A unified design model for aeroengine intercoolers integrating compressible aerodynamics and supercritical coolant thermodynamics

The design of conformal intercoolers for advanced aeroengines is complicated by high compressibility and variable flow area. This paper presents a refined design methodology based on a fully coupled system of ordinary differential equations (ODEs), derived from first principles to solve axial gradients of static pressure and temperature. The model inherently captures friction, heat transfer, and area-change effects, overcoming limitations of conventional tools such as the LMTD method in converting between static and total parameters. The methodology is applied to design a conformal air-to-supercritical nitrogen intercooler and is rigorously validated against high-fidelity CFD simulations and a state-of-the-art segmented LMTD model. The results demonstrate that the proposed ODE model achieves excellent agreement with CFD in predicting both overall performance metrics and local parameter distributions. In contrast, the classic and enhanced segmented LMTD models exhibit significant deviations, with total pressure-drop prediction errors reaching 17.9–45.4 % on the air side, whereas the proposed ODE model reduces this to within 10 % under the design condition. These findings highlight the limitations of LMTD-based approaches in handling strongly coupled problems. This work provides a computationally efficient yet physically robust tool for the high-fidelity design and optimization of advanced thermal management components in high-speed propulsion systems.