Question

20 E2) An idealized reheat-regenerative vapour power cycle having two feedwater heaters (one closed, one open) operates with a boiler delivery pressure and temperature of 8.0 MPa and 480 °C, respectively. A portion of the steam, y, is extracted at 2.0 MPa after the first turbine expansion stage for the CFWH. The remainder expands to 0.7 MPa and is then reheated to 440°C. The reheated steam then enters the third turbine stage, expands to 0.3 MPa and has a portion, z, extracted for the OFWH. The remainder expands through the final turbine stage to the condenser pressure of 0.008 MPa. Feedwater exits the CFWH at 205 °C and 8.0 MPa, and condensate exits as a saturated liquid at 2.0 MPa. The fluid exiting the OFWH is a saturated liquid at 0.3 MPa. If the cycle has a net power output of 100 MW, determine: a) the system thermal efficiency [%] b) the total steam flow rate [kg/hr] S T -440°C SC enter 0.0CB MP2 You Ti - 205"CL

Answer 1

Solution frist page Assumptions to be considered 1 Each components in the cycle is analyzed as a Control volume at starter state 2) No stray Heat transfer from components to its sorroundings 3) Working fluid undergoes internally reversible process as it passes through componente like turbines, pumps, etc. = 4 Trap expansion is throttling process that 5) KE and PE: effects of energy are negligible 6) Condensate exits the closed FWH as saturated liquid at ampa, feed water exits open heater as saturated liquid at 0.3 ropa Condensate exits condensor as saturated lique Temperatief entropy(s)

река (1-y) ③ Boiles word Jopen FWH (1) Cylyng To Condeisers pump PT trap out to all Finding enthalpies at principal states of the cycle. State I is super heated steams & h, 3348.4 kJ/kg and S. 26.6586 kJ/kg k an state & is fixed by P2 = 2mpa and sp. entropy S₂ = 51. By interpolation, a 2953.5 kilkg State at exit of first turbine is fixed by P220 Ampa and 33-S, By interpolation, h32 2741. 8 kJ/kg. State 4 is super heated vapos at 0.7mpa, 44800, giving 342 3353. 3 kJ/kg, s427.7571 kJ legk. with P520.3mla sed ss² Sur 7.7571 k3 ling the he 3101.5 k3 lkg. I

At & noe het nehega 2403. 1 kg. I rd page / condenser exist bg=173.88 k]/leg. Speatic enthalpy at first pump exit, hqa hat V₂ (Pg - Pq) = 174. 15 k3 lleg. hiquid leaving open FWH at state 9 is saturated liquid at 0.3 mPa. specific enthalpy is hq 2561.47 k] 1 kg. The specific enthalpy at exit of second pump is hroa hatva (Pro-Pa) - 569.73 kJ/kg. Condensate leaving closed heat as saturated at 2mpas h22 908.79 kisg. The fluid passing through trap undergoes a thoottling process, so hi3=908.79 10 3/ky. The specific enthalpy of feed water exiting closed heater at 8mpa and 20500 should be modified for the pressure hil I het of (Pn-Psat) = 882.4k3/19 where he saturated liquid specific enthalpy at 205°c. 4 specific volume at 2056. Peat & Satisation pressure & la at 2050 The fractions of total flow diverted to closed heater and open heater respectively are y'= nelim, y = molin, where in mass flow rate entering first torbice The fraction y can be determined by application of mass and energy sate balances to a control volume enclosing closed hecte .

Irth page 01522 y'a hithio = 882.4 - 569.73 1₂-hiz 29635-908.79 - The fraction yn can be determined by application of mass and anera rate balance to a control volume enclosing the opers heater, resulting en : or y hg+ (1-yny") hg + y histha y"=(1-9) hgry h13-ha -0.0941 - S ho-hs The following work and heat transfers values are expressed on the basis of unit mass entering first turbine. The work developed by first turbine t-whit mass entering is the sum? Wts - Chi-ha) + (1 - ₂ -hz) = 572.9 kJ/kg similarly for second turbine Wie (1-y) (bg-hs) + (1-yl- y") (hs-ho) = 7 2017 le 3 kg Wg mi for pumps; Wei=C1 - y - y") (ng - ha) = 0.22 ke 3 kg Wipes alho-ha) – 8.26 k3 kg Total added heat is sum of energy added by heat transfer dursing boiling / superheating and reheating when expressed in basis of und mass entering first turbine, this is an din (hi-hu) + (1-y) (24 h 3) = 2984.4 kJ / kg with foregoing values the thermal efficiency is: na Whlm, & Wtelm, - Weilm, - Weelm mg = 0.431 (43.1%) Binsin, mi

Ith page The mass flow rate entering the first turbine can be determined using the givers value of net power output Wise Wegeleht 22.8x10 kg/h Walim & Weslin - Wp lim - Welne - u bosos ro colo