Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session H29: Nonlinear Dynamics: Model Reduction |
Hide Abstracts |
Chair: Themistoklis Sapsis, MIT Room: 310 |
Monday, November 23, 2015 10:35AM - 10:48AM |
H29.00001: A variational principle for the extraction of time-dependent modes associated with transient instabilities Themistoklis Sapsis, Hessam Babaee We introduce a variational formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of phase space associated with finite-time instabilities. While these instabilities have finite lifetime they can play a crucial role either by altering the system dynamics through the activation of other instabilities, or by creating sudden nonlinear energy transfers that lead extreme responses. However, their essentially transient character makes their description a particularly challenging task. Here we develop a variational framework that focus on the optimal approximation of the system dynamics over finite-time intervals under the orthonormal basis constraint. This variational formulation results in differential equations that evolve a time-dependent basis so that it optimally approximates the most unstable directions over finite times. [Preview Abstract] |
Monday, November 23, 2015 10:48AM - 11:01AM |
H29.00002: Time-dependent modes associated with finite time instabilities in unstable fluid flows Hessam Babaee, Themistoklis Sapsis We apply a recently developed variational formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures the directions associated with finite-time instabilities. We demonstrate the capability of the method for two problems: the Orr-Sommerfeld/Squire operator and the vertical jet in crossflow. In the first problem we demonstrate that the time-dependent subspace captures the strongly transient non-normal energy growth (in the short time regime), while for longer times the modes capture the expected asymptotic behavior of the dynamics. We also consider the vertical jet in crossflow at the jet Reynolds number of $Re_j = 900$. We demonstrate that the subspace instantaneously captures the most unstable directions of the time-dependent flow. We explore the connection between the shear flow, non-normal growth and persistent instabilities. [Preview Abstract] |
Monday, November 23, 2015 11:01AM - 11:14AM |
H29.00003: Nonlinear reduced order models for fluids systems using extended dynamic mode decomposition Scott Dawson, Clarence Rowley The development of techniques that can extract simple, accurate, and computationally tractable models from fluids data is of importance for enhanced prediction, control, and fundamental understanding of such systems. Modeling approaches can take the form of identifying modes upon which to project the governing equations (e.g., Galerkin projection onto a set of POD modes), or in determining (or calibrating) the temporal dynamics from data, such as in dynamic mode decomposition (DMD), or various modifications to Galerkin projection. Here, we demonstrate that choosing appropriate observables (such as linear and quadratic monomials of POD coefficients) can allow for nonlinear behavior to be accurately captured using the recently proposed extended DMD algorithm. For cylinder wake data spanning the transient and vortex shedding limit cycle regimes, the identified nonlinear models show significant improvement in accuracy and robustness over standard DMD and Galerkin projection. Compared to traditional DMD, this approach should also allow for a better global approximation of the Koopman operator for the dynamical system. We make connections with other related model identification algorithms, and additionally investigate the performance of the method upon spatially sparse and noisy data. [Preview Abstract] |
Monday, November 23, 2015 11:14AM - 11:27AM |
H29.00004: Network Structure of Two-Dimensional Homogeneous Turbulence Kunihiko Taira, Aditya Nair, Steven Brunton The network structure of two-dimensional incompressible homogeneous turbulence is characterized by highlighting the vortical interactions in the flow field. By analyzing the degree distribution of the turbulence network, it is observed that turbulence has an underlying scale-free network that describes how vortical structures are interconnected. In the network-theoretic framework, we can identify strong vortices that serve as hubs that are strongly connected to other vortical hubs. Smaller and weaker eddies are found to be predominantly influenced by the neighboring hubs. These observations complement previous knowledge of turbulence based on vortex dynamics. The time evolution of the fluid flow network shows that the scale-free property is achieved when turbulence is sustained but is not observed when the flow reaches a laminar regime through dissipation. The finding that turbulence has a scale-free interaction network enables us to identify the type of perturbations that turbulence is resilient against. These insights from network analysis enable us to examine how the behavior of turbulent flows can be modified. [Preview Abstract] |
Monday, November 23, 2015 11:27AM - 11:40AM |
H29.00005: Introducing Spectral Proper Orthogonal Decomposition: Superior identification of coherent structures in turbulent flows Moritz Sieber, Kilian Oberleithner, C. Oliver Paschereit The identification of coherent structures from experimental or numerical data is an essential task in fluid dynamics. Today's commonly used approaches employ the construction of a modal base that captures the dominant flow structures. Typically, these modes are either energy (POD) or frequency (Fourier decomposition) ranked. However, there are numerous examples where the relevant coherent structures occur at low energies or at multiple frequencies. To overcome the shortcoming of the current ``rigid'' approaches, we propose a new method - Spectral Proper Orthogonal Decomposition (SPOD). It is based on classical POD and it applies to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. It allows for a continuous shifting from the energy ranked POD to the frequency ranked Fourier decomposition by changing a single parameter. In this presentation we demonstrate the SPOD on experimental data of some flow cases, where the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures that might be hidden in noise or spread over a wide frequency range. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD is still comparable to the snapshot POD. [Preview Abstract] |
Monday, November 23, 2015 11:40AM - 11:53AM |
