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P.O. Box 2134
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Phone: (301) 919-9670
E-Mail: info@engineering-4e.com
http://www.e...
Energy Conversion Analysis Webinar
Objectives
In this webinar, the student gets familiar with the ideal simple and basic p...
This webinar consists of the following three major sections:
• Power Cycles (Carnot, Brayton, Otto and Diesel)
• Power Cyc...
The energy conversion analysis presented in this webinar considers ideal (isentropic) operation when air,
argon, helium an...
Basic Conservation Equations
Continuity Equation
m = ρvA [kg/s]
Momentum Equation
F = (vm + pA)out - in [N]
Energy Equatio...
Ideal Gas State Equation
pv = RT [kJ/kg]
Perfect Gas
cp = constant [kJ/kg*K]
Kappa
χ = cp/cv [/]
Basic Engineering Equatio...
Basic Engineering Equations
Physical Properties
Gas Constant
[kJ/kg*K]
0.2867
0.2801
2.0785
0.2969
Specific Heat
[kJ/kg*K]...
Power Cycles Engineering Equations
Carnot Cycle Efficiency
 = 1 - TR/TA
Otto Cycle Efficiency
 = 1 - 1/ε(χ-1)
Brayton Cy...
Power Cycles Engineering Equations
Otto Cycle
wnet = qh - ql = cv(T3 - T2) - cv(T4 - T1) [kJ/kg]
Wnet = wnetm [kW]
Brayton...
Carnot Cycle Schematic Layout
Compressor
Heat Exchanger
Gas Turbine
1
32
4
Heat Addition
Heat Exchanger
Heat Rejection
Car...
Carnot Cycle T - s Diagram
1
32
4
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Carnot Cycle
Carnot Cycle Efficiency
0
20
40
60
80
500 600 700 800 900 1,000
CarnotCycleEfficiency[%]
Heat Addition Temperature [K]
Com...
Carnot Cycle Efficiency
0
20
40
60
80
278 288 298 308 318 328
CarnotCycleEfficiency[%]
Heat Rejection Temperature [K]
Turb...
Brayton Cycle (Gas Turbine) Schematic Layout -- Open Cycle
Compressor
Combustor
Gas Turbine
1
32
4
Fuel
Brayton Cycle (Gas...
Brayton Cycle Schematic Layout -- Closed Cycle
Compressor
Heat Exchanger
Gas Turbine
1
32
4
Heat Addition
Heat Exchanger
H...
Brayton Cycle (Gas Turbine) T - s Diagram
1
3
2
4
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Brayton Cycle (Gas Turbine)
Brayton Cycle (Gas Turbine) Efficiency
0
20
40
60
80
5 10 15 20 25
Compression Ratio (P2/P1) [/]
BraytonCycle(GasTurbine)E...
Brayton Cycle (Gas Turbine) Specific Power
Output
0
500
1,000
1,500
2,000
2,500
900 1,200 1,500
Gas Turbine Inlet Temperat...
Brayton Cycle (Gas Turbine) Power Output
0
100
200
300
400
50 100 150
Working Fluid Mass Flow Rate [kg/s]
BraytonCycle(Gas...
Brayton Cycle (Gas Turbine)
Oxidant Composition
Fuel Composition
C
[kg/kg]
0.000
H
[kg/kg]
0.000
S
[kg/kg]
0.000
N
[kg/kg]...
Brayton Cycle (Gas Turbine)
Combustion Products Composition on Weight and Mole Basis
CO2
[kg/kg]
0.015
0.036
0.058
H2O
[kg...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O N2 O2
CombustionProducts[kg/kg]
90...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O N2 O2
CombustionProducts[kmol/kmol]
...
Brayton Cycle (Gas Turbine) Specific Fuel
Consumption
0.00
0.01
0.02
0.03
900 1,200 1,500
Gas Turbine Inlet Temperature [K...
Brayton Cycle (Gas Turbine) Stoichiometry
0
4
8
12
900 1,200 1,500
Gas Turbine Inlet Temperature [K]
BraytonCycle(GasTurbi...
Otto Cycle p - V Diagram
1
3
2
4
Pressure--p[atm]
Volume -- V [m^3]
Otto Cycle
Otto Cycle T - s Diagram
1
3
2
4
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Otto Cycle
Otto Cycle Efficiency
0
20
40
60
80
2.5 5 7.5 10 12.5
Compression Ratio (V1/V2) [/]
OttoCycleEfficiency[%]
V1/V2
Working F...
Otto Cycle Power Output
100
200
300
400
1,200 1,500 1,800
Combustion Temperature [K]
OttoCyclePowerOutput[kW]
5 10
Compres...
Otto Cycle
Oxidant Composition
Fuel Composition
C
[kg/kg]
0.860
H
[kg/kg]
0.140
S
[kg/kg]
0.000
N
[kg/kg]
0.000
O
[kg/kg]
...
Otto Cycle
Combustion Products Composition on Weight and Mole Basis
CO2
[kg/kg]
0.053
0.074
0.097
H2O
[kg/kg]
0.021
0.030
...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O N2 O2
CombustionProducts[kg/kg]
1,...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O N2 O2
CombustionProducts[kmol/kmol]
...
Otto Cycle Specific Fuel Consumption
0.00
0.01
0.02
0.03
0.04
1,200 1,500 1,800
Combustion Temperature [K]
OttoCycleSpecif...
Otto Cycle Stoichiometry
0
2
4
6
1,200 1,500 1,800
Combustion Temperature [K]
OttoCycleStoichiometry[/]
Stoichoimetry
Comp...
Diesel Cycle p - V Diagram
1
32
4
Pressure--p[atm]
Volume -- V [m^3]
Diesel Cycle
Diesel Cycle T - s Diagram
1
3
2
4
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Diesel Cycle
Diesel Cycle Efficiency
0
20
40
60
80
7.5 10 12.5 15 17.5
Compression Ratio (V1/V2) [/]
DieselCycleEfficiency[%]
3 4
Worki...
Diesel Cycle Efficiency
20
40
60
80
1,500 1,800 2,100
Combustion Temperature [K]
DieselCycleEfficiency[%]
10 15
Compressio...
Diesel Cycle Cut Off Ratio
0
1
2
3
4
1,500 1,800 2,100
Combustion Temperature [K]
DieselCycleCutOffRatio[/]
10 15
Compress...
Diesel Cycle Power Output
200
300
400
500
600
1,500 1,800 2,100
Combustion Temperature [K]
DieselCyclePowerOutput[kW]
10 1...
Diesel Cycle
Oxidant Composition
Fuel Composition
C
[kg/kg]
0.860
H
[kg/kg]
0.140
S
[kg/kg]
0.000
N
[kg/kg]
0.000
O
[kg/kg...
Diesel Cycle
Combustion Products Composition on Weight and Mole Basis
CO2
[kg/kg]
0.054
0.084
0.115
H2O
[kg/kg]
0.022
0.03...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O N2 O2
CombustionProducts[kg/kg]
1,...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O N2 O2
CombustionProducts[kmol/kmol]
...
Diesel Cycle Specific Fuel Consumption
0.00
0.01
0.02
0.03
0.04
1,500 1,800 2,100
Combustion Temperature [K]
DieselCycleSp...
Diesel Cycle Stoichiometry
0
2
4
6
1,500 1,800 2,100
Combustion Temperature [K]
DieselCycleStoichiometry[/]
Stoichoimetry
...
Power Cycles Conclusions
The Carnot Cycle efficiency increases with an increase in the heat addition temperature when the ...
Isentropic Compression
T2/T1 = (p2/p1)(χ-1)/χ [/]
T2/T1 = (V1/V2)(χ-1) [/]
p2/p1 = (V1/V2)χ [/]
wc = cp(T2 - T1) [kJ/kg]
W...
Combustion is ideal, complete with no heat loss and
fuel reacts with air and oxygen enriched air as the
oxidant at differe...
Isentropic Expansion
T1/T2 = (p1/p2)(χ-1)/χ [/]
T1/T2 = (V2/V1)(χ-1) [/]
p1/p2 = (V2/V1)χ [/]
we = cp(T1 - T2) [kJ/kg]
We ...
Compression Schematic Layout
Working Fluid In
Working Fluid Out
Compressor
1
2
Compression
Compression T - s Diagram
2
1
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Compression
Compression Specific Power Input
0
1
2
3
4
5 10 15
CompressionSpecificPowerInput[MJ/kg]
Air Argon Helium Nitrogen
Compress...
