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Power Cycle Components/Processes

The document analyzes power cycle components and processes, focusing on isentropic compression and combustion for various fuels. It includes governing equations, input data, results, and conclusions regarding the effects of compression ratios and mass flow rates on power input. Additionally, it presents a combustion analysis for different fuels, detailing their chemical properties, compositions, and resulting emissions.

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Power Cycle Components/Processes -- i -- Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Power Cycle Components/Processes by Engineering Software Copyright © 1996
Power Cycle Components/Processes -- 1 -- Table of Contents Compression ..................................................................................................................................................................2 Analysis .....................................................................................................................................................................2 Assumptions...............................................................................................................................................................5 Governing Equations .................................................................................................................................................6 Input Data ..................................................................................................................................................................6 Results .......................................................................................................................................................................6 Conclusions................................................................................................................................................................8 Combustion....................................................................................................................................................................9 Analysis .....................................................................................................................................................................9 Assumptions.............................................................................................................................................................14 Governing Equations ...............................................................................................................................................15 Input Data ................................................................................................................................................................16 Results .....................................................................................................................................................................17 Figures .....................................................................................................................................................................18 Conclusions..............................................................................................................................................................25 Expansion ....................................................................................................................................................................26 Analysis ...................................................................................................................................................................26 Assumptions.............................................................................................................................................................29 Governing Equations ...............................................................................................................................................30 Input Data ................................................................................................................................................................30 Results .....................................................................................................................................................................30 Conclusions..............................................................................................................................................................32
Power Cycle Components/Processes -- 2 -- Compression This section provides an isentropic compression analysis when the working fluid is air. Analysis In the presented compression analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a compressor at point 1 and it exits the compressor at point 2. Isentropic compression is considered with no entropy change. Figure 1 presents a compression schematic layout. Figure 1 - Compression Schematic Layout
Power Cycle Components/Processes -- 3 -- Figure 2 presents a compression temperature vs entropy diagram. Figure 2 - Compression Temperature vs Entropy Diagram Figure 3 presents compression specific power input requirements for a few typical compression ratio values. It should be noted that the air enters the compressor at standard ambient conditions of 298 [K] and 1 [atm] of absolute pressure.
Power Cycle Components/Processes -- 4 -- Figure 3 - Compression Specific Power Input Figure 4 presents compression power input requirements for two typical compression ratio values and a few different working fluid mass flow rate values.
Power Cycle Components/Processes -- 5 -- Figure 4 - Compression Power Input One can notice that both compression specific power input and power input increase with an increase in the compression ratio values. As the working fluid mass flow rate increases for a fixed compression inlet temperature value, the compression power input requirements increase too. Assumptions Working fluid is air. There is no friction and heat transfer. Compression is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
Power Cycle Components/Processes -- 6 -- Governing Equations T2/T1 = (p2/p1)(ϰ-1)/ϰ ϰ = cp/cv cp - cv = R pv = RT w = cp(T2 - T1) W = cp(T2 - T1)m Input Data T1 = 298 [K] p1 = 1 [atm] p2 = 5, 10 and 15 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = 1.4 [/] m = 50, 100 and 150 [kg/s] Results Specific Power Input vs Compression Ratio Compression Inlet Temperature = 298 [K] Compression Ratio [/] Specific Power Input [kW/kg/s] 5 174 10 278 15 349
Power Cycle Components/Processes -- 7 -- Power Input vs Compression Ratio for a few Mass Flow Rates Compression Inlet Temperature = 298 [K] Power Input [MW] Mass Flow Rate [kg/s] Compression Ratio [/] 50 100 150 5 8.68 17.37 26.05 15 17.47 34.94 52.41
Power Cycle Components/Processes -- 8 -- Conclusions Both compression specific power input and power input increase with an increase the compression ratio values. As the working fluid mass flow rate increases for a fixed compression inlet temperature value, the compression power input requirements increase too. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.
Power Cycle Components/Processes -- 9 -- Combustion This section provides a combustion analysis for a few typical fuel cases (carbon, hydrogen, sulfur, coal, oil and gas) when the fuel reacts with air at stoichiometric conditions. Analysis In the presented combustion analysis, both fuel and air are at standard inlet combustion conditions of 298 [K] and 1 [atm] of absolute pressure. Furthermore, combustion at constant pressure is complete and with no heat loss. During combustion, a large amount of reactants' chemical energy gets released in the form of thermal energy. Fuel higher heating value (HHV) or heat of combustion is the difference between the reactants enthalpy value and the combustion products enthalpy value per unit mass amount of fuel at the standard reference temperature, which is 298 [K]. When the reactants specific enthalpy value is equal to the combustion products specific enthalpy value, one can calculate the combustion products flame temperature or adiabatic temperature. Figure 1 presents how the reactants and combustion products specific enthalpy values change with an increase in the temperature.
