arXiv subjects

Marek Morzyński

Publications and source records attributed to Marek Morzyński.

9 recordsLinked to original sources

arXiv2021

Cluster-based hierarchical network model of the fluidic pinball -- Cartographing transient and post-transient, multi-frequency, multi-attractor behaviour

We propose a self-supervised cluster-based hierarchical reduced-order modelling methodology to model and analyse the complex dynamics arising from a sequence of bifurcations for a two-dimensional incompressible flow of the unforced fluidic pinball. The hierarchy is guided by a triple decomposition separating a slowly varying base flow, dominant shedding and secondary flow structures. All these flow components are kinematically resolved by a hierarchy of clusters, starting with the base flow in the first layer, resolving the vortex shedding in the second layer and distilling the secondary flow structures in the third layer. The transition dynamics between these clusters is described by a directed network, called the cluster-based hierarchical network model (HiCNM) in the sequel. Three consecutive Reynolds number regimes for different dynamics are considered: (i) periodic shedding at $Re=80$, (ii) quasi-periodic shedding at $Re=105$, and (iii) chaotic shedding at $Re=130$, involving three unstable fixed points, three limit cycles, two quasi-periodic attractors and a chaotic attractor. The HiCNM enables identifying the transient and post-transient dynamics between multiple invariant sets in a self-supervised manner. Both the global trends and the local structures during the transition are well resolved by a moderate number of hierarchical clusters. The proposed reduced-order modelling provides a visual representation of transient and post-transient, multi-frequency, multi-attractor behaviour and may automate the identification and analysis of complex dynamics with multiple scales and multiple invariant sets.

physics.flu-dyn↗

arXiv2021

Dynamiques transitoires de sillage dans le pinball fluidique

In this work, we are interested in the transient dynamics of a fluid configuration consisting of three fixed cylinders whose axes distribute over an equilateral triangle in transverse flow << fluidic pinball >>. As the Reynolds number is increased on the route to chaos, its transient dynamics tell us about the contribution of the elementary degrees of freedom of the system to the lift and drag coefficients.

physics.flu-dyn↗

arXiv2021

Reduced-order modeling of the fluidic pinball

The fluidic pinball is a geometrically simple flow configuration with three rotating cylinders on the vertex of an equilateral triangle. Yet, it remains physically rich enough to host a range of interacting frequencies and to allow testing of control laws within minutes on a laptop. The system has multiple inputs (the three cylinders can independently rotate around their axis) and multiple outputs (downstream velocity sensors). Investigating the natural flow dynamics, we found that the first unsteady transition undergone by the wake flow, when increasing the Reynolds number, is a Hopf bifurcation leading to the usual time-periodic vortex shedding phenomenon, typical of cylinder wake flows, in which the mean flow field preserves axial symmetry. We extract dynamically consistent modes from the flow data in order to built a reduced-order model (ROM) of this flow regime. We show that the main dynamical features of the primary Hopf bifurcation can be described by a non-trivial lowest-order model made of three degrees of freedom.

physics.flu-dyn↗

arXiv2021

Route to Chaos in the Fluidic Pinball

The fluidic pinball has been recently proposed as an attractive and effective flow configuration for exploring machine learning fluid flow control. In this contribution, we focus on the route to chaos in this system without actuation, as the Reynolds number is smoothly increased. It was found to be of the Newhouse-Ruelle-Takens kind, with a secondary pitchfork bifurcation that breaks the symmetry of the mean flow field on the route to quasi-periodicity.

physics.flu-dyn↗

arXiv2021

Galerkin force model for transient and post-transient dynamics of the fluidic pinbal

We propose an aerodynamic force model associated with a Galerkin model for the unforced fluidic pinball, the two-dimensional flow around three equal cylinders with one radius distance to each other. The starting point is a Galerkin model of a bluff-body flow. The force on this body is derived as a constant-linear-quadratic function of the mode amplitudes from first principles following the pioneering work of Noca (1997, 1999) and Liang & Dong (2014). The force model is simplified for the mean-field model of the unforced fluidic pinball (Deng et al. 2020) using symmetry properties and sparse calibration. The model is successfully applied to transient and post-transient dynamics in different Reynolds number regimes: the periodic vortex shedding after the Hopf-bifurcation and the asymmetric vortex shedding after the pitchfork bifurcation comprising six different Navier-Stokes solutions. We foresee many applications of the Galerkin force model for other bluff bodies and flow control.

physics.flu-dyn↗

arXiv2021

Stabilization of the fluidic pinball with gradient-enriched machine learning control

