## 1 Introduction
[PERSON] et al. (2018) proposed an actively cooled TPS based on a corrugated sandwich structure, studying the influence effect of the inlet velocity and flow direction on its thermal characteristics, and its response under thermal-mechanical loading. In Ref. [PERSON] et al. (2018), the authors introduce another actively cooled TPS using pyramid core sandwich panels with cooling channels in the top panel to maintain a safe temperature range for the underlying structure. The study analyzed the flow fields and mechanisms in four types of cooling channels and discusses the impact of the flow conditions on the thermal-fluid performance. [PERSON] et al. [PERSON] et al. (2018) studied the thermal-hydraulic performance of bend tubes with different section shapes (circular, rectangular, and pentagonal) in an actively cooled TPS for hypersonic aircraft. Through a comparative analysis, they proposed a diamond-shaped channel using RP-3 as the coolant. The feasibility and advantages of this design were subsequently verified through numerical simulation. In Ref. [PERSON] et al. (2018), the previously proposed \"Diamond\" channel was further improved by adding discrete inclined ribs. The cooling effects and the impacts of different parameters were numerically investigated. To address the complex and time-consuming issue of evaluating the actively cooled effects through experimental or numerical methods, [PERSON] et al. [PERSON] et al. (2018) propose an efficient analytical model capable of accurately predicting the maximum temperature and temperature distribution. Recently, the layout of the active cooling network throughout the aircraft was analyzed by [PERSON] et al. [PERSON] et al. (2018, 2019) from a thermal management perspective. This analysis covered various components, such as the windward and leeward sides of the fuselage and the wings, air rudders, and power systems. Moreover, fractal channels have received much attention. As bionic channels, they produce significantly efficient cooling channels by mimicking natural evolution and may be an ideal candidate for the cooling channels of air rudders. [PERSON] et al. [PERSON] et al. (2019) propose a combined parametric model to describe fractal channels of Y, V, and T shapes and provide a fast-parametric modeling method. The results indicate that, among these configurations, the V-shaped network exhibits a better cooling performance, while the Y-shaped network demonstrates a superior flow performance. It is evident that there exists a substantial research gap concerning active cooling thermal protection systems (TPSs) for air rudders. Hence, this work proposed two distinct cooling schemes with varying flow paths and structural designs and developed six cooling channel configurations by modifying the leading-edge details. The cooling efficiency was assessed under simulated flight conditions (30 km altitude, Mach 8), with an emphasis on managing the temperatures and optimizing the coolant flow rates. Both series and parallel cooling circuit arrangements were analyzed, incorporating suitable settings for the inlet flow rates and temperatures. A thorough evaluation was performed to assess the temperature distributions, flow dynamics, and thermal-mechanical behaviors of the different cooling channel designs. These findings establish a foundation for future research and practical applications of actively cooled air rudders.