Numerical study on transpiration cooling heat transfer characteristics under dynamic heat flux conditions with feedforward compensation

Modern closed-loop control-based transpiration cooling systems for hypersonic vehicles suffer from delayed temperature response, substantial steady-state errors, and insufficient robustness under dramatically changing heat flow conditions, necessitating complex parameter tuning across flight regimes to maintain stability. To address the core issues, this paper revisits the relay-based closed-loop thermal control strategy and demonstrate that, with a novel and carefully devised feedforward compensation module, it enables prompt and effective thermal management without runtime parameter adjustments. This feedforward module is driven by a predictive coolant flow model that incorporates two key factors: heat transfer hysteresis between the porous medium and the coolant, and inertial resistance to coolant flow, based on the local thermal non-equilibrium model and Darcy - Forchheimer equations. Based on it, the relay controller dynamically adjusts the coolant flow rate in advance, optimizing the longitudinal temperature distribution across the porous medium and improving the temperature gradient control. Simulation results show that the feedforward compensation module significantly mitigates the limitations imposed by non-equilibrium heat transfer and flow resistance, reducing temperature overshoot by 53.9%–93.2 %, response delay by 39.3 %–75.0 %, and mean absolute error by 15.9 %–65.5 % compared to traditional PID control under step, sine wave, and square wave heat flux disturbances. Under complex operating conditions, the proposed strategy outperforms conventional strategies in temperature accuracy, response speed, coolant efficiency, and overall control robustness, demonstrating superior dynamic adaptability.