Engineering Software
P.O. Box 2134
Kensington, MD 20891
Phone (301) 919-9670
E-Mail: info@engineering-4e.com
http://www.en...
Power Cycles and Combustion Analysis
Webinar Objectives
In this webinar, the engineering students and professionals get fa...
This webinar consists of the following two major sections:
• Power Cycles (Carnot, Brayton, Otto and Diesel)
• Combustion
...
The energy conversion analysis presented in this webinar considers ideal (isentropic) operation and air, argon,
helium and...
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...
Power Cycles Engineering Equations
Isentropic Compression
T2/T1 = (p2/p1)(χ-1)/χ [/]
T2/T1 = (V1/V2)(χ-1) [/]
p2/p1 = (V1/...
Power Cycles Engineering Equations
Isentropic Expansion
T1/T2 = (p1/p2)(χ-1)/χ [/]
T1/T2 = (V2/V1)(χ-1) [/]
p1/p2 = (V2/V1...
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]
Stoichoimetry [/]
Com...
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) [/]
V1/V2 [/]
Working Fluid: Air
Otto Cycl...
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]
Stoichoimetry [/]
Compression Ratio (V1/V2) ...
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]
Stoichoimetry [/]
Compression Ratio (V1/V2...
Power Cycles Conclusions
The Carnot Cycle efficiency increases with an increase in the heat addition temperature when the ...
Combustion Engineering Equations
Combustion is ideal, complete with no heat loss and
fuel reacts with air at different sto...
Combustion Schematic Layout
Fuel
Oxidant
Combustion Products
Combustion
Specific 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 ...
Combustion h - T Diagram
SpecificEnthalpy--h[kJ/kg]
Temperature -- T [K]
Reactants
Products
TflameTreference
Combustion
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
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]
0.0...
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]
0.000
H
[kg/kg]
0.000
S
[kg/kg]
0.000
N
[kg/kg]
0.000
O
[kg/kg]
...
Combustion
Combustion Products Composition on Weight and Mole Basis
CO2
[kg/kg]
0.151
0.078
0.052
0.040
0.032
0.026
H2O
[k...
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]
...
Combustion Products Flame Temperature
600
900
1,200
1,500
1,800
2,100
2,400
1 2 3 4 5 6
Flame Temperature [K]
Combustion
S...
Combustion Oxidant to Fuel Ratio
0
30
60
90
120
1 2 3 4 5 6
Oxidant to Fuel Ratio [/]
Combustion
Stoichiometry [/]
Fuel an...
Combustion Conclusions
Hydrogen as the fuel has the highest flame temperature, requires the most mass
amount of oxidant in...
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Power Cycles and Combustion Analysis Webinar

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Engineering webinar material dealing with power cycles (Carnot, Brayton, Otto and Diesel) and combustion when air, argon, helium and nitrogen are considered as the working fluid.

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Power Cycles and Combustion Analysis Webinar

