9.1 Basic considerations in power cycle analysis. Thermal efficiency of a power cycle : th = Wnet/Qin

Size: px

Start display at page:

Download "9.1 Basic considerations in power cycle analysis. Thermal efficiency of a power cycle : th = Wnet/Qin"

Pauline Bennett
5 years ago
Views:

1 Chapter 9 GAS POWER CYCLES 9.1 Basic considerations in power cycle analysis. Thermal efficiency of a power cycle : th = Wnet/Qin Gas-power cycles vs. vapor-power cycles: T p 1 p 2 p 3 Vapor cycle Gas cycle v (a) Gas power cycles : low operating pressures, but specific volume during compression ~ spec. vol. during expansion -> high back work ratio (= compression work/expansion work) (b) Vapor power cycles : high operating pressure, low bwr. Ideal power cycles : (a) All processes are internally reversible. Thus, wb = pdv; w rev, steady-flow = - vdp; qrev = Tds, etc. 1

2 (b) Heat transfer from the pipe surfaces to the surroundings and friction losses are negligible. 2

3 Gas power cycle assumptions : (a) Air-standard assumptions: working fluid is air; combustion proc. is replaced by a heat addition proc., etc. (b) Cold-air-standard-assumptions: air-standard assumptions + constant spec. heats evaluated at 25 oc. Heat engines operating on gas-power cycles : (1) Reciprocating engines (spark-ignition and compressionignition engines) (a) CS analysis. (b) Tmax ~ 2800 K, moderate bwr. (c) Definitions : bore, stroke, TDC & BDC, compression ratio (r = VBDC/VTDC), displacement volume, clearance, MEP, etc. 3

4 (2) Gas turbines (a) CV analysis (b) Tmax ~ 1600 K, high bwr Carnot power cycle: T q in T H T L q out s th = w net /q in = 1 - T L /T H where T H = heat addition temp., T L = heat rejection temp. Enclosed area = net heat input per kg = net work output per kg 4

5 9.2 SI (Spark-Ignition) engines 5

6 The air-standard Otto cycle S.P. Piston movement p 3 T q in 3 q in 2 s s 4 1 q out TDC BDC v Fig Fig First law for a closed system : q - w = u qin = (u3 - u2) qout = - (u1 - u4) wnet = qin - qout = qnet th,otto = wnet/qin = 1 - (u4 - u1)/(u3 - u2) (for constant spec. heats :) = 1 - [cv(t4 - T1 )]/[cv(t3 - T2)] v v 4 q out = 1 - T1/T2 = 1-1/(rk-1) s where r = compression ratio, k = specific heat ratio 6

7 7

8 9.3 CI (Compression-Ignition) engines The air - standard Diesel cycle Piston movement Fuel injector p T 3 q q in in p s 4 4 q out q s 1 1 v out TDC BDC v Fig. 8.21(a) Fig. 8.21(b) Proc. 2-3 : Constant-pressure heat addition. s m(u3 - u2) = Q23 - W23 qin = Q23/m = (u3 - u2) + p(v3 - v2) = h3 - h2 qout = u4 - u1 wnet = qin - qout th, Diesel = 1 - (u4 - u1)/(h3 - h2) where rc = cutoff ratio = v3/v2 8

9 9.4 The air-standard Brayton cycle Basic components of a simple gas turbine 9

10 p T 3 q q in in 2 3 p s s 2 4 q 1 q 4 out 1 p out v s Fig. 8.31(b) Fig. 8.31(a) For a CV undergoing steady -flow processes : h = q w (if ke and pe negligible) w rev, steady-flow = - vdp wt = h3 - h4 wc = h2 - h1 qin = h3 - h2 qout = h4 - h1 th = (wt - wc)/qin = [(h3 - h4) - (h2 - h1)]/(h3 - h2) bwr = wc/wt = (h2 - h1)/(h3 - h4) ~ 40-80%!!! Proc. 1-2 : Reversible adiabatic compression -> isentropic (s = constant) (a) Constant-spec. heats : T2 = T1 (p2/p1)(k-1)/k th = [cp(t3 - T4) - cp(t2 - T1)]/[cp(T3 - T2)] = 1 - (T4 - T1)/(T3 - T2) = 1-1/[(p2/p1)(k-1)/k] (b) Variable spec. heats : Use p1/p2 = pr(t1)/pr(t2), etc. Optimum pressure ratio : wnet = wmax when p2/p1 = (T2/T1) k/[2(k-1)] or when T2 = T4 = (T1T3)0.5 10

