Page 368 - Advanced thermodynamics for engineers

16.4 DIESEL (COMPRESSION IGNITION) ENGINES 357

first fuel that is injected into the cylinder is not ready to ignite until it has evaporated and produced the
necessary conditions for hypergolic combustion. This takes a finite time, referred to as the ignition
delay period, during which the fuel is prepared but not yet ignited. At the end of this period, there is
rapid combustion of the premixed fuel and air, which gives rise to a high rate of heat release and
produces high temperatures in the combustion chamber. This period has a major effect on the amount
of NO x produced in the engine. Typical equations for the ignition delay period are:

0:446 e ð4650=T igÞ
t ig ¼ 1:19 ms (16.15a)
p ig
Or one developed by Hardenberg and Hase (1979)

h i
0:63

1 1 21:2
E A <T 17190 p 12:4
t ig ¼ 0:36 þ 0:22V p e crank angle (16.15b)
where
V p ¼ mean piston speed (m/s)
p ¼ pressure (bar)
T ¼ temperature (K)
E A ¼ activation energy ¼ 618,840/(CN þ 25)
CN ¼ cetane number
Both Eqns (16.15a) and (16.15b) have a similar form, and are related to the Arrhenius equation
introduced in Section 14.3 to define the rate equations. Equation (16.15b) is a more recent formulation
than Eqn (16.15a), and has a more complex structure. Both equations are the result of experimental
tests on engines with a range of fuels, and cannot be extended far beyond the regime under which they
were evaluated, but they do give a basic structure for ignition delay. It should be noted that Eqn
(16.15b) contains a term for the CN of the fuel. The value of E A reduces as the CN increases and this
means that the ignition delay is inversely related to CN. A mechanical method for limiting the overall
ignition delay is to use two-stage or split injection. In this type of system, a small quantity of pilot fuel
is injected into the cylinder some time prior to the main injection process. The pilot charge is prepared
and ready to ignite before the main charge enters the chamber, and in this way, the premixed
combustion is limited to the pilot charge.
After the premixed period is over the main combustion period commences, and this is dominated
by diffusion burning, controlled by the mixing of the fuel and air. Whitehouse and Way (1970)
attempted to model both periods by the two equations given below.
Reaction rate
Z a

E A
K p O 2
R ¼ p ffiffiffiffi e T ðP RÞda (16.16a)
N T
a inj
and, preparation rate
0
P ¼ K m ð1 xÞ x Þ z (16.16b)
u
i m ðp O 2