  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. Power Cycles and Combustion Analysis Webinar Objectives In this webinar, the engineering students and professionals get familiar with the ideal simple and basic power cycles and combustion 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 and combustion and their T - s, p - V and h - T diagrams Be familiar with Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle and combustion operation Understand general Carnot Cycle, Brayton Cycle, Otto Cycle, Diesel Cycle and combustion performance trends
  3. 3. This webinar consists of the following two major sections: • Power Cycles (Carnot, Brayton, Otto and Diesel) • Combustion 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. Power Cycles and Combustion Analysis Webinar
  4. 4. The energy conversion analysis presented in this webinar considers ideal (isentropic) operation and 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 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. Power Cycles Engineering Equations 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]
  11. 11. Power Cycles Engineering Equations 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]
  12. 12. Carnot Cycle Schematic Layout Compressor Heat Exchanger Gas Turbine 1 32 4 Heat Addition Heat Exchanger Heat Rejection Carnot Cycle
  13. 13. Carnot Cycle T - s Diagram 1 32 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Carnot Cycle
  14. 14. 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
  15. 15. 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
  16. 16. 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
  17. 17. Brayton Cycle Schematic Layout -- Closed Cycle Compressor Heat Exchanger Gas Turbine 1 32 4 Heat Addition Heat Exchanger Heat Rejection Brayton Cycle (Gas Turbine)
  18. 18. Brayton Cycle (Gas Turbine) T - s Diagram 1 3 2 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Brayton Cycle (Gas Turbine)
  19. 19. 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)
  20. 20. 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]
  21. 21. 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)
  22. 22. 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
  23. 23. 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 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 H2O [kmol/kmol] 0.020 0.047 0.075 O2 [kmol/kmol] 0.187 0.158 0.127 Stoichiometry [/] 10.05 4.35 2.68
  24. 24. 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]
  25. 25. 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]
  26. 26. 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]
  27. 27. Brayton Cycle (Gas Turbine) Stoichiometry 0 4 8 12 900 1,200 1,500 Gas Turbine Inlet Temperature [K] Stoichoimetry [/] Compression Ratio (P2/P1) = 15 [/] Brayton Cycle (Gas Turbine) Compressor Inlet Temperature: 298 [K] BraytonCycle(GasTurbine)Stoichiometry[/]
  28. 28. Otto Cycle p - V Diagram 1 3 2 4 Pressure--p[atm] Volume -- V [m^3] Otto Cycle
  29. 29. Otto Cycle T - s Diagram 1 3 2 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Otto Cycle
  30. 30. Otto Cycle Efficiency 0 20 40 60 80 2.5 5 7.5 10 12.5 Compression Ratio (V1/V2) [/] V1/V2 [/] Working Fluid: Air Otto Cycle OttoCycleEfficiency[%]
  31. 31. 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
  32. 32. 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
  33. 33. 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
  34. 34. 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]
  35. 35. 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]
  36. 36. 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]
  37. 37. Otto Cycle Stoichiometry 0 2 4 6 1,200 1,500 1,800 Combustion Temperature [K] Stoichoimetry [/] Compression Ratio (V1/V2) = 10 [/] Otto Cycle Ambient Temperature: 298 [K] OttoCycleStoichiometry[/]
  38. 38. Diesel Cycle p - V Diagram 1 32 4 Pressure--p[atm] Volume -- V [m^3] Diesel Cycle
  39. 39. Diesel Cycle T - s Diagram 1 3 2 4 Temperature--T[K] Entropy -- s [kJ/kg*K] Diesel Cycle
  40. 40. 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
  41. 41. 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]
  42. 42. 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]
  43. 43. 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) [/]
  44. 44. 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
  45. 45. 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 Combustion Products Flame Temperature and Oxidant to Fuel Ratio H2O [kmol/kmol] 0.035 0.054 0.073 O2 [kmol/kmol] 0.153 0.123 0.091 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
  46. 46. 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]
  47. 47. 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]
  48. 48. 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]
  49. 49. Diesel Cycle Stoichiometry 0 2 4 6 1,500 1,800 2,100 Combustion Temperature [K] Stoichoimetry [/] Compression Ratio (V1/V2) = 15 [/] Diesel Cycle Ambient Temperature: 298 [K] Cut Off Ratio (V3/V2) = 1.70, 2.05 and 2.39 [/] DieselCycleStoichiometry[/]
  50. 50. 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 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.
  51. 51. Combustion Engineering Equations Combustion is ideal, complete with no heat loss and fuel reacts with air at different stoichiometry values (stoichiometry => 1) and air (oxidant) inlet temperature values. Also, Flame Temperature [K] hreactants = hproducts [kJ/kg]
  52. 52. Combustion Schematic Layout Fuel Oxidant Combustion Products Combustion
  53. 53. Specific 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 O2 N2 C(S) S(S) H2 CO2 SO2 H2O H2O(L) CH4 Combustion SpecificEnthalpy[kJ/kg] Temperature [K]
  54. 54. Combustion h - T Diagram SpecificEnthalpy--h[kJ/kg] Temperature -- T [K] Reactants Products TflameTreference Combustion
  55. 55. 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
  56. 56. Combustion 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 14.694 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 Stoichiometric Combustion Combustion Products Composition on Weight and Mole Basis
  57. 57. 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]
  58. 58. 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]
  59. 59. 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 Flame Temperature [K] Combustion Fuel and Oxidant Inlet Temperature: 298 [K] FlameTemperature[K]
  60. 60. Combustion Stoichiometric Oxidant to Fuel Ratio 0 5 10 15 20 25 30 35 40 Carbon Hydrogen Sulfur Coal Oil Gas Stoichiometric Oxidant to Fuel Ratio [/] Combustion Fuel and Oxidant Inlet Temperature: 298 [K] StoichiometricOxidanttoFuelRatio[/]
  61. 61. 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] Combustion Fuel and Oxidant Inlet Temperature: 298 [K] HHV[Btu/lbm]
  62. 62. 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
  63. 63. 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
  64. 64. 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
  65. 65. Combustion 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
  66. 66. Combustion Combustion Products Composition on Weight and Mole Basis CO2 [kg/kg] 0.151 0.078 0.052 0.040 0.032 0.026 H2O [kg/kg] 0.124 0.064 0.043 0.032 0.026 0.022 N2 [kg/kg] 0.725 0.745 0.753 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 0.020 0.018 Stoichiometry [/] 1 2 3 4 5 6 N2 [kmol/kmol] 0.715 0.750 0.763 0.770 0.774 0.776 Combustion Products Flame Temperature and Oxidant to Fuel Ratio 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 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 Stoichiometry [/] 1 2 3 4 5 6
  67. 67. 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 2 3 4 5 6 Fuel and Oxidant Inlet Temperature: 298 [K] Combustion Stoichiometry [/]
  68. 68. 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 2 3 4 5 6 Fuel and Oxidant Inlet Temperature: 298 [K] Combustion Stoichiometry [/]
  69. 69. Combustion Products Flame Temperature 600 900 1,200 1,500 1,800 2,100 2,400 1 2 3 4 5 6 Flame Temperature [K] Combustion Stoichiometry [/] Fuel and Oxidant Inlet Temperature: 298 [K] FlameTemperature[K]
  70. 70. Combustion Oxidant to Fuel Ratio 0 30 60 90 120 1 2 3 4 5 6 Oxidant to Fuel Ratio [/] Combustion Stoichiometry [/] Fuel and Oxidant Inlet Temperature: 298 [K] OxidanttoFuelRatio[/]
  71. 71. Combustion Conclusions Hydrogen as the fuel has the highest flame temperature, 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, air, preheat temperature increases for a fixed stoichiometry value. The flame temperature decreases as the stoichiometry values increase.

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