Availability simulation of a lithium bromide absorption heat pump

Heat Recovery Systems & C H P Vol. 8, No. 2, pp. 157-171, 1988

0890-4332/88 $3.00 +0.00 Pergamon Press plc

Printed in Great Britain

A V A I L A B I L I T Y S I M U L A T I O N OF A L I T H I U M BROMIDE ABSORPTION HEAT PUMP WOLF J. KOmtLER, WARREN E. IBELE Heat Transfer Laboratory, Mechanical Engineering Department, University of Minnesota, 111 Church Street S.E., Minneapolis, MN 55455, U.S.A. JOSEPH SOLTF~ a n d EDGAR R. W ~ Lehrstuhl C fiir Thermodynamik, Technische Universit~t Mfinchen, Mfinchen, West Germany (Received 16 July 1987)

AhotrmetuAvailabilitydata of aqueous solutions of lithium bromide are calculated. A groundwater-fed, solar-assisted absorption heat pump with LiBr-H20 as working fluid is simulated. In particular, a second law analysis is applied to detect internal losses quantitatively and to describe ways for physically realistic cost aRi~nment to internal devices. A parameter study shows ways for system optimization.

NOMENCLATURE C

costs

COP f h L

coeff~ent of performance function mthal~ [lO kS-R] avnilab/lity loss rate [kW ( k W h ) - ' ] mare flow rate [kss-']

m

P

o.

$

S T W x

7"

prmum [I.,]

heat flow rate [kW (kWh,) -~] entropy [ld (ks K)-'] entropy ,tow rate [kW (K kW~o~,) -~] tempmuare [K, °C if stated] work [kW (kW~,~) -t] mass fraction of LiBr in solution effectivenem modified effectiveness (equation 15) availability [kJ ks - '] availability flow rote (kW ( k W h ) - ' ]

Subscripts

AW CW e, ex EW GW hi i

absorber water circuit condenser water circuit exit evaporator water circuit generator water circuit high inlet, internal

irr 1o s

iii~versible

t x o0 01 02 2L I, II

low saturated technical at concentration x state of surroundings pure solvent (water) pure solute (LiBr) second law per unit mass flow of concentration I or II INTRODUCTION

R e c e n t d e v e l o p m e n t s in c o o l i n g a n d h e a t i n g systems s h o w a g r o w i n g interest in the a p p l i c a t i o n o f a b s o r p t i o n cycles. Since a n a b s o r p t i o n cycle c a n b e d r i v e n b y l o w t e m p e r a t u r e t h e r m a l e n e r g y 157

158

WOLF J. KOEHLEg et al.

it provides a constructive way to convert waste heat to useful purposes. Employing nontoxic, odorless aqueous solutions of lithium bromide as working fluid is safe and comfortable. Low cost and simple handling favor water as a refrigerant despite its high freezing point, while low temperatures of crystallization, high heat capacity and low viscosity are advantages of aqueous solutions of lithium bromide as absorbent. Since energy conservation has grown more important, there is a need for optimizing processes for minimum consumption of energy. The second law analysis is a simple but effective tool to detect where and how much of the input energy of a system is lost. Moreover, this method gives information about how losses at different devices are interdependent and where a given design should be modified for best performance.

AVAILABILITY The availability of a pure substance is generally given as ~k = (h - Toos) - (hoo - T~os~) = f ( T , p )

where contributions due to potential and kinetic energies are neglected. The subscript oo denotes the state of the ambient. However, in a binary mixture such as LiBr and water, the concentration of the mixture must be taken into account for availability calculations. Due to the irreversible nature of any mixing process, the least potential of a mixture for doing useful work is given when it is in a saturated state at Too and poo. Therefore

¢ = ¢ (T,p,x)

(l)

for a mixture. For a given environmental state we can treat the availability as a state function and thus may choose a convenient path from any given state to the dead state of the environment: V/(T,p, x) = Cx(T,p) + ¢~(x).

(2)

The temperature and pressure dependent part of the availability of a mixture of a given state x is ~k~(T,p) = [ h ( T , p , x ) - Toos(T,p, x)] - [h(Too,p~, x ) - T ~ s ( T o o , p ~ , x)].

