P ISTON E NGINE AND C OMBUSTION P ROCESS
6.4 Examples
6.4.1 Case Study – Octane Fuel Analysis
A chemical reaction is presented by equation (89), where liquid octane is used in a complete combustion process with theoretical air (enthalpy of formation data along with the heat values are presented in Table 21)—
8 18 12.5 2 3.76 2 9 2 8 2 47 2
C H O N H O CO N . Calculate:
(a) adiabatic flame temperature, and (b) analyze the combustion process.
To calculate the adiabatic flame temperature, equation (102) is applicable, which is a simplified form of equations (99) and (100). This is an adiabatic process happening at standard combustion conditions (i.e., 25 °C, 101.325 kPa). The enthalpy of ideal gases as a function of the temperature is available in the literature. In this situation, the total enthalpy of formation of the products is the same as that of the reactants—equation (102)—
meaning that the difference is zero when maximum flame temperature is reached. Employing the enthalpy for different temperatures results in the balance of energy expressed by equations (103) and (104).
i f o f
i o
R P
n h h n h h
(102)flight.indb 119
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1 249,952 0 12.5 0 0 47 0 0
249,952 kJ kmol
i f
R i
n h h
(103)
2 2
2 2 2
2 2 2
9 241, 827 8 393, 522
47 0 0 0 5, 324, 619 9
8 47 0 kJ
kmol
o f H O CO
P o
N O H O
CO N O
n h h h h
h h h
h h h
(104) Figure 41 shows temperature versus the total heat release in the chemical reaction presented by equation (89). Based on the previous discussion, the total heat release is to be zero (x 0) for the adiabatic flame temperature to be calculated, meaning that the heat release associated with the reactants—equation (103) and equation (104)—should be equal. Using a trial and error technique, an adiabatic flame temperature of 2,412.1 K is found for theoretical air for the 12.5 moles of air mixture available for the combustion process. This is the maximum temperature that the engine may be exposed to; therefore, it can be used as a design criterion when selecting the material for the piston and cylinder in addition to making engine performance calculations. For 12 percent excess air (i.e., 14 moles of air mixture), an adiabatic flame temperature of 2,225.7 K is obtained.
FIGURE 41 Absolute adiabatic flame temperature versus the total heat release for equation (89) for octane.
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With the increase of excess air, the adiabatic flame temperature decreases as shown in Figure 42 and Figure 43—meaning the process does not require exerting itself for complete combustion to occur. For actual air that is four times the amount of theoretical air (A/At), an adiabatic flame temperature of 945.4 K is obtained. This means that if the fuel mixture is to be enriched in a piston engine, the fuel consumption will increase, and if the amount of air molecules decreases—for example, in higher
FIGURE 42 T otal heat release versus the absolute adiabatic flame temperature for octane-heptane for different mass ratios of the actual air to the theoretical air.
FIGURE 43 To tal heat release versus the mass ratio of the actual air to the theoretical air for octane-heptane for different absolute adiabatic flame temperatures.
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altitudes—the fuel consumption may be decreased by leaning the mixture in a piston engine. It is possible that a concave diagram curving downward is obtained, provided that more data points are added to the diagram of the mass ratio of the actual air to the theoretical air—Figure 44 and Figure 45.
Neverthele ss, it is possible to predict the adiabatic flame temperature trend by interpolating the three sets of data given a valid trend based on the linear relationship (Figure 44) or the power relationship (Figure 45) to present the mass ratio of the actual air to the theoretical air versus the heat release.
It is possible to present the total heat release as a function of the combustion temperature or the mass ratio of the actual air to the theoretical air (A/At) (Figure 44 and Figure 45). The individual models depicting the influence of each of these single variables on the heat release during combustion have been presented inside the diagrams for the upper and lower limits of either temperature or the mass ratio of the actual air to the theoretical air. Performing regression analysis, you may obtain a relationship that considers both variables as independent components into the expression for heat release of combustion presented by equation (105)—where T is the absolute temperature (K) and Qc v. .is the heat release during combustion (kJ/kmol).
FIGURE 44 Total heat release and mass ratio of the actual air to the theoretical air versus the absolute adiabatic flame temperature for octane, linear curve-fit.
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FIGURE 45 Total h eat release and mass ratio of the actual air to the theoretical air versus the absolute adiabatic flame temperature for octane, power curve-fit.
Table 22 and Figure 46 present the analysis summary and normal probability plot for the regression analysis. It is seen that the relationship between the heat releases of combustion and air ratios as well as absolute temperatures are statistically significant and may be expressed with a confidence level above 87 percent. At adiabatic conditions, no heat enters or leaves the control volume, so term Qc v. .(kJ/kmol) is ignored and T(K) would approximately be the adiabatic flame temperature, which varies with the mass ratio of the actual air to the theoretical air.
. . 15909509 2333822 7554
c v
Q A T
At (105)
Heat release as a fun ction of the temperature presented by equation (105) in kJ/kmol may be multiplied by the molecular mass in kmol/kg of the fuel to obtain the energy per mass of the fuel (kJ/kg)—also known as the specific energy. This energy then may be employed per duration of operation to represent the specific energy per time that is also known as horsepower per unit mass of the fuel (specific horsepower) in combination with the engine efficiency.
TABLE 22 Model summa ry for the regression analysis for the heat release combustion model for octane as a function of the mass ratio of the actual air to the theoretical air
and adiabatic flame temperature presented by equation (105).
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FIGURE 46 Normal proba bility plot for the regression analysis for the heat release combustion model for octane as a function of the mass ratio of the actual air to the theoretical air and adiabatic flame temperature presented by equation (105).