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P. Colonna, S. Rebay, J. Harinck and A. Guardone The effect of the different fluid models on the fluid dynamics is evaluated by comparing the distributions of various parameters along the blade surface. These are shown in Fig. 3 and 4. It should be noted that this nozzle has been designed for inlet conditions corresponding to a slightly superheated vapor at a reduced pressure P01/Pc ≈ 0.56 (see Table 1), with a large expansion ratio so that the process evolves very rapidly toward lower pressure states (near ideal gas). Significant real gas effects are therefore present only in the initial phase of the expansion through the blade nozzle (i.e. only along the first half of the blade surface). The predicted performance of the nozzle blade is therefore not heavily affected by the chosen thermodynamic model even if some differences have indeed been put in evidence. The Mach number distribution is given in Fig. 3(a). The line that indicates early expansion (with a maximum in the Mach number) pertains to the suction side of the blade, the line with retarded expansion to the pressure side. At the location S/C = 0.52- 0.6 the Mach number distribution of the suction side does not vary smoothly, indicating irregular expansion, which might indicate an imperfection in the design of the blade. The Mach number distribution appears surprisingly similar for all EoS models. How- ever, in the first part of the expansion along the blade, the Mach number distribution computed with the PIG model shows a large relative difference with respect to the one computed with the SW EoS, as becomes apparent from Fig. 4(c). In fact, at the leading edge (S/C = 0), the Mach number is 10% lower according to the PIG EoS. This is caused by the fact that the first portion of the expansion process occurs in the more nonideal gas thermodynamic region, as indicated by the compressibility factor in Table 1. The initial high nonideality has, however, little effect on the absolute value of the Mach number since the latter is initially very low. Further downstream, at S/C ≈ 0.7 on the suction side as well as at S/C ≈ 0.9 on the pressure side, the Mach number based on the PIG EoS is 5% higher. The maximum difference in Mach number predicted by the PRSV model is only 0.5%. The sound speed, denoted by c, is shown in Fig. 3(c). According to the PIG model, the sound speed of MDM is high (c ≈ 137 m/s) and decreases slightly, which, under ideal gas theory, is always the case for an isentropic expansion. PRSV and SW, on the other hand, predict a much lower sound speed (c = 93 m/s) in the initial phase of the expansion, which is more realistic since the inlet state is close to the critical point. The initial error in the sound speed predicted by the PIG model is approximately 48%. Furthermore, as the fluid expands, PRSV and SW predict an increase in sound speed, ultimately reaching a value of c ≈ 128 m/s. Such an increase in sound speed across an isentropic expansion can occur only for molecularly complex fluids within a certain thermodynamic region19 as is discussed in the following. The relative difference in Mach number among the PIG and the real gas models (SW and PRSV) is at maximum 10%, which is significant, but small compared to the relative difference in sound speed, which is at maximum 48%. This results from the fact that the 9PDF Image | REAL-GAS EFFECTS IN ORC TURBINE FLOW SIMULATIONS
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