(3)

To find Coo(x) imagine a mixture at Too,p® undergoing a change of state from given x to the dead state x, by admixing an amount of solute at Too,p~. For steady conditions the first and second law for such a process are: Q -

w t = re, h, -

m,~h,, -

(4)

Amo2ho2

Sir, = re, s, - m,,sx - Amo2So2-- -Q-

(5)

To

where the subscripts s and x denote saturated and actual concentration, while 02 stands for the admixed solute. Combining equations (4) and (5) yields: Wt + TooSi,, = mx(hx - Toosx) + ~m%2(ho2 - T®so2) - m,(h, - T ~ s , ) .

(6)

The left hand side of equation (6) gives--for the ideal case regarding the second law--the maximum ( = reversible) amount of work which can be obtained from a solution at given To0,p® and x: (7)

Wid = W, + T ~ S , ~ .

W~d related to a unit of mass flow m~ gives the availability of a mixture at this state: X s oo - - X

~boo = ( h , , - T®s,,).~ ~'--~,.-~ [(ho2- rooso~)- ( h , -

r~os,,r,) ] - ( h , -

T~s,)

(8)

where x,, ~ -

x =

1 -- xs, ~

m , -- m ~

mx

(9)

Lithium bromide absorption heat pump

159

,oo V 6S0 600

"~

550

-

5OO 450

A

i 'I

-

4O0

30O

2OO /

mso

1.00 eC

i IOOi O'C SQ --

~

o -

-eo

2 5"C

I

0

I0

I

I

ZO

1

3O

Morns p e r c e n t

4O

I

5O

I

Im

I

7O

L i B r in s o l u t i o n

Fig. 1. Availability of aqueous solution of LiBr for three d i i T ~ t temperatures, 0°C, 25°C and 100°C

at T® --25°C. From this one can obtain, for instance, the availabifity of the pure solvent: ~(x =O)=(ho.-

T®so.)-t

x.,® [(ho2- T®s,-(h.- T®s,)]-(h.- r®s.).

I -xL~

(I0)

The difference in availability of two mixtures at T®, p® and x~ and T®, p® and x., related to the unit mass of m~, is then: q/. - q'l ffi 11---xl x.

(h~,.- T®sx.,)-(hx,!-

T,

~ " XI ~ X I I ' ®s xj,-t-l_--~(ne~T®so2).

(11)

Substituting equations (3) and (8) into equation (2) we get: O(T,p, x) = [h(T,p, x) - T®s(T,p, x)] -t x~® - x [(h02- T®se2) - (h, - T®s.)] 1 - - X~,®

-[h.(T®,p®,x,)- T®s.(T®,p®,x.)] (12) This gives the desired availability of a binary mixture. Availability values of aqueous solutions of LiBr were calculated using this formula. The results for three different temperatures and an ambient temperature of 25°C are shown in Fig. 1. MODEL FOR SIMULATION The model r e p r d e d consists of an internal and an external system (Fig. 2). The external system represents the connection between the internal system and the surroundings. The internal system is a standard absorption cycle containing evaporator, condenser, absorber, generator, pump, two expansion valves and two heat exchangers. The external system is given by four open water circuits carrying heat from or to the internal system. The model operates as follows. Pure saturated refrigerant of state Is is heated to state 1 by the internal heat exchanger of the cooling cycle (HECC). In the absorber the refrigerant vapor is

160

WOLF J. KOEHLERet al. Heat rejecting side AWi Cond. water

Abs water

Condenser ~

~

Heat exchanger (HECC)

Absorber

Expan~on

volve solar cycte 6PU

Heat

exchon~ (HESC) Exponsion volve cooling cycle

Evaporator

I" - ' a Is

Evap. water I---1

~

Generator

GWi r - -

Gen.water

EWe

-

__d

GWe Heat absorbing side

Fig. 2. Model for simulation.

absorbed by the absorbent of concentration x8 and cooled to state 5 by the absorber water (AW). The refrigerant-rich solution of state 5 is pumped to state 6PU (high pressure level, Phi) and heated to state 6 by the internal heat exchanger of the solution cycle (HESC). In the generator the refrigerant-rich solution is heated further by the generator water (GW), evaporating refrigerant of state 2. In the heat exchanger HESC the weak solution is cooled to state 7 before it is throttled to low pressure (p~, state 8). If the solution at state 7 is near saturated liquid, during the throttling process part of the liquid will flash into vapor, absorbing heat from the remaining liquid and cooling it to temperature Ts. Otherwise the expansion occurs in the pure liquid phase while the temperature remains constant. In the condenser, refrigerant vapor from the generator is condensed to saturated water, state 3s. The heat removed is transferred to the condenser water (CW). In the heat exchanger of the cooling cycle (HECC) the refrigerant liquid is subcooled to state 3 before it is throttled to low pressure (state 4). The heat absorbed in the evaporator is transferred from the evaporator water (EW). For the calculation it was assumed and confirmed that the minimum temperature differences at absorber and generator occur at state 5 and 7G, respectively. Thus /'5

=

TAwi + A T^

/'7 = T ~ w i - ATo.

