# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 4 Results and Discussion
In particular, the core flow energization and compression by secondary injection allows for the mitigation of the viscous chocking occurring toward the exit section, with significant improvement downstream jet 1 at \(x>0.002\) m.  
Figure 7: 3D representation of the water vapor flow into the micro-nozzle through contour plot of the Mach number in combination with streamline visualization: (**a**) test case H2O_1 (baseline); (**b**) test case H2O_2 (additional mass flow rate with jet 1 = ON, jet 2 = OFF); (**c**) test case H2O_3 (additional mass flow rate with jet 1 = ON, jet 2 = ON). To compare the effect of secondary injection in nitrogen-fed CGs with the water-propelled VLMs, similar mass flow rates and overall momentum co-efficients have been used. As a result, a higher improvement of the thrust co-efficient \(c_{T}\) is retrieved when operating with gaseous nitrogen in CG mode. More specifically, the test cases N2_5 and N2_6 have exhibited the highest performance enhancement, with percent thrust co-efficient augmentation equal to +21.6% and +32.6%, respectively, and percent increment of total mass flow rate of 15.2% and 24.8%, respectively. The beneficial impact of secondary injection on the jet thrust is even greater: \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +26.0% and \(\Delta^{\%}\)or\({}_{lgp,Fjet}\) = +9.3% for the test case N2_5, and \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +36.1% and \(\Delta^{\%}\)or\({}_{lgp,Fjet}\) = +9.1% for the test case N2_6. By reducing the momentum co-efficient, the percent thrust augmentation decreases, too: at \(c_{\mu}\) = 0.0556 (test case N2_4), it is \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +14.2%, and \(\Delta^{\%}\)or\({}_{lgp,Fjet}\) = +3.9%, with \(\Delta^{\%}\)or\({}_{\textbf{Tjet}}\) = +10.0%. It is worth observing that the stronger impact of secondary injection in nitrogen-fed CGs is likely due to the location of micro-jets in relation to the operating conditions. In fact, the quality of the expansion process of the nitrogen gaseous flow is higher than the one experienced by the water vapor flow, as highlighted by the contour plot of the Mach number in Figure 9a. This produces a thinner sub-sonic packet along sidewalls, which starts to form just before the location of the jet 1. Furthermore, for a given \(c_{\mu}\), the kinetic energy of the micro-jet, and hence, the penetration length, in nitrogen-fed CG mode is higher than the one observed in water-fed VLM mode. The enhancement of the expansion process is clearly underlined in the contour plots of the Mach number shown in Figure 9. In fact, with respect to the baseline configuration (Figure 9a), the isoline \(M\) = 1.4 moves downstream for the test case N2_2 (Figure 9b), approaching to the exit section for test cases N2_3 (Figure 9c) and N2_4 (Figure 9d). By increasing \(c_{\mu}\) (test cases N2_5 and N2_6), the flow undergoes a second expansion process with \(M\) > 1.4 at the micro-nozzle exit. The 3D representation of the flow in Figure 10 confirms that the expansion improvement is due to the formation of the recirculating vortexes just before and after the jet 1. Comparing to the water-fed cases shown in Figure 7, test cases N2_5 and N2_6 exhibit stronger and larger vortical structures, which affect the core flow more deeply up to break the expansion process in correspondence of jet 1. This allows the core flow to gain energy and expand more efficiently downstream of the jet 1. The Schlieren images in Figure 9 show the impact of secondary injection on the density gradients. In general, in comparison with the water-fed VLM cases, a more pronounced gray is computed along the sonic line due to the smaller sub-sonic pocket and the more abrupt density change: this confirms the higher effectiveness of such flow control strategy when operating in nitrogen-fed CG mode. As expected, the most significant impact on the expanding flow is retrieved at the highest \(c_{\mu}\) (test cases N2_5 and N2_6): the jet 1 deeply penetrates the core flow, shrinking it and producing an enlargement of the sub-sonic region.