Analysis Code for High Altitude Balloons - FedOA - Università degli ...
Analysis Code for High Altitude Balloons - FedOA - Università degli ...
Analysis Code for High Altitude Balloons - FedOA - Università degli ...
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ACHAB: <strong>Analysis</strong> <strong>Code</strong> <strong>for</strong> <strong>High</strong> <strong>Altitude</strong> <strong>Balloons</strong> Chapter 3<br />
For free convection between the external skin and the air the following <strong>for</strong>mulation<br />
of the Nusselt number is considered:<br />
Nu =<br />
free<br />
HC<br />
free<br />
Diameter<br />
Nusselt numbers <strong>for</strong> free convection problems are usually correlated to Rayleigh<br />
numbers. The general <strong>for</strong>m is:<br />
k<br />
air<br />
Nu a0<br />
a1Ra<br />
+ =<br />
where Rayleigh number is the product of the Grashof number and Prandtl number<br />
( Ra = GrPr ), and 0 a , a 1 and n are usually determined experimentally.<br />
The Nusselt number used in this model is taken from Ref. 9, 17, 18, 20. The Grashof<br />
number <strong>for</strong> air Gr air is defined as:<br />
Gr<br />
External Forced Convection.<br />
air<br />
2<br />
ρ air g T film − Tair<br />
Diameter<br />
=<br />
T µ<br />
This kind of convection depends on the vertical velocity of the balloon that <strong>for</strong>ces the<br />
relative movement of air with respect to the external skin.<br />
The <strong>for</strong>mulations of the Nusselt number ( Nu <strong>for</strong>ced ) <strong>for</strong> external <strong>for</strong>ced convection<br />
used in this model are those reported in Ref. 9, 18, 20.<br />
Hence, this yields to the following coefficient:<br />
air<br />
2<br />
air<br />
kair<br />
HC <strong>for</strong>ced =<br />
Nu<br />
Diameter<br />
n<br />
<strong>for</strong>ced<br />
3<br />
39
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