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Topology optimization of transitional flows

Time: Fri 2023-12-15 10.00

Location: E3, Osquars backe 14, Stockholm

Language: English

Subject area: Engineering Mechanics

Doctoral student: Harrison Nobis , Teknisk mekanik

Opponent: Professor Paolo Luchini, Universita di Salerno, Italien

Supervisor: Professor Dan Henningson, ; Professor Philipp Schlatter,

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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.