Physically, these assumptions are not necessary, but simplify the calculations considerably. Furthermore it was assumed that the refrigerant vapor leaving the generator is in thermodynamic equilibrium with the saturated absorbent of concentration xt. Consequently the state of the vapor entering the condenser is fully determined by the boiling temperature of the refrigerant-rich solution at p~ and x6. This assumption follows the calculation procedure of Bosnjacovic [2]. Isenthalpic expamfion was pr,~umed for both throttle valves. Finally it was assumed that the pressure levels p~ and Pk, can be perfectly controlled. The substance data of the LiBr solution were taken from the approximation equations given in [3,8, 10].

Lithium bromide absorption heat pump

161

i

The input data of the analysis were: the ambie/it ~ i ~ r a t u r e , T®; the inlet temperatures of the external water circuits, TEwi, Towt, T^w~, Towt; the change of temperature of the external water circuits, ATEw, ATcw, AT^w, ATGw; the minimum temperature difference between external water and internal mixture at each device, ATe, ATc, AT^, ATo; and the COPs of the internal heat exchangers, ~/,ecc and ~sesc. The standard conditions were assumed as follows: all extensive properties per KW output; ambient temperature T® = 278.15 K = 5°C; for the evaporator circuit, ground water of 12°C is solar heated to 16°C, ATew = 4 K; the peak temperature of the condenser- and absorber-water circuits is 50°C, where the temperature change along the device is 25°C. Hence Tcw~= T^wi = 25°C, ATcw -- AT^w = 25°C; the heat source is water of 120°C, Towi = 120°C, ATG = 25°C; the minimum temperature difference at all major devices is 5 K: ATe = A T c = AT^ = ATo = 5 K; both internal heat exchangers have a 50% efficiency: t/HeCC= r/HeSC= 0.5. These standard conditions lead to pressures of 1000 Pa and 15730Pa in the system, while the concentrations are 51.1% and 64.9%. A complete result of the analysis is given in the Appendix. ANALYSIS

Usefulness and limitations of a second law analysis Employing the availability analysis we are primarily interested in three quantities: the COP, the second law efficiency ( ~ effectiveness) of the system and the availability losses at the four major devices. The latter indicates where a design concept should be modified to improve the system performance. The performance of a given system in turn is described best by the COP and the effectiveness. These two quantities are used to find the system performance which yields the lowest cost under given conditions. But do optimum effectiveness and optimum COP always lead to the same result? If not, which one is to be preferred? The standard definitions of COP and effectiveness are given as: COP -~ Qp,eat .~

Qi,~

Qc + Q^

(13)

mow × ~ w

~p~at = m c w x A ~cw + maw x A ~^w 1~2L "~" ~inlmt

mow

X

(I4)

~l~OWi

If the costs of the energy source used are charged according to the energy input, the COP is the quantity to be optimized; if they are charged according to the availability input, the effectiveness should be maximized. However, it is questionable to express the profit of a heat pump in terms of work potential. The availability profit might actually change due to a change in the layout parameters, while the energetic profit remains constant. If the layout conditions are modified such that the input energy is reduced, the COP will increase. The effectiveness will only increase if the decrease in availability input is higher than a possible decrease in the availability profit. Thus an optimum effectiveness does not necessarily lead to lowest-cost performance, even if the cost is proportional to the availability input. Expressing the profit of the system as the actual energetic profit in which we are interested eliminates that difficulty. Hence we can define a modified effectiveness as:

Qp,o~,

(I5)

Using t/~L and the COP will not lead to contradicting optimization trends. For a given design concept, the availability losses indicate which part it is most worthwhile to improve. A second law analysis visualizes the losses, quantifies their nmgnitude and shows clearly their interdel~ndence. Although the qualitative behaviour of the losses can be inferred from proper physical intuition, their magnitude can only be determined by means of a second law analysis. This is similar to other areas of fluid flow and heat transfer where qualitative solutions of problems were known long before quantitative solutions could be predicted by numerical methods.

162

WOLF J. KOEHLERet al.

