NBS

PUBLICATIONS

AlllDS Mfi3b3ti

NATL INST OF STANDARDS & ^ECH R.I.C,

A11 102483636

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*<"?EAO Ot *

I/) O NBS TECHNICAL NO rr 1218

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

hQC

100

.U5753

No. 1218

1986

C.2

Modeling of a

Heat Pump

Charged With a

Non-Azeotropic

Refrigerant IVIixture

Piotr Domanski
Tm he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

^ Bureau's overall goal is to strengthen and advance the nation's science and technology and facilitate their effective application for public benefit. To this end, the Bureau conducts research and provides: (1) a

basis for the nation's physical measurement system, (2) scientific and technological services for industry and

government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety.

The Bureau's technical work is performed by the National Measurement Laboratory, the National

Engineering Laboratory, the Institute for Computer Sciences and Technology, and the Institute for Materials

Science and Engineering

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• Basic Standards^

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The Institute for Computer Sciences and Technology

Conducts research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and economy in Government

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Conducts research and provides measurements, data, standards, reference

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'Headquarters and laboratories at Gailhersburg, MD, unless otherwise noted; mailing address Caiihersburg, MD 20899. 'Some divisions within the center arc located at Boulder, CO 80303. 'Located at Bouldci , CO, with some elements ai Gailhersburg, MD.
NES EESEARCH iNFOEJIAtlOH CENTER

Modeling of a Heat Pump Charged ^^

With a Non-Azeotropic Refrigerant Mixture u^y^s

Piotr Domanski

'^^^

National Bureau of Standards

Center for Building Technology

Building Equipment Division

Gaithersburg, Maryland 20899

January 1986

Sponsored by:

Electric Power Research Institute

Palo Alto, California 94303

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
National Bureau of Standards Technical Note 1218

Natl. Bur. Stand. (U.S.), Tech. Note 1218, 391 pages (Jan. 1986)

CODEN: NBTNAE

US. Government Printing Office

Washington: 1986

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402
ABSTRACT

An analysis of the vapor compression cycle and the main components of an airto-air heat pump charged with a binary non-azeotropic mixture has been performed for steady-state operation. The general heat pump simulation model

HFBI has been formulated which is based on independent, analytical models of

system components and the logic linking them together. The logic of the

program requires an iterative solution of refrigerant pressure and enthalpy

balances, and refrigerant mixture and individual mixture component mass

inventories.

The modeling effort emphasis was on the local thermodynamic phenomena which

were described by fundamental heat transfer equations and equation of state

relationships among material properties. In the compressor model several

refrigerant locations were identified and the processes taking place between

these locations accounted for all significant heat and pressure losses.

Evaporator and condenser models were developed on a tube-by-tube basis where

performance of each coil tube is computed separately by considering the cross- flow heat transfer with the external air stream and the appropriate heat and mass transfer relationships. A constant flow area expansion device model was formulated with the aid of Fanno flow theory. Equation of state for mixtures

is described and equation constants for a R13B1/R152a mixture are given.

The developed heat pump model was validated by checking computer results

against laboratory tests data of one heat pump at two cooling and two heating

rating points.

Program HFBI can be used to evaluate potentials of non-azeotropic mixtures

working in a split residential heat pump. User's Manual and listing of the

program is included in the report.

Key words: air conditioner; capillary tube; coil; compressor; condenser;

expansion device; heat pump; modeling; mixture; non-azeotropic

refrigerant; vapor modeling cycle

iii
ACKNCWLEDGEMENTS

Hie author wishes to acknowledge the assistance received from Graham Morrison,

William Nnlroy, Reinhard Radermacher. Howard Ross, and especially David Didion

who directed the Group's non-azeotropic mixture research.

Appreciation is due Preston McNall, Victor Goldschmidt and Jesse Galloway for

their comments on the report.

This work was funded by the Electric Power Research Institute, with Jim Calm

serving as the project manager.

Iv
TABLE OF CONTENTS

Page

ABSTRACT iii

ACKNOffLEDGEMENTS iv

DISCLAIMER vii

METRIC CONVERSION FACTORS viii

LIST OF TABLES ix

LIST OF FIGURES x LIST OF SYMBOLS xii

1

.

INTRODUCTION 1

2. GUIDELINES FOR MODEL DEVELOPMENT 7

3. EVALUATION OF THERMODYNAMIC AND TRANSPORT PROPERTIES OF A

NON-AZEOmOPIC MIXTURE, R13B1/R152a 9

3.1. Evaluation of Thermodynamic Properties 9

3.2. Evaluation of Transport Properties 19

4. OPERATION OF A HEAT PUMP WITH A CONSTANT FLOW AREA EXPANSION

DEVICE 23

5

.

