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7.4 Modeling of a small ORC The ORC model is built by interconnecting several sub-models related to the components: scroll expander, heat exchanger and pump models. These sub-models will be described in the following paragraphs. 7.4.1 The scroll expander model Volumetric expanders, such as scroll, screw or reciprocating technologies present an internal built-in volume ratio corresponding to the ratio between the inlet pocket volume and the outlet pocket volume. Under-expansion occurs when the internal pressure ratio imposed by the expander is lower than the system pressure ratio. In that case, the pressure in the expansion chambers at the end of the expansion process (Pin) is higher than the pressure in the discharge line (Pex). Over-expansion occurs when the internal pressure ratio imposed by the expander is higher than the system pressure ratio. Under and over expansion losses can be modeled by splitting the expansion into two consecutive steps (Zanelli and Favrat, 1994): Isentropic expansion: w1=hsu –hin hin being the isentropic enthalpy at pressure Pin. Isochoric expansion: (7.1) w2=vin Pin -Pex w2 is positive in case of under-expansion, and negative in case of over-expansion (Figure 7.2). Figure 7.2 - Under and over-expansion losses The total expansion work is then obtained by summing w1 and w2. Other losses such as internal leakage, supply pressure drop, heat transfers and friction are lumped into one single mechanical efficiency ηmech. Thus, the actual expander work is expressed as: (7.2) Page | 167PDF Image | Low-Grade Heat Conversion into Power Using Small Scale Organic Rankine Cycles
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