Download - Chapter 7 and 8 (Power Cycles)
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Power Cycles
Chapter 7 & 8
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Outline of Power Cycles
Heat engines
Steam power plants
1. Carnot cycle
2. Rankine cycle
Turbines/compressors – Chap 7
Internal combustion engines
1. Otto engine
2. Diesel engine
3. Gas turbine engines
Regenerative cycle
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Heat into work
Most present day methods based on the evolution of heat and subsequent conversion of part of the heat into useful work.
Fossil fuel steam power plants (Efficiency: 35%) Combined cycle plants (Efficiency: 50%) – advanced
technology gas turbines Conversion of chemical energy directly into electrical
energy Eg.: Electrochemical cell (battery), fuel cell (Efficiency: 50%
and more)
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Heat engines
Internal combustion energy Conversion of chemical energy of fuel directly into internal
energy Eg: Otto engine, Diesel engine, gas turbines Power plants Working fluid such as steam is separated from heat source and
heat is transferred across a physical boundary
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Heat Engine Cycle
Heat engines operate in a cyclic manner, adding energy in the form of heat in one part of the cycle and using that
energy to do useful work in another part of the cycle.
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Revision
Specific volumes at constant temperature and states within the vapor dome in a liquid-vapor system
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Boiler – part of heat from fuel oil converts water to steam at high T and P QH
Turbine – shaft work by a turbine Ws
Condenser – condenses exhaust steam at low T QC Pump – pumps water back to boiler. Ws
Simple steam power plant
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Carnot engine
The most efficient heat engine cycle is the Carnot cycle, consisting of two isothermal processes and two adiabatic processes.
When the second law of thermodynamics sets the limiting value on the fraction of the heat which can be so used.
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Carnot efficiency
H
C
T
T1
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Issues in Carnot cycle
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Turbines (Expanders - gas)
• The expansion of a gas in a nozzle to produce a high velocity stream • Converts internal energy into kinetic energy and finally shaft work • Consists of alternate sets of nozzles and rotating blade through which vapour flows in an expansion process
Conversion of a high pressure stream into shaft work
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Shaft work, Ws
In open systems, DH = Q + Ws
For turbines, Ws = DH = H2 – H1
If the fluid in turbine expands reversibly and adiabatically isentropic process
Isentropic: S2 = S1
Ws (isentropic) = (DH)s
Ws (isentropic) is the maximum that can be obtained
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Adiabatic expansion process in turbine
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Turbine efficiency
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Values of range from 0.7 – 0.8
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Adiabatic expansion process in turbine
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Compressors
Expansion process (turbines): pressure reduction in a flowing fluid
Compression process (compressor): pressure increases (by reducing volume)
Compressors are similar to pumps: both increase the pressure on a fluid and both can transport the fluid through a pipe
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Adiabatic compression
P1
P2
W
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Compressor efficiency
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A steam turbine with rated capacity of 56400kW operates with steam at
inlet conditions at 8600 kPa and 500oC, and discharges into a condenser at
a pressure of 10kPa. Assuming the turbine efficiency at 0.75, determine the
state of the steam at discharge and the mass flow rate of the steam.
1) Determine quality, x2’
2) Find (DH)s
M=Ml +xvDMlv
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3) Find H2 actual using efficiency and determine new quality, x2
4) Find S2 actual and actual shaft work, Ws
H=Hl +xvDHlv
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What if the fluid is not steam?
How can the isentropic shaft work be calculated?
Where will you obtain data from?
Let’s say the stream going through the turbine is a gas eg. ethylene – you have two options:
1. Ideal gas assumption
)( 12 TTCHH
ig
P D
D2
11
2
1
2 lnlnT
T
ig
PP
PR
T
TCS
For isentropic conditions, DS=0
)()()( 12 TTCsHisentropicWsH
ig
P D
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Alternatively…
2. Choose an appropriate generalised equation
),,(
10
OMEGAPRTRHRBRT
H
RT
H
RT
H
c
R
c
R
c
R
),,(
10
OMEGAPRTRSRBR
S
R
S
R
S RRR
RR
H
ig
P HHTTCH 1212 )( D
RRT
T
ig
P SSP
PR
T
dTCS 12
1
22
1
ln D
RR
H
ig
P HHTTCsHisentropicWs 1212 )()()( D
Refer to Example 7.7
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Simple steam power plant
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Turbine and pump work Work output of the cycle (Steam turbine), Wturbine and work
input to the cycle (Pump), Wpump are:
Wturbine = m (h2-h1) (negative value) Wpump = m (h4-h3)
where m is the mass flow of the cycle. Heat supplied to the cycle (boiler), QH and heat rejected from the cycle (condenser), QC are:
QH = m (h4-h1) QC = m (h3-h2) (negative value)
The net work of the cycle is:
W = Wturbine + Wpump
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Rankine Cycle
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Practical power cycle - Rankine
Rankine Cycle
Carnot Cycle
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Rankine Cycle
1. Saturated or superheated steam enters the turbine at state 1, where it expands isentropically to the exit pressure
2. The steam is then condensed at constant pressure and temperature to a saturated liquid.
3. The heat removed from the steam in the condenser is typically transferred to the cooling water. The saturated liquid then flows through the pump
4. The pump increases the pressure to the boiler pressure where the water is heated to the saturation temperature, boiled and typically superheated to state 1.
