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REAL-GAS EFFECTS IN ORC TURBINE FLOW SIMULATIONS

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REAL-GAS EFFECTS IN ORC TURBINE FLOW SIMULATIONS ( real-gas-effects-in-orc-turbine-flow-simulations )

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P. Colonna, S. Rebay, J. Harinck and A. Guardone higher sound speed is compensated by a velocity magnitude that is similarly higher, as is shown in Fig. 4(b). The figure shows the percentage difference of velocity magnitude for the PIG EoS with respect to the SW EoS. As the difference in sound speed decreases (Fig. 3(c)), the difference in velocity magnitude also decreases (Fig. 4(b)), thus limiting the relative difference in the Mach number (Fig. 4(c)) to a maximum of 6% further downstream. This leads to an Mach number distribution that, even in relative terms, does not differ as much between EoS models as the sound speed and the velocity magnitude. As stated above, one of the main peculiarities of dense vapor flows of complex molecules is the variation of the speed of sound with density. The fundamental derivative, denoted by Γ, is the parameter that, if negative, indicates the possible occurrence of the so-called nonclassical gasdynamic behavior.20,21,19 It is defined as: (6) Γ≡1−c ∂v s v ∂c􏰁 Here, v is the specific volume and s is the entropy. Fluids which have Γ < 0 over a finite range of pressures and temperatures in the single-phase regime are referred to as Bethe- Zel’dovich-Thompson (BZT) fluids after the authors who first recognized the importance of (6). The molecules of these fluids have a high number of degrees of freedom, which is often the case for fluids that have a high molecular weight. Their molecular complexity enables them to exhibit nonclassical fluid dynamic behavior such as expansion shocks and compression fans.19 For the less stringent condition Γ < 1, the isentropic relation between sound speed and temperature is inverted with respect to the ideal gas behavior: the sound speed increases across an isentropic expansion and decreases across an isentropic compression. Fig. 3(d) shows the distribution of the fundamental derivative. The results for the SW EoS show that the entire expansion process occurs at Γ < 1, which is in accordance with the increase in sound speed observed in Fig. 3(c) for the PRSV and SW models. Initially, its value is Γ = 0.56 (SW) and Γ = 0.59 (PRSV) and it increases to Γ = 0.67. With respect to the SW model, PRSV model predicts a 5% higher Γ at the leading edge. Although MDM can be considered a molecularly complex fluid (0 < Γ < 1 in this expansion process), nonclassical fluid dynamic behavior is not possible as it is known that MDM is not a BZT fluid, i.e., Γ > 0.10 The PIG EoS incorrectly predicts a value of 1.0087, since it is known20 that for ideal gas (6) reduces to Γ = 1/2(γ + 1). The distribution of the pressure coefficient defined as CP = P01 − P , (7) P01 − P2 where P01 is the total inlet pressure and P2 the static outflow pressure, is shown in Fig.3(b). Its trend is similar to the one of the Mach number. Note that the same pressure values are prescribed at the inflow and outflow boundary for all EoS. 10

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