Geometry-driven thermal–fluid topology optimization using B-spline geometric primitives

Abstract

Topology optimization has been widely applied to thermal–fluid design, particularly for channel-based systems. However, many conventional approaches rely on implicit density-field representations, making it difficult to preserve geometrically interpretable channel features and directly obtain editable CAD models. This study develops a geometry-driven topology optimization framework for cooling-system design based on a three-dimensional loft-based channel representation. Each channel is parameterized by a B-spline centerline and spatially varying cross-sectional profiles, enabling simultaneous control of its trajectory and sectional shape. The resulting geometry is mapped onto a fixed background mesh through a distance-field-based explicit–implicit formulation for thermal–fluid analysis. A predominantly analytical sensitivity scheme is developed for the geometry-to-field mapping, with finite-difference evaluation restricted to the computationally inexpensive rotation-minimizing-frame term. The local nature of the mapping is further exploited through narrow-band evaluation to improve computational efficiency. Curvature, domain-feasibility, adhesion, and self-support constraints are incorporated to preserve design intent and additive manufacturability. Numerical examples demonstrate that the method can generate complex two- and three-dimensional channels while retaining explicit geometric control, computationally efficient gradient evaluation, and direct reconstruction of editable CAD geometries.