MODELING OF A HEAT PUMP 29

5.1. Logic of a Model of a Heat Pump Charged with a Non-Azeotropic Mixture Refrigerant 29

5.2. Modeling of a Reciprocating, Hermetic Compressor 33

5.2.1. Compressor Operation 33

5.2.2. Theory and Governing Relations 33

5.3. Modeling of a Constant Flow Area Expansion Device 47

5.3.1. Available Capillary Tube Performance Data 47

5.3.2. Available Short Tube Restrictor Performance Data .... 50

5.3.3. Critical Flow 50

5.3.4. Model Formulation 53

5.4. Modeling of an Evaporator and a Condenser 56

5.4.1. Modeling Methodology 56

5.4.2. Heat Transfer Rate for a Tube of a Cross-Flow

Arrangement 56

5.4.3. Refrigerant and Air Mass Flow Rates Associated

with a Tube 61

5.4.4. Overall Heat Transfer Coefficient for a Dry

Finned Tube 62

5.4.5. Forced Convection Heat Transfer Inside a Tube 63

5.4.6. Forced Convection Heat Transfer at the Air-Side

of a Flat-Finned Tube 66

5.4.7. Overall Heat Transfer Coefficient for a Wet

Finned Tube 67

5.4.8. Pressure Drop in a Tube 74

5.5. Modeling of Additional Heat Pump Components 77

5.6. Refrigerant Mass Inventory in a Heat Pump 79

6

.

MODEL VERIFICATION 85
7. SUMMARY AND CONCLUSIONS 89

8. REFERENCES 91

APPENDIX A. Calculations of Properties of Moist Air 95

APPENDIX B. Calculation of Water and Frost Properties 97

APPENDIX C. Calculation of Critical Pressure for TVro-Phase

Fanno Flow of a Non-Azeotropic Mixture 99

APPMDIX D. The Logic of the Main Program, BMAIN 103

APPENDIX E. Compressor Simulation Subroutine, COMPRE 107

APPENDIX F. Capillary Tube Simulation Subroutine, CAPIL 109

APPENDIX 6. Evaporator and Condenser Subroutines, EVAPHX and CONDHX .. Ill

APPENDIX H. User' s Manual 113

HI. General Information 113

H2 . Input and Output Data Coding 113

H2.1 Refrigerants Constants 113

H2.2 Heat Pump Data 113

H2.3 Run Controlling Data, Indoor and Outdoor

Air Conditions, Refrigerant Parameters

and Output Data 114

APPMDIX I. Example of Run of the Program, HPBI 131

APPENDIX J . Listing of the Program, HPBI 215

vi
DISCLAIMER

In view of the presently accepted practice of the building industry in the

United States and the structure of the computer software used in this project,

common U.S. units of measurement have been used in this report. In recognition of the United States as a signatory to the General Conference of Weights

and Measures, which gave official status to the SI system of units in 1960,

appropriate conversion factors have been provided in the table below. The

reader interested in making further use of the coherent system of SI units is

referred to: NBS SP330, 1972 Edition. 'The International System of Units, ' or E380-72, ASTM Metric Practice Guide (American National Standard 2210.1).

Vll
METRIC CONVERSION FACTORS

Length

Area

Volume

Temperature

Temperature

Interval

Mass

Mass Per Unit

Volume

Energy

Specific Heat

Gallon

1 inch (in) = 25.4 millimeters (mm)

1 foot (ft) = 0.3048 meter (m)

1 ft2 = 0.092903 m^

1 ft3 = 0.028317 m3

F = 9/5 C + 32

1»F = 5/90C or K

1 pound (lb) = 0.453592 kilogram (kg)

1 lb/ft3 = 16.0185 kg/m^

1 Btu = 1.05506 kilojoules (kJ)

1 Btu/ [(lb) (OF)] = 4.1868 kJ/[(kg)(K)]

1 gallon = 0.0037854 m^

Vlll
LIST OF TABLES

Page

1. Eqmttlon of State Constants for Refrigerants 13B1 and 152a 11

2. Coefficients to be Used in Equations (17), (18), and (19) 18

3. Coefficients to be Used in Correlations for Fin Efficiency

(Equation ( 89) ) 70

4. Laboratory Test and Ccnpnter Simnlation Results in the

Cool ing Mode 87

5. Laboratory Test and Computer Simulation Results in the

Heating Mode 88

Bl. Water Property Evaluation Constants vhioh are Used in

Equation (Bl) 98

HI. Refrigerant Property Single Precision Functions and

Subroutines 119

H2. Refrigerant Property Double Precision Functions and

Subroutines 121

H3. Functions and Subroutines for Heat Pump Component Simulation,

Heat Transfer and Fluid Mechanic Calculations 122

H4. Data File Containing Constants for Evaluation of Thermodynamic

Properties of R13Bl/RlS2a Mixture 123

H5 . Heat Pump Input Data Code to Program HPBI 124

H6. Example of a Heat Pump Data File 129

ix
LIST OF FIGURES

Page

1. Oversimplified thermodynamic cycle of a heat pomp 2

2. Schematic of a heat pump 3

3. Thermodynamic cycle realized by a heat pump 5

4. Flow chart for calculating the saturation pressure of single

component refrigerant 12

5. Flow chart for calculating the bubble point temperature of a non-azeotropic binary mixture 15

6. Temperature-composition diagram for a non-azeotropic binary

mixture 16

7. Simplified thermodynamic cycle realized by a heat pump

charged with refrigerant 22 in the cooling mode at different

outdoor temperatures 25

8. Schematic of an accumulator 26

9. Overall logic of a program simulating a heat pump employing a constant flow area expansion device and charged with a non-azeotropic binary refrigerant mixture 30

