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 From Figure 1 the steady-state internal heat flows of the vessels are as follows. Evaporator: Q = m& ⋅ ( h − ) & (1) E, int v 10 h8 Condenser: Q = m& ⋅ ( h − ) & (2) C, int v 7 h8 Q& = & & & & (3) , m ⋅ h − m ⋅ h + m − m ⋅ h Absorber: A int v 10 sol, w 1 ( sol, w v ) 5 Q& = & & & & (4) , m ⋅ h + m − m ⋅ h − m ⋅ h Generator: G int v 7 ( sol, w v ) 4 sol, w 3 In equations (1) to (4), & is the mass flow of the diluted solution and m& v is the mass flow m sol , w of the refrigerant water vapour which is of equal value at state points 7 and 10 in Figure 1. Equations (1) to (4) are based on the calculation of internal enthalpies for LiBr/water solution and refrigerant vapour which requires sound knowledge of these properties. For computational purposes this means that a property database of both LiBr/water and water vapour has to be implemented into the simulation model and usually requires timeconsuming iterations. The main aim of the model presented is to account for the dynamics. Therefore, no detailed steady-state simulation with all state points was performed but a simpler approach was taken which considers the most important physical properties only. This may be refined later on but is not intended to be the focus of this work. This kind of refinement will not change the basic findings of this report. So, to keep the model fast, equations (1) to (4) can be simplified using the latent heat of evaporation and sorption, r and l, as shown in equations (6) to (9). This approach has been proposed by Ziegler [4] to avoid a detailed enthalpy calculation for each state point. Please note that the latent heat is taken at condenser pressure. The dependency of latent heat on temperature is treated according to Plank’s rule [4]. Moreover, not all internal temperatures in Figure 1 are being calculated in the model. Instead, each vessel is being modelled using external and internal mean temperatures of the respective fluids (heat carrier and working fluid) as well as a mean vessel temperature. External mean heat carrier temperatures ϑX are being calculated using the arithmetic mean temperature of inlet and outlet temperature. Internal mean temperatures page 64 T X are assumed to be the mean of the equilibrium temperatures of strong and weak solution and of the
IEA SHC Task 38 Solar Air Conditioning and Refrigeration Subtask C2-A, November 9, 2009 condensing or evaporating refrigerant. Mean vessel temperatures mean temperature of the external and internal mean temperatures. T X are the arithmetic The boiling temperature of saturated LiBr/water solution can be calculated using the Duehring relation, as described by Feuerecker [5]. In the model, this temperature is by definition the mean of the equilibrium temperatures of strong (or weak) solution, T x . T x = A ( X ) + B ( X ) ⋅ D (5) d d with X being the mole fraction and D being the dew point temperature of the water vapour. A d and B d are the Duehring coefficients which depend on the solution concentration but are constant with regard to the dew point [5]. Some simplifying assumptions have been made for the model. These are: (a) There is no heat loss to or gain from the ambient. (b) The pump work is neglected. (c) The LiBr/water solution leaving generator and absorber tube bundle is saturated. (d) The external inlet temperatures t 11 , t 13 , t 17 are used as control parameters. (e) The absorber cooling water outlet temperature equals the condenser inlet temperature (t 14 =t 15 ). (f) The solution heat exchanger has a constant effectiveness η SHX (g) Water and LiBr/water solution have constant property data. (h) The external and internal heat transfer coefficients (UA-values) are constant. (i) (j) (k) Evaporation and solution enthalpy are constant. Constant pumping rate: The mass flow of weak solution from absorber to generator is constant (state points 1, 2 and 3). The generator pressure equals the condenser pressure; the absorber pressure equals the evaporator pressure. . Equations (1) to (4) do not account for dynamic effects. One way of accounting for a more precise dynamic calculation is the introduction of different vapour mass flows for state points 7 and 10. The vapour mass flow from generator to condenser, m & v , G (state point 7), and from evaporator to absorber, & (state point 10), are therefore used in equations (6) to (9) which m v , A describe the simplified internal enthalpy calculations. E = m& , int v, A ⋅ ( pc) p, v ( r − c ⋅ ( T − T ) Q & (6) C E page 65
- Page 490 and 491: IEA SHC Task 38 Solar Air Condition
- Page 492 and 493: IEA SHC Task 38 Solar Air Condition
- Page 494 and 495: IEA SHC Task 38 Solar Air Condition
- Page 496 and 497: IEA SHC Task 38 Solar Air Condition
- Page 498 and 499: IEA SHC Task 38 Solar Air Condition
- Page 500 and 501: IEA SHC Task 38 Solar Air Condition
- Page 502 and 503: IEA SHC Task 38 Solar Air Condition
- Page 504 and 505: IEA SHC Task 38 Solar Air Condition
- Page 506 and 507: IEA SHC Task 38 Solar Air Condition
- Page 508 and 509: IEA SHC Task 38 Solar Air Condition
- Page 510 and 511: IEA SHC Task 38 Solar Air Condition
- Page 512 and 513: IEA SHC Task 38 Solar Air Condition
- Page 514 and 515: IEA SHC Task 38 Solar Air Condition
- Page 516 and 517: IEA SHC Task 38 Solar Air Condition
- Page 518 and 519: IEA SHC Task 38 Solar Air Condition
- Page 520 and 521: IEA SHC Task 38 Solar Air Condition
- Page 522 and 523: IEA SHC Task 38 Solar Air Condition
- Page 524 and 525: IEA SHC Task 38 Solar Air Condition
- Page 526 and 527: IEA SHC Task 38 Solar Air Condition
- Page 528 and 529: IEA SHC Task 38 Solar Air Condition
- Page 530 and 531: IEA SHC Task 38 Solar Air Condition
- Page 532 and 533: IEA SHC Task 38 Solar Air Condition
- Page 534 and 535: IEA SHC Task 38 Solar Air Condition
- Page 536 and 537: IEA SHC Task 38 Solar Air Condition
- Page 538 and 539: IEA SHC Task 38 Solar Air Condition
- Page 542 and 543: IEA SHC Task 38 Solar Air Condition
- Page 544 and 545: IEA SHC Task 38 Solar Air Condition
- Page 546 and 547: IEA SHC Task 38 Solar Air Condition
- Page 548 and 549: IEA SHC Task 38 Solar Air Condition
- Page 550 and 551: IEA SHC Task 38 Solar Air Condition
- Page 552 and 553: IEA SHC Task 38 Solar Air Condition
- Page 554 and 555: IEA SHC Task 38 Solar Air Condition
- Page 556 and 557: IEA SHC Task 38 Solar Air Condition
- Page 558 and 559: IEA SHC Task 38 Solar Air Condition
- Page 560 and 561: IEA SHC Task 38 Solar Air Condition
- Page 562 and 563: IEA SHC Task 38 Solar Air Condition
- Page 564 and 565: IEA SHC Task 38 Solar Air Condition
- Page 566 and 567: IEA SHC Task 38 Solar Air Condition
- Page 568 and 569: IEA SHC Task 38 Solar Air Condition
- Page 570 and 571: IEA SHC Task 38 Solar Air Condition
- Page 572 and 573: Task 38 Solar Air-Conditioning and
- Page 574 and 575: IEA SHC Task 38 Solar Air Condition
- Page 576 and 577: IEA SHC Task 38 Solar Air Condition
- Page 578 and 579: IEA SHC Task 38 Solar Air Condition
- Page 580 and 581: IEA SHC Task 38 Solar Air Condition
- Page 582 and 583: IEA SHC Task 38 Solar Air Condition
- Page 584 and 585: IEA SHC Task 38 Solar Air Condition
- Page 586 and 587: IEA SHC Task 38 Solar Air Condition
- Page 588 and 589: IEA SHC Task 38 Solar Air Condition
<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 />
condensing or evapor<strong>at</strong>ing refrigerant. Mean vessel temper<strong>at</strong>ures<br />
mean temper<strong>at</strong>ure of the external <strong>and</strong> internal mean temper<strong>at</strong>ures.<br />
T<br />
X<br />
are the arithmetic<br />
The boiling temper<strong>at</strong>ure of s<strong>at</strong>ur<strong>at</strong>ed LiBr/w<strong>at</strong>er solution can be calcul<strong>at</strong>ed using the<br />
Duehring rel<strong>at</strong>ion, as described by Feuerecker [5]. In the model, this temper<strong>at</strong>ure is by<br />
definition the mean of the equilibrium temper<strong>at</strong>ures of strong (or weak) solution, T<br />
x<br />
.<br />
T<br />
x<br />
= A ( X ) + B ( X ) ⋅ D<br />
(5)<br />
d<br />
d<br />
with X being the mole fraction <strong>and</strong> D being the dew point temper<strong>at</strong>ure of the w<strong>at</strong>er vapour. A d<br />
<strong>and</strong> B d are the Duehring coefficients which depend on the solution concentr<strong>at</strong>ion but are<br />
constant with regard to the dew point [5]. Some simplifying assumptions have been made for<br />
the model. These are:<br />
(a) There is no he<strong>at</strong> loss to or gain from the ambient.<br />
(b) The pump work is neglected.<br />
(c)<br />
The LiBr/w<strong>at</strong>er solution leaving gener<strong>at</strong>or <strong>and</strong> absorber tube bundle is s<strong>at</strong>ur<strong>at</strong>ed.<br />
(d) The external inlet temper<strong>at</strong>ures t 11 , t 13 , t 17 are used as control parameters.<br />
(e) The absorber cooling w<strong>at</strong>er outlet temper<strong>at</strong>ure equals the condenser inlet<br />
temper<strong>at</strong>ure (t 14 =t 15 ).<br />
(f) The solution he<strong>at</strong> exchanger has a constant effectiveness η<br />
SHX<br />
(g) W<strong>at</strong>er <strong>and</strong> LiBr/w<strong>at</strong>er solution have constant property d<strong>at</strong>a.<br />
(h) The external <strong>and</strong> internal he<strong>at</strong> transfer coefficients (UA-values) are constant.<br />
(i)<br />
(j)<br />
(k)<br />
Evapor<strong>at</strong>ion <strong>and</strong> solution enthalpy are constant.<br />
Constant pumping r<strong>at</strong>e: The mass flow of weak solution from absorber to gener<strong>at</strong>or<br />
is constant (st<strong>at</strong>e points 1, 2 <strong>and</strong> 3).<br />
The gener<strong>at</strong>or pressure equals the condenser pressure; the absorber pressure<br />
equals the evapor<strong>at</strong>or pressure.<br />
.<br />
Equ<strong>at</strong>ions (1) to (4) do not account for dynamic effects. One way of accounting for a more<br />
precise dynamic calcul<strong>at</strong>ion is the introduction of different vapour mass flows for st<strong>at</strong>e points<br />
7 <strong>and</strong> 10. The vapour mass flow from gener<strong>at</strong>or to condenser, m &<br />
v , G<br />
(st<strong>at</strong>e point 7), <strong>and</strong> from<br />
evapor<strong>at</strong>or to absorber,<br />
& (st<strong>at</strong>e point 10), are therefore used in equ<strong>at</strong>ions (6) to (9) which<br />
m<br />
v , A<br />
describe the simplified internal enthalpy calcul<strong>at</strong>ions.<br />
E<br />
= m&<br />
, int v,<br />
A<br />
⋅<br />
( pc)<br />
p,<br />
v<br />
( r − c ⋅ ( T − T<br />
)<br />
Q & (6)<br />
C<br />
E<br />
page 65
Change language