Gas Power Cycles Dr.Mohammad Tarawneh
) Carnot cycle 2) Otto cycle ) Diesel cycle - Today 4) Dual Cycle 5) Stirling cycle 6) Ericsson cycles 7) Brayton cycle
Carnot Cycle Reversible isothermal expansion Reversible adiabatic expansion Reversible isothermal compression Reversible adiabatic compression T 2 4 s
Otto cycle : The ideal cycle for spark-ignition (SI) engines P q in T q in 2 4 q out 2 q 4 out TDC BDC v s P-v diagram T-s diagram
Diesel cycle : The ideal cycle for compression ignition (CI) engines Processes: -2 Compression (s = Const) 2- Combustion (P = Const.) -4 Expansion (s = Const) 4- Exhaust (V = Const) P q in 2 4 T q out 2 q in 4 q out v (a) P-v diagram (b) T-s diagram Eliminates pre-ignition of the fuel-air mixture when compression ratio is high. s The combustion process in CI engines takes place over a longer interval and is approximated as constant-pressure heat addition process.
A. Diesel cycle : The ideal cycle for compression ignition (CI) engines
A. Diesel cycle : The ideal cycle for compression ignition (CI) engines Named after Rudolph Diesel (858 9) developed an engine designed for the direct injection of liquid fuel into combustion chamber in 897
Rudolf Christian Karl Diesel (858-9) 9) born on March 8, 858. His parents were Bavarian. Diesel pursued his education in England and at the Polytechnic School in Munich. He worked as a mechanic and parts designer for two years at the Sulzer Machine Works of Winterthur in Switzerland. joined the Linde Refrigeration Enterprises and worked as a refrigerator engineer.
He envisioned an engine in which air is compressed to such a degree that there is an extreme rise in temperature.
When fuel is injected into the piston chamber with this air, the fuel is ignited by the high temperature of the air, exploding it, forcing the piston down. Diesel designed his engine in response to the heavy resource consumption and inefficiency of the steam engine, which only produced 2% efficiency.
A. Diesel cycle : The ideal cycle for CI engines An CI power cycle useful in many forms of automotive transportation, railroad engines, and ship power plants Replace (the spark plug + carburetor) in SI by fuel injector in CI engines. Spark plug Fuel injector Air-fuel mixture Fuel spray Gasoline engine Diesel engine
A. Diesel cycle : The ideal cycle for CI engines () Inlet valve open and fresh air is drawn into the cylinder (2) Temperature rise about the autoignition temperature of the fuel. () Intake compression Diesel fuel is sprayed into the combustion chamber. Evaporation, mixing, ignition and combustion of diesel fuel. In the later stages, expansion process occur. Combustion Exhaust (4) Burned gases is pushed out to the exhaust valve
A Diesel cycle : The ideal cycle for CI engines Processes: -2 Compression (s = Const) 2- Combustion (P = Const.) -4 Expansion (s = Const) 4- Exhaust (V = Const) P q in 2 4 T q out 2 q in 4 q out v (a) P-v diagram (b) T-s diagram Eliminates pre-ignition of the fuel-air mixture when compression ratio is high. s The combustion process in CI engines takes place over a longer interval and is approximated as constant-pressure heat addition process.
2.6 Diesel cycle : The ideal cycle for CI engines Energy balance for closed system: q q in in w = q q b out 2 out = = u w 2 2 = P ( v = ( h = q q 4 out 2 + ( u h 2 v ) u 2 2 ) ) + ( u = c = w+ u p ( T u 2 T qout = ( u4 u) = cv ( T4 T ) 4 4 = ( u u) 2 ) ) p = Constant 2 qout qin 4 V = Constant s η th,diesel = w q net in = q q out in = T4 T K( T T 2 ) = T kt ( T4 / T ) ( T / T ) 2 2
A. Diesel cycle : The ideal cycle for CI engines Define a new quantity r cutoff r c c V V ratio cylinder after combustion cylinder before combustion = V V 2 = v v 2 η th, diesel r k c = where r= k r k( rc ) v v 2 k rc k( r c ) > η th, > η otto th,diesel
A. Diesel cycle : The ideal cycle for CI engines As the cut off ratio decreases, increases η The th diesel engines operate at much higher r and usually more efficient than spark-ignition engines. The diesel engines also burn the fuel more completely since they usually operate at lower rpm than SI engines. CI engines operate on lower fuel costs.
