IEA Solar Heating and Cooling Programm - NachhaltigWirtschaften.at

IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009
x(j-1,j)
•
x(i-1,j)
•
x(i,j)
•
∆z
∆θ
D(i,j)
Figure 22: Current and neighbor nodes
The estimation of the partial derivatives is done using an upwind interpolation that permits
expressing the frontiers values in function of the considered node and in function of the
previous node.
The derivative with respect to θ:
( x i
− x )
∂ x , j i − 1,
j
=
∂θ ∆θ
The derivative with respect to z:
∂x
=
∂z
( x − x )
i,
j
∆z
i,
j−1
The moist air enthalpy is expressed by:
a
pa
a
a
( h c T )
h = c . T + w + .
(35)
fg
pv
a
The desiccant enthalpy is expressed following Brandemuehl and Banks [18] and Stabat [11]
H = c
pd
T
d
+ c
pv
W T
d
h
+
fg
∆λ
e
k
−kW
−1
(36)
Replacing the enthalpies and derivative by the above equations, for each node (i,j) we have
finally:
Mass conservation equation
( W −W
) + m '( w − w ) + m * ( w − w ) 0
M (37)
d
'
i, j i−1,
j a a i,
j a i−1,
j a a i,
j a i,
j−1
=
Mass transfer equation
( Wi
j
Wi
j
) − hmS'
wa
i j
= −hmS
weq i j
M
d
'
, 1,
,
'
,
−
−
(38)
Heat conservation equation
page 50