## 1 Introduction  
Scramjets are the most promising power devices in air-breathing hypersonic flight, which has received increasing attention. As the flight Mach number increases, the thermal protection of combustion chambers becomes a critical issue due to its extremely thermal environment [1, 2, 3, 4, 5]. Active regenerative cooling technology is proposed as the most feasible thermal protection method, in which the hydrocarbon fuel of a scramjet is used as a coolant [2, 6, 7]. During the cooling process, hydrocarbon fuel provides not only physical heat sink but also additional chemical heat sink through endothermic reactions (also known as thermal cracking or pyrolysis [8]). Much research has been conducted on the flow and heat transfer characteristics of hydrocarbon fuels with the consideration of fuel pyrolysis under supercritical conditions in straight cooling channels. [PERSON] et al. [9] and [PERSON] et al. [10] investigated the heat transfer and thermal cracking behaviors of aviation kerosene. [PERSON] [11] and [PERSON] [12] studied the pressure effect on heat transfer and fuel pyrolysis. [PERSON] et al. [13, 14] quantitatively analyzed the coupling relationship between the flow and pyrolysis reactions of hydrocarbon fuel in a mini channel. Results reveal that, in a regenerative cooling system, the flow field and heat transfer are significantly influenced by fuel pyrolysis. A curved channel is an important component and widely applied in the design of regenerative cooling technology, such as the cavity flame-holder, near the nozzle throat region and the connection area of a combustion chamber [15]. In curved cooling channels, the secondary flow is induced by the centrifugal force in the cross section [16; 17]. Some literature [15; 18; 19; 20; 21; 22] has been published on the influence of secondary flow on the flow field and heat transfer of hydrocarbon fuels without fuel pyrolysis. Results revealed that, compared to straight channels, the secondary flow enhanced flow mixing and promoted heat transfer in curved channels. However, these investigations ignore the pyrolysis process of hydrocarbon fuels. Until recently, there was a lack of knowledge about the effect of curved configurations on flow field, heat transfer, and fuel pyrolysis. In a relevant paper, [PERSON] et al. [23] investigated the flow and heat transfer characteristics of aviation kerosene in sharply curved cooling channels at supercritical pressures using a simplified pyrolytic reaction mechanism. [PERSON] et al. [24] numerically studied the effect of centrifugal force on the flow field, heat, and mass transfers of hydrocarbon fuel in a helical channel, using the PPD model [25]. However, the results carried out by the PPD model were limited to situations with low fuel conversion. The reason is that many important secondary chemical reactions were ignored. In a curved channel (e.g., a surrounding cavity flame-holder or nozzle throat), the wall heat flux is very high, and a secondary reaction occurs, which makes the conversion of hydrocarbon fuel exceed the mildly cracked regime [26]. The secondary chemical reaction significantly influences the flow and heat transfer of supercritical hydrocarbon fuel in cooling channels [27]. However, there is little information available in the literature about the flow and heat transfer characteristics of hydrocarbon fuel with secondary reactions in curved cooling channels. In this paper, numerical studies are carried out to analyze the flow and heat transfer characteristics of supercritical China RP-3 aviation kerosene under a wide range of fuel pyrolysis conditions in a 3D rectangular curved cooling channel. The detailed chemical reaction mechanism of RP-3 in Ref. [28] is adopted to simulate the fuel pyrolysis process. In addition, the influence of mass flow rate and curvature on flow and heat transfer in curved cooling channels is also investigated. The numerical model and its validation are described in Section 2. The model setup for the simulation is presented in Section 3.