# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 4 Results and Discussion
\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 H2O\_1 & OFF & OFF & \(5.00\times 10^{-6}\) & - & \(5.00\times 10^{-6}\) & - & - & - & - & - \\ H2O\_2 & ON & OFF & \(5.00\times 10^{-6}\) & \(0.63\times 10^{-6}\) & \(5.63\times 10^{-6}\) & 1.09 & - & \(1.26\times 10^{-1}\) & - & \(1.26\times 10^{-1}\) \\ H2O\_3 & ON & ON & \(5.00\times 10^{-6}\) & \(0.96\times 10^{-6}\) & \(5.96\times 10^{-6}\) & 1.09 & 0.55 & \(1.28\times 10^{-1}\) & \(4.02\times 10^{-2}\) & \(1.68\times 10^{-1}\) \\ H2O\_4 & ON & OFF & \(4.50\times 10^{-6}\) & \(0.50\times 10^{-6}\) & \(5.00\times 10^{-6}\) & 0.95 & - & \(1.11\times 10^{-1}\) & - & \(1.11\times 10^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Test matrix and micro-jet blowing conditions: water vapor flow. Jet temperature \(T_{jet1}=T_{jet2}=505.58\) K.  
Figure 4: Contour plot of the Mach number for the baseline configuration of the water vapor flow (test case H2O_1). Figure 5: Contour plot of the Mach number for the baseline configuration of the nitrogen gaseous flow (test case N2_1). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test Case** & \(\hat{\mathbf{m}}_{tot}\) & \(\mathbf{A^{*}}\) & \(\mathbf{p_{0}}\) & \(\mathbf{T}\) & \(\mathbf{I_{sp}}\) & \(\mathbf{c_{T}}\) & \(\mathbf{\Delta\%}_{\hat{m}}\) & \(\mathbf{\Delta\%}_{\hat{m}}\) \\  & [kg/s] & [mm\({}^{2}\)] & [Pa] & [mN] & [s] & [-] & [\%] & [-] \\ \hline H2O\_1 & \(5.00\times 10^{-6}\) & 0.018 & \(2.15\times 10^{5}\) & 4.489 & 89.8 & 1.160 & - & - \\ H2O\_2 & \(5.63\times 10^{-6}\) & 0.018 & \(2.15\times 10^{5}\) & 5.140 & 91.3 & 1.328 & +12.6 & 14.5 \\ H2O\_3 & \(5.96\times 10^{-6}\) & 0.018 & \(2.15\times 10^{5}\) & 5.449 & 91.4 & 1.408 & +19.2 & 21.4 \\ H2O\_4 & \(5.00\times 10^{-6}\) & 0.018 & \(1.95\times 10^{5}\) & 4.531 & 90.6 & 1.291 & +0.0 & 11.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance analysis of the micro-nozzle: water vapor flow. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test Case** & \(\mathbf{T}_{jet}\) & \(\mathbf{\Delta\%}_{T,jet}\) & \(\mathbf{I_{sp,jet}}\) & \(\mathbf{\Delta\%}_{sp,jet}\) & \(\mathbf{\delta^{*}_{xy}}\)1  & \(\mathbf{\theta_{xy}}\)1  & \(\mathbf{\delta^{*}_{xx}}\)2  & \(\mathbf{\theta_{xx}}\)2  \\  & [mN] & [\%] & [s] & [\%] & [\%] & [\%] \\ \hline H2O\_1 & 2.801 & - & 56.0 & - & 132.3 & 23.2 & 7.6 & 2.5 \\ H2O\_2 & 3.247 & +15.9 & 57.7 & +3.0 & 187.2 & 19.9 & 8.5 & 2.5 \\ H2O\_3 & 3.433 & +22.6 & 57.6 & +2.9 & 174.7 & 9.7 & 6.1 & 2.1 \\ H2O\_4 & 2.839 & +0.9 & 56.8 & +1.4 & 162.8 & 18.4 & 7.9 & 2.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Analysis of the flow expansion into the micro-nozzle: water vapor flow. Concerning the water vapor flow, the test cases H2O_2 and H2O_3 correspond to the secondary injection with increased total mass flow rate with respect to the baseline configuration without actuation: the former refers to single jet configuration with \(\Delta^{\infty}\%_{\dot{m}}=12.6\%\), while the latter results from activation of both micro-jets with \(\Delta^{\infty}_{\dot{m}}=19.2\%\). If the total thrust is considered, it rises from 4.489 mN of the baseline test case (H2O_1) to 5.140 mN and 5.449 mN for test cases H2O_2 and H2O_3, respectively. This leads to an improvement of the thrust co-efficient up to about 21.4%, from \(c_{T}=1.16\) of test case H2O_1 to \(c_{T}=1.408\) of the test case H2O_3. However, when considering the activation of the jet 1 at same total mass flow rate of the baseline configuration (test case H2O_4) through bypass, i.e., \(\Delta\%_{\dot{m}}=0.0\%\), the feeding pressure at the micro-nozzle entrance decreases due to the reduced inlet mass flow rate.