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Assimilation and extension of particle image velocimetry data of turbulent Rayleigh–Bénard convection using direct numerical simulations

Bauer, Christian and Schiepel, Daniel and Wagner, Claus (2022) Assimilation and extension of particle image velocimetry data of turbulent Rayleigh–Bénard convection using direct numerical simulations. Experiments in Fluids, 63 (22), pp. 1-17. Springer. doi: 10.1007/s00348-021-03369-3. ISSN 0723-4864.

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Official URL: http://link.springer.com/content/pdf/10.1007/s00348-021-03369-3.pdf

Abstract

A novel method for assimilating and extending measured turbulent Rayleigh-Bénard convection data is presented, which relies on the fractional step method also used to solve the incompressible Navier-Stokes equation in direct numerical simula-tions. Our approach is used to make measured tomographic particle image velocimetry (tomo PIV) fields divergence-free and to extract temperature fields. Comparing the time average of the extracted temperature fields with the temporally averaged temperature field, measured using particle image thermometry in a subdomain of the flow geometry, shows that extracted fields correlate well with measured fields with a correlation coefficient of CTT=0.84 . Additionally, extracted temperature fields as well as divergence-free velocity fields serve as initial fields for subsequent direct numerical simulations with and without feedback which generate small-scale turbulence initially absent in the experimental data. Although the tomo PIV data set was spatially under-resolved and did not include any information on the boundary layers, the here-proposed method successfully generates velocity and temperature fields featuring small-scale turbulence and thermal as well as kinetic boundary layers, without disturbing the large-scale circulation contained in the original experimental data significantly. The latter is underpinned by high vertical and horizontal velocity correlation coefficients--computed from velocity fields averaged in time and horizontal x-direction obtained from the measurement and from the simulation without feedback--of Cvv=0.92and Cww=0.91 representing the large-scale structure. For simulations with feedback, the generated velocity fields resemble the experimental data increasingly well for higher feedback gain values, whereas the temperature fluctuation intensity deviates noticeably from the values obtained from a direct numerical simulation without feedback for gain values \alpha \ge 1 . Thus, a feedback gain of \alpha=0.1 was found optimal with correlation coefficients of Cvv=0.96 and Cww=0.95 as well as a realistic temperature fluctuation intensity profile. The xt-averaged temperature fields obtained from the direct numerical simulations with and without feedback correlate somewhat less with the extracted temperature field (CTT~0.6), which is presumably caused by spatially under-resolved and temporally oscillating initial tomo PIV fields reflected by the extracted temperature field.

Item URL in elib:https://elib.dlr.de/147972/
Document Type:Article
Title:Assimilation and extension of particle image velocimetry data of turbulent Rayleigh–Bénard convection using direct numerical simulations
Authors:
AuthorsInstitution or Email of AuthorsAuthor's ORCID iD
Bauer, ChristianChristian.Bauer (at) dlr.dehttps://orcid.org/0000-0003-1838-6194
Schiepel, Danieldaniel.schiepel (at) dlr.dehttps://orcid.org/0000-0002-3703-3514
Wagner, ClausClaus.Wagner (at) dlr.deUNSPECIFIED
Date:4 January 2022
Journal or Publication Title:Experiments in Fluids
Refereed publication:Yes
Open Access:Yes
Gold Open Access:No
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:63
DOI :10.1007/s00348-021-03369-3
Page Range:pp. 1-17
Editors:
EditorsEmailEditor's ORCID iD
UNSPECIFIEDSpringerUNSPECIFIED
Publisher:Springer
ISSN:0723-4864
Status:Published
Keywords:data assimilation, Rayleigh-Bénard convection, direct numerical simulation, temperature field extraction
HGF - Research field:Aeronautics, Space and Transport
HGF - Program:Transport
HGF - Program Themes:Rail Transport
DLR - Research area:Transport
DLR - Program:V SC Schienenverkehr
DLR - Research theme (Project):V - NGT BIT
Location: Göttingen
Institutes and Institutions:Institute for Aerodynamics and Flow Technology > Ground Vehicles
Deposited By: Bauer, Christian
Deposited On:05 Jan 2022 08:36
Last Modified:05 Jan 2022 08:36

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