Power Cycle Components/Processes -- 10 -- Figure 1 - Reactants and Combustion Products Specific Enthalpy vs Temperature Physical properties for both reactants and combustion products are very important and need to be known in order to carry out successful combustion calculations. Figure 2 depicts how the reactants and combustion products species specific enthalpy values change with the temperature. The physical properties provided in Figure 2 come from the JANAF Thermochemical Data - Tables, 1970.
Power Cycle Components/Processes -- 11 -- Figure 2 - Reactants and Combustion Products Species Specific Enthalpy vs Temperature It is interesting to note that the specific enthalpy value for basic combustion elements such as carbon (C), hydrogen (H2), sulfur (S), oxygen (O2) and nitrogen (N2) is equal to zero at the standard combustion conditions of 298 [K] and 1 [atm]. Also, it should be mentioned that for ideal gas species, the specific enthalpy values are only dependent on the temperature. In addition to knowing the reactants and combustion products physical properties, for any kind of combustion analysis and calculations, it is important to know both oxidant and fuel compositions. Oxidant composition is usually given on the mole/volume basis. For solid and liquid type fuels, the fuel composition is given on the weight basis for a unit mass amount. For the gas type fuels, the fuel composition is provided on the mole/volume basis for a unit volume amount. In this analysis, methane (CH4) is considered as the gas fuel. In order to keep the combustion analysis simple and straightforward, the CH4 composition is provided on the weight basis.
Power Cycle Components/Processes -- 12 -- Table 1 provides the standard air composition. Table 1 - Oxidant Composition Oxidant N [kg/kg] O [kg/kg] N [kmol/kmol] O [kmol/kmol] Air 0.767 0.233 0.790 0.210 Table 2 provides the fuel composition. Table 2 - Fuel Composition Fuel C [kg/kg] H [kg/kg] S [kg/kg] N [kg/kg] O [kg/kg] H2O [kg/kg] CH4 [kg/kg] Carbon 1.000 0.000 0.000 0.000 0.000 0.000 - Hydrogen 0.000 1.000 0.000 0.000 0.000 0.000 - Sulfur 0.000 0.000 1.000 0.000 0.000 0.000 - Coal 0.780 0.050 0.030 0.040 0.080 0.020 - Oil 0.860 0.140 0.000 0.000 0.000 0.000 - Gas - - - - - - 1.000 Again, in this combustion analysis, only the stoichiometric combustion is analyzed. Results of such analysis are provided, including combustion products composition on weight and mole/volume basis, flame temperature, stoichiometric oxidant to fuel ratio and fuel higher heating value (HHV). Table 3 provides the combustion products composition on the weight basis. Table 3 - Combustion Products Composition on the Weight Basis Fuel CO2 [kg/kg] H2O [kg/kg] SO2 [kg/kg] N2 [kg/kg] O2 [kg/kg] Carbon 0.295 0.000 0.000 0.705 0.000 Hydrogen 0.000 0.255 0.000 0.745 0.000 Sulfur 0.000 0.000 0.378 0.622 0.000 Coal 0.249 0.041 0.005 0.705 0.000 Oil 0.202 0.080 0.000 0.718 0.000 Gas 0.151 0.124 0.000 0.725 0.000
Power Cycle Components/Processes -- 13 -- Table 4 provides the combustion products composition on the mole basis. Table 4 - Combustion Products Composition on the Mole Basis Fuel CO2 [kmol/kmol] H2O [kmol/kmol] SO2 [kmol/kmol] N2 [kmol/kmol] O2 [kmol/kmol] Carbon 0.210 0.000 0.000 0.790 0.000 Hydrogen 0.000 0.347 0.000 0.653 0.000 Sulfur 0.000 0.000 0.210 0.790 0.000 Coal 0.170 0.068 0.002 0.759 0.000 Oil 0.132 0.129 0.000 0.739 0.000 Gas 0.095 0.190 0.000 0.715 0.000 When considering coal, oil and gas as the fuel, coal has the largest amount of CO2 in the combustion products on both weight and mole basis. Table 5 provides the combustion products flame temperature, stoichiometric oxidant to fuel ratio and the fuel higher heating value. Table 5 - Combustion Products Flame Temperature, Stoichiometric Oxidant to Fuel Ratio and Fuel Higher Heating Value Fuel Flame Temperature [K] Stoichiometric Oxidant to Fuel Ratio [/] HHV [Btu/lbm] Carbon 2,460 11.444 14,094 Hydrogen 2,525 34.333 60,997 Sulfur 1,972 4.292 3,982 Coal 2,484 10.487 14,162 Oil 2,484 14.649 20,660 Gas 2,327 17.167 21,563 Stoichiometric oxidant to fuel ratio is the mass of air required for complete combustion of a unit mass of fuel. Thus, 1 [kg] of carbon fuel requires 11.444 [kg] of air for complete, ideal combustion. Today, global warming is becoming more evident and it is being said that it is primarily caused by CO2 emissions. A detailed combustion analysis, as it is provided here, can be very useful in determining different fuel and technology scenarios that would result in the reduction of current CO2 emissions.
