# An Analysis of the Factors Influencing Dual Separation Zones on a Plate
## 3 Simulation Method and Numerical Validation
### Numerical Validation  
To validate the reliability of the numerical method, validation experiments were conducted using a dual-separation-zone model in a free jet wind tunnel at Mach 4. The validation model is illustrated in Figure 3. Since the SWBLI exhibits pronounced three-dimensional characteristics and pronounced unsteady behaviors, it is necessary to conduct wind tunnel experiments to verify the reliability of the two-dimensional steady-state computational results. The interaction between dual separation zones is facilitated by the movement of the bottom plate derived by a step motor. The plate is 414 mm long and 95 mm wide, and the height of SG is 46 mm, with an angle of 14 deg.  
The two curves in Figure 4 compare the numerically calculated wall pressure distributions with experimentally obtained wall pressure data, respectively, under two scenarios: when dual separation zones are far apart and when they are critically close to merging.  
The calculated pressure peaks in SZI under different movement distances are slightly higher than the experimental data, while the results corresponding to SZII are in good agreement with the experiments. The overall variation trend of the simulated wall pressure remains consistent with the experimental results. It is concluded that the two-dimensional steady numerical method adopted in this study can meet the requirements for investigating the evolution process of a dual-separation-zone flow field.  
The research object in this investigation displays a significant difference compared to studies conducted by other scholars. Essentially, the dual-separation-zone model in our study differs from previous research. The existing studies on dual separation zones are  
\begin{table}
\begin{tabular}{c c c c} \hline
**Incoming Flow** & **Total Pressure** & **Unit Reynolds Number** & **Boundary Layer** \\
**Mach Number** & **(kPa)** & **(/m)** & **Thickness (mm)** \\
**M\({}_{0,\epsilon}\)** & **P\({}_{\text{tc}}\)** & **Re\({}_{\text{x}}\)** & **8\({}_{\text{x}}\)** \\ \hline
3 & 101.325 & 7.53 \(\times\) 10\({}^{7}\) & 7.38 \\ \hline \end{tabular}
\end{table}
Table 1: Flow condition for simulations.  
Figure 4: Comparison between calculation pressure curves and experimental data.  
Figure 3: Validation model of dual separation zones in the wind tunnel.  
basically set in dual-shock-wave models, whose mergence/re-separation process between dual separation zones exhibits a rapidly dynamic evolution. It requires sensors with high sampling rates to resolve the high-frequency information of transient flow field during the state transition. Therefore, the aforementioned studies mostly focused on the steady parameters in one single state (e.g., the length of the merged separation zone [15,16]) and the critical decoupling criterion between the merged and decoupled state [17]. There is a lack of a detailed depiction of flow field evolution from a decoupled state to a merged state. However, the transition between different states in our study is a rather smooth process compared to other research. It is adequate to use the steady simulation method to reveal the regularity of state transitions for our model, as the comparison between the numerical results and experimental data demonstrates.