Compression Power Input
0
100
200
300
400
500
50 100 150
Working Fluid Mass Flow Rate [kg/s]
CompressionPowerInput[MW]
Air...
Combustion Schematic Layout
Fuel
Oxidant
Combustion Products
Combustion
Enthalpy vs Temperature
-20,000
-10,000
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
80,000
90,000
500 800 1,100 1,4...
Enthalpy - Temperature h - T Diagram
Enthalpy--h[kJ/kg]
Temperature -- T [K]
Reactants
ProductsHHV
TflameTreference
Combus...
Combustion
Oxidant Composition
Fuel Composition
C
[kg/kg]
1.000
0.000
0.000
0.780
0.860
-
H
[kg/kg]
0.000
1.000
0.000
0.05...
Combustion
Stoichiometric Combustion
Combustion Products Composition on Weight and Mole Basis
CO2
[kg/kg]
0.295
0.000
0.00...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products Flame Temperature
1,900
2,000
2,100
2,200
2,300
2,400
2,500
2,600
Carbon Hydrogen Sulfur Coal Oil Gas
...
Combustion Stoichiometric Oxidant to Fuel Ratio
0
5
10
15
20
25
30
35
40
Carbon Hydrogen Sulfur Coal Oil Gas
Stoichiometri...
Higher Heating Value (HHV)
0
10,000
20,000
30,000
40,000
50,000
60,000
70,000
Carbon Hydrogen Sulfur Coal Oil Gas
HHV[Btu/...
Combustion
Oxidant Composition
Fuel Composition
C
[kg/kg]
1.000
0.000
0.000
0.780
0.860
-
H
[kg/kg]
0.000
1.000
0.000
0.05...
Combustion
Stoichiometric Combustion
Flame Temperature
Hydrogen
[K]
2,525
2,583
2,640
2,689
2,757
2,818
2,879
2,942
Sulfur...
Combustion Products Flame Temperature
0
1,000
2,000
3,000
298 400 500 600 700 800 900 1,000
FlameTemperature[K]
Carbon Hyd...
Combustion
Oxidant Composition
Fuel Composition
C
[kg/kg]
1.000
0.000
0.000
0.780
0.860
-
H
[kg/kg]
0.000
1.000
0.000
0.05...
Combustion
Combustion Products Composition on Weight and Mole Basis
Combustion Products Flame Temperature and Oxidant to F...
Combustion
Combustion Products Composition on Weight and Mole Basis
Flame Temperature
[K]
2,525
1,645
1,269
1,059
924
830
...
Combustion
Combustion Products Composition on Weight and Mole Basis
Flame Temperature
[K]
1,972
1,229
949
799
705
641
Oxid...
Combustion
Combustion Products Composition on Weight and Mole Basis
Fuel: Coal
CO2
[kg/kg]
0.249
0.130
0.088
0.067
0.053
0...
Combustion
Combustion Products Composition on Weight and Mole Basis
Flame Temperature
[K]
2,484
1,555
1,187
989
863
776
Ox...
Combustion
Combustion Products Composition on Weight and Mole Basis
Flame Temperature
[K]
2,327
1,480
1,137
951
832
750
Ox...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products Flame Temperature
600
1,100
1,600
2,100
2,600
1 2 3 4 5 6
FlameTemperature[K]
Carbon Hydrogen Sulfur C...
Combustion Oxidant to Fuel Ratio
0
40
80
120
160
200
240
1 2 3 4 5 6
OxidanttoFuelRatio[/]
Carbon Hydrogen Sulfur Coal Oil...
Combustion
Oxidant Composition
N
[kmol/kmol]
0.790
0.580
0.370
O
[kmol/kmol]
0.210
0.420
0.630
N
[kg/kg]
0.767
0.550
0.340...
Combustion
Stoichiometric Combustion
Combustion Products Composition on Weight and Mole Basis
Combustion Products Flame Te...
Combustion
Fuel: Hydrogen
CO2
[kg/kg]
0.000
0.000
0.000
H2O
[kg/kg]
0.255
0.482
0.686
SO2
[kg/kg]
0.000
0.000
0.000
N2
[kg...
Combustion
Fuel: Sulfur
CO2
[kg/kg]
0.000
0.000
0.000
H2O
[kg/kg]
0.000
0.000
0.000
SO2
[kg/kg]
0.378
0.623
0.796
N2
[kg/k...
Combustion
Fuel: Coal
CO2
[kg/kg]
0.249
0.448
0.610
H2O
[kg/kg]
0.041
0.074
0.100
SO2
[kg/kg]
0.005
0.009
0.013
N2
[kg/kg]...
Combustion
Fuel: Oil
CO2
[kg/kg]
0.202
0.369
0.511
H2O
[kg/kg]
0.081
0.148
0.204
SO2
[kg/kg]
0.000
0.000
0.000
N2
[kg/kg]
...
Combustion
Fuel: Gas
CO2
[kg/kg]
0.151
0.280
0.390
H2O
[kg/kg]
0.124
0.229
0.319
SO2
[kg/kg]
0.000
0.000
0.000
N2
[kg/kg]
...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products -- Weight Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kg/kg...
Combustion Products -- Mole Basis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CO2 H2O SO2 N2 O2
CombustionProducts[kmol/km...
Combustion Products Flame Temperature
0
1,000
2,000
3,000
4,000
5,000
O2 - 0.21 O2 - 0.42 O2 - 0.63
FlameTemperature[K]
Ca...
Combustion Stoichiometric Oxidant to Fuel Ratio
0
10
20
30
40
O2 - 0.21 O2 - 0.42 O2 - 0.63
StoichiometricOxidanttoFuelRat...
Expansion Schematic Layout
Working Fluid In
Working Fluid Out
Turbine
1
2
Expansion
Expansion T - s Diagram
1
2
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Expansion
Expansion Specific Power Output
0
2
4
6
5 10 15
ExpansionSpecificPowerOutput[MJ/kg]
Air Argon Helium Nitrogen
Turbine Inle...
Expansion Power Output
0
200
400
600
800
50 100 150
Working Fluid Mass Flow Rate [kg/s]
ExpansionPowerOutput[MW]
Air Argon...
Power Cycle Components/Processes
Conclusions
The compression specific power input increases with an increase in the compre...
The flame temperature decreases as the stoichiometry values increase.
For stoichiometric combustion conditions, the amount...
Sonic Velocity
vs = (χ RT)1/2 [m/s]
Mach Number
M = v/vs [/]
Compressible Flow Engineering Equations
Isentropic Flow
Tt/T = (1 + M2(χ - 1)/2) [/]
pt/p = (1 + M2(χ - 1)/2)χ/(χ-1) [/]
ht = (h + v2/2) [kJ/kg]
Tt = (T + v2/(2cp...
Nozzle Schematic Layout
Working Fluid In Working Fluid Out
Nozzle
1 2
Nozzle
Nozzle T - s Diagram
1
2
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Nozzle
Nozzle Performance
1.00
1.10
1.20
1.30
1.40
1.50
0.39 0.67 1.00
Mach Number [/]
Tstagnation/Tstatic[/]
Air Argon Helium Ni...
Nozzle Performance
1.00
1.30
1.60
1.90
2.20
2.50
0.39 0.67 1.00
Mach Number [/]
Pstagnation/Pstatic[/]
Air Argon Helium Ni...
Diffuser Schematic Layout
Working Fluid In Working Fluid Out
Diffuser
1 2
Diffuser
Diffuser T - s Diagram
2
1
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Diffuser
Diffuser Performance
1.00
1.10
1.20
1.30
1.40
1.50
0.29 0.58 0.95
Mach Number [/]
Tstagnation/Tstatic[/]
Air Argon Helium ...
Diffuser Performance
1.00
1.30
1.60
1.90
2.20
2.50
0.29 0.58 0.95
Mach Number [/]
Pstagnation/Pstatic[/]
Air Argon Helium ...
Thrust Schematic Layout
Working Fluid Out
Nozzle
21
Working Fluid at Still
Thrust
Thrust T - s Diagram
1
2
Temperature--T[K]
Entropy -- s [kJ/kg*K]
Thrust
Thrust
500
1,000
1,500
2,000
2,500
3,000
900 1,200 1,500
Nozzle Inlet Stagnation Temperature [K]
Thrust[N]
Air Argon Heliu...
