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Requiring a limited maximum pressure of 20 bar is seen to cause modestly reduced efficiencies compared to the SI constraint. At levels 4 and 3, the LP constraint reduces efficiency by about 2%, while at levels 2 and 1 reductions of 7% and 14%, respectively, are seen. Under the SI con- straint, the reduction is about 8% at levels 4 and 3; while at levels 2 and 1, 22% and 28% have been found, respectively. With the LP and SI constraints combined, an cumulative effect is found only at hazard levels 2 and 1, where the reductions in efficiencies are 34% and 44%, respectively. Results of the optimisation for hazard levels up to 3 are shown in Table 4. Fluids at level 4 do not seem to be relevant, since they do not offer higher efficiencies and are extremely hazardous. The best three fluids under each of the constraints are shown in order to present alterna- posed the Figure of Merit (FOM) using the conden- sation and evaporation temperatures (Te): F OM = J a0.1 (Tco /Te )0.8 . For the optimised results shown in Figures 3, 4 and 5, the F OM was found; see Figure 7. Excluded are results with supercritical pressures since FOM cannot be calculated in those cases. 0.3 0.25 0.2 R2 = 0.896 ηth = −1.2342F OM + 0.5052 0.16 0.18 0.2 0.22 0.24 0.26 0.28 Figure of Merit cases are of very different fluids, with a relatively Figure The the effi treate that th dicted bound 4. Di In t timum shown dry flu as the cases. than t superh Those Inthre factor, larger evapor limitf timum tives with similar net work output. Again the fluid type Table 4: Simulation results - hazard level 2 is notably different when one compares the process with large range of pressures and different process config- Fluid (pressure) FH HH PH ηth andwithoutrecuperator.Therangeofefficienciesamong Figure 7: Thermal efficiency vs. Figure of Merit at temperatures NO R245CA (37.0) 1 2 0 24.5 optimised processes anRd23fl6uEiAds(5a7.t7)hazar0d lev1el 3 is1 see2n3.6to be within about 11%. RC318 (97.2) 0 1 2 23.4 fromaut1ur8ar0etsitofrno3sm60(w◦1C8i0thtoo3r6w0iCthoutpreheating,superheating and recuperation). Results from imposing hazard level 2 as the maximum btyepmesadoef wRitahnkvienrey pgroocdesaspesp,roflxuimidastiaondhapvreinssguarens LP R245CA (20.0) 1 2 0 22.7 of Rankine processes, fluids and pressures treated in the C5F12 (20.0) 2 ? ? 20.8 2 arepresentedinTable5.Allthefluidsinthetableexcept Rtreavtaeludei(nthtehecoperffiesceiennttwoofrdke,tearrmeinshaotwion)inofFabigourte present work, are shown in Figure 8 along with results 08.9a0l.ongTwhitshisresruemltsarokbatbalienebdeactauasdedithioenaolpteimipsedr- R236EA (19.9) 0 1 1 20.3 cyclo-propane are compounds containing fluor atoms and SI C-Propane (99.7) 2 2 0 19.1 are associated with a Rh2ig45hCgAlo(3b7a.1l)warm1ing p2otent0ial1[82.3]. obtained at additional temperature levels. R2 = 0.9957 0.1817ln(T ) − 0.7497 0.3 R2 = 0.9924 0.166ln(T ) − 0.6669 0.25 0.2 R245FA (39.6) 0 2 1 17.0 ature levels. 8 The efficiencies are strongly influenced by the constraints. Figure 7: Thermal efficiency vs. Figure of Merit at temper- ◦ ITthisesoepentimfruom therfimgaulreffithcaietnacileisneaacrotsrsenadllctahne The optimum thermal efficiencies across all the types LP+SI R245CA (20) 1 2 0 16.3 It is seen that there are relatively large differences between R245FA (20) 0 2 1 14.9 the best fluids and theR2s3e6cEoAnd(19a.n9)d the0third1 best1(wi1t3h.3in the same constraints). For cases at hazard level 1 the fluids are of the same type as feotrahl.azfaorudndlevtehlat2,thweitrhatsioimoiflasrenpsriebslseurhealtevterlasn,s- althoughfeffirctoienlactiesntarheealotwoefreivnagpeonreartaiol.n,calledtheJacob number, Ja = cp∆T/he, is a good