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Adjoint optimization of natural convection problems: differentially heated cavity
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-9627-5903
KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.ORCID iD: 0000-0001-7864-3071
2017 (English)In: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250, Vol. 31, no 5-6, p. 537-553Article in journal (Refereed) Published
Abstract [en]

Optimization of natural convection-driven flows may provide significant improvements to the performance of cooling devices, but a theoretical investigation of such flows has been rarely done. The present paper illustrates an efficient gradient-based optimization method for analyzing such systems. We consider numerically the natural convection-driven flow in a differentially heated cavity with three Prandtl numbers (Pr= 0.15 - 7 ) at super-critical conditions. All results and implementations were done with the spectral element code Nek5000. The flow is analyzed using linear direct and adjoint computations about a nonlinear base flow, extracting in particular optimal initial conditions using power iteration and the solution of the full adjoint direct eigenproblem. The cost function for both temperature and velocity is based on the kinetic energy and the concept of entransy, which yields a quadratic functional. Results are presented as a function of Prandtl number, time horizons and weights between kinetic energy and entransy. In particular, it is shown that the maximum transient growth is achieved at time horizons on the order of 5 time units for all cases, whereas for larger time horizons the adjoint mode is recovered as optimal initial condition. For smaller time horizons, the influence of the weights leads either to a concentric temperature distribution or to an initial condition pattern that opposes the mean shear and grows according to the Orr mechanism. For specific cases, it could also been shown that the computation of optimal initial conditions leads to a degenerate problem, with a potential loss of symmetry. In these situations, it turns out that any initial condition lying in a specific span of the eigenfunctions will yield exactly the same transient amplification. As a consequence, the power iteration converges very slowly and fails to extract all possible optimal initial conditions. According to the authors’ knowledge, this behavior is illustrated here for the first time.

Place, publisher, year, edition, pages
Springer, 2017. Vol. 31, no 5-6, p. 537-553
Keywords [en]
Adjoint optimization, Arnoldi method, Differentially heated cavity, Natural convection, Power iterations
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-218117DOI: 10.1007/s00162-016-0398-5ISI: 000414941500006Scopus ID: 2-s2.0-85033476369OAI: oai:DiVA.org:kth-218117DiVA, id: diva2:1160094
Note

QC 20171124

Available from: 2017-11-24 Created: 2017-11-24 Last updated: 2018-05-16Bibliographically approved

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Saglietti, ClioSchlatter, PhilippHenningson, Dan S.

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Stability, Transition and ControlLinné Flow Center, FLOW
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