= 1 T 4 T 1 T 3 T 2. W net V max V min. = (k 1) ln ( v 2. v min
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1 SUMMARY OF GAS POWER CYCLES-CHAPTER 9 OTTO CYCLE GASOLINE ENGINES Useful Wor, Thermal Efficiency 1-2 Isentropic Compression (s 1=s Isochoric Heat Addition (v 2= v Isentropic Expansion (s 3=s Isochoric-Heat Rejection (v 4= v 1 For isochoric process 1-2 Q 12 = Q Added Heat = m(u 3 u 1 = mc v (T 3 T 2 = c v (T 3 T 2 For isochoric process 4-1 Q 41 = Q Rejection = m(u 4 u 1 = mc v (T 4 q out = c v (T 4 η th Otto = W net = q out In the isentropic process: ds = 0 = 1 T 4 T 3 T 2 ds = du T + P T dv du + Pdv = 0 for ideal gas: c vdt + Pdv = 0 P = RT v, MEP = W net V max V min dt + RT dv = 0 dt vc v T + R dv c v v = 0 R = c p c v dt T = (1 c p dv c v v Integrating dt T = ( 1 dv v yields: is the specific heat ratio = c p c v ln T 2 = ( 1 ln ( v 2 v 1 T 2 = ( v 2 v 1, η th Otto = 1 1 r where r = v max v min = v 1 v 2 T-s diagram P-v College of Engineering Taibah University 1
2 DIESEL CYCLE DIESEL ENGINES Useful Wor, Thermal Efficiency 1-2 Isentropic Compression (s 1=s Isochoric Heat Addition (v 2= v Isentropic Expansion (s 3=s Isochoric-Heat Rejection (v 4= v 1 For isochoric process 1-2 = P 2 (v 3 v 2 + (u 3 u 2 = h 3 h 2 = c p (T 3 T 2 q out = (u 4 u 1 = c v (T 4 η Diesel = W net = 1 T 4 (T 3 T 2 Thermal Efficiency ( T 4 T 1 = 1 1 T 2 ( T, 3 T 1 2 P 1 v 3 = RT 3, P 1 v 1 = R r c = v 3, r = v 1 Max. Volume = v 2 v 2 Mini. Volume r c is a Cutt off Ratio is the ratio of the cylinder volumes and after and beforethe combustion proces. The efficiency becomes: η Diesel = W net P 4 v 4 = RT 4, P 2 v 2 = RT 2 = 1 T 4 (T 3 T 2 = 1 r c 1 r (r c 1 DUAL CYCLE DIESEL+GASOLINE ENGINES The dual cycle is a diesel and a gasoline cycle which has a constant pressure and a constant volume at the heat addition College of Engineering Taibah University 2
3 1-2 Isentropic Compression process (s 1=s Isochoric and Isobaric Heat Addition process (v 2= v X, P 3=P x 3-4 Isentropic Expansion process (s 3=s Isochoric-Heat Rejection process (v 4= v 1 = c v (T X T 2 + c p (T 3 T X q out = (u 4 u 1 = c v (T 4 η Dual = W net P-v diagram BRAYTON CYCLE TURBOJET ENGINES = h 3 h 2 = c p (T 3 T 2 P 2 = P 3 q out = h 4 h 1 = c p (T 4 Isentropic process: P 2 = P 3 and P 1 = P 4 T 2 = ( P 2 \\\\ P 1 ( η Brayton and T 3 T 4 = ( P 3 P 4 = 1 = 1 1 r P ( T 4 1 T 2 ( T 3 T 2 1, r P = P 2 P 1 The actual cycle of Brayton cycle: η C = h 2s h 1 h 2a h 1 η T = h 3 h 4a h 3 h College of Engineering Taibah University 3
4 A. Brayton Cycle with Regeneration q regen, act = h 5 h 2, andq regen, max = h 5 h 2 = h 4 h 2 The extent to which a regenerator approaches and ideal regenerator is called and is defined as = h 5 h 2 h 4 h 2 η Brayton, generation = (1 ( r T P 3 Regeneration cycle B. Brayton Cycle with intercooling, Reheating, and Regeneration P 2 P 1 = P 4 P 3, and P 6 P 7 = P 8 P 6 Closed Gas- Turbine Regenerator with reheating and intercooler College of Engineering Taibah University 4
5 College of Engineering Jet Propulsion Ideal Engines: 1-3 Isentropic Compression (s 1=s Isobaric Heat Addition (P 3= P Isentropic Expansion (s 4=s Isobaric-Heat Rejection (P 6= P 1 The thrust net force can be calculated as: F thurst = m (V eixt V inlet Propulsive efficiency: η P = W P Q in W comp = W Turbine T 3 = T 4 T 6 ( No inetic or Potentail Energy h 1 + V = h 2 + V = T 2 + V V 1 2c p 1-3 Isentropic Compression (s 1=s 2 T 4, also T 3 = ( P 3 P 1 T 6 = ( P 4 P 6 Stirling and Ericson Cycles Stirling Cycle: 1-2 T= constant expansion (heat addition from the external source 2-3 v = constant regeneration (internal heat transfer from the woring fluid to the regenerator 3-4 T= constant compression (heat rejection to the external tan 4-1 v = constant regeneration (internal heat transfer from the regenerator bac to the woring College of Engineering Taibah University 5
6 W net = mr(t H T L ln ( V max = mr(t V H T L ln ( v 3 min v 4 Q regen = m c v (T 2 T 3 = mc v ( T 4 T H is at P max = P 1 and T L is at P in = P 3. = c v (T H T L + w 34 w 34 = RT 4 ln ( P 4 P 3 η th = w net Ericson Cycle: Q regen = m c p (T 2 T 3 = mc p ( T 4 W net = mr(t H T L ln ( V max V min = mr(t H T L ln ( v 2 v College of Engineering Taibah University 6
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