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600 400 200 0 0.2 0 -0.2 -0.4 600 500 400 300 200 100 0 0 0.2 0.4 0.6 0.8 1 x 0.6 0.4 0.2 0 -0.2 -0.4 Chapter 8 (a) Pure linear siloxanes. (b) Values for mixtures of MDM/MD6M (•) and MD5M/MD6M (◦). Figure 8.4: Molecular weight MW (—), active degrees of freedom evaluated at the critical tem- perature N (· · · ) and minimum value of Γ along the dew line (- - -) for selected linear siloxanes. Properties are calculated with the iPRSV equation of state for the pure fluids, see Ref. [69], while the equation of state is complemented by the Wong–Sandler mixing rules for the mixtures [78]. sure Pc, critical temperature Tc, critical density ρc and minimum value of the fundamental derivative of gasdynamics Γmin for the mixture of siloxane fluids MDM and MD6M are reported. Thermody- namic properties are calculated using the iPRSV-WS thermodynamic model. As it is well known, the critical point coordinates in table 8.1 depend in a non-linear fashion on the mixture composition x, with the critical pressure, temperature and density exhibiting a local maximum. Admittedly, the negative-Γ region of fluids MD5M and MD6M is partially or completely past the TSL, see figure 8.3. Although mixtures are expected to be more thermally stable than their pure components, such high values of operating temperatures are unrealistic, if stainless steel is the containing material. Moreover, for MD5M and MD6M the negative-Γ region is very close to the liquid-vapour saturation point, where the value of Γ is expected to diverge to infinity [21]. In this region, an accurate evaluation of the thermodynamic properties, including Γ, would require the inclusion of a critical point scaling law and of a cross-over model, linking the latter with the ana- lytical EoS. In the present qualitative study, fluid MD6M was considered in order to maximize the strength of non-classical phenomena for illustration purposes; thermal decomposition and critical point effects are to be carefully assessed before selecting this fluid for the experiments. However, it is remarkable that, similarly to previous studies on non-classical gasdynamics, the present findings are directly applicable to less complex molecules, because the qualitative fluid dynamic behaviour is similar to that of MD6M. Results shown in figure 8.4 are a preliminary evaluation of the dependence of the minimum value of Γ on the molecular weight and on the molecular complexity, which is defined here as the equivalent number of active translational, rotational and vibrational degrees of freedom of the molecules at the critical temperature and in the dilute gas limit, see Ref. [79]. The molar compo- sition is also indicated for mixtures. As it is known, in the case of pure fluids the minimum value 210 MW [g/mol], N Γmin MW [g/mol], N Γmin MD M 6 MD M 5 MD M 4 MD M 3 MD M 2 MDMPDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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