1

A11102 140327 NBS

PUBLICATIONS

v NBSIR 82-2606

AlllOb 41L7L.2

A Mode! of the Steady-State

Performance of An Absorption

Heat Pump

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, DC 20234

October 1 982

. (J56 U.S. DEPARTMENT OF COMMERCE

c32-2606 NATI0NAL bureau of standards

1982

C.2

NBSIR 82-2606

* • * A MODEL OF THE STEADY-STATE

PERFORMANCE OF AN ABSORPTION

HEAT PUMP

RATIONAL BUREAU

PF STANDARDS

LIBRARY DEC 1 1982

O'O'V cxcc.- CvCC*

GiC V°°

. ou>

<L->

Dr. S. A. Klein

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Building Technology

Washington, DC 20234

October 1 982

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

A mathematical model of the steady-state performance of an absorption heat pump

is described. The model is compared with experimental data from a residentialsized water chiller. It is also used to determine the sensitivity of the heat

pump performance to its design variables.

iii
TABLE OF CONTENTS

Page

ABSTRACT iii

LIST OF FIGURES v

LIST OF TABLES vi

1. INTRODUCTION 1

2. DESCRIPTION OF THE MODEL 2

3. EXPERIMENTAL DATA 3

4. COMPARISON OF THE MODEL TO EXPERIMENTAL DATA 21

5. EFFECTS OF MODEL PARAMETERS 27

6. CONCLUSIONS 30

REFERENCES 31

ACKNOWLEDGMENT 32

APPENDIX A. PROPERTY DATA ROUTINES A-l

APPENDIX B. PROGRAM LISTING B-l
LIST OF FIGURES

Page

Figure 1. Schematic Diagram of the ARKLA Chiller, Model No. ACC-36-00 .. 3

Figure 2. Thermocouple Locations 16

v
«

LIST OF TABLES

Page

Table 1. ARKLA Unit Thermocouple Locations 17

Table 2. Steady-state Test Data at 80°F 18

Table 3. Steady-state Test Data at 95°F 19

Table 4. Steady-state Test Data at 100. 5°F 20

Table 5. Parameter Values Used in Comparisons 22

Table 6. Calculated Results for Ta-j_ r = 95°F 23

Table 7. Calculated Results for Taar = 80°F 25

Table 8. Calculated Results for Taj[ r = 100. 5°F 26

vi
1 . INTRODUCTION

A mathematical model of the steady-state performance of an absorption heat pump

has been developed and coded into a FORTRAN program. The model is based on mass and energy balances about each system component and it incorporates heat

transfer rate limitations. A detailed description of the model appears in

section 2.

One application for this model is to check the consistency of experimental

data. Thus far, the model has been compared with the steady-state performance

of an ARKLA 3-ton ammonia-water chiller (model no. ACC 3600). The experimental

data are reported in section 3. Comparisons of the model to these data appear

in section 4.

The model can also be a useful tool in the analysis and design of absorption

heat pumps through sensitivity studies. Used in this manner, the model

indicates how the steady-state performance is affected by changes in the design

parameters or operating conditions. The results of a sensitivity study are reported in section 5.

The model has been written to be independent of the absorbent-refrigerant

system; any absorbent-refrigerant system for which property data are available

can be used with the model. The required property data subroutines are described in appendix A. A listing of the program appears in appendix B.

1
2. DESCRIPTION OF THE MODEL

The absorption heat pump model is coded in a modular manner; i.e., a separate

FORTRAN subroutine is used for each system component. There are several advantages to this modular approach. First, it allows simulation of many different

system configurations without major changes to the model since additional heat

exchangers, pumps, throttles, etc. can be included as desired. Second, the

modular approach simplifies the program development in that improved component

models can be incorporated as they are developed. A disadvantage of the modular

approach is that the set of equations describing the heat pump performance can

not be solved explicitly. An iterative solution is required.

There are three distinct types of information associated with each component

model: parameters, inputs, and outputs. The parameters are the design

specifications of the component. In the component models described below, the

parameters are primarily factors to account for heat transfer limitations. The

inputs to a component are the characteristics of the fluid streams flowing into

that component. Each stream has six characteristics:

T - temperature [°F]

P - pressure [psia] x - overall composition [lb ref rigerant/lb solution]

h - enthalpy [BTU/lb]

q - quality [lb vapor/lb liquid + vapor]

A - flow rate [lb/hr]

(Other stream characteristics are density, viscosity, thermal conductivity,

specific heat, etc., but they are not needed in this model.) The outputs of a component are the characteristics of the outlet streams and any external heat

flows such as the evaporator heat input. In steady-state operation, the inputs

and outputs are constants with respect to time. The distinction between parameters and inputs is that parameters are known constants specified by the user;

the inputs are generally unknown and must be found by an iterative solution

technique

.

The iterative solution proceeds in the following way. Each component subroutine

is designed to calculate the outputs of the component using the supplied parameter and input values. The outputs of one component are inputs to other com- ponents in the system. The component subroutines are executed and with each

iteration, the input/output values are improved. The order in which the subroutines are executed is unimportant. The iteration proceeds until the outputs

(and thus the inputs) of all routines converge. The final solution is thus

found by successive substitution.

A schematic diagram of an ARKLA 3-ton chiller is shown in figure 1. Due to its

modular form, the model is not limited to absorption machines of this particular

configuration, but the model was developed for the ARKLA unit. Sixteen flow

stream locations are identified by numbers in the diagram and are referred to

in the component model descriptions below.

9
Figure 1 . Schematic diagram of ARKLA chiller model ACC-36-00

3

Solution

Pump
2 . 1 SOLUTION PUMP

SUBROUTINE PUMP

PARAMETERS

:

1. m - solution flow rate [lb/hr]

2. Phigh “ pressure on high side of cycle [psia]

INPUTS: Stream 1

OUTPUTS: Stream 2

The solution pump requires a relatively small work input and has little effect

on thermodynamic properties other than pressure. The model is simplistic in

that the work input is assumed to be negligible and the flow rate must be

specified. A mathematical description is as follows.

2.2

m2 — m (2.1.1)

p 2 = phigh (2.1.2)

T2 = Ti (2.1.3)

x2 = Xi (2.1.4)

h2 = hi (2.1.5)

q2 =

<u (2.1.6)

RECTIFIER

SUBROUTINE RECT

PARAMETERS

:

1. (UA) rect - overall heat conductance

INPUTS: Streams 2, 5

OUTPUTS: Streams 3, 6, 13

The purpose of the rectifier is to condense water vapor from the ammonia-water

vapor mixture leaving the generator. In the ARKLA unit, the rectifier is a heat exchange coil acting as a partial condenser. In the model, it is assumed

that the rectifier is adiabatic and that streams 6 and 13 are in equilibrium

so that

T6 = T13 ( 2 . 2 . 1 )

p 6 = p 13

4

( 2 . 2 . 2 )
Mass balances yield

m3 = m2 (2.2.3)

X3 = X2 (2.2.4)

• • • m^ + m ^

3

= 1115 (2.2.5)

• • • mftx^ + m13 x 13 = m5 x5 (2.2.6)

Pressure losses are assumed to be negligible.

P 5 = P 5 (2.2.7)

P 3 = P 2 (2.2.8)

The rate of heat transfer between the stream flowing within the coil and the

condensing vapor is expressed in terms of an overall heat conductance and a log mean temperature difference.

Q = (UA) rect ATlm (2.2.9)

where

(Tc - To) - (T fi - To)

ATim = —2. 2 2 £-

T - T

ln(_5 3

) t 6 - t 2

( 2 . 2 . 10 )

An energy balance requires that

• • • • • Q = m2 (h3 - h2 ) = 015115 - m^h^ - m^h^ (2.2.11)

Equations 2.2.5 through 2.2.11 are solved iteratively as follows. A guess is

made for T 5 (= T 13 ). This temperature is used with the property data subroutines

to determine the composition and specific enthalpy of streams 6 (vapor) and 13

(liquid)

.

x13 = XLPT(P 13 , T 13 )

h 13 = HL(x 13 , T 13 , P 13 )

x6 = xv ( x 13> p 6>

h6 = ^V( x i 3 , x6 , T5 , P^)

• • The mass flow rates, m^ and m^, are found from equations 2.2.5 and 2.2.6.

Using these flow rates, the rate of heat transfer is evaluated form the righthand side of equation 2.2.11, which then determines >13 , The temperature of

state 3 is fixed by its enthalpy, pressure, and composition, and it can be

determined from the property data subroutines as follows.

5
TH(x3 , h3 , P3 ) if T3 < TSAT(x3 , P3 ) t3 = TQ(x3 , P3 , h3 , q3 ) otherwise

This value of T3 is then used with equations 2.2.9 and 2.2.10 to determine the

rate of heat transfer. The difference between this result and that obtained

from equation 2 . 2.11 is used to find an improve value of T 5 (= T]^ 3 ) by the

Secant method. (D

2.3 SOLUTION - COOLED ABSORBER

SUBROUTINE ABSSC

PARAMETERS

1. (UA) absg - overall heat conductance

INPUTS: Streams 3, 11, 14

OUTPUTS: Streams 4, 12

Absorption of refrigerant in the ARKLA unit occurs in two components; a solution-cooled and an air-cooled absorber. In the solution-cooled absorber, the

hot weak (in refrigerant) solution from the generator is sprayed over a coil

containing the cooler rich solution which is thereby preheated before it enters

the generator during this process. The refrigerant vapor is partially absorbed

in the weak solution. It is also entrained so that a two-phase solution exits

the absorber at state 12 .

Mass balances require that

• • m4 = m3 (2.3.1)

x4 = x3 (2.3.2)

• • • m 12 = mll + m14 (2.3.3)

• • • m12 x 12 = mll x ll + m14 x 14 (2.3.4)

Pressure losses are neglected.

P 4 = P 3

p 12 = P 11

The rate of heat transfer between the stream flowing in the coil and the

absorbent is expressed in terms of an overall heat conductance and a log mean

temperature difference.

Q = (UA) abss ATlm (2.3.7)

(2.3.5)

(2.3.6)

6
where

(2.3.8)

Energy balances require that

Q = 013(114 - I13 ) = miihn + m^h^ - 2^1

2

(2.3.9)

Equations 2.3.7 through 2.3.9 must be solved iteratively for T 4 and T]^* A

guess is made for T 4

. The enthalpy at state 4 is then obtained from property

data routines. If the guess value of T4 is less than the saturation temperature,

stream 4 is subcooled. In this case

h4 = HL (

X

4 , T4 , P4 ) for T4 < TSAT(x4 , P4 )

94 = 0

For two-phase conditions (T4 > TSAT(x4 , P4 )),

The enthalpy of state 12 and rate of heat transfer can now be evaluated from

equation 2.3.9. The temperature and quality of state 12 are fixed by the

pressure, overall composition and enthalpy of the mixture and can be determined

from property data routine TQ.

T i2 = TQ(x 12 , Pi 2 > h12 , 912)

The rate of heat transfer can now be calculated from equations 2.3.7 and 2.3.9.

The difference between the values of Q calculated from equations 2.3.7 and

2.3.9 is used to find an improved value of T4 by the Secant method. The iterations are terminated when two successive values of T 4 are within a specified

tolerance

.

