CHAPTER 13. Mathematical Modelling and Computation for Rapid Expansion of Supercritical Solutions

Yamamoto, Satoru; Furusawa, Toshiaki

doi:10.1039/9781788013543-00395

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“…Strictly speaking, unlike ideal flows, it is practically impossible to derive an explicit relation between static to total quantities. The current available models of real gas thermal properties such as equations of state (EOS) [2,3] or database look-up table method [4,5] appear in extremely complex and nonlinear form. Furthermore, the speed of the sound is determined by both pressure and temperature, increasing the difficulties to theoretically derive isentropic relations which describe the dynamic physics.…”

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The Real Gas Effect on the Stagnation Properties for Supercritical Carbon Dioxide Flows

Xiao

Himeno

Watanabe

2020

JGPP

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This paper presents a comprehensive study on the stagnation properties namely the total pressure and total temperature for supercritical CO 2 flows including the methodology, applications and detailed analysis. Due to the high nonlinear real gas effect, it is practically impossible to have explicit expressions between static and its corresponding stagnation properties. The equations of obtaining the real gas stagnation properties as well as their physical meanings related to fluid dynamics need to be reconsidered. In this paper, the stagnation pressure and temperature for sCO 2 flows are accurately calculated in a way that implicitly iterated from stagnation enthalpy and entropy without any addendum assumptions. Accordingly, this approach is applied to typical applications that essentially exert stagnation properties. The total pressure and total temperature of typical sCO 2 flows in which contain significant real gas characteristics are numerically studied by using our in-house CFD code coupled with real gas models. It is found that the real gas tends to preserve more internal energy than the ideal gas during irreversible flow process especially with the presence of shockwaves. Finally, as a regular indicator of viscous flow loss, the total pressure loss for a sCO 2 compressor cascade is evaluated. NOMENCLATURE U Velocity in x-direction m/s V Velocity in y-direction m/s W Velocity in z-direction m/s T Static temperate K P Static pressure Pa h Static enthalpy J kg −1 K −1 s Static entropy J kg −1 K −1 u Magnitude of flow velocity m/s ρ Density Kg/m 3 T c Critical temperature 304.13K P c Critical pressure 7.3773MPa Non-dimensional parameters Z Compression factor

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