## 4 Results and Analysis  
### Flow Field Analysis  
Figure 6 shows the contours of the instantaneous axial velocity in non-swirling and swirling turbulent impinging jets in the XOY and YOZ planes. Compared with the MCIJ, SJJ has a larger obstruction effect on the jet flow due to the spiral channels. Most of the jet is collected in the central region of the nozzle, resulting in a larger axial velocity of the potential flow core in the jet space for the 45\({}^{\circ}\) spiral nozzle. Due to the effect of the swirl on the jets, it can also be seen that SJJ has a large tangential velocity and the effect to entrain the surrounding low-speed airflow is stronger, while the entraining airflow from the top of the jet space is higher. Under the action of the processing vortices, the entraining airflow is rapidly mixed with the potential flow, so that the jet with high speed under the nozzle exit, the blue region shown in Figure 6b, becomes gradually weak, which decays more rapidly along the flow direction. At the periphery of the potential flow, the mixed airflow forms the \"skirt type\" green region with a larger diffusion area. For the MCIJ issuing from the 0\({}^{\circ}\) straight nozzle, the injected groove velocity is slightly lower than that at the central region of the nozzle due to the effect of the wall boundary layer, while it has a longer potential flow in the jet space and forms a \"taper-foot-type\" green region with a relatively smaller diffusion area compared with the SJJ. After the jet impacts the concave target, the rebound axial velocity from the wall free jet in the YOZ plane (\(u_{y}/U_{b}=0.8\)) is much larger than that in the XOY plane (\(u_{y}/U_{b}=0.3\)) due to flow delay on the curved surface for the MCIJ, while the rebound axial velocities in the XOY and YOZ planes (\(u_{y}/U_{b}=0.6\)) are comparable due to the entrainment effect of the velocity component of the swirl. Therefore, it can be inferred from the flow phenomenon that the swirl flow by the 45\({}^{\circ}\) spiral nozzle struggles more to escape from the curved and flat surfaces. As a result, the cooling effect may be improved on the curved surface with a more uniform heat transfer. It is worth noting that the range of legend values in Figure 6 is the actual range of solution values. Even though the color is the same, the value is not the same. Figure 7 shows the distribution of pressure in the XOY and YOZ planes. For the MCIJ, there are a series of blue regions with negative pressure (marked in red circle) around the potential flow, which are generated from Kelvin-Helmholtz instability in the shear layer, resulting in a series of vortex pairs. Under the entrainment effect of the airflow in the free shear layer, the jet in the stagnation zone deflects quickly, escapes outward in the radial direction, forms wall free jet at about \(x/D=1\) with the negative pressure in the blue region near the wall, and tends to gradually entrain the low-speed ambient gas above the wall. The secondary blue region near the wall occurs at \(x/D=1.8\), where the escaped airflow with the dominant radial velocity meets with the entrained ambient gas from the outlet. For the SJJ, there are not any vortex pairs in the jet space, and many blue regions of high negative pressure with a small scale are distributed disorderly throughout the whole downstream flow of the nozzle. It indicates that the addition of tangential velocity resulted in a more complex entrainment mixing jet. Accordingly, many small-scale complex vortices form and distribute anywhere around the central-jet impinging zone. A peak of high negative pressure near the wall at \(x/D=0.8\) can be seen in the XOY plane, which indicates that the wall-free jet at that position is more intense than that of the non-swirling jet. Compared with the MCIJ, the red region of high positive pressure in the stagnation zone for the SJJ is  
bigger, which is attributed to the potential flow in the central region developing closer to the target surface.