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Topology optimization of unsteady flows using the spectral element method
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Stability, Transition and Control.ORCID iD: 0000-0002-7760-2523
KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Fluid Mechanics and Engineering Acoustics.ORCID iD: 0000-0001-9627-5903
Umeå Univ, Dept Comp Sci, Umeå, Sweden.;Karlstad Univ, Dept Math & Comp Sci, Karlstad, Sweden..
Umeå Univ, Dept Comp Sci, Umeå, Sweden..
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2022 (English)In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 239, p. 105387-, article id 105387Article in journal (Refereed) Published
Abstract [en]

We investigate the applicability of a high-order Spectral Element Method (SEM) to density based topology optimization of unsteady flows in two dimensions. Direct Numerical Simulations (DNS) are conducted relying on Brinkman penalization to describe the presence of solid within the domain. The optimization procedure uses the adjoint-variable method to compute gradients and a checkpointing strategy to reduce storage requirements. A nonlinear filtering strategy is used to both enforce a minimum length scale and to provide smoothing across the fluid-solid interface, preventing Gibbs oscillations. This method has been successfully applied to the design of a channel bend and an oscillating pump, and demonstrates good agreement with body fitted meshes. The precise design of the pump is shown to depend on the initial material distribution. However, the underlying topology and pumping mechanism is the same. The effect of a minimum length scale has been studied, revealing it to be a necessary regularization constraint for the oscillating pump to produce meaningful designs. The combination of SEM and density based optimization offer some unique challenges which are addressed and discussed, namely a lack of explicit boundary tracking exacerbated by the interface smoothing. Nevertheless, SEM can achieve equivalent levels of precision to traditional finite element methods, while requiring fewer degrees of freedom. Hence, the use of SEM addresses the two major bottlenecks associated with optimizing unsteady flows: computation cost and data storage.

Place, publisher, year, edition, pages
Elsevier BV , 2022. Vol. 239, p. 105387-, article id 105387
Keywords [en]
Topology optimization, Spectral element method, Unsteady, Direct numerical simulations, Length scale control, Non-linear filtering
National Category
Fluid Mechanics and Acoustics
Identifiers
URN: urn:nbn:se:kth:diva-312979DOI: 10.1016/j.compfluid.2022.105387ISI: 000793263500001Scopus ID: 2-s2.0-85126644608OAI: oai:DiVA.org:kth-312979DiVA, id: diva2:1661760
Note

QC 20220530

Available from: 2022-05-30 Created: 2022-05-30 Last updated: 2023-11-25Bibliographically approved
In thesis
1. Topology optimization of transitional flows
Open this publication in new window or tab >>Topology optimization of transitional flows
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Topologioptimering av strömning med omslag till turbulens
Abstract [en]

This thesis is concerned with the application of topology optimization in thedesign of structures that control fluids. A framework is developed in the high-order Spectral Element Method (SEM) code Nek5000, extending Nek5000 fromits original capabilities, performing Direct Numerical Simulations (DNS), toperforming density-based topology optimization. The optimization processemploys the adjoint-variable method for gradient computations and, at times, acheckpointing strategy to reduce data storage requirements.

The applicability of the SEM for topology optimization is assessed in2D, successfully applying the methodology to design a channel bend and anoscillating pump, and demonstrating strong agreement with body-fitted meshes. A nonlinear filtering strategy was used to enforce a minimum length scale andfound to be a necessary regularization constraint for meaningful pump designs.

Moving attention to laminar–turbulent transition, the framework is used tooptimize spanwise arrays of roughness elements that generate steady streaks inboundary layers to attenuate the growth of Tollmien-Schlichting (TS) waves.The optimized designs significantly dampen downstream TS wave amplitudecompared to a reference Miniature Vortex Generator (MVG) of similar size. Energy budget and local stability analyses are conducted to study the optimizeddesigns and the streaky baseflows they induce.

Topology optimization was used to design the macroscopic layout of Super-Hydrophobic Surfaces (SHSs) in channels to delay subcritical K-type transition. In a temporal setting, the optimized designs inhibit the growth of secondaryinstability modes. This methodology was extended to optimizing over anensemble of initial perturbations. In a spatial setting, the optimized surfacesexhibited an asymmetry in design between the top and bottom surfaces, breakingthe classical K-type symmetry. While this breaking of the symmetry was foundto be beneficial, the major contributing factor to the delay in transition was,again, the inhibition of the growth of secondary instability modes.

This framework was also applied to conjugate heat transfer problems. The thermal performance of a heat sink in a differentially heated cavity was alsoimproved by the application of topology optimization.

Abstract [sv]

Avhandlingen behandlar topologioptimering av strukturer i syfte att påverkavätske- och luftströmmingar. Ett ramverk har utvecklats i programvaran Nek5000,som numeriskt löser Navier–Stokes ekvationer med hjälp av en högre ordningensspektralelementmetod (SEM). Ramverket utökar Nek5000 ursprungliga kapa-citet så att densitetsbaserad topologioptimering kan utföras inom ramen fördirekta numeriska simuleringar (DNS).

Användingen av SEM för topologioptimering utvärderades först i två di-mensioner med en framgångsrik tillämpning av metodiken för utformning aven oscillerande pump. Resultatet verifierades genom beräkningar med kropps-anpassade nät. En icke-linjär filtreringsstrategi användes för att upprätthållaen minimalängdskala på den optimerade geometrin, en strategi som visade sigvara nödvändig för att erhålla meningsfulla pumpkonstruktioner.

Programvaran användes sedan för att optimera uppsättningar av ytstruk-turer som genererar s.k. stråk i laminära gränsskikt. Syftet med optimeringenvar att dämpa tillväxten av Tollmien–Schlichting- (TS) vågor. De optimeradestrukturerna dämpar TS-vågamplituden avsevärt bättre än tidigare användaminiatyrvirvelgeneratorer. De optimerade strukturerna och de nya basflöden deinducerar studerdes med energibudget- och lokala stabilitetsanalys.

Topologioptimering användes också för makroskopisk utformning av super-hydrofobiska ytor i kanalströmning i syfte att fördröja laminärt till turbulentomslag. Först betraktades en liten periodisk domän, och resultaten indikeraratt de optimerade ytorna minskar tillväxten av de sekundärinstabiliteter somorsakar omslag till turbulens. Sedan utökades domänen till att studera spa-tiellt utvecklande strömning. Där visar de optimerade ytorna en strukturellasymmetri mellan topp- och bottenytor, vilket bryter den klassiska symme-trin i omslag av s.k. K-typ. Även om detta symmetribrott visade sig varafördelaktigt, är den huvudsakliga orsaken till fördröjningen av omslaget återigenen tillväxtsbegränsning av den sekundära instabiliteten.

Det utvecklade Nek5000-ramverket användes också för att optimera värme-överföringsproblem. Den termiska prestandan av en kylfläns i en differentielltuppvärmd kavitet förbättrades genom att utforma kylflänsen med användandeav topologioptimering.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2023. p. 35
Series
TRITA-SCI-FOU ; 2023:57
Keywords
Direct Numerical Simulation, Topology Optimization, Laminar– Turbulent Transition, Spectral Element Method, Direkt numerisk simulering, topologioptimering, laminär–turbulent omslag, spektralelementmetod
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
urn:nbn:se:kth:diva-340054 (URN)978-91-8040-773-1 (ISBN)
Public defence
2023-12-15, E3, Osquars backe 14, Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2023-11-27 Created: 2023-11-25 Last updated: 2023-11-27Bibliographically approved

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Nobis, HarrisonSchlatter, PhilippHenningson, Dan S.

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