Untitled - Aerobib - Universidad Politécnica de Madrid

13.15. DROPLET EVAPORATION 329
1
0.9
0.8
0.7
0.6
m/m 0
0.5
0.4
0.3
0.2
0.1
c T /q =2
p1 ∞ l 4 6 8 10
0
0 1 2 3 4 5 6 7 8 9 10
x
Figure 13.7: The ratio m/m 0 as a function of x = c p1(T ∞ − T s)/q l for some values of
c p1T ∞/q l .
Figure 13.7 gives m/m 0 as a function of x, for some values of c p1 T ∞ /q 1 .
When the evaporation velocity is high the fast decrease of the evaporation constant
can be seen due to the transport of enthalpy done by the vapour motion.
The previous formulae do not take into account the influence of convection.
Such effect has been studied by Frössling [32], who obtained the following relation
between the evaporation velocity m c with convection and the evaporation velocity at
rest
m c
m = (
1 + 0.276 Sc 1/3 Re 1/2) . (13.106)
Here Sc = µ/ρD 12 and Re = ρvd s /µ are, respectively, the Schmidt number
and the Reynolds number of the motion, µ is the gas viscosity coefficient, d s the
droplet diameter and v the motion velocity. Ranz and Marshall [33] have experimentally
verified this formula. Fig. 13.8 gives m c /m as a function of Sc 2/3 Re.
Formula (13.105) was obtained from experiments at ambient temperature. Ingebo
[34] gives the following empirical formula which represents with good approximation
the experimental results obtained by him from 30 ◦ C to 500 ◦ C
m c
m = ( 1 + 0.151(Sc Re) 0.6) . (13.107)