Density-based topology optimization for aerodynamic and thermofluid optimal design

Topology optimization (TO) methods are referred to a set of numerical techniques that are ultimately flexible in terms of modifying a design’s geometry to maximize its desired performance during the course of an optimization process. More precisely, TO methods are not only capable of modifying geometrical sizes and shapes but also the topological characteristics, by manipulating the material spatial distribution. Such ultimate design freedom significantly reduces the dependency on providing a reasonable initial guess to initiate the design process or providing any particular geometrical parametrization, which makes these methods superior to shape optimization techniques. Consequently, TO often relies on no particular information to be provided by a designer, and can be regarded as an independent (automated) design tool, which can start the designing process from scratch; a highly demanding feature that can be considered the main strength of TO methods. Two main approaches have been extensively studied and developed for TO techniques, namely: density-based and level-set methods (LSM). In the first approach, the material volumetric distribution in space is used for topological descriptions of the geometry of the design, however, in the second approach often the (zero) level-set contours of a higher-dimensional topological function are utilized to define the material domains by their boundaries associated with those contours. Both approaches demonstrate specific strengths and weaknesses, and one should use them depending on the intended purpose. For instance, LSM methods mostly lack a robust zone-nucleation technique, and consequently, their outcomes are often considered sensitive to the provided initial guess and demand special care from the designer. However, the density-based approach is intrinsically capable of nucleating new zones, increasing its robustness concerning the seeding baseline, effectively making it an ideal choice for an independent design tool. Hence, as iv v investigating an automated design process is concerned in this work, the density-based method is utilized. In flow TO problems using density-based approaches, the solid material distributions are often modeled by a highly impermeable porosity field using the Brinkman penalized Navier–Stokes equations. Brinkman penalized Navier–Stokes equations are often used for flow TO problems using density-based approaches. Therefore, the solid material distribution is then modeled by introducing a highly impermeable porosity (scalar) field. Using such a porosity field on a fixed mesh, however, lacks providing explicit material interfaces, i.e. no-slip boundary condition, which either leads to material grayness or stair-steps (non-smooth) interfaces. Therefore, in this work, several techniques have been developed to improve the modeling accuracy of the density-based approach while maintaining reasonable computational performance. In the first step, the high-order pseudo-spectral CFD method is used as a primal flow solver to improve the accuracy of the density-based TO on fixed grids. This tool is then used to design optimal fin arrays that minimize flow pressure losses. Next, this tool is equipped with a thermal finite-element solver and employed for the optimal design of pin-fin forced convection heat sinks, using a pseudo-3D conjugate heat-transfer model. In the second step, an automated aerodynamic TO-based design tool is developed in the OpenFOAM environment, targeting external flow design problems for the first time. To achieve satisfying modeling accuracy at reasonable computational costs, the multi-stage optimization process with a sequence of design space block-mesh refinements is proposed. In addition, the operator-based analytical differentiation is developed to precisely and efficiently compute the primal solver derivatives, required for the discrete adjoint sensitivities. The utility of the developed tool in designing from scratch is comprehensively demonstrated by rigorously investigating (2D and 3D) topology-optimized aerodynamic geometries in the laminar regimes. For instance, the present tool has been utilized for designing the 3D planform of micro-air vehicles (MAV) at low speeds in order to demonstrate its utility in finding optimal aerodynamic solutions in a more effective manner and using disruptive and new technology. The findings strongly confirmed that with further developments, TO could play an important role in the future of aircraft design projects, by achieving optimal performances via unconventional designs.