Page 353 - Advanced thermodynamics for engineers

342 CHAPTER 15 COMBUSTION AND FLAMES

It is not proposed to discuss Eqn (15.22), but just to show how complex flame speed models can
become. This equation includes a whole range of terms similar to those shown in Fig. 15.9, and this
indicates that an incredibly detailed knowledge of the flow in the engine combustion chamber would
be required before the equation could be used.

15.4.7 DIFFUSION FLAMES
The previous sections all related to premixed flames of the type found in Bunsen burners, or spark-
ignition engines. The other major class of flames is called diffusion flames; in these flames the rates
of reaction are not controlled by the laminar flame speed but by the rate at which the fuel and air can be
brought together to form a combustible mixture. This type of combustion occurs in
• Open flames, when mixing with secondary air enables combustion of a rich premixed core to
continue to completion;
• Gas turbine combustion chambers, when the liquid fuel sprays are mixed with the air in the
combustion chamber;
• Diesel engines, when the injected fuel has to mix with the air in the chamber before
combustion can take place.

A typical arrangement of a diffusion flame might be that shown in Fig. 15.12.Thisisa
simple example of a jet of hydrogen passing into an oxygen atmosphere. The principle is the same if
the fuel is a more complex gaseous one passing into air, the major difference will be that the products
of combustion will be more complicated. The three sections across the jet (at A, B and C) show the
wayinwhich theoxygendiffusesintothe jet, usually by turbulent mixing brought about by the jet
entraining the surrounding oxygen. At Section A the hydrogen and oxygen are completely separate,
as indicated bythe mass fraction curves.BySection B, some wayfromthe endofthe nozzle,
the hydrogen has been mixed with the oxygen just outside the jet diameter due to turbulent
entrainment. There has not yet been any mixing of hydrogen and oxygen in the potential core. Some
combustion has also taken place by this section, as indicated by the mass fraction of water. Section C
is located almost at the end of the mixing zone, after the end of the potential core and there
is no pure hydrogen left in the jet. The edge of the mixing zone is now well within the diameter of
the jet.
Considering the concentration of hydrogen and oxygen along the centreline of the jet, it can be seen
that there is pure hydrogen right up to the end of the potential core. After that the hydrogen and oxygen
on the centreline combine to form water, and it is not until the end of the mixing zone that the oxygen
concentration starts to rise again, as the water and oxygen mix and dilute each other.
In this example it has been assumed that the oxygen and hydrogen burn as soon as they come
intimately in contact. This presupposes that the chemical reaction rate is much faster than the diffusion
rates: this is usually a reasonable assumption.
A similar, but more complex analysis may be made of the injection of diesel fuel into the cylinder
of a diesel engine. In this case the entrainment of the fuel and air does not take place in the gaseous
phase, but occurs because the droplets of fuel leaving the nozzle impart their momentum on the
surrounding air by aerodynamic drag. Once the fuel and air are mixed it is possible for the droplets to
evaporate to create a combustible mixture. The details of diesel combustion are beyond this text, but
the principles are similar to the combustion of gaseous jets. Diesel engine combustion is discussed in