Transcript
Air-standard cycles CH. 2 Air-standard analysis: Prepared by Ar Assim Al Daraje
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Cold-air-standard assumptions: When the working fluid is considered to be air with constant specific heats at room temperature (25°C). Air-standard cycle: A cycle for which the air-standard assumptions are applicable. Air-standard analysis is a simplification of the real cycle ۲
Air-standard assumptions: 1.The working fluid is air, which continuously circulates in a closed loop and always behaves as an ideal gas. 2.All the processes that make up the cycle are internally reversible. 3.The combustion process is replaced by a heat-addition process from an external source. 4.The exhaust process is replaced by a heatrejection process that restores the working fluid to its initial state. ۳
The combustion process is replaced by a heat-addition process in ideal cycles. ٤
OTTO CYCLE
The two-stroke engines are generally less efficient than their four-stroke counterparts but they are relatively simple and inexpensive, and they have high power-to-weight and power-to-volume ratios.
Four-stroke cycle 1 cycle = 4 stroke = 2 revolution Two-stroke cycle 1 cycle = 2 stroke = 1 revolution
T-s diagram of the ideal Otto cycle. 5
Schematic of a two-stroke reciprocating engine.
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In SI engines, the compression ratio is limited by auto ignition or engine knock.
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Thermal efficiency of the ideal Otto cycle as a function of compression ratio and k. ۸
The thermal efficiency of the Otto cycle increases with the compression ratios. ۹
Diesel Cycle • Invented by Rudolf Christian Karl Diesel in 1893 • First engine was powered by powdered coal • Achieved a compression ratio of almost 80 • Exploded, almost killed Diesel • First working engine completed 1894 generated 13 hp ۱۰
Thermodynamic Cycles for CI engines In early CI engines the fuel was injected when the piston reached TDC • and thus combustion lasted well into the expansion stroke. In modern engines the fuel is injected before TDC (about 15o)•
Fuel injection starts Early CI engine
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Fuel injection starts Modern CI engine
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combustion process in the early CI engines is best approximated by a constant pressure heat addition process Diesel Cycle • The combustion process in the modern CI engines is best approximated by a combination of constant volume and constant pressure Dual Cycle
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The p - V diagrams of two-stroke and four-stroke diesel engine
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DIESEL CYCLE: THE IDEAL CYCLE FOR COMPRESSION-IGNITION ENGINES In diesel engines, only air is compressed during the compression stroke, eliminating the possibility of auto ignition (engine knock). Therefore, diesel engines can be designed to operate at much higher compression ratios than SI engines, typically between 12 and 24.
In diesel engines, the spark plug is replaced by a fuel injector, and only air is compressed during the compression process.
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Cut-off ratio:
Air-Standard Diesel cycle rc = Process a b
Isentropic compression
Process b c Constant pressure heat addition Process c d Isentropic expansion Process d a Constant volume heat rejection - a=1,b=2,etc…for book
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v vc = 3 (BOOK ) vb v2
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Thermal Efficiency
η Diesel cycle
Qout m u4 − u1 = 1− = 1− Qin m h3 − h2
For cold air-standard the above reduces to:
ηDiesel const cV
k −1 r ) 1 1 (c recall, = 1− k−1 ⋅ r k (rc −1)
ηOtto = 1 −
1 r
k −1
Note the term in the square bracket is always larger than one so for the same compression ratio, r, the Diesel cycle has a lower thermal efficiency than the Otto cycle So why is a Diesel engine usually more efficient? ۲۱
Thermal Efficiency
Typical CI Engines 15 < r < 20
When rc (= v3/v2)1 the Diesel cycle efficiency approaches the efficiency of the Otto cycle Higher efficiency is obtained by adding less heat per cycle, Qin, run engine at higher speed to get the same power. ۲۲
The cut-off ratio is not a natural choice for the independent variable a more suitable parameter is the heat input, the two are related by: as Qin 0, rc1
k = 1.3
k − 1 Qin 1 k −1 rc = 1 − k P1V1 r W net MEP = Vmax − Vmin
k = 1.3
- compares performance of engines of the same size ۲۳
Modern CI Engine Cycle and the Thermodynamic Dual Cycle Fuel injected at 15o before TDC
A I R Air
Combustion Products
Actual Cycle Intake Stroke
Compression Stroke
Power Stroke
Qin Dual Cycle
Air
Exhaust Stroke
Qin
Qout
TC BC
Compression Process ۲٤
Const volume heat addition Process
Const pressure heat addition Process
Expansion Process
Const volume heat rejection Process
Dual Cycle
Process 1 2 Isentropic compression Process 2 2.5 Constant volume heat addition Process 2.5 3 Constant pressure heat addition Process 3 4 Isentropic expansion Process 4 1 Constant volume heat rejection
Qin = (u2.5 − u2 ) + (h3 − h2.5 ) = cv (T2.5 − T2 ) + c p (T3 − T2.5 ) m Q 2.5
3
in
3
Qin
2
4
2.5
4
2
1 1
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Qout
η Dual cycle
Thermal Efficiency Qout m u4 − u1 = 1− = 1− (u2.5 − u2 ) + (h3 − h2.5 ) Qin m
η Dual const cv
αrck − 1 1 = 1 − k −1 r (α − 1) + αk (rc − 1)
where rc =
v3
v2.5
and α =
P3
P2
Note, the Otto cycle (rc=1) and the Diesel cycle (a=1) are special cases:
ηOtto = 1 − ۲٦
1 r
k −1
η Diesel const cV
( (
) )
k 1 1 rc − 1 = 1 − k −1 ⋅ r k rc − 1
The use of the Dual cycle requires information about either: i) the fractions of constant volume and constant pressure heat addition (common assumption is to equally split the heat addition), or ii) maximum pressure P3. Transformation of rc and a into more natural variables yields
α − 1 k − 1 Qin 1 1 P3 α= k k −1 − rc = 1 − αk P1V1 r k −1 r P1 For the same initial conditions P1, V1 and the same compression ratio:
ηOtto > η Dual > η Diesel
For the same initial conditions P1, V1 and the same peak pressure P3 (actual design limitation in engines): ۲۷
η Diesel > η Dual > ηotto
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Thermal efficiency of the ideal Diesel cycle as a function of compression and cutoff ratios (k=1.4).
