Question

A Rankine power cycle with reheat uses water as the working fluid. The inlet conditions of the first stage turbine are 14MPa and 600°C. All the turbines are known to have isentropic efficiency of 85%, however the pump is assumed as an isentropic pump. If the maximum temperature is kept at 600°C and the condenser pressure is 6 kPa, by constructing a suitable plot, show that having more than 2 reheat stages is not practical. (Hint: Take at least three reheat pressures between 2 to 12 MPa) Note: You may construct the plot on Microsoft Excel or manually on a graph paper. However, all the calculations involved must be performed manually, in details and must be shown clearly. (30 marks)

Answer 1

solution: 600c the 1st Stage turbine, J = Given, Inlet temperature of Inlet pressure P = 14MPa = 140 bar -0.85 I sentropic efficiency of the each ta bine 1t - 85% 600°c Maximum temperature in the Cycle Condensen pressure, Peft = 6 kPa = 0.06bas such that the AS given in the problem we choose 3 reheat pressures outlet quality of the steam from the final stage is greater than 0.9 (or) 0.88. Here we choose O intermedite pressures as Lallows. the = 40 bar PG=20 bar 80 bar 5 line diagram on T-S plot. P3 the following figure shows the 6 1 600c 140 bar 8obar 40 bar -45 TA Lobar 8 0.06 baur IS 7 Sg

steam tables, Now from the mollier chart and hi = 3591.94 Kilky h5 : 3674085 Kilis h2= 3642042 Kblys h6= 3190 kilks ha= hy + x hay = 151.484 +0.91(2415:17) 2349.29 Kilts at Condensen Pressme Wilk x=0.91 has = 151.484 kilks Assuming the pump is is entropic, work done WAP specitic volumex prescue by the pumb , Wp 10 - ²x (140-0606x10 13.994 Kjlis Wp = But (ho- has) = 13.994 ho = 13.994 thes = 165.488 kilks steam tables we have Now from saturated has = 2758.61 kilps hus = 2800.9 kilks and his = 12798,38 kilks Heat addition, a, = (hi-h8)+(hz-h2s) + (hs-hys) 7th6-655) - - 3426.452 +883.81 +873.95€ 891.62 6075.832 %)/19

work of the tesbines, W7o Chi - has) +(hs hus) ths - hss) the th=) = 0.85(833-33+ 341152 +876-47+ 345.71) = 38921031(kil 13) X0185 Network done, What = 3308.2 Wy - Wp 3308.2 z 789 2008) – 13.994 347473 K 3294.206 iliy Efficiency of the cycle, Rayce What 3378.037 3294.206 -X100 6075.832 0.542x100 こ cycle. 54,2). Such that Now clotie 2 stages only we choose pressure, as Robar, and Quality of steam at outtet of the turbine. as oral. ܩܢ 600 luober 20bar T ooobbar 748

Heat supplied, or = Chr. hg) + (ha-has) = 3426.452 +(3680– 2758.61) z 4357.842 kilks work done by the turbine, wy = Et [ch, - hus) + (ho-ha 2 0.85 833,33 + 1340.71] z 1847.934 Whet z Wr-we 1847 13.884 z 1833194 Kjlis Wnet Meych Weet 1833.54 4357184 x 100 Myle 42.08) So As in the est Case the heat supplied is very high when compared to Caye a. reheat Cycle more than & stages are not recomended.
as if we choose 35 bar and 0.88 dryness fraction, the efficiency may be some what high. Try that one.