Power Cycle Components/Processes -- 14 -- Assumptions Both fuel and air are at standard inlet combustion conditions of 298 [K] and 1 [atm] of absolute pressure. Furthermore, combustion is complete and with no heat loss. Combustion Schematic Layout Species Molecular Weight Species C H2 S O2 N2 CO2 H2O SO2 CH4 Molecular Weight [kg/kmol] 12 2 32 32 28 44 18 64 16
Power Cycle Components/Processes -- 15 -- Stoichiometric Oxidant and Combustion Products Mole Flow Rates for 1 [kmol] of Fuel Species Fuel Composition Oxidant Composition Combustion Products Composition Fuel C [kmol] H2 [kmol] S [kmol] CH4 [kmol] O2 [kmol] N2 [kmol] CO2 [kmol] H2O [kmol] SO2 [kmol] O2 [kmol] N2 [kmol] Carbon 1 0 0 0 1 3.762 1 0 0 0 3.762 Hydrogen 0 1 0 0 0.5 1.881 0 1 0 0 1.881 Sulfur 0 0 1 0 1 3.762 0 0 1 0 3.762 Coal 1 1 1 0 2.5 9.404 1 1 1 0 9.404 Oil 1 1 0 0 1.5 5.642 1 1 0 0 5.642 Gas 0 0 0 1 2 7.524 1 2 0 0 7.524 Stoichiometric Oxidant to Fuel Ratio, Oxidant and Combustion Products Mass Flow Rates for 1 [kmol] of Fuel Species Fuel Composition Oxidant Composition Combustion Products Composition Stoichiometric Oxidant to Fuel Ratio [/]Fuel C [kg] H2 [kg] S [kg] CH4 [kg] O2 [kg] N2 [kg] CO2 [kg] H2O [kg] SO2 [kg] O2 [kg] N2 [kg] Carbon 12 0 0 0 32 105.336 44 0 0 0 105.336 11.444 Hydrogen 0 2 0 0 16 52.668 0 18 0 0 52.668 34.333 Sulfur 0 0 32 0 32 105.336 0 0 64 0 105.336 4.292 Coal 12 2 32 0 80 263.312 44 18 64 0 263.312 7.463 Oil 12 2 0 0 48 157.976 44 18 0 0 157.976 14.712 Gas 0 0 0 16 64 210.672 44 36 0 0 210.672 17.167 Governing Equations Fuel higher heating value (HHV) or heat of combustion is the difference between the reactants enthalpy value and the combustion products enthalpy value per unit mass amount of fuel at the standard reference temperature, which is 298 [K]. When the reactants specific enthalpy value is equal to the combustion products specific enthalpy value, one can calculate the combustion products flame temperature or adiabatic temperature.
Power Cycle Components/Processes -- 16 -- Input Data Table 1 - Oxidant Composition Oxidant N [kg/kg] O [kg/kg] N [kmol/kmol] O [kmol/kmol] Air 0.767 0.233 0.790 0.210 Table 2 - Fuel Composition Fuel C [kg/kg] H [kg/kg] S [kg/kg] N [kg/kg] O [kg/kg] H2O [kg/kg] CH4 [kg/kg] Carbon 1.000 0.000 0.000 0.000 0.000 0.000 - Hydrogen 0.000 1.000 0.000 0.000 0.000 0.000 - Sulfur 0.000 0.000 1.000 0.000 0.000 0.000 - Coal 0.780 0.050 0.030 0.040 0.080 0.020 - Oil 0.860 0.140 0.000 0.000 0.000 0.000 - Gas - - - - - - 1.000
Power Cycle Components/Processes -- 17 -- Results Table 3 - Combustion Products Composition on the Weight Basis Fuel CO2 [kg/kg] H2O [kg/kg] SO2 [kg/kg] N2 [kg/kg] O2 [kg/kg] Carbon 0.295 0.000 0.000 0.705 0.000 Hydrogen 0.000 0.255 0.000 0.745 0.000 Sulfur 0.000 0.000 0.378 0.622 0.000 Coal 0.249 0.041 0.005 0.705 0.000 Oil 0.202 0.080 0.000 0.718 0.000 Gas 0.151 0.124 0.000 0.725 0.000 Table 4 - Combustion Products Composition on the Mole Basis Fuel CO2 [kmol/kmol] H2O [kmol/kmol] SO2 [kmol/kmol] N2 [kmol/kmol] O2 [kmol/kmol] Carbon 0.210 0.000 0.000 0.790 0.000 Hydrogen 0.000 0.347 0.000 0.653 0.000 Sulfur 0.000 0.000 0.210 0.790 0.000 Coal 0.170 0.068 0.002 0.759 0.000 Oil 0.132 0.129 0.000 0.739 0.000 Gas 0.095 0.190 0.000 0.715 0.000 Table 5 - Combustion Products Flame Temperature, Stoichiometric Oxidant to Fuel Ratio and Fuel Higher Heating Value Fuel Flame Temperature [K] Stoichiometric Oxidant to Fuel Ratio [/] HHV [Btu/lbm] Carbon 2,460 11.444 14,094 Hydrogen 2,525 34.333 60,997 Sulfur 1,972 4.292 3,982 Coal 2,484 10.487 14,162 Oil 2,484 14.649 20,660 Gas 2,327 17.167 21,563
Power Cycle Components/Processes -- 18 -- Figures Figure 1 - Reactants and Combustion Products Specific Enthalpy vs Temperature
Power Cycle Components/Processes -- 19 -- Figure 2 - Reactants and Combustion Products Species Specific Enthalpy vs Temperature
