Chapter 8.
Production of Power from Heat
Introduction
Production of Power
Energy from the sun : Photovoltaic cells
Kinetic Energy from atmospheric wind : windmills
Fossil fuels, atomic fuels
- Chemical Energy Heat Power (Electrical Work) - Efficiencies are low (35 – 50 %)
Fuel cell
- Chemical Energy Power (Electrical Work) - Greater efficiency (85 %)
Use of Fossil Fuels
Steam Power Plant : Fossil fuel and nuclear
Internal combustion engines
Otto engines
Diesel engines
Gas turbine
Jet engines
8.1 Steam Power Plant
Simple steam power plant
Diagram of a real power plant
Steam Plant…
Carnot cycle
H C
H
T
T Q
W
1 1
Efficiency increases as
T
Hincreases T
Cdecreases
T
S
1 2
4 3 T
HT
CVaporization process in the boiler Reversible, adiabatic expansion of
saturated vapor into two-phase (turbine)
Condensation (condenser)
Isentropic compression (pump)
Rankine Cycle
In a Carnot cycle, several steps are almost impossible for practical reasons
23 : Steams with liquid content causes erosion problems in turbine blades
41 : Pumping of gas-liquid mixture is difficult
Carnot vs. Rankine Cycles
Two major differences
Heating step 12 : Heating beyond vaporization
Cooling step 34 : Complete Condensation
Rankine Cycle : alternative standard for power plant
Two modification from Carnot cycle
12 : Heating beyond vaporization
34 : Complete Condensation
T
S
2
1
3 4
Heating of subcooled liquid
(const P)
Vaporization at const T and P
Superheating of vapor well above the
saturation T
(Reversible, adiabatic) Expansion
(reduced moisture contents)
Condensation (Const P, const T) Pumping of sat.
liquid to boiler temperature
Real path due to irreversibility
Steam Power Plant
Turbine (Ch.7)
Pump (Ch.7)
Boiler and Condenser
Heat transfer process
S s
s
) H (
H )
isentropic (
W
W
) H H
( H
W
s
3
2H ) H ( W
) isentropic (
W
Ss s
) H H
( H
W
s
1
4H Q
, H m
Q
Example 8.1
Steam generated in a power plant at a pressure of 8,600 kPa and a temperature of 500
oC is fed to a turbine. Exhaust from the turbine enters a condenser at 10 kPa, where it is condensed to saturated liquid, which is then pumped to the boiler.
(a) The thermal efficiency of a Rankine cycle
(b) The thermal efficiency of a practical cycle if the turbine efficiency
and pump efficiency are both 0.75
Example 8.1
(a)
8,600 kPa500 oC
H2 = 3391.6 kJ/kg
10 kPa
H3 = 2117.4 kJ/kg 10 kPa
Tsat= 45.83 oC H4 = 191.8 kJ/kg Isentropic pumping (process 4 1)
(H)S = 8.7 kJ/kg (Ex 7.10) H1 = H4 + (H)S = 200.5 kJ/kg
the turbine operate under the same condition as Ex. 7.6
H
S 1 , 274 . 2 kJ / kg
3966 .
1 0 . 191 , 3
5 . 1265 )
boiler (
Q
) Rankine (
W
kg / kJ 5 . 265 , 1 6
. 925 , 1 1 . 191 , 3 )
condenser (
Q ) boiler (
Q )
Rankine (
W or
kg / kJ 5 . 265 , 1 7
. 8 2 . 1274 )
pump (
W ) turbine (
W ) Rankine (
W
kg / kJ 1 . 191 , 3 5 . 200 6
. 391 , 3 H H
) boiler (
Q
kg / kJ 6 . 925 , 1 4
. 117 , 2 8 . 191 H
H ) condenser (
Q
S S S
1 2
3 4
Example 8.1
(b)
2961 .
