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Session: Poster session & Sponsor Exhibition
Session starts: Monday 07 October, 14:00

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Tiemo Mathijssen (Delft University of Technology)
Alberto Guardone (Politecnico di Milano)
Piero Colonna (Delft University of Technology)

Abstract:
As it is well known, thermodynamic models based on analytic equations of state fail to reproduce the singular behaviour at the vapour-liquid critical point. For example, cubic equations of state provide inaccurate value of all properties close to the critical point [1]. Multi-parameter equations of state provide accurate estimations of the primary properties thanks to the inclusion of so-called critical terms in the functional form, but derived quantities are affected by the inherently incorrect functional form and departure from physical behaviour becomes apparent, especially if first and second order derivative of primary properties are considered [2]. Balfour and collaborators formulated an equation of state using the method of non-classical scaling that is capable to accurately predict the thermodynamic properties at and in the close proximity of the critical point [3]. In order to simulate compressible flows in the vicinity of the critical point, we implemented the non-classical scaling thermodynamic model in our in-house thermodynamic library [4]. A comparison is reported between the values of relevant primary and derived thermodynamic properties for CO2 obtained with the scaling-laws model, the Span-Wagner [5] equation of state and measurement data close to critical conditions, to assess the predictive capabilities of the non-classical scaling model. In particular, the divergence of the fundamental derivative of gasdynamics Gamma to minus infinity approaching the critical point from the two-phase region is predicted by the non-classical scaling model [2]. The negative value of the fundamental derivative of gasdynamics Gamma heralds possible non-classical gasdynamic behaviour in the two-phase critical region. To investigate these phenomena, our in-house real-gas solver, coupled to the thermodynamic library, is used. In particular, numerical simulations of the formation and propagation of non-classical two-phase rarefaction shock waves are carried out. The computed shock velocity and strength are assessed against the exact theory of Rankine-Hugoniot. Non-classical gasdynamic behaviour at the critical point is predicted to impact the design of fluid devices operating in the close proximity of the critical region, such as expanders for advanced Organic Rankine Cycle power systems [6]. [1] M. M. Abbott, "Cubic equations of state", AIChE J., vol. 19, p. 596, 1973. [2] N. Nannan, A. Guardone, and P. Colonna, "On the fundamental derivative of gas dynamics in the vapor-liquid critical region of single-component typical fluids," Fluid Phase Equilibria, vol. 337, pp. 259-273, 2013. [3] F. W. Balfour, J. V. Sengers, M. R. Moldover, and J. M. H. L. Sengers, "Universality, revisions and corrections to scaling in fluids", Phys. Lett. A, vol. 65, pp. 223-225, 1978. [4] P. Colonna, T. P. van der Stelt, and A. Guardone, "FluidProp (Version 3.0): A program for the estimation of thermophysical properties of fluids." http://www.fluidprop.com/, 2010. A program since 2004. [5] R. Span and W. Wagner, "A new equation of state for carbon dioxide covering the fluid region from the triple-point temperature to 1100 K at pressures up to 800 MPa," J. Phys. Chem. Ref. Data, vol. 25, no. 6, pp. 1509-1596, 1996. [6] E. Casati, A. Galli, and P. Colonna, "Thermal energy storage for solar powered organic Rankine cycle engines", Solar Energy, 2013. Submitted for publication.