# MEMS Vaporizing Liquid Microthruster: A Comprehensive Review
## 4 Instability Control into VLMs
### Active Control of Flow Instability  
The flow into VLM undergoes fast phase change phenomena in an open-loop system at high wall temperature and full vaporization conditions. An in-depth analysis of the dynamic flow instabilities is required for active control purposes, but it is still missing to date. The dynamic analysis of two-phase oscillations (TPOs) into microchannels has always involved microchannel systems operating below the dry-out condition. As underlined in [29; 30], TPOs into parallel microchannels systems have been mapped depending on the heat flux to mass flux (\(q/G\)) ratio and inlet subcooling condition. This has allowed distinguishing two main kinds of TPOs, i.e., high-frequency TPOs (above 2 Hz) and low-frequency TPOs (below 2 Hz). In particular, for a given degree of subcooling, at low \(q/G\) the former is experienced, characterized by a pressure drop, temperature, and mass flow rate fluctuating at low amplitudes. As \(q/G\) increases, the oscillating frequencies reduce, coupled with the growth of the fluctuation amplitudes, and the second TPO regime establishes. Furthermore, it has been found that the unstable operating region of \(q\) and \(G\) extends by reducing the subcooling degree. The role of flow and thermal coupling in the presence of flow oscillations was investigated in [38; 39] by considering a two parallel microchannels system. The first work demonstrates that controllable oscillations could benefit the mitigating flow uneven distribution and achieve a uniform temperature distribution. The second work focuses on the influence of the Ledingg instability on the thermal performance of two thermally isolated parallel channels operating at a constant pressure and using HFE-7100 as a coolant. Results show that the boiling incipience in one of the channels triggered the Ledingg instability due to the increased flow resistance. With an increasing heat flux, the Ledingg instability triggered a severe uneven distribution of the flow between channels coupled with a strong temperature excursion on the flow-starved channel (experiencing boiling) owing to a deteriorated heat transfer coefficient. The temperature excursion per  
Figure 9: Schematic sketch of backflow [32]. sists until boiling occurrence in the second channel, which hinders the uneven distribution of the flow. As a result, the wall temperature of both channels reduces significantly. In the context described above, two main approaches were considered for the active control of flow instability. The first relies on the feeding pressure/mass flow rate control, for instance, using a micro-valving system placed upstream the inlet section [40; 41; 42; 43], bubble seeding [44; 45], or synthetic jet in the crossflow [46] demonstrating the heat transfer coefficient enhancement (see Figure 11). This approach is typically applied in partially vaporized heating systems after performing a predictive analysis of the dynamic response of the thermal system [47]. However, oscillations of the mass flux would directly affect the propulsive performance of VLMs. Furthermore, VLMs experience the occurrence of the CHF and the dry-out condition into the heating chamber due to the need for total vaporization and overheating of the propellant flow. The second approach of flow boiling active control focuses on heat flux-based control through the design of the heating system in combination with the temporal heating law. The interest in a pulsed heating strategy has continuously increased in recent years for thermal management applications. [PERSON] et al. [48] experimentally characterized transient phenomena in a water-fed single microchannel heat exchanger during pulsed heating (frequency \(f_{s}=8\) Hz and pulse duration \(t_{s}=31\) ms). The authors observed that low-frequency/high-duration pulsed heating leads to an increase in the average hotspot temperature. Similarly, [PERSON] and [PERSON] [49] investigated the microscale boiling phenomenon under pulse heating (\(t_{s}=2\) ms) on a silicon-based microchannel with an integrated platinum microheater.