X

4 = XLPT (

P

4

> T

4

)

*4 = XV( X

L,

P

4

)

*4 = HL(x|, T

4

, P

4

)

h^ = hv(x£, xj, t

4

, p

4

)

94 = (x4 - x^)/(x| - x^;)

h

4 = (1 “ 94)^4 + 9 4

h

4

7
2.4 AIR-COOLED ABSORBER

SUBROUTINE CONABS

This subroutine is used for evaluating the performance of the air-cooled

absorber as well as for the condenser as outlined below.

PARAMETERS

1. (UA) absa - overall heat conductance

2. Taj_ r - air temperature

INPUTS: Stream 12

OUTPUTS: Stream 1, Qab sa A two-phase mixture enters the air-cooled absorber and it is cooled (and

condensed) by heat transfer to the air stream. Continuity requires that

• • ml =m12 (2.4.1)

xi = xi2 (2.4.2)

Pressure losses are neglected.

Pi = P12 (2.4.3)

The rate of heat transfer between the solution and the air is expressed using

a log-mean temperature difference relation.

Qabsa = (UA) absa AT]_m (2.4.4)

where

T — T

ATlm = 11 I (2.4.5)

T - T

In ( 12 air ') T 1 “ Tair

An energy balance requires that

• • Qabsa = (^12 " ^l^ml (2.4.6)

Equation 2.4.4 through 2.4.6 are solved iteratively. A guess is made for T^

and Qabsa is evaluated with equation 2.4.4. The enthalpy of state 1 can also

be found using the assumed temperature. If state 1 is subcooled then

h]_ = HKxi, T ]_ , P]_) for Ti < TSAT(x L , P]_)

q i = o

If state 1 is two-phase then T^ _> TSAT (xj_, P]_) and

8
= XLPTCPp T

l

)

xj = XV(x^, P

x

)

h\ = HL(x^, T p

P

L

)

h* = hv( x

l, x

J,

T pp

x

)

q 1 = (x

1 - xL)/( x

V -

h

l = (i “ + q : hj

Qabsa can now calculated from equation 2.4.6. The difference between this

result and the value of Qabsa found from equation 2.4.4 is used to find an improved value of by the Secant method.

2.5 GENERATOR

SUBROUTINE GEN

PARAMETERS

:

1 • Qgen “ rate of heat input

2 . e L- heat transfer effectiveness between the exiting weak solution

and the entering rich solution

3. ey - heat transfer effectiveness between the exiting vapor and the

entering rich solution

INPUTS: Streams 4, 13

OUTPUTS: Streams 5, 14

Refrigerant is separated from the absorbent by the heat input to the generator.

The high pressure of the boiling refrigerant forces the weak solution at the

lower part of the generator through a pipe leading to the solution-cooled

absorber. In the ARKLA unit, the pipe is arranged so that the weak solution is

placed in a heat exchange situation with the entering rich solution. Similarly,

heat exchange occurs between the exiting vapor, and the incoming rich solution.

Mass balances yield

• • • • m5 + m14 = m4 + m13 (2.5.1)

• • • • 1115 x5 + m^ 4 X |4 = 104 x4 + m^x^ (2.5.2)

Pressure losses are neglected

P 5 = P 14 = P4 = P i3 (2.5.3)

9
Internal heat exchanges between the incoming rich solution and the exiting

streams are described in terms of effectiveness factors. For the exiting vapor,

T5 = Tgen - ey^gen “ T 4 ) (2.5.4)

and for the exiting weak solution,

Ti 4 = Tgen - e l/Tgen ~ T 4 ) (2.5.4)

where Tg en is the temperature of the weak solution at the lower part of the

generator where it enters the pipe.

An energy balance around the generator requires that

• • • • • 1115115 + m^4h^4 = m]_3h^3 + 1114114 + Qgen ( 2 . 5 . 6 )

The above equations are solved iteratively. A guess is made for Tgen . The

concentration (at equilibrium) of the weak solution is thus established.

x 14 = XLPT(Pi4> Tgen)

The temperatures of the exiting streams are determined from equations 2.5.4 and

2.5.5. These temperatures are used to determine the specific enthalpies of the

exiting streams and the composition of the vapor.

h 14 = HL(x l4 , T^ 4 , P 14 )

x

5 = XV(xcj , P5

)

hcj = HV(xg, Xg , Tg, Pg)

where x^ = XLPT(P

5

, Tg)

With the concentrations of the exiting streams determined, equations 2.5.1 and

2.5.2 are used to determine the mass flow rates, which are then used with the

calculated enthalpies in equation 2.5.6. The difference between the left and

right hand sides of equation 2.5.6 is used to find an improved value of Tgen by

the Secant method. The iterations are terminated when two successive values of

Tgen are within a specified tolerance.

2.6 CONDENSER

SUBROUTINE CONABS

PARAMETERS

1. (UA) conci - overall heat conductance

2 . Taj_ r - air temperature

10
INPUTS: Stream 6

OUTPUTS: Stream 7, Q ccmd

Rerigerant vapor, along with a small amount of water is condensed and possibly

subcooled in the condenser.

Continuity requires that

• • my = m^ (2.6.1)

X7 = (2.6.2)

Pressure losses are neglected

P7 = P6 (2.6.3)

The heat transfer rate between the refrigerant and the air is expressed using

a log-mean temperature difference relation.

Qcond (UA) conci AT]_m (2.6.4)

where

T - T

ln(J> air)

^7 “ ^air

An energy balance requires that

• • Qcond = ( h6 “ ^7

)

m7 (2.6.6)

The heat transfer processes occurring in the condenser are identical to those

in the air-cooled absorber. As a result, the same subroutine is used for both

components. The program logic is described in section 2.4.

2.7 REFRIGERANT HEAT EXCHANGER

SUBROUTINE HXLV

PARAMETERS

1 . (UA)ftx

- overall heat conductance

INPUTS: Streams 7, 10

OUTPUTS: Streams 8 , 11

11
Liquid refrigerant from the condenser is cooled further in the refrigerant heat

exchanger by the refrigerant vapor leaving the evaporator. Mass balances

require that

• • • • mg = m n = m7 = m10 (2.7.1)

x8 = X 11 = x7 = x 10 (2.7.2)

Pressure losses are neglected

p8 = P 11 = p7 = p 10 (2.7.3)

The rate of heat exchange between the streams entering and exiting the

evaporator is expressed

Qhx - (UA) hX

(T8 - T

10 ) - (T

? - T n ) T _ T

ln(_J! L2)

Ty - Tn

(2.7.4)

Also, an energy balance requires that

Qhx = ( h ll “ h 10) m10 = ( h8 “ h7 )m7 (2.7.5)

Equations 2.7.4 and 2.7.5 are solved iteratively. A guess is made for Tg , which

establishes the enthalpy of Tg.

hg = HL ( xg , Tg, Pg)

The enthalpy of state 11 is then directly determined from equation 2.7.5 which

establishes its temperature and quality.

Tn = TQ(xg , Pg, hg, qg)

With Tg and Tn known, the rate of heat exchange can be calculated from

equation 2.7.4. The difference in the values of Q^x obtained from equations 2.7.4 and 2.7.5 is used to improve the estimate of Tg using the Secant

method. Iteration stops when two successive values of Tg are within a specified

tolerance

.

2.8 RESTRICTOR

SUBROUTINE THROT

PARAMETERS

:

1. Pevap

“ Tow side pressure [psia]

INPUTS: Stream 8

OUTPUTS: Stream 9

12
In the ARKLA chiller, the refrigerant leaving the condenser is reduced to the

evaporator pressure as it passes through two refrigerent restrictors. In the

model, the drop in pressure is obtained by a single restrictor. Mass and

energy balances require that

• • mg = mg (2.8.1)

xg = xg (2.8.2)

hg = h8 (2.8.3)

The restrictor outlet stream will be a two-phase mixture. The temperature and

quality of this stream can be determined since its composition, pressure and

enthalpy are known.

Tg = TQ(xg, Pg, hg , qg)

2.9 EVAPORATOR

PARAMETERS

1. (UA) evap - overall heat conductance between the evaporating refrigerant

and the chilled water

INPUTS: Streams 9, 15

OUTPUTS: Streams 10, 16, Qevap

In the ARKLA chiller, water is cooled as is drips over a coil through which

the evaporating refrigerant flows. The refrigerant may exit the evaporator

in a two-phase or superheated state.

In earlier versions of this program, the small amount of water (2-3 percent on

a weight basis) with the refrigerant was neglected. It was found however, that

the water has substantial effect on the evaporator performance and it must be

accounted for.

Mass balances require that

m10 = mg (2.9.1)

x10 = xg (2.9.2)

•m16

• = m 15 (2.9.3)

Pressure losses are neglected

*10 = P9 (2.9.4)

13
The rate of heat transfer between the refrigerant and the water is expressed

Qevap = (UA) evap^lm (2.9.5)

where

(2.9.6)

The log-mean temperature difference assumes this form since the design of the

evaporator causes the refrigerant at both the inlet and outlet of the evaporator

to be in heat exchange contact with the entering chilled water.

An energy balance requires that

• • • Qevap = ( h 10 “ h9) m9 = ( h 16 “ h 15)m15 (2.9.7)

Equations 2.9.5 through 2.9.7 are solved iteratively. A guess is made for T^q.

The log-mean temperature difference and rate of heat transfer are then

calculated from equations 2.9.6 and 2.9.5, respectively.

With water present in the refrigerant, the refrigerant always exits in

two-phase. Its enthalpy and quality are found as follows:

xL

10 = XLPT (

P

10’ T

10 )

x

V

10 - > P 10>

q 10 (x

10 - x

10 )/( x10 - x10

h

10 - HLfx^j ’ P 10>

"To

* • x 10’ T 10’ P 10 )

h

10 = (1 - q 10 )h 10 + q 10 h

10

Using this enthalpy, the rate of heat transfer is calculated from equation 2.9.7.

The difference between the values obtained from equations 2.9.5 and 2.9.7 is

used to improve the estimate of T]_q the Secant method. Iteration is

stopped when two successive values of T]_q are within a specified tolerance.

ATim =

T

10 ~ T

9

T „ - T

ln(JJL_JL)

15 - T 10

14
3 . EXPERIMENTAL DATA

The steady-state performance of an ARKLA water chiller (model no. ACC 36 00) was measured in an environmental chamber at air temperatures of 80°F, 95°P,

and 100°F. In all tests, 55°F water was supplied to the unit at 7.2 GPM.

The test apparatus and procedures were as described by Lindsay and Didion(2)

with the following modifications.

1. A micro-computer (CROMEMCO) was interfaced with the FLUKE data logger to

improve the analysis of the experimental data. Temperatures were measured

at 48 locations shown in figure 2 and listed in table 1. After steadystate operation was achieved, these data were recorded at two minute

intervals for 30 minutes and averaged over this period.

2. To measure the generator heat input, the CO 2 and O 2 content of the exiting

flue gas were independently measured using a LIRA Model 300 Infrared Analyzer

and a LYNN Model 6000-B Combustion Analyzer, respectively. The flue gas

temperature was measured with a six-junction averaging thermocouple

(location 30) and the gas usage was measured in cubic feet by a Spraque

dry test meter. None of these measurements varied significantly with air

temperature. Assuming the gas to be pure methane, the CO2 and O 2 measurements indicate a theoretical amount of air ranging between 153 percent and

168 percent. A combustion analysis results in the generator heat input

between 58100 and 58800 BTU/h.

