# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 4 Results and Discussion
Consequently, the super-sonic core flow is compressed when crossing the jet 1 region; then, it expands immediately after with suppression of the viscous choking toward the exit section. The comparison between test cases N2_6 and N2_8 analyzes the use of secondary injection in relation to the similar increase of total mass flow rate in the core flow (i.e., \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +24.8%) without any fluidic flow control. As reported in Tables 8 and 9, a weak difference is retrieved in percent jet augmentation: \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +36.1% in presence of micro-jet blowing (N2_6) and \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +32.8% with equivalent core mass flow rate increase (N2_8). However, the more the core mass flow rate is, the higher the feeding pressure must be and, consequently, the more the cost per unit of thrust results. In fact, \(p_{0}\) increases from 1.287 \(\times\) 10\({}^{5}\) Pa to 1.608 \(\times\) 10\({}^{5}\) Pa for test case N2_8, and the percent increase of the thrust co-efficient is reduced from +32.9% (test case N2_6) to \(\Delta^{\%}\)or\({}_{\textbf{T}}\) = +2.9% (test case N2_8). Similar finding results are achieved by comparing the baseline test case N2_1 with the test case N2_7, owning active micro-jet blowing and bypassed mass flow rate (\(\Delta^{\%}\)or\({}_{\textbf{T}}\) = +0.0%): \(\Delta^{\%}\)or\({}_{\textbf{T}}\) = +13.3%, with \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +2.0%, and \(\Delta^{\%}\)or\({}_{lgp,jet}\) = +2.8%. Figure 11a shows the profile of the axial velocity \(U_{x}\) along the centerline: in presence of secondary injection, the higher \(c_{\mu}\) is, the sooner the flow slows down and compresses after the initial flow expansion, and the more it re-expands toward the exit section. This is in accordance with the 2D and 3D analysis previously discussed and shown in Figures 9 and 10. Figure 9: Contour plot of the Mach number and Schlieren computations: (**a**) test case N2_1 (baseline); (**b**) test case N2_2 (additional mass flow rate, jet 1 = ON, jet 2 = OFF); (**c**) test case N2_3 (additional mass flow rate, jet 1 = ON, jet 2 = OFF); (**d**) test case N2_4 (additional mass flow rate, jet 1 = ON, jet 2 = ON); (**e**) test case N2_5 (additional mass flow rate, jet 1 = ON, jet 2 = OFF); (**f**) test case N2_6 (additional mass flow rate, jet 1 = ON, jet 2 = ON); (**g**) test case N2_7 (bypassed mass flow rate, jet 1 = ON, jet 2 = OFF): (**h**) test case N2_8 (additional mass flow rate, jet 1 = OFF, jet 2 = OFF). Instead, Figure 11b highlights the increase of the axial velocity \(U_{x}\) at the micro-nozzle exit (\(x\) = 0.00301 m) by showing the modification of \(U_{x}\) in the symmetry plane along the width-wise direction (y-coordinate). With respect to the baseline test case N2_1 (blue line with circles), the more \(c_{\mu}\) increases, the more the flow accelerates in both the subsonic boundary layer and the super-sonic fully developed flow region; consequently, the maximum expansion enhancement is observed at the highest \(c_{\mu}\) (test cases N2_5 and N2_6). Figure 11: Profiles of the axial velocity \(U_{x}\) for the water vapor flow in the symmetry plane (0,\(x\),\(y\)): (**a**) at \(y\) = 0 m (along the symmetry axis); (**b**) at \(x\) = 0.00301 m (along the width-wise direction). Test cases: N2_1 (baseline); N2_2 (additional mass flow rate, jet 1 = ON, jet 2 = OFF); N2_3 (additional mass flow rate, jet 1 = ON, jet 2 = OFF); N2_4 (additional mass flow rate, jet 1 = ON, jet 2 = ON); N2_5 (additional mass flow rate, jet 1 = ON, jet 2 = OFF); N2_6 (additional mass flow rate, jet 1 = ON, jet 2 = ON); N2_7 (bypassed mass flow rate, jet 1 = ON, jet 2 = OFF): N2_8 (additional mass flow rate, jet 1 = OFF, jet 2 = OFF).