Design and Simulation of Two Stroke Engines

£2 =
Pi
P2
I Pi J
Chapter 4 - Combustion in Two-Stroke Engines
m u2 x V ul
m ul V u2) (A4.2.11)
The volume of the unburned zone, VU2, is the only unknown in the above equation. Consequently,
the volume of the burned zone is:
Vb2 = V2-Vu2
(A4.2.12)
and the temperatures in the two zones may be found using Eq. A4.2.10.
This is arguably a more accurate solution for the single-zone theory described in Sec.
4.4.2. There, the average gas properties for the entire cylinder space are determined as in Eqs.
A4.2.5-A4.2.7, but the individual properties of the trapped air and the burned gas are determined
less realistically using the average cylinder temperature, Ti, instead of the zone temperatures,
Tui and Tbi, employed here. In the example given below, it is clear that this will
induce errors; while not negligible, they are small.
The use of this theory within an engine simulation
In Chapters 4-7, a chainsaw engine is frequently employed as a design example for a
computer simulation. The data used here for the computation are given in Sec. 5.5.1 for the
standard engine. The fuel employed in the simulation is unleaded gasoline with a stoichiometric
air-to-fuel ratio of 14.3. The results of a computer simulation with air-to-fuel ratios of
12, 13, 14, 15 and 16, are shown in Fig. A4.2, on which are displayed the cylinder temperatures
as predicted by this two-zone combustion model. The mean cylinder temperature, and
the temperatures in the burned and unburned zones, are indicated on this figure around the tdc
period. The rapid rise of temperature in the burned zone to nearly 2400°C is clearly visible,
and this peaks at about 10° atdc. The mean cylinder temperature peaks at about 2000°C, but
this occurs at some 30° atdc. The temperature in the unburned zone has a real peak at about
15° atdc, whereas the spike at 50° atdc indicates the engulfement of, and disappearance of,
the unburned zone by the combustion process. The maximum burn zone temperatures recorded
during the simulations are shown in Fig. A4.3, with the highest value shown to be at
an AFR of 13, and not closer to the stoichiometric point, i.e., where X is unity.
The formation of nitric oxide (NO)
The formation of oxides of nitrogen is very, indeed exponentially, dependent on temperature.
In Fig. A4.3, as captured from Fig. A4.2, the results of a simulation incorporating the
two-zone burn model show the peak temperatures in both the burned and the unburned zones
with respect to the same fueling changes. The burn zone temperature reaches a maximum
before the stoichiometric air-to-fuel ratio. The unburned zone encounters its highest peak
temperature at the richest air-fuel ratio.
The Zeldovitch [4.39] approach to the computation of NO formation, as in Eq. A4.1.14,
takes all of these factors into account. The profile of the calculated NO formation, shown in
Fig. A4.4 with respect to air-fuel ratio, is quite conventional and correlates well with the
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