3. A sample valve was installed in the line carrying the weak solution from

the generator to the absorber (approximately at the location of thermocouple 3). This valve allowed the composition of the weak solution to be

determined by titrating a known mass of sample with dilute sulfuric acid

of known normality.

4. To install the sample valve (and two other valves intended to improve the

cyclic performance of the chiller) it was necessary to remove the ammonia.

The unit was recharged in a trial and error procedure until its capacity

no longer was affected by small changes in the charge. The capacities

measured in the steady-state tests agreed nearly identical to within

2 percent of those reported by Lindsay and Didion.(2) The evaporator and

generator pressure measured in these tests, however, differ significantly

from those reported by Lindsay and Didion. Pressure gauges were calibrated

directly before these tests were run.

The experimental results for the steady-state tests at 80°F, 95°F, and 100°F are summarized in tables 2, 3, 4, respectively. The COP appearing in these

tables is the ratio of the capacity to the generator heat input; it does not

account for electrical power usage nor inefficiencies in combustion.

15
R*<(i(*««nl

H«»t

fwh»nf*r

f

Figure 2. Thermocouple Locations.

16
Table 1 ARKLA Unit, Thermocouple Locations

Chanel No. Location

0

12

3

4

5

6

78

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

Icebath

Pump in

Pump out

Solution out of Generator

Solution in to Generator

Solution into Absorber Heat Exchanger

Unit Plenum Air DB

Ammonia to Condenser

Ammonia out of Condenser

Ammonia into Evaporator

Ammonia out of Evaporator

Ammonia into Absorber

Liquid Ammonia into Refr. Heat Ex.

Liquid Ammonia out of Refr. Heat Ex.

Generator Top

Generator Middle

Generator Bottom

Solution cooled Absorber Top

Solution cooled Absorber Bottom

Air cooled Absorber Bottom

Air cooled Absorber Middle

Air cooled Absorber Top

Condenser Top

Condenser Middle

Condenser Bottom

Evaporator Top

Evaporator Middle

Evaporator Bottom

Air Inlet

Air off Condenser Coils

Stack Gases

Water Inlet

Water Outlet

Water Bypass

Ambient Air DB

Ambient Air TO

Temperature Difference Water Inlet/Outlet

Evaporator Water Discharge Line

Evaporator Water Bottom

Evaporator Water Middle

Evaporator Water Top

Evaporator Water Inlet Line

Solution out of Absorber

Solution out of Absorber Coils

Absorbent into Absorber

Refrigerant into R.efr. Heat Ex.

Gas Supply Temperature

Icebath

17
Table 2. Steady-State Test Data at 80°F

Evaporator Pressure - 56.5 psia

Generator Pressure - 276.5 psia

Capacity - 35435 BTU/hr

C02% in Stack Gas - 9.0%

02% in Stack Gas - 7.5%

Generator Heat Input - 58100 to 58830 BTU/hr

Electrical Power Consumption - 1052 W

Weak Solution Concentration - 0.053 lbm NH3 /lbm soln.

COP - 0.602 to 0.610

Temperatures

(Thermocouple Location = Temperature °F)*

0= 32. 49 1 = 106. 16

4=220. 56 5= 139. 08

3= 94. 92 9= 87. 43

12= 94. 62 13= 79. 89

16= 172. 29 17= 168. 98

20= 139. 93 21 = 124. 44

24= 116. 99 25= 55. 18

28= 79. 89 29= 123. 43

32= 45. 21 33= 57. 46

36= 3. 44 37= 44. 96

40= 39. 94 41 = 115. 82

44=213. 49 45= 96. OO

2= 104. 20 3=231. 54

6= 57. 96 7= 131. 04

10= 69. 21 h-L

I-*- II 83. 46

14=219. 74 15=235. 27

13= 144. 41 19= 141. 91

22= 121. 75 23= 113. 13

26= 34. 46 27= 33. 07

30=446. 13 31 = 55. 1 1 34= 77. 73 35= 77. 93

38= 43. 69 39= 40. 98

42= 155. 96 43= 103. 98

46= 72. 14 47= 32. 64

* Channel 36 is a millivolt reading which yields the difference in temperature

between the inlet and outlet chilled water when multiplied by 2.8539.

18
Table 3. Steady-State Test Data at 95°F

Evaporator Pressure - 324.6 psia

Generator Pressure - 71.6 psia

Capacity - 32755 BTU/hr

CC> 2 % in Stack Gas - 7.3%

02% in Stack Gas - 8.6%

Generator Heat Input - 58100 to 58830 BTU/hr

Electrical Power Consumption - 1056 W

Weak Solution Concentration - 0.087 lbm NH3 /lbm soln.

COP - 0.556 to 0.564

Temperatures

(Thermocouple Location = Temperature °F)*

0= 32. 32 1 = 121. 64 2= 119. 60 3=240. 57

4=230. 23 5= 152. 94 6= 51. 20 7= 194. 00

8= 1 19. 37 9= 85. 04 10= 66. 69 11 = 85. 40

12= 93. 78 13= 74. 51 14=230. 70 15=242. 71

16= 169. 58 17= 184. 27 18= 156. 66 19= 155. 18

20= 152. 96 21 = 140. 03 22= 135. 59 23= 131. 19

24= 129. 74 25= 53. 06 26= 45. 31 27= 43. 19

28= 95. 01 29= 137. 46 30=446. 23 31 = 54. 81

32= 45. 69 33= 58. 36 34= 92. 09 35= 92. 38

36= 3. 18 37= 45. 36 38= 45. 19 39= 44. 68

40= 45. 09 41 = 133. 81 42= 168. 29 43= 119. 55

44=228. 44 45= 95. 49 46= 71. S3 47= 32. 51

* Channel 36 is a millivolt reading which yields the difference in temperature

between the inlet and outlet chilled water when multiplied by 2.8539.

19
Table 4. Steady-State Test Data at 100. 5°F

Evaporator Pressure - 340 psia

Generator Pressure - 73.5 psia

Capacity - 29050 BTU/hr

C02% in Stack Gas - 7.3%

02% in Stack Gas - 8.9%

Generator Heat Input - 58103 to 58830 BTU/hr

Electrical Power Consumption - 1068 W

Weak Solution Concentration - 0.085 lbm N^/lbm soln.

COP - 0.494 to 0.50

Temperatures

(Thermocouple Location = Temperature °F)*

0= 32. 53 1 = 126. 79 2= 125. 01 3=247. 46

4=233. 51 5= 158. 76 6= 49. 21 7= 199. 71

8= 127. 70 9= 76. 66 10= 62. 50 1 1 = 75. 89

12= 87. 03 13= 61. 56 14= 237. 02 15=24S. 13

16= 167. 58 17= 189. 44 18= 157. 93 19= 159. 33

20= 157. 58 21 = 144. 12 22= 139. 98 23= 135. 40

24= 133. 78 25= 52. 36 26= 46. S3 27= 44. 74

28= 100. 46 29= 141. 84 30=449. 32. 31 = 55. 12

32= 46. 97 33= 59. 86 34= 98. 09 35= 97. 97

36= 2. 82 37= 46. 72 33= 46. 53 39= 46. 24

40= 46. 43 41 = 139. 23 42= 170. 58 43= 124. 55

44=231. 46 45= 89. 85 46= 72. SO 47= 32. 64

* Channel 36 is a millivolt reading which yields the difference in temperature

between the inlet and outlet chilled water when multiplied by 2.8539.

20
4. COMPARISON OF THE MODEL TO EXPERIMENTAL DATA

Table 5 lists the parameters which must be specified to apply the steady-state

model described in section 2; also listed are the values of these parameters

used in the comparisons with the experimental data.

The heat transfer parameters were selected in a trial and error process by

matching the calculated and experimental temperatures and capacity. A trial

and error process was needed because the effects of these parameters are interrelated; a change in any one affects the temperatures at all other points in

the cycle. One set of heat transer parameters was selected for all operating

conditions based on the experimental results in table 3 for T a^ r = 95°F.

The calculated performance of the cycle for a 95°F air temperature and these

parameters values appears in table 6. The tabular data in this table lists the

location (figure 1), and corresponding temperature (T = °F), pressure (P = psia),

composition (x = lb NH3 /lb soln), enthalpy (H = BTU/lb) flow rate (M = lb/hr)

and quality (Q = lb vapor/lb liquid + vapor). The last two columns give the

thermocouple number in figure 2 corresponding to the locatio and the experimental

temperature (TOBS = °F) at this point. The calculated capacity appears in the

table as QEVAP in BTU/h.

As indicated previously, the heat transfer parameters in table 5 were chosen to

cause the calculated temperatures, capacity, and weak solution composition to

agree with the experimental data for Taj_ r = 95°F. The calculated capacity for

this case is 32630 BTU/h which agrees well with the experimental value of

32755 BTU/h from table 3. The calculated weak solution composition is

0.085 lbm NH3 /lbm soln; the experimental value is 0.087 lb N^/lb soln. The

calculated and experimental temperatures in table 6 are in reasonably good

agreement. However, there are significant differences in the area of the evaporator and refrigerant heat exchanger (locations 8-11). For example, location

9 is downstream of the refrigerant restrictor and the temperature at this point

should be the lowest refrigerant temperature in the cycle. The experimental

value, however, is 85°F which is clearly not possible. An investigation of

thermocouple 9 revealed that it is positioned at the refrigerant restrictor,

rather than downstream of the restrictor as indicated in figure 2. A more

reliable indication of the refrigerant temperature in the evaporator is

provided by thermocouple 27, which indicated 43.2°F.

The temperature of the refrigerant exiting the evaporator (location 10) cannot

be warmer than the inlet water (55°F) without violating the Second Law, yet

the experimental value is 66.7°F. Thermocouple 10 was examined, calibrated

with an ice bath and reinstalled with additional insulation. However, its

reading did not change significantly. Perhaps the measurement is affected by

conduction along the pipe.

The calculated temperature of the liquid overflow returning to the generator

from the rectifier (location 13) is significantly higher than measured. It is

likely, however, that the experimental value is low in this case because the

overflow pipe was in an awkward location and as a result, poorly insulated.

21
Table 5. Parameter Values Used in Comparisons

Qgen " 58460 BTU/h

m - 200 lb/h

— 7.2 gpm

T 15 - 55°F

(UA) rect - 80 BTU/°F-h

(UA) abss - 550 BTU/°F-1

(UA)hx “ 55 BTU/°F-h

(UA) evap - 3000 BTU/°F-

(UA) absa - 1000 BTU/ °F'

(UA) Cond - 750 BTU/°F-1

e b

- 0.8

£y - 0.9

^air ^evap

°F psia

80 56.5

95 71.6

100.4 73.5

h

h

Pgen

psia

275

325

340

22
Table 6. Calculated Results for Ta± r = 95°F

NO OF ITERATIONS 3 1?

AIR TEMPERATURE 3 95*0

LACK OF CLOSURE 3 -20*92

QGEN= 58460

0

COOLING COP 3

Q E V A P 3

.5582

32630.

