Question

3a. A gas-turbine power plant operates on the simple Brayton cycle between the pressure limits of 14.7 and 200 psia. Air enters the compressor at 77°F at a rate of 28 lbm/s and leaves at 750°F. Fuel is burned in the combustion chamber and the combustion gases enter the turbine at 2000°F. Combustion gases leave the turbine whose isentropic efficiency is 85 percent. Treating the combustion gases as air and using constant specific heats evaluated at 900°F, determine (a) the isentropic efficiency of the compressor (10), (b) the net power (10), and (c) the thermodynamic efficiency (10)

Answer 1

For finding the isentropic efficiency of compressor, net work produced and thermal efficiency of the cycle, we just need temperatures at all the 4 points. Missing values of temperatures are obtained using isentropic relationship between pressure and temperature.

Please refer to attached images for solution of given problem. Do comment in case of any query, all the best!!

* Given: Pressure limite ane 14.7psia and 2oo psa. P = Py - 14.7psia and P2 = P3 2oopsia Air enters the compressor at T, = 77F 533°R. at mass Flow rate or 28 lbm's and leaves the compressor at 750°F = 1210°R. Combuston gases (taken as aar) enter the turbine at T3 = 2000°€ Zubor. I sentropic 95 efficiency of turbine 0.85. ! n = 85% . RT

Let's start solving the given problem by first drawing Tas diagram of brayton cycle. 3 25 45 Process 9.22 ideal Casentropic) compression Proces 9 - 2 9 actocil compression qe qdeal Cientropic) Росе ( 3- це expansion. Procen 3-u is actual expansion Process 2-3 a constant pressure heat addation whole process 4-1 constant pressure heat rejection * ca) To determine isentropic efficiency OR compressor and Mathematically he work supplied in icentropic compression work supplied in actual compression.

no has -ha hathi im .Cp. (Izz-T) mcp. (T2-Ti) no ( Tas T,) ( Tz- Ti) We have all the valves except Tzs (temperature of cair at end OR asentropie compression). It be derived can TD n. .. Tzsa Too (Palp,) ( 200 ) teyl 1.U. Tara 537 ܕ ܝܕܐ 1132. 12R values an equation 1, placing all have we 1132.12 - 537 0.8842 12 537 Isentropic efferiency efficiency of compressor & ne= 88.4%.

Net power: as The net power output of a brayton cycle difference of worth obtained by turbine and work supplied to compresor. Whet = (Turbine work) (compres: work . inet moc kz-hi) mchz-hu) Whet mo Cp. (T3-T4) ni Cp CT2~T;) * Ine have values of of TA Tz, and Tz. Tu Cactual temperature of air after ex pansion be calculated osing Pormula of asentropic efficheny for Turbine) an

NT- actual work produced is entropic work produced hz-hy hthys, nr- (T3-T4) mo Cp. (T3-Tu) mo. (p CT3 Tush (Tz- Tus) Now Esentropic relation, rat T3/Tus (P3/p4) Tys 6 temp after sentopic expansion Tus T3 (P3/py) 2460 tu-) 200 14.7 e' Tusa 1166.86°R. → Placing above value in @ we have

0.85= 2460 - Tu 2u60 - 1166.86 Tus 1360.831°R kinet 26 x 0.259#x (2460-1360-631) 26x0.2597 x 41210 - 537 & Cp @ 900°F 0.2597 BTU lor i Net power produced a linet 3098.93 BTO * Thermodynamic efficiency - Network Heat supplied. n ther. 3098.93 mi (hy h2o 3098.93 mo Cp (Tz-Tz) in therm. 3098.93 28* 0-259+x (2460 - 1210) 0.3u og in thermat 34:09.