# Experimental Identification of Characteristic Curves of
## 2 Literature Review  
Plenty of literature has been written on experiments with supersonic nozzles. Regarding operational and geometric parameter studies, [PERSON] [10] explored nozzle positioning for industrial supersonic ejectors, and [PERSON] [11] validated the significance of Fabri-choking; however, the TET was not mentioned. [PERSON] [12; 13] optimized the efficiency of ejector refrigeration through geometric adjustments and integration of renewable energy, while [PERSON] [14] analyzed the pressure distribution in a two-stage multi-nozzle system. [PERSON] [15; 16] studied R-134a ejector refrigeration systems, focusing on pressure recovery and mixing chamber designs. His experiments revealed a transition point where the secondary flow rate changes from supersonic to subsonic, which is critical for current research. [PERSON] [17] validated a CFD model for a supersonic air ejector, high  
Figure 1: Ejector internal geometry showing the two most important flows. The flow direction is from the left to the right.  
lighting accurate turbulence modeling, while [PERSON] [18] validated a numerical model improving suction flow rate and reducing incidence time in vacuum ejectors, both with experimentation, highlighting the importance of the TET. Others have focused their research on the optimization and performance enhancement of ejectors. [PERSON] [19] developed a validated optimization method for a supersonic ejector compressor used in vehicle waste heat recovery, while [PERSON] [20] explored the optimal position of the nozzle for subsonic ejectors through experimental and CFD analysis. [PERSON] et al. [21; 22; 23] provided extensive experimental results on two-phase R134a ejectors, highlighting that a convergent-divergent nozzle improves the entrainment ratio, while a convergent nozzle is less affected by subcooling variations. Experimenting with the adjustable multistage ejector, [PERSON] et al. [24; 25] found that two-stage ejector refrigeration systems driven by dual heat sources offer better refrigerating effects at condensation temperatures below 21.7 \({}^{\circ}\)C compared to single-stage systems.  
[PERSON] [26] examined adjustable ejectors with axial spindles, showing that a smaller nozzle throat area increases the entrainment ratio but reduces the discharge pressure, suggesting more economical design possibilities. In mixing characteristics, [PERSON] [27] found that tabs and ejectors reduced noise but less so than expected due to flow instability. [PERSON] [28] showed experimentally that the entrainment ratio in a rectangular supersonic ejector varies with the expansion mode and Mach number ratio. As noted above, the polytropic coefficient is crucial in the process of discharging an air-filled tank, as highlighted in previous studies by the authors [6]. [PERSON] [29] developed a model to predict the pressure and temperature of the tank during charging and discharging, noting that the polytropic exponent varies with the conditions and time. Many studies, such as those by [PERSON] et al. [21] and [PERSON] et al. [24], focus heavily on experimental validation and system-specific designs. While valuable, these approaches often lack generalization to unbuilt systems. Similarly, [PERSON] [17] and [PERSON] [20] emphasize CFD and numerical analyses, but their dependence on idealized conditions limits their practical applicability.  
This paper introduces a predictive TET that does not require physical prototypes or substantial computational resources, thus filling a significant gap in the literature and industry. Despite TET's acknowledged significance in the industrial market and literature [30], no empirical models for PTET have been found. By adding something new to an understudied field, this work expands on developments in ejector research.