Combustion Process

P ISTON E NGINE AND C OMBUSTION P ROCESS

6.2 Combustion Process

For an incompressible flow, where central locations of the inlet and constricted areas are at the same level, equation (87) may be simplified to equation (88)—assuming that the volumetric flow rate (Q) is constant throughout the tube.

i i i c c c o o o

m  A v   A v   A v (86)

 

1 2

2 1

i c

c i

i c

c c

c c i i

P P

g z z

m A

A A

 

  

 

 

 

    

   

 

 (87)

 

2

2 1

i c

c

c i

P P Q A

A A

 

  

  

  

 

(88)

of the fuel (also known as the octane number). In diesel engines, the lower the octane number and the higher the cetane number (inverse of the octane number) is, the better the performance is expected to be. These two numbers both indicate ignition readiness, if the fuel ignites spontaneously or not. Spark plugs ignite the air-fuel mixture at the end of the compression phase in a piston engine. An increased fuel compression ratio is necessary to reduce the knocking that is common for fuels with higher octane numbers.

The optimum balance between octane and heptane numbers is 0.9 to 1.

Any fuel mixture with a high likelihood of knocking has an ideal octane to heptane ratio—also known as an octane rating—of 90. Any combustion process using an amount of air that deviates from that of the stoichiometric one either includes excess air among the by-products or leads to an incomplete process with formation of carbon monoxide and nitrogen oxide as its by-products. The existence of contamination (e.g., water, debris, and color variation) in the fuel may be spotted by discharging some from the fuel tank sump into a clear bottle and investigating the content of the bottle.

In reality, more air molecules are needed for a combustion process to be complete for efficiencies that are less than ideal. For example, for gasoline piston engines to operate close to their peak, the air-to-fuel ratio of 14 to 1 is recommended for operation, which is 12 percent extra air than the theoretical air shown previously. This ratio is to be honored to comply with fuel economics. As the aircraft climbs, the air density decreases with increasing altitude, and fewer molecules are available per unit volume of air; therefore, to make the same air-to-fuel ratio possible you need to lean the mixture. This becomes particularly important for long haul flights—for example, your favorite cross-country. The chemical reaction for this combustion process is presented by equation (90), where fourteen molecules of oxygen are mixed with one octane molecule. It is seen that the combustion by-products consist of molecules of water (H₂O), carbon dioxide (CO₂), nitrogen (N₂), and oxygen (O₂). Note that in a complete combustion process with excess air, the possibility for creation of nitrogen oxides (NO_x) exists; however, it has been ignored in this case.

 

8 18 14 2 3.76 2 9 2 8 2 52.64 2 1.5 2

C H  O  N ^ H O CO  N  O (90)

Assuming that the combustion process is incomplete, meaning that carbon monoxide (CO) and nitrogen oxides (NO_x) are also a by-product of the process, the chemical reaction may be represented by equation (91)—

where y is the number of released oxygen molecules given by equation (92) and m and n are multipliers for the ideal process that is larger than one.

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 

8 18 14 2 3.76 2

nC H  m O  N ^

   

2 2 2 2

9nH O8CO 8 n1 CO 52.64m t N yO 2tNO_x (91)

28 17 8 2

2

m n tx

y   

 (92)

Theoretical air for a complete combustion process to occur when burning AVGAS consisting of an octane-heptane combination is presented by equation (93). It is seen that the combustion by-products consist of molecules of water (H₂O), carbon dioxide (CO₂), and nitrogen (N₂).

 

8 18 7 16 23.5 2 3.76 2 17 2 15 2 88.36 2

C H C H  O  N ^ H O CO  N (93) As mentioned earlier, more oxygen molecules are needed to make the combustion process a complete one. If the same excess air (112 percent) as used earlier for complete combustion of the octane is now employed for an octane-heptane combination, equation (94) is obtained.

 

8 18 7 16 2 2 2 2

2 2

26.32 3.76 17 15

98.96 2.82

C H C H O N H O CO

N O

    

  (94)

Assuming that you do not know the optimum value for the fuel-to-air ratio for a complete combustion process of octane-heptane, this chemical reaction can be presented by equation (95)—where y is the number of released oxygen molecules given by equation (96) and r is the number of oxygen and nitrogen molecules that is larger than one.

 

8 18 7 16 2 2 2 2

2 2

23.5 3.76 17 15

88.36

C H C H r O N H O CO

rN yO

    

 

(95)

 

47 1

2

y r

 (96)

If an incomplete combustion of octane-heptane is employed that affects both engine efficiency and the environmental impact of gasoline burning into the atmosphere, chemical reaction (97) may be written—where y is the number of released oxygen molecules given by equation (98), and n and p are multipliers for the ideal process that are larger than one.

   

8 18 7 16 23.5 2 3.76 2 9 8 2 15 2

nC H pC H  q O  N ^ n p H O CO 



8n7p15



CO



88.36q0.5t N



2yO2tNO_x (97) 47 17 15 15

2

q n p tx

y    

 ⁽⁹⁸⁾

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Using any of the previous chemical reactions, you are able to calculate the heat of combustion using the enthalpy of the input and output products.