Test of calculation procedure The simulation program used in this work was compared with data from [4]. Whereas there is almost a perfect agreement with their theoretical calculations, the COP predicted by simulation of the ideal cycle was in average about 40% higher than their experimental data. The predictions of generator temperature and gross temperature lift ( T o - T E ) proved to be very accurate (deviations of + 2.8°C and + 1.9°C, respectively), but the curvature of the temperature lift cannot be predicted by the ideal model. However, the ideal model can well be taken to predict the behaviour of a real system, while the calculated COPs should be corrected towards lower values.

Profitside ~'cw.

I

~'A.,,

~,w~

Evoporotort =[ Gen.water I.I

I.ow,

dl

Costintensiveside Fig. 3. Availability flow chart of chosen model.

Analysis of the layout system An availability flow balance of the system (Fig. 3) reveals that

= ~'~vi + ~'cwi + ~VAWi+ ~POWi-- ~PEwc-- ~Pcwc- PAW, -- ~OWc"

(16)

Defining exit loss and availability profit as: L=~ = ~VGw~ + ~VEw~

(17)

and ~'~a, = ~Vcw~+ ~VAW,- ~CWi- ~VAWi

(18)

the net loss can be expressed as: L=t = ~'owi + ~Ewi - ~p,om - Lex-

(19)

Obviously, the net loss equals the total internal losses, thus E Li.in, "~ Lex = ~I'/Gwi "[- ~l'/EWi -- ~T'/profit

J

(20)

where Li,i,, denotes the availabifity loss of an internal device. From this relationship the specific cost of a device in the system can be determined. If we denote the net cost associated with the right hand side of equation (20) with C,~I we can write: Ci =

Li,i,t I~GWi + t~EWi I

C,~t. tJ~profit

(21 )

Lithium bromide absorption heat pump

163

The results of the analysis of the layout system are .~h0~ in the Appendix. It may be noted here that the iteration process to determine the temperature and vapor content at the inlet to the absorber resulted in slightly too low entropies at state 8 if the vapor content was very low. However, for the purpose of this work, this problem was insignificant.

Various influences and their effects Deviating from the layout data set, the influences of various parameters were investigated. The parameters were: the quality of the four major devices, evaporator, condenser, absorber and generator, measured in terms of the minimum temperature difference across the device; the existence and quality of the two internal heat exchangers, measured in terms of COP; the mass flow rates in the external heat carrier circuits, measured in terms of temperature change which the water undergoes along the device; the heat transfer from the internal cycle to the heat carrier circuit or vice versa is determined as (2, = mnv x cp x ATnv, where I stands for either E, C, A or G. Suppose Q~ and cp to be constant, then mnv is a reciprocal function of ATnv; The results are shown in Figs 4-13.

Discussion of results From the Appendix one can see that the internal losses~make up only 20% of the losses to be accounted for, the remaining 80% are exit losses. Among the internal losses the condenser losses are the highest with 37.6%, whereas the remaining three main devices have about equal percentage ( ~ 17%). Thus first of all the influence of the quality of the condenser should be investigated. For more detailed design improvement the devices themself have to be broken into subsystems and analyzed alike. That, however, can only be done for one particular real system. A better quality of the internal heat exchangers of course leads to reductions of availability losses at the actual heat exchanger (Figs 4 and 5). However, the main benefit for the system comes from reduced losses at the four major devices, noting that the losses at the internal heat exchangers are ! o+-

I

Evaporator tosses Absorber

A_ =-

tosses

[ o-System tosses 8 [ * - Rrst tOWefficiency

Condenser Losses Generator Losses

I I

--E.xi't tosses xlO" I , - Second tow efficiency / 2

t--

J

)<

T L6

~,

-:~ v

o

1.2 ~ "0 c

8

3

•

-,

_*

JL,

.O

0.8

o

~ ir

2

-

q o

0.6

~' o. ~

~ 0.2

~ o.3

....~ o.4

? o,~

~ oe

o.2 0.7

Efficiency of ~Lernok heat e~changer

Fig. 4. Influence of the quality of the heat exchanger in the solution cycle on internal ~ pcl'fOITllancc.

and system

164

J.

WOLF

o-

+-

[

o-

8 /

"~-

K.OEHLER

el al.

