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6.1 Cycle efficiency The efficiency of the cycle is the net amount of useful work (the work of the expander minus the work of the pump) divided by the amount of heat provided by the cycle. The work of the pump by kg of fluid is defined by : w pump=h1−h8 And the heat provided in the boiler is given by : qboil=h4−h1 In order to obtain the powers, the intensive variables must be multiplied by the mass flow rate : W ̇ e x p [ W ] = M ̇ ⋅ w e x p W ̇ pump[W]=M ̇⋅wpump Q ̇ b o i l [ W ] = M ̇ ⋅ q b o i l The efficiency is then defined by : = W ̇ e x p – W ̇ p u m p = w e x p – w p u m p = h 4 – h 5 – h 1 – h 8 Q ̇ boil qboil h4−h1 It should be noted that this relation is only valid for adiabatic expansion and compression. In the case of a heat transfer between the expander (or the pump) and the surroundings, a heat balance gives : W ̇ e x p = M ̇ ⋅ h 4 – h 5 – Q ̇ a m b , e x p W ̇ pump=M ̇ ⋅h1 – h8– Q ̇ amb , pump Where Q ̇ amb is the heat power exchanged between the expander (or the pump) and the environment or “ambiance”. The efficiency becomes : η = W ̇ e x p – W ̇ p u m p = M ̇ ⋅ h 4 – h 5 – Q ̇ a m b , e x p − M ̇ ⋅ h 1 – h 8 – Q ̇ a m b , p u m p M ̇ ⋅ h 4 − h 1 M ̇ ⋅ h 4 − h 1 6.2 Effectiveness In an adiabatic expansion, the entropy increase principle states that dS ≥0 . reversible process, and hence to the maximum work output. dS= 0 corresponds to a Let's consider the expansion of the R245fa in vapor state, at 110°C from the pressure of 14 bar down to 0.78 bar. The starting point of the expansion will be located at the intersection of the T1=110°C line with the 14 bar isobaric line. The final point of the expansion must be located on the 0.78 bar isobaric line. In the ideal case of an isentropic expansion (1 – 2s) the line joining the two points is vertical (no entropy increase). A temperature jump of T 1−T 2s is stated. 13PDF Image | An introduction to thermodynamics applied to Organic Rankine Cycles
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