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Job Record #15510
TitleAugmentation of PIV data of the flow around a bluff body
LocationFrance, Meudon
InternationalYes, international applications are welcome
Closure DateMonday, December 31, 2018
Title: Augmentation of experimental measurements of the flow around a bluff body
at high Reynolds numbers through data assimilation

Experimental fluid dynamics (EFD) is by essence the preferred means to obtain
information about real-world flows, such as flows around airfoils, bluff bodies
or in more complex geometries. However, data obtained from EFD approaches are
usually limited in space and time, and can not provide a full
description of the flow. Among EFD techniques, particle image velocimetry (PIV)
[1] appears nowadays as an attractive approach to obtain unsteady velocity
fields in a whole domain of interest in complex and turbulent flow
configurations. However, this technique is still limited in terms of spatial and
temporal resolutions, since higher resolved measurements are more likely to be
corrupted by noise. Various interpolation techniques [2,3] have been proposed in
order to complete sparse/poorly-resolved experimental data, but such methods do
not generally allow to satisfy all the physical constraints of the flow.

An emerging and promising approach to increase the resolution of PIV data
consists in combining them with computational fluid dynamics (CFD) tools, so
that the measurements are extrapolated, and their resolution and smoothness
improved, while being constrained by the numerically resolved conservation
laws of fluid motion. This so-called data assimilation (DA) [4] approach has
been implemented in two different ways so far. The first one consists in
minimizing the discrepancies between the PIV data and the predictions of a CFD
solver relying on optimal control theory [5,6]. While indeed providing enhanced
estimations of the measured flow fields, a drawback of this technique is the
need of the development of the adjoint model associated to the considered CFD
solver, which may be a tedious task. The second approach is based on Kalman
filtering [7,8], where the statistics related to the confidence in a numerical
prediction are sequentially updated in time using the available PIV data. This
technique does not require the coding of an adjoint model, and can thus be
readily implemented. However, a limitation of this approach may be the
relatively large computational cost required to propagate in time the covariance
matrix associated to the flow state, which is usually equivalent to 10-100
forward simulations. In a recent study [8], several approximations were proposed
to drastically lighten the burden of the covariance matrix propagation step in
the case of incompressible flows, thus greatly facilitating the application of
Kalman filtering to complex configurations.

The primary goal of this internship is the implementation of a technique similar
to that proposed in [8] and to assess the latter in the context of flow
estimation based on PIV data. The developed approach should allow to augment PIV
measurements at a limited computational cost (not superior to a few forward
simulations) and for various flow configurations. The first step of the
internship will consist in implementing the Kalman filter-based approach in a
solver for incompressible flows, which will be validated using synthetic data.
Improvements in terms of temporal and spatial resolutions will be
assessed and compared with some reference DA results that have already been
obtained with the adjoint-based approach [9]. In a second step, this technique
will be employed to improve flow estimation from available 3D time-resolved PIV
data on the flow around a wall-mounted cube in the presence of laminar or
turbulent boundary layer and at Reynolds numbers ranging from 2000 to 8000. The
developed approach should allow to denoise and increase the spatial resolution
of the data, in particular close to the wall regions.

[1] Raffel, Willert, Wereley and Kompenhans, Particle Image Velocimetry: A
practical Guide, Springer,2007.
[2] Gunes, Sirisup and Karniadakis, Gappy data: To Krig or not to Krig?, J.
Comput. Phys., 2006.
[3] Willcox, Unsteady flow sensing and estimation via the gappy proper
orthogonal decomposition,Comput. Fluids, 2006.
[4] Lewis, Lakshmivarahan and Dall, Dynamic Data Assimilation approach: A Least
Squares Approach, Cambridge University Press, 2006.
[5] Gronskis, Heitz and Mémin, Inflow and initial conditions for direct
numerical simulation based on adjoint data assimilation, J. Comput. Phys., 2013.
[6] Yegavian, Leclaire, Champagnat and Marquet, Performance assessment of PIV
super-resolution with adjoint-based data assimilation, 11 th Int, symp, on
particle image velocimetry, Santa Barbara, USA, 2015.
[7] Suzuki, Reduced-order Kalman-filtered hybrid simulation combining particle
tracking velocimetry and direct numerical simulation, J. Fluid Mech., 2012.
[8] Meldi, Poux, A reduced order model based on Kalman filtering for sequential
data assimilation of turbulent flows, J. Comput. Phys., 2017.
[9] Yegavian, Model-based approaches for flow estimation using Particle Image
Velocimetry, Thèse de doctorat de l'Université Paris-Saclay, Spécialité
Mécanique des fluides, 2017.

Period: February-August 2019

Profile of the candidate: Master 2/Engineer school student in Fluid Mechanics
Contact Information:
Please mention the CFD Jobs Database, record #15510 when responding to this ad.
NameVincent Mons
Email ApplicationYes
8 rue des Vertugadins
92190, Meudon, France
Record Data:
Last Modified14:26:45, Thursday, December 06, 2018

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