Snapshot Lagrangian Proper Orthogonal Decomposition of Cylinder Wake Flow

2016 ◽  
Author(s):  
Jack S. Rossetti ◽  
John Dannenhoffer ◽  
Melissa A. Green
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Wake Flow ◽  
Cylinder Wake ◽  
Proper Orthogonal

Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition

2008 ◽  
Vol 610 ◽  
pp. 1-42 ◽  
Author(s):  
STEFAN G. SIEGEL ◽  
JÜRGEN SEIDEL ◽  
CASEY FAGLEY ◽  
D. M. LUCHTENBURG ◽  
KELLY COHEN ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Proper Orthogonal Decomposition ◽  
Limit Cycle ◽  
Dynamic Behaviour ◽  
Orthogonal Decomposition ◽  
Wake Flow ◽  
Data Sets ◽  
Cylinder Wake ◽  
Low Dimensional ◽  
Proper Orthogonal

For the systematic development of feedback flow controllers, a numerical model that captures the dynamic behaviour of the flow field to be controlled is required. This poses a particular challenge for flow fields where the dynamic behaviour is nonlinear, and the governing equations cannot easily be solved in closed form. This has led to many versions of low-dimensional modelling techniques, which we extend in this work to represent better the impact of actuation on the flow. For the benchmark problem of a circular cylinder wake in the laminar regime, we introduce a novel extension to the proper orthogonal decomposition (POD) procedure that facilitates mode construction from transient data sets. We demonstrate the performance of this new decomposition by applying it to a data set from the development of the limit cycle oscillation of a circular cylinder wake simulation as well as an ensemble of transient forced simulation results. The modes obtained from this decomposition, which we refer to as the double POD (DPOD) method, correctly track the changes of the spatial modes both during the evolution of the limit cycle and when forcing is applied by transverse translation of the cylinder. The mode amplitudes, which are obtained by projecting the original data sets onto the truncated DPOD modes, can be used to construct a dynamic mathematical model of the wake that accurately predicts the wake flow dynamics within the lock-in region at low forcing amplitudes. This low-dimensional model, derived using nonlinear artificial neural network based system identification methods, is robust and accurate and can be used to simulate the dynamic behaviour of the wake flow. We demonstrate this ability not just for unforced and open-loop forced data, but also for a feedback-controlled simulation that leads to a 90% reduction in lift fluctuations. This indicates the possibility of constructing accurate dynamic low-dimensional models for feedback control by using unforced and transient forced data only.

Optimal Feedback Control of Vortex Shedding Using Proper Orthogonal Decomposition Models

2001 ◽  
Vol 123 (3) ◽  
pp. 612-618 ◽  
Author(s):  
Sahjendra N. Singh ◽  
James H. Myatt ◽  
Gregory A. Addington ◽  
Siva Banda ◽  
James K. Hall
Keyword(s):  
Feedback Control ◽  
Proper Orthogonal Decomposition ◽  
Control Function ◽  
Orthogonal Decomposition ◽  
Wake Flow ◽  
Optimal Feedback Control ◽  
Stabilizing Feedback Control ◽  
Decomposition Models ◽  
System Mode ◽  
Proper Orthogonal

This paper treats the question of control of two-dimensional incompressible, unsteady wake flow behind a circular cylinder at Reynolds number Re=100. Two finite-dimensional lower order models based on proper orthogonal decomposition (POD) are considered for the control system design. Control action is achieved via cylinder rotation. Linear optimal control theory is used for obtaining stabilizing feedback control systems. An expression for the region of stability of the system is derived. Simulation results for 18-mode POD models obtained using the control function and penalty methods are presented. These results show that in the closed-loop system mode amplitudes asymptotically converge to the chosen equilibrium state for each flow model for large perturbations in the initial states.

scholarly journals Proper Orthogonal Decomposition and Spectral Analysis of a Wall-Mounted Square Cylinder Wake

2018 ◽  
Vol 10 ◽  
Author(s):  
Henrique Fanini Leite ◽  
Ana Cristina Avelar ◽  
Leandra de Abreu ◽  
Daniel Schuch ◽  
André Cavalieri
Keyword(s):  
Spectral Analysis ◽  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
Cylinder Wake ◽  
Square Cylinder ◽  
Proper Orthogonal
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