Nozzle -- Thrust Performance
1.14
1.17
1.20
1.23
1.26
900 1,200 1,500
Nozzle Inlet Stagnation Temperature [K]
Tstagnation/...
Nozzle -- Thrust Performance
1.58
1.62
1.66
1.70
1.74
900 1,200 1,500
Nozzle Inlet Stagnation Temperature [K]
Pstagnation/...
Compressible Flow Conclusions
Nozzle stagnation over static temperature and pressure ratio values increase with an
increas...
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Energy Conversion Analysis Webinar -- Long Version

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Engineering webinar material dealing with power cycles (Carnot, Brayton, Otto and Diesel), power cycle components/processes (compression, combustion and expansion) and compressible flow (nozzle, diffuser and thrust) when air, argon, helium and nitrogen are considered as the working fluid.

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Energy Conversion Analysis Webinar -- Long Version

  1. 1. Engineering Software P.O. Box 2134 Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com http://www.engineering-4e.com Copyright © 1996
  2. 2. Energy Conversion Analysis Webinar Objectives In this webinar, the student gets familiar with the ideal simple and basic power cycles, power cycle components/processes and compressible flow and their T - s, p - V and h - T diagrams, operation and major performance trends when air, argon, helium and nitrogen are considered as the working fluid. Performance Objectives: Introduce basic energy conversion engineering assumptions and equations Know basic elements of Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle, compression, combustion and expansion processes and compressible flow (nozzle, diffuser and thrust) and their T - s, p - V and h - T diagrams Be familiar with Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle, compression, combustion, expansion and compressible flow (nozzle, diffuser and thrust) operation Understand general Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle, compression, combustion, expansion and compressible flow (nozzle, diffuser and thrust) performance trends
  3. 3. This webinar consists of the following three major sections: • Power Cycles (Carnot, Brayton, Otto and Diesel) • Power Cycle Components/Processes (compression, combustion and expansion) • Compressible Flow (nozzle, diffuser and thrust) In this webinar, first overall engineering assumptions and basic engineering equations are provided. Furthermore, for each major section, basic engineering equations, section material and conclusions are provided. Energy Conversion Analysis Webinar
  4. 4. The energy conversion analysis presented in this webinar considers ideal (isentropic) operation when air, argon, helium and nitrogen are considered as the working fluid. Furthermore, the following assumptions are valid: Power Cycles Single species consideration -- fuel mass flow rate is ignored and its impact on the properties of the working fluid Basic equations hold (continuity, momentum and energy equations) Specific heat is constant Power Cycle Components/Processes Single species consideration Basic equations hold (continuity, momentum and energy equations) Specific heat is constant Compressible Flow Single species consideration Basic equations hold (continuity, momentum and energy equations) Specific heat is constant Thermodynamic and Transport Properties Single species consideration Ideal gas approach is used (pv=RT) Specific heat is not constant Coefficients describing thermodynamic and transport properties were obtained from the NASA Glenn Research Center at Lewis Field in Cleveland, OH -- such coefficients conform with the standard reference temperature of 298.15 K (77 F) and the JANAF Tables Engineering Assumptions
  5. 5. Basic Conservation Equations Continuity Equation m = ρvA [kg/s] Momentum Equation F = (vm + pA)out - in [N] Energy Equation Q - W = ((h + v2/2 + gh)m)out - in [kW] Basic Engineering Equations
  6. 6. Ideal Gas State Equation pv = RT [kJ/kg] Perfect Gas cp = constant [kJ/kg*K] Kappa χ = cp/cv [/] Basic Engineering Equations
  7. 7. Basic Engineering Equations Physical Properties Gas Constant [kJ/kg*K] 0.2867 0.2801 2.0785 0.2969 Specific Heat [kJ/kg*K] 1.004 0.519 5.200 1.038 χ [/] 1.4 1.67 1.66 1.4 Working Fluid Air Argon Helium Nitrogen
  8. 8. Power Cycles Engineering Equations Carnot Cycle Efficiency  = 1 - TR/TA Otto Cycle Efficiency  = 1 - 1/ε(χ-1) Brayton Cycle Efficiency  = 1 - 1/rp (χ-1)/χ Diesel Cycle Efficiency  = 1 - (φχ-1)/ (χε(χ-1)(φ-1)) Cycle Efficiency  = Wnet/Q [/] Heat Rate HR = (1/)3,412 [Btu/kWh] rp = p2/p1 [/]; ε = V1/V2 [/]; φ = V3/V2 [/]
  9. 9. Power Cycles Engineering Equations Otto Cycle wnet = qh - ql = cv(T3 - T2) - cv(T4 - T1) [kJ/kg] Wnet = wnetm [kW] Brayton Cycle wnet = qh - ql = cp(T3 - T2) - cp(T4 - T1) [kJ/kg] Wnet = wnetm [kW] Diesel Cycle wnet = qh - ql = cp(T3 - T2) - cv(T4 - T1) [kJ/kg] Wnet = wnetm [kW]
  10. 10. Carnot Cycle Schematic Layout Compressor Heat Exchanger Gas Turbine 1 32 4 Heat Addition Heat Exchanger Heat Rejection Carnot Cycle
  11. 11. Carnot Cycle T - s Diagram 1 32 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Carnot Cycle
  12. 12. Carnot Cycle Efficiency 0 20 40 60 80 500 600 700 800 900 1,000 CarnotCycleEfficiency[%] Heat Addition Temperature [K] Compressor Inlet Temperature: 298 [K] Carnot Cycle
  13. 13. Carnot Cycle Efficiency 0 20 40 60 80 278 288 298 308 318 328 CarnotCycleEfficiency[%] Heat Rejection Temperature [K] Turbine Inlet Temperature: 800 [K] Carnot Cycle
  14. 14. Brayton Cycle (Gas Turbine) Schematic Layout -- Open Cycle Compressor Combustor Gas Turbine 1 32 4 Fuel Brayton Cycle (Gas Turbine) Heat Addition Working Fluid In Working Fluid Out
  15. 15. Brayton Cycle Schematic Layout -- Closed Cycle Compressor Heat Exchanger Gas Turbine 1 32 4 Heat Addition Heat Exchanger Heat Rejection Brayton Cycle (Gas Turbine)
  16. 16. Brayton Cycle (Gas Turbine) T - s Diagram 1 3 2 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Brayton Cycle (Gas Turbine)
  17. 17. Brayton Cycle (Gas Turbine) Efficiency 0 20 40 60 80 5 10 15 20 25 Compression Ratio (P2/P1) [/] BraytonCycle(GasTurbine)Efficiency[%] Air Argon Helium Nitrogen Brayton Cycle (Gas Turbine)
  18. 18. Brayton Cycle (Gas Turbine) Specific Power Output 0 500 1,000 1,500 2,000 2,500 900 1,200 1,500 Gas Turbine Inlet Temperature [K] BraytonCycle(GasTurbine)SpecificPower Output[kJ/kg] Air Argon Helium Nitrogen Compression Ratio (P2/P1) = 15 [/] Brayton Cycle (Gas Turbine) Compressor Inlet Temperature: 298 [K]
  19. 19. Brayton Cycle (Gas Turbine) Power Output 0 100 200 300 400 50 100 150 Working Fluid Mass Flow Rate [kg/s] BraytonCycle(GasTurbine)PowerOutput[MW] Air Argon Helium Nitrogen Compression Ratio (P2/P1) = 15 [/] Compressor Inlet Temperature: 298 [K] -- Gas Turbine Inlet Temperature: 1,500 [K] Brayton Cycle (Gas Turbine)
