Untitled - Aerobib - Universidad Politécnica de Madrid

13.2. ATOMIZATION 303
lem has been reviewed by Heinze [10], who studied in detail the action of its various
factors.
Atomization is characterized by the average size of the droplets and by their
distribution in sizes. The average size of the spray droplets is characterized by the
Sauter diameter d s [11]. This is the diameter that would be obtained in an ideal atomization
where all the droplets were of equal size and where the surface and total
volume of the fuel were equal to those of actual atomization. The value d s depends
on the variables that characterize the particular conditions of atomization, according
to rules empirically determined (see Ref. [9], p. 117 and f.).
The size distribution in characterized by the mass fraction R (d/d s ) of the fuel
corresponding to droplets of a diameter larger than d. Therefore, the size distribution
dR
function is
d (d/d s ) . Several empirical formulas have been proposed for R (d/d s) or
dR
, [12]. The two formulas generally used are the Rosin-Rammler formula [13]
d (d/d s )
and the Nukiyama-Tanasawa formula [14]. The results given by these two formulas
are in fair agreement with the distributions experimentally observed [15], [16]. These
formulas are as follows.
Rosin-Rammler:
or else
( ) δ−1
dR d
d (d/d m ) = δ e −(d/d m) δ , (13.1)
d m
R = 1 − e −(d/d m) δ , (13.2)
In these formulas d m is an average diameter, characteristic of the size of atomization,
which is related to the Sauter diameter through formula
d m
d s
(
= Γ 1 − 1 )
, (13.3)
δ
where Γ is the factorial function, 1 and δ is a characteristic parameter of size uniformity.
When δ increases the distribution becomes more uniform.
Nukiyama-Tanasawa:
( ) 5
dR
d (d/d m ) = δ d
e −(d/d m) δ (13.4)
Γ (6/δ) d m
1 Also called gamma function, defined as Γ(a) = R ∞
0 ta−1 e −t dt, Ed.