A computationally efficient flow reconstruction technique is proposed, exploiting homogeneity in a given direction, to recreate three-dimensional instantaneous turbulent velocity fields from snapshots of two dimension planar fields. This methodology, termed as ’snapshot optimisation’ or SO, can help to provide 3D data sets for studies which are currently restricted by the limitations of experimental measurement techniques. The SO method aims at optimising the error between an inlet plane with a homogeneous direction and snapshots, obtained over a sufficient period of time, on the observation plane. The observations are carried out on a plane perpendicular to the inlet plane with a shared edge normal to the homogeneity direction. The method is applicable to all flows which display a direction of homogeneity such as cylinder wake flows, channel flow, mixing layer, and jet (axisymmetric). The ability of the method is assessed with two synthetic data sets, and three experimental PIV data sets. A good reconstruction of the large-scale structures is observed for all cases. The small-scale reconstruction ability is partially limited especially for higher dimensional observation systems. POD-based SO method and averaging SO variations of the method are shown to reduce discontinuities created due to temporal mismatch in the homogenous direction providing a smooth velocity reconstruction. The volumetric reconstruction is seen to capture large-scale structures for synthetic and experimental case studies. The algorithm run time is found to be in the order of a minute providing results comparable with the reference. Such a reconstruction methodology can provide important information for data assimilation in the form of initial condition, background condition, and 3D observations.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Adrian RJ (1984) Scattering particle characteristics and their effect on pulsed laser measurements of fluid flow: speckle velocimetry vs particle image velocimetry. Appl Opt 23(11):1690–1691
Braud C, Heitz D, Braud P, Arroyo G, Delville J (2004) Analysis of the wake mixing layer interaction using multiple plane PIV and 3d classical POD. Exp Fluids 37(1):95–104
Brücker C (1995) Digital-particle-image-velocimetry (DPIV) in a scanning light-sheet: 3d starting flow around a short cylinder. Exp Fluids 19(4):255–263
Brücker C, Hess D, Kitzhofer J (2012) Single-view volumetric PIV via high-resolution scanning, isotropic voxel restructuring and 3d least-squares matching (3d-LSM). Meas Sci Technol 24(2):024001
Casey TA, Sakakibara J, Thoroddsen ST (2013) Scanning tomographic particle image velocimetry applied to a turbulent jet. Phys Fluids 25(2):025102
Chandramouli P, Memin E, Heitz D, Laizet S (2018) Coarse large-eddy simulations in a transitional wake flow with flow models under location uncertainty. Comput Fluids 168:170–189
Chandramouli P, Heitz D, Memin E (2017) 4D turbulent wake reconstruction using large eddy simulation based variational data assimilation. 2nd workshop on data assimilation & CFD processing for particle image and tracking velocimetry. Delft
Le Dimet F-X, Talagrand O (1986) Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 38(2):97–110
D’adamo J, Papadakis N, Mémin E, Artana G (2007) Variational assimilation of POD low-order dynamical systems. J Turbul 8:N9
Foucaut J-M, Coudert S, Stanislas M, Delville J (2011) Full 3d correlation tensor computed from double field stereoscopic PIV in a high Reynolds number turbulent boundary layer. Exp Fluids 50(4):839–846
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):989–996
Ganapathisubramani B, Lakshminarasimhan K, Clemens NT (2008) Investigation of three-dimensional structure of fine scales in a turbulent jet by using cinematographic stereoscopic particle image velocimetry. J Fluid Mech 598:141–175
Gesemann S, Huhn F, Schanz D, Schröder A (2016) From noisy particle tracks to velocity, acceleration and pressure fields using B-splines and penalties. 18th international symposium on applications of laser and imaging techniques to fluid mechanics. Lisbon, pp 4–7
Gronskis A, Heitz D, Mémin E (2013) Inflow and initial conditions for direct numerical simulation based on adjoint data assimilation. J Comput Phys 242:480–497
Hamdi J, Assoum H, Abed-Meraïm K, Sakout A (2018) Volume reconstruction of an impinging jet obtained from stereoscopic-PIV data using POD. Eur J Mech B/Fluids 67:433–445
Kit E, Krivonosova O, Zhilenko D, Friedman D (2005) Reconstruction of large coherent structures from SPIV measurements in a forced turbulent mixing layer. Exp Fluids 39(4):761–770
Kähler CJ, Kompenhans J (2000) Fundamentals of multiple plane stereo particle image velocimetry. Exp Fluids 29(1):S070–S077
Laizet S, Lamballais E (2009) High-order compact schemes for incompressible flows: A simple and efficient method with quasi-spectral accuracy. J Comput Phys 228(16):5989–6015
Laizet S, Li N (2011) Incompact3d: a powerful tool to tackle turbulence problems with up to O(105) computational cores. Int J Numer Methods Fluids 67(11):1735–1757
Lions J (1971) Optimal control of systems governed by partial differential equations problèmes aux limites. Springer, Berlin
Mons V, Chassaing J-C, Gomez T, Sagaut P (2016) Reconstruction of unsteady viscous flows using data assimilation schemes. J Comput Phys 316:255–280
Robinson C (2015) Image assimilation techniques for large Eddy scale models: application to 3D reconstruction. Scientific, Université de Rennes 1, Rennes
Scarano F (2012) Tomographic PIV: principles and practice. Meas Sci Technol 24(1):012001
Schanz D, Gesemann S, Schröder A (2016) Shake-the-box: Lagrangian particle tracking at high particle image densities. Exp Fluids 57(5):70
Schneiders JFG, Scarano F (2016) Dense velocity reconstruction from tomographic PTV with material derivatives. Exp Fluids 57(9):139
de Silva CM, Philip J, Marusic I (2013) Minimization of divergence error in volumetric velocity measurements and implications for turbulence statistics. Exp Fluids 54(7):1557
Sodjavi K, Carlier J (2013) Experimental study of thermal mixing layer using variable temperature hot-wire anemometry. Exp Fluids 54(10):1599
Stansby PK (1974) The effects of end plates on the base pressure coefficient of a circular cylinder. Aeronaut J 78(757):36–37
Steinberg AM, Driscoll JF, Ceccio SL (2009) Three-dimensional temporally resolved measurements of turbulence-flame interactions using orthogonal-plane cinema-stereoscopic PIV. Exp Fluids 47(3):527–547
van Bladel J (1958) On Helmholtz’s theorem in finite regions. Midwestern Universities Research Association, & U.S. Atomic Energy Commission. Midwestern Universities Research Association, Madison, Wisconsin
Wang H, Gao Q, Wang S, Li Y, Wang Z, Wang J (2018) Error reduction for time-resolved PIV data based on Navier–Stokes equations. Exp Fluids 59(10):149
Wang C, Gao Q, Wang H, Wei R, Li T, Wang J (2016) Divergence-free smoothing for volumetric PIV data. Exp Fluids 57(1):15
Yang Y, Robinson C, Heitz D, Mémin E (2015) Enhanced ensemble-based 4DVar scheme for data assimilation. Comput Fluids 115:201–210
Zhang W, Hain R, Kähler CJ (2008) Scanning PIV investigation of the laminar separation bubble on a SD7003 airfoil. Exp Fluids 45(4):725–743
The authors would like to thank Anthony Guibert for providing the experimental data sets (cases 3 and 5), and Sylvain Laizet for the channel flow DNS data set.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Chandramouli, P., Memin, E., Heitz, D. et al. Fast 3D flow reconstructions from 2D cross-plane observations. Exp Fluids 60, 30 (2019). https://doi.org/10.1007/s00348-018-2674-1