  20. 20. Brayton Cycle (Gas Turbine) Oxidant Composition Fuel Composition C [kg/kg] 0.000 H [kg/kg] 0.000 S [kg/kg] 0.000 N [kg/kg] 0.000 O [kg/kg] 0.000 H2O [kg/kg] 0.000 CH4 [kg/kg] 1.000 Fuel Gas N [kmol/kmol] 0.790 O [kmol/kmol] 0.210 N [kg/kg] 0.767 O [kg/kg] 0.233 Oxidant Air
  21. 21. Brayton Cycle (Gas Turbine) Combustion Products Composition on Weight and Mole Basis CO2 [kg/kg] 0.015 0.036 0.058 H2O [kg/kg] 0.012 0.029 0.047 N2 [kg/kg] 0.762 0.756 0.750 O2 [kg/kg] 0.208 0.177 0.143 CO2 [kmol/kmol] 0.010 0.023 0.037 Stoichiometry [/] 10.05 4.35 2.68 N2 [kmol/kmol] 0.781 0.771 0.759 H2O [kmol/kmol] 0.020 0.047 0.075 O2 [kmol/kmol] 0.187 0.158 0.127 Combustion Products Flame Temperature and Oxidant to Fuel Ratio Flame Temperature [K] 900 1,200 1,500 Oxidant to Fuel Ratio [/] 172.574 74.675 46.007 Stoichiometry [/] 10.05 4.35 2.68
  22. 22. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O N2 O2 CombustionProducts[kg/kg] 900 1,200 1,500 Brayton Cycle (Gas Turbine) Fuel Temperature: 298 [K] -- Oxidant Temperature: 646 [K] Gas Turbine Inlet Temperature [K]
  23. 23. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O N2 O2 CombustionProducts[kmol/kmol] 900 1,200 1,500 Brayton Cycle (Gas Turbine) Fuel Temperature: 298 [K] -- Oxidant Temperature: 646 [K] Gas Turbine Inlet Temperature [K]
  24. 24. Brayton Cycle (Gas Turbine) Specific Fuel Consumption 0.00 0.01 0.02 0.03 900 1,200 1,500 Gas Turbine Inlet Temperature [K] BraytonCycle(GasTurbine)SpecificFuel Consumption[kg/kg] HHV Combustion Compression Ratio (P2/P1) = 15 [/] Brayton Cycle (Gas Turbine) Compressor Inlet Temperature: 298 [K]
  25. 25. Brayton Cycle (Gas Turbine) Stoichiometry 0 4 8 12 900 1,200 1,500 Gas Turbine Inlet Temperature [K] BraytonCycle(GasTurbine)Stoichiometry[/] Stoichoimetry Compression Ratio (P2/P1) = 15 [/] Brayton Cycle (Gas Turbine) Compressor Inlet Temperature: 298 [K]
  26. 26. Otto Cycle p - V Diagram 1 3 2 4 Pressure--p[atm] Volume -- V [m^3] Otto Cycle
  27. 27. Otto Cycle T - s Diagram 1 3 2 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Otto Cycle
  28. 28. Otto Cycle Efficiency 0 20 40 60 80 2.5 5 7.5 10 12.5 Compression Ratio (V1/V2) [/] OttoCycleEfficiency[%] V1/V2 Working Fluid: Air Otto Cycle
  29. 29. Otto Cycle Power Output 100 200 300 400 1,200 1,500 1,800 Combustion Temperature [K] OttoCyclePowerOutput[kW] 5 10 Compression Ratio (V1/V2) [/] Working Fluid: Air Ambient Temperature: 298 [K] -- Number of Revolutions: 60 [1/s] For Given Geometry of the Four Cylinder and Four Stroke Otto Engine Otto Cycle
  30. 30. Otto Cycle Oxidant Composition Fuel Composition C [kg/kg] 0.860 H [kg/kg] 0.140 S [kg/kg] 0.000 N [kg/kg] 0.000 O [kg/kg] 0.000 H2O [kg/kg] 0.000 CH4 [kg/kg] 0.000 Fuel Gasoline N [kmol/kmol] 0.790 O [kmol/kmol] 0.210 N [kg/kg] 0.767 O [kg/kg] 0.233 Oxidant Air
  31. 31. Otto Cycle Combustion Products Composition on Weight and Mole Basis CO2 [kg/kg] 0.053 0.074 0.097 H2O [kg/kg] 0.021 0.030 0.039 N2 [kg/kg] 0.754 0.749 0.743 O2 [kg/kg] 0.172 0.147 0.122 CO2 [kmol/kmol] 0.035 0.049 0.063 Stoichiometry [/] 4.01 2.84 2.16 N2 [kmol/kmol] 0.777 0.771 0.766 Combustion Products Flame Temperature and Oxidant to Fuel Ratio H2O [kmol/kmol] 0.034 0.047 0.062 O2 [kmol/kmol] 0.155 0.133 0.109 Flame Temperature [K] 1,200 1,500 1,800 Oxidant to Fuel Ratio [/] 58.742 41.603 31.642 Stoichiometry [/] 4.01 2.84 2.16
  32. 32. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O N2 O2 CombustionProducts[kg/kg] 1,200 1,500 1,800 Otto Cycle Fuel Temperature: 298 [K] -- Oxidant Temperature: 748.5 [K] Combustion Temperature [K]
  33. 33. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O N2 O2 CombustionProducts[kmol/kmol] 1,200 1,500 1,800 Otto Cycle Fuel Temperature: 298 [K] -- Oxidant Temperature: 748.5 [K] Combustion Temperature [K]
  34. 34. Otto Cycle Specific Fuel Consumption 0.00 0.01 0.02 0.03 0.04 1,200 1,500 1,800 Combustion Temperature [K] OttoCycleSpecificFuelConsumption[kg/kg] HHV Combustion Compression Ratio (V1/V2) = 10 [/] Otto Cycle Ambient Temperature: 298 [K]
  35. 35. Otto Cycle Stoichiometry 0 2 4 6 1,200 1,500 1,800 Combustion Temperature [K] OttoCycleStoichiometry[/] Stoichoimetry Compression Ratio (V1/V2) = 10 [/] Otto Cycle Ambient Temperature: 298 [K]
  36. 36. Diesel Cycle p - V Diagram 1 32 4 Pressure--p[atm] Volume -- V [m^3] Diesel Cycle
  37. 37. Diesel Cycle T - s Diagram 1 3 2 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Diesel Cycle
  38. 38. Diesel Cycle Efficiency 0 20 40 60 80 7.5 10 12.5 15 17.5 Compression Ratio (V1/V2) [/] DieselCycleEfficiency[%] 3 4 Working Fluid: Air Cut Off Ratio V3/V2 [/] Diesel Cycle
  39. 39. Diesel Cycle Efficiency 20 40 60 80 1,500 1,800 2,100 Combustion Temperature [K] DieselCycleEfficiency[%] 10 15 Compression Ratio (V1/V2) [/] Diesel Cycle Ambient Temperature: 298 [K]
  40. 40. Diesel Cycle Cut Off Ratio 0 1 2 3 4 1,500 1,800 2,100 Combustion Temperature [K] DieselCycleCutOffRatio[/] 10 15 Compression Ratio (V1/V2) [/] Diesel Cycle Ambient Temperature: 298 [K]
  41. 41. Diesel Cycle Power Output 200 300 400 500 600 1,500 1,800 2,100 Combustion Temperature [K] DieselCyclePowerOutput[kW] 10 15 Working Fluid: Air Diesel Cycle Ambient Temperature: 298 [K] -- Number of Revolutions: 60 [1/s] For Given Geometry of the Four Cylinder and Four Stroke Diesel Engine Compression Ratio (V1/V2) [/]
  42. 42. Diesel Cycle Oxidant Composition Fuel Composition C [kg/kg] 0.860 H [kg/kg] 0.140 S [kg/kg] 0.000 N [kg/kg] 0.000 O [kg/kg] 0.000 H2O [kg/kg] 0.000 CH4 [kg/kg] 0.000 Fuel Diesel N [kmol/kmol] 0.790 O [kmol/kmol] 0.210 N [kg/kg] 0.767 O [kg/kg] 0.233 Oxidant Air
  43. 43. Diesel Cycle Combustion Products Composition on Weight and Mole Basis CO2 [kg/kg] 0.054 0.084 0.115 H2O [kg/kg] 0.022 0.033 0.046 N2 [kg/kg] 0.754 0.747 0.739 O2 [kg/kg] 0.170 0.136 0.100 CO2 [kmol/kmol] 0.036 0.055 0.075 Stoichiometry [/] 3.90 2.50 1.81 N2 [kmol/kmol] 0.776 0.769 0.761 H2O [kmol/kmol] 0.035 0.054 0.073 O2 [kmol/kmol] 0.153 0.123 0.091 Combustion Products Flame Temperature and Oxidant to Fuel Ratio Flame Temperature [K] 1,500 1,800 2,100 Oxidant to Fuel Ratio [/] 57.131 36.622 26.514 Stoichiometry [/] 3.90 2.50 1.81
  44. 44. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O N2 O2 CombustionProducts[kg/kg] 1,500 1,800 2,100 Diesel Cycle Fuel Temperature: 298 [K] -- Oxidant Temperature: 880.3 [K] Combustion Temperature [K]
  45. 45. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O N2 O2 CombustionProducts[kmol/kmol] 1,500 1,800 2,100 Diesel Cycle Fuel Temperature: 298 [K] -- Oxidant Temperature: 880.3 [K] Combustion Temperature [K]
  46. 46. Diesel Cycle Specific Fuel Consumption 0.00 0.01 0.02 0.03 0.04 1,500 1,800 2,100 Combustion Temperature [K] DieselCycleSpecificFuelConsumption[kg/kg] HHV Combustion Compression Ratio (V1/V2) = 15 [/] Diesel Cycle Ambient Temperature: 298 [K]
  47. 47. Diesel Cycle Stoichiometry 0 2 4 6 1,500 1,800 2,100 Combustion Temperature [K] DieselCycleStoichiometry[/] Stoichoimetry Compression Ratio (V1/V2) = 15 [/] Diesel Cycle Ambient Temperature: 298 [K] Cut Off Ratio (V3/V2) = 1.70, 2.05 and 2.39 [/]