Power Cycle Components/Processes -- 20 -- Combustion Products - Weight Basis
Power Cycle Components/Processes -- 21 -- Combustion Products - Mole Basis
Power Cycle Components/Processes -- 22 -- Combustion Products Flame Temperature
Power Cycle Components/Processes -- 23 -- Combustion Stoichiometric Oxidant to Fuel Ratio
Power Cycle Components/Processes -- 24 -- Higher Heating Value (HHV)
Power Cycle Components/Processes -- 25 -- Conclusions Hydrogen as the fuel has the highest flame temperature, requires the most mass amount of oxidant/air 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/air, there is no CO2 present in the combustion products. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.
Power Cycle Components/Processes -- 26 -- Expansion This section provides an isentropic expansion analysis when the working fluid is air. Analysis In the presented expansion analysis, only air is considered as the working fluid behaving as a perfect gas - - specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a turbine at point 1 and it exits the turbine at point 2. Isentropic expansion is considered with no entropy change. Figure 1 presents an expansion schematic layout. Figure 1 - Expansion Schematic Layout
Power Cycle Components/Processes -- 27 -- Figure 2 presents an expansion temperature vs entropy diagram. Figure 2 - Expansion Temperature vs Entropy Diagram Figure 3 presents expansion specific power output values for a few typical expansion ratio values. It should be noted that the air enters the turbine at the temperature of 1,500 [K] and the turbine exhaust pressure is always equal to the standard ambient pressure -- 1 [atm] of absolute pressure.
Power Cycle Components/Processes -- 28 -- Figure 3 - Expansion Specific Power Output Figure 4 presents expansion power output values for two typical expansion ratio values and a few different working fluid mass flow rate values.
Power Cycle Components/Processes -- 29 -- Figure 4 - Expansion Power Output One can notice that both expansion specific power output and power output increase with an increase in the expansion ratio values. As the working fluid mass flow rate increases for a fixed expansion inlet temperature value, the expansion power output values increase too. Assumptions Working fluid is air. There is no friction and heat transfer. Expansion is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
Power Cycle Components/Processes -- 30 -- Governing Equations T1/T2 = (p1/p2)(ϰ-1)/ϰ ϰ = cp/cv cp - cv = R pv = RT w = cp(T1 - T2) W = cp(T1 - T2)m Input Data T1 = 1,500 [K] p1 = 5, 10 and 15 [atm] p2 = 1 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = cp/cv - for air ϰ = 1.4 [/] m = 50, 100 and 150 [kg/s] Results Specific Power Output vs Expansion Ratio Expansion Inlet Temperature = 1,500 [K] Expansion Ratio [/] Specific Power Output [kW/kg/s] 5 555 10 726 15 811
Power Cycle Components/Processes -- 31 -- Power Output vs Expansion Ratio for a few Mass Flow Rates Expansion Inlet Temperature = 1,500 [K] Power Output [MW] Mass Flow Rate [kg/s] Expansion Ratio [/] 50 100 150 5 27.76 55.51 83.27 15 40.56 81.13 121.69
Power Cycle Components/Processes -- 32 -- Conclusions Both expansion specific power output and power output increase with an increase in the expansion ratio values. As the working fluid mass flow rate increases for a fixed expansion inlet temperaure, the expansion power output values increase too. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.

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Power Cycle Components/Processes

  • 1.
    Power Cycle Components/Processes --i -- Engineering Software P.O. Box 2134, Kensington, MD 20891 Phone: (301) 919-9670 E-Mail: info@engineering-4e.com Web Site: http://www.engineering-4e.com Power Cycle Components/Processes by Engineering Software Copyright © 1996
  • 2.
