In density-based topology optimization of flow problems, flow in the solid domain is generally inhibited using a penalization approach. Setting an appropriate maximum magnitude for the penalization traditionally requires manual tuning to find an acceptable compromise between flow solution accuracy and design convergence. In this work, three penalization approaches are examined, the Darcy (D), the Darcy with Forchheimer (DF), and the newly proposed Darcy with filtered Forchheimer (DFF) approach. Parameter tuning is reduced by analytically deriving an appropriate penalization magnitude for accuracy of the flow solution. The Forchheimer penalization is found to be required to reliably predict the accuracy of the flow solution. The state-of-the-art D and DF approaches are improved by developing the novel DFF approach, based on a spatial average of the velocity magnitude. In comparison, the parameter selection in the DFF approach is more reliable, as convergence of the flow solution and objective convexity are more predictable. Moreover, a continuation approach on the maximum penalization magnitude is derived by numerical inspection of the convexity of the pressure drop response. Using two-dimensional optimization benchmarks, the DFF approach reliably finds accurate flow solutions and is less prone to converge to inferior local optima.

The design of high-performing fluid and thermal devices is crucial for many aerospace
applications such as heat exchangers and flow manifolds. These systems often operate
under transient conditions, adding another layer of complexity to their design. Conventional
design principles have limitations as they depend on engineers to propose the
principal structure. In this dissertation, topology optimization (TO) is investigated as a method to design transient flow and thermal devices. To date, the use of TO for transient flow or thermal problems remains limited to experts in the field. Performing successful optimization heavily relies on the tuning of model and optimization parameters. By systematically investigating and improving the algorithms, their parameters and their characteristics, this thesis provides engineers with guidelines for their use.

In topology optimization of transient problems, memory requirements and computational costs often become prohibitively large due to the backward-in-time adjoint equations. Common approaches such as the Checkpointing (CP) and Local-in-Time (LT) algorithms reduce memory requirements by dividing the temporal domain into intervals and by computing sensitivities on one interval at a time. The CP algorithm reduces memory by recomputing state solutions instead of storing them. This leads to a significant increase in computational cost. The LT algorithm introduces approximations in the adjoint solution to reduce memory requirements and leads to a minimal increase in computational effort. However, we show that convergence can be hampered using the LT algorithm due to errors in approximate adjoints. To reduce memory and/or computational time, we present two novel algorithms. The hybrid Checkpointing/Local-in-Time (CP/LT) algorithm improves the convergence behavior of the LT algorithm at the cost of an increased computational time but remains more efficient than the CP algorithm. The Parallel-Local-in-Time (PLT) algorithm reduces the computational time through a temporal parallelization in which state and adjoint equations are solved simultaneously on multiple intervals. State and adjoint fields converge concurrently with the design. The effectiveness of each approach is illustrated with two-dimensional density-based topology optimization problems involving transient thermal or flow physics. Compared to the other discussed algorithms, we found a significant decrease in computational time for the PLT algorithm. Moreover, we show that under certain conditions, due to the use of approximations in the LT and PLT algorithms, they exhibit a bias toward designs with short characteristic times. Finally, based on the required memory reduction, computational cost, and convergence behavior of optimization problems, guidelines are provided for selecting the appropriate algorithms.

Modeling of fluid flows in density-based topology optimization forms a longstanding challenge. Methods based on the Navier–Stokes equations with Darcy penalization (NSDP equations) are widely used in fluid topology optimization. These methods use porous materials with low permeability to represent the solid domain. Consequently, they suffer from flow leakage in certain areas. In this work, the governing equations for solid/fluid density-based topology optimization are reevaluated and reinterpreted. The governing equations are constructed using the volume averaged Navier–Stokes (VANS) equations, well known in the field of porous flow modeling. Subsequently, we simplify, interpret and discretize the VANS equations in the context of solid/fluid topology optimization, and analytically derive lower bounds on the Darcy penalization to sufficiently prevent flow leakage. Based on both the NSDP and VANS equations, two flow solvers are constructed using the Finite Volume method. Their precision and the lower bound on the Darcy penalization are investigated. Subsequently, the solvers are used to optimize flow channels for minimal pressure drop, and the resulting designs and convergence behavior are compared. The optimization procedure using the VANS equations is found to show less tendency to converge to inferior local optima for more precise flow solutions and is less sensitive to its parameter selection.