## 3 Results
### Turbine Performance at a Rotor Outlet Pressure of 150 kPa  
This section presents the results of the computational analysis conducted on a turbine operating at a constant outlet pressure of 150 kPa. Simulations were conducted for three rotational speeds (3600 rpm, 3000 rpm, and 1500 rpm) and various inlet pressures (ranging from 330 kPa to 780 kPa) in order to evaluate the turbine's performance under different operating conditions and to ascertain the impact of rotational speed and inlet pressure on efficiency and power output. For the turbine operating at 3600 rpm, the isentropic efficiency exhibited a range of 66.16% to 70.6%. Upon reducing the rotational speed to 3000 rpm, the efficiency values exhibited a slight decline, ranging from 60% to 67%. The lowest efficiencies were observed at 1500 rpm, with values ranging from 38.6% to 47.9%. These findings suggest that higher rotational speeds contribute to enhanced turbine efficiency under the specified conditions. A comparable pattern was discerned in the mechanical power generated by the turbine. The highest power output of 132.5 kW was achieved at an inlet pressure of 780 kPa and a rotational speed of 3600 rpm. Conversely, the lowest power output of 25.4 kW occurred at an inlet pressure of 380 kPa and a rotational speed of 1500 rpm. Figure 7 illustrates the relationship between power output and efficiency across the different operating conditions. In order to evaluate the turbine's regulatory capabilities and adapt the cycle parameters to its characteristics, the mass flow rate through the turbine was determined as a function of the inlet pressure (Figure 8). At an inlet pressure of 330 kPa, the mass flow rate was approximately 2.6 kg/s, increasing to nearly 6.3 kg/s at an inlet pressure of 780 kPa. The significant variation in mass flow rate with inlet pressure underscores the necessity for precise control of operating conditions to guarantee optimal turbine performance within the ORC system. Figure 9 illustrates the axial force exerted on the turbine rotor, a pivotal factor in the selection of thrust bearings, and comprehensive mechanical design considerations. The lowest axial force in the direction of flow was 14.6 kN, obtained at an inlet pressure of 330 kPa. The highest axial force of 64.3 kN was recorded at the maximum inlet pressure of 780 kPa. As there were negligible differences in axial forces at different rotational speeds, the results are presented solely for a rotational speed of 3000 rpm. Figure 7: Comparison of efficiency and power output at varying inlet pressures and rotational speeds. These findings underscore the considerable influence of rotational speed and inlet pressure on the turbine's efficiency, power output, mass flow rate, and axial force. A comprehensive understanding of these relationships is crucial for optimizing turbine operation and effectively integrating it into an ORC system, particularly when harnessing variable waste heat sources. The results indicate that operating the turbine at higher rotational speeds and carefully managing inlet pressures can enhance performance but also necessitate meticulous mechanical design to accommodate increased axial forces. The velocity vectors (Figure 10), streamlines (Figures 11-13), and entropy contours (Figures 14 and 15) were subjected to analysis for the centrifugal turbine operating at an inlet pressure of 780 kPa and a rotational speed of 3000 rpm. Profile losses were observed on the suction side of the rotor blades across the first, second, and third stages of the turbine. These losses occurred over a significant portion of the blade height, indicating areas where the flow separated from the blade surface, which ultimately resulted in a reduction in  
Figure 8: Variation in mass flow rate with inlet pressure for different flow conditions. Figure 9: Axial force at varying inlet pressures. efficiency. Moreover, a substantial blade wake was discernible in the stator blades of the second and third stages.