Design and Simulation of Two Stroke Engines

Chapter 4 - Combustion in Two-Stroke Engines
The researchers, Lavoie et al. [4.41], have suggested that the reaction described by,
O + OH f) 02 + H (A4.1.13)
should also be included. This statement should not be disregarded as the argument for its
inclusion with the Zelovitch equations from above is that during rich and near stoichiometric
air-fuel ratios this third, rate-limiting condition prevails. If this model is used to predict the
formation rate of NO in the cylinder of a compression-ignition engine, where the richest
trapped air-fuel ratio will approximately be a value of 20, then the NO rate model may be able
to exclude this third, rate-limiting equation.
The NO formation rate is much slower than the combustion rate and most of the NO is
formed after the completion of the combustion due to the high temperatures present in the
combustion zone. Therefore Eqs. A4.1.11 and A4.1.12 are decoupled from the combustion
model.
It was reported by researchers [4.41,4.42] that measurements of the NO formed in the
post-flame-front zone was greater than that predicted by the reaction kinetics. Several models
have been formed to deal with this scenario, which is due to "prompt NO" formation.
The reaction kinetics which are an integral part of the model are generally formulated
under ideal laboratory conditions in which the combustion occurs in a shock tube, but clearly
this is somewhat remote from the closed cycle combustion taking place in the spark-ignition
or the compression-ignition engine.
The temperature calculated in the cylinder as a product of the increase in pressure corresponding
to the period of burn is the average in-cylinder temperature. This temperature is the
product of two distinct zones in the cylinder, namely the burn zone comprising the products of
combustion and the unburned zone composed of the remaining air and exhaust gas residual.
From researcher De Soete [4.42], it was proposed that a greater rate of NO formation was
recorded in the post-flame zone whose temperature has been raised by the passing flame. To
emulate this, the NOx model uses the average temperature, Tb, in the burn zone. As described
previously, the flame packet contains air, fuel and exhaust gas residual. This packet mass
varies with time step and its position during the heat release process. At the conclusion of the
burning of each packet in the computation time step, normally about 1° crankshaft, the burn
zone has new values of mass, volume, temperature, and oxygen and nitrogen mass concentrations.
The NO rate formation model may now be generally described as follows:
dNO , .
= k xf
dt
m b02> m bN2' V b> T b] (A4.1.14)
where Vb is the volume of the burn zone, Tb is the temperature in the burn zone and k is a ratelimiting
constant. The symbols, mb 0 and mb N refer to the mass of oxygen and nitrogen,
respectively, within the burn zone. Once the formation of NO is determined as a function of
time, its formation in any given time-step of an engine simulation is determined, and the
summation of that mass increment over the combustion period gives the total mass formation
of the oxides of nitrogen.
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