A. Diesel cycle : The ideal cycle for CI engines At r c =, the Diesel and Otto cycles have the same efficiency. Physical implication for the Diesel cycle: No change in volume when heat is supplied. A high value of k compensates for this. For r c >, the Diesel cycle is less efficient than the Otto cycle.
Q : Example 9.45 An air standard Diesel cycle has a compression ratio of 6 and cut off ratio of 2. At beginning of the compression process, air is at 95kPa and 27 o C. Accounting for the variation of specific heat with temperature, determine a) Temperature after the heat additional process. b) Thermal efficiency c) The mean effective pressure Solution : Answer : a),724.8k b) 56.% c) 675.9kPa
Q Solution : P q in 2 4 q out T 2 (a) P-v diagram v (b) T-s diagram s q in 4 q out
Q
Dual cycle: A more realistic ideal cycle model for modern, high-speed compression ignition engine. P-v diagram of an ideal dual cycle.
A. Diesel cycle : The ideal cycle for CI engines The ideal Dual cycle The dual cycle is designed to capture some of the advantages of both the Otto and Diesel cycles. It it is a better approximation to the actual operation of the compression ignition engine.
A. Diesel cycle : The ideal cycle for CI engines The ideal Dual cycle p qin,v` qin,p 4 s = Constant 2 5 qout,v V
A. Diesel cycle : The ideal cycle for CI engines The ideal Dual cycle qin,v qin,p 4 2 5 qout,p r = r c = V V 2 V V 4 V
Q2 : Example The compression cycle of an ideal dual cycle is 4. Air is at 00kPa and 00K at beginning of the compression process and at 2,200K at the end of heat addition process. Heat transfer process to air is take place partly at constant volume and partly at constant pressure and its amount to,520.4 kj/kg. Assume variable specific heat for air, determine the thermal efficiency of the cycle. 9-54
Q2 Solution 9-54
Q2
Q2
B. Stirling and Ericsson cycles
HISTORY OF STIRLING ENGINE REV.ROBERT STIRLING The Stirling engine was invented by Rev. Robert Stirling in 86. He was a Scottish minister. At that time, Stirling engines were recognized as a safe engine that could not explode like steam engines of that era often did.
B. External Combustion Engine : Stirling and Ericsson cycles This is the Stirling engine that he created in his era
B. External Combustion Engine : Stirling and Ericsson cycles He create a safer alternative to the steam engines of the time, Whose boilers often exploded due to the high pressure of the steam and the primitive materials of the time. Stirling engines convert heat (actually, any temperature differential) directly to movement. They use a displacer piston to move enclosed air back and forth between cold and hot reservoirs. most important invention was the "regenerator" or "economizer"
HISTORY OF ERICSSON ENGINE JOHN ERICSSON Ericsson was invented the "hot air engine" in 852 Used hot air instead of steam as a propellant Inspired by his earlier attempts of fume heat engines in Sweden.
B. External Combustion Engine : Stirling and Ericsson cycles
B. External Combustion Engine : Stirling and Ericsson cycles 86 he developed a screw mechanism for boat propulsion, which he called a "propeller. Then,Ericsson claimed priority of invention a tubular heat exchanger form of regeneration, Robert Stirling had in fact patented a similar system in 86. 85 Ericsson managed to persuade his financial backers to build the Caloric Ship "Ericsson. This engine was no success. In spite of this, Ericsson was awarded the Rumford Prize in 862.
