Skip to main content Accessibility help

Reduced-order Kalman-filtered hybrid simulation combining particle tracking velocimetry and direct numerical simulation

  • Takao Suzuki (a1)

The capability of state-of-the-art techniques integrating experimental and computational fluid dynamics has been expanding recently. In our previous study, we have developed a hybrid unsteady-flow simulation technique combining particle tracking velocimetry (PTV) and direct numerical simulation (DNS) and demonstrated its capability at low Reynolds numbers. Similar approaches have also been proposed by a few groups; however, applying algorithms of this type generally becomes more challenging with increasing Reynolds number because the time interval of the frame rate for particle image velocimetry (PIV) becomes much greater than the required computational time step, and the PIV/PTV resolution tends to be lower than that necessary for computational fluid dynamics. To extend the applicability to noisy time-resolved PIV/PTV data, the proposed algorithm optimizes the data input temporally and spatially by introducing a reduced-order Kalman filter. This study establishes a framework of the Kalman-filtered hybrid simulation and proves the concept by tackling a planar-jet flow at as an example. We evaluate the filtering functions as well as convergence of the proposed algorithm by comparing with the existing PTV–DNS hybrid simulation, and show some techniques available to hybrid velocity fields by analysing vortical motion in the shear layers of the jet.

Hide All
1. Alvarez, L., Castaño, C. A., Garca, M., Krissian, K., Mazorra, L., Salgado, A. & Sánchez, J. 2007 Variational second-order flow estimation for PIV sequences. Exp. Fluids 44 (2), 291304.
2. Bewley, T. R. & Liu, S. 1998 Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365, 305349.
3. Bewley, T. R., Moin, P. & Temam, R. 2001 DNS-based predictive control of turbulence: an optimal benchmark for feedback algorithm. J. Fluid Mech. 447, 179225.
4. Bucy, R. S. & Joseph, P. D. 1968 Filtering for Stochastic Processes with Applications to Guidance. John Wiley & Sons.
5. Charonko, J. J., King, C. V., Smith, B. L. & Vlachos, P. P. 2010 Assessment of pressure field calculations from particle image velocimetry measurements. Meas. Sci. Technol. 21 (10), 105401.
6. Druault, P., Guibert, P. & Alizon, F. 2005 Use of proper orthogonal decomposition for time interpolation from PIV data: application to the cycle-to-cycle variation analysis of in-cylinder engine flows. Exp. Fluids 39 (6), 10091023.
7. Evensen, G. 1994 Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99 (C5), 1014310162.
8. Evensen, G. 2009 Data Assimilation: The Ensemble Kalman Filter, 2nd edn. Springer.
9. Fujii, K. 2005 Progress and future prospects of CFD in aerospace – wind tunnel and beyond. Prog. Aerosp. Sci. 41, 455470.
10. Fujisawa, N., Tanahashi, S. & Srinivas, K. 2005 Evaluation of pressure field and fluid forces on a circular cylinder with and without rotational oscillation using velocity data from PIV measurement. Meas. Sci. Technol. 16 (4), 989996.
11. Fukumori, I. & Malanotte-Rizzoli, P. 1995 An approximate Kalman filter for ocean data assimilation: an example with an idealized Gulf Stream model. J. Geophys. Res. 100 (C4), 67776793.
12. Grinstein, F. F. 2001 Vortex dynamics and entrainment in rectangular free jets. J. Fluid Mech. 437, 69101.
13. Gunes, H. & Rist, U. 2007 Spatial resolution enhancement/smoothing of stereo-particle-image-velocimetry data using proper-orthogonal-decomposition-based and Kriging interpolation methods. Phys. Fluids 19, 064101.
14. Heitz, D., Héas, P., Mémin, E. & Carlier, J. 2008 Dynamic consistent correlation-variational approach for robust optical flow estimation. Exp. Fluids 45 (4), 595608.
15. Hogberg, M., Bewley, T. R. & Henningson, D. S. 2003 Linear feedback control and estimation of transition in plane channel flow. J. Fluid Mech. 481, 149175.
16. Jameson, A. & Martinelli, L. 1998 Mesh refinement and modelling errors in flow simulation. AIAA J. 36 (5), 676686.
17. Julier, S. J. & Uhlmann, J. K. 1997 A new extension of the Kalman filter to nonlinear systems. In Proceedings of the 1997 Meeting of the SPIE Aerosense Conference (ed. Kadar, Ivan ). Society of Photographic Instrumentation Engineers.
18. Kalman, R. E. 1960 A new approach to linear filtering and prediction problems. Trans. ASME: J. Basic Engng 82 (D), 3545.
