Abstract
For successful feedback flow control, an accurate estimation of the flow state is necessary. Proper Orthogonal Decomposition (POD) has been used to achieve this. However, if the POD modes are derived from a set of snapshots obtained from one flow condition only, the resulting modes will become less and less valid for a flow field that is for example altered by the effect of feedback flow control. In the past, a shift mode has been added to account for the change in the mean flow. Here, we present a new scheme that allows for the derivation of shift modes for all of the original POD modes. This DPOD mode set thus may span a range of flow conditions that are different in forcing, Reynolds number or other parameters affecting the modes. Artificial Neural Network Estimation (ANNE) allows for real time monitoring of the time coefficients associated with these DPOD modes.
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References
Noack, B. R.; Afanasiev, K.; Morzynski, M.; Tadmor, G., Thiele, F., ‘A hierarchy of low-dimensional models for the transient and post-transient cylinder wake’, J. Fluid Mechanics, 497, 2003
Luchtenburg, M., G. Tadmor, O. Lehmann, B.R. Noack, R. King, M. Morzyinski, ‘Tuned POD Galerkin models for transient feedback regulation of the cylinder wake’, 44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, AIAA-2006-1407, 2006
M. Bergmann, L. Cordier, and J.-P. Brancher, ‘Optimal rotary control of the cylinder wake using POD reduced order model’, 2nd AIAA Flow Control Conference, AIAA 2004-2323, 2004
Siegel, S.; Cohen, K.; McLaughlin, T., ‘Feedback Control Of A Circular Cylinder Wake In Experiment And Simulation (invited)’, 33rd AIAA Fluid Dynamics Conference, Orlando, AIAA 2003-3569, 2003
Siegel, S., Cohen, K., Seidel, J., McLaughlin, T., ‘Short Time Proper Orthogonal Decomposition for State Estimation of Transient Flow Fields’, 43rd AIAA Aerospace Sciences Meeting, Reno, AIAA2005-0296, 2005
Siegel, S., Cohen, K., Seidel, J., McLaughlin, T., ‘Two Dimensional Simulations Of A Feedback Controlled D-Cylinder Wake’, AIAA Fluid Dynamics Conf Toronto, ON, CA, AIAA 2005-5019, 2005
Holmes P., Lumley, J. L., Berkooz, G., 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry, Cambridge University Press
Cohen, K., Siegel S., and McLaughlin T.,“A Heuristic Approach to Effective Sensor Placement for Modeling of a Cylinder Wake”, Computers and Fluids, Volume 35, Issue 1, January 2006, pp. 103–120.
Nelles, O., Nonlinear System Identification, Springer-Verlag, Berlin, Germany, 2001, Chap. 11.
Nørgaard, M., Ravn., O., Poulsen, N.K., Hansen, L.K., Neural Networks for Modeling and Control of Dynamic Systems, 3rd printing, Springer-Verlag, London, U.K., 2003, Chap. 2.
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© 2007 Springer-Verlag Berlin Heidelberg
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Siegel, S., Cohen, K., Seidel, J., McLaughlin, T. (2007). State Estimation of Transient Flow Fields Using Double Proper Orthogonal Decomposition (DPOD). In: King, R. (eds) Active Flow Control. Notes on Numerical Fluid Mechanics and Multidisciplinary Design (NNFM), vol 95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71439-2_7
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DOI: https://doi.org/10.1007/978-3-540-71439-2_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71438-5
Online ISBN: 978-3-540-71439-2
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