In this paper we propose a method to reconstruct the flow at a given time over a region of space using partial instantaneous measurements and full-space proper orthogonal decomposition (POD) statistical information. The procedure is tested for the flow past an open cavity. 3D and 2D POD analysis are used to characterize the physics of the flow. We show that the full 3D flow can be estimated from a 2D section at an instant in time provided that some 3D statistical information—i.e., the largest POD modes of the flow— is made available.
Issue Section:
Technical Papers
1.
Moin
, P.
, and Mahesh
, K.
, 1998, “Direct Numerical Simulation: A Tool in Turbulence Research T.R. Bewley and D.S. Henningson
,” Annu. Rev. Fluid Mech.
0066-4189, 30
, pp. 539
–578
.2.
Bonnet
, J. P.
, and Delville
, J.
, 2001, “Review of Coherent Structures in Turbulent Free Shear Flows and Their Possible Influence on Computational Methods
,” Appl. Sci. Res.
0003-6994, 66
(4
), pp. 333
–353
.3.
Bonnet
, J. P.
, and Delville
, J.
, 2001, “Review of Coherent Structures in Turbulent Free Shear Flows and Their Possible Influence on Computational Methods
,” Flow, Turbul. Combust.
1386-6184, 66
, pp. 333
–353
.4.
Lumley
, J. L.
, 1967, The Structure of Inhomogeneous Turbulent Flows in Atmospheric Turbulence and Wave Propagation
, A. M.
Yaglom
and V. I.
Tatarski
, eds., Nauka
, Moscow
, pp. 166
–178
.5.
Murray
, N.
, and Ukeiley
, L.
, 2002, “Estimating the Shear Layer Velocity Field Above an Open Cavity From Surface Pressure Measurements
,” AIAA Paper No. 2002–2866.6.
Picard
, C.
, and Delville
, J.
, 2000, “Pressure Velocity Coupling in a Subsonic Round Jet
,” Int. J. Heat Fluid Flow
0142-727X, 21
, pp. 359
–364
.7.
Boree
, J.
, 2003, “Extended Proper Orthogonal Decomposition: A Tool to Analyze Correlated Events in Turbulent Flows
,” Exp. Fluids
0723-4864, 35
(2
), pp. 188
–192
.8.
Taylor
, J.
, and Glauser
, M.
, 2002, “Toward Practical Flow Sensing and Control Via POD and lse-based low-dimensional tools
,” ASME 2002 Fluids Engineering Division Summer Meeting, Montreal, Quebec, 14–18 July.9.
Maurel
, S.
, Boree
, J.
, and Lumley
, J. L.
, 2001, “Extended Proper Orthogonal Decomposition: Application to Jet/Vortex Interaction
,” Flow, Turbul. Combust.
1386-6184, 67
, pp. 125
–136
.10.
Rempfer
, D.
, 2000, “On low-dimensional Galerkin Models for Fluid Flow
,” Theor. Comput. Fluid Dyn.
0935-4964, 14
, pp. 75
–88
.11.
Lusseyran
, F.
, Faure
, T.
, Eschenbrenner
, C.
, and Fraigneau
, Y.
, 2004, “Shear Layer Instability and Frequency Modes Inside an Open Cavity
,” Proceedings ICTAM 2004
, Varsaw, Poland, 15–21 Aug.12.
Williams
, D. R.
, Rowley
, C. W.
, Fabris
, D.
, Colonius
, T.
, and Murray
, R. M.
, 2002, “Model-Based Control of Cavity Oscillations, Part I: Experiments
,” in Proceedings 40th AIAA Aerospace Meeting
, AIAA
.13.
Podvin
, B.
, 2001, “Low-Order P.O.D-Based Models for the Flow in a Differentially Heated Cavity
,” Phys. Fluids
1070-6631, 13
(11
), pp. 3204
–3214
.14.
Lumley
, J. L.
, 1967, “The Structure of Inhomogeneous Turbulent Flows
,” in Atmospheric Turbulence and Radio Wave Propagation
, A. M
Iaglom
and V. I.
Tatarski
, eds., Nauka
, Moscow, pp. 221
–227
.15.
Berkooz
, G.
, Holmes
, P.
, and Lumley
, J. L.
, 1993, “The Proper Orthogonal Decomposition in the Analysis of Turbulent Flows
,” Annu. Rev. Fluid Mech.
0066-4189, 25
, pp. 539
–575
.16.
Holmes
, P.
, Lumley
, J. L.
, and Berkooz
, G.
, 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry
, Cambridge University Press
, Cambridge, MA.17.
Sirovich
, L.
, 1987, “Turbulence and the Dynamics of Coherent Structures Part I: Coherent Structures
,” Q. Appl. Math.
0033-569X, 45
(3
), pp. 561
–571
.18.
Gadouin
, E.
, Le Quéré
, P.
, and Daube
, O.
, 2001, “A General Methodology for Investigating Flow Instability in Complex Geometries: Application to Natural Convection in Enclosures
,” Int. J. Numer. Methods Fluids
0271-2091, 37
(2
), pp. 175
–208
.19.
Leonard
, B. P.
, 1979, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream interpolation
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 19
, pp. 59
–98
.20.
Hirsch
, C.
, 1987, Numerical Computation of Internal and External Flows
, Wiley
, New York.21.
Rockwell
, D.
, and Naudascher
, E.
, 1979, “Self-Sustained Oscillations of Impinging Free Shear Layers
,” Annu. Rev. Fluid Mech.
0066-4189, 11
, pp. 67
–94
.22.
Lusseyran
, F.
, Rambert
, A.
, Gougat
, P.
, Fraigneau
, Y.
, Elcafsi
, A.
, and Quénot
, G.
, 2002, “Relationship Between Fourier-Modes and Spatial Structures in a Cavity—Boundary Layer Interaction at Moderate Reynolds Numbers
,” in Proceedings 11th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics
, Lisboa.23.
Rockwell
, D.
, 1977, “Prediction of Oscillation Frequencies for Unstable Flow Past Cavities
,” ASME J. Fluids Eng.
0098-2202, 99
, pp. 294
–300
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