## 4 Results and Analysis
### Flow Field Analysis
It is worth noting that the range of legend values in Figure 7 is the actual range of solution values. Even though the color is the same, the value is not the same. Figure 8 shows the streamlines and velocity vectors in the XOY and YOZ planes. For the MCIJ, the surrounding airflow from the top of jet space is carried by the free shear layer,  
Figure 6: The contours of the instantaneous axial velocity in the XOY and YOZ planes. Figure 7: The distribution of pressure in the XOY and YOZ planes. moving downstream to the target surface with some vortex pairs, and deflecting to the radial direction at \(x/D=0.5\)-0.8 with a similar corner vortex. When the jet impinges the stagnation point, the rebounded airflow near the wall also deflects to the radial direction and meets the shear tangential flow (marked red curves), which results in a large-scale recirculation vortex at about \(x/D=1\) in the XOY plane. A similar vortex occurs at \(z/D=1.25\) in the YOZ plane due to the hamper effect of the curved cylinder concave target on the rebounded tangential airflow. It should be noted that the recirculation vortices produce a certain suppression on the deflected airflow in the stagnation zone to escape along the radial direction, which would weaken the heat transfer in this region to some extent. In the range of \(x/D=1\)-1.5, the escaped velocity near the wall gradually increases and the entrainment effect of shear flow above the wall also gradually enhances. In the range of \(x/D=1.5\) away from the stagnation point, the escaped airflow near the wall would hold steady. However, shear flow meets the entrained airflow from the outlet, resulting in a large-scale recirculation vortex at \(x/D=2.3\) near the exit of jet space. Indeed, the discharge capacity of axial flow along the wall would be suppressed by the vortex, and heat transfer would be the same. For the SIJ, the potential flow in the central region has a bigger axial velocity, and the airflow of the free shear layer around the potential flow has a stronger entrainment effect on the surrounding gas. It can be seen that lots of marked blue oblique curves of entrainment flow come from the top of jet space. Compared with the non-swirling case, these curves are denser without any large-scale vortex. At the same time, there is no obvious flow structure of vortex pairs around the potential flow, and no complicated similar corner vortex in the range of \(x/D=0.5\)-0.8 in the XOY plane. These disappeared large-scale vortices may be attributed to tangential velocity of the swirl jet. The escaped airflow near the wall in the XOY plane has a higher radial velocity, resulting in a stronger shear flow. It shows that the whole recirculation vortex appears earlier at \(x/D=2\) and a large-scale semi-vortex follows downstream near the exit. Three obvious vortices above the concave wall form in the YOZ plane as shear flow meets with the entrained airflow from the top of jet space. It can be seen that the positions of vortex center are at \(z/D=0.7\), 1.2, and 2.3 for the MCIJ, while these positions are at \(z/D=0.9\), 1.8, and 2.3 for SIJ. Two upstream vortices for the SIJ are not only further from the stagnation point, but also higher above the wall compared with the MCIJ. Moreover, for the MCIJ, one more unformed recirculation vortex appears near the exit except three vortices. It should be pointed out that these different flow structures for the SIJ would be beneficial to improve heat transfer on the semi-cylinder concave surface. Figure 8: _Cont_. Figure 9 shows the instantaneous Q-criterion. [PERSON] et al. [28] proposed the Q-criterion based on the positive second invariant of velocity gradient or the complex eigenvalues of velocity gradient; their definition can accurately identify the vortex core in flows where the vortex geometry is intuitively clear.