# Experimental Study of the Formation and Evolution of Gas Jets in Supersonic Combustion Chambers
## 2 Test and Observation Setup
### Test System
#### 2.1.2 Jet Generating Device  
The modular jet generator shown in Figure 3 was designed to explore the influence of jet angle and momentum flux ratio on the formation and evolution of the nitrogen jet in a supersonic inlet flow. Different jet angles can be realized by replacing the jet generator. The jet angle \(\alpha\) was defined between supersonic mainstream and jet velocity directions. Five different jet angles were tested and analyzed: 30\({}^{\circ}\), 60\({}^{\circ}\), 90\({}^{\circ}\), 120\({}^{\circ}\), and 150\({}^{\circ}\). It should be emphasized that though the skew of the nozzle leads to uneven Mach number distribution at the nozzle outlet, this was ignored in the present analysis. The following Cartesian coordinate system was defined to facilitate the subsequent discussion. The positive X axis direction (streamwise direction) is the same as that of the mainstream velocity, the positive Y axis direction (longitudinal direction) is the same as that of the sonic jet velocity, and the positive Z axis direction (spanwise direction) is the same as the camera viewing direction. The momentum flux ratio of the nitrogen jet is given by the following equation [31]:  
\[J=\frac{\left(\rho u^{2}\right)_{j}}{\left(\rho u^{2}\right)_{\infty}}, \tag{1}\]  
where the subscript \(j\) denotes the jet outlet condition, and \(\infty\) denotes the supersonic mainstream condition at the front of the bow shock. The momentum flux ratio of jet was controlled by changing the total pressure of jet (\(Pt_{j}\)). Three values of \(Pt_{j}\) of efflux were used during the experiment, namely, 1.8, 2.4, and 3.0 Mpa. Due to the flow loss caused by pipeline deformation and other factors, the total pressures at the jet outlet and upstream were not consistent. In this work, the total \begin{table}
\begin{tabular}{c c c c} \hline
**Parameter** & **Symbol** & **Unit** & **Value** \\ \hline Mach number & \(M_{\infty}\) & / & 2.6 \\ Velocity & \(U_{\infty}\) & m/s & 1445 \\ Total temperature & \(Tt_{\infty}\) & K & 1636 \\ Static temperature & \(T_{\infty}\) & K & 820 \\ Static pressure & \(p_{\infty}\) & MPa & 0.079 \\ Density & \(\rho_{\infty}\) & kg/m\({}^{3}\) & 0.337 \\ \hline \end{tabular}
\end{table} 
Table 1: Supersonic crossflow conditions. Figure 2: Schematic of the direct-connect experimental setup. pressure at the outlet of the jet was determined by the position of the Mach disk, which was generated when the jet expanded in free space. The empirical formula for the Mach disc position and the jet total (\(Pt_{j}\)) and back (\(P_{eb}\)) pressures was proposed by [PERSON] and [PERSON] [32], namely:  
\[\frac{y_{1}}{d}=0.67\cdot(\frac{Pt_{j}}{P_{eb}})^{0.5}, \tag{2}\]  
where \(y_{1}\) is the height of the Mach disk. The flow field observation technique (described in Section 2.2) was used to obtain the free expansion results of the efflux for the above-named three upstream total pressures, as shown in Figure 4. In addition, Formula (2) was used to obtain the total pressure at the jet outlet. Other parameters at the jet outlet were obtained using NASA thermodynamic calculation software [33], as shown in Table 2. The numerical results showed that the momenta flux ratio of the jet was 0.49, 0.88, and 1.46, for pressures 1.8, 2.4, and 3.0 Mpa, respectively. A total of 15 experimental tests were carried out to explore all the combinations of the five jet angles and three jet momentum flux ratios. The identification number and working conditions of all the tests are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **Symbol** & **Unit** & & **Values** & \\ \hline Mach number & \(M_{j}\) & & 1 & \\ Stagnation pressure & \(Pt_{j}\) & MPa & 0.475 & 0.849 & 1.422 \\ Velocity & \(U_{j}\) & m/s & & 322.3 & \\ Density & \(\rho_{j}\) & kg/m\({}^{3}\) & 3.38 & 6.05 & 10.13 \\ Jet-to-freestream Momentum & \(j\) & & 0.49 & 0.88 & 1.46 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Resulting jet exit flow properties at the sonic orifice.