# Investigation of a Solar-Driven Organic Rankine Cycle with Reheating
## 3 Results and Discussion
### Thermodynamic Analysis of the ORCs in the Steady-State Analysis  
The first step in this work is the thermodynamic analysis of the reheat cycle and the conventional (simple) cycle. Figure 3 illustrates the ORC thermodynamic efficiency for \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Volume of the tank & \(V\) & 5 m\({}^{3}\) \\ Solar field area & \(A_{\text{cal}}\) & 300 m\({}^{2}\) \\ Tank’s thermal losses coefficient & \(U_{\text{tank}}\) & 0.5 W/m\({}^{2}\) K \\ Pinch Point of the HRS & \(PP\) & 5 K \\ Superheating in the high-pressure turbine & \(\Delta T_{\text{s}h}\) & 5 K \\ Minimum temperature approach in the recuperator & \(\Delta T_{\text{s}rc}\) & 5 K \\ Pump isentropic efficiency & \(\eta_{\text{s},pump}\) & 80\% \\ Mechanical efficiency & \(\eta_{\text{m}}\) & 99\% \\ Electrical generator efficiency & \(\eta_{\text{s}on}\) & 98\% \\ Motor efficiency & \(\eta_{\text{t}motor}\) & 80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Details of the thermodynamic analysis and the solar field. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Project life span & \(N\) & 25 years \\ Discount factor & \(d\) & 3\% \\ Cost for operation and maintenance & (O\(\xi M\)) & 0.5\% \(\cdot\)\(C_{0}\) \\ Solar cost per area & \(K_{\text{cal}}\) & 150 \(\xi\)/m\({}^{2}\) \\ Tank cost per volume & \(K_{\text{tank}}\) & 500 \(\xi\)/m\({}^{3}\) \\ Simple ORC per electrical power & \(K_{\text{ORC,simple}}\) & 2500 \(\xi\)/k\(W_{\text{el}}\) \\ Reheat ORC per electrical power & \(K_{\text{ORC,}\text{t}ntant}\) & 3000 \(\xi\)/k\(W_{\text{el}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Details of the economic evaluation. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Examined Cases**} & \multicolumn{2}{c}{**EES Model**} & \multicolumn{2}{c}{**Literature [29]**} & \multicolumn{2}{c}{**Deviation**} \\ \hline
**Working** & \(m\) & \(p_{h}\) & \(p_{l}\) & \(P_{el}\) & \(\eta_{\text{s}or}\) & \(P_{el}\) & \(\eta_{\text{s}or}\) & \(P_{el}\) & \(\eta_{\text{s}or}\) \\ \cline{2-10}
**Fluid** & **(kg/s)** & **(bar)** & **(bar)** & **(kW)** & **(\%)** & **(kW)** & **(\%)** & **(\%)** \\ \hline R245 fa & 0.020 & 7.05 & 2.09 & 139.1 & 2.83 & 139.1 & 2.84 & 0.000 & 0.352 \\ R1224 yd(Z) & 0.020 & 6.10 & 1.94 & 76.5 & 1.80 & 76.9 & 1.81 & 0.520 & 0.552 \\ R1233 zd(E) & 0.020 & 6.82 & 1.82 & 174.1 & 3.66 & 174.8 & 3.67 & 0.400 & 0.272 \\ R245 fa & 0.035 & 9.68 & 2.23 & 311.7 & 4.07 & 317.5 & 4.08 & 1.827 & 0.245 \\ R1233 zd(E) & 0.035 & 8.74 & 1.94 & 268.1 & 3.46 & 270.2 & 3.45 & 0.777 & 0.290 \\ R1224 yd(Z) & 0.035 & 9.21 & 2.19 & 286.7 & 4.19 & 286.5 & 4.15 & 0.070 & 0.964 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Validation of the simple ORC system with experimental data [29]. different operating conditions for both the reheat and simple cycle. More specifically, the saturating temperature in the ORC's HRS and the condenser temperature are the studied parameters. Practically, these temperature levels are associated with the operating pressure levels and the pressure ratio. In the present study, isentropic efficiency is dependent on the expand pressure ratio, a critical fact that affects a lot of the results. More specifically, Figure 3 indicates that for every condenser temperature, the curves of the simple cycle are maximized for a specific saturation temperature and after this point, the efficiency curves have decreasing rates. Practically, after this limit, the increase in saturation temperature increases the pressure ratio a lot, something that reduces the efficiency of the expander and consequently of all the system. On the other hand, this behavior is not observed for the case with two expanders because a turbine has a smaller pressure ratio (the square root of the respective value in the simple case).