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Compression Introduction 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 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.
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.
Figure 4 - Compression Power Input One can notice that both compression specific power input and power input increase with the compression ratio. As the working fluid mass flow rate increases, 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. Governing Equations T2/T1 = (p2/p1)(k-1)/k k = cp/cv w = cp(T2 - T1) W = cp(T2 - T1)m Input Data T1 = 298 [K] p1 = 1 [atm] cp = 1.004 [kJ/kg*K] k = cp/cv - for air k = 1.4
[/] Results Specific Power Input vs Compression Ratio
Power Input vs Compression Ratio for a few Mass Flow Rates
Figures
Conclusions Both compression specific power input and power input increase with the compression ratio. As the working fluid mass flow rate increases, the compression power input requirements increase too. References JANAF Thermochemical Data - Tables, 1970 Stoichiometric Combustion (Carbon, Hydrogen, Sulfur, Coal, Oil and Gas) Introduction 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 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 minus the combustion products enthalpy value at the standard reference temperature, which is 298 [K]. When the reactants enthalpy value is equal to the combustion products enthalpy value, one can calculate the combustion products flame temperature or adiabatic temperature. Figure 1 presents the reactants and combustion products enthalpy value change with an increase in the temperature.
Figure 1 - Reactants and Combustion Products 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 presents how the reactants and combustion products species enthalpy values change with the temperature. The physical properties provided in Figure 2 come from the JANAF Thermochemical Data - Tables, 1970.
Figure 2 - Reactants and Combustion Products Species Enthalpy vs Temperature It is interesting to note that the 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 enthalpy value is 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 fuel and oxidant compositions. 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 the only gas fuel considered. In order to keep the combustion analysis simple and straightforward, the CH4 composition is provided on the weight basis. Oxidant composition is usually given on the mole/volume basis. Table 1 provides the fuel composition. Table 1 - Fuel Composition
Table 2 provides the standard air composition. Table 2 - Oxidant Composition
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
Table 4 provides the combustion products composition on the volume basis. Table 4 - Combustion Products Composition on the Volume Basis
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 fuel higher heating value. Table 5 - Combustion Products Flame Temperature,
Stoichiometric Oxidant to Fuel Ratio
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 11.433 [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. 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.
Species Molecular Weight
Stoichiometric Fuel, Oxidant and Combustion
Products
Stoichiometric Fuel, Oxidant and Combustion Products
Governing Equations Fuel higher heating value (HHV) or heat of combustion is the difference between the reactants enthalpy value minus the combustion products enthalpy value at the standard reference temperature, which is 298 [K]. When the reactants enthalpy value is equal to the combustion products enthalpy value, one can calculate the combustion products flame temperature or adiabatic temperature. Input Data Table 1 - Fuel Composition
Table 2 - Oxidant Composition
Results Table 3 - Combustion Products Composition on the Weight Basis
Table 4 - Combustion Products Composition on the Volume Basis
Table 5 - Combustion Products Flame Temperature,
Stoichiometric Oxidant to Fuel Ratio
Figures
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 the largest fuel higher heating value. When hydrogen reacts with oxidant/air, there is no CO2 present in the combustion products. References JANAF Thermochemical Data - Tables, 1970 Expansion Introduction 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 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.
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.
Figure 4 - Expansion Power Output One can notice that both expansion specific power output and power output increase with the expansion ratio. As the working fluid mass flow rate increases, 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. Governing Equations T1/T2 = (p1/p2)(k-1)/k k = cp/cv w = cp(T1 - T2) W = cp(T1 - T2)m Input Data T1 = 1,500 [K] p1 = 5, 10 and
15 [atm] cp = 1.004 [kJ/kg*K] k = cp/cv - for air k = 1.4
[/] Results Specific Power Output vs Expansion Ratio
Power Output vs Expansion Ratio for a few Mass Flow Rates
Figures
Conclusions Both expansion specific power output and power output increase with the expansion ratio. As the working fluid mass flow rate increases, the expansion power output values increase too. References JANAF Thermochemical Data - Tables, 1970 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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