Simulation of a Feedback-Controlled Cylinder Wake Using Double Proper Orthogonal Decomposition

2007 ◽  
Author(s):  
Stefan Siegel ◽  
Kelly Cohen ◽  
Jürgen Seidel ◽  
Selin Aradag ◽  
Thomas McLaughlin
Keyword(s):  
Proper Orthogonal Decomposition ◽  
Orthogonal Decomposition ◽  
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.

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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