Heats of combustion for octane (44.427 MJ/kg  19,104 BTU/lb) and hep- tane (44.566 MJ/kg  19,163 BTU/lb) are available in the literature—with the heptane generating more energy of about 139 kJ/kg (59.76 BTU/lb) of fuel. As a 2,2,4-trimethylpentane, isooctane generates about 44.310 MJ/kg (19,053 BTU/lb) of energy, falling behind heptane by 260 kJ/kg (111.78 BTU/

lb) of fuel. Heats of combustion for most commonly used AVGAS fuels are presented in Table 21 [135,136,137,138].

Let us discuss the energy exchange proc e ss t ha t fuel is to achieve in order to ensure an effective and efficient combustion and hence an im- proved engine performance. The first law of thermodynamics expressed by equation (53)—dU  dQ  dW—states the conservation of energy principle in the form of heat and work. For a flow moving inside and outside of a control volume, similar to the venturi flow shown in Figure 37, the inflow and outflow share this energy transfer. This energy is in the form of kinetic energy (due to the flow velocity), potential energy (due to the elevation), and internal energy. Change in internal energy is due to changes in tem- perature of the fluid molecules and also due to the changes in pressure and the boundaries of the control volume interacting with the fluid. The combi- nation of internal, kinetic, and potential energy is the energy that is brought in or taken away by the flow. Conservation of energy then is defined using equation (99)—where “R” and “P” are the subscripts for reactants (inputs) and products (outputs), respectively.

. . . .

c v i f c v o f

i o

R P

Q 



n h ^ hW 



n h ^ h ⁽⁹⁹⁾ It is assumed that the enthalpy of formation for the elements at 25 °C and 101.325 kPa is zero—this is the reference point where the element, gas, solute, or substance is at its pure one-phase form or the most stable state. Flow enthalpy at a desired temperature is the enthalpy value at the reference point and enthalpy difference between the desired state and the reference point. For example, when carbon dioxide is produced from elements of oxygen and carbon, the enthalpy of the formation of the carbon dioxide product is the amount of heat required to create it by joining the reactants. This enthalpy of formation may be negative or positive depending on whether the process is exothermic or endothermic—

meaning that the standard enthalpy of the products is less or more than the standard enthalpy of the reactants. The formation of carbon dioxide (CO₂) from the original elements is an exothermic process, meaning that energy is released to the environment, and therefore its enthalpy of formation is

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negative (393,522 kJ/kmol); on the other hand, the formation of ozone is an endothermic process, meaning that energy is absorbed, and therefore its enthalpy of formation is positive (142,700 kJ/kmol). The third atom of oxygen in the ozone molecule (O₃) is the atom that is reattached to other molecules and as a result changes their chemical composition and their interaction with other molecules. Vegetation generally can absorb up to 20 percent of the ozone produced by the atmosphere, and that is the testament to their paramount role in keeping other living creatures safe.

During heat waves where plants are stressed and close the small pores on their leaves (stomata) so that water evaporation is reduced, they do not absorb pollutants and ozone. The excess ozone in the atmosphere therefore creates adverse health conditions such as damaged lungs, chest pain, throat irritation, and different types of respiratory problems—an example is the loss of 460 lives in the United Kingdom during the heat waves of the summer of 2006 [139,140]. The enthalpies of formation of some aviation reactants and products are given in Table 21.

TABLE 21 Heat values of common AVGAS fuels (“l” and “g” stand for liquid and gas) [135,136,137,138].

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If the process of combustion is adiabatic, and there is neither work nor heat generated—that is, no heat transfer occurs—the products reach the adiabatic burn (flame) temperature, and only enthalpy terms remain in equation (99). This is the maximum temperature to which the reactants may be exposed, since there is no waste of heat from the initial elements or as the by-product of the incomplete combustion.

Figure 38 shows the enthalpy of formation versus the absolute temperature for water vapor. Three sets of curves are presented, with two labeled as modeled for heat capacities at constant pressure, both temperature-dependent and temperature-independent. The one from the published data in thermodynamic tables is somewhat closer to those of the temperature-dependent heat capacities at constant pressure; however, they underpredict the value of heat formation. For lower values of absolute temperature, the first and second order terms may be ignored, and therefore the predicted relationship shows a linear relationship between the enthalpy of formation and absolute temperature.

Figure 39 shows the mass ratio of the actual air to the theoretical air versus the absolute adiabatic flame temperature for the octane and octane- heptane fuels using equations (105) and (108), which will be discussed in the case studies. The temperatures for the given air mole mixture for these two fuels are very similar; therefore, the average of the two is curve-fitted and represents the adiabatic flame temperature versus the air ratios as a design criterium guidance for similar scenarios. The details of the models are presented in the case studies at the end of this section.

FIGURE 38 Enthalpy of formation for water vapor versus the absolute temperature for constant and temperature-dependent heat capacities.

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FIGURE 39 Mass ratio of the actual air to the theoretic al air versus the absolute adiabatic temperature for octane and octane-heptane fuels.