Untitled - Aerobib - Universidad Politécnica de Madrid

324 CHAPTER 13. COMBUSTION OF LIQUID FUELS
1) Augmentation of the energy transmitted by radiation from the flame to the droplet
which increases very rapidly with pressure.
2) Augmentation of the rate of chemical reactions which could be very significant
if the burning velocity of the droplet would depend, even if only slightly, on the
said reaction rate, contrary to what is postulated in the present theory.
3) Augmentation of the free convection effects due to the increase of the Grashof
number with pressure.
The theoretical study of such effects is very arduous as it implies taking into
account the influence of radiation, finite thickness of the flame and free convection.
So far this study has not been satisfactorily accomplished.
13.13 Influence of convection
The present theory excludes convection effects. Experiments with suspended droplets
show that the influence of free convection is not significant. Less experimental information
is available for the case of forced convection. Spalding [24] has performed
some measurements for very large Reynolds numbers (from 400 to 4 000). His experiments
show that for this range the burning velocity of droplets with forced convection
can be computed by applying the Frössling formula 11 for the evaporation with no
combustion. Spalding’s experiments bring forth the fact that, at least in the analyzed
range, two different combustion states can exist. For convection velocities lower than
a given critical value, a semi-spherical flame surrounds the front part of the droplet,
whilst in the opposite side a long wake forms with a strong formation of carbon. If the
convection velocity is larger than the critical value the front flame extinguishes and
the wake flame remains. It is questionable whether this second state also produces in
the case of very small droplets.
Spalding explains this extinction as follows. Even in the present theory the
thickness of the flame is assumed to be zero, actually it is finite. Now, the convection
activates evaporation and increases the flame thickness in order to burnt the largest
quantity of fuel that must be consumed per second. But such an increase in thickness
is accompanied by a decrease in the maximum temperature of the flame. Since reaction
rate changes very rapidly with temperature if the said decrease is large enough
the reaction is incomplete and combustion extinguishes. The same occurs in diffusion
flames. 12
11 See Eq. (13.106)
12 See chapter 12.
When assuming a reaction rate of the Arrhenius type, Spalding’s calcula-