1

GC0ND =-41703 .9 QABS =-49407.2

LOC * T P X H M G TC T0B

1 120.3 71.6 . 436 -11.3 200.0 000 1 121 . n 120.3 325.0 .436 -11.3 200.0 .000 2 119 . 3 150.3 325.0 .436 23.3 200.0 .000 5 152.

4 224.9 325.0 436 107.4 200 .

0

.000 4 228

.

5 240.4 325.0 941 661.5 85.3 1.000 14 230.

6 203.0 325.0 . 978 623.0 78.6 1.000 7 194 . 7 118.7 325.0 . 978 92.8 78.6 . 000 8 119.

8 83.3 325.0 . 978 53.0 78.6 .000 13 71 . 9 40.6 71.6 . 978 53.0 78.6 .102 Q 85 . 10 47.0 71 .

6

. 978 468.1 78.6 854 10 66 . 1

1

56.1 71.6 .978 507.9 78.6 .917 1

1

85.

12 180.5 71.6 . 436 235.8 200.0 . 266 42 168 . 13 203.0 325.0 .510 83.4 6 .

7

. 000 16 169 . 14 255.9 325.0 . 085 198.2 121.4 . 000 3 240 . 15 55.0 20.0 . 000 23.0 3610.0 .000 31 54 . 16 46.0 20.0 .000 14.0 3610.0 . 000 -r n \~J A.. 45.

c

6

23

\i

CO

QO'

W

\lO

\l

O

\l

'O

l>
It is possible that the agreement between the calculated and measured

performance could be improved by further manipulation of the heat transfer

parameters

The parameters selected for the 95°F air temperature test were used to calculate

the cycle performance at 80°F and 100°F air temperatures; the results appear in

tables 7 and 8, respectively. The model predicts that capacity decreases with

increasing air temperature, as observed experimentally. However, the calculated

capacities are 3 percent high at 80°F and 6 percent high at 100°F compared to

the experimental results in tables 2 and 4. The discrepancy results from using

the parameters for the 95°F air temperature case. The agreement between the

calculated and experimental temperatures is good. As for the 95°F case, significant differences occur primarily in the area of the evaporator and refrigerant

heat exchanger. The calculated weak solution composition changed only slightly

with changing air temperatures. The low value (0.053 lb N^/lb soln) observed

experimentally for the 80°F test suggests that the solution flow rate is not

constant with changing air temperature as assumed.

24
Table 7. Calculated Results for T 80°F a^ r =

NO OF ITERATIONS* 28

AIR TEMPERATURE* 80*0

LACK OF CLOSURE* 59,77

QGEN= 58460,0

COOLING C0P=

Q E V A P = ,6244

36503,7 QC0ND =-42277 5 QABS = -52 626.4

LOC, T P X H M Q TC T0BS

1 106.9 56.5 . 434 -25.

e

200.0 . 000 1 106.0

2 106,9 275,0 , 434 -25,9 200,0 ,000 2 104.2

3 137,6 275.0 . 434 9.0 200.0 000 5 139.1

4 214.0 275,0 .434 97.1 200.0 003 4 220.6

5 229,2 275,0 .943 655.3 85,1 1.000 14 219.7

6 189,7 275,0 .981 616,7 78.3 1 , 000 7 1S1 .0

7 103.9 275,0 .981 77.1 78.3 ,000 8 94,9

8 81 ,

5

275.0 .981 51 .

7

78.3 , 000 13 79 .

9

9 29.2 56.5 ,981 51.7 78,3 . 131 9 94.9

10 50.5 56,5 . 981 517,9 78,3 .940 10 69.2

11 73,9 56,5 , 981 543,3 78.3 .960 1

1

83.5

12 171.2 56.5 .434 237,7 200.0 .279 4 2 156.0

13 189,7 275,0 ,510 68.4 6.7 .000 16 172.3

14 244.4 275,0 .082 185.7 121.7 , 000 3 231 ,5

15 55.0 20.0 , 000 23.0 3610.0 , 000 31 55 .

1

16 44,9 20.0 , 000 12,9 3610,0 , 000 — n4mm 45.2

25

cnw

o

cn

ro

-o

o

-oo

-J

a-

<-* r

jo
Table 100. 5°F 8. Calculated Results for Tai r =

NO. OF ITERATIGNS= 22

AIR TEMPERATURE=100.5

LACK OF CLOSURE = 100 07

QGEN = 58460.0 Q E V A P = 30890.0 QCOND =-41613. 6 QABS = -476 36.3

COOLING C0P= 5284

LOC . T P X H M Q TC TOBS

1 124.7 73.5 436 4.3 200.0 .017 1 126.8

2 124.7 340.0 . 436 4.3 200.0 . 000 2 125.0

3 162.2 340.0 .436 36.7 200.0 . 000 5 158.8

4 226.0 340.0 . 436 108.7 200*0 .000 4 233.5

5 241.9 340.0 .942 661.7 85.3 1.000 14 237.0

6 207.0 340.0 .977 625.2 79.1 1.000 7 199.7

7 124.6 340.0 .977 99.1 79.1 . 000 8 127.7

8 85.5 340.0 .977 55.0 79.1 .000 13 61.6

9 41 .9 73.5 .977 55.0 79.1 .103 9 76.7

10 47.0 73.5 977 445.8 79.1 .813 10 62.5

11 52.1 73.5 .977 489.9 79.1 .888 11 75.9

12 183.4 73.5 . 436 243.1 200.0 .271 42 170.6

13 207.0 340.0 .509 87.8 6.3 . 000 16 167.6

14 257.8 340.0 .083 200.8 121.0 . 000 3 247 .

15 55.0 20.0 .000 23.0 3610.0 . 000 31 55 .

16 46.4 20.0 .000 14 .3610.0 * 000 32 47.0

26
5. EFFECTS OF MODEL PARAMETERS

The steady-state model described in section 2 is of limited value for

interpolation or extrapolation of experimental data since it requires as input

the values of the parameters listed in table 5; these parameter values must be

determined from experimental data. A more detailed model would provide values

for these parameters based on the physical dimensions of the components and

their operating conditions. This model is, however, useful as an analysis and

design tool in that the sensitivity of the heat pump performance to these

design parameters can be assessed, indicating the components in the cycle for

which the design is most critical.

Each of the parameters in table 5 was independently varied and the cycle

performance was recalculated for the 95°F air temperature. The results of this

sensitivity study are summarized in table 9 which lists the percent increase in

capacity resulting from an increase in each parameter value from 5 percent below

to 5 percent above its base value.

Relatively large sensitivities are observed to the inlet chilled water

temperature (T^) and the evaporator pressure, which affects the temperature of

the evaporating refrigerant. These results indicate that, at a 95°F air temperature, the performance of the heat pump is constrained by the rate of heat

transfer in the evaporator. This constraint becomes more apparent as the air

temperature (and thus the evaporator pressure) is increased, causing a precipitous drop in capacity (as observed experimentally) between the 95°F and 100°F

tests. It is unlikely that the experimental performance will be as sensitive

to inlet water temperature as suggested in table 9 since the calculated result

does not consider the effect the inlet water temperature will have on evaporator

pressure

.

The generator heat input appears to have only a small effect on capacity in the

range of its base value of 58460 BTU/h. Both the increase and the decrease in

generator heat input resulted in a slight decrease in capacity, indicating that

capacity is maximized at the base value of the generator heat input. As the

generator heat input is increased, the refrigerant vapor flow rate increases,

but so do the temperatures of the vapor and the weak solution. Higher temperature vapor results in a higher percentage of water in the refrigerant after

rectification. The higher weak solution temperature results in less effective

absorption of refrigerant. These two effects counteract the beneficial effect

of increased vapor flow rate. The coefficient of performance (ratio of evaporator to generator heat inputs) is reduced 9.6 percent by the increase in

generator heat input.

The solution flow rate (m) has a marked effect on the weak solution composition,

but its effects on the refrigerant composition and the capacity are small. From

a design standpoint, it appears that little improvement in performance could be

expected from using a variable speed solution pump controlled as a function of

operating conditions.

The capacity decreases slightly with the increase in (UA) ab ss , the heat transfer

conductance for the solution-cooled absorber. This non-intiutive result

27
Table 9. Sensitivity of the Calculated Performance to the Design Parameters

(changed from 5 percent below to 5 percent above the base values)

% Increase

Variable Base Value in Capacity

•Qgen 58460 BTU/h 0.4

•m 200 lbm/h 1.8

•% 3610 gpm 0

*15 55 °F 13.2

( UA) rect 80 BTU/°F-h 0.7

( UA) abgs 550 BTU/°F-h -1.1

(UA)hx 65 BTU/°F-h 0.3

( UA) evap 3000 BTU/°F-h 2.4

(UA) absa 1000 BTU/°F-h 0.8

(UA) cond 750 BTU/°F-h 0.8

e L 0.8 2.0

e V 0.9 5.3

^evap 71.6 psia -11.2

P gen 325 psia 0.9

28
illustrates an interaction between the components. The generator is designed

to allow contact between the exiting refrigerant vapor and the entering rich

solution, as a result the vapor temperature approaches the rich solution

temperature. This internal heat transfer improves performance since the rich

solution is preheated and the water content of the refrigerant is reduced.

(In the model, the temperature difference between the vapor and the rich solution is controlled by the effectiveness factor, e v

. Capacity is relatively

sensitive to this parameter.) An increase in (UA) abss increases the heat transfer rate in the solution-cooled absorber and thus the temperature of the rich

solution. The increased heat transfer rate tends to increase the capacity

since it increases the rate of absorption of refrigerant in the solution-cooled

absorber. However, the higher rich solution temperature reduces the capacity

since it causes the refrigerant vapor leaving the generator to be at a higher

temperature. These competing effects indicate that there is an optimum value

for (UA) a.bss*

Only a small increase in capacity is observed to occur as a result of increases

in the heat transfer parameters. Additional heat transfer surface area would

not cause a significant improvement in the steady-state performance.

29
6 . CONCLUSIONS

The usefulness of the sensitivity study in section 5 rests on the assumption

that a small change in any one of the model parameters does not significantly

affect any of the others. If these interaction effects can be neglected, the

results of the sensitivity study reveal a number of interesting conclusions

concerning the design of the ARKLA ACC-3600 chiller.

1. The unit is designed to operate at maximum capacity, rather than

maximum coefficient of performance, at a 95°F air temperature.

2. There is an optimum heat exchanger surface area in the solution-cooled

absorber.

3. Internal heat exchange between the streams entering and exiting

the generator significantly improves the performance of the unit.

4. The rate at which the rich solution is pumped has only a small effect

on the chiller performance. The rich solution at the pump inlet may

be in two-phase under some operating conditions.

5. The chilled water inlet temperature has a significant affect on performance with higher temperatures resulting in increased capacity.

The absorption heat pump model presented here is simplistic in that pressure

losses are not considered and heat transfer parameters must be supplied. In

a more fundamental model, pressure losses and heat transfer coefficients would

be calculated as a function of the physical characteristics of the system

components and the operating conditions. Development of a model of this type

would be a complex, but worthwhile project.

30
REFERENCES

1 . The Secant method is a modification of the Newton-Raphson iteration method

in which the derivative of the function with respect to the dependent

variable is found numerically,

2. Lindsay, T. M. and Didion, D. A., "Investigation of the Cyclic Performance

of a Gas-Fired Absorption Chiller," NBS internal report.

3. Jain, P. C. and Gable, G. K. , "Equilibrium Property Data Equations for

Aqua-Ammonia Mixtures," ASHRAE Trans., 77, 149, (1971).

31
ACKNOWLEDGMENT

The author is grateful to Reinhard Radermacher for his help in obtaining the

experimental data and for his many suggestions concerning the model.

32
APPENDIX A

PROPERTY DATA ROUTINES

Equilibrium relationships between binary mixture properties are provided by

eight FORTRAN function subprograms. A brief description of the independent

variables and purpose of each subprogram is as follows:

FUNCTION TSAT(XL, P)

TSAT returns the bubble point temperature of a mixture at a total pressure P and

a liquid refrigerant mass fraction XL.

FUNCTION XV (XL, P)

XV returns the mass fraction of refrigerant in the vapor phase which is in

equilibrium with a liquid at total pressure P and refrigerant mass fraction XL.

FUNCTION HL (XL, T, P)

HL returns the specific enthalpy of the liquid phase at temperature T,

pressure P, and refrigerant mass fraction XL.

FUNCTION HV (XL, XV, T, P)

HV returns the specific enthalpy of the vapor phase at teperature T, pressure P,

and refrigerant mass fraction XV. XL is the refrigerant mass fraction of the

liquid phase in equilibrium with the vapor.

FUNCTION PSAT (XL, T, PIC)

PSAT returns the bubble point pressure of a mixture at temperature T and liquid

refrigerant mass fraction XL. PIC is used as the first guess in the iterative

solution.

FUNCTION TH(XL, H, P, TIC)

TH returns the temperature of a liquid at pressure P, refrigerant. Mass

fraction XL, and specific enthalpy H. TIC is used as the first guess.

FUNCTION XLPT (P, T, XLIC)

XLPT returns the equilibrium refrigerant mass fraction of a liquid at pressure P

and temperature T. XLIC is used as the first guess in the iterative solution.

FUNCTION TQ (X, P, H, Q)

TQ returns the temperature and quality (Q) of a two-phase mixture having an overall refrigerant mass fraction x and enthalpy H at a total pressure P.

A-l
The property data for ammonia-water mixtures used in this report were provided

by the polynomial equations of Jain and Gable (3). If a property was not given

explicitly by these equations, it was found iteratively using the Secant method.
o

rji

t-4

r-J

o

'o

co

'-.j o

c_n

_t>

c»4

ro

h

o

co

'•j

oc.n

-t>

c-4

rj

APPENDIX B

COMPUTER PROGRAM LISTING

SCABS' ( 1 > fi A

I

N ( 4

)

1

4

cr

6

*7/u9

10

ii

"i ~

u> O

*7 Q

£u

10

11

12

111

7 0 / u

SO

DIMENSION I THL (16) » TUBS ( 16

)

COMMON T (20) t P ( 2 0 ) > X ( 2 0

)

> H ( 2 0 ) » F L COMMON /LU/ LUR f LUW f LUF

COMMON /TOLS/ T0L1 ? T0L2? ITERMX

COMMON /DD/ IP

LUR = 5 L U W =

6

(20) » Q (20)

WRITE (LUWt2)

FORMAT ( IX f' ENTER FILE NUMBER')

READ ( LUR f *

)

LUF

ITERMX=100

WRITE < LUW f 3

)

FORMAT ( lXi ' ENTER T0L1 > T0L2 » TOLP ')

READ ( LUR ? % ) T0L1 > T0L2 > TOLP

I C Y =

0

WRI TE ( LUW ? 5

)

FORMAT ( IX >

' ENTER IPfITPCMX ')

READ (LUR ft) IP f ITPCMX

FORMAT (415)

READ (LUF f % ) TAIR

READ (LUF f t ) NP

DO 10 1=1 fNP

READ ( LUF f * ) T ( I ) f P ( I ) f X ( I ) f H ( I ) f FL ( I ) f Q ( I

)

CONTINUE

DO 11 1 = 1 fNP

READ (LUF ft) ITHL(I) fTOBS(I)

CONTINUE

FORMAT ( 15 f F10 * 0

)

D1C = 0

CPC=1»0

P E 0 A P = P ( 9

)

F L 0 W = F L ( 1

)

WRITE (LUWf73)

FORMAT ( IX f 'ENTER UA J RECT» iC: 1 H X f E v A P f A B S A C f :ond

NPUT ' )

READ (LUR f * ) UAREC ? UAABSS f UALVHX f UAEUAP f UAABSA , UACOND

WRITE (L’JW >t) UAREC f UAABSS fUALUHX? UAEUAP ? UAABSA f UACOND

WRITE ( LUW f 30)

FORMATdXf 'ENTER GENERATOR HEAT

READ(LURft) Q G E

N

WRI I E ( L U W ? t ) U G E N IF ( QGEN . LT *0.0) STOP

WRITE (LUW? 31

)

FORMAT ( IX f 'ENTER GENERATOR

READ (LUR

y

i ) EFFL

WRITE ( LUW f * ) EFFL

WRITE (LUWf33

)

FORMATdXf 'ENTER GENERATOR HEAT TRANSFER EFF

- R ? t ) EFFU

{EAT TRANSFER EFFEi LIQUID

B-l
4? WRITE ( LUW

,

t ) EFFV

50 1/ FORMAT ( 6F10 0

)

51 C.

r.n O i. 1000 CONTINUE

53 I T E R P C = 0

54 1005 CONTINUE

cr c

J J ITERPC*ITERPC+1

J 6 IF (ITERPC.LT. ITPCMX) GO TO 1006

t=!"7 o / CALL BIAG< ITERPCf 0)

=!0 o u STOP 3

=:q u / 1006 CONTINUE

60 ICY = I C Y +

1

61 C. CYCLE CALCULATIONS - NO PRESSURE DROPS

62 CALL F'UMF'd »2»P(5) »FL0U)

63 IF (IP.LT.O) CALL DI AG ( ITERF'C »1

)

64 CALL RECT(5,2,6,3,13,UAREC)

65 IF (IP.LT.O) CALL DI AG ( ITERF'C , 2

)

i ^ u u CALL ABSSC(1-1»14»12»3»4»UAABSS)

67 IF (IP.LT.O) CALL DI AG ( ITERF'C » 3

)

68 CALL CONABS ( 12,1 » TAIR > UAABSA , QABS

)

6? IF (IP.LT.O) CALL DI AG ( ITERF'C , 4

)

70 CALL GEN(4,13,14,5,QGEN,EFFL,EFFV)

71 IF (IP.LT.O) CALL DI AG ( ITERF'C , 5

)

?9 CALL CONABS ( 6, 7 , TAIR , UACOND , QCOND

)

73 IF (IP.LT.O) CALL DI AG ( ITERF'C , 6

)

74 CALL HXLV(10,7»11,S,UALVHX)

75 IF (IP.LT.O) CALL DI AG ( ITERF'C , 7

)

76 CALL THROT (8,9, F'EVAF'

)

-7 “7 / / IF (IP.LT.O) CALL DI AG ( ITERF'C , 3

)

7S CALL EVAP(9»10»15»16»UAEVAPfCPC»QEVAP>

7? IF (IP.LT.O) CALL DI AG ( ITERF'C , 9

)

30 1010 CONTINUE

0 1 U J. D1=QGEN+QEVAP+QC0ND+QABS

00U 4L IF (ABS(DI-DIC) .LT.TOLP*QGEN) GO TO 1008

33 D 1 C = D

1

34 GO TO 1005

85 1008 CONTINUE

36 9000 CONTINUE

37 C. PRINT' SUMMARY

q 0 O U WRITE ( LUU , 901 0 ) ITERF’C

3? 9010 FORMAT ( /IX , 'NO. OF ITERATIONS*

, 13 ) 90 URITE(LUW, 9015) TAIR

91 9015 FORMAT ( IX » 'AIR TEMPERATURE*» F5 . 1

)

oo/ WRITE(LUW,9020) DI

93 9020 FORMAT (IX? ' LACK OF CLOSURE* ', F 10 . 2 ) 94 WRITE (LUU ,9030) QGEN , QEVAP , QCOND , QABS

95 9030 FORMAT ( IX »

' QGEN*' , F8.

1

,

' QEVAP*

, F8 . 1 ,

y QCOND* '

? F 8 . 1 ? 96 1

7 QABS*'»F8.1)

97 C0P = QEVAF7QGEN

93 URI TE ( LUU , 9040 ) COP

99 9040 FORMAT ( IX ,' COOLING C0P=',F8.4/)

100 WRITE ( LUU , 9050

)

101 9050 FORMAT (3X» 'LOC. '»3X, 'V »7Xi 'P' »8X» 'X' ,6X, 'H' ,7X, 'H' ,8X, 'G'

,

102 1 4X ,

' TC ' , 4X ,

' TOBS '

)

103 DO 9100 1=1, NP
104 9100 WRITE ( LUU » 91 10) I » T ( I

)

r P ( I ) » X ( I) ? H ( I ) , FL ( I ) » Q ( I ) ; ITHL ( I ) ; TOBS ( I

)

105 9110 FORMAT ( IX ? I4»2F3.1»F8.3»2F3.1»F3*3f I5»F3*1)

106 99 CONTINUE

107 WRITE (LUU f 59

)

P

-*• O CO 59 FORMAT (/)

109 D 1 C = 1 0 0 0 0 0 0 * 110 GO TO 111

111 END

48SABSU) *PUMP(0)

1 SUBROUTINE RUHR ( IL » JL > F'HIGH > FLOW

)

2 COMMON T ( 20 ) » F'( 20 ) » X ( 20 ) » H ( 20 ) > FL ( 20 ) > Q ( 20

)

3 C* IL - LIQUID FROM AIR-COOLED ABSORBER

4 C* JL - LIQUID TO RECTIFIER HX

5 T ( JL ) =T ( IL

)

6 R ( J L ) = F H I G H

7 . FL ( JL ) =FLOW

8 H ( JL ) =H ( IL

)

9 X ( JL ) =X ( IL

)

10 RETURN

11 END

* r. .j. a r. r

*7 O -f rt D z

1

j4

trJ

i Z

1 n

R E C T ( 6 ) > SUBROUTINE R E C T ( I V , I L 1 » J V » J L 1 > J L 2 , U A > COMMON T ( 20 ) » P ( 20 ) » X ( 20 ) » H ( 20 ) , FL ( 20 ) > Q ( 20

)

COMMON /TOLS/ T0L1 ? T 0L2 j ITERMX

C 0 ri H 0 N / D D / I C K COMMON /LU/ LUR ? LUU » LUF

C. IV - VAPOR FROM GENERATOR

C, I LI - LIQUID FROM SOLUTION PUMP

C* JV - VAPOR TO CONDENSOR

C. JL 1 - LIQUID TO ABSORBER HX

C. JL2 - LIQUID RETURN TO GENERATOR

P( JV)=P(IV)

p : jli ) =p ( i l i

)

FL ( JL1 > =FL ( IL1

)

X ( JLI ) =X ( IL1

)

I T E R = 0

T 1 = ( 7 C I V ) rT ( I L 1

)