    Power Cycle Components/Processes --1 -- Table of Contents Compression ..................................................................................................................................................................2 Analysis .....................................................................................................................................................................2 Assumptions...............................................................................................................................................................5 Governing Equations .................................................................................................................................................6 Input Data ..................................................................................................................................................................6 Results .......................................................................................................................................................................6 Conclusions................................................................................................................................................................8 Combustion....................................................................................................................................................................9 Analysis .....................................................................................................................................................................9 Assumptions.............................................................................................................................................................14 Governing Equations ...............................................................................................................................................15 Input Data ................................................................................................................................................................16 Results .....................................................................................................................................................................17 Figures .....................................................................................................................................................................18 Conclusions..............................................................................................................................................................25 Expansion ....................................................................................................................................................................26 Analysis ...................................................................................................................................................................26 Assumptions.............................................................................................................................................................29 Governing Equations ...............................................................................................................................................30 Input Data ................................................................................................................................................................30 Results .....................................................................................................................................................................30 Conclusions..............................................................................................................................................................32
  • 3.
    Power Cycle Components/Processes --2 -- Compression This section provides an isentropic compression analysis when the working fluid is air. Analysis In the presented compression analysis, only air is considered as the working fluid behaving as a perfect gas -- specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a compressor at point 1 and it exits the compressor at point 2. Isentropic compression is considered with no entropy change. Figure 1 presents a compression schematic layout. Figure 1 - Compression Schematic Layout
  • 4.
    Power Cycle Components/Processes --3 -- Figure 2 presents a compression temperature vs entropy diagram. Figure 2 - Compression Temperature vs Entropy Diagram Figure 3 presents compression specific power input requirements for a few typical compression ratio values. It should be noted that the air enters the compressor at standard ambient conditions of 298 [K] and 1 [atm] of absolute pressure.
  • 5.
    Power Cycle Components/Processes --4 -- Figure 3 - Compression Specific Power Input Figure 4 presents compression power input requirements for two typical compression ratio values and a few different working fluid mass flow rate values.
  • 6.
    Power Cycle Components/Processes --5 -- Figure 4 - Compression Power Input One can notice that both compression specific power input and power input increase with an increase in the compression ratio values. As the working fluid mass flow rate increases for a fixed compression inlet temperature value, the compression power input requirements increase too. Assumptions Working fluid is air. There is no friction and heat transfer. Compression is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
  • 7.
    Power Cycle Components/Processes --6 -- Governing Equations T2/T1 = (p2/p1)(ϰ-1)/ϰ ϰ = cp/cv cp - cv = R pv = RT w = cp(T2 - T1) W = cp(T2 - T1)m Input Data T1 = 298 [K] p1 = 1 [atm] p2 = 5, 10 and 15 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = 1.4 [/] m = 50, 100 and 150 [kg/s] Results Specific Power Input vs Compression Ratio Compression Inlet Temperature = 298 [K] Compression Ratio [/] Specific Power Input [kW/kg/s] 5 174 10 278 15 349
  • 8.
    Power Cycle Components/Processes --7 -- Power Input vs Compression Ratio for a few Mass Flow Rates Compression Inlet Temperature = 298 [K] Power Input [MW] Mass Flow Rate [kg/s] Compression Ratio [/] 50 100 150 5 8.68 17.37 26.05 15 17.47 34.94 52.41
  • 9.
    Power Cycle Components/Processes --8 -- Conclusions Both compression specific power input and power input increase with an increase the compression ratio values. As the working fluid mass flow rate increases for a fixed compression inlet temperature value, the compression power input requirements increase too. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.
  • 10.
    Power Cycle Components/Processes --9 -- Combustion This section provides a combustion analysis for a few typical fuel cases (carbon, hydrogen, sulfur, coal, oil and gas) when the fuel reacts with air at stoichiometric conditions. Analysis In the presented combustion analysis, both fuel and air are at standard inlet combustion conditions of 298 [K] and 1 [atm] of absolute pressure. Furthermore, combustion at constant pressure is complete and with no heat loss. During combustion, a large amount of reactants' chemical energy gets released in the form of thermal energy. Fuel higher heating value (HHV) or heat of combustion is the difference between the reactants enthalpy value and the combustion products enthalpy value per unit mass amount of fuel at the standard reference temperature, which is 298 [K]. When the reactants specific enthalpy value is equal to the combustion products specific enthalpy value, one can calculate the combustion products flame temperature or adiabatic temperature. Figure 1 presents how the reactants and combustion products specific enthalpy values change with an increase in the temperature.
  • 11.
    Power Cycle Components/Processes --10 -- Figure 1 - Reactants and Combustion Products Specific Enthalpy vs Temperature Physical properties for both reactants and combustion products are very important and need to be known in order to carry out successful combustion calculations. Figure 2 depicts how the reactants and combustion products species specific enthalpy values change with the temperature. The physical properties provided in Figure 2 come from the JANAF Thermochemical Data - Tables, 1970.
