## 4 Results and Discussion  
### Effect of Secondary Flow on Pyrolysis and Heat Transfer  
According to the previous analysis, the secondary flow in a curved channel enhances the fluid mixing and thermal exchange. In this paper, a case was also calculated in a straight channel for the purpose of comparison. The fuel conversion and heat transfer coefficient  
Figure 3: Schematic and dimensions of simulation model: (**a**) cross section of channel (**b**) schematic of channel along axial direction. Figure 2: The flow-path configuration of engine [37]. were numerically conducted in a straight channel and a curved channel to analyze the effect of the secondary flow on pyrolysis and heat transfer. The sectional geometry and boundary conditions of the straight channel were consistent with the curved channel, except that the bending radius is infinite. The conversion of RP-3, \(Z_{\text{RP-3}}\), is defined as [39]:  
\[Z_{\text{RP-3}}=\left(1-\frac{\int_{A}\rho u_{\text{KP-3}}dA}{\int_{A}\rho udA} \right)\times 100\%, \tag{12}\]  
where \(u\) is the velocity of fluid, and \(A\) is the surface area of the channel. The distributions of fuel temperature and conversion at the cross sections of \(0^{\circ}\), \(15^{\circ}\), \(45^{\circ}\), and \(75^{\circ}\) in the curved cooling channel, and at the same positions in the straight cooling channel, are presented in Figures 4-7. The cooling channel was made of alloy and had high thermal conductivity. Although the channel was one-side-heated, the temperature of the hydrocarbon fuel in the near-wall regions increased first. Due to the higher fluid temperature, the fluid in the near-wall region had a higher chemical reaction rate than that in the main flow in both kinds of channels. Moreover, under the action of molecular viscous force, the hydrocarbon fuel in the near-wall region had a smaller axial velocity and longer residence time than that in the main flow. Therefore, in both curved and straight channels, the fuel conversion was high in the near-wall region and low in the main flow. Figure 4: Temperature distribution at different cross sections: (**a**) curved channel and (**b**) straight channel. Figure 5: Fuel temperature in the centerline along \(y\) axis at different cross sections. However, in the curved channel, the secondary flow pattern appeared in cross sections because of the centrifugal force, as shown in Figure 8. The secondary flow drove the fluid with low velocity near the wall inward, while the fluid with high velocity in the main flow swept outward [40]. The intensity of the secondary flow can be characterized by the secondary flow velocity [40], which is calculated as \(V_{Sec}=\sqrt{\left(u_{y}\right)^{2}+\left(u_{z}\right)^{2}}\). In the curved cooling channel, the high-temperature fluid in the near-wall region moved to the main flow due to the secondary flow. The fuel in the central region flowed towards the wall, as shown in Figure 8. The secondary flow transferred energy and components from the near-wall region to the main flow, and the radial heat and mass transfers were promoted. Therefore, compared with the straight cooling channel, the fuel in the curved cooling channel absorbed more heat. Meanwhile, due to the secondary flow, the main flow temperature increased faster in the curved cooling channel (as shown in Figure 5), and the chemical reaction rate was larger. Fuel conversion in the main flow of the curved channel was higher, as shown in Figure 7. Moreover, as the secondary flow enhanced mass transfer, the non-cracked hydrocarbon fuel in the main flow was pushed to the near-wall region, and the pyrolytic products in the near-wall region were transported to the main flow, and more hydrocarbon fuel underwent pyrolysis. For these two reasons, in the curved cooling channel, fuel conversion was higher, and the chemical heat absorption was larger, as shown in Figures 7 and 9. At the outlet, the average fuel conversion of the curved channel was 34.25%, and that of the straight channel was 27.17%.