H29.00006: Dynamic reconstruction of sub-sampled data using Optimal Mode Decomposition Jakub Krol, Andrew Wynn The Nyquist-Shannon criterion indicates the sample rate necessary to identify information with particular frequency content from a dynamical system. However, in experimental applications such as the interrogation of a flow field using Particle Image Velocimetry (PIV), it may be expensive to obtain data at the desired temporal resolution. To address this problem, we propose a new approach to identify temporal information from undersampled data, using ideas from modal decomposition algorithms such as Dynamic Mode Decomposition (DMD) and Optimal Mode Decomposition (OMD). The novel method takes a vector-valued signal sampled at random time instances (but at Sub-Nyquist rate) and projects onto a low-order subspace. Subsequently, dynamical characteristics are approximated by iteratively approximating the flow evolution by a low order model and solving a certain convex optimization problem. Furthermore, it is shown that constraints may be added to the optimization problem to improve spatial resolution of missing data points. The methodology is demonstrated on two dynamical systems, a cylinder flow at Re $=$ 60 and Kuramoto-Sivashinsky equation. In both cases the algorithm correctly identifies the characteristic frequencies and oscillatory structures present in the flow. [Preview Abstract] |
Monday, November 23, 2015 11:53AM - 12:06PM |
H29.00007: Data-driven reduced order model for prediction of wind turbine wake dynamics Mithu Debnath, Christian Santoni, Mario A. Rotea, Stefano Leonardi, Giacomo Valerio Iungo Wind turbine wakes are highly turbulent flows for which coherent vorticity structures lead to complex dynamics and instabilities. In this study, high-fidelity large eddy simulations (LES) data of a utility-scale wind turbine is analyzed through proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) in order to detect the main dynamic contributions to the temporal and spatial evolution of a wind turbine wake. Eigenmodes obtained from modal decomposition are clustered as a function of their physical origin, energy, spectral contribution and growth rate. A subset of the eigenmodes is then selected accordingly to a customized objective function in order to represent an optimal blend of the different dynamic contributions. The selected eigenmodes are embedded in a time-marching algorithm enabling the prediction of the wake velocity field and loads on downstream turbines. This reduced order model is characterized by a relatively low rank compared to the dimension of the physical space of the original LES data, thus by a low computational cost. The reduced order model is then embedded within a Kalman filter in order to perform data assimilation of new available observations in order to maximize agreement between the forecast and observations. [Preview Abstract] |
Monday, November 23, 2015 12:06PM - 12:19PM |
H29.00008: Network-based representation of energy transfer in unsteady separated flow Aditya Nair, Kunihiko Taira We construct a network-based representation of energy pathways in unsteady separated flows using a POD-Galerkin projection model. In this formulation, we regard the POD modes as the network nodes and the energy transfer between the modes as the network edges. Based on the energy transfer analysis performed by Noack {\it et al.} (2008), edge weights are characterized on the interaction graph. As an example, we examine the energy transfer within the two-dimensional incompressible flow over a circular cylinder. In particular, we analyze the energy pathways involved in flow transition from the unstable symmetric steady state to periodic shedding cycle. The growth of perturbation energy over the network is examined to highlight key features of flow physics and to determine how the energy transfer can be influenced. Furthermore, we implement closed-loop flow control on the POD-Galerkin model to alter the energy interaction path and modify the global behavior of the wake dynamics. The insights gained will be used to perform further network analysis on fluid flows with added complexity. [Preview Abstract] |
Monday, November 23, 2015 12:19PM - 12:32PM |
H29.00009: Principal interval decomposition framework for POD-based model reduction of convective flows Omer San, Jeff Borggaard A principal interval decomposition (PID) framework is proposed to build more reliable reduced-order models for unsteady flow problems. The PID method optimizes the lengths of the time windows over which proper orthogonal decomposition (POD) is performed and can be highly effective in building reduced-order models for convective problems. The performance of these POD models with and without using the PID approach is investigated by applying these methods to the unsteady lock-exchange flow problem modeled by solving the Boussinesq equations in vorticity-streamfunction formulation. This benchmark problem exhibits a strong shear flow induced by a temperature jump and results in the Kelvinâ€“Helmholtz instability. This is considered a challenging benchmark problem for the development of reduced order models. The predictive performance of our model is then analyzed over a wide range of computational modeling and physical parameters. It is shown that the PID approach provides a significant improvement in accuracy over the standard Galerkin POD reduced-order model. Our numerical assessment of the PID shows that it may represent a reliable model reduction tool for convection-dominated, unsteady-flow problems. [Preview Abstract] |
Monday, November 23, 2015 12:32PM - 12:45PM |
H29.00010: Reduced-order modeling of the flow around a high-lift configuration with unsteady Coanda blowing Richard Semaan, Laurent Cordier, Bernd Noack, Pradeep Kumar, Marco Burnazzi, Gilles Tissot We propose a low-dimensional POD model for the transient and post-transient flow around a high-lift airfoil with unsteady Coanda blowing over the trailing edge. This model comprises the effect of high-frequency modulated blowing which mitigates vortex shedding and increases lift. The structure of the dynamical system is derived from the Navier-Stokes equations with a Galerkin projection and from subsequent dynamic simplifications. The system parameters are determined with a data assimilation (4D-Var) method. The boundary actuation is incorporated into the model with actuation modes following Graham et al.(1999); Kasnako\u{g}lu et al.(2008). As novel enabler, we show that the performance of the POD model significantly benefits from employing additional actuation modes for different frequency components associated with the same actuation input. In addition, linear, weakly nonlinear and fully nonlinear models are considered. The current study suggests that separate actuation modes for different actuation frequencies improve Galerkin model performance, in particular with respect to the important base-flow changes. [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2023 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
1 Research Road, Ridge, NY 11961-2701
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700