Networked-oscillator-based modeling and control of unsteady wake flows

Abstract

A networked-oscillator-based analysis is performed to examine and control the transfer of kinetic energy for periodic bluff body flows. The dynamics of energy fluctuations in the flow field are described by a set of oscillators defined by conjugate pairs of spatial proper orthogonal decomposition (POD) modes. To extract the network of interactions among oscillators, impulse responses of the oscillators to amplitude and phase perturbations are tracked. Tracking small energy inputs and using linear regression, a networked-oscillator model is constructed that reveals energy exchange among the modes. The model captures the nonlinear interactions among the modal oscillators through a linear approximation. A large collection of system responses is aggregated to capture the general network structure of oscillator interactions. The present networked-oscillator model describes the modal perturbation dynamics more accurately than the empirical Galerkin reduced-order model. The linear network model for nonlinear dynamics is subsequently utilized to design a model-based feedback controller. The controller suppresses the modal amplitudes that result in wake unsteadiness leading to drag reduction. The strength of the proposed approach is demonstrated for a canonical example of two-dimensional unsteady flow over a circular cylinder. The present formulation enables the characterization of modal interactions to control fundamental energy transfers in unsteady bluff body flows.

Thel1-based sparsification of energy interactions in unsteady lid-driven cavity flow

“…In addition, sparsity identification methods have been applied, so far, to relatively small Galerkin models (Loiseau & Brunton 2018), and it is not yet understood if these can be utilised to identify and extract relevant interactions in larger models in agreement with the established picture of energy interactions in turbulent flows. In this sense, our approach is closer to the recent work of Nair & Taira (2015), Taira, Nair & Brunton (2016) and Nair, Brunton & Taira (2018). These authors employed network-theoretic sparsification approaches (Newman 2018) to identify key vortex-to-vortex interactions in two-dimensional homogeneous turbulence, obtaining sparse models that capture the essential physics of unsteady fluid flow with a reduced number of interactions between the same large number of states.…”

Cluster-based feedback control of turbulent post-stall separated flows

“…Such modulation results from a sub-optimal pressure recovery closer to the trailing edge. Previous studies with model-based feedback control have shown that suppressing this low-frequency modulation can yield additional performance benefits (Nair, Brunton & Taira 2018). There is an opportunity for a model-free extension to suppress the low-frequency modulation using the current feedback control strategy using additional clusters (G-Michael, Gunzburger & Peterson 2018).…”

Identifying vortical network connectors for turbulent flow modification

“…2015; Hadjighasem et al. 2016), oscillator-based representation of the energy fluctuations (Nair, Brunton & Taira 2018), time series of fluid-flow properties (Scarsoglio, Cazzato & Ridolfi 2017), triadic interactions in turbulence (Gürcan 2017; Gürcan, Li & Morel 2020) and the effects of perturbations on time-varying vortical flows (Yeh, Gopalakrishnan Meena & Taira 2020) have been studied using a network-theoretic framework. The formulations have been extended to characterize various turbulent flows, including two-dimensional isotropic turbulence (Taira, Nair & Brunton 2016), turbulent premixed flames and combustors (Godavarthi et al.…”

“…In recent years, network formulations have been introduced to quantify and capture the interactions in fluid flows. The induced velocity amongst vortical elements (Nair & Taira 2015), Lagrangian motion of fluid elements (Ser-Giacomi et al 2015;Hadjighasem et al 2016), oscillator-based representation of the energy fluctuations (Nair, Brunton & Taira 2018), time series of fluid-flow properties (Scarsoglio, Cazzato & Ridolfi 2017), triadic interactions in turbulence (Gürcan 2017;Gürcan, Li & Morel 2020) and the effects of perturbations on time-varying vortical flows (Yeh, Gopalakrishnan Meena & Taira 2020) have been studied using a network-theoretic framework. The formulations have been extended to characterize various turbulent flows, including two-dimensional isotropic turbulence (Taira, Nair & Brunton 2016), turbulent premixed flames and combustors (Godavarthi et al 2017;Singh et al 2017;Krishnan et al 2019b), wall turbulence (Iacobello, Scarsoglio & Ridolfi 2018b), mixing in turbulent channel flow (Iacobello et al 2018a(Iacobello et al , 2019a and isotropic magnetohydrodynamic turbulence (Gürcan 2018).…”