2 0 . 188 , 3
0 . 944 )
boiler (
Q
) Rankine (
W
kg / kJ 2 . 188 , 3 4 . 203 6
. 391 , 3 H H
) boiler (
Q
kg / kJ 4 . 203 6
. 11 8 . 191 H
H H
kg / kJ 0 . 944 75
. 11 6 . 955 )
pump (
W ) turbine (
W ) Rankine (
W
kg / kJ 75 . 75 11
. 0
676 . ) 8 pump (
H W H
, 10 . 7 Ex From
kg / kJ 0 . 436 , 2 6 . 955 6
. 391 , 3 H H
H
kg / kJ 6 . 955 2
. 274 , 1 75 . 0 ) turbine (
W H
H , 6 . 7 Ex From
S
1 2 4
1
S S
S
S S
2 3
S S
The Regenerative Cycles
Higher efficiencies
Increased Boiler Temperature Increased Boiler Pressure Increased cost for construction
Lower condenser temperature Lower condenser pressure practical condensation controlled by ambient temp
Most modern power plants operate on a modification of the Rankine cycle that incorporates feed water heaters
Water from the condenser is first heated by steam extracted from the turbine
In Rankine cycle, water from the condenser is pumped directly back to the boiler
The Regenerative Cycles
Stagewise preheating the feed water can improve efficiencies
Simple steam power plant
steam power plant by regenerative cycle
Example 8.2
Determine the thermal efficiency of the power plant in
Figure, assuming turbine and pump efficiency of 0.75.
Example 8.2 – Section I
From energy balance
kg / kJ 4 . 240 )
5 . 320 (
75 . 0
H H
WS S
) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H
H ) liq . sat ( H H
) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H
kg / kJ 5 . 971 )
liq . sat ( H
H ) liq . sat ( H H
kg / kJ 2 . 151 , 3
4 . 240 6
. 391 , 3 H
balance Energy
Basis
Example 8.2 – Section II
From energy balance
SS H H
W
) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H
H ) liq . sat ( H H
) 25 . 7 eq , 7 . CH ( P ) T 1 ( V H
kg / kJ 5 . 971 )
liq . sat ( H
H ) liq . sat ( H H
H S 2. 151 , 3 H
balance Energy
Example 8.2
To get the thermal efficiency of whole process,
Complete the calculation on turbine (section I – V)
3276 .
6 0 . 418 , 2
4 . 792 )
boiler (
Q
) Rankine (
W
kJ 6 . 418 , 2 0 . 973 6
. 391 , 3 H )
boiler (
Q
kJ 4 . 792 6
. 11 0
. 804 )
pump (
W )
turbine (
W )
Rankine (
W
kg / kJ 6 . 75 11
. 0
676 . ) 8 pump (
H W H
, 10 . 7 Ex From
) V I tion (sec turbine
for kJ 0 . 804 W
S
S S
S
S S
S
8.2 Internal – Combustion Engines
Characteristics of Steam Power Plant
Steam is an inert medium heat is transferred from a burning fuel
Large heat transfer surfaces
- Absorption of heat by the steam at a high T in the boiler, and rejection of heat from the steam at a relatively low T in the condenser
- Thick walls to withstand high T, P impose a limit on heat absorption.
Complicated structure
Characteristics of Internal-Combustion Engines
Combustion are carried out within engine
- The combustion products serve as the working medium, acting on a piston in a cylinder - High temperatures are internal, and do not involve heat-transfer surfaces
Complex thermodynamic analysis
No working fluid undergoes a cyclic process
The Otto Engine
No working fluid undergoes cyclic process
An imaginary cyclic engine with air as working fluid
- The combustion step is replaced by the addition to the air of an equivalent amount of heat
Equivalent in performance to actual internal-combustion engine
The most common internal-combustion engine
The Otto engine
- Used in automobiles
Otto Engine Cycle
Air / fuel mixture fed into the engine Air / fuel mixture are
compressed by the piston
Combustion of fuel : So rapid so that the volume remains const.
Adiabatic expansion
Valve opened and exhaust gas vented
Piston pushes remaining exhaust
gases
Idealized Otto Cycle
Increasing the compression ratio is to increase the efficiency of engine. (Proof ?)
Using idealized Otto engine
Two adiabatic & two const V steps
The working fluid is air (ideal gas with constant Cp)
Reversible adiabatic compression Sufficient heat is absorbed by the air at
constant volume (P and T increase)
Reversible adiabatic expansion
Cooling at constant volume
Thermodynamic Analysis of Otto Engine
Increasing the compression ratio is to increase the efficiency of engine. (Proof ?)