TT = T 1 ASSIGN 100 TO I GO TO SCO
21 100 F1 = F H9 T2=Tlf2*

07A. xJ 110 TT=T2

24 ASSIGN 120 TO IJP

25 GO TO 300

26 120 F2 = F 27 ITER=ITER+1

oox. U IF ( ITER * LT * ITERMX ) GO TO 150

nojL / WRITE ( LUU » 130 ) T< JL1 ) »QX»DTLM»H( JL1 ) >X( JV)

30 130 FORMATdXj / ***RECT*** / »6F8»3)

31 STOP

"TO ii 150 CONTINUE

33 T ( JO > = T 2 - F 2 / ( F2-F1 ) * ( T2-T1

)

34 IF ( ABS ( T ( JV ) -T2 ) LT T0L1 ) RETURN

7 nr u •J F1 = F2

O T 1 = T2

7

xj / T2=T( JO)

7 O \-> u GO TO 110

3? 800 CONTINUE

40 T ( JL2 ) =TT

41 X( JL2)=XLPT(P( JL2) »T( JL2) >X( JL2)

)

42 X ( JV ) = XV ( X ( JL2 ) » F’ ( JV )

)

43 FL ( JO ) =FL ( I V ) * ( X ( IV ) -X ( JL2 ) ) / < X ( JV ) -X ( JL2

)

44 FL ( JL2 ) =FL ( I V

) -FL ( JV ) 45 H( JV) =HV(

0

. 9» X ( JV) >TT »F’( JV)

)

46 H ( JL2 ) =HL ( X ( JL2

)

t T ( JL2 ) > P ( JL2

)

) 47 QX=FL ( JV)*H ( JV) tFL

(

JL2

)

( JL2) -FL ( IV ) #H (IV

48 H(JL1)=H(IL1)-QX/FL(IL1)

49 T M = T S A T (X(JL1) » P ( J L 1 ) ) cr

xJ V T (

J

L

1

) = T H ( X (

J

L

1

) ? H ( J L

1

) ? P ( J L

1

) > 1 50 »

)

~ 1X Q ( J L

1

) = 0

J IF ( T ( JL1 ) * GT , TM ) T ( JL1 ) =TQ (X( JL1 )

»

P ( JL1 )

»

J \3 IF (ICK.EQ.7) WRITE ( LUU > 7 ) TT ? T ( IV ) ? T ( JL1 ) 54 7 FORMAT ( IX f 5F1

0

3 ) cr c*. xJ A R G = ( T ( I V

) -T ( JL1 ) ) / ( TT-T ( IL1 )

)

“ L

i_i •_? IF ( ARG GT * 0 0 ) GO TO 810

cr *7

\j / D T L M = 0 * cr n

vj O GO TO 820

cr n

•J 7 310 CONTINUE

60 DTLM= ( T ( IV

)

-T ( JL1 ) -TT + T < III )

)

/ALQG ( ARG ) 61 O O A

U i- V CONTINUE

/ n O A- GXC=-UA*DTLM

63 F = Q X - Q X C 64 GO TO IJP

65 END

QX

4 3 & A B S ( 1 ) * A hi S b' C ( 9

i SUBROU

COMMON

T XJ p ApCCTf T!l. Tl 1 . |! 1 , i 17 L H D O O b \ X Y ? i i- 1 7 J U. i 7 I ( 2 0 ) ? P ( 2 0 ) ? X < 2 0 ) ? H < 2

L 2 ,* J L 2 ? U A

)

) ? F L ( 2 0 ) ? Q ( 2 0

)
COMMON /T0LS/ T0L1 ? T0L2 ? ITERMX

4 COMMON /DD/ ICI- 5 COMMON /LU/ LUR>LUU»LUF

6 C. IV - VAPOR FROM EVAPORATOR HX

7 C. IL1 - LIQUID FROM GENERATOR

oU C< JL1 - LIQUID TO AIR-COOLED ABSORBER

9 C. IL2 - LIQUID FROM RECTIFIER

10 C. JL2 - LIQUID TO GENERATOR

11 C * 12 X ( JL2 ) =X ( I L2

)

13 P< JL2)=P(IL2)

14 FL ( JL2 ) =FL ( IL2)

15 FL ( JL 1

) =FL ( I V ) +FL ( I LI

)

16 X ( JL1 ) = ( FL ( IV 5 IX ( I V > +FL ( IL1 ) *X ( IL1

17 P( JL1 )=P( IV)

1 QL u I T E R = 0

1? T1=T ( IL2 ) t40

20 TT = T1

21 ASSIGN 100 TO IJP

99 GO TO SOO

n "7 100 F1 = F 24 ASSIGN 120 TO IJP

n c

x. J T2=Tl+5

26 110 TT = T2

n "7 GO TO SOO

o O

<_ w 120 n-c » X. — 1 nox. / ITER=ITER+1

30 IF (ITER. LT. ITERMX) 60 TO 150

L> i WRITE (LUU> 130) T ( JL2

)

t QX » DTLM t XLIQ

”7 O vJ X. 130 FORMAT

(

IX » ‘ IIIABSSCIII '? SFS . 3 ) o o RETURN

34 150 CONTINUE

•4 J T( JL2)=T2-F2/(F2-F1 )I(T2-T1

)

•2) u IF (ABS(T( JL2)-T2) .LT.T0L1) RETURN

“7

_> / F 1 =F2

“7 r« O T 1 = T 2

o u 7 40

T2=T ( JL2

)

GO TO 110

*7 i o 0 \J CONTINUE

42 TM = TSAT (

X

( JL2

)

? P

(

JL2 ) ) 4 >4 IF CT-JL2) .GT.TM) GO TO 320

4-£ 8'-J 1X nv CONTINUE

r O

•16 4 7

SUBCOOLED LIQUID

H(JL2)=HL(X(JL2)»TT»P'

Q ( JL2 ) =0 * GO TO 330

jl:

4? 320 CONTINUE

50 C. TWO--PHASE MIXT URE

51 X L I Q = X L P T ( P (

J

I n L. X. ) ? TT j 0

* \

sr •—« j ^ XVAP=XV (

X

L I Q j P( JL2

)

\

ir -7 Q ( J L 2 ) = ( X ( JL2 )- XLIQ ) / ( X V A P 34 HLIQ=HL (

X

LIQ? TT ? P (

J

L2

)

) U \J HVAP=HV (

X

LI Q f VII A V AP ? T T ? P ( JL2

cr /, H ( JL2 ) = (

1

,0-Q ( J L 2 ) ) IHL IQ-rQ

•J / u Jj v CONTINUE
CJo

QX=FL( JL2)*(H( JL2)-H(IL2)

)

H ( JL1 ) = ( FL ( I V ) *H ( IV ) +FL ( IL1 ) *H ( IL1 ) -QX ) /FL. ( JL1

)

T( JL1)=TQ(X( JL1) »P( JL1) ,H< JL1) »Q( JL1)

)

IF (ICK.EQ.9) WRITE(LUU»*) T ( IL1 ) > TT » T ( JL1 ) , T ( IL2 ) > QX

AR6=(T(IL1)-TT)/(T( JLD-KIL2)

)

IF ( A R G G T 0 ) GO TO 840

DTLM=0

GO TO 845

840 CONTINUE

DTLM= ( T ( IL1 ) -TT-T ( JL1 ) +T ( IL2) ) /ALQG ( ARG

)

345 CONTINUE

QXC=UA*DTLM

F=QX-QXC

GO TO IJP

END

GEN ( 6

)

SUBROUTINE GEN( IL1 » IL2UL1 » JV» QGEN» EFFL >EFFV

)

COMMON T (20) > P ( 2 0 > > X ( 2 0 ) > H ( 2 0 ) ?FL(20) >0(20)

COMMON / T 0 L 3 / TOLU T0L2 » ITERMX

COMMON /DD/ ICK

COMMON /LU/ LURUUUjLUF

. Ill - LIQUID FROM ABSORBER

, IL2 - LIQUID FROM RECTIFIER

C. JL1 - LIQUID TO SOLUTION-COOLED ABSORBER

C, JO - VAPOR TO RECTIFIER

TGEN1=T( JO)

P(JL1)=P(IL1)

ITERG=0

TH0LD=TGEN1

ASSIGN 10 TO IJP1

GO TO 1000

10 F1=F

TGEN2=TGEN1t5

20 TH0LD=TGEN2

ITERG=ITERG+1

IF (ITERG.LT. ITERMX) GO TO 25

WRITE (LUU» 24) TGEN , P ( JL1

)

, X ( JL 1 ) ? H < JL1

)

f FL ( JL 1

)

24 FORMAT < IX f ' »F10.3)

RETURN

25 CONTINUE

assign so to i j p

GO TO 1000

30 F2=F

TG£N=TGEN2-F2/ ( F2-F1

)

t ( TGEN2-TGEN1

)

IF ( ABSCTGEN-TGEN2) .LT.T0L1) GO TO SO

T G E N 1 = T G E N 2

F 1 = F 2
«

37

38

7 0 \J / 40

41

1 o T jL 43

44

45

46

47

48

4?

50

5

1

c* o

vJ

54

nr c

•JJ 56

GO TO 20

60 CONTINUE

T( JL1 )=T6EN-EFFL* ( TGEN-T ( IL1 >

)

RETURN

1000 CONTINUE

T( JL1)=THQLD-EFFL*(TH0LD-T< IL1)

)

C* EFFL IS A HEAT EXCHANGE EFFECTIVENESS BETWEEN THE EXITING WEAK

C, SOLUITION AND THE INCOMING STRONG SOLUTION

X< JL1)=XLPT(P< JL1) »TH0LD>0.35)

H(JL1)=HL(X(JL1) > T (JL1) ? P ( J L 1 ) ) C, NOTE THAT LIQUID IS SUBCOOLED BEFORE LEAVING GENERATOR IF EFFL>0

C. EFFV IS A HEAT TRANSFER EFFECTIVENESS BETWEEN THE ENTERING LIQUID AND

C. THE EXITING VAPOR AT THE TOP OF THE GENERATOR

T( JV)=THOLD-EFFV*(THOLD-T(ILi)

)

P( JV)=P( JL1

)

X L T 0 P = X L P T ( P ( JV ) ? T ( JV ) * 0 * 40 ) IF (ICK.EQ.10) WRITE CLUW»*) XLTOP » P ( JV ) > T ( JV ) ? THOLD » X ( JL 1

)

1 »T<JL1)

X ( JV ) =XV ( XLTOP ? P ( JV ) ) FL ( JL 1 ) = ( FL ( IL 1 ) *X ( I L 1 ) TFL ( I L2 ) *X ( I L2 ) - ( FL ( I L 1 ) +FL ( I L2 ) ) *X ( JV )

)

1 / ( X ( JLl)-X(JV)

)

FL( JV)=FL( IL1 )tFL( IL2J-FLC JL1

)

H ( JV ) =HV (XLTOP > X ( JV ) » T ( JV ) » P ( JV )

)

F=FL ( IL1 ) #H< IL1 )+FL ( IL2 ) *H ( IL2 ) -FL < JV ) #H( JV ) -FL ( JL 1 ) *H ( JL1 ) + QGEN

GO TO IJP1

END

- *

a

r> cm \ ’'T'ni.'w v i /

' * C0NAB3 (4)