•"-- Condenser Losses - Generotor Losses =-Exit Losses x l O -~ • - S e c o n d Low e f f i c i e n c y

E v a p o r a t o r Losses A b s o r b e r Losses S y s t e m Losses First Low e f f i c i e n c y

2

|

<~.

b

C-,,

~

¢--

C)

,

"

~

~" . . i

18

.:l

T

!6 6

--

$ u

F4 5 --

i2

hC

I >,

3 •[ " _ _ i

•

~w8

"--t

T

,"

;

"--"

O8

2 ~-


h

O6 x

-

-

x

~,,,, x

x - - ~

0 ~. 02

02

04

06

98

Efficiency of internal heat exchonger

Fig. 5. Influence of the quality of the heat exchanger in the cooling cycle on internal losses and system p©l'foHnance.

about one order of magnitude less than those at the major devices. The effect of the heat exchanger of the solution cycle on the system is mainly described by lower losses at absorber and generator. Following the results of the study, the generator losses can be reduced by 59% by increasing the COP of this heat exchanger from zero to 70%. Consequently, the heat exchanger in the solution

o " + x

-

Evaporotor Condenser Absorber Generator

180

178

!

025

~

0.245

,~6

o 240

i

:~ "$

.

I 74

17

--

l

l

I

I

2

4

6

8

Temperature difference

~

ozz5 I0

(K)

Fig. 6. Influence of the quality of the four major devices on system performance.

Lithium bromide absorption heat pump

o- Evo~r

tosses

165

[ |

•" - C ~ r

tosSes x . Generator Losses • - E x i t tosses xlO -~ • - Second Low efficiency

+ - Absorber tosses

o - System losses * - First low efficiency 6

2

b

tl.=,,.,.~.

,3.

~--

-- I.----.....

41.....,...

/

T 1.6

6

o (J

~4

]=

5 --

!

12 4 I

3 Z-

JD

9

• • --" '

.:."

~. ,

-'.

~

n

g

0.8

2 -

~'--"'--'T

•

Ip.

* • , ,, ~ * ~

e,,.,---,-~.

i

2

3

4

6

0

5

0.6

02 7

Temperature difference (K)

Fig. 7. Influenceof the quality of the evaporator on internal losses and system performance.

cycle b.~ a ~ effect on the COP and effectiveness (here: 5.3°4 and 4.8%, respectively). The heat exchanger in the cooling cycle has only little impact on the system performance. Interestingly the relative changes of COP and effectivene=ts have the same magnitude. A similar behaviour of the COP and the effectiveness is observed when the quality of the four major devices is varied (Fig. 6). Both numbers are strongly influenced by the quality of the evaporator, whereas the quality of the generator has only little effect over the range of the varied

+- Absorber

tos~,~

x - Ger~w-ub~

O- System Losses • - First tow effiaency

• - Exit Losms xlO "j • - Second Low efficiency .......

8

2

o_ x T

"6

.

_

C

-

-

~

II,

16 6

0 1.4 5 o 12

J

4 --

I

0

o

0.6

! 0

i

7

?'

~'

P--?'

2

3

4

5

6

:i

,~

7

8

04

Temperoture difference (K) FiB. 8. Influence o f the quality o f the condenser o n internal l o a m M.R.$.

$/2--.G

and system performance.

166

WOLF J. KOEHLER el al. ~ - Condenser Losses x - Generotor Losses * - E x i t losses x IO -= B - S e c o n d l o w efficiency

o - E v o p o r o t o r Losses + - Absorber Losses o- Systern losses = - Furst l o w e f f i c i e n c y 8

2

x T

t4

~x-

~2 N

'8

+

+

u:

+ ~

I o =---=--=--~--~--m--np-.-m--m--~--0

3

6

9

;

• 02

12

~5

Temperoture difference (K)

Fig. 9. lnflumtc¢ of the quality of the al~orber on intcrtBl losses and system performarc¢.

parameters. Although the absolute losses at the condenser are higher than at the evaporator, a better quality of condenser has less impact on the system performance than a better quality of evaporator. When the quality of a device declines, the availability losses at this devke increase linearly (Figs 7-10). This follows from theory, but for rather complex devices like absorber or generator this is not trivial. It is striking that increasing losses at the evaporator, condenser or absorber change the cycle conditions such that the generator losses decrease (Figs 7-9); On the o- Evoporotor Losses + - Absorber tosses I o - System tosses e i --~-irst Low efficiency

b x

" - Condenser losses x- Generotor Losses * - Exit Losses x IO-' e-Second tow efficiency

| 7

0

~

.

¢

,

C

¢•

~•

¢ •

*8

0•

7

v

_go

--

1(3

--

14

'~

--

12

"~u

-

4

.go

.>5 <~

2~

"-

+

--=

.0

_

_

tt.

=_ 1 o¸6

+

i

04

1 ~02 0

2

4

6

8

Temperoture difference ( K )

Fig. 10. Influence of the quality of the generator on internal losses and system performance.

Lithium bromide absorption heat pump ,,=

o+O•-

....

167

,

EvaDomtor Losses Absorber tosses System tosses First t~w efficiency

, ,,

z~- Condenser ~c~sses ] x - Generator ~osses I • - Exit tosses x I0 < [ m- Second tow efficiency I

8

I 2

T °

~

-

6 -

1,6

g

,_

0,6 ~

__It__

oi 1

I'

1'

2

3

,

,

1"

"

4

~"

mo. z

5

6

Temperature difference (K)

Fig. l 1. Infll~-qme of the mass flow rate in the evaporator water circuit on internal losses and system pfrformance.

other hand, increasing losses at the generator are made up by diminished losses at the absorber, while the net losses increase slightly (Fig. 10). From this, one might conclude that in order to improve the system performance, first of all the quality of the evaporator should be increased. Given an entry temperature TEwi, a decreased mass flow in the evaporator water circuit will lead o - [ v o l ~ r o t o r tosses + - A b s o r b e r tosses o - s y s t e m tosses * - First tow efficiency

~- Condor tosses. x-Generotor toIiel a - E x i t t o m s xlO "~ s - S e c o n d Low efficiency

8

b

i. 5 0

j,

o

w

~

+

t,,

_

;

- :

0

+

i I0

15

+~

i~ . . . .

20

25

~x.,...~

,,- ,

06

,

02 30

Temperotum difference (K)

Fig. 12. Influence of the mass flow rate in the condenser and almuH'ber water circuit on internal tomes and system performance.

W O L F J. KOEHLER et al.

168

to a lower evaporator temperature, which in turn will lead to an increased temperature lift in the cooling cycle. Thus the calculated decrease of the COP and rhL meets our expectations. Interestingly, the increasing loss at the evaporator will be partly compensated by lower losses at generator and absorber. The steep increase of the exit losses is mainly due to the higher mass flow in the evaporator water circuit. Therefore this does not concern us and a high mass flow rate here can be recommended (Fig. 11). Decreased mass flows in the condenser and absorber circuits lead to higher losses at condenser and generator, while the losses at the evaporator and absorber are almost constant and decreasing, respectively (Fig. 12). The counter effect at condenser and absorber may be explained by the increase/decrease of the mean temperature difference at the appropriate device. While the decrease of the effectiveness corresponds to the increase of the internal system losses, the COP increases at the same time. Here we encounter a situation discussed earlier, that COP and effectiveness yield contradicting results. A decreasing mass flow causes a considerably lower availability profit and a moderate decrease of availability input. Hence the effectiveness diminishes. On the contrary the constant heat profit and the reduced input to the system result in an increasing COP (Fig. 12). The modified effectiveness ~/~Lwould show the same trend as the COP. In this case, the highest value of either COP or r/~Lboth lead to the lowest cost performance. The appearing contradiction of the behaviour of COP and availability losses can be resolved when the exit losses after the generator are taken into account: the total losses decrease with decreasing mass flow. A higher mass flow in the generator water circuit (Fig. 13) causes much higher exit losses and only slightly higher generator losses. Whereas the COP is insensitive to this, the effectiveness (and the modified effectiveness) increase steeply. Therefore a rather low mass flow in the generator water circuit should be chosen. CONCLUSIONS 1. It was shown that the second law analysis quantitatively visualizes losses within the system and gives clear trends for system design optimization.

o - Evoporator + -

¢ - System

K

7

IL

~ - Condenser x - Generator

tosses

* - Exit tosses

tow efficiency

• - First

o--

Losses

Absorber Losses

!t

• - Second

tosses x I 0 -~

tow effic~r)cy

a.e

~

~

~

16

6

g

ig,

,4 ~

"

'5 --

0 "0

~

>"

<[

g

3

0.8 -

0

•

Z

, ; -

~ ....