11 Deviation of actual gas - turbine cycles from idealized ones : Irreversibilities : heat and friction losses, non - isentropic compression and expansion, etc. (Fig. 9-36) 11

12 Isentropic efficiencies (Fig.9-37): (1) Turbine : t = wt/wts ~ (h3 - h4a)/(h3 - h4s) (2) Compressor : c = wcs/wc ~ (h2s-h1)/(h2a - h1) 9.5 The Brayton cycle with regeneration The regenerator (a counter-flow heat exchanger) preheats the air prior to combustion. -> higher heat addition T and lower heat rejection T -> higher thermal eff. Regenerator effectiveness = qreg, act/qreg, max = (h5 - h2)/(h4 - h2) 12

13 The Brayton cycle with intercooling, reheating, and regeneration Basic components (Fig. 9-43) 9.5 Jet propulsion T-s diagram Basic components and T s diagram of a turbojet engine 13

14 wcomp,in = h3 - h2 = wturb,out = h4 - h5 Thrust F = m(vexit - Vinlet) Propulsive power Wp = F Vaircraft Propulsive eff. p = Wp/Qin Other air-breathing engines 14

15 Appendices I. Thermodynamic analysis of 2016 Honda Accord 4-cylinder engine I. 1 Spec sheet 15

16 I. 2 Thermodynamic analysis (a) Assumptions : T 1 = 300 K and p 1 = 101 kpa (for naturally aspirated engines) T max = 2700 K (for Aluminum-alloy engine) Constant specific heats at 300 K (b) Analysis : Proc. 1-2: isentropic compression V 1 /V 2 = 11.1; V 1 V 2 = displacement volume = 2356 E-6 m 3 V 1 = m 3 16

17 m = p 1 V 1 /(R T 1 ) = kg of air per cycle T 2 /T 1 = (V 1 /V 2 ) k-1 p 2 /p 1 = (V 1 /V 2 ) k T 2 = 785 K p 2 = 2.93E6 Pa T 3 = T max p 3 = p 2 (T 3 /T 2 ) = 10.1E6 Pa T 4 /T 3 = (V 3 /V 4 ) k-1 = (V 2 /V 1 ) k-1 p 4 /p 3 = (V 2 /V 1 ) k T 4 = 1032 K p 4 = 0.35E6 Pa u 1 = c v T 1 = 215 kj/kg air; u 2 = 564; u 3 = 1939; u 4 = 741 w c = u 2 u 1 = 348; q in = u 3 u 2 = 1375; w p = u 3 u 4 = 1198 w net = w p w c = 850 Power = m x w net x (# of cycles/s) = 138 kw = 184 HP at 6400 RPM II. Turbo-charging and inter-cooling 17

18 P > 1 atm T > atm. air temp. Intake valve Exhaust valve Exhaust gas Turbine Piston Carburetor Or fuel injection system Compressor Atmospheric air (a) Turbo-charged engine P > 1 atm T ~ atm. air temp. Intake valve Exhaust valve Exhaust gas Turbine Piston Carburetor Or fuel injection system Compressor Heat exchanger Atmospheric air (b) Turbo-charged engine with intercooling. 18

19 Assumptions : T a = 300 K and p a = 101 kpa p 1 = 2 p a II. 1 Turbo-charging only Isentropic compression from a to 1: (T 1 /T a ) = (p 1 /p a ) (k-1)/k T 1 = 366 K, m = kg, q in = 1251 Power = m x w net x (# of cycles/s) = 276 HP at 6400 RPM II. 2 Turbo-charging + Inter-cooling T 1 = T a m = kg, q in = 1375 Power = 368 HP at 6400 RPM III. p-v and T-s charts 19

20 20

21 21

Teaching schedule *15 18

Teaching schedule *15 18 Teaching schedule Session *15 18 19 21 22 24 Topics 5. Gas power cycles Basic considerations in the analysis of power cycle; Carnot cycle; Air standard cycle; Reciprocating engines; Otto cycle; Diesel