  • 12.
    Power Cycle Components/Processes --11 -- Figure 2 - Reactants and Combustion Products Species Specific Enthalpy vs Temperature It is interesting to note that the specific enthalpy value for basic combustion elements such as carbon (C), hydrogen (H2), sulfur (S), oxygen (O2) and nitrogen (N2) is equal to zero at the standard combustion conditions of 298 [K] and 1 [atm]. Also, it should be mentioned that for ideal gas species, the specific enthalpy values are only dependent on the temperature. In addition to knowing the reactants and combustion products physical properties, for any kind of combustion analysis and calculations, it is important to know both oxidant and fuel compositions. Oxidant composition is usually given on the mole/volume basis. For solid and liquid type fuels, the fuel composition is given on the weight basis for a unit mass amount. For the gas type fuels, the fuel composition is provided on the mole/volume basis for a unit volume amount. In this analysis, methane (CH4) is considered as the gas fuel. In order to keep the combustion analysis simple and straightforward, the CH4 composition is provided on the weight basis.
  • 13.
    Power Cycle Components/Processes --12 -- Table 1 provides the standard air composition. Table 1 - Oxidant Composition Oxidant N [kg/kg] O [kg/kg] N [kmol/kmol] O [kmol/kmol] Air 0.767 0.233 0.790 0.210 Table 2 provides the fuel composition. Table 2 - Fuel Composition Fuel C [kg/kg] H [kg/kg] S [kg/kg] N [kg/kg] O [kg/kg] H2O [kg/kg] CH4 [kg/kg] Carbon 1.000 0.000 0.000 0.000 0.000 0.000 - Hydrogen 0.000 1.000 0.000 0.000 0.000 0.000 - Sulfur 0.000 0.000 1.000 0.000 0.000 0.000 - Coal 0.780 0.050 0.030 0.040 0.080 0.020 - Oil 0.860 0.140 0.000 0.000 0.000 0.000 - Gas - - - - - - 1.000 Again, in this combustion analysis, only the stoichiometric combustion is analyzed. Results of such analysis are provided, including combustion products composition on weight and mole/volume basis, flame temperature, stoichiometric oxidant to fuel ratio and fuel higher heating value (HHV). Table 3 provides the combustion products composition on the weight basis. Table 3 - Combustion Products Composition on the Weight Basis Fuel CO2 [kg/kg] H2O [kg/kg] SO2 [kg/kg] N2 [kg/kg] O2 [kg/kg] Carbon 0.295 0.000 0.000 0.705 0.000 Hydrogen 0.000 0.255 0.000 0.745 0.000 Sulfur 0.000 0.000 0.378 0.622 0.000 Coal 0.249 0.041 0.005 0.705 0.000 Oil 0.202 0.080 0.000 0.718 0.000 Gas 0.151 0.124 0.000 0.725 0.000
  • 14.
    Power Cycle Components/Processes --13 -- Table 4 provides the combustion products composition on the mole basis. Table 4 - Combustion Products Composition on the Mole Basis Fuel CO2 [kmol/kmol] H2O [kmol/kmol] SO2 [kmol/kmol] N2 [kmol/kmol] O2 [kmol/kmol] Carbon 0.210 0.000 0.000 0.790 0.000 Hydrogen 0.000 0.347 0.000 0.653 0.000 Sulfur 0.000 0.000 0.210 0.790 0.000 Coal 0.170 0.068 0.002 0.759 0.000 Oil 0.132 0.129 0.000 0.739 0.000 Gas 0.095 0.190 0.000 0.715 0.000 When considering coal, oil and gas as the fuel, coal has the largest amount of CO2 in the combustion products on both weight and mole basis. Table 5 provides the combustion products flame temperature, stoichiometric oxidant to fuel ratio and the fuel higher heating value. Table 5 - Combustion Products Flame Temperature, Stoichiometric Oxidant to Fuel Ratio and Fuel Higher Heating Value Fuel Flame Temperature [K] Stoichiometric Oxidant to Fuel Ratio [/] HHV [Btu/lbm] Carbon 2,460 11.444 14,094 Hydrogen 2,525 34.333 60,997 Sulfur 1,972 4.292 3,982 Coal 2,484 10.487 14,162 Oil 2,484 14.649 20,660 Gas 2,327 17.167 21,563 Stoichiometric oxidant to fuel ratio is the mass of air required for complete combustion of a unit mass of fuel. Thus, 1 [kg] of carbon fuel requires 11.444 [kg] of air for complete, ideal combustion. Today, global warming is becoming more evident and it is being said that it is primarily caused by CO2 emissions. A detailed combustion analysis, as it is provided here, can be very useful in determining different fuel and technology scenarios that would result in the reduction of current CO2 emissions.
