), which is similar to input-output analysis in classical control theory. Although we refer to recent review articles (Taira et al, 2017; for the details of these methods, mathematical relationships among them, and their applications, there is no doubt that these methods have substantially advanced our understanding of flow physics and provided important implications to flow control (e.g., Nakashima et al 2017;Kawagoe et al, 2019). However, these linear theory-based methods are not always suited to directly extract nonlinear dynamics.…”