IEA Solar Heating and Cooling Programm - NachhaltigWirtschaften.at

IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009
As stated in equation (14) above, the mass flow of weak solution is set constant. In equation
(12) it is assumed that the mass flow entering the absorber tube bundle at time interval i
equals the mass flow which has left the generator c 1 time intervals ago. Doing so, the
physical incompressibility of the solution in the piping between generator and absorber is not
modelled correctly. In reality, the mass flow entering the tube at time interval i should equal
the mass flow leaving the tube at time interval i. The assumption, however, had to be made
in order to achieve a correct salt balance in equation (22). The result is a hidden mass
storage term in the solution tube. However, the amount of stored solution in the tube is only
0.6 % of the total amount of stored solution in the sumps [3]. The error introduced by this
assumption is therefore negligible.
Mass balances
The vessel sumps (see Figure 2) are assumed to be fully mixed at each time interval. Thus
vessel sump and solution leaving the vessel are assumed to have the same salt
concentration, x sA,i and x wG,i , respectively. The outlet of each tube bundle is assumed to
exhibit the equilibrium concentration x sG,i and x wA,i . The total solution mass stored in
generator and absorber sump at time i is expressed by
M
sol st,
G,
i
M
,
,
and
sol, st,
A i
, respectively.
We know that the total mass (or salt mass, respectively) in the sump at time interval i equals
the total mass (or salt mass) at time interval (i-1) plus the difference of ingoing and outgoing
solution (or salt) flows at time interval i. The balances for the total solution contents in the
sumps are given in equations (15) and (16).
∆ t is the time between two simulation intervals.
M
sol,
, G,
i
− M
sol,
, G,
i−1
Generator: m& , , ,
− m&
, ,
−
st
st
sol tb G i sol sG i
= 0
(15)
∆t
M
sol,
st,
A,
i
− M
sol,
st,
A,
i−1
Absorber: m& , , ,
− m&
sol tb A i sol,
wA,
i
−
= 0
(16)
∆t
The fraction term in equations (15 and 16) is the amount of solution which is added to the
solution stored in either generator or absorber sump during the time
simulation intervals i and (i-1).
∆ t between consecutive
The salt flow balance, analogously, in both sumps can be written as:
Generator
M
sol,
, G,
i
⋅ xsA,
i
− M
sol,
, G,
i−1
⋅ xsA,
i−1
m& , , ,
⋅ x
,
− m&
, ,
⋅ x
,
−
st
st
= 0 (17
sol tb G i sG i sol sG i sA i
∆t
:
)
Absorber
:
M
sol,
st,
A,
i
⋅ xwG
, i
− M
sol,
st,
A,
i−1
⋅ xwG
, i−1
m& , , ,
⋅ x
,
− m&
sol tb A i wA i sol,
wA,
i
⋅ xwG
, i
−
= 0 (18
∆t
)
page 68