Effect of Gasoline Fuel Additives on Combustion and Engine Performance

2.4.1
 
Heat Release Analysis 
The most widely used technique for determining combustion efficiency and 
characteristics in IC engines is heat release analysis. In cases where optical access is 
not possible or suited, pressure change caused by the combustion can be used to 
characterise the combustion rate. Stone [163] explains that heat release analysis allows 
for calculation of the quantity of heat required to cause an observed pressure change 
within a control volume. Applying the 1
st
Law of Thermodynamics to a control volume 
with no mass transfer allows the heat released by a combustion event to be expressed 
as: 
𝛿𝑄
ℎ𝑟
= 𝑑𝑈 + 𝛿𝑊 + 𝛿𝑄
ℎ𝑡
2.12 
Assuming the reactants and products have same properties and that there is no 
temperature gradient throughout the gas mixture, the terms in Equation 2.12 can be 
evaluated as follows: 

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2.4 Combustion Analysis 
62 
𝑑𝑈 = 𝑚𝑐
𝑣
𝑑𝑇
2.13 
and 
𝛿𝑊 = 𝑝 𝑑𝑉
2.14 
Rearranging the equation of state,
𝑝𝑣 = 𝑚𝑅𝑇,
gives: 
𝑚𝑑𝑇 =
1
𝑅
(𝑝𝑑𝑉 + 𝑉𝑑𝑃)
2.15 
Substituting Equation 2.15 into Equation 2.13: 
𝑑𝑈 =
𝑐
𝑣
𝑅
(𝑝𝑑𝑉 + 𝑉𝑑𝑃)
2.16 
Substituting Equations 2.14 and 2.16 into Equation 2.12 gives: 
𝑑𝑄
ℎ𝑟
𝑑𝑡
=
𝑐
𝑣
𝑅
(𝑝
𝑑𝑉
𝑑𝑡
+ 𝑉
𝑑𝑝
𝑑𝑡
) + 𝑝
𝑑𝑉
𝑑𝑡
+
𝑑𝑄
ℎ𝑡
𝑑𝑡
2.17 
Assuming
𝛾 =
𝑐
𝑝
𝑐
𝑣
, 
𝑅 = 𝑐
𝑝
− 𝑐
𝑣
and
𝑑𝑄
𝑛𝑒𝑡
𝑑𝑡
=
𝑑𝑄
ℎ𝑟
𝑑𝑡
− 
𝑑𝑄
ℎ𝑡
𝑑𝑡
, Equation 2.17 can be 
expressed as: 
𝑑𝑄
𝑛𝑒𝑡
𝑑𝑡
=
γ
γ − 1
𝑃
𝑑𝑉
𝑑𝑡
+ 
1
γ − 1
𝑉
𝑑𝑃
𝑑𝑡
2.18 
Equation 2.18 includes both, the pressure and volume change terms and takes 
into account of heat lost to the cylinder walls. Frequently, the in-cylinder pressure data 
of an engine is coupled with the piston position to determine the instantaneous volume 
of the cylinder. In that case, the net heat release is usually represented in terms of 
incremental crank angle change, dϑ, instead of time, dt. Heat release analysis can also 
be used in conjunction with optical methods and is utilised in rigs other than research 
engines [164]. 

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2.4 Combustion Analysis 
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