# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 5 Conclusions  
The present work provides a numerical investigation of thrust augmentation of a planar convergent-divergent micro-nozzles by means of steady micro-jet blowing. The aim of such active flow control consists in hindering the viscous losses and suppress the chocking of the flow into the divergent section due to the growth of boundary layer thickness. The analysis of the micro-nozzle performance involved both water vapor and nitrogen gas as propellant, operating in a vaporizing liquid micro-thruster mode and cold gas micro-resistojet mode, respectively. Concerning the active control configuration, two micro-injectors have been placed into the divergent region along the sidewalls, injecting a secondary flow of propellant perpendicularly to the wall where they have been located, i.e., at \(75^{\circ}\) of injection angle with respect to the micro-nozzle axis. The secondary injection has been supposed symmetric with respect to the micro-nozzle axis, leading to symmetric expanding flow. Each micro-jet blowing configuration has been defined by the overall momentum coefficient \(c_{\mu}\), i.e., the sum of the ratios between the momentum of each secondary jet and the momentum of the core flow at the injection section. The impact of the micro-jet blowing on the micro-nozzle performance has been evaluated in terms of percent variation of the thrust co-efficient, the jet thrust \(\Delta^{\%}\)or\({}_{\textbf{J}\textbf{e}\textbf{t}}\) and the jet specific impulse \(\Delta^{\%}\)or\({}_{\textbf{J}\textbf{e}\textbf{t}}\), and the estimation of the momentum thickness along the width-wise direction \(\theta_{xy}\) at the exit section. Results highlight that, at similar \(c_{\mu}\), \(\Delta^{\%}\)or\({}_{\textbf{J}\textbf{e}\textbf{t}}\) significantly increases when considering the secondary injection of gaseous nitrogen in comparison to the water vapor one. As revealed by the 3D contour plot of the Mach number in combination with stream  
Figure 12: Momentum thickness along the width-wise direction \(\theta_{\textbf{xy}}\) at the exit section in the symmetry plane as a function of the overall momentum co-efficient of secondary injection \(c_{\mu}\): (**a**) nitrogen gaseous flow; (**b**) water vapor flow. lines visualization, this is due to the formation of larger vortical structures close to jet 1, which cause a stronger energization of the core flow expanding into the divergent section, and the consequent better expansion process just downstream to jet 1. The greatest performance improvement is retrieved at the maximum \(c_{\mu}\) for both water vapor and nitrogen gaseous flows. Concerning the former, it is \(\Delta\%_{\textbf{T},\textbf{jet}}=+22.6\) % and \(\Delta\%_{\textbf{L}\textbf{S}\textbf{P},\textbf{T}\textbf{jet}}=+2.9\)% at \(c_{\mu}=0.168\), while the latter exhibits \(\Delta\%_{\textbf{T},\textbf{jet}}=+36.1\) % and \(\Delta\%_{\textbf{L}\textbf{S}\textbf{P},\textbf{T}\textbf{jet}}=+9.1\)% at \(c_{\mu}=0.297\). The axial profiles of the centerline velocity and the velocity profile at the micro-nozzle exit along the width-wise direction highlight the mitigation of the viscous chocking of the core flow thanks to secondary injection, with enhanced flow expansion in both the subsonic pocket region close to walls and the supersonic core flow region. Furthermore, a relevant advantage in using micro-jet blowing has been pointed out by computing the percent variation of thrust coefficient \(\Delta\%_{\textbf{T}}\). By comparing the baseline test case without secondary injection and test cases owning active micro-jet blowing with by-passed mass flow rate (percent total mass flow rate \(\Delta\%_{\dot{m}}=0.0\)%), \(\Delta\%_{\textbf{T}}\) is higher than +10%, even though with negligible \(\Delta\%_{\textbf{T},\textbf{jet}}\) and \(\Delta\%_{\textbf{L}\textbf{S}\textbf{P},\textbf{jet}}\). This is related to the reduction of the \"cost\" of micro-nozzle feeding, since the pressure at the micro-nozzle entrance decreases due to the reduced inlet mass flow rate.