B. External Combustion Engine : Stirling and Ericsson cycles Concept of Stirling Engine Energy in Hot source Cold air displace by piston Compression Energy out Expansion Hot air displace by piston Cold source
B. External Combustion Engine : Stirling and Ericsson cycles Concept of Stirling Engine Energy in Hot source Isochoric regeneration Isothermal Compression Energy out Isothermal Expansion Isochoric regeneration Cold source
B. External Combustion Engine : Stirling and Ericsson cycles Operation of a Stirling cycle (4) Isochoric regeneration qin () Isothermal compression Isothermal expansion () qout (2) Isochoric regeneration
B. External Combustion Engine : Stirling and Ericsson cycles
B. External Combustion Engine : Stirling and Ericsson cycles Indicated diagram for Stirling cycle p T qin qin 2 T H = constant 4 qout Regeneration 2 Regeneration T L = constant v 4 qout s
B. External Combustion Engine : Stirling and Ericsson cycles Operation of a Ericsson cycle
B. External Combustion Engine : Stirling and Ericsson cycles Indicated diagram for Ericsson cycle p T 4 qin qin 2 T H = constant qout Regeneration Regeneration T L = constant 2 v 4 qout s
B. External Combustion Engine : Stirling and Ericsson cycles
B. External Combustion Engine : Stirling and Ericsson cycles Thermal efficiency η th stirling = η = η = th Ericsson th Carnot T T L H Advantages. Potential for higher efficiency and better emission control 2. Suitable for variable fuels Disadvantages. Difficult to achieve in practice due to heat transfer
Example An ideal Stirling engine using helium as the working fluid operates between temperature limit 00K and 2,000K and pressure limits of 50 and,000 kpa. Assuming the mass of the helium used in the cycle is 0.2kg, determine : a) The thermal efficiency of the cycle. b) The amount of heat transfer rate in the regenerator. c) The work output per cycle. 9-64
B External Combustion Engine : Stirling and Ericsson cycles Indicated diagram for Stirling cycle p T qin qin 2 T H = constant 4 qout Regeneration 2 Regeneration T L = constant v 4 qout s
Example
C. Brayton cycle : The ideal cycle for gas-turbine engines
History The Brayton cycle is a constant-pressure cycle named after George Brayton (80 892), 892), the American engineer who developed it. It is also sometimes known as the Joule cycle. In 872, Brayton filed a patent for his "Ready Motor" which, unlike the Otto or Diesel cycles, used a separate compressor and expansion cylinder. Today the Brayton cycle is generally associated with gas turbines Like other internal combustion power cycles, The Brayton cycle is an open system, though for thermodynamic analysis it is conventionally assumed that the exhaust gases are reused in the intake, enabling analysis as a closed system.
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Proposed by George Brayton around 870. Operate on an open cycle Application in commercial aircraft, military aircraft
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Model The term Brayton cycle has more recently been given to the gas turbine engine. This also has three components: A gas compressor A burner (or combustion chamber) An expansion turbine
2.8 Brayton cycle : The Ideal Cycle for Gas Turbine Engines Operation of an open cycle gas turbine engine
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Schematic diagram for the open cycle gas turbine engine
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines The air standard turbine cycle Open system modeled as a closed system - fixed with fixed mass flow. Air is the working fluid. Ideal gas assumptions are applied. Approximate the combustor as the high temperature source. Internally reversible processes.
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Simplification of gas turbine engine in close cycle -2 Isentropic compression (in a compressor) 2- Isobaric heat addition -4 Isentropic expansion (in turbine) 4- Isobaric heat rejection
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Thermodynamics analysis Compressor w 2 = h know that w h 2 h = h = c p dt 2= wcomp = c p T ( T 2) Combustion chamber q q 2 in = = h c p h ( T T ) 2 2
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Thermodynamics analysis Turbine w = h h = c p T ) 4 4 ( T4 w = c ( T T ) p 4 turb Heat exchanger q q 4 out = = h c p h ( T T ) 4 4
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Thermodynamics analysis Thermal efficiency η η η th th th = = work net heat supplied c p = ( T ( T ( T 4 T c p 4 ( T T T 2 ) ) ) c = p T ( T 2 = w w ) 2 turb q q out in q T in ) comp
( ) ( ) 2 2 2 Processes- 2 and - 4 are isentropic, T P P T k k k k C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines 2 )/ ( th Brayton 4 2 2 2 where pressure ratio, P P r r T T P P P P T T p k k p = = = = = η