  • 15.
    Power Cycle Components/Processes --14 -- Assumptions Both fuel and air are at standard inlet combustion conditions of 298 [K] and 1 [atm] of absolute pressure. Furthermore, combustion is complete and with no heat loss. Combustion Schematic Layout Species Molecular Weight Species C H2 S O2 N2 CO2 H2O SO2 CH4 Molecular Weight [kg/kmol] 12 2 32 32 28 44 18 64 16
  • 16.
    Power Cycle Components/Processes --15 -- Stoichiometric Oxidant and Combustion Products Mole Flow Rates for 1 [kmol] of Fuel Species Fuel Composition Oxidant Composition Combustion Products Composition Fuel C [kmol] H2 [kmol] S [kmol] CH4 [kmol] O2 [kmol] N2 [kmol] CO2 [kmol] H2O [kmol] SO2 [kmol] O2 [kmol] N2 [kmol] Carbon 1 0 0 0 1 3.762 1 0 0 0 3.762 Hydrogen 0 1 0 0 0.5 1.881 0 1 0 0 1.881 Sulfur 0 0 1 0 1 3.762 0 0 1 0 3.762 Coal 1 1 1 0 2.5 9.404 1 1 1 0 9.404 Oil 1 1 0 0 1.5 5.642 1 1 0 0 5.642 Gas 0 0 0 1 2 7.524 1 2 0 0 7.524 Stoichiometric Oxidant to Fuel Ratio, Oxidant and Combustion Products Mass Flow Rates for 1 [kmol] of Fuel Species Fuel Composition Oxidant Composition Combustion Products Composition Stoichiometric Oxidant to Fuel Ratio [/]Fuel C [kg] H2 [kg] S [kg] CH4 [kg] O2 [kg] N2 [kg] CO2 [kg] H2O [kg] SO2 [kg] O2 [kg] N2 [kg] Carbon 12 0 0 0 32 105.336 44 0 0 0 105.336 11.444 Hydrogen 0 2 0 0 16 52.668 0 18 0 0 52.668 34.333 Sulfur 0 0 32 0 32 105.336 0 0 64 0 105.336 4.292 Coal 12 2 32 0 80 263.312 44 18 64 0 263.312 7.463 Oil 12 2 0 0 48 157.976 44 18 0 0 157.976 14.712 Gas 0 0 0 16 64 210.672 44 36 0 0 210.672 17.167 Governing Equations Fuel higher heating value (HHV) or heat of combustion is the difference between the reactants enthalpy value and the combustion products enthalpy value per unit mass amount of fuel at the standard reference temperature, which is 298 [K]. When the reactants specific enthalpy value is equal to the combustion products specific enthalpy value, one can calculate the combustion products flame temperature or adiabatic temperature.
  • 17.
    Power Cycle Components/Processes --16 -- Input Data Table 1 - Oxidant Composition Oxidant N [kg/kg] O [kg/kg] N [kmol/kmol] O [kmol/kmol] Air 0.767 0.233 0.790 0.210 Table 2 - Fuel Composition Fuel C [kg/kg] H [kg/kg] S [kg/kg] N [kg/kg] O [kg/kg] H2O [kg/kg] CH4 [kg/kg] Carbon 1.000 0.000 0.000 0.000 0.000 0.000 - Hydrogen 0.000 1.000 0.000 0.000 0.000 0.000 - Sulfur 0.000 0.000 1.000 0.000 0.000 0.000 - Coal 0.780 0.050 0.030 0.040 0.080 0.020 - Oil 0.860 0.140 0.000 0.000 0.000 0.000 - Gas - - - - - - 1.000
  • 18.
    Power Cycle Components/Processes --17 -- Results Table 3 - Combustion Products Composition on the Weight Basis Fuel CO2 [kg/kg] H2O [kg/kg] SO2 [kg/kg] N2 [kg/kg] O2 [kg/kg] Carbon 0.295 0.000 0.000 0.705 0.000 Hydrogen 0.000 0.255 0.000 0.745 0.000 Sulfur 0.000 0.000 0.378 0.622 0.000 Coal 0.249 0.041 0.005 0.705 0.000 Oil 0.202 0.080 0.000 0.718 0.000 Gas 0.151 0.124 0.000 0.725 0.000 Table 4 - Combustion Products Composition on the Mole Basis Fuel CO2 [kmol/kmol] H2O [kmol/kmol] SO2 [kmol/kmol] N2 [kmol/kmol] O2 [kmol/kmol] Carbon 0.210 0.000 0.000 0.790 0.000 Hydrogen 0.000 0.347 0.000 0.653 0.000 Sulfur 0.000 0.000 0.210 0.790 0.000 Coal 0.170 0.068 0.002 0.759 0.000 Oil 0.132 0.129 0.000 0.739 0.000 Gas 0.095 0.190 0.000 0.715 0.000 Table 5 - Combustion Products Flame Temperature, Stoichiometric Oxidant to Fuel Ratio and Fuel Higher Heating Value Fuel Flame Temperature [K] Stoichiometric Oxidant to Fuel Ratio [/] HHV [Btu/lbm] Carbon 2,460 11.444 14,094 Hydrogen 2,525 34.333 60,997 Sulfur 1,972 4.292 3,982 Coal 2,484 10.487 14,162 Oil 2,484 14.649 20,660 Gas 2,327 17.167 21,563
  • 19.