19. Kampanis, N. A. & Ekaterinaris, J. A. 2006 A staggered grid, high-order accurate method for the incompressible Navier–Stokes equations. J. Comput. Phys. 215 (2), 589613.
20. Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59, 308323.
21. Kurtulus, D. F., Scarano, F. & David, L. 2007 Unsteady aerodynamic forces estimation on a square cylinder by TR-PIV. Exp. Fluids 47 (2), 185196.
22. Liu, X. & Katz, J. 2006 Instantaneous pressure and material acceleration measurements using a four-exposure PIV system. Exp. Fluids 41 (2), 227240.
23. Ma, Q., Rossmann, T., Kinght, D. & Jaluria, Y. 2007 Utilization of laser-based measurements and numerical simulation for analysis of fluid-thermal systems by dynamic data driven application systems. AIAA paper 2007-0875.
24. Ma, X., Karniadakis, G. E., Park, H. & Gharib, M. 2003 DPIV-driven flow simulation: a new computational paradigm. Proc. R. Soc. Lond. A 459, 547565.
25. Misaka, T., Obayashi, S. & Endo, E. 2008 Measurement-integrated simulation of clear air turbulence using a four-dimensional variational method. J. Aircraft 45 (4), 12171229.
26. Moser, R. D. & Rogers, M. M. 1993 The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence. J. Fluid Mech. 247, 275320.
27. Murai, Y., Nakada, T., Suzuki, T. & Yamamoto, F. 2007 Particle tracking velocimetry applied to estimate the pressure field around a Savonius turbine. Meas. Sci. Technol. 18 (8), 24912503.
28. Navarrete, J. A. & Meade, A. J. 2004 Fusion of experimental data and mathematical models in the simulation of aerodynamic coefficients. AIAA paper 2004-0952.
29. Nishino, K., Kasagi, K. & Hirata, M. 1989 Three-dimensional particle tracking velocimetry based on automated digital image processing. Trans. ASME: J. Fluids Engng 111, 384391.
30. Nisugi, K., Hayase, T. & Shirai, A. 2004 Fundamental study of hybrid wind tunnel integrating numerical simulation and experiment in analysis of flow field. JSME Intl J. Ser. B 47 (3), 593604.
31. van Oudheusden, B. W., Scarano, F. & Casimiri, E. W. 2006 Non-intrusive load characterization of an aerofoil using PIV. Exp. Fluids 40 (6), 988992.
32. Ruhnau, P., Kohlberger, T., Schnörr, C. & Nobach, H. 2005 Variational optical flow estimation for particle image velocimetry. Exp. Fluids 38 (1), 2132.
33. Ruhnau, P., Stahl, A. & Schnörr, C. 2007 Variational estimation of experimental fluid flows with physics-based spatio-temporal regularization. Meas. Sci. Technol. 18 (3), 755763.
34. Sirisup, S., Karniadakis, G. E., Yang, Y. & Rockwell, D. 2004 Wave-structure interaction: simulation driven by quantitative imaging. Proc. R. Soc. Lond. A 460, 729755.
35. Stanley, S. A., Sarkar, S. & Mellado, J. P. 2002 A study of the flow field evolution and mixing in a planar turbulent jet using direct numerical simulation. J. Fluid Mech. 450, 377407.
36. Stengel, R. F. 1994 Optimal Control and Estimation. Dover.
37. Suzuki, T., Ji, H. & Yamamoto, F. 2009a Unsteady PTV velocity field past an aerofoil solved with DNS. Part 1. Algorithm of hybrid simulation and hybrid velocity field at . Exp. Fluids 47 (6), 957976.
38. Suzuki, T., Ji, H. & Yamamoto, F. 2010 Instability waves in a low-Reynolds-number planar jet investigated with hybrid simulation combining particle tracking velocimetry and direct numerical simulation. J. Fluid Mech. 655, 344379.
39. Suzuki, T., Sanse, A., Mizushima, T. & Yamamoto, F. 2009b Unsteady PTV velocity field past an aerofoil solved with DNS. Part 2. Validation and application at Reynolds numbers up to . Exp. Fluids 47 (6), 977994.
40. Takehara, K., Adrian, R. J., Etoh, G. T. & Christensen, K. T. 2000 A Kalman tracker for super-resolution PIV. Exp. Fluids 29 (7), S34S41.
41. Tinoco, E. N. 2008 Validation and minimizing CFD uncertainty for commercial aircraft applications. AIAA paper 2008–6902.
42. Tsorng, S. J., Capart, H., Lai, J. S. & Young, D. L. 2006 Three-dimensional tracking of the long time trajectories of suspended particles in a lid-driven cavity flow. Exp. Fluids 40 (2), 314328.
43. Venturi, D. & Karniadakis, G. E. 2004 Gappy data and reconstruction procedures for flow past a cylinder. J. Fluid Mech. 519, 315336.
44. Watanabe, S., Kuchi-ishi, S., Aoyama, T., Fujita, N., Kato, H. & Matsuo, Y. 2009 Digital/analog hybrid wind tunnel: a prototype system toward EFD/CFD integration. In 4th Symposium on Integrating CFD and Experiments in Aerodynamics.
45. Yamagata, T., Hayase, T. & Higuchi, H. 2008 Effect of feedback data rate in PIV measurement-integrated simulation. J. Fluid Sci. Technol. 3 (4), 477487.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed