IEA Solar Heating and Cooling Programm - NachhaltigWirtschaften.at
IEA Solar Heating and Cooling Programm - NachhaltigWirtschaften.at IEA Solar Heating and Cooling Programm - NachhaltigWirtschaften.at
IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009 A int G int C = m& , int v, G ⋅ ( pc) p, v ( r + c ⋅ ( T − T ) Q & (7) ( r pc l pc c p w ( TG TA )) Q& ( ) + ( ) + ⋅ − SHX = mv, G ⋅ , G Q & & + , (8) ( r pc l pc c p v ( TG TE ) c p w ( TG TA ) Q& ( ) + ( ) − , ⋅ − + ⋅ − SHX Q & & + , (9) = mv, A ⋅ , C The solution heat exchanger does not exchange the maximum possible heat between its two flows. The difference between actual and ideal heat transfer can be assumed as a parasitic heat flow which has to be added to the generator and has to be removed at the absorber. For a constant heat exchanger effectiveness η SHX it can be calculated as Q& SHX ( 1 −η ) ⋅ m& ⋅ c ⋅ ( T − T ) = SHX sol, sG p, sol, s G A . (10) In equation (10), & is the mass flow rate of the strong solution from generator to m sol , sG absorber [4]. The dynamic performance of the absorption chiller is influenced by various time-dependent effects, caused by complex heat transfer phenomena in the internal and external heat exchangers. In order to keep the model simple, not all of the dynamic effects have been taken into account. Only the three effects with the estimated biggest influence on chiller performance have been chosen. These include a time delay in the solution transport between generator and absorber, mass storage in the vessel sumps, and thermal storage in the external and internal heat exchangers. These dynamic terms are the backbone of the model and will be discussed in detail. Dynamic Modelling Both generator and absorber vessel have been modelled as a serial connection of a tube bundle heat exchanger and a solution sump. The tube bundle is the active part; the sump is a storage and mixing device. Solution can accumulate in absorber and generator sump according to the actual load, however there is also some solution which is always stored on the tube bundle. This hold-up, usually, is small as compared to the amount of liquid in the sump because the film is less than half a millimetre thick. Moreover, the bundle should be wetted all the time with the consequence that the amount of liquid on the bundle will not change significantly. Therefore the amount of liquid on the bundle is neglected. Due to the storage effect, we have to distinguish between the solution flow entering the vessel, the one leaving the bundle and entering the sump, and the one leaving the sump. Moreover, we have to consider different concentrations at the inlet of the bundle, at the exit page 66
IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009 of the bundle dripping into the sump, and at the exit of the sump. Figure 2 shows the concentration and mass flow definitions, introducing time-discrete parameters (index i). Figure 2. Definition of concentrations and mass flows in generator/absorber. Solid lines: strong solution, dotted lines: weak solution, white arrows: vapour. Solution transport delay A transport delay (c) is assumed to occur in both solution circuit legs. Referring to Figure 2, the inlet values of solution mass flow & * and concentration m sol, sA, i ∗ x sA , i at the absorber at time interval i are assumed to equal the generator outlet values of time interval (i-c 1 ). The superscript * symbolizes the time-delayed arrival of the solution at absorber and generator inlet. By analogy, the inlet value of concentration x ∗ wG i , at the generator at time interval i is assumed to equal the outlet value of the absorber at time step (i-c 2 ). Constants c 1 and c 2 account for the time which the solution needs to flow from generator to absorber and vice versa. They are integers representing a number of simulation steps. Absorber: x = x (11) ∗ sA, i sA, i−c1 m& = & (12) * sol, sA, i msol, sG, i−c1 Generator: x = x (13) ∗ wG , i wG , i−c2 m& * , , m& , , 2 const. (14) sol wG i = sol wA i−c = page 67
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<strong>IEA</strong> SHC Task 38 <strong>Solar</strong> Air Conditioning <strong>and</strong> Refriger<strong>at</strong>ion Subtask C2-A, November 9, 2009<br />
of the bundle dripping into the sump, <strong>and</strong> <strong>at</strong> the exit of the sump. Figure 2 shows the<br />
concentr<strong>at</strong>ion <strong>and</strong> mass flow definitions, introducing time-discrete parameters (index i).<br />
Figure 2. Definition of concentr<strong>at</strong>ions <strong>and</strong> mass flows in gener<strong>at</strong>or/absorber. Solid lines: strong solution,<br />
dotted lines: weak solution, white arrows: vapour.<br />
Solution transport delay<br />
A transport delay (c) is assumed to occur in both solution circuit legs. Referring to Figure 2,<br />
the inlet values of solution mass flow<br />
& * <strong>and</strong> concentr<strong>at</strong>ion<br />
m<br />
sol,<br />
sA,<br />
i<br />
∗<br />
x<br />
sA , i<br />
<strong>at</strong> the absorber <strong>at</strong> time<br />
interval i are assumed to equal the gener<strong>at</strong>or outlet values of time interval (i-c 1 ). The<br />
superscript * symbolizes the time-delayed arrival of the solution <strong>at</strong> absorber <strong>and</strong> gener<strong>at</strong>or<br />
inlet. By analogy, the inlet value of concentr<strong>at</strong>ion<br />
x<br />
∗<br />
wG i<br />
,<br />
<strong>at</strong> the gener<strong>at</strong>or <strong>at</strong> time interval i is<br />
assumed to equal the outlet value of the absorber <strong>at</strong> time step (i-c 2 ). Constants c 1 <strong>and</strong> c 2<br />
account for the time which the solution needs to flow from gener<strong>at</strong>or to absorber <strong>and</strong> vice<br />
versa. They are integers representing a number of simul<strong>at</strong>ion steps.<br />
Absorber:<br />
x<br />
= x<br />
(11)<br />
∗<br />
sA, i sA,<br />
i−c1<br />
m& = &<br />
(12)<br />
*<br />
sol,<br />
sA,<br />
i<br />
msol,<br />
sG,<br />
i−c1<br />
Gener<strong>at</strong>or:<br />
x<br />
= x<br />
(13)<br />
∗<br />
wG , i wG , i−c2<br />
m& *<br />
, ,<br />
m&<br />
, , 2<br />
const.<br />
(14)<br />
sol wG i<br />
=<br />
sol wA i−c<br />
=<br />
page 67