  48. 48. Power Cycles Conclusions The Carnot Cycle efficiency increases with an increase in the heat addition temperature when the heat rejection temperature does not change at all. Furthermore, the Carnot Cycle efficiency decreases with an increase in the heat rejection temperature when the heat addition temperature does not change at all. The Carnot Cycle efficiency is not dependent on the working fluid properties. The Brayton Cycle efficiency depends on the compression ratio and working fluid properties. The efficiency increases with an increase in the compression ratio values. Also, the efficiency increases with the higher value for ϰ, which is a ratio of gas specific heat values (cp/cv). The Brayton Cycle specific power output increases with an increase in the gas turbine inlet temperature for a fixed compression ratio. Also, the Brayton Cycle specific power output and power output increase for the working fluid having higher specific heat values. The Brayton Cycle power output increases with an increase in the working fluid mass flow rate for the fixed gas turbine inlet temperature and compression ratio values. The Otto Cycle efficiency increases with an increase in the compression ratio values. Also, the Otto Cycle power output increases with an increase in the combustion temperature. The Otto Cycle power output is greater for the higher compression ratio values for the given combustion temperature values and geometry of the four cylinder and four stroke Otto engine. The Diesel Cycle efficiency increases with an increase in the compression ratio and with a decrease in the cut off ratio values. Also, the Diesel Cycle power output increases with an increase in the compression ratio values for the given combustion temperature values and geometry of the four cylinder and four stroke Diesel engine. For Brayton Cycle, Otto Cycle and Diesel Cycle, specific fuel consumption is greater for the ideal and complete combustion calculations than for the calculations based upon fuel higher heating value.
  49. 49. Isentropic Compression T2/T1 = (p2/p1)(χ-1)/χ [/] T2/T1 = (V1/V2)(χ-1) [/] p2/p1 = (V1/V2)χ [/] wc = cp(T2 - T1) [kJ/kg] Wc = cp(T2 - T1)m [kW] Power Cycle Components/Processes Engineering Equations
  50. 50. Combustion is ideal, complete with no heat loss and fuel reacts with air and oxygen enriched air as the oxidant at different stoichiometry values (stoichiometry => 1) and oxidant inlet temperature values. Also, Flame Temperature [K] hreactants = hproducts [kJ/kg] Higher Heating Value (HHV) [Btu/lbm] HHV = hreactants - hproducts [kJ/kg] Power Cycle Components/Processes Engineering Equations
  51. 51. Isentropic Expansion T1/T2 = (p1/p2)(χ-1)/χ [/] T1/T2 = (V2/V1)(χ-1) [/] p1/p2 = (V2/V1)χ [/] we = cp(T1 - T2) [kJ/kg] We = cp(T1 - T2)m [kW] Power Cycle Components/Processes Engineering Equations
  52. 52. Compression Schematic Layout Working Fluid In Working Fluid Out Compressor 1 2 Compression
  53. 53. Compression T - s Diagram 2 1 Temperature--T[K] Entropy -- s [kJ/kg*K] Compression
  54. 54. Compression Specific Power Input 0 1 2 3 4 5 10 15 CompressionSpecificPowerInput[MJ/kg] Air Argon Helium Nitrogen Compressor Inlet Temperature: 298 [K] Compression Compression Ratio (P2/P1) [/]
  55. 55. Compression Power Input 0 100 200 300 400 500 50 100 150 Working Fluid Mass Flow Rate [kg/s] CompressionPowerInput[MW] Air Argon Helium Nitrogen Compression Ratio (P2/P1) = 15 [/] Compression Compressor Inlet Temperature: 298 [K]
  56. 56. Combustion Schematic Layout Fuel Oxidant Combustion Products Combustion
  57. 57. Enthalpy vs Temperature -20,000 -10,000 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 500 800 1,100 1,400 1,700 2,000 2,300 2,600 2,900 3,200 3,500 3,800 4,100 4,400 4,700 5,000 Temperature [K] Enthalpy[kJ/kg] O2 N2 C(S) S(S) H2 CO2 SO2 H2O H2O(L) CH4 Combustion
  58. 58. Enthalpy - Temperature h - T Diagram Enthalpy--h[kJ/kg] Temperature -- T [K] Reactants ProductsHHV TflameTreference Combustion
  59. 59. Combustion Oxidant Composition Fuel Composition C [kg/kg] 1.000 0.000 0.000 0.780 0.860 - H [kg/kg] 0.000 1.000 0.000 0.050 0.140 - S [kg/kg] 0.000 0.000 1.000 0.030 0.000 - N [kg/kg] 0.000 0.000 0.000 0.040 0.000 - O [kg/kg] 0.000 0.000 0.000 0.080 0.000 - H2O [kg/kg] 0.000 0.000 0.000 0.020 0.000 - CH4 [kg/kg] - - - - - 1.000 Fuel Carbon Hydrogen Sulfur Coal Oil Gas N [kmol/kmol] 0.790 O [kmol/kmol] 0.210 N [kg/kg] 0.767 O [kg/kg] 0.233 Oxidant Air
  60. 60. Combustion Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis CO2 [kg/kg] 0.295 0.000 0.000 0.249 0.202 0.151 H2O [kg/kg] 0.000 0.255 0.000 0.041 0.080 0.124 SO2 [kg/kg] 0.000 0.000 0.378 0.005 0.000 0.000 N2 [kg/kg] 0.705 0.745 0.622 0.705 0.718 0.725 O2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 CO2 [kmol/kmol] 0.210 0.000 0.000 0.170 0.132 0.095 Fuel Carbon Hydrogen Sulfur Coal Oil Gas SO2 [kmol/kmol] 0.000 0.000 0.210 0.002 0.000 0.000 N2 [kmol/kmol] 0.790 0.653 0.790 0.759 0.739 0.715 Combustion Products Flame Temperature, Stoichiometric Oxidant to Fuel Ratio and HHV Flame Temperature [K] 2,460 2,525 1,972 2,484 2,484 2,327 Stoichiometric Oxidant to Fuel Ratio [/] 11.444 34.333 4.292 10.487 14.649 17.167 HHV [Btu/lbm] 14,094 60,997 3,982 14,162 20,660 21,563 Fuel Carbon Hydrogen Sulfur Coal Oil Gas H2O [kmol/kmol] 0.000 0.347 0.000 0.068 0.129 0.190 O2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000
  61. 61. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel and Oxidant Inlet Temperature: 298 [K]
  62. 62. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel and Oxidant Inlet Temperature: 298 [K]
  63. 63. Combustion Products Flame Temperature 1,900 2,000 2,100 2,200 2,300 2,400 2,500 2,600 Carbon Hydrogen Sulfur Coal Oil Gas FlameTemperature[K] Flame Temperature Combustion Fuel and Oxidant Inlet Temperature: 298 [K]
  64. 64. Combustion Stoichiometric Oxidant to Fuel Ratio 0 5 10 15 20 25 30 35 40 Carbon Hydrogen Sulfur Coal Oil Gas StoichiometricOxidanttoFuelRatio[/] Stoichiometric Oxidant to Fuel Ratio Combustion Fuel and Oxidant Inlet Temperature: 298 [K]
  65. 65. Higher Heating Value (HHV) 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 Carbon Hydrogen Sulfur Coal Oil Gas HHV[Btu/lbm] HHV Combustion Fuel and Oxidant Inlet Temperature: 298 [K]
  66. 66. Combustion Oxidant Composition Fuel Composition C [kg/kg] 1.000 0.000 0.000 0.780 0.860 - H [kg/kg] 0.000 1.000 0.000 0.050 0.140 - S [kg/kg] 0.000 0.000 1.000 0.030 0.000 - N [kg/kg] 0.000 0.000 0.000 0.040 0.000 - O [kg/kg] 0.000 0.000 0.000 0.080 0.000 - H2O [kg/kg] 0.000 0.000 0.000 0.020 0.000 - CH4 [kg/kg] - - - - - 1.000 Fuel Carbon Hydrogen Sulfur Coal Oil Gas N [kmol/kmol] 0.790 O [kmol/kmol] 0.210 N [kg/kg] 0.767 O [kg/kg] 0.233 Oxidant Air
  67. 67. Combustion Stoichiometric Combustion Flame Temperature Hydrogen [K] 2,525 2,583 2,640 2,689 2,757 2,818 2,879 2,942 Sulfur [K] 1,972 2,045 2,118 2,191 2,267 2,343 2,421 2,501 Coal [K] 2,484 2,551 2,618 2,686 2,756 2,827 2,899 2,972 Oil [K] 2,484 2,551 2,616 2,683 2,751 2,820 2,891 2,963 Preheat Temperature [K] 298 400 500 600 700 800 900 1,000 Combustion Products Stoichiometric Oxidant to Fuel Ratio and HHV Stoichiometric Oxidant to Fuel Ratio [/] 11.444 34.333 4.292 10.487 14.649 17.167 HHV [Btu/lbm] 14,094 60,997 3,982 14,162 20,660 21,563 Fuel Carbon Hydrogen Sulfur Coal Oil Gas Gas [K] 2,327 2,391 2,455 2,520 2,586 2,653 2,721 2,791 Carbon [K] 2,460 2,531 2,602 2,674 2,747 2,822 2,898 2,976
  68. 68. Combustion Products Flame Temperature 0 1,000 2,000 3,000 298 400 500 600 700 800 900 1,000 FlameTemperature[K] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel Inlet Temperature: 298 [K] Oxidant Preheat Temperature for Stoichiometric Combustion Conditions
  69. 69. Combustion Oxidant Composition Fuel Composition C [kg/kg] 1.000 0.000 0.000 0.780 0.860 - H [kg/kg] 0.000 1.000 0.000 0.050 0.140 - S [kg/kg] 0.000 0.000 1.000 0.030 0.000 - N [kg/kg] 0.000 0.000 0.000 0.040 0.000 - O [kg/kg] 0.000 0.000 0.000 0.080 0.000 - H2O [kg/kg] 0.000 0.000 0.000 0.020 0.000 - CH4 [kg/kg] - - - - - 1.000 Fuel Carbon Hydrogen Sulfur Coal Oil Gas N [kmol/kmol] 0.790 O [kmol/kmol] 0.210 N [kg/kg] 0.767 O [kg/kg] 0.233 Oxidant Air
  70. 70. Combustion Combustion Products Composition on Weight and Mole Basis Combustion Products Flame Temperature and Oxidant to Fuel Ratio Flame Temperature [K] 2,460 1,506 1,145 952 831 748 Oxidant to Fuel Ratio [/] 11.444 22.889 34.333 45.778 57.222 68.667 Stoichiometry [/] 1 2 3 4 5 6 Fuel: Carbon CO2 [kg/kg] 0.295 0.153 0.104 0.083 0.063 0.053 H2O [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 SO2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kg/kg] 0.705 0.735 0.745 0.751 0.754 0.756 O2 [kg/kg] 0.000 0.112 0.151 0.171 0.183 0.191 CO2 [kmol/kmol] 0.210 0.105 0.070 0.053 0.042 0.035 Stoichiometry [/] 1 2 3 4 5 6 SO2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kmol/kmol] 0.790 0.790 0.790 0.790 0.790 0.790 H2O [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 O2 [kmol/kmol] 0.000 0.105 0.140 0.157 0.168 0.175
  71. 71. Combustion Combustion Products Composition on Weight and Mole Basis Flame Temperature [K] 2,525 1,645 1,269 1,059 924 830 Oxidant to Fuel Ratio [/] 34.333 68.667 103.000 137.333 171.667 206.000 Stoichiometry [/] 1 2 3 4 5 6 Fuel: Hydrogen CO2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 H2O [kg/kg] 0.255 0.129 0.087 0.065 0.052 0.043 SO2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kg/kg] 0.745 0.756 0.760 0.761 0.763 0.763 O2 [kg/kg] 0.000 0.115 0.154 0.173 0.185 0.193 CO2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 Stoichiometry [/] 1 2 3 4 5 6 SO2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kmol/kmol] 0.653 0.715 0.738 0.751 0.758 0.763 H2O [kmol/kmol] 0.347 0.190 0.131 0.100 0.081 0.068 O2 [kmol/kmol] 0.000 0.095 0.131 0.150 0.161 0.169 Combustion Products Flame Temperature and Oxidant to Fuel Ratio
  72. 72. Combustion Combustion Products Composition on Weight and Mole Basis Flame Temperature [K] 1,972 1,229 949 799 705 641 Oxidant to Fuel Ratio [/] 4.292 8.583 12.875 17.167 21.458 25.750 Stoichiometry [/] 1 2 3 4 5 6 Fuel: Sulfur CO2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 H2O [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 SO2 [kg/kg] 0.378 0.209 0.144 0.110 0.089 0.075 N2 [kg/kg] 0.622 0.687 0.712 0.725 0.733 0.738 O2 [kg/kg] 0.000 0.104 0.144 0.165 0.178 0.187 CO2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 Stoichiometry [/] 1 2 3 4 5 6 SO2 [kmol/kmol] 0.210 0.105 0.070 0.053 0.042 0.035 N2 [kmol/kmol] 0.790 0.790 0.790 0.790 0.790 0.790 H2O [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 O2 [kmol/kmol] 0.000 0.105 0.140 0.158 0.168 0.175 Combustion Products Flame Temperature and Oxidant to Fuel Ratio
  73. 73. Combustion Combustion Products Composition on Weight and Mole Basis Fuel: Coal CO2 [kg/kg] 0.249 0.130 0.088 0.067 0.053 0.045 H2O [kg/kg] 0.041 0.021 0.014 0.011 0.009 0.007 SO2 [kg/kg] 0.005 0.003 0.002 0.001 0.001 0.001 N2 [kg/kg] 0.705 0.735 0.745 0.750 0.754 0.756 O2 [kg/kg] 0.000 0.111 0.151 0.171 0.183 0.191 CO2 [kmol/kmol] 0.170 0.087 0.059 0.044 0.035 0.030 Stoichiometry [/] 1 2 3 4 5 6 SO2 [kmol/kmol] 0.002 0.001 0.001 0.001 0.001 0.000 N2 [kmol/kmol] 0.760 0.774 0.779 0.782 0.783 0.785 H2O [kmol/kmol] 0.068 0.035 0.024 0.018 0.014 0.012 O2 [kmol/kmol] 0.000 0.103 0.138 0.156 0.166 0.174 Flame Temperature [K] 2,484 1,544 1,178 981 856 769 Oxidant to Fuel Ratio [/] 10.487 20.992 31.497 42.002 52.507 63.013 Stoichiometry [/] 1 2 3 4 5 6 Combustion Products Flame Temperature and Oxidant to Fuel Ratio
  74. 74. Combustion Combustion Products Composition on Weight and Mole Basis Flame Temperature [K] 2,484 1,555 1,187 989 863 776 Oxidant to Fuel Ratio [/] 14.694 29.298 43.947 58.596 73.244 87.893 Stoichiometry [/] 1 2 3 4 5 6 Fuel: Oil CO2 [kg/kg] 0.202 0.104 0.070 0.053 0.042 0.035 H2O [kg/kg] 0.080 0.042 0.028 0.021 0.017 0.014 SO2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kg/kg] 0.718 0.742 0.750 0.754 0.757 0.758 O2 [kg/kg] 0.000 0.113 0.152 0.172 0.184 0.192 CO2 [kmol/kmol] 0.132 0.068 0.046 0.035 0.028 0.023 Stoichiometry [/] 1 2 3 4 5 6 SO2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kmol/kmol] 0.739 0.764 0.772 0.777 0.779 0.781 H2O [kmol/kmol] 0.129 0.067 0.045 0.034 0.027 0.023 O2 [kmol/kmol] 0.000 0.102 0.137 0.155 0.166 0.173 Combustion Products Flame Temperature and Oxidant to Fuel Ratio
  75. 75. Combustion Combustion Products Composition on Weight and Mole Basis Flame Temperature [K] 2,327 1,480 1,137 951 832 750 Oxidant to Fuel Ratio [/] 17.167 34.333 51.500 68.667 85.833 103.000 Stoichiometry [/] 1 2 3 4 5 6 Fuel: Gas CO2 [kg/kg] 0.151 0.078 0.052 0.039 0.032 0.026 H2O [kg/kg] 0.124 0.064 0.043 0.032 0.026 0.022 SO2 [kg/kg] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kg/kg] 0.725 0.745 0.752 0.756 0.758 0.760 O2 [kg/kg] 0.000 0.113 0.152 0.172 0.184 0.192 CO2 [kmol/kmol] 0.095 0.050 0.034 0.026 0.021 0.017 Stoichiometry [/] 1 2 3 4 5 6 SO2 [kmol/kmol] 0.000 0.000 0.000 0.000 0.000 0.000 N2 [kmol/kmol] 0.715 0.751 0.763 0.770 0.774 0.776 H2O [kmol/kmol] 0.190 0.100 0.068 0.051 0.041 0.034 O2 [kmol/kmol] 0.000 0.100 0.135 0.153 0.165 0.172 Combustion Products Flame Temperature and Oxidant to Fuel Ratio
  76. 76. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] 1 2 3 4 5 6 Combustion Stoichiometry [/] Fuel: Carbon Fuel and Oxidant Inlet Temperature: 298 [K]
  77. 77. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] 1 2 3 4 5 6 Combustion Stoichiometry [/] Fuel: Carbon Fuel and Oxidant Inlet Temperature: 298 [K]