~

~ , ~ ,

o" , ~ ' 5

~

to

~+,~*---'---

~ ' ~ ' ~ ~

L

l

,

k

15

2o

25

30

Temperature

difference

F i g . 13. I n f l u e n c e o f the mass flow rate in t h e g e n e r a t o r performance.

o2 l o 35

(K)

water circuit o n i n t e r n a l losses and system

Lithium bromide absorption heat pump

169

2. The use of an effectiveness in order to find the lowest cost performance of a given system can be misleading and is of limited benefit. 3. It was demonstrated that specific cost can be assigned to each device of the system on the basis of a physically realistic second law analysis. 4. The highest losses occur at the condenser, even if it has ideal behavior. 5. For given layout conditions, the system is most sensitive to the quality of the evaporator. 6. The internal heat exchanger in the solution cycle has a large effect, whereas the one in the cooling cycle has only little impact. 7. The losses of the various devices are highly interdependent and can only be treated as such. AcknowledgementsmThe principal author wants to acknowledge the following institutions, whose support made this work possible: Academic Computing Services and Systems (ACSS); German Academic Exchange Service (DAAD); Department of Mechanical Engineering, University of Minnesota.

REFERENCES 1. T. Badoh, Exergie, Universititsbibliothek der Technischen Universit~t Berlin-Abt. Publikationen, Berlin (1981). 2. F. Bosfijakovic, Wd~melehreund W~rmewirtschaft in Einzeldarstellungen Bd. 12, Teclmische Thermodynamik II. Theodor Steinkopff, Dresden (1960). 3. M. F. Brunk, Thermodynamische und physikadische Eigenschaften der L6sung Lithiumbromid/Wasser ads Grundlage ffir die Prozel~imulafion yon Absorptions Kilteanlagen, Ki fflima-IG~lte-Hebung 1O, 463--470 (1982). 4. S. K. Chandhari, D. V. Paranjape, M. A. Eisa and F. A. Holland, A study of the operating characteristics of a water--fithium bromide absorption heat pump, J. Heat Recovery Systems 5, 285-297 (1985). 5. R. T. Ellington, G. Kunst, R. E. Peck and J. F. Reed, The absorl3tion cooling process, Inst. Gas Technol. Chicago, Res. Bull. 14 (August 1957). 6. N. Ehner, Grundlagen der Technischen Thermodynamik. Vicweg + Sohn, Braunschweig/Wiesbaden (1980). 7. K. F. Knoche, D. Stehnufier, Exergetic Criteria for the Development of Absorption Heat Pumps, Chem. Engng Communs 17, 183-194 (1982). 8. W. Koehler, W. E. lbele, E. R. Winter and J. Soltes, Entropy values of aqueous solutions of lithium bromide and approximation equation, ASHRAE Trans. 93(2) (1987). 9. H. L6wer, Thermodynami~che und Physikafische Eigenschaften der w~srigen LiBr-L6sung, Dissertation, Technische

Hochschule, Karbruhe (1960). 10. L. A. McNecly, Thermodynamic properties of aqueous solutions of lithium bromide, ASHRAE Trans. gS, 413-434 (1979). 1I. Second law aspects of thermal design, ASME-Heat Transfer Division, HTD-Vol. 33, A. Bejan and R. L. Reid (eds) presented at The 22nd National Heat Transfer Conference and Exhibition, Niagara Falls, N.Y. (5-8 August 1984).

APPENDIX

COMPUTATION FOR LAYOUT CONDITIONS ''"'"

INPUT QUANTITIES * " " " ' " * " " " " ' * * " ' " * ' ' " ' " * * * * " ENVIRONMENTAL TEMPERATURE: TINF [K] =

278.15

TEMP. OF INLET WATEROF EXT.SYS.

TAWI

298.15

EXTERNAL ASSUMPTIONS: DLTTCW DLTTAW DLTTGW

= 25. = 25. = 25.

INTERNAL ASSUMPTIONS: DLTTC K DLTTA DLTTG ETAHESC

= 5. : 5. = 5. .5

TGWI

393.15

WOLF J. KOEHLEP.et al.

170

" ' = = " POINTS OF STATE OF FIRST EXT.SYS. ============================= EWI .

.

.

.

.

.

.

EWE

.

.

.

.

.

.

.

.

.

CWl .

.

.

.

..

.

.

CWE .

.

.

.

.

.

.

.

AWl .

.

.

.

.

.

.

.

AWE .

.

.

.

.

.

.

GWI .

.

.

.

.

.

.

GWE .

.

.

.

.

.

.