We stabilize the flow past a cluster of three rotating cylinders, the fluidic pinball, with automated gradient-enriched machine learning algorithms. The control laws command the rotation speed of each cylinder in an open- and closed-loop manner. These laws are optimized with respect to the average distance from the target steady solution in three successively richer search spaces. First, stabilization is pursued with steady symmetric forcing. Second, we allow for asymmetric steady forcing. And third, we determine an optimal feedback controller employing nine velocity probes downstream. As expected, the control performance increases with every generalization of the search space. Surprisingly, both open- and closed-loop optimal controllers include an asymmetric forcing, which surpasses symmetric forcing. Intriguingly, the best performance is achieved by a combination of phasor control and asymmetric steady forcing. We hypothesize that asymmetric forcing is typical for pitchfork bifurcated dynamics of nominally symmetric configurations. Key enablers are automated machine learning algorithms augmented with gradient search: explorative gradient method for the open-loop parameter optimization and a gradient-enriched machine learning control (gMLC) for the feedback optimization. gMLC learns the control law significantly faster than previously employed genetic programming control. The gMLC source code is freely available online.

physics.flu-dyn↗

arXiv2020

Explorative gradient method for active drag reduction of the fluidic pinball and slanted Ahmed body

We address a challenge of active flow control: the optimization of many actuation parameters guaranteeing fast convergence and avoiding suboptimal local minima. This challenge is addressed by a new optimizer, called explorative gradient method (EGM). EGM alternatively performs one exploitive downhill simplex step and an explorative Latin hypercube sampling iteration. Thus, the convergence rate of a gradient based method is guaranteed while, at the same time, better minima are explored. For an analytical multi-modal test function, EGM is shown to significantly outperform the downhill simplex method, the random restart variant, Latin hypercube sampling, Monte Carlo iterations and the genetic algorithm. EGM is applied to minimize the net drag power of the two-dimensional fluidic pinball benchmark with three cylinder rotations as actuation parameters. The net drag power is reduced by $40\%$ employing direct numerical simulations at a Reynolds number of $100$ based on the cylinder diameter. This optimal actuation leads to $98\%$ drag reduction employing Coanda forcing for boat tailing and partial stabilization of vortex shedding. The price is an actuation energy corresponding to $58\%$ of the unforced parasitic drag power. EGM is also used to minimize drag of the $35^\circ$ slanted Ahmed body employing distributed steady blowing with 10 inputs. $17\%$ drag reduction are achieved using Reynolds-Averaged Navier-Stokes simulations (RANS) at the Reynolds number $Re_H=1.9 \times 10^5$ based on the height of the Ahmed body. The optimal actuation emulates boat tailing by inward-directed blowing with velocities which are comparable to the oncoming velocity. We expect that EGM will be employed as efficient optimizer in many future active flow control plants.

physics.flu-dyn↗

arXiv2020

Cluster-based network model

We propose an automatable data-driven methodology for robust nonlinear reduced-order modelling from time-resolved snapshot data. In the kinematical coarse-graining, the snapshots are clustered into few centroids representable for the whole ensemble. The dynamics is conceptualized as a directed network, where the centroids represent nodes and the directed edges denote possible finite-time transitions. The transition probabilities and times are inferred from the snapshot data. The resulting cluster-based network model constitutes a deterministic-stochastic grey-box model resolving the coherent-structure evolution. This model is motivated by limit-cycle dynamics, illustrated for the chaotic Lorenz attractor and successfully demonstrated for the laminar two-dimensional mixing layer featuring Kelvin-Helmholtz vortices and vortex pairing, and for an actuated turbulent boundary layer with complex dynamics. Cluster-based network modelling opens a promising new avenue with unique advantages over other model-order reductions based on clustering or proper orthogonal decomposition.

physics.flu-dyn↗

arXiv2020

Towards human-interpretable, automated learning of feedback control for the mixing layer

We propose an automated analysis of the flow control behaviour from an ensemble of control laws and associated time-resolved flow snapshots. The input may be the rich data base of machine learning control (MLC) optimizing a feedback law for a cost function in the plant. The proposed methodology provides (1) insights into control landscape which maps control laws to performance including extrema and ridge-lines, (2) a catalogue of representative flow states and their contribution to cost function for investigated control laws and (3) a visualization of the dynamics. Key enablers are classification and feature extraction methods of machine learning. The analysis is successfully applied to the stabilization of a mixing layer with sensor-based feedback driving an upstream actuator. The fluctuation energy is reduced by 26\%. The control replaces unforced Kelvin-Helmholtz vortices with subsequent vortex pairing by higher-frequency Kelvin-Helmholtz structures of lower energy. These efforts target a human interpretable, fully automated analysis of MLC identifying qualitatively different actuation regimes, distilling corresponding coherent structures, and developing a digital twin of the plant.

physics.flu-dyn↗