Internal Cooling Design Using Multiphysics Topology Optimization

Abstract: This thesis investigates topology optimization (TO) as a tool for designing optimal internal cooling configurations in components subjected to external hot gas streams. The work is motivated by the challenge of simultaneously considering objectives from multiple physics domains, and the rapid development of additive manufacturing (AM) in the industry, which makes it possible to realize highly complex TO designs. Against this background, a multi-physics TO approach is employed, involving the following physics domains: • Fluid mechanics: describes the flow of the coolant • Heat transfer: describes the coolant and component temperatures • Solid mechanics: describes the structural behaviour of the component Density-based TO is used to parametrize the design, such that the interpolation between solid and fluid material properties is governed by a spatially varying design variable. Temperature measures are considered as objectives in the non-convex optimization problems, and coolant mass flow and structural stiffness measures are considered as constraints. The design process is iterative: for a given design, the flow velocities are computed and used to calculate the temperature distribution, which in turn influences the domain’s structural response. These three equilibrium state problems are solved sequentially, followed by solving corresponding adjoint problems in reversed order, to acquire first-order sensitivity information used by the gradient-based optimization solver. Numerical simulations are carried out for geometries of varying degrees of complexity, resembling gas turbine guide vanes. The simulations cover a range of fidelity levels: from simpler 2D setups to more complex 3D setups with fine resolution, intended for execution on high-performance computing (HPC) clusters. Low-fidelity flow models are utilized in the TO process, while more advanced flow models are employed for design comparisons, and flow and heat response comparisons for given TO designs. The thesis consists of two parts: the first provides the theoretical framework, and the second includes appended papers. In Paper I, only the heat problem is included when modelling convection on internal boundaries identified using the design gradient. Fluid and solid mechanics are introduced in Paper II, where a conjugate heat transfer problem is augmented with a structural model coupled through thermal strains, with numerical examples in 3D. In Paper III, the simultaneous consideration of flow and heat objectives is formulated as a mathematical game between two players trying to minimize the average temperature in the domain and the coolant mass flow through the domain, respectively, with examples in 2D and 3D. The flow problems are the computational bottlenecks, and therefore, Paper IV demonstrates a 3D implementation investigating two different numerical techniques for solving the flow problem, with a voxelization approach for efficient meshing of complex geometries. Paper V presents an efficient, massively parallel HPC implementation for three-field flow-heat-structural models, and addresses further implementation details. This thesis highlights challenging aspects of large-scale multiphysics TO considering fluid mechanics, heat transfer, and solid mechanics.