## 1 Introduction  
Energy-saving topic gains more attention globally. This is a logical consequence of the increase in people's awareness all over the world regarding the limited fossil energy resources. It keeps depleting and eventually will become extinct. To solve this issue, many researchers have been searching for renewable energy resources as well as developing efficient technologies to utilize that energy. These attempts have led researchers to various ideas such as an idea to use ejectors in refrigeration systems to compress the refrigerant. Instead of using electricity, an ejector is able to utilize thermal energy to do the compression. An ejector is a device that entrains a fluid at low pressure (secondary flow) by accelerating another fluid at high pressure (primary flow) via a nozzle. Then, the primary and secondary flows mix inside the device and leave through an outlet at an intermediate pressure. In an ejector refrigeration system, the secondary flow is the refrigerant leaving the evaporator, and the ejector acts as a compressor through which this refrigerant is compressed. A typical structure of an ejector can be seen in Figure 1. In this work, the mixing section consists of a converging mixing section, also called constant pressure mixing section, and a constant area mixing section, also called ejector throat (ET) (Figure 1). A supersonic ejector operation can be divided into three modes, i.e., critical (double-choked) mode, sub-critical (single-choked) mode, and malfunction mode [1]. Figure 2 shows various ejector operation modes at a fixed primary and secondary inlet pressures. The ejector is in a critical mode operation when the primary and secondary flows are both choked. This means that both mass flow rates are constant with respect to the change of ejector outlet pressure, \(P_{4}\). The secondary flow is choked because it accelerates until it reaches sonic speed through a hypothetical converging annular duct formed by the outer boundary of the primary flow jet and the wall of the ejector [2]. As we increase the outlet pressure, the secondary flow will not be choked anymore (only the primary flow is choked). This pressure threshold is referred to as critical pressure, \(P_{crit}\). Beyond this pressure, the ejector will enter the sub-critical mode operation within which an increase in \(P_{4}\) will decrease the secondary mass flow rate but has no effect on the primary mass flow rate. As the outlet pressure is increased further, it reaches a pressure, \(P_{mal}\), at which the ejector starts to malfunction. There will be no secondary flow or, even, reverse flow through the secondary inlet will occur. In practice, an ejector is usually required to operate in the critical mode/condition, and hence, it is also called the on-design condition. Designing an ejector is an important task so that the system utilizing this device is not only able to operate functionally, but also efficiently. To know/predict the performance of an ejector, analytical and computational fluid dynamics (CFD) models are usually used before experiment. The one-dimensional analytical model has an advantage over the CFD for its simplicity and quick result. It does not require the time-consuming generation of the discretized  
Figure 1: Schematic of a typical ejector. Figure 2: Various ejector operation modes at a fixed primary and secondary inlet pressures. Entrainment ratio (the y-axis) is the ratio of secondary to primary mass flow rates. computational domain. Furthermore, the calculation time is also short, in the order of a few minutes or even seconds, compared to that of CFD which can take hours. Due to these advantages, the one-dimensional model is attractive to predict the global performance of an eject such as predicting the primary and secondary mass flow rates (\(\dot{m}_{p}\) and \(\dot{m}_{s}\)) and the ejector outlet pressure (\(P_{4}\)). To improve the model's accuracy, the effects of local flow phenomena have to be included [1].