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Figure 16 shows the output power for both rows in all the analyzed cases. The continuous lines represent the model prediction, while the dashed lines represent the 2D configuration and the dotted lines are their averages. The asterisks represent the 3D configuration which was analyzed in a single Int. J. Turbomach. Propuls. Power 2020, 5, 19 14 of 17 frame. Figure 16. Output power as a function of time. Figure 16. Output power as a function of time. The isentropic efficiency of the whole turbine is about 0.82; however, to make a comparison with the CFD results, only the first two rows are to be considered. Therefore, the isentropic efficiency The isentropic efficiency of the whole turbine is about 0.82; however, to make a comparison with decreases to 0.759 because of the low efficiency of the first row. For the 2D configuration, the efficiency the CFD results, only the first two rows are to be considered. Therefore, the isentropic efficiency for the first two rows, calculated on the basis of the average power and enthalpy drop, is about decreases to 0.759 because of the low efficiency of the first row. For the 2D configuration, the 0.762—for the 3D configuration, about 0.751. The reduction in efficiency from the 2D to the 3D efficiency for the first two rows, calculated on the basis of the average power and enthalpy drop, is configuration is caused by the increase in the frictional losses, in particular in the hub and tip boundary about 0.762—for the 3D configuration, about 0.751. The reduction in efficiency from the 2D to the 3D layers. In fact, since the Soderberg loss model takes into account 3D losses, the slightly higher value configuration is caused by the increase in the frictional losses, in particular in the hub and tip of the efficiency in the 2D analysis compared with the “analytical” efficiency can be attributed to the boundary layers. In fact, since the Soderberg loss model takes into account 3D losses, the slightly neglection of wall friction (on the disks), which are instead considered in the 3D analysis. higher value of the efficiency in the 2D analysis compared with the “analytical” efficiency can be Now that the effectiveness of the proposed design algorithm has been demonstrated via the above attributed to the neglection of wall friction (on the disks), which are instead considered in the 3D described CFD simulations, it is possible to formulate an educated assessment of the suitability of the analysis. Ljungström turbine for different low-T thermal sources by using different working fluids in different Now that the effectiveness of the proposed design algorithm has been demonstrated via the Int. J. Turbomach. Propuls. Power 2019, 4, x FOR PEER REVIEW 14 of 16 ranges of power: above described CFD simulations, it is possible to formulate an educated assessment of the suitability Figure 17 clearly shows that, as the range of power increases, higher density working fluids are of thFeiLgujurneg1s7trcölmeartluyrsbhinoewfsotrhdaitf,faesretnhtelroawng-Te othfepromwaelrsionucrceeassebsy, huisgihnegrdieffnesrietnytwoorkrkininggflfuluididssarine required to match the Ljungström turbine characteristics. rdeiqffueirreendt troanmgaetscohftphoewLejurn: gström turbine characteristics. Figure 17. Different power output for different working fluids. Figure 17. Different power output for different working fluids. 4. Conclusions To the best of our knowledge, there is not a commercially available Ljungström blade design software, and therefore the present study proposes the use of the kinematic efficiency as a new relevant design parameter in the Ljungström design. However, as discussed in section 2, such a choice opens up a lot of points worthy of further discussion and investigation. The main reason is that thisPDF Image | Optimal Design of a Ljungstrom Turbine for ORC Power
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