# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 4 Results and Discussion  
The use of secondary injection has two main purposes, namely thrust augmentation by mass addition and thrust augmentation by viscous loss reduction and flow expansion enhancement. Concerning the latter, the boundary layer growth at walls causes the establishment of the viscous choking into the divergent section and severely inhibits the super-sonic expansion of the flow, which mainly occurs into the exhaust plume downstream of the micro-nozzle exit, as confirmed in the contour plots of the Mach number in Figures 4 and 5, referred to as the water vapor flow and the nitrogen gaseous flow, respectively. In the present section, the impact of secondary injection on the super-sonic expansion of the flow into the micro-nozzle has been evaluated by coupling the analysis of the overall performance in terms of thrust force, specific impulse, and thrust co-efficient with the analysis of the flow expansion into the divergent region. The last one is based on the computation of the boundary layer thicknesses at the exit section and percent variation of the jet thrust and specific impulse related to the jet thrust, as specified in Section 2.3. Results and comparisons are summarized in Tables 7 and 8 for the water vapor flow and Tables 8 and 9 in the case of nitrogen gas flow. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Test Case** & **Jet 1** & **Jet 2** & \begin{tabular}{c} \(\hat{m}_{0}\) \\ **[kg/s]** \\ \end{tabular} & \
\begin{tabular}{c} \(\hat{m}_{jet,1}+\hat{m}_{jet,2}\)** \\ **[kg/s]** \\ \end{tabular} &
\begin{tabular}{c} \(\hat{m}_{tot}\) \\ **[kg/s]** \\ \end{tabular} & \(M_{jet,1}\) & \(M_{jet,2}\) & \(\epsilon_{p,jet1}\) & \(\epsilon_{p,jet2}\) & \(\epsilon_{p,tot}\) \\ \hline N2\_1 & OFF & OFF & \(5.00\times 10^{-6}\) & - & \(5.00\times 10^{-6}\) & - & - & - & - & - \\ N2\_2 & ON & OFF & \(5.00\times 10^{-6}\) & \(0.15\times 10^{-6}\) & \(5.15\times 10^{-6}\) & 0.43 & - & \(8.58\times 10^{-3}\) & - & \(8.58\times 10^{-3}\) \\ N2\_3 & ON & OFF & \(5.00\times 10^{-6}\) & \(0.29\times 10^{-6}\) & \(5.29\times 10^{-6}\) & 0.86 & - & \(3.95\times 10^{-2}\) & - & \(3.95\times 10^{-2}\) \\ N2\_4 & ON & ON & \(5.00\times 10^{-6}\) & \(0.50\times 10^{-6}\) & \(5.50\times 10^{-6}\) & 0.86 & 0.43 & \(4.28\times 10^{-2}\) & \(1.38\times 10^{-2}\) & \(5.66\times 10^{-2}\) \\ N2\_5 & ON & OFF & \(5.00\times 10^{-6}\) & \(0.76\times 10^{-6}\) & \(5.76\times 10^{-6}\) & 1.71 & - & \(1.93\times 10^{-1}\) & - & \(1.93\times 10^{-1}\) \\ N2\_6 & ON & ON & \(5.00\times 10^{-6}\) & \(1.24\times 10^{-6}\) & \(6.24\times 10^{-6}\) & 1.71 & 0.86 & \(2.33\times 10^{-1}\) & 6.40\(\times 10^{-2}\) & \(2.97\times 10^{-1}\) \\ N2\_7 & ON & OFF & \(4.50\times 10^{-6}\) & \(0.50\times 10^{-6}\) & \(5.00\times 10^{-6}\) & 1.31 & - & \(1.19\times 10^{-1}\) & - & \(1.19\times 10^{-1}\) \\ N2\_8 & OFF & OFF & \(6.24\times 10^{-6}\) & - & \(6.24\times 10^{-6}\) & - & - & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Test matrix and micro-jet blowing conditions: nitrogen gaseous flow. Jet temperature \(T_{jet1}=T_{jet2}=293\) K.