## 3 Results and Analysis  
### Time-Averaged Results  
Figure 6 presents the time and spanwise averaged pressure coefficient distribution. On the upper wing surface, the IDDES predicted an average shock wave position located at around x/c = 0.25, which is approximately one-third ahead of the experimentally observed average shock wave position. The average shock wave position obtained with DDES was slightly closer to the upstream, and the pressure distribution in the trailing edge region was noticeably lower than the experimental results. In comparison, the average shock wave position predicted by ZDES in this study were essentially consistent with the experimental results. During the oscillation of the shock wave, the flow on the lower surface remained attached, and both global and zonal DES provided pressure distribution results consistent with the experiment.  
The streamwise velocity distributions obtained with DDES and ZDES at different positions are compared in Figure 7. At the x/c = 0.28 location, which was at the upstream position of the shock wave, the flow remained attached, and both the DDES and ZDES  
Figure 5: Schematic of OAT15A segmented computation.  
Figure 6: Averaged pressure coefficient distribution; [PERSON] 2014 [11], [PERSON] 2012 [12].  
velocity distributions agree well with the measured results. At the x/c = 0.45 location, near the average position of the shock wave, the ZDES result predicted a velocity distribution in agreement with the experimental results. However, the DDES yielded a thicker boundary layer and lower velocities outside the boundary layer, due to the predicted advance of the average shock wave position by the DDES. This also led to slight discrepancies between the DDES and the experiment at the x/c = 0.60 and x/c = 0.75 locations. Overall, the streamwise velocity distribution obtained with ZDES better matched the experimental results.  
The distribution of root-mean-square pressure fluctuations on the upper surface of the airfoil is illustrated in Figure 8. In the upstream region of the separation area, the flow remains fully attached throughout the entire oscillation cycle. Therefore, both global and ZDES predicted relatively low levels of pressure fluctuations. Under the influence of the transonic shock buffet, the level of surface pressure fluctuations rapidly increased, reaching approximately 30% of the maximum peak level at x/c = 0.45, and then quickly receded. The maximum fluctuation level obtained with DDES was approximately 36%, while the IDDES predicted a maximum peak value of 39%, both significantly higher than the experimental data. The root mean square of surface pressure fluctuations also partially reflected the range of shock wave motion. The shock wave motion range obtained with IDDES was overall shifted forward compared to the experimental results, consistent with the average shock wave position reflected in Figure 8.  
Figure 7: Mean streamwise velocity distribution at different streamwise locations on the upper surface of the airfoil, Grossi 2014 [11].  
From Figure 8, it can be observed that the maximum pressure fluctuation level calculated with ZDES is slightly lower than the experimental value. This may be because the mesh currently in use may not be dense enough. In the separation region downstream of the shock wave, the pressure fluctuation levels obtained with DDES and IDDES were significantly higher than the experimental values. This may be influenced by the shedding of large-scale vortex structures at the trailing edge. Overall, the ZDES results are in good agreement with the experimental data.