    Power Cycle Components/Processes --18 -- Figures Figure 1 - Reactants and Combustion Products Specific Enthalpy vs Temperature
  • 20.
    Power Cycle Components/Processes --19 -- Figure 2 - Reactants and Combustion Products Species Specific Enthalpy vs Temperature
  • 21.
    Power Cycle Components/Processes --20 -- Combustion Products - Weight Basis
  • 22.
    Power Cycle Components/Processes --21 -- Combustion Products - Mole Basis
  • 23.
    Power Cycle Components/Processes --22 -- Combustion Products Flame Temperature
  • 24.
    Power Cycle Components/Processes --23 -- Combustion Stoichiometric Oxidant to Fuel Ratio
  • 25.
    Power Cycle Components/Processes --24 -- Higher Heating Value (HHV)
  • 26.
    Power Cycle Components/Processes --25 -- Conclusions Hydrogen as the fuel has the highest flame temperature, requires the most mass amount of oxidant/air 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/air, there is no CO2 present in the combustion products. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.
  • 27.
    Power Cycle Components/Processes --26 -- Expansion This section provides an isentropic expansion analysis when the working fluid is air. Analysis In the presented expansion analysis, only air is considered as the working fluid behaving as a perfect gas - - specific heat has a constant value. Ideal gas state equation is valid -- pv = RT. Air enters a turbine at point 1 and it exits the turbine at point 2. Isentropic expansion is considered with no entropy change. Figure 1 presents an expansion schematic layout. Figure 1 - Expansion Schematic Layout
  • 28.
    Power Cycle Components/Processes --27 -- Figure 2 presents an expansion temperature vs entropy diagram. Figure 2 - Expansion Temperature vs Entropy Diagram Figure 3 presents expansion specific power output values for a few typical expansion ratio values. It should be noted that the air enters the turbine at the temperature of 1,500 [K] and the turbine exhaust pressure is always equal to the standard ambient pressure -- 1 [atm] of absolute pressure.
  • 29.
    Power Cycle Components/Processes --28 -- Figure 3 - Expansion Specific Power Output Figure 4 presents expansion power output values for two typical expansion ratio values and a few different working fluid mass flow rate values.
  • 30.
    Power Cycle Components/Processes --29 -- Figure 4 - Expansion Power Output One can notice that both expansion specific power output and power output increase with an increase in the expansion ratio values. As the working fluid mass flow rate increases for a fixed expansion inlet temperature value, the expansion power output values increase too. Assumptions Working fluid is air. There is no friction and heat transfer. Expansion is isentropic -- there is no entropy change. Ideal gas state equation is valid -- pv = RT. Air behaves as a perfect gas -- specific heat has a constant value.
  • 31.
    Power Cycle Components/Processes --30 -- Governing Equations T1/T2 = (p1/p2)(ϰ-1)/ϰ ϰ = cp/cv cp - cv = R pv = RT w = cp(T1 - T2) W = cp(T1 - T2)m Input Data T1 = 1,500 [K] p1 = 5, 10 and 15 [atm] p2 = 1 [atm] R = 0.2867 [kJ/kg*K] cp = 1.004 [kJ/kg*K] ϰ = cp/cv - for air ϰ = 1.4 [/] m = 50, 100 and 150 [kg/s] Results Specific Power Output vs Expansion Ratio Expansion Inlet Temperature = 1,500 [K] Expansion Ratio [/] Specific Power Output [kW/kg/s] 5 555 10 726 15 811
  • 32.
    Power Cycle Components/Processes --31 -- Power Output vs Expansion Ratio for a few Mass Flow Rates Expansion Inlet Temperature = 1,500 [K] Power Output [MW] Mass Flow Rate [kg/s] Expansion Ratio [/] 50 100 150 5 27.76 55.51 83.27 15 40.56 81.13 121.69
  • 33.
    Power Cycle Components/Processes --32 -- Conclusions Both expansion specific power output and power output increase with an increase in the expansion ratio values. As the working fluid mass flow rate increases for a fixed expansion inlet temperaure, the expansion power output values increase too. When you get a chance, please visit the following URL: http://www.engineering-4e.com The above URL provides lots of free online and downloadable e-material and e-solutions on energy conversion.