Question

PROBLEM 2

Problem 1 (40 pts): A power plant runs on a steam cycle that closely approximates a Rankine cycle with one exception: the turbine is adiabatic but not isentropic, and has an isentropic efficiency of 85%. The cycle operates between 20 kPa and 20 MPa and steam achieves a maximum temperature of 600 °C. The cycle receives heat from a combustion chamber at 1500 K and rejects heat to the surrounding. a) Calculate the net work output and thermal efficiency of the cycle. (15 pts) b) Calculate the entropy generated in each component of the cycle and the total exergy destroyed by the cycle. (25 pts) Problem 2 (60 pts): In order to enhance the performance of the cycle, you are brought in as a consultant to assess the gains associated with turning the cycle (in Problem 1) into a re-heat cycle. The pressure and temperature at the inlet of the low-pressure turbine are 4.5 MPa and 600 °C, respectively. The low-pressure turbine has the same isentropic efficiency as the original high-pressure turbine. a) Make a schematic of the re-heat cycle and show the processes on a T-s diagram, clearly indicating the states. (5 pts) b) Calculate the percent increase in net work ouput compared to the original cycle. (20 pts) c) Compare the thermal efficiency of the re-heat cycle to that of the original cycle. (15 pts) d) Compare the total exergy destroyed by the re-heat cycle to that by the original cycle. Briefly comment on the result. (20 pts) NOTE: this problem set involves multiple steps and things might get messy. Please make sure your solution is organized and easy to follow and that the key answers are clearly labeled. In other words, make it easy for the grader to give you the credit you deserve.

Answer 1

V Original cycle ? si 1533k combatan per Combustion chamber 7 20 mpa, 6ooºc. Boiler Pompa 바 Turcbind 20 mpa pump Rokpan 2okpa Condensetre 20kpa lookpa, 290k (he surround fig schematic diagram, Veso entropic of turbine = 0.85

At gokpa y = 0.021017.mai A+ 20 mpa, boo's h= 3536, 6 5 = 6.5052 ose kolegom = 2311 31 49 748 hong = 2 35865 21 ss = 0.8313 4T / regie sp= 7.9090 kJ/kgile Sfg = 70771 Kegik alow, h, = 251.31 kJ/ka. .: Wp = Ý (R-P.)°= 0.001017(20005-20) We = 20.32 KI shah, = wp » h = We the th=20132 +251.31 > h₂ = 271.63 KB /kg = 3536.61 19/g Now, $a = 54 6.5352 = 0.8313 +X x7.0777 x= 0.8016 h4 = 251.31 + o.fb 16 *2358.65 his 2142.142 K7 Wartuah zsentric Wideo 0.85 hz-hi ► 0185 = 3536.61-ha 35 3661-2142.142 → ha = 2351.3125 KT)

. (6 a who = Wq -Wp. = (haha) -(ha-hy). = (3536.61 - 2351.3125)-(271.63 – 251.31) = 1164.47 Tag, cliç ha-ha = (3536.61 – 271.63) = 3264.98 kg - din harha=0 Whenen = 0.3568 = 35.68%. 2351, 3125 -251:31 NOU "sa 0.09+273). que -6.3046+ o. 8313 120kpa → 54-5, = 6.3046 $54–63046 + 0.8913' (1?S, = ss Igokea 048313) * S2 = 7,136 kkk from entreopy balance equation, cele - th-Sova) +.of, + 42, - Song) + y + sten-free)$ (t) system i pump Turebne pump e n-Sout) + 1 2 +Sgen. Condenser

for steady state, (S) Surteo for Pump 40,8 fin = fout fore turbine sint sout Abow, Poiler= hy h₂ = 3264.98 ling Landensere = hy th, = 2351.3125 - 251.31 = 2100 Kthers (ne. Relected 'heat) =Dandenser = – 210a Kathy Content orgine sagen = ($-$) - + (5 =) - 4 +(**) Segen = - 1964, 48 + 2009 (5475.) » Sagen = 5,065 15 Agus • Exergy destroyed = Tox Sagen = 290 5,065 = 1466 77 KT Reheat cyerel - Highline High pressure Low pressure Low WHAT torebhe. WLPT to Combato Chambra 100+ pump,

2o MPa. V . . . .. . 4 4.5 Mpa 20 kpa abous, h = 251.31 kJ/eg. 1 h = 271+63 kg ha = 3536.61 Kitting And so = 6i5os2 *57kgok : * -S41 = 6.5052 RT/kaur * from Steam table, corresponding to $, 565352 K37kg.K., h = 3081.585 KT7 Wart vol to Wedeal Vissentreopic 0.5 = _3535.6 che ? 353616-3061. ha = 5149.63 K47. 4 = 3666 1375 kng f = 7.3088 Kokg. So sci 7366 = 0.6313 4X X 7,0 777 X= 0.9152 = 251.31 0.9152 x 2358 65 = 2409,992 Kolka And

Wattual Now, Wissentrepic Widec 7085= ho ho ng-her 50.85 = 3666.375-ho he = 2598.4076 kg7e 3666.375- 2409,942 .. Whet - Wattipit +Whip.it -wp. = (-hy) + (13- ha) – Chertha) = (3536.6i – 3149183) +(3666+ 395 – 2598.4076) - (271.63–251.31) they = 14 34. 427 lang?

3149.83 3781.52 = (3536161– 27163) + (3666.375 os (electing net = 578): 528 YT/kg - Wherencia entre from entropy balance equastion, -= 0.3793 = 37.93, sys Boiler + -Sop) + (Sin Sout) +$, +(Sen-Soun) + q: +(cm 504) + 9 +5 Reheater - TI - Condensere

For pump! - gzo, & Sin Sout. For both HIPT & LIPIT. Q=o, & Sth# south- pi' ger Boiler w Reheater + Sony -ov)-of. + Focus Sede), os son = (652) - Photo + 6 +50" +(35–6) - lei + (64-59)76-) » gan= lehen et Pool & Sgen = - 3781.525 1500 2347.09 - 5,572 290 Klan 7 (- Crep = haha V = 251-31-2598407 = -2347,09 KPK . Exergy destroyed = Tox Sgen. = 240 * 5.572 = 1616.002

16 Weeheat - Woreiginal % increase - cycle chere in work Woriginal cycle 1436 427 - 1164.97 1164.97 = 23.137. - Veeneat - Voriginal y. increase in efficiency Voriginal 0.3793 – 0.3568 0.3568 = 6:37. (c) 1 Id y increase in exergy 1616.002–1468.77 - 1468,77 = 10.02%. less
In T-S diagram of reheat cycle, I forgot to mark the point "6" It is slightly towards right of point "6"