Investigation of a scale-variable multi-objective optimization method for heat pipe–Stirling coupled nuclear power systems

Heat pipe cooled reactors coupled with Stirling engines are a preferred pathway for space and deep-sea nuclear power, yet their conceptual design faces an inherent trade-off between efficiency and compactness. This paper proposes a scale-variable multi-objective optimization method based on Organ's similarity theory and the Beale number. A thermal resistance network model describes the sodium heat pipe, and a second-order Improved Simple model for the β-type Stirling engine incorporates both thermal and power loss mechanisms, coupled by damped Newton iteration. The swept volume is introduced as a continuous decision variable, and a geometric scaling law links engine geometry, thermodynamic performance, and system volume. The NSGA-II algorithm solves the efficiency–specific power Pareto front. The efficiency ranges from 38.8% to 42.5% and the specific power from 435 to 926 W/L, with Beale numbers of 0.112–0.127. Morris analysis shows that the swept volume affects specific power 35 times more than efficiency, so changing the engine size primarily affects compactness rather than efficiency. Two controlled numerical comparisons confirm a 0.8% higher specific power with a 21% smaller engine and an 11% lower frequency. The reactor core is represented at its thermal interface with a bounded temperature error of about 20 K; full neutronics is outside the scope. The proposed method provides effective engineering guidance for the power rating–compactness trade-off in the conceptual design of heat pipe–Stirling nuclear power systems.