Troels Dyhr Pedersen.indd - Solid Mechanics

9 Heat release calculations
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9.1 The Heat Release analysis
In order to visualize the rate of the combustion it is necessary to perform a heat release
analysis. This analysis can provide the crank angle resolved rate of combustion.
The heat release analysis [18] looks as follows:
dQ V
HR dQwall
d(
m c T ) γ dV 1 dp
+ + = p ⋅ + V ⋅
dθ
dθ
dθ
γ − 1 dθ
γ − 1 dθ
In this expression the terms on the left hand side are the chemical heat release, the wall
heat transfer and the energy loss related to mass escaping the process. The mass loss is
most often insignificant and is therefore usually not included.
The heat transfer is in the order of +/- 2 Joule per CAD for a 1 liter cylinder. The heat
release is in the order of 10-100 Joule per CAD or higher. The magnitude and shape of
the heat release rate are therefore not affected much by the heat transfer. In many
situations it is therefore irrelevant to improve the accuracy with the additional term for
heat transfer. Only if the accumulated heat release and combustion efficiency is of
interest should this be required.
9.2 Location of TDC
The mechanical TDC position of the engine is possibly the most critical parameter in the
heat release analysis. The impact of a deviation between the estimated and real TDC
position on the IMEP with a typical combustion cycle can be seen in table 2.
Table 2: Influence of TDC offset on IMEP calculation
Position offset (CAD) -2.0 -1.0 -0.5 -0.1 0 +0.1 +0.5 +1.0 +2.0
IMEP 406 446 467 483 487 491 507 527 567
Deviation (%) -16 -8 -4 -0.8 0 +0.8 +4 +8 +16
It is clear that even a minor deviation from the correct TDC results in a significant error
in the IMEP calculation.
The peak pressure may be used as a preliminary indicator of the TDC. This assumption
will result in a certain deviation depending on the engine size, as heat losses will reduce
the pressure and cause it to peak shortly before TDC. For 4-stroke engines in typical
vehicles the peak pressure may appear around 0.5 CAD before TDC, whereas for small
two stroke engines the peak pressure may appear as much as 2 CAD before TDC due to
relatively high heat losses in such small engines.
It is possible to locate the TDC with reasonable accuracy with the cylinder head removed.
Positioning the crank angle encoder so that the z-pulse occurs exactly in this position is