Beyond Laminar Limits: Fractal Geometry Theory Inspired Topology Optimization of Liquid Cooling plates in Turbulent Flow Regime

Multi-objective topology optimization (TO) has been widely applied in the design of high-performance liquid cooling plates. However, most TO methods are limited to laminar flow, and the existing turbulent TO studies suffer from overly simplified optimized structures that results in suboptimal thermal performance. In this study, the turbulent TO method is developed by the fractal geometry theory (TFGTO), which explicitly optimizes convective heat transfer through its objective function to achieve better thermal and hydraulic performances. Compared to turbulent TOs that are performed with conventional thermal objective, the TFGTO achieves more complex structural topologies and improved performance, with heat transfer area augmented by 51.1%, average temperature reduced by 18.1 K, and the PEC improved by 31.1%. Compared to the widely-used pin fin liquid cooling plate (PFLCP), the average and maximum temperatures of the TFGTO results are reduced by 6.9 K and 33.3 K, respectively, while the pressure drop is reduced by up to 62%. Varying the weight parameters fails to effectively manipulate the optimization results under turbulent flow conditions, and the overall structure resembling parallel straight channels that compromises thermal performance is generated at extreme thermal weight. The optimized liquid cooling plates by turbulent and laminar TO methods exhibit remarkable distinctions in structure and performance, which is attributed to the differences in flow and heat transfer characteristics between turbulent and laminar flow regimes. The turbulent and laminar TO results are proved to be suitable only for the corresponding operating conditions, otherwise, the performance of the optimized liquid cooling plates might be severely compromised.