Display omitted •Conformal cooling channels are designed for various of axisymmetric castings.•Two-dimensional simplification is performed inspired by origami technique.•Comprehensive design flow is proposed following theoretical analysis.•Topology optimization processes are customized within a unified framework. To address the unacceptable computational burden in three-dimensional topology optimization, this paper presents an origami-inspired strategy that directly applies two-dimensional topology optimization to design three-dimensional conformal cooling channels. A comprehensive design flow incorporating theoretical analysis is proposed stepwise, aiming at axisymmetric castings. Various two-dimensional simplification styles are evaluated, following geometric configuration analysis on channel space. Multiple topology optimization processes are customized on the simplified domain, following thermal analysis of the casting and Reynolds number analysis on the bending transition. The objective is to design a conformal cooling channel with superior cooling performance at a steady state. Numerical simulations are performed to verify the cooling performance of optimized results. Two feasible designs are obtained for a given regular hexahedral casting, with one conducting two-dimensional simplification along the intersection axis of multiple planes exhibiting better steady-state cooling performance. It achieves a 6.7 K reduction in casting temperature and an 11.06 % decrease in pressure drop compared to the other design. In addition, the study explores the application of castings of increasing geometric complexity, including regular tetrahedron, octahedral, dodecahedral, and spherical shapes. For a given spherical casting, a trade-off analysis between average cooling spacing and optimization domain area is conducted as the number of segmentations increases. The optimal design, achieved with 12-part segmentations, results in a casting temperature of 308.05 K under a coolant inlet pressure of 400 Pa at a steady state. This study provides an efficient approach that circumvents the computationally intensive topology optimization process.