for the same compression ratio 29
QUESTIONS
Dual cycle: A more realistic ideal cycle model for modern, high-speed compression ignition engine.
Diesel engines operate at higher air-fuel ratios than gasoline engines. Why? Despite higher power to weight ratios, two-stroke engines are not used in automobiles. Why? The stationary diesel engines are among the most efficient power producing devices (about 50%). Why?
P-v diagram of an ideal dual cycle. 30
What is a turbocharger? Why are they mostly used in diesel engines compared to gasoline engines.
Modern CI Engine Cycle and the Thermodynamic Dual Cycle Fuel injected at 15o before TDC
A I R Air
Combustion Products
Actual Cycle Intake Stroke
Compression Stroke
Power Stroke
Qin Dual Cycle
Air
Exhaust Stroke
Qin
Qout
TC BC
Compression Process ۳۱
Const volume heat addition Process
Const pressure heat addition Process
Expansion Process
Const volume heat rejection Process
Dual Cycle
Process 1 2 Isentropic compression Process 2 2.5 Constant volume heat addition Process 2.5 3 Constant pressure heat addition Process 3 4 Isentropic expansion Process 4 1 Constant volume heat rejection 2.5
Qin
3
Qin
2
4 1
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2.5 4
2
1
3
Qout
Qin = (u2.5 − u2 ) + (h3 − h2.5 ) = cv (T2.5 − T2 ) + c p (T3 − T2.5 ) m
The use of the Dual cycle requires information about either: i) the fractions of constant volume and constant pressure heat addition (common assumption is to equally split the heat addition), or ii) maximum pressure P3. Transformation of rc and α into more natural variables yields
α − 1 k − 1 Qin 1 k −1 − rc = 1 − αk P1V1 r k −1
1 P3 α= k r P1
For the same initial conditions P1, V1 and the same compression ratio:
ηOtto > η Dual > η Diesel
For the same initial conditions P1, V1 and the same peak pressure P3 (actual design limitation in engines):
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η Diesel > η Dual > ηotto
S.No Petrol Engine 1. The petrol engine works on Otto cycle i.e. on constant volume. The air and petrol are mixed in 2. the carburetor before they enter into the cylinder. The petrol engine compresses 3. a mixture of air and petrol which is ignited by an electric spark. Compression ratio is low. 4. Less power is produced due to 5. lower compression ratio. Petrol engine is fitted with a 6. spark plug Burns fuel that has high 7. volatility.
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Diesel Engine The diesel engine works on diesel cycle i.e. on constant pressure. The fuel is fed into the cylinder by a fuel injector and is mixed with air inside the cylinder. The diesel engine compresses only a charge of air and ignition is done by the heat of compression. Compression ratio is higher in diesel engine. Due to higher compression ratio more power is produced. It is fitted with a fuel injector. Burns fuel that has low volatility.
8. They are used in light vehicles which requires less power Eg: car, jeep, motorcycle, scooters etc. Fuel consumption in 9. petrol engine is high. Lighter 10. 1 Petrol engine requires 1. frequent overhauling. 1 Lesser starting problem. 2. 1 Lower initial cost. 3. 1 Lower maintenance cost. 4.
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They are used in heavy vehicles which require high power. Eg: bushes, trucks, locomotive etc. Fuel consumption in diesel engine is less. Heavier Overhauling of diesel engine is done after a long time. Greater starting problem. Higher initial cost. Higher maintenance cost.
OTTO CYCLE
1. Heat addition takes place at constant volume. 2. Petrol engines work on this cycle. 3. At constant volume, heat rejection takes place. 4. Compression ratio is less. It is 7:1 to 10:1. 5. Efficiency is less.
DIESEL CYCLE
Heat addition takes place at constant pressure. Diesel engines work on this cycle. in diesel cycle also the heat rejection takes place at constant volume. Compression ratio is more. It is 11:1 to 22:1. Efficiency is more.
6. Adiabatic expansion takes place After the heat addition is cutduring the complete backward off in the backward stroke, the stroke of the piston. adiabatic expansion takes place during the remaining portion of stroke. ۳٦
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An air-standard Dual cycle operates with a compression ratio of 14. The conditions at the beginning of compression are 100 kPa and 300 K. The maximum temperature in the cycle is 2200 K and the heat added at constant volume is twice the heat added at constant pressure. Determined, (a) The pressure, temperature, and specific volume at each corner of the cycle, (b) The thermal efficiency of the cycle, and (c) The mean effective pressure. Solution
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