## 2 Materials and Methods
### Theoretical Model
\[Ex_{des,cond}=\dot{m}_{ref}[(h_{2}-h_{3})-T_{o}(s_{2}-s_{3})]-\dot{Q}_{h} \frac{\overline{T}_{H}-T_{O}}{\overline{T}_{H}} \tag{14}\]  
where \(\dot{Q}_{h}\) and \(\overline{T}_{H}\) are the heating capacity and the entropy-averaged temperatures of the secondary fluid at the condenser, respectively [25]. Equation (15) can be employed to calculate the exergy destruction of the evaporator [27]:  
\[Ex_{des,cond}=\dot{Q}_{c}\frac{\overline{T}_{C}-T_{O}}{\overline{T}_{C}}+\dot {m}_{i}[(h_{1}-h_{i})-T_{o}(s_{1}-s_{i})] \tag{15}\]  
where \(\dot{Q}_{c}\) and \(\overline{T}_{C}\) are the cooling capacity and the entropy-averaged temperatures of the secondary fluid in the evaporator, respectively [27]. The subscript \(i\) in this equation is the evaporator's inlet point, which would be points 4, 5, and 7 for the SS, IHX, and ECO configurations, respectively. It is noted that \(\dot{m}_{i}\) is the mass flow rate passing the evaporator, which is equal to the total refrigerant mass flow rate for the SS and IHX configurations. By contrast, it is smaller for the ECO configuration than for the refrigerant's total mass flow rate, as one portion of the refrigerant goes directly to the compressor from the vapor injection line. The entropy averaged temperatures can be calculated using Equations (16) and (17) [27]. \[\overline{T}_{H}=\frac{T_{sf\ cond,out}-T_{sf\ cond,in}}{ln\Big{(}T_{sf\ cond, out}/T_{sf\ cond,in}\Big{)}} \tag{16}\]  
\[\overline{T}_{C}=\frac{T_{HS\ evap,in}-T_{HS\ evap,out}}{ln\big{(}T_{HS\ evap,in}/T_{HS\ evap,out}\big{)}} \tag{17}\]  
The exergy destruction at the expansion valve is:  
\[Ex_{des,EV}=\dot{m_{i}}\ T_{o}(s_{EV,out}-s_{EV,in}) \tag{18}\]  
where \(s_{EV,in}\) and \(s_{EV,out}\) are the entropy at the inlet and outlet of the expansion valve in different configurations, and \(\dot{m_{i}}\) is the refrigerant mass flow rate passing each expansion value. The exergy destruction of the internal heat exchanger in the second configuration (IHX) was calculated as shown in Equation (19) [27]. \[Ex_{des,IHX}=\dot{m}_{ref}[(h_{3}-h_{4})-(h_{1}-h_{6})]-T_{o}[(s_{3}-s_{4})-(s_{1 }-s_{6})] \tag{19}\]  
The exergy destruction of the flash tank is shown in Equation (20). \[ \begin{array}{ll}Ex_{des,ECO}=&\dot{m}_{7}[(h_{7}-h_{o})-T_{o}(s_{7}-s_{o})] -\dot{m}_{8}[(h_{8}-h_{o})-T_{o}(s_{8}-s_{o})]\\ &-\dot{m}_{9}[(h_{9}-h_{o})-T_{o}(s_{9}-s_{o})]\end{array}  \tag{20}\]  
The total exergy efficiency of the refrigeration system was calculated as shown in Equation (21) [27]. \[\eta=1-\frac{Ex_{des,\ total}}{\dot{W}_{comp}} \tag{21}\]  
where \(Ex_{des,\ total}\) is the total exergy destruction of the system. Another parameter that takes into account the contribution of each component of the system is relative irreversibility (\(RI\)) and can be defined for the component \(i\) using Equation (22) [26]:  
\[RI_{i}=\frac{Ex_{des,\ i}}{Ex_{des,\ total}} \tag{22}\]  
Relative irreversibility provides valuable information about the potential for improvement regardless of the exergy efficiency. A component with a higher \(RI\) has greater potential to improve. TEWI is employed to measure the global warming impact of a cooling/heating sector. This environmental metric incorporates direct and indirect greenhouse gas emissions from a refrigeration system and can be defined as shown in Equation (23) [28]:  
\[TEWI=GWP\cdot L\cdot n+\left[GWP\cdot m\cdot\left(1-\alpha_{recovery}\right) \right]+n\cdot E_{annual}\cdot\beta \tag{23}\]  
where \(L\), \(n\), \(m\), \(\alpha_{recovery}\), \(E_{annual}\), and \(\beta\) are the leakage rate (kg per year), the system's lifetime (year), the optimal refrigerant charge (kg), the recovery factor at the end of life, annual energy consumption (kWh per year), and the carbon emission factor (kgCO\({}_{2}\)-eq kWh\({}^{-1}\)) related to electricity generation, respectively.