# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 4 Results and Discussion
Despite the negligible variations of the total thrust and the specific impulse, this gives an improvement of \(c_{T}\) of about 11.3%, which underlines a significant benefit in using secondary injection: the reduction of the energetic cost proportional to the feeding pressure. If the jet thrust contribution is considered, the percent jet thrust augmentation \(\Delta^{\%}\mathbf{r}_{\mathbf{jet}}\) is equal to +15.9% for the test case H2O_2 and +22.6% for the test case H2O_3, as confirmed in Table 7. The last one is given by two different contributions, namely the percent mass flow rate variation \(\Delta\%_{\dot{m}}\) and the percent variation of the specific impulse \(\Delta^{\infty}\%_{\mathit{1}\mathit{jet}}\), which are equal to 12.6% and 3%, respectively, for test case H2O_2 and 19.2% and 2.9%, respectively, for test case H2O_3. Concerning the test case H2O_4, the increase of jet thrust is negligible (below 1%), as the total mass flow rate is not varied. The improvement of the super-sonic expansion thanks to micro-jet blowing is confirmed in Figure 6, which compares the contour plots of the Mach number of all test cases in combination with Schlieren computations. In general, the flow experiences a blocking effect due to the viscous growth of the boundary layer at the walls, as underlined by the isolines of the Mach number. However, in comparison with the baseline configuration (test case H2O_1 in Figure 6a), the presence of  
Figure 6: Contour plot of the Mach number and Schlieren computations: (**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); (**d**) test case H2O_4 (bypassed mass flow rate with jet 1 = ON, jet 2 = OFF). secondary injection mitigates these losses for test cases H2O_2 and H2O_3 (see Figure 6b,c), as highlighted by the elongation of the isoline \(M\) = 1.2 toward the micro-nozzle exit. This couples with an elongation of the super-sonic plume immediately after the micro-nozzle exit, which slightly moves the first Mach diamond region further downstream. Schlieren computations provide a more detailed view of the compressibility effects: the darkest structure appearing along the sidewalls in the divergent region reveals the presence of strong density gradients across the sonic line separating the super-sonic region (M > 1) to the sub-sonic region (M < 1), which start to develop close to the inner walls due to the boundary layer growth and then enlarge as the blocking of the flow occurs, coupled with the formation of the sub-sonic pocket region. Due to the viscous choking, the core flow is compressed as it moves toward the exit section; consequently, the intensity of the high-density gradient region softens. In presence of secondary injection, the shadow structure along the sonic line extends downstream, thanks to the energization of the main flow provided by micro-jets. In fact, by analyzing the 3D flow structures (see Figure 7), the formation of two vortical structures upstream and downstream of jet 1 is revealed, placed in the sub-sonic zone close to sidewalls. The intensity of these recirculating vortexes is proportional to \(c_{\mu,1}\), inducing forces that accelerate the core flow along the axial direction (x-direction) and shrink it in the width-wise direction (y-direction), while pushing the sub-sonic flow upward toward sidewalls. The enhancement of the flow expansion in the flow blocking region is also underlined in Figure 8a, comparing the axial profiles of the centerline velocity of all test cases.