Page 350 - Advanced thermodynamics for engineers

15.4 FLAMES 339

Burned Burned Unburned
gas gas gas

Laminar Turbulent (wrinkled)
flame flame

FIGURE 15.11
Comparison of laminar and turbulent flames.

The theory of turbulent flames was initiated by Damkohler (1940) who showed that the ratio of
turbulent to laminar flame speeds, based on large scale eddies in the flow, is
r ffiffiffi
u t ε
¼ ; (15.14)
u [ n
where
ε ¼ eddy diffusivity
v ¼ kinematic viscosity of the unburned gas.
Experience shows that in spark-ignition engines the flame speed factor is a strong function of
engine speed but not greatly affected by load. Experiments by Lancaster et al. (1976) have also shown
that the level of turbulence intensity in an engine cylinder increases with engine speed, but is not quite
proportional to it. This means that while turbulence increases the flame speed significantly the length
of the burning period increases as engine speed is increased, which explains why the ignition timing
has to be advanced.

15.4.6 ENGINE COMBUSTION MODELS
The main aims of an engine combustion model are to be able to predict:

• the rate of burning in the cylinder
• the power output of the engine
• the emissions of the process
• the heat transfer to the cylinder liner to evaluate the thermal stresses
• the exhaust gas conditions

The combustion model should also enable the emissions to be calculated prior to the catalyst, the
flow in the exhaust system, and the energy for matching a turbocharger. In addition it might be able to
predict the cyclic irregularity that might occur under certain conditions. An excellent summary of
engine combustion models is given in Heywood (1994).