Untitled - Aerobib - Universidad Politécnica de Madrid

13.12. COMPARISON WITH EXPERIMENTAL RESULTS AND LIMITATIONS OF THE THEORY 323
0.5
0.4
r 2 s × 102 (cm 2 )
0.3
0.2
0.1
0.0
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
t (s)
Figure 13.5: Experimental results showing the linear dependence between r 2 s and time, obtained
for isooctane in air at ambient pressure.
On the other hand a comparison of the theoretical and experimental radius
of the flame [20] shows that the former is two or three times larger than the latter.
Although formula (13.76) shows that ratio r l /r s is practically independent from
pressure, Wise, Lovell and Wood [26] have experimentally observed that this ratio
increases as pressure decreases. The authors explain theoretically this effects as a
consequence of free convection. Photographic evidence shows that combustion is accompanied
by strong free convection flows due to which the spherical flame appears
only in the lower half of the droplet whilst in the upper half it takes a considerably
elongate shape. The intense formation of carbon observed makes difficult the optical
study of this region. This convection effect may account for the difference between
the theoretical and experimental values of the flame radius making the values of k
predicted by theory agree with the experimental values as previously seen.
Formula (13.73) shows that the burning velocity of a droplet is practically independent
from pressure. In fact, its only influence shows small reduction of latent
heat of evaporation that accompanies and increase in pressure. However, Hall and
Diederichsen [23] have experimentally checked that the burning velocity of a droplet
is approximately proportional to the 4th root of pressure. It has been suggested [20]
that the following factors could account for this effect, aside from the aforementioned
decreases in evaporation heat: