# Correction of Aero-Optical Effect with Blow-Suction Control for Hypersonic Vehicles
## 2 Physical Model and Correction Method
### Correction Method  
In order to cool the optical seeker's window, two different jet cooling methods are employed. The low temperature jet separates the optical window from the high-temperature incoming flow, effectively cooling it. The cooling nozzle is positioned upstream of the window, at a slope angle of 15\({}^{\circ}\) with respect to the projectile body axis, as depicted in Figure 2 below. The direction of the cooling jet is indicated by the red arrow. For selecting an appropriate jet medium, low-temperature nitrogen is chosen due to its easy availability and relatively low cost, with a jet temperature set to 77 K. The incoming flow conditions consist of air at Mach numbers of 3 and 5, a specific heat ratio of 1.4, and the wall temperature maintained at 300 K. Other detailed parameters, such as static pressure and static temperature can be found in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Density** & **Fusing Point** & **Elastic Modulus** & **Specific Heat Capacity** & **Thermal Conductivity** & **Yield Strength** & **Poisson’s Ratio** \\ \hline
3980 kg/m\({}^{3}\) & 2050 K & 344 GPa & 750 J/(kg\(\cdot\)K) & 36 W(m\(\cdot\)K) & 300 MPa & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical properties of optical window [22]. Figure 1: (a) THAAD-like seeker geometry parameters. (b) Geometric parameters near the optical window. As previously mentioned, the key aspect in suppressing the aero-optical effect lies in mitigating density pulsations. Currently, there are two primary approaches: one involves reducing the intensity of density pulsations through cooling; and the other aims to disintegrate large-scale vortex structures into smaller ones via flow control, thereby diminishing the intensity of density pulsations [21]. In this study, we will investigate the corrective impact of the latter method on aero-optical effects. The model employed remains based on the THAAD-like seeker model described above, with a series of MVGs positioned 4 mm upstream from the window, as depicted in Figure 3. The dimensions of the MVGs are indicated in Figure 3, with a spacing of 1 mm between adjacent MVGs, as denoted in the lower right corner. In order to further optimize the flow field structure near the optical window, a suction device is introduced at the compression corner adjacent to the window end, aiming to investigate whether it can enhance the light transmission performance of the flow field. The blow-suction control diagram is depicted in Figure 4 below. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & \multicolumn{3}{c}{**Flow Field Parameter**} & \multicolumn{2}{c}{**Blowing**} & \multicolumn{2}{c}{**MVGs**} & \multicolumn{1}{c}{**Suction**} \\ \hline  & \(Ma_{\infty}\) & \(P\) (Pa) & \(T\) (K) & \(P_{j}\) (kPa) & \(m_{0}\) (kg/s) & \(\theta\) & & \\ \hline
0 & 3 & 5529 & 216 & - & 0 & - & without & without \\
1 & 5 & 5529 & 216 & - & 0 & - & without & without \\
2 & 3 & 5529 & 216 & 11 & 0.05 & 15\({}^{\circ}\) & without & without \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Incoming flow parameters and cooling jet parameters. Figure 4: Schematic diagram of blow and suction control near optical window. Figure 3: Schematic diagram of MVGs. Figure 2: Schematic diagram of two jet-cooling modes: (**a**) \(\theta=15^{\circ}\) and (**b**) \(\theta=90^{\circ}\). According to relevant references [23], the upper limit of the total mass of the cooling gas is 1 kg, and the time interval from the beginning of pneumatic heating to hitting the target is 10-20 s when the hood is removed. Therefore, in this section, where jet cooling research is conducted, a maximum jet flow rate of 0.05 kg/s should be used. Among other parameters, \(Ma_{\infty}\) represents the incoming Mach number, \(P0\) represents the incoming pressure at this height, \(T0\) represents the local static temperature, \(Pj\) represents the cooling jet pressure, and \(mj\) represents the jet flow of a specific jet mode.