CBS-based topology optimization of thermal-fluid problems

Efficient thermal management is critical for high-power-density electronic and electromechanical devices. This work presents a feature-driven topology optimization framework for the integrated design of cooling systems by simultaneously optimizing cooling efficiency and energy consumption governed by coupling steady-state Navier-Stokes equations and heat conduction. To overcome the limitations of post-processing and geometric reconstruction inherent in conventional density-based methods, Closed B-spline (CBS) features are employed as the fundamental design primitives for representing fluid/solid domains. The geometric parameters of CBS features serve as design variables, and their material layout is described via an implicit level-set function (LSF) with a relaxed Heaviside projection, ensuring compatibility with fixed computational meshes. The primary contribution of this work is the development of a novel adaptive insertion strategy, which mitigates the initial layout dependency common to feature-driven methods. Unlike approaches reliant on complex topological derivatives, this strategy identifies potential insertion locations using the sensitivity of the objective function with respect to pseudo-density variables, derived analytically via the discrete adjoint method. Numerical examples demonstrate that the framework effectively generates optimized channel layouts, and that adaptive insertion strategy yields superior performance. The approach provides a practical and mesh-compatible method for feature-driven thermal-fluid topology optimization.