Vaporization of JP-8 Jet Fuel in a Simulated Aircraft Fuel Tank ...

APPENDIX A: REVIEW OF FUEL VAPORIZATION MODEL
The model used in this thesis is presented in reference [11] and will be summarized here
in the appendix.
Several principal assumptions were made in the model to simplify the
calculations. The flow field in the tank was assumed driven entirely by natural
convection between the heated liquid fuel on the tank floor and the unheated tank ceiling
and sidewalls. The ullage gas was considered well mixed with no thermal or
concentration gradients existing within the ullage, which was justified by the fact that the
natural convection flow in the tank was in the turbulent region, since the magnitude of the
Raleigh number, based on the floor to ceiling temperature difference and the distance
between them, was typically of order (10 9 ).
Initially it was assumed that the ullage gas mixture would be composed of N
species, consisting of N-1 fuel vapor components and atmospheric air. As the species
concentrations were low for the purposes of these experiments, the vaporization rate of
the fuel species considered was expressed by the relationship:
( y − y ) , i = → N
65
m ei = A1hi
ρ fi gi 1
( 1 )
The analogy between heat and mass transfer allowed for the species Sherwood number to
be expressed in terms of the Nusselt number:
1/
3
Pr ⎟ hi
L ⎛ Sci
⎞
Sh i = = Nu⎜
( 2 )
D ⎝ ⎠
On the horizontal surfaces the Nusselt number was found by [38]:
i
( ) 3 / 1
Nu = 0. 14 Ra
( 3 )