1X SUBROUTINE CONABS ( I

V

» JL , TAIR , UA t QCDND

)

C COMMON T ( 20 ) > P ( 20 > > X ( 20 ) * H ( 20 ) > FL ( 20 ) » Q (20

)

G COMMON /TOLS/ T0L1 ? T0L2 > ITERMX

4 COMMON /LU/ LUR > LUW ? LUF

cr COMMON /DD/ ICK

G 0, IV - VAPOR FROM RECTIFIER

7 C* JL - LIQUID TO EVAPORATOR MX

q FL( JL)=FL< IV)

9 P( JL ) =P ( I V > 10 X ( J L ) = X ( IV)

u I T E R = 0

i G

X X. T l = TAIR + 20

.L G TT = T 1

‘ A ASSIGN 100 TO IJP

15 GO TO 800

i C* 100 F1=F

17 T2 = T 1 i5 >

1 n

1 O 110 TT = T2

19 ASSIGN 200 TO IJP

20 GO TO 300

n 4X 200 F2=F
•>

Ci

'

O'

cn

cn

cn

cn

cn

cn

cn

li

w

u

w

>

t-j

oj

c.r

c-j

cj

c

-4

c»J

on

or

or

ro

ro

ro

to

ro

ro

ro

ro

cn

fo

o

'O

co

'' j

cn

cn

-t»

co

ro

*

'o

o

co

'j

ocn

-o

co

ro

h*

o

o

co

-i

O'

cn

_t»

co

ro

ho

o

ra

nj

cn

cn

.o

04

ro ITER=ITER+i

IF ( ITER.LT. ITERMX) GO TO 210

URITE(LUW»230) TT»H(JL) »QC0ND»T(IV) »X( JL)

230 FORMATCIX? ' **:*C0ND*** ' » 5F10 . 3)

STOP 230

210 CONTINUE

T(JL)=T2-F2/(F2-F1)*(T2-T1)

IF (ABS(T(JL)-T2)*LT.T0L1) RETURN

F 1 = F 2

T1 = T2

T2=T( JL)

GO TO 110

300 CONTINUE

ARG=(T(IV)-TAIR)/(TT-TAIR)

IF (ARG.GT.0.0) GO TO 810

DTLM=0

GO TO 820

310 CONTINUE

DTLM=(T(IV)-TT)/AL0G(ARG)

820 CONTINUE

QC0ND=-UA*DTLM

THAX=TSAT(X( JL) rP( JL)

IF ( TT GT THAX ) GO TO 850

C. SUBC00L D ED AT OUTLET

Q ( JL ) =0 * H ( JL ) =HL ( X ( JL ) ? TT r P ( JL )

GO TO 380

850 CONTINUE

• C. TWO-PHASE AT OUTLET

XLI Q=XLPT ( P ( JL ) » TT > 0 8

XVAP=XV(XLIQ»P( JL)

HLIQ=HL(XLIQ>TT»P( JL)

H 0 A P = H V (XLIQ»XVAPjTT >P( JL )

330

6

Q ( JL ) = ( X ( JL ) -XLIQ ) / ( XUAP-XLIQ

H ( J L ) = ( 1 , - 9 ( JL ) ) *HL I Q + Q ( JL ) * HV AP

CONTINUE

Q C 0 N D C = ( H ( JL ) -H ( IV ) ) *FL ( JL > F=QC0ND-QC0NDC

IF ( ICK EQ « 6 ) WRITE (LUUU)

r Q < JL) f T( IV)

FORMAT ( IX » SF9 3

GO TO IJP

END

TT j THAX f XLI Q > XVAP t HL I Q » HVAP »

JL)

0 O 4 S n & S V i )

1 SUBROUTINE EVAP

COMMON T(20)?P(

COMMON / D D / I C

I L ? J v > I W t J W ? U A i CPC

0 ) ? X ( 2 0 ) t H ( 2 0 ) ? F L (

n r 1

a o \ Lx tvni / 0 ) ) Q ( 2 0

COMMON /T0LS/ TOLL > T0L2r ITERMX
c COMMON /LU/ LUR»LUW»LUF

6 C, IL - LIQUID FROM THROTTLE

7 C. JV - VAPOR TO HEAT EXCHANGER

0 C, IW - COOLANT WATER INLET

9 c. jy -- CHILLED WATER OUTLET

10 c 11 X ( JV > =X ( IL

)

12 FL( JV)=FL(IL)

1

3

F( JV)=P( IL)

i P( JW)=P(IW)

1 C' 1 J FL(JW)=FL(IW)

1 £ i 0 X(JW)=0.

i "7

j. / T M A X = T ( I U

) -0 * 000

1

13 T 1=TMAX

1 O j. / TT = T 1 20 ASSIGN 110 TO IJP

? 1 GO TO 300

?? 110 F 1 = F 23 ASSIGN 120 TO IJP

24 T2=Tl-2

.

•-*1 cr I TER=0

n lU 115 TT = T2

27 GO TO 300

00U 120 F2 = F 29 ITER=ITERt1

vJ1 v* IF (ITER.LT, ITERMX) 60 TO 5 31 URI TE ( LUW } 3 ) T( JO) , DTLM » QEVAP » H ( JV) »Q( JV)

TO RETURN

5 CONTINUE

34 IF ( ICK + EQ + 4) WRITE ( LUW r

t

> TT » T ( IL ) » T ( IW ) » FL ( IL

T c* \j J T ( JV ) =T2-F2/ ( F2-F1 ) * ( T2-T1

)

36 IF (ABS(T(JV)-T2) .LT.T0L1) RETURN

37 T1=T2

33 F 1 = F 2

"7 O T2=T( JV)

40 GO TO 115

41 300 CONTINUE

.4 0

~r DTLM = ( TT-T ( I L ) ) /ALOG ( ( T ( I W

) -T ( I L ) ) / ( T ( I W ) -TT )

)

43 Q E V A P C = U A % D T L M 44 XLIQ=XLPT ( F ( JV ) ? T T ? 0 8

)

a cr n yj X V A F‘ = X V ( X L I Q » P ( J V )

)

*7 O Q ( JV ) = ( X ( J V

) -XL I Q ) / ( XVAP-XL I Q

)

£t / HLIQ=HL(XLIQ»TT»P( JV)

)

,4 O ~T •«' H V A P = H V ( XLIQ » XVAP » TT » P ( JV )

)

O "7 / H ( JV ) = (

1

, -Q ( JV )

)

*HL I Q+Q ( JV ) *HVAP

\j !J QEV AP= ( H

(

J V

) -H ( I L ) ) *FL ( I

L

) C 4 J i F=QEVAP-QEV AF’C 0 *2 IF (ICKtEQ.4) WRITE ( LUW 1 3 ) TT ? DTLH > QEVAP ? H ( J V )

?

^ 7

*7 FORMAT ( IXf 6F 10.2)

O ^7 H ( JW ) =H ( I

W

) -QEVAPC/FL ( I W

)

ui -J T ( JW ) =T ( I

W

) +

(

H ( JW ) -H (I

W

)

)

/CPC

cr / •J O 30 TO IJP

irJ j END
0348$ ABS ( 1 ) * H X L V ( 7

)

1 SUBROUT I NE HXLV ( IV » IL > JV > JL > UA

)

n COMMON T(20) »P(20) »X(20) »H(20) iFL(20) »Q(20)

u COMMON /T0LS/ T0L1 » T0L2 > ITERMX

A COMMON /DD/ ICK

5 COMMON /LU/ LUR>LUW>LUF

6 C. IV - VAPOR FROM EVAPORATOR

“7

/ C, JV - VAPOR TO ABSORBER

O

u C. IL - LIQUID FROM CONDENSQR

O

/ C. JL - LIQUID TO EVAPORATOR

10 Lr 11 FL( JV)=FL( IL)

.1 *- FL ( IV ) =FL ( IL

)

13 FL( JL)=FL( IL)

14 X( JV)=X( IV)

15 X ( J L ) = X ( I L

)

16 P(JV)=P(IV)

17 P(JL)=P(IL)

13 ITER=0

1? T 1 = T (IL) — 15*

20 TT=T1

21 ASSIGN 100 TO IJP

•n o GO TO 800

7 7

*1. u 100 F1=F

24 T2=Tl+5

25 ASSIGN 120 TO IJP

26 110 TT = T2

97 GO TO 800

28 120 F2 = F 29 ITER=ITER+1

30 IF (ITER. LT. ITERMX) GO TO 150

31 U R I T E ( L U W > 1 3 0 ) T ( JL ) » QX > DTLM » QX1 » H ( JL ) , H ( JV

)

7 °

U il 130 FORMAT ( IX ?

' $$$HXLV$$$ ' j 6F8. 3

)

33 STOP

34 150 CONTINUE

-? nr 0 J T(JL)=T2-F2/(F2-F1)$(T2~T1)

36 IF (ABS(T( JL)-T2) .LT.TQL1) RETURN

7 7 F 1 = F 2

70u u T1 = T2

7 0 T2=T( JL)

40 GO TO 110

4

3 0 0 CONTINUE

42 Q ( J L ) = 0

43 H( JL ) =HL ( X ( JL) ?TT»P( JL)

)

44 QX= ( H ( IL ) -H ( JL) )*FL(IL)

45 H ( JV ) =H ( I V ) TQX/FL ( IV

)

46 T ( JV ) =TQ ( X ( JV ) » P ( JV ) , H ( JV

)

, Q ( JV )

)

47 IF ( T ( JV ) GE T ( IL ) ) T ( J V ) = T < I L

) — 0 * 1

*1 0O A R G = ( T T - T (IV) ) / ( T ( I L

) -T ( JV )

)

4? IF (ICK.EQ.il) WRITE ( LUW ? %

)

T T > T ( I V ) ? T ( I L ) j T (
50 DTLM= ( TT-T ( IV ) -T ( IL ) +T ( JV ) ) /ALOG ( ARG

)

51 QX1=UA*DTLM

52 F=QX-QX1

53 GO TO IJF' 54 END

348#ABS( 1

)

1

4

5

6

10

END PR

I

THROT(O)

SUBROUTI NE THROT ( IL ?JL> PSAT

)

COMMON T(20) »P(20) »X(20) »H(20) »FL(20) >0(20)

P( JL)=PSAT

I T E R T = 0

X F = X ( I L

)

H ( JL ) =H ( IL > X ( J L ) = X ( I L ) FL ( JL ) =FL ( IL)

T( JL)=TQ(X( JL) »P( JL) »H( JL) »Q( JL)

>

RETURN

END

34S*ABS(1 ) D I A G ( 1

)

6

“7

3o

1

0

24

9110

SUBROUTINE DIAG ( ITERPC > LOO

COMMON T(20) »P(20) >X<20) »H(20) »FL( 20) »Q(20)

COMMON /LU/ LUR»LUW»LUF

URITE(LUW»23> ITERPCjLOC

FORMAT ( IX > ' ITERATION 3 '> 1 5

»

LOCATION 3 '

? 1 5

)

DO 24 1 = 1 , 16

WRITE ( LUU* 91 10) I » T ( I ) > P ( I ) » X ( I ) > H ( I ) , FL (

I

FORMAT (1X>I5»6F10*3)

RETURN

END

? L-i

!

