Untitled - Aerobib - Universidad Politécnica de Madrid

330 CHAPTER 13. COMBUSTION OF LIQUID FUELS
24
20
Ingebo (S c
=0.65)
m c
/ m
16
12
Frössling
8
4
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
2/3
S Re × 10
−3
c
Figure 13.8: Experimental relations of Frössling and Ingebo, giving m c/m as a function of
Sc 2/3 Re.
This formula is represented by the dash line in Fig. 13.8. It is seen that the Frössling
formula underestimates the evaporation velocity for the large Reynolds numbers.
Miesse [35] has lately calculated the motion of an evaporating droplet by assuming:
1) The coefficient of the aerodynamic drag of the droplet is inversely proportional
to the Reynolds number (laminar flow).
2) The evaporation velocity of the droplet follows the Frössling law.
Miesse has obtained solutions for the case where the air velocity changes linearly with
distance. Such solutions allow the calculation of the distance covered by the droplet
as a function of the reduction of its diameter and the distance needed for complete
evaporation, etc. His work contains interesting practical applications. However, when
trying to extend his conclusions to the case of sprays the remarks made at the beginning
of this paragraph should be taken into account. On the other hand the possible
interaction of evaporation and aerodynamic drag of the droplet is neglected.
Penner [36] has calculated the evaporation time of a propellant droplet within
the combustion chamber of a rocket by assuming that the droplet is isothermal but its
temperature changes with time. He has estimated the possible influence of the radiation
energy on the evaporation process reaching the conclusion that such influence is
of no significance.