  78. 78. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] 1 2 3 4 5 6 Combustion Fuel: Hydrogen Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  79. 79. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] 1 2 3 4 5 6 Combustion Fuel: Hydrogen Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  80. 80. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] 1 2 3 4 5 6 Combustion Fuel: Sulfur Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  81. 81. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] 1 2 3 4 5 6 Combustion Fuel: Sulfur Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  82. 82. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] 1 2 3 4 5 6 Combustion Fuel: Coal Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  83. 83. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] 1 2 3 4 5 6 Combustion Fuel: Coal Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  84. 84. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] 1 2 3 4 5 6 Combustion Fuel: Oil Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  85. 85. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] 1 2 3 4 5 6 Combustion Fuel: Oil Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  86. 86. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] 1 2 3 4 5 6 Combustion Fuel: Gas Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  87. 87. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] 1 2 3 4 5 6 Combustion Fuel: Gas Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  88. 88. Combustion Products Flame Temperature 600 1,100 1,600 2,100 2,600 1 2 3 4 5 6 FlameTemperature[K] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  89. 89. Combustion Oxidant to Fuel Ratio 0 40 80 120 160 200 240 1 2 3 4 5 6 OxidanttoFuelRatio[/] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometry [/]
  90. 90. Combustion Oxidant Composition N [kmol/kmol] 0.790 0.580 0.370 O [kmol/kmol] 0.210 0.420 0.630 N [kg/kg] 0.767 0.550 0.340 O [kg/kg] 0.233 0.450 0.660 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Fuel Composition C [kg/kg] 1.000 0.000 0.000 0.780 0.860 - H [kg/kg] 0.000 1.000 0.000 0.050 0.140 - S [kg/kg] 0.000 0.000 1.000 0.030 0.000 - N [kg/kg] 0.000 0.000 0.000 0.040 0.000 - O [kg/kg] 0.000 0.000 0.000 0.080 0.000 - H2O [kg/kg] 0.000 0.000 0.000 0.020 0.000 - CH4 [kg/kg] - - - - - 1.000 Fuel Carbon Hydrogen Sulfur Coal Oil Gas
  91. 91. Combustion Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis Combustion Products Flame Temperature and Stoichiometric Oxidant to Fuel Ratio Stoichiometric Oxidant to Fuel Ratio [/] 11.444 5.889 4.037 Fuel: Carbon CO2 [kg/kg] 0.295 0.532 0.728 H2O [kg/kg] 0.000 0.000 0.000 SO2 [kg/kg] 0.000 0.000 0.000 N2 [kg/kg] 0.705 0.468 0.272 O2 [kg/kg] 0.000 0.000 0.000 CO2 [kmol/kmol] 0.210 0.420 0.630 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 SO2 [kmol/kmol] 0.000 0.000 0.000 N2 [kmol/kmol] 0.790 0.580 0.370 H2O [kmol/kmol] 0.000 0.000 0.000 O2 [kmol/kmol] 0.000 0.000 0.000 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Flame Temperature [K] 2,460 3,985 > 5,000
  92. 92. Combustion Fuel: Hydrogen CO2 [kg/kg] 0.000 0.000 0.000 H2O [kg/kg] 0.255 0.482 0.686 SO2 [kg/kg] 0.000 0.000 0.000 N2 [kg/kg] 0.745 0.518 0.314 O2 [kg/kg] 0.000 0.000 0.000 CO2 [kmol/kmol] 0.000 0.000 0.000 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 SO2 [kmol/kmol] 0.000 0.000 0.000 N2 [kmol/kmol] 0.653 0.408 0.227 H2O [kmol/kmol] 0.347 0.592 0.773 O2 [kmol/kmol] 0.000 0.000 0.000 Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis Stoichiometric Oxidant to Fuel Ratio [/] 34.333 17.667 12.111 Combustion Products Flame Temperature and Stoichiometric Oxidant to Fuel Ratio Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Flame Temperature [K] 2,525 3,625 4,294
  93. 93. Combustion Fuel: Sulfur CO2 [kg/kg] 0.000 0.000 0.000 H2O [kg/kg] 0.000 0.000 0.000 SO2 [kg/kg] 0.378 0.623 0.796 N2 [kg/kg] 0.622 0.377 0.204 O2 [kg/kg] 0.000 0.000 0.000 CO2 [kmol/kmol] 0.000 0.000 0.000 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 SO2 [kmol/kmol] 0.210 0.420 0.630 N2 [kmol/kmol] 0.790 0.580 0.370 H2O [kmol/kmol] 0.000 0.000 0.000 O2 [kmol/kmol] 0.000 0.000 0.000 Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis Stoichiometric Oxidant to Fuel Ratio [/] 4.292 2.208 1.514 Combustion Products Flame Temperature and Stoichiometric Oxidant to Fuel Ratio Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Flame Temperature [K] 1,972 3,167 4,125
  94. 94. Combustion Fuel: Coal CO2 [kg/kg] 0.249 0.448 0.610 H2O [kg/kg] 0.041 0.074 0.100 SO2 [kg/kg] 0.005 0.009 0.013 N2 [kg/kg] 0.705 0.469 0.277 O2 [kg/kg] 0.000 0.000 0.000 CO2 [kmol/kmol] 0.170 0.326 0.470 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 SO2 [kmol/kmol] 0.002 0.005 0.007 N2 [kmol/kmol] 0.759 0.538 0.335 H2O [kmol/kmol] 0.068 0.131 0.189 O2 [kmol/kmol] 0.000 0.000 0.000 Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis Flame Temperature [K] 2,484 3,889 4,913 Stoichiometric Oxidant to Fuel Ratio [/] 10.487 5.388 3.688 Combustion Products Flame Temperature and Stoichiometric Oxidant to Fuel Ratio Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63
  95. 95. Combustion Fuel: Oil CO2 [kg/kg] 0.202 0.369 0.511 H2O [kg/kg] 0.081 0.148 0.204 SO2 [kg/kg] 0.000 0.000 0.000 N2 [kg/kg] 0.718 0.483 0.284 O2 [kg/kg] 0.000 0.000 0.000 CO2 [kmol/kmol] 0.132 0.248 0.351 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 SO2 [kmol/kmol] 0.000 0.000 0.000 N2 [kmol/kmol] 0.739 0.510 0.307 H2O [kmol/kmol] 0.129 0.242 0.343 O2 [kmol/kmol] 0.000 0.000 0.000 Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis Stoichiometric Oxidant to Fuel Ratio [/] 14.649 7.538 5.167 Combustion Products Flame Temperature and Stoichiometric Oxidant to Fuel Ratio Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Flame Temperature [K] 2,484 3,836 4,789
  96. 96. Combustion Fuel: Gas CO2 [kg/kg] 0.151 0.280 0.390 H2O [kg/kg] 0.124 0.229 0.319 SO2 [kg/kg] 0.000 0.000 0.000 N2 [kg/kg] 0.725 0.492 0.291 O2 [kg/kg] 0.000 0.000 0.000 CO2 [kmol/kmol] 0.095 0.174 0.240 Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 SO2 [kmol/kmol] 0.000 0.000 0.000 N2 [kmol/kmol] 0.715 0.479 0.281 H2O [kmol/kmol] 0.190 0.347 0.479 O2 [kmol/kmol] 0.000 0.000 0.000 Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis Flame Temperature [K] 2,327 3,505 4,300 Stoichiometric Oxidant to Fuel Ratio [/] 17.167 8.833 6.056 Combustion Products Flame Temperature and Stoichiometric Oxidant to Fuel Ratio Oxidant [kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63
