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Chapter 4: Modeling W ̇ i n = M ̇ i n ⋅ w i n = M ̇ i n ⋅ ( w i n , s + w i n , v ) =M ̇ i n⋅((hsu ,2−hin)+vi n⋅(pi n−pex)) (15) =M ̇ i n⋅((hsu ,2−hin)+rv ,in⋅vsu ,2⋅(pi n−pex)) The expander mechanical power can be split into the internal expansion power and the mechanical losses W ̇ loss . These losses can be expressed as a function of a mechanical losses torque Tm and the rotational speed of the expander. The expander mechanical power is given by W ̇ sh=W ̇ i n−W ̇ loss=W ̇ in−2⋅π⋅Nexp⋅Tm (16) A fictitious envelope of uniform temperature Tw is assumed to be sufficient to represent the three heat transfer modes. Tw is determined by establishing a steady state energy balance on this envelope, as proposed by (Winandy et al., 2002): W ̇ loss−Q ̇ ex+Q ̇ su−Q ̇ amb=0 (17) Supply and exhaust heat transfers are described by introducing fictitious semi- isothermal heat exchangers characterized by global heat transfer conductances AUsu and AUex . The latter can be correlated to the refrigerant mass flow rate according to the following law (suitable for turbulent regime): AU=AU M ̇ 0.8 n ( M ̇ n ) (18) The variables involved in the ORC model are of three types: input variables, output variables and parameters. They are summarized in Figure 32. It should Figure 32: Expander model 4PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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