T: 289.15 285.15 298.15 323.15 298.15 323.15 393.15 368.15 H: 6 7 . 0 1 50.25 104.73 209.51 104.73 209.51 502.88 398.10 S: . 2 3 5 2 . 1 7 7 1 . 3 6 3 8 . 7 0 3 8 . 3 6 3 8 . 7 0 3 8 1.5276 1.2514 PSI: 1.2978 . 6 8 8 8 3.2235 13.438.1 3.2235 13.4381 77.6622 49.7153 ='''"

POINTS OF STATE IN INT.SYS. =================================== T

lS 1 2 3S 3 4 5 6PU 6 7G 7 8

P VAPCO

280.15 304•15 357.02 328.15 317,37 280,15 303.15 303.15 330•90 388.15 345,66 331.12

1000 1000 15730 15730 15730 1000 1000 15730 15730. 15730. 15730. 1000.

1.000 1,000 1.000 .000 ,000 ,063 .000 ,000 ,000 ,000 ,000 .009

XI

H

.0 0 0 0 0 0 51 1 51 1 51 1 64 9 64 9 64 9

S

PSl

2513.76 8.9610 647.72 2558.96 9.1332 645.03 2656.09 8.1181 1024.51 230.46 . 7 6 8 6 643.15 1 8 5 . 2 6 . 6 2 7 6 637.18 1 8 5 . 2 6 . 6 5 9 7 628•22 -174.05 . 2 8 3 1 53.74 -174.04 . 2 8 3 1 53.76 -113.92 . 4 7 2 1 61.30 -20.02 .6848 9.87 ~ 9 6 . 3 3 , 4 6 8 0 -6.14 -96,33 . 4 6 7 2 -5.92

MISCELLANEOUS QUANTITIES ~ S W l S l S S S ~ m I ~ S S S ~ I S S S S ~ t S ~ w ~ I ~ HEATS AND WORK

QE = OC

2328.494KJ/KG

= QA =

-2425.631Kd/KG -3021.585 KO/KG

OG = WPU =

3118.657KO/KG •064 Kd/KG

OR OR OR OR OR

.427465 KWI(KW PROFIT) -.445297 KWI(KW PROFIT) -.554703 KW/(KW PROFIT) .572523 KW/(KW PROFIT) .000012 KW/(KW PROFIT)

MASS FLOWS IN [(KG/S)/(KWPROFIT)] DDOT = MEW = MAW =

.184E'03 .255E-01 .529E-02

FDOT = MCW = ~W =

.865E-03 .425E-02 .546E-02

CHECK OF ALL ENERGYBALANCES: ALL ENERGYBALANCESARE SATISFIED • ==='=

ANALYSES = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = FIRST LAW ANALYSIS FUNCTION DEVICE

EVAPORATOR CONDENSER ABSORBER

GENERATOR PUMP EXP.VALV.CC EXP.VALV.SC HEATEXCH.CC HEATEXCH.SC SYSTEM

ENERGY PERCENT INPUT OF TOTAL KW/KW INP OUT

.427

42.7 .0 -.555 .0 •573 57.3 .000 .0 .000 .0 .000 .0 .000 .0 .000 .0 -.445

0 445 555 0 0 0 0 0 0

EN. COP PROF. KW/KW • 000 • 000 .000 . OOO .000 .000 • 000 .000 .000

444 833 758 402 700

OOO 000 500 500

.000 100.0 100.0 -1.000 1.747

MASS

1.000 1.000 1.000 1.000 1.000 1,000 4.713 4.713 4.713 3.713 3•713 3.713

.

.

.

Lithium bromide absorption heat pump

171

SECOND LAW ANALYSIS FUNCTION

DEVICE

LOSS IN KW/KW

EXITLOSS AVAIL AFTER DEV PROF. PRC KW/KW KW/KW

E2L

16.9 37.6 19.5 15.5 .0 2.3 -.2 2.2 6.2

01756 O00OO O00OO 27166 00000 O000O 00000 OOOO0 00000

.00000 00000 00000 00000 00000 00000 00000 00000 00000

230 620 797 928

.07076 100.0

.28923

.09749

::::::::::::::::::::::::::::::::::::::::::::::::::::::

EVAPORATOR CONDENSER ABSORBER GENERATOR PUMP EXP.VALV.CC EXP.VALV.SC HEATEXCH.CC HEATEXCH.SC SYSTEM

.01195 .02660 .01381 .01094 .00000 .00164 -.00015 .00159 .00438

1 000

000 000 000 598 .230