Experimental and Numerical Analysis of a PCM-Supported ...
Experimental and Numerical Analysis of a PCM-Supported ...
Experimental and Numerical Analysis of a PCM-Supported ...
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Appendix B<br />
B1. Pressure drop calculations (Stichlmair et al. [29])<br />
Stichlmair et al. [29] shows the advantages <strong>of</strong> the particle model. In this model<br />
structure, the real packing is replaced by a system <strong>of</strong> spherical particles which have<br />
the same surface <strong>and</strong> void fraction as the original packing. With these equivalence<br />
conditions, the equivalent diameter <strong>of</strong> the particle d p is:<br />
d 6<br />
1 <br />
p<br />
(B.1)<br />
a<br />
Thus, the originally r<strong>and</strong>om structure <strong>of</strong> the packing is made accessible to<br />
calculation. Stichlmair et al. [29] show that the correlations for fluidized beds can<br />
also be applied to a system <strong>of</strong> fixed particles. The analysis <strong>of</strong> the pressure drop on<br />
the air side in a packed column was based on the computation <strong>of</strong> the dry column<br />
pressure drop <strong>and</strong> a correction term to account for the effect <strong>of</strong> liquid flow rate.<br />
Equation (27) describes the basic equation <strong>of</strong> the particle model. The dry column<br />
pressure drop per unit height that utilizes the single particle friction factor as well as<br />
the bed porosity ε is given by the following correlation [29]:<br />
d<br />
4.65 2<br />
<br />
<br />
gVg<br />
d<br />
p<br />
P Z 3 4 f<br />
<br />
(B.2)<br />
0<br />
1<br />
where V g is the air superficial velocity <strong>and</strong> f is the friction factor given by the following<br />
equation:<br />
f<br />
0.5<br />
0<br />
C1<br />
Re<br />
g<br />
C2<br />
Re<br />
g<br />
C<br />
(B.3)<br />
3<br />
where the friction factor f 0 for a single particle is a function <strong>of</strong> gas Reynold’s number:<br />
Re V d <br />
(B.4)<br />
g<br />
g<br />
g<br />
p<br />
g<br />
The friction factor f 0 is derived from the dry pressure drop <strong>of</strong> the original packing.<br />
Therefore, it is one <strong>of</strong> the characteristic parameters <strong>of</strong> a r<strong>and</strong>om <strong>and</strong> structured<br />
packing, together with the geometric surface a <strong>and</strong> the void fraction ε. The constants<br />
C 1 , C 2 <strong>and</strong> C 3 in equation (B.3) are available in Stichlmair et al [29] for different<br />
packing elements other than spherical packing. As long as the friction factor can be<br />
expressed in the same form <strong>of</strong> equation (B.3), the model can be applied for spherical<br />
packing (or any other packing geometry).<br />
Bird et al. [19] provides a simple <strong>and</strong> useful empirical expression for the friction<br />
factor for creeping flow around a sphere that matches the form <strong>of</strong> equation (B.3):<br />
24 Re 0. 2<br />
f<br />
0<br />
<br />
g<br />
5407 for Re < 6000 (B.5)<br />
194