  97. 97. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Carbon Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  98. 98. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Carbon Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  99. 99. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Hydrogen Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  100. 100. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Hydrogen Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  101. 101. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Sulfur Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  102. 102. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Sulfur Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  103. 103. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Coal Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  104. 104. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Coal Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  105. 105. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Oil Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  106. 106. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Oil Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  107. 107. Combustion Products -- Weight Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kg/kg] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Gas Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  108. 108. Combustion Products -- Mole Basis 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 CO2 H2O SO2 N2 O2 CombustionProducts[kmol/kmol] O2 - 0.21 O2 - 0.42 O2 - 0.63 Combustion Fuel: Gas Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  109. 109. Combustion Products Flame Temperature 0 1,000 2,000 3,000 4,000 5,000 O2 - 0.21 O2 - 0.42 O2 - 0.63 FlameTemperature[K] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  110. 110. Combustion Stoichiometric Oxidant to Fuel Ratio 0 10 20 30 40 O2 - 0.21 O2 - 0.42 O2 - 0.63 StoichiometricOxidanttoFuelRatio[/] Carbon Hydrogen Sulfur Coal Oil Gas Combustion Fuel and Oxidant Inlet Temperature: 298 [K] Stoichiometric Combustion
  111. 111. Expansion Schematic Layout Working Fluid In Working Fluid Out Turbine 1 2 Expansion
  112. 112. Expansion T - s Diagram 1 2 Temperature--T[K] Entropy -- s [kJ/kg*K] Expansion
  113. 113. Expansion Specific Power Output 0 2 4 6 5 10 15 ExpansionSpecificPowerOutput[MJ/kg] Air Argon Helium Nitrogen Turbine Inlet Temperature: 1,500 [K] Expansion Expansion Ratio (P1/P2) [/]
  114. 114. Expansion Power Output 0 200 400 600 800 50 100 150 Working Fluid Mass Flow Rate [kg/s] ExpansionPowerOutput[MW] Air Argon Helium Nitrogen Expansion Expansion Ratio (P1/P2) = 15 [/] Turbine Inlet Temperature: 1,500 [K]
  115. 115. Power Cycle Components/Processes Conclusions The compression specific power input increases with an increase in the compression ratio values. As the working fluid mass flow rate increases for the fixed compression ratio and compression inlet temperature values, the compression power input requirements increase too. The compression specific power input and power input increase for the working fluid having higher specific heat values. Hydrogen as the fuel has the highest flame temperature (when reacting with air at stiochiometric conditions), requires the most mass amount of oxidant in order to have complete combustion per unit mass amount of fuel and has the largest fuel higher heating value. When hydrogen reacts with oxidant, there is no CO2 present in the combustion products. The flame temperature increases as the oxidant preheat temperature increases for a fixed stoichiometry value.
  116. 116. The flame temperature decreases as the stoichiometry values increase. For stoichiometric combustion conditions, the amount of oxidant decreases as the oxygen enriched air level in the oxidant increases. Also, the flame temperature for such combustion conditions increases. The expansion specific power output increases with an increase in the expansion ratio values. As the working fluid mass flow rate increases for the fixed expansion ratio and expansion inlet temperature values, the expansion power output values increase too. The expansion specific power output and power output increase for the working fluid having higher specific heat values. Power Cycle Components/Processes Conclusions
  117. 117. Sonic Velocity vs = (χ RT)1/2 [m/s] Mach Number M = v/vs [/] Compressible Flow Engineering Equations
  118. 118. Isentropic Flow Tt/T = (1 + M2(χ - 1)/2) [/] pt/p = (1 + M2(χ - 1)/2)χ/(χ-1) [/] ht = (h + v2/2) [kJ/kg] Tt = (T + v2/(2cp)) [K] Thrust = vm + (p - pa)A [N] Compressible Flow Engineering Equations
  119. 119. Nozzle Schematic Layout Working Fluid In Working Fluid Out Nozzle 1 2 Nozzle
  120. 120. Nozzle T - s Diagram 1 2 Temperature--T[K] Entropy -- s [kJ/kg*K] Nozzle
  121. 121. Nozzle Performance 1.00 1.10 1.20 1.30 1.40 1.50 0.39 0.67 1.00 Mach Number [/] Tstagnation/Tstatic[/] Air Argon Helium Nitrogen Nozzle Nozzle Inlet Stagnation Conditions -- Temperature: 1,500 [K] and Pressure: 10 [atm]
  122. 122. Nozzle Performance 1.00 1.30 1.60 1.90 2.20 2.50 0.39 0.67 1.00 Mach Number [/] Pstagnation/Pstatic[/] Air Argon Helium Nitrogen Nozzle Nozzle Inlet Stagnation Conditions -- Temperature: 1,500 [K] and Pressure: 10 [atm]
  123. 123. Diffuser Schematic Layout Working Fluid In Working Fluid Out Diffuser 1 2 Diffuser
  124. 124. Diffuser T - s Diagram 2 1 Temperature--T[K] Entropy -- s [kJ/kg*K] Diffuser
  125. 125. Diffuser Performance 1.00 1.10 1.20 1.30 1.40 1.50 0.29 0.58 0.95 Mach Number [/] Tstagnation/Tstatic[/] Air Argon Helium Nitrogen Diffuser Diffuser Inlet Static Conditions -- Temperature: 298 [K] and Pressure: 1 [atm]
  126. 126. Diffuser Performance 1.00 1.30 1.60 1.90 2.20 2.50 0.29 0.58 0.95 Mach Number [/] Pstagnation/Pstatic[/] Air Argon Helium Nitrogen Diffuser Diffuser Inlet Static Conditions -- Temperature: 298 [K] and Pressure: 1 [atm]
  127. 127. Thrust Schematic Layout Working Fluid Out Nozzle 21 Working Fluid at Still Thrust
  128. 128. Thrust T - s Diagram 1 2 Temperature--T[K] Entropy -- s [kJ/kg*K] Thrust
  129. 129. Thrust 500 1,000 1,500 2,000 2,500 3,000 900 1,200 1,500 Nozzle Inlet Stagnation Temperature [K] Thrust[N] Air Argon Helium Nitrogen Working Fluid Mass Flow Rate: 1 [kg/s] Thrust Nozzle Outlet Static Conditions -- Mach Number: 0.85 [/] Nozzle Inlet Stagnation Pressure: 10 [atm] and Ambient Conditions Pressure: 1 [atm]
  130. 130. Nozzle -- Thrust Performance 1.14 1.17 1.20 1.23 1.26 900 1,200 1,500 Nozzle Inlet Stagnation Temperature [K] Tstagnation/Tstatic[/] Air Argon Helium Nitrogen Thrust Nozzle Outlet Static Conditions -- Mach Number: 0.85 [/] Nozzle Inlet Stagnation Pressure: 10 [atm] and Ambient Conditions Pressure: 1 [atm]
  131. 131. Nozzle -- Thrust Performance 1.58 1.62 1.66 1.70 1.74 900 1,200 1,500 Nozzle Inlet Stagnation Temperature [K] Pstagnation/Pstatic[/] Air Argon Helium Nitrogen Thrust Nozzle Outlet Static Conditions -- Mach Number: 0.85 [/] Nozzle Inlet Stagnation Pressure: 10 [atm] and Ambient Conditions Pressure: 1 [atm]
  132. 132. Compressible Flow Conclusions Nozzle stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. Diffuser stagnation over static temperature and pressure ratio values increase with an increase in the Mach Number. Thrust increases with an increase in the inlet stagnation temperature. The nozzle, diffuser and thrust performance increases for the working fluid having higher specific heat values.

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