-j 4 3 * H !• S 1 / * T b H T » 'J i

1 FUNCTION T S A T ( X L ? P

)

2 C, THESE CURVE FITS ARE TAKEN FROM

;

3 C* EQUILIBRIUM PROPERTY DATA EQUATIONS FOR AQUA-AMMONIA MIXTURE

4 C * r’iCt J A I N A N D G K GABLE ASHRAE (19 / 1

)
10

11

12

13

14

15

C. ENGLISH units: t = f, X=LB/LB S0LN» F‘ = PSIA

IF ( P * L T 2 0 0 * ) GO TO 100

TSAT= ( ( ( (-24Q.11*XL+346.31)*XL-27.120)*XL+166.94)#XL-535.76)*XL

1 + (0*033839-0 .18053E-03*P )*XL*P+305.04+( 0,44631

2 0.24284E-03*P)*P

RETURN

100 CONTINUE

T S A T = ( ( ( (-692.82*XL+1673.3)#XL-1424.98)*XL+787.79)*XL-584.7B)*XL

1 +( -0.34428+0. 0001 1334*P)*P*XL+203. 80+ (1. 3362-0. Q060111#P)#P

RETURN

END

034SIABS ( 1 ) *XV( 1

)

1

4

7 100

oU7 1 10 200

11

12

FUNCTION X V ( X L ? P

)

IF (XL. GT. 0.9999) XL=0.9999

IF (P.LT.200.) GO TO 100

R=( ( ( ( 10 .749*XL-17 . 369 ) *XL+4 . 0279 ) *XL-1 3©=d6 ) *XL + 2 . 5622E-03

*P*XL)*XL-4.256E-03:4'P + 7.l|B8

GO TO 200

CONTINUE

R=( ( ( (108.485*XL-229.009)*XL+155.247)*XL-41 . 0442) *XL)*XL

+11 .2925-0. 031256*P+0.0213337*P#XL#*2

XV=1.-(1*-XL)**R

RETURN

END

0348$ABS ( 1 ) HL ( 0

)

1

O

u9

10

FUNCTION H L ( X L > T ? P

)

IF (P.LT.200*) GO TO 100

HL= ( ( ( ( 561 . S6*XL-1929 * 6 ) KXL+2343 * 3 ) sXL-828 * 4 1 ) *XL-103 . 48 > *XL

-76*82411 . 1 2 7 0 3 4c T RETURN

CONTINUE

HL=( ( (-6!

-57*1775 + 1. 09174 4: T RETURN

END

100

i’ V I sj vj I ) T- A i_
0348*ABS<1) HV ( 0

)

1

456

/3

o

/ 10

11

12

13

14

15

16

\ "7 x / 13

19

1

50

1

100

FUNCTION HV(XL»XV»T>P)

IF (P.LT.200.) GO TO 100

XVT=ALQG(0* 00004)

IF ( XV LE 0 * 99996

)

IF ( XL . LT 0 36 ) GO TO 50

HV=< ( (0.063765*XVT+2.0794)*XVT+24.8: 9 ) * XVT-M 44 4 63 ) *XVT+91 1 1 \ >2E-05*T+0, 027252 >#T-5. 9429)

*T)*(1.-XV)+0*54663*T*(1.-XV)**2 i3i;

RETURN

CONTINUE

Hv= ^ \ -l«i42 fjo»Xv + 2954 4 ) #XV- -. T U W T W / M* V 1 W / J. +8.370E-09*T**4+< ( <-3,7752E-05*T+0.Q27252)*T5 * 9429 )

%

T ) # ( 1

. -XV ) +0 . 54663* T* ( 1. -XV ) **2-3 . 1 31

3

RETURN

CONTINUE

HV=( <-4.94BE-06*T+l*49518E-03)#T+0.415871>*T+530.976

+ ( ( (4 * 05554E-05*T-0 *0290022 >*T+A 79126 ) *T ) * ( 1 -XV

)

RETURN

END

0348* ABS ( 1 ) * P 6 A T ( 1

)

1 FUNCTION PSAT(XL»T»P1C>

n COMMON /TOLS/ T0L1 » T0L2 » ITERMX

3 COMMON /LU/ LUR»LUU»LUF

4 I T E R = 0

5 P 1 = P 1

C

6 F 1 = T - T S A T ( X L > P 1

)

7

/ P 2 = P 1 + 1

,

Ow 10 CONTINUE

Q ITER=ITER+1

10 IF ( ITER * LT ITERMX) GO TO 15

11 U R I T E ( L U U > 1 6 ) XL»T»PSAT» ITER

i O

x x. 16 FORMAT ( / IX >

***PSAT*** ' »3F10.3»I5

13 RETURN

14 1

5

CONTINUE

1

5

F 2 = T - T 3 A T ( X L ? P 2

)

16 P S A T = F’ 2 - F 2 / ( F2-F1 ) * ( P2-P1

)

i 7

X i IF ( ABS ( P3AT-P2 ) LT T0L1 ) RETURN

1 q P 1 = P 2

19 F 1 =F2

20 P 2 = P S A T

9

• GO TO 10

? 9 END
9

48*ABS(1) TH ( 1

1 FUNCTION TH(XLfHfPfTIC)

COMMON /TOLS/ T0L1 » T0L2 > ITERMX

“I COMMON /LU/ LURfLUWfLUF

4 I T E R = 0

5 T 1 =T 1C

6 Fl=H-HL(XL»TlfP)

/ T2 = T 112 4 Ou 10 CONTINUE

9 ITER=ITER+

10 IF ( ITER * LT 4 ITERMX ) 60 TO 15

11 WRITE ( LUW f 16 ) XLfHfTHfP

12 16 FORMAT ( /IX f '***TH*** ' f4F10*3)

i "I

J. v_‘ RETURN

14 15 CONTINUE

15 F2=H-HL(XLfT2fP)

16 TH=T2-F2/(F2-F1 ) * ( T2-T1

17 IF ( AES ( TH-T2* LT 0 01 ) RETURN

13 T 1 = T 2

i o F 1 = F 2 20 T2=TH

n i jL X GO TO 10

99 END

0 u 4 d -T- A B b ( 1 ) A L f ! \ 0 }

X FUNCTION XLPT(PfTfXLIC)

9 COMMON /TOLS/ T0L1 f T0L2f ITERMX

u COMMON /LU/ LURfLUUfLUF

4 I T E R = 0

cr X L 1 = X L1C

O F1=T-TSAT(XL1 fP)

7 XL2 = XL1 +0 * 01

n

u 10 CONTINUE

9 I T E R = I T E R + 1 10 IF ( I TER * LT * ITERMX) 60 TO 15

11 WRITE ( LUW f6 ) PfTfXLPT

•< -”» i jL

i L

x u FORMAT ( /IX f '***XLPT*** 7 f3F10.3)

13 RETURN

14 15 CONTINUE

15 F 2 = T - T 3 A T ( X L 2 f P )

1 6 XLF'T =XL2-F2/ ( F2-F1 ) % ( XL2-XL1

1 7 IF ( ABS ( XLPT-XL2 ) * LT ( T0L2 ) RETURN

i O

i u X L 1 = X L 2

1 9 F1 = F2

20 X L 2 = X L P T h i

Xm X 60 TO 10
END

48* ABS i: 1 ) . THU ( 1

1 FUNCTION THU ( XL ? XV ? H > F' » TIC

)

9 COMMON /TOLS/ T0L1 » TQL2 t ITERMX

7

u COMMON /LU/ LUR>LUU>LUF

A"7 I T E R = 0

cr T 1 =T 1

O F1=H-HV(XL»XV»T1»P)

7 T2 = T 1 +2 * Ou 10 CONTINUE

9 ITER=ITER+1

10 IF (ITER. LT. ITERMX) GO TO 15

11 WRITE ( LUU > 16) XL>XV»H>P>THV

12 16 FORMAT (1X»'***TH**4 ' >5F9,3)

13 RETURN

14 15 CONTINUE

15 F 2 = H - H 0 ( X L j X 0 > T 2 ? P

)

16 THU=T2-F2/ ( F2-F1 )*(T2-T1

)

17 IF (ABS(THV-T2) .LT.T0L1) RETURN

13 T 1 = T 2

1 Q J. i FI =F2

20 T 2 = T H 0

21 GO TO 10

22 END

1o

~i A

-r

nr\j

/O

O

u

i ‘J 11

FUNCTION T Q ( X j P > H ? Q

)

COMMON /TOLS/ T0L1 >T0L2? ITERMX

COMMON /LU/ LUR»LUW>LUF

COMMON /DO/ ICK

ITERT=0

T 1 = T S A T ( X i F'

TT=T 1 ASSIGN 670 TO IJPT

GO TO 300

0 CONTINUE

FT1=FT

T2 = T 142

ASSIGN 675 TO IJPT

L1

TT-T-1 i I 1 Am r.n t n uu i O

1 soo
17 ITERT=ITERT+1

IS IF (ITERT.LT. ITERMX) 60 TO 680

19 UR I T E ( LUW >681) TT » FVXF , X6 » HF > HG t Q > H 20 681 FORMAT ( IX > '***TQ*** # f8F7.2)

21 RETURN

00 680 CONTINUE

77jL w IF (ICK.EQ.5) WRITE ( LUW >681) TT»P»XF»XG»HF»HG»Q»H

24 TT=T2-FT2/(FT2-FT1)*(T2-T1>

n c IF ( AES < TT-T2 ) .LT.T0L1) 60 TO 690

26 T1 = T2

n 7 FT1=FT2

n n

iL O T2 = TT

?9 GO TO 673

30 690 CONTINUE

31 TQ = TT

32 RETURN

O 800 CONTINUE

34 XF=XLPT(P>TT»X)

1 ET

vJ J IF (XF.6T. 0.9999) XF=0.9999

vJ U HF=HL(XF»TT»P)

T*7 o / XG=XV(XF»P)

1 O

u.' U 0= ( X-XF ) / ( XG-XF ) 39 HG=HV(XF»XG»TT»P)

40 FT=Q*HG+<1 .-Q)*HF-H

41 60 TO I.JF'T 42 END

END PRT
»

NBS-114A (REV. 2-80

U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

SHEET (See instructions

)

REPORT NO.

NBSIR 82-2606 October 1982

4. TITLE AND SUBTITLE

A Model of the Steady-State Performance of an Absorption Heat Pump

5. AUTHOR(S)

S. A. Klein

6. PERFORMING ORGANIZATION (If joint or other than NBS, see instructions) 7. Contract/Grant No. national bureau of standards

DEPARTMENT OF COMMERCE i. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

U.S.. Department of Energy Oak Ridge National Laboratory

Washington, D.C. 20585

10. SUPPLEMENTARY NOTES

| | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most si gnificant information. If document includes a significant

bibliography or literature survey, mention it here)

A mathematical model of the steady-state performance of an absorption heat

pump is described. The model is compared with experimental data from a residential-sized water chiller. It is also used to determine the sensitivity

of the heat pump performance to its design variables.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

absorption heat pump; ammonia-water; ARKLA water chiller; experimental performance;

mathematical model; steady-state performance

13. AVAILABILITY 14. NO. OF

lY | Unlimited

PRINTED PAGES

| j For Official Distribution. Do Not Release to NTIS 56

1 j Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402. 15. Price

p£~| Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $9.00
T

y

’