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Figure 7.1: Saturation and Γ = 0 curves in the vR − PR plane of reduced specific volume and pressure, as computed by the SW thermodynamic model [19], for siloxane D6 (dodecamethylcy- clohexasiloxane, C12H36O6Si6): MW = 444.9 [g mol−1], TCR = 372.7 [oC], PCR = 9.61 [bar], ρCR = 246.8 [kg m−3]. Reduced thermodynamic variables are made dimensionless by their critical point values. The non-classical region (BZT region) is bounded by the saturation curve and the Γ = 0 curve. admissible is that the fundamental derivative of gas dynamics ρ∂c v3 ∂2P Γ≡1+ = , (7.1) Commissioning of the FAST setup 1.0 0.9 0.8 Liquid phase V apour phase BZT region Γ=0 Critical point Two-phase region 0.5 11.522.5 v r c ∂ρ 2c2 ∂v2 ss a thermodynamic property of the fluid first introduced by Hayes [12], is negative in part of the covered domain. In definition (8.1), ρ is the density, s is the entropy, P is the pressure, v = 1/ρ is the specific volume, and c is the zero-frequency speed of sound c ≡ (∂P/∂ρ)s. If Γ is negative in a finite thermodynamic region, RSWs are admissible, among other so-called non-classical waves [9]. From basic gas dynamics theory [9, 12], an expansion perturbation entirely embedded in the Γ < 0 region necessarily evolves as a discontinuity, namely as a non-classical rarefaction shock wave, whereas a compression disturbance disintegrates into an isentropic non-classical compression wave. After the names of the above mentioned scientists, substances characterized by thermodynamic states featuring negative values of Γ in the dense vapour phase are called Bethe-Zel’dovich-Thompson (BZT) fluids. Much attention has recently been devoted to the computation of the negative-Γ region, and to the identification of BZT compounds among both pure fluids, see Ref. [13] for a review, and binary mixtures [14]. Currently, there are three classes of substances predicted to be BZT by the most accurate thermodynamic models available, namely hydrocarbons [15], perfluorocarbons [15–17], and siloxanes [18]. Figure 7.1 shows the saturation curve and the non-classical (Γ < 0) region of the cyclic siloxane D6. Experimental evidence of non-classical gas dynamics is available only for flows displaying liq- uidvapour phase transition, see Refs. [20–22], or in allotropic phase changes in solid-solid sys- tems [23]. In the single-phase vapour region, only classical gas dynamics phenomena have been 179 P r Saturation curvePDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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