# Thrust Augmentation of Micro-Resistojets by Steady Micro-Jet Blowing into Planar Micro-Nozzle
## 1 Introduction
Later, in [18], it was shown that the Mach number near the downstream position of the micro-nozzle's throat is lower than that in the conventional nozzle and that the position of the sonic point moves away from the throat toward the outlet if the size of the nozzle decreases. This specific behavior is ascribed to the higher viscous dissipation in micro-nozzles with respect to the macro-scale flow nozzles. More recently, viscous losses on boundary layer of rarefied gas flows inside micro-nozzles in the slip regime condition could lead to a reduction of the nozzle performance of about the 95%, as shown in [9]. In large-scale nozzles, the use of secondary injection as active fluidic flow control strategy has been investigated since the 1960s using both gaseous [19] and liquid [20] secondary jets to extend the propulsive performance of different kinds of nozzles, such as single expansion ramp nozzles for scramjets [21], dual-throat nozzles [22; 23], dual-bell nozzles [24], aero-spike nozzles [25], and biconical nozzles [26]. More recently, many numerical and experimental works have followed to extend the knowledge of the transition phenomena involved in the interaction between the secondary jet and the super-sonic flow expanding into the nozzle, such as [27], and to optimize the effectiveness of such active control system over a variety of parameters, for instance, injector location, number, shape, angles, cross section, and flow momentum [28; 29; 30; 31]. Despite the large amount of literature on the use of secondary injection in large-scale nozzles, there is a lack about the implementation of steady micro-jet blowing into planar micro-nozzles for viscous losses mitigation and thrust augmentation. The present work aims to fill this knowledge gap by providing a numerical investigation of the impact of such active fluid flow control of performance of a planar tornco-conical micro-nozzle geometry applied to MEMS-based micro-resistojets operating as water VLM or nitrogen CG. The overall investigation has been conducted on the planar geometry designed by [PERSON] and [PERSON] [32], where the entity of viscous losses is increased due to the relatively long divergent. The analysis is based on 3D CFD computations conducted using NS with Maxwellian partial slip at walls with a tangential momentum accommodation co-efficient (TMAC) equal to 0.80. The estimation of the global performance of the micro-nozzle was performed in terms of percent variation of thrust force, specific impulse, and mass flow rate, coupled with the calculation of the boundary layer thicknesses at the micro-nozzle exit. Furthermore, a qualitative description of the flow behavior based on the Mach number contour plot highlighted the differences among the investigated cases. The paper is structured as follows: Section 2 describes the micro-nozzle geometry and the active flow control configuration; Section 3 provides the description of the numerical setup and the overall investigation logic and methodology; Section 4 presents and discusses the results underlining the most interesting findings; and finally, Section 5 is devoted to conclusions and final remarks.