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η CNCA =1− τ=1− TL TH Tαβ(1− τ)2 α+β [5.2.9] [5.2.10] & WCNCA = H Where the subscript CNCA gives credit to Chambadal, [1958], Novikov, [1958], and Curzon & Ahlborn [1975] who first showed this result. For a visual appreciation of equation [5.2.9] equations [5.2.1] through [5.2.6] can be solved for efficiencies ranging between 0 and the Carnot efficiency (defined by the ratio of the thermal resource temperatures). Doing this reveals a parabolic relationship between power and cycle thermal efficiency. The parabolic relationship implies that, as a power cycle approaches its maximum efficiency, its power output will approach zero. Figure 5.2 shows this analysis applied to a Carnot cycle operating between thermal resources of 20oC and 300oC to be indicative of typical ORC operating conditions. Figure 5.2 shows the power output of this cycle as a function of Carnot cycle efficiency for a range of plant sizes (expressed in terms of UA). Maximum power increases with increasing UA. Figure 5.2: Results of a finite-time analysis of a Carnot cycle operating between 20oC and 300oC showing a parabolic relation between first-law efficiency and power at constant UA. Each line is for constant (evenly-spaced, linearly-increasing) UA. Figure 5.2 shows that in order to increase cycle efficiency while maintaining a constant power output, the power cycle size (UA) must increase, as indicated by points A, B, and 67PDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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