Modeling and numerical analysis of PID-controlled phase-change transpiration cooling

This paper innovatively introduces PID control to the phase-change transpiration cooling process and numerically investigates the multi-physics process of coupled control, flow, and heat transfer through mathematical modeling. Based on numerical simulations, the critical equal-amplitude oscillation characteristics in PID-controlled phase-change transpiration cooling, the PID tuning method for the cooling system's fast stabilization, and the applicability of PID tuning strategies at various control conditions are discussed. The discussions show that liquid phase change significantly influences the PID-controlled response process. The response process is prone to large temperature fluctuations and overshoots when the final phase change position is far from that in the corresponding open-loop process. In addition, the classical tuning parameters from the Ziegler-Nichols critical proportional tuning method are not fully applicable due to the significant heat transfer hysteresis in the liquid phase change and must be revised. After revision, the PID tuning strategy can contribute to excellent control consistency and reliability when the target temperature keeps away from the saturated temperature of the coolant or the feedback location moves within the superheated vapor area.