Nørgaard, Sebastian Arlund

Denne afhandling demonstrerer anvendelsen af lattice Boltzmann metoden til topolo-gioptimeringsproblemer. Mere specifikt er fokus på problemer for hvilke tidsafhængige væskestrømninger er betydningsfulde for ydeevnen af de apparater der skal optimeres. Afhandlingen introducerer nye topologioptimeringsproblemer for både isotermiske og termiske væskestrømninger, og det demonstreres at topologioptimering kan tage højde for tidsafhængige strømningse˙ekter under optimeringsprocessen.De introducerede optimeringsproblemer løses ved hjælp af en gradient baseret fremgangsmåde, og design sensitiviteterne beregnes med en diskret adjoint metode. For nemmere at håndtere kompleksiteten af den diskrete adjoint metode, introduceres en fremgangmåde til at beregne den baseret på automatisk di˙erentiation, som kan tilpasses til enhver lattice Boltzmann model. For eksempel vises det at fremgangsmå-den nemt kan tilpasses til en termisk lattice Boltzmann model, på trods af at den er udledt for en isotermisk model.Endelig sammenlignes den forudsete adfærd af et optimeret design med den ækvivalente forudsigelse fra en kommerciel finite element løser. Det konstateres at lattice Boltzmann metodens svagt kompressible natur fører til en uoverensstemmelse mellem de forudsete resultater. Yderligere forskning er påkrævet for at afgøre hvilken forudsigelse der er mest nøjagtig, samt hvilke konsekvenser uoverensstemmelsen har for de optimerede design.This thesis demonstrates the application of the lattice Boltzmann method for topology optimization problems. Specifically, the focus is on problems in which time-dependent flow dynamics have significant impact on the performance of the devices to be optimized. The thesis introduces new topology optimization problems for both isothermal and thermal flows, and it is demonstrated that topology optimization can account for unsteady flow effects during the optimization process.The introduced optimization problems are solved using a gradient based approach, and the design sensitivities are computed using a discrete adjoint approach. To handle the complexity of the discrete adjoint approach more easily, a method for computing it based on automatic differentiation is introduced, which can be adapted to any lattice Boltzmann type method. For example, while it is derived in the context of an isothermal lattice Boltzmann model, it is shown that the method can be easily extended to a thermal model as well. Finally, the predicted behavior of an optimized design is compared to the equiva-lent prediction from a commercial finite element solver. It is found that the weakly compressible nature of the lattice Boltzmann method leads to a discrepancy in the predicted outcomes. Further research is required to determine which prediction is more accurate, and what implications the discrepancy has for the optimized designs

Online Research Database In Technology

Topology optimization and lattice Boltzmann methods

http://orbit.dtu.dk/ws/files/143487031/Sebastian_A_N_rgaard_PhD_Thesis.pdf

Topology optimization and lattice Boltzmann methods

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Online Research Database In Technology