Using idealized Otto engine
) (
A DV
DA
C T T
Q
) T T
( C
Q
BC
V C
B
D A
C B
D A
V
B C
V D
A V
DA BC DA
DA net
T T
T 1 T
T T
C
T T
C T
T C
Q Q Q
Q W
Otto Engine - Analysis
The Compression ratio, r ≡ V
C/V
D r increases : efficiency increases
The thermal efficiency increases rapidly at low value of r, but more slowly at higher value of r
T TCA T T
DB
1
nRT PV
const PV
1
11
r
D C
V r V
Derive yourself! (Page 304)
Diesel Engine
Difference from Otto Engine
Compression is high, combustion is initiated spontaneously
High compression ratio, high efficiency
Efficiency in Diesel – Example 8.3
The thermal efficiency of Diesel cycle
The compression ratio, r (≡ V
C/V
D)
The expansion ratio, r
e(≡ V
B/V
A)
) T T
( C
Q
DA
P A
D) T T
( C
Q
BC
V C
B
D A
C B
D A
P
B C
V
DA BC DA
BC DA
T T
T T
1 1 T
T C
T T
1 C
Q 1 Q Q
Q Q
RT PV
V / V r
V / V r
V T V
T
V T V
T
A B e
D C
1 C C 1
D D
1 B B 1
A A
r / 1 r / 1
) r / 1 ( ) r / 1 ( 1 1
r / r 1
) r / 1 )(
r / r ( )
r / 1 ( 1 1
e e
e
1 e
1 e
Derive yourself!
(Page 306)
The Gas-Turbine Engine
Otto & Diesel engines
Direct use of the energy of high T and P gases, acting on a piston within a cylinder
However, turbines are more efficient than reciprocating engines
Gas Turbine Engine
Advantage of high T and P for internal combustion engine
Advantage of using turbine rather than reciprocating engine
Gas-Turbine Engine
The gas turbine is driven by high-T gases from a combustion chamber
The entering air is compressed before combustion
The centrifugal compressor operates on the same shaft as the turbine
Part of the work of the turbine serves to drive the compressor
Brayton Cycle
Brayton cycle
The idealization of the gas-turbine engine
The working fluid is taken as air, ideal gas with const Cp
Reversible adiabatic compression Heat QBC is added at
constant P
(replacing combustion) Reversible adiabatic
expansion (Isentropic)
Cooling at constant pressure
Thermodynamic Analysis of Brayton Engine
) T T
( C
Q
BC
P C
B) T T
( C H
H
W
AB
B
A
P B
AB C
A D
BC AB CD
BC net
T T
T 1 T
Q W W
Q W
) T T
( C
Q
DA
P A
D) T T
( C
W
CD
P C
D
/ ) 1 (
A B /
) 1 (
C D C
D
/ ) 1 (
A B A
B
P P P
P T
T
P and P T
T
/ ) 1 (
B A
P
1 P
8.3 Jet Engines, Rocket Engines
Previous power cycles
High T, P gas expands in a turbine (steam power plant or gas turbine) or in the cylinders with reciprocating pistons (Otto or Diesel engine)
The power become available through a rotating shaft!
Turbojet (or jet) engine
A nozzle for expanding the hot gases
The power is available as kinetic energy in the jet of exhaust gases leaving the nozzle
Turbojet engine (or jet engine)
Turbojet engine (or jet engine)
Compression by an axial-flow compressor
Combustion of the fuel with air
The hot gases pass through a turbine
- The expansion provides enough power to drive the compressor - The remainder of the expansion accomplished in the nozzle
- The velocity of exhaust gases increases Provide a force on the engine in the forward direction
For adiabatic and reversible compression and expansion
- The jet engine cycle is identical to the ideal gas turbine cycle (Brayton cycle)
Rocket engine
Rocket engine
Difference from a jet engine The oxidizing agent is carried with the engine (not surrounding air for burning the fuel)
Can operate in a vacuum such as in outer space
The combustion and expansion steps
- Same as an ideal jet engine