## 2 Materials and Methods
### Theoretical Model  
According to the law of conservation of mass and the energy balance, the following equations were derived. The total refrigerant mass flow rate for SS and IHX configurations was calculated as shown in Equation (1) [24]. \[\dot{m}_{ref}=\frac{\dot{Q}_{c}}{h_{evap,out}-h_{evap,in}} \tag{1}\]  
where \(\dot{Q}_{c}\) is the cooling capacity, and \(h_{evap,out}\) and \(h_{evap,in}\) are the enthalpy at the inlet and outlet of the evaporator. For the third configuration with vapor injection and ECO, mass balance gives the following equations:  
\[h_{3}\dot{m}_{ref}=h_{6}\left(\dot{m}_{ref}-\dot{m}_{5}\right)+h_{5}\dot{m}_{5} \tag{2}\]  
\[\dot{m}_{5}=\dot{m}_{ref}\frac{(h_{3}-h_{6})}{(h_{5}-h_{6})} \tag{3}\]  
The subscript numbers in all equations are referenced from the notation in the configurations shown in Figure 1. The heating capacity in all configurations is shown in Equation (4). \[\dot{Q}_{h}=\dot{m}_{ref}(h_{3}-h_{2}) \tag{4}\]  
The effectiveness of the IHX cycle was defined as shown in Equation (5) [24]  
\[\varepsilon_{IHX}=\frac{T_{cold,out}-T_{cold,in}}{T_{hot,in}-T_{cold,in}}=\frac{ T_{1}-T_{6}}{T_{3}-T_{6}} \tag{5}\]  
and Equation (6). \[\dot{m}_{3}h_{3}+\dot{m}_{6}h_{6}=\dot{m}_{4}h_{4}+\dot{m}_{1}h_{1} \tag{6}\]  
\(\dot{W}_{comp}\) is the power consumption of the system and was calculated for the SS and IHX cycles as shown in Equation (7) [24]. \[\dot{W}_{comp}=\frac{\dot{m}_{ref}\Delta h_{is,comp}}{\eta_{is}} \tag{7}\]  
where \(\eta_{is}\) is isentropic efficiency, and \(\Delta h_{is,comp}\) isentropic enthalpy difference. For the ECO cycle, the compressor work depends on the refrigerant mass flow rates \(m_{1}\) and \(\dot{m}_{5}\) and the changes of the enthalpies in the two lines and can be written as shown in Equation (8) [25]:  
\[\dot{W}_{comp}=\frac{\dot{m}_{1}\big{(}h_{1^{\prime},is}-h_{1}\big{)}}{\eta_{is }}+\frac{\dot{m}_{2}(h_{2,is}-h_{1^{\prime\prime}})}{\eta_{is}} \tag{8}\]  
where \(h_{1^{\prime},is}\) and \(h_{2,is}\) are the specific enthalpies of refrigerant vapor at the end of the first and second compression processes under the isentropic compression processes, and \(h_{1}\) and \(h_{1^{\prime\prime}}\) are the specific enthalpies of refrigerant fluids at the compressor inlet and the beginning of the second compression process. Finally, the COP of the heating mode was calculated using Equation (9). \[COP_{h}=\frac{\dot{Q}_{h}}{\dot{W}_{comp}} \tag{9}\]  
The total and specific exergy of a fluid were calculated using Equations (10) and (11), respectively [26]:  
\[h_{3}\dot{m}_{ref}=h_{6}\left(\dot{m}_{ref}-\dot{m}_{5}\right)+h_{5}\dot{m}_{5} \tag{2}\]0  
\[h_{3}\dot{m}_{ref}=h_{6}\left(\dot{m}_{ref}-\dot{m}_{5}\right)+h_{5}\dot{m}_{5} \tag{2}\]1where \(h\) is specific enthalpy, \(s\) is the specific entropy, and \(h_{o},s_{o}\), and \(T_{o}\) are the enthalpy, entropy, and temperature at the dead (reference) state, respectively. The reference temperature was fixed at zero degrees. This study presents exergy parameters as relative deviations, so a change in reference temperature does not significantly influence the presented results. The exergy destruction for the compressor of the SS and IHX configurations can be calculated as shown in Equation (12). \[h_{3}\dot{m}_{ref}=h_{6}\left(\dot{m}_{ref}-\dot{m}_{5}\right)+h_{5}\dot{m}_{5} \tag{2}\]2  
The exergy destruction for the compressor of the ECO configuration was calculated as shown in Equation (13). \[ \begin{array}{ll}Ex_{des,comp}=&\dot{W}_{comp}+\dot{m}_{1}[(h_{1}-h_{o})-T_{ o}(s_{1}-s_{o})]-\dot{m}_{2}[(h_{2}-h_{o})-T_{o}(s_{2}-s_{o})]\\ &\quad+\dot{m}_{5}[(h_{5}-h_{o})-T_{o}(s_{5}-s_{o})]\end{array}  \tag{13}\]  
where \(\dot{m}_{1}\), \(\dot{m}_{2}\), and \(\dot{m}_{5}\) are the refrigerant mass flow rate passing the evaporator, the flash tank vapor injection, and the condenser (total mass flow rate), respectively. The exergy destruction of the condenser was calculated using Equation (14) [27].