C. Brayton cycle : The Ideal Cycle for Gas Turbine Engines Thermodynamics analysis : Turbine efficiency T 2 2 4 η η T T = = actual work isentropic work h h h h 4' 4 = T T T T 4' 4 = wa w 4 s
Thermodynamics analysis : Compressor efficiency T η η C C = = isentropic work actual work h h 2 2' h h = T T 2 2' T T = w w a 2 2 4 4
Thermodynamics analysis : actual thermal efficiency T 2 2 4 η = η = w q net in ( T T4' ) ( T2' T ) ( T T 2 ') 4
work Compressor Turbine w turbine w net w compressor Back work
Thermodynamics analysis work Compressor Turbine w turbine w net w compressor Back work Work ratio r r w w = Back work ratio w T = T w turb comp ( T T4 ) ( T2 T ) r r w 4 bw bw turb = = T T w w 4 = comp turb = ( T ( T ( T 2 T T T 4 ) ) 4 )
η th Brayton =, r ( k )/ k p Depends on the pressure ratio and specific heat ratio
Example The open cycle gas turbine operate on Brayton cycle with pressure ratio 4.5/. Air enter the compressor at 2 0 C and heated to 780 0 C at entry to the turbine. If mass flow rate is 40kg/min, Determine : a) Cycle efficiency b) Power output from the plant. k=.4, c p =.005kJ/kgK Data : r p =4.5, T =294K, T =05K, m=2.kg/s
Process -2, isentropic compression Process -4, isentropic expansion Consider kg of heat supply,
Heat rejection Net work output Cycle efficiency
Net work output per second
Example A gas turbine power plant operating on an ideal Brayton cycle has a pressure ratio of 8. The gas temperature is 00K at compressor inlet and,00k at turbine inlet. Utilizing the air standard assumption, determine : a) The gas temperature at exit of the compressor and turbine, (Answer = 770K) b) the back work ratio, (Answer = 0.40) c) The thermal efficiency (Answer = 0.426)
Solution Process -2, isentropic compression on ideal gas T 2 = at compressor exit Process -4, isentropic expansion on ideal gas T 4 = at Turbine exit
Pressure Drop.Pressure drop during heat addition and heat rejection process 2.Actual work input to compressor is more.actual work from the turbine is less
Thermodynamics analysis : Turbine efficiency T 4' 4' T a T work isentropic work actual T T h h w s w = = = = η η s 2 4 4 2 4 4 T T T h h
Thermodynamics analysis : Compressor efficiency T η η C C = = isentropic work actual work h 2 h T 2 T = h h T T 2' 2' = w s w a 2 2 4 4
Thermodynamics analysis : actual thermal efficiency T η = η = w q ( T net in T4' ) ( T2' ( T T ) 2' T ) 2 2 4 4
Example A gas turbine power plant operating on brayton cycle has a pressure ratio of 8. the gas temperature is 00K at compressor inlet and,00k at turbine inlet. Utilizing the air standard assumption, and assuming compressor efficiency of 80% and turbine efficiency is 85%, determine back work ratio
Solution Compressor Turbine Turbine
D. The Brayton cycle with regeneration
Cycle Improvements Regeneration Reduces heat input requirements and lowers heat rejected.
Regeneration is accomplished by preheating the combustor air with the exhaust gas from the turbine.
T,h Q H 2 6 5 Q H 4 2 5 6 4 W COMP W TURB Q C s Internal heat transfer, States 2 - x.
6 2 5 Q H 4 W COMP W TURB
Act and max heat transfer from the exhaust gas to air : q regen,act = h 5 h 2 q regen,max = h 5 h 2 = h 4 - h 2 q regen,act h 5 h 2 Effectiveness, = = q regen,max h 4 - h 2
The maximum benefit of regeneration is obtained when the exhaust temperature T 6 is brought to temperature T 2 by the regenerative heat exchanger or regenerator. Increase the thermal efficiency of the Brayton cycle Decrease the heat input (thus fuel) requirements Is use when the turbine exhaust temperature is higher than the compressor exit temperature
Example A gas turbine power plant operating on an Brayton cycle has a pressure ratio of 8. the gas temperature is 00K at compressor inlet and,00k at turbine inlet. Utilizing the air standard assumption, and assuming compressor efficiency of 80% and turbine efficiency is 85%, regenerator having effectiveness of 80% is is install, determine the thermal efficiency.
q regen,act h 5 h 2a Effectiveness, = = q regen,max h 4a - h 2a = 0.80, h 5 = 825.7kJ/kg q in = h - h 5 = 570.6kJ/kg
E. The Brayton cycle with intercooling, reheating and regeneration
Cycle Improvements Regeneration Reduces heat input requirements and lowers heat rejected. Inter-cooling Lowers mean temperature of the compression process Reheat Raises mean temperature of the heat addition process
T = T T6 = T8 P2 = P4 P = P
Decrease the total compression work Improve the back work ratio If the number of compression and expansion stages is increased, the ideal turbine cycle with intercooling, reheating and regeneration approaches the Ericsson cycle
T qin 2 Regeneration 4 qout s Multistage intercooling, reheat and regeneration gas turbine cycle The ideal Ericsson cycle
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