indicator of the 3.3.EfficpienrfcoiremsanccroesosfththeesoflluitdioindaonmOaiRnCprocess.cpis the average specific heat at constant pressure, ∆T As argued by Kuo et al. [7] no single fluid property is the temperature difference during heating and NO 2 SI seems to allow the prediction of the fluid performance in h is the latent heat of evaporation [20]. In order e the Rankine process. However, Kuo et al. found that the R 0.1404ln(T ) − 0.5473 LP to generalize the prediction ability, Kuo et al. pro- = 0.9924 ratio of sensible heat transfer to latent heat of evapora- posed the Figure of Merit (FOM) using the conden- tion, called the Jacob number, Ja = cp∆T/he, is a good 180 210 240 270 300 330 360 Heat source temperature ◦C sation and evaporation temperatures (T ): F OM = indicator of the performance of the fluid in an ORC pro- )0.8 . cess. c is the average specific heat at constant pressure, J a0.1 (T /T co e p ∆T is the temperature difference during heating and he For the optimised results shown in Figures 3, 4 and 5, the F OM was found; see Figure 7. Excluded Figure 8: Thermal efficiency vs. heat source temperature Figure 8: Thermal efficiency vs. heat source temperature is the latent heat of evaporation [7]. In order to general- are results with supercritical pressures since FOM ize the prediction ability, Kuo et al. proposed the Figure cannot be calculated in those cases. The graphs present strong correlations between of Merit (FOM) using the condensation and evaporation temperatures (Te): FOM = Ja0.1(Tco/Te)0.8. The graphs present strong correlations between the ef- For the optimised results shown in Figures 3, 4 and 0.3 5, the FOM was found; see Figure 7. Excluded are re- sults with supercritical pressures since FOM cannot be calculated in those cases. treated constraints (NO, SI and LP). Thus it seems It is seen from the figure that a linear trend can be 0.25 2 made with very good approximation having an R value 4. Discussion (the coefficient of determination) of about 0.90. This is re- markable because the optimised cases are of very different fluids, with a r0el.a2tively large range of pressures and dif- ferent process configur2ations (with or without preheating, R = 0.896 superheating and recηuthp=er−at1i.o23n4)2.F OM + 0.5052 0.16 0.18 0.2 0.22 0.24 0.26 0.287 Figure of Merit Figure 7: Thermal efficiency vs. Figure of Merit at temper- atures from 180 to 360◦C 4. Discussion e the efficiencies and the temperatures for each of the ficiencies and the temperatures for each of the treated con- straints (NO, SI and LP). Thus it seems that the maximum that the maximum obtainable efficiency can be pre- obtainable efficiency can be predicted from the tempera- dicted from the temperature alone, with the given ture alone, with the given boundary conditions. boundary conditions. 4.1. General influence of the heat source inlet temperature In the optimisation of the individual fluid at op- Itnimtuhme oprteimssiusraetioandofptrhoeceinssdiivnideuaclhfluoifdtahteocpatsiemsum presshuorwenanindFprigouceress3in,4eaacnhdo5f,ththeectarsensdshwoawsnthinatFtihgeures 3, 4drayndflu5i,dsthweetrreenodptwimaissetdhawtithethderyevflaupidorsawtoerrePoPpti- miseadstwhiethlimthietienvgafpaocrtaotro.rTPhPisawsatshtehleimcaitsienginfa2c0torf.3T6his cases. In 13 cases the evaporator ∆Tpp was larger than the minimum allowable, and the limit for the superheater approach limited further optimisation. Those cases were mostly wet or isentropic fluids. In three cases the recuperator PP was the limiting factor, and the evaporator PP and the ∆Tsh were It is seen from the figure that a linear trend can larger than the minimum allowable. 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