## 3 Results and Discussion
### Comparison of the ORC\({}_{\text{CTE}}\) System and ORC\({}_{\text{DTE}}\) System  
The radial-inflow turbine efficiency is obtained based on the prediction model in Section 2.3. Figure 7 shows the variation of the turbine efficiency with evaporation and condensation temperature. It is evident that turbine efficiency decreases with the increasing evaporation temperature, and increases with the increasing condensation temperature. It can be concluded that turbine efficiency increases with the decreasing pressure ratio. The maximum turbine efficiency is 0.746, and the minimum is 0.543, the relative difference reaches 27.21%. The maximum difference between the constant turbine efficiency and the predicted turbine efficiency reaches 0.157, and the relative error is 22.43%. From the above data, it can be found that turbine efficiency is not constant, and will vary with operating parameters. Therefore, it is necessary to couple the ORC system with the radial-inflow turbine efficiency prediction model. Figure 7: Radial-inflow turbine efficiency at different evaporation and condensation temperature. Multi-objective optimization is conducted for the ORC\({}_{\text{CTE}}\) system and the ORC\({}_{\text{DTE}}\) system with respect to thermodynamic and economic performance. The multi-objective optimization Pareto frontier of both ORC systems is shown in Figure 8. It is apparent that there is a significant difference in the distribution of the Pareto frontier between the ORC\({}_{\text{CTE}}\) system and the ORC\({}_{\text{DTE}}\) system. Compared with the ORC\({}_{\text{CTE}}\) system, the thermal efficiency of the ORC\({}_{\text{DTE}}\) system lies at a lower level, and the specific investment cost of the ORC\({}_{\text{DTE}}\) system is distributed over a wider range. Figure 8 also shows the turbine efficiency value corresponding to the Pareto frontier of the ORC\({}_{\text{DTE}}\). The turbine efficiency value is less than the constant turbine efficiency (0.7), and the lower turbine efficiency value leads to lower net power output. Thus, the thermal efficiency of the ORC\({}_{\text{DTE}}\) system is less than that of the ORC\({}_{\text{CTE}}\) system, and the specific investment cost of the ORC\({}_{\text{DTE}}\) system is higher than that of the ORC\({}_{\text{CTE}}\) system. It can also be found that the deviation of the distribution of the Pareto frontier between the ORC\({}_{\text{CTE}}\) system and the ORC\({}_{\text{DTE}}\) system increases with the decreasing turbine efficiency. It should be noted that each point on the Pareto frontier is a potential solution for the multi-objective optimization. There is not an optimal point to maximize the thermal efficiency and minimize the specific investment cost simultaneously. Therefore, it is necessary to conduct a decision-making process based on engineering experience. The aid of ideal point method is used to conduct the process of decision-making in this paper [32]. Taking the Pareto frontier of ORC\({}_{\text{CTE}}\) system as an example, the decision-making process using the aid of ideal point method is presented in Figure 8. The ideal point has the highest thermal efficiency and the lowest specific investment cost simultaneously but this point does not actually exist. The point on the Pareto frontier that has the shortest distance from the ideal point is selected as the final optimal solution. The final optimal solutions for the ORC\({}_{\text{CTE}}\) system and the ORC\({}_{\text{DTE}}\) system are listed in Table 1. Compared with the ORC\({}_{\text{CTE}}\) system, the ORC\({}_{\text{DTE}}\) system has a lower optimal evaporation temperature but a higher evaporation temperature. Due to the low turbine efficiency, the ORC\({}_{\text{DTE}}\) system has lower thermal efficiency and a higher specific investment cost. Therefore, the assumption of constant turbine efficiency in the ORC system would lead to errors in the determination of the optimal operating evaporation temperature and condensation temperature.