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Isentropic conditions
1 to 2: Isentropic expansion (Steam turbine)
2 to 3: Isobaric heat rejection (Condenser)
3 to 4: Isentropic compression (Pump)
4 to 1: Isobaric heat supply (Boiler)
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Rankine efficiency
The efficiency of the Rankine cycle is not as high as Carnot cycle but the cycle has less practical difficulties
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Internal Combustion Engines
Does not require heat transfer areas such as in steam power plant
Internal combustion engines burn fuel within the engine
Does not happen in cyclic process for the working medium such as steam in power plants, therefore the cyclic process is imagined with air as the working fluid
First presented in qualitative description than quantitative using air as an ideal gas
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The Otto Engine
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Stage 1: Beginning of the intake stroke of the engine. The pressure is near atmospheric pressure and the gas volume is at a minimum. The pressure remains constant, and the gas volume increases as fuel/air mixture is drawn into the cylinder through the intake valve. Stage 2: Compression stroke of the engine with the closing of the intake valve. Between Stage 2 and Stage 3, the piston moves back into the cylinder, the gas volume decreases, and the pressure increases because work is done on the gas by the piston. Stage 3: Combustion of the fuel/air mixture. The combustion occurs very quickly and the volume remains constant. Heat is released during combustion which increases both the temperature and the pressure, according to the equation of state.
Internal –Combustion Engines
- The Otto Engine
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Stage 4: Power stroke of the engine. Between Stage 4 and Stage 5, the piston is driven towards the crankshaft, the volume in increased, and the pressure falls as work is done by the gas on the piston. Stage 5: Exhaust valve is opened and the residual heat in the gas is exchanged with the surroundings. The volume remains constant and the pressure adjusts back to atmospheric conditions. Stage 6: Exhaust stroke of the engine during which the piston moves back into the cylinder, the volume decreases and the pressure remains constant. At the end of the exhaust stroke, conditions have returned to Stage 1 and the process repeats itself.
Internal –Combustion Engines
- The Otto Engine
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Idealised Air Standard Cycle
•Heat is transferred at
constant volume during 1-2.
•The gas expands
reversibly and adiabatically
during 2-3, where work is
done.
•Heat is rejected at
constant volume at low
temperature during 3-4.
•The gas is compressed
reversibly and adiabatically
in 4-1.
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The thermal efficiency of an Otto cycle with a perfect gas as working fluid is: It can be shown that: where, r = V1/V2= Compression ratio g = constant depending on specific heat capacity
The Otto Engine efficiency
Ideal Otto cycle thermal efficiency
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Diesel engine
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Diesel Cycle
1 to 2: Isentropic compression 2 to 3: Reversible constant pressure heating 3 to 4: Isentropic expansion 4 to 1: Reversible constant volume cooling
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•Heat is supplied reversibly at constant pressure in 1-2.
•Reversible adiabatic expansion during which work is done in 2-3.
•Heat is rejected reversibly at constant volume in 3-4.
•Gas is compressed reversibly and
adiabatically in 4-1.
Diesel Cycle
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- Advantages of internal combustion and those of the
steam turbine are combined in the gas-turbine engine.
- Driven by high temperature gases from combustion chamber, compressed to several bars
Gas Turbine Engine
PA
PB
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Ideal cycle: Brayton cycle Working fluid is air as ideal gas
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Idealisation of gas turbine is known as the Brayton cycle
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Comparison of efficiency
g = 1.4 for ideal cycle conditions
Both k and g may be used. However they represent the same constant
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Example 8.1 from textbook
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Turbine – as done previously
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For condenser and boiler,
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Thermal efficiency
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When turbine efficiency = 0.75,
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If rating of power cycle = 80000kW,
what is the steam rate, QB and QC
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Regenerative cycle
The incremental steps of heat transfer to the feedwater increases the cycle efficiency over having all of the heat transfer taking place within the boiler. The steam from the turbine releases its heat to the feedwater, reducing the amount of heat rejected in the condenser.
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After emerging from the condenser as a subcooled liquid the working fluid is heated by steam tapped from the hot portion of the cycle. On the diagram shown, the fluid at 2 is mixed with the fluid at 4 (both at the same pressure) to end up with the saturated liquid at 7.
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Tutorial Questions
Attempt the following from textbook (7th Edition):
Chapter 7: 10, 18, 23
Chapter 8: 1, 4, 6, 7