Design and Simulation of Two Stroke Engines

Chapter 4 - Combustion in Two-Stroke Engines
over a crankshaft interval, d0. The increment of fuel mass vaporized and burned during this
time and crankshaft interval is given by dmvap, thus:
dmvap = dmbe = (B0b+de - B0b)mtfhvap
(4.3.40)
Consequently, the loss of heat from the cylinder contents, 5Qvap, for this crankshaft interval,
d0, is found by the employment of the latent heat of vaporization of the fuel, hvap. Numerical
values of latent heat of vaporization of various fuels are to be found in Table 4.1.
5Qvap = dmvaphvap
(4.3.41)
It should be noted that this equation provides a "positive" number for this heat loss, in
similar fashion to the application of Eq. 4.3.34, and that this is soluble only if the mass fraction
burned is available as numerical information.
4.3.6 Heat release data for spark-ignition engines
Already presented and discussed is the heat release and mass fraction burned data for the
QUB LS400 engine in Figs. 4.4 and 4.5. A simple model of the profile of the heat release rate
curve is extracted from the experimental data and displayed in Fig. 4.6. The heat release
period is b°, with a rise time of b°/3 equally distributed about tdc. The ignition delay period is
10°. It will be noted that the heat release rate profile has a "tail" of length b°/3, falling to zero
from about one-sixth of the maximum value of heat release. The total area under the profile in
Fig. 4.6 is the total heat released, QR, and is given by simple geometry, where QR0 is the
maximum rate of heat release:
14b°QRfl
QR = ,. (4.3.42)
36
The actual value of QR0 in Fig. 4.4 is 28.8 J/deg and the period, b°, is 60°. The area under
the model profile in Fig. 4.6 is 672 J, which corresponds well with the measured value of
662.6 J. For a theoretical total heat release of 662.6 J, one would predict from the model a
maximum heat release rate, QR0, of 28.4 J/deg.
The Vibe approach
It is possible to analyze a mass fraction burned curve and fit a mathematical expression to
the experimental data. This is often referred to as the Vibe method [4.36]. The mathematical
fit is exponential with numerical coefficients, a and m, for the mass fraction burned, B0 , at a
particular crankshaft angle, 0b, from the onset of heat release and combustion for a total crank
angle duration of b°. It is expressed thus:
'a \m+l
B0 =l-e
'6b
W ) (4.3.43)
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