Question

Fure shows a combined gas turbine vapor power plant operating of steady state. The gives data at these numbered states. The total ne power output is 45 MW and the mass flow 4 turbines numbered 1-5. The vapor parte numbered as the accompany rate of the water flowing through the vapour power plants 6 Air flows through the as turbine power plant, and the ideal gas made applies to the Stray heat transfer and the effects of motion and gravity can be ignored at 300K, 100 kPa. Determine the mass flow rate of the air flowing through the gas turbine, in (4 marks) the netrate exere carried out with the exhaust stream, len in MW (4 marks) i) the rate of energy destruction in the compressor and pump, each in MW. 14 marks) in the net rate of energy increase of the air flowing through the combustor, (on-Pol in MW (4 marks) v Devise and evaluate an energetic efficiency for the overall combined power plant. (4 marks [20 marks) Vapour Cycle state state Gas Turbine ki/ke) 300.19 669.79 1515.42 85802 400.98 2 3 4 5 sik/kg 1.7020 2.5088 3.3620 2.7620 1.9919 6 2 B 9 SK 0.5975 6.3634 6.7282 0.5926 183 96 3130 30 2104.74 173.88 Table 04. Data for the combined gas vapor power plant

Answer 1

Date: Page no: 1 soln. Givendata: Mass flow tate of water, Mw = 15.6 kg/s Net Power output , WNet = 45 mW Ambient temperature g To = 300k Ambient Pressure, Po= 100 kPa 2 Schematics P₂ = P2 = 1200 kPa comtuste Tg = 14ook 2 3 Gtas ttcotte Compressed Tuchinc Wgos = Wt - We T=300k ALL Inlet 14 Wigart=450 In Exhaust T5 = 400k PS = P4 = 100 kPa = Good Plz = Empo Woad=Wf-Wp to Hent exchange 2010 My = 150648/s chill 8+ condemes mains down 1988) Pg = P8 8 kPa Assumptions: (1) control volume at steady state enclose Principal components and the overall system (2) The effects of motion and gravity are negligible (3) Foe rach control volume, Qev=o. (4) the air is modeled as an ideal gas

Date: Page no: (20 Analysis : () An energy tate Balance for the heat exchange Reduces to, 0 = Qev - Wout ma Cha-h5) + mv Cho -ht) A stray heat transfes and work done fot control volume could be neglected mafha-hs) + mucho-hz) = 0. The mass flow rate of the air flowing through the gas turbine could be defined as following ma = my (hr-ho hy-h5 ma = (15.6 kg/s) ( ma = 100.84 kg/s. 3138.3-183-96 858.02 - 400.98 An 9 (ii) The net tate Igy is carried out with the exchaust ait Stream could be defined as following (Éps - Éft) = ma [hs-hi - To CS5-5,)] ÉQ5 - Eft = ma [hs-hi - Tox( SETJS(T-Ren P5)] PL Since P5=Pt. 9 Éks - Åfi = ma [hs-hi-ToxCss (TS) - S'CT+))] ĖLs -ÉRL = (100:84k9/s)[400-98 - 300:19 - 300(1-9919 - 1:7021KW Eps-Éli 1.39 mW 103k5/5 Ans

Date: Page no: (111) The tate of exergy dutruction in the compellot could be defined as following Éd = Toxocv since, & dj + m (3.-52) + ocv = 0 Éd = max Tox (S, -S.) PL Éd = to ( s'CL) - sº(IL) - Ren Ed = (100-84kg/s) (300k) [ 2.5088-1:70 20 - 8.314 en 1200] {mw 28.97 100 LokJ S Éd = 2-83 mW Anis The rate of energy destruction in the pump could be defined as following = To x ocv Ed = my To (So- Sg) Éd = (15.6 kg/s) (300K) (0.5975 - 0«5926.) kJ / 1 mW kgk (103 kJ/s) Éd = 0.02 mW Am

Date: Page no (N) The net tate of excergy increase of the air flousing through the combustor could be defined following (Efe - É42) = ma [ hi-he - To (Sa-S2)] ( Égs - ÉR2) = (100-84 ks) [1515:42 -669:79 - 300 (3.3620–9:5088)74mW (Efs - ÉR2) = 59.46 mW Ans (v.) The energy Provided to the overall system obtained in Paxt (d) so an exergetio efficiency for the overall combined power plant could be defined as following, E = Wnet 45 mW Ép3 - É42 59.46 mW € 0.757 = 75.7 % Ans.