Untitled - Aerobib - Universidad Politécnica de Madrid

13.5. NOTATION 307
2) The phenomenon is quasi-stationary.
3) Combustion takes place at constant pressure.
4) The droplet temperature is uniform and equal to the boiling temperature of the
fuel at ambient pressure.
5) The chemical reaction takes place upon a spherical surface, named the flame
front. Fuel vapours and oxygen diffuse in the stoichiometric ratio towards this
flame front from which the burnt gases flow. The gases that reach the flame front
react instantaneously. Thereby, on the flame front both the mass fractions of fuel
vapours and of oxygen are zero.
6) Only three chemical species exist, namely: fuel, oxygen and inert gases.
These assumptions allow a simple analysis of the problem and lead to results
which have been experimentally confirmed. Such a treatment of the problem has been
applied by Godsave [19] and Spalding [3] in England, and by Penner and Goldsmith
[20] in the U.S.A. Aside from the aforementioned assumptions Godsave and Spalding
also assume that transport coefficients are independent from temperature by adopting
a mean value for these coefficients. This rather arbitrary assumption reduces appreciably
the suitability of the method. In fact, for the existing range of temperatures, these
coefficients can vary in a ratio of ten to one. Goldsmith and Penner take into account
this variation as well as that of heat capacities. The following study is mainly based
on the work of these two authors but it assumes that heat capacities are independent
from temperature since their variation has no substantial influence on the results.
13.5 Notation
In the present study the notation used in the preceding chapter will be completed with
the following (see Fig. 13.1):
M = Droplet mass
m = Mass flow across a closed surface surrounding the droplet.
q l = Latent heat of evaporation per unit mass of fuel.
r = Radial distance to the center of the droplet.
v = Radial velocity of the mixture.
v j = Radial velocity of species A j .
v jd = Radial diffusion velocity of species A j .
Y j = Mass fraction of species A j .
ν = Stoichiometric ratio of oxygen mass to fuel mass.