Question

Question 3 [30 marks]

A reheat Rankine cycle is designed for a steam power plant. Steam enters both the high- and low- pressure turbines at 600oC. The maximum and minimum pressures of the cycle are 20 MPa and 20 kPa, respectively. Steam leaves the condenser as a saturated liquid. The moisture content of the steam at the exit of the low-pressure turbine is 4% if the actual expansion process is adiabatic; 8.5% if the ideal expansion process is isentropic. The isentropic efficiencies of the high-pressure turbine and compressor are both at 89%.

(a) Sketch the cycle on a T-s diagram, clearly indicating the pressures and temperature given. (5 marks)

(b) Calculate the operating pressure (MPa) of the low-pressure turbine. (5 marks)

(c) Calculate the isentropic efficiency of the low-pressure turbine. (2 marks)

(d) What is the minimum mass flowrate of steam (kg/s) if at least 20 MW of power is generated?(16 marks)

(e) Calculate the thermal efficiency of the cycle. (5 marks)

Answer 1

60 z 5 reheat Rantine cycle : Pressure at entrance of hp. entrance of hp turbine in 20MPa and Temp is 600°c Jemp at entrance of (p turbine 18 600°c Pressure at ext of Up turbine 20 kPa 20 MPas 200 tar 20 kpa 6.2 bar: La العربيلا 3 Condensen 5 RA o.ltau Se at point o, Pi = 200 bar, 7, = 600** 3538 kJ / kg, SF = 6505 ks/kg. K hi

Og no 225 Properties at Point ① & ② can't be known without pressure In the low pressare steam at torbune, troislave conteni a erit 4.1. it actual Expansion process adiabatic ideal capansion process ingentropic 8.5.1. it steam leaves Condenser point saturated liquid so at If 0.001017 with his 251.4.KJ J/kg m3/19 8.54 moisture content ideal peont at ip turbine east is hy = hp + (1-0.085) bifg - g S4= 251.4 +(0.915% (2610-251.4)) = hu 2409.5 kJ/kg S4+ (1 - 0.055) Sfg : 0,$ 32 +0,9152 (4.908 -0.532) - Su = 7-306 kilky.k. with 44 moisture content', actual point at la turbine exit is. 25), 41+(0.96(26 10-25). 4)) hf (1-0.0 hing hus kilig. has 2515.65

Ideally the proces at pants. Smo 325 is iseotropic, S3 = Su :4.306 ks) kg K. so from mollien's diagram at botc. hz 3660 KJ/kg k (appro21 50 bar (5 MPa) and pressure appor So far Ponte 50 Point, bar at point $2 = SI 6.505 kJ l reg K. at superheated region kg 11e4 Copprox) Again from mollien 3 diagram is by 3100 Given is 89/ e fficiency of of hp turbine so (h, - hos) - 0.39 Chi - 12) = 0.39(3538 - 3100) hi - has 389.82 of his hi- 389.82 3146.18 K . 43/kg For lp lp tarbine hz hus nep (hz - hu) 65 3660 2515 nlp = 0.975) 3666 - 2409.5 Mip 91.51). for pump Dork, ho-hs lop --N's Aps 0.00017 Y(200 -0 2x10

Pg no u 4 5 20.3), kulrg 20319.661 sho - hy 20.319 - 251.41 + 20,517 21). 419 Ky lleg hat actual pump work in Apump & wp . ( his hos) (opreme ? pump's top : 0.89 x 20.3191 18.08 kg leg. has hot (0.89 x 20.319) 251.4 + 18-08 269.48 Kylreg. T-s diagram drawn in first page b. Operating pressure of lp turbine is so bar 5 MPa (approx) vi I sentropic efficiency of ip turbine 2 91.5) . d let 3. is to produce flow rate กาง3.5 20 Mo Mo of power Iele work done per sea m [(b.- has) a (har hus)] 6 => " {(359.52 +1144.35 ) = 20x10x tons 3 13.03 11 kg/sec 1534214

Po 525 Thermal Efficiency of cycle net work done Rcycle Work input ett With wp (hi-has) + (hz-hus)-(hos-hs) (hechas) + (ha-has) 13.0s 15 34.14 u (35 3538 269.48) + (3660-3148.13 O. 4010 ? cycle = 40.14