Enhanced transient thermal analysis of finite-length PDE tubes under cyclic severe internal heating using a hybrid analytical–numerical approach

Pulse detonation engines (PDEs) are among the most promising propulsion technologies for future aerospace applications due to their potential for lower mechanical complexity and higher thermodynamic efficiency. However, their intense and cyclic thermal loading creates a unique transient heat transfer environment within the detonation tube that challenges long-term reliability and thermal design. This work presents a comprehensive analytical and numerical study of the transient thermal response of a finite-length detonation tube subjected to high-frequency, rapid, and severe internal heating representative of PDE operation. To model realistic PDE conditions, a detailed thermal loading profile based on the full engine cycle, including detonation, thrust, purging, and refilling phases, has been validated and developed. The novelty of this work lies in the verification and development of a cycle-based thermal loading model, and in providing a combined analytical-numerical solution for the transient temperature distribution across the tube wall. The analytical model, based on the separation of variables in cylindrical coordinates, provides closed-form expressions for thermal behavior under cyclic heating. These are cross-validated with finite element simulations in ABAQUS and benchmarked against experimental data reported in the literature. Validation against experimental data at an operating frequency of 3.077 Hz shows that the model accurately predicts an outer wall temperature rise of approximately 21.19°C to 22.53°C after 28 cycles, closely matching the experimental observation of 23.7°C. Results further demonstrate that while the tube temperature rises sharply without cooling, implementing external convection (h = 200 to 2000 W/m 2 K) effectively stabilizes the thermal response over 1000 operating cycles. The findings quantify the critical time scales for thermal penetration, showing a 1°C increase at the outer wall within approximately 2 s of operation. This hybrid modeling approach provides a precise and computationally efficient tool for the long-term thermal management and structural optimization of pulse detonation systems.