10. Schematic of a hermetic compressor 34

11. lypical speed (RPM) versus load curve for a permanent

split-capacator two pole electric motor [15] 36

12. Simplified indicator diagram for a reciprocating compressor 38

13. Typical efficiency versus load curve for a permanent

split-capacitor two pole electric motor [15] 40

14. Pressure and temperature distribution along typical capillary

tube [23] 48

15. Mass balance for an element of fluid in one-dimensional steady

flow in a constant area duct 51

16. Momentum balance for an element of fluid in one-dimensional

flow in a horizontal > constant area duct 51

17. Energy balance for an element of fluid in one-dimensional,

adiabatic, steady flow in a horizontal, constant area duct 52

18

Fanno 1 ine 52
19. Schematic of a heat pump heat exchanger 57

20. Example of coil circuitry 58

21. Approximation method for treating a rectangular-plate fin of

uniform thickness in terms of a flat circular-plate fin of

equal area 59

22. Cross section of a flat-finned tube indicating parameters which

affect the air-side heat transfer coefficient 68

23. Efficiency for a circular-plate fin of uniform thickness 69

24. Refrigerant phase in heat pump components 80

CI. Logic to evaluate the quality of the Fanno flow of a given

pressure for a mon-azeotropic mixture 101

Dl. Overall logic of program HFB I 105

Fl. Logic of a constant flow area expansion device simulation

program, CAPIL 110

61. Flow chart for coil performance simulation programs 112

xi
LIST OF SYMBOLS

A = flow cross section area

Af = fin siirface area

At = heat transfer surface area

A . = coefficients in equation (89)

A £ = pipe inside surface area

A^ ^ = pipe isean surface area

A - pipe total outside surface ares

al,a2,a3 = coefficients in equation (45)

CP = pressure drop parameter

CQ = heat traasfer parameter

C„ = correction factor in equation (34)

C = clearance Yolraae, in fraction of compressor stroke volume

Cp - specific heat at constant pressure

Cv ~ specific heat at constant volume

D - tube inside diameter

D„ = tube outside diameter

oDj = fin tip diameter

dl,d2 = dimensions representing arrangement of tubes in a coil, as per

figure 21

E = electrical power input

F1,F2 = dimensionless parameters used in equation (83)

f = Fanning friction factor

f^ L

~ friction factor for the liquid portion of two-phase flow, flowing

alone in the tube

G = —, mass flux, or Gibbs free energy

A

^max ~ ^^^ mass flux between two adjacent fins

H = liquid refrigerant level in an accumulator

h = heat transfer coefficient, h refers to air-side forced convection

heat transfer coefficient for wet air, h^ ^ refers to air-side

xli
forced convection heat transfer coefficient for dry air, h. refers

to inside tube convection heat transfer coefficient

hn ^ - air-side mass transfer coefficient

D, o hp = horse power

i = enthalpy

ifg = latent heat of evaporation or condensation

J = the mechanical equivalent of heat

K = flow contraction coefficient

Kf = J * ifg * Ax/L, boiling number

k = thermal conductivity

L = tube length

Le = —^^— , Lewis number

^D,oCPa

M = mass of refrigerant, or molecular weight

m = mass flow rate

Nu =

' ^ , Nusselt number

n = polytropic index

P = pressure

Pr = 1L_1_C£^ Prandtl number

k

Q = heat transfer rate

R = rate of moisture removal per unit area, or universal gas constant

R' = rate of moisture removal per unit width of a fin

Re = ^ ' ^ , Reynolds number

Re^ j^ = Reynolds number for the liquid portion of two-phase, flowing alone

in the tube

RPN = compressor number of revolutions per minute

S = tube perimeter

s = entropy

T = temperature

xiii
Tj V = fin base temperature

Tj = mean fin temperature

T« = refrigerant saturation temperature

r,g

t = fin thickness

U = overall heat transfer coefficient

V = velocity

Vs = conpressor swept volume

V = volume

V = specific volume or molar volume

W- = mechanical power available for compression process

W = mechanical power input

w„ = humidity ratio of air, w„ t refers to tube row inlet, w„ ^ refers a a,x a^o

to tube row outlet

w = humidity ratio of saturated air at temperature of wetted water film

XL - molar composition of liquid phase

XM = molar composition of mixture

XV = molar composition of vapor phase

XW = weight composition of mixture

Xtt = ( ^ 7

^

) 1^1 (— ) , Lockhart-Martinelli parameter

V,v/ Vl

my

m*T + mj

, quality

X = pipe wall thickness

y = fin height

Z. = fraction of the tube in the two-phase region for the tube with

liquid and two-phase flow

Zy = fraction of the tube in the superheated vapor region for the tube

with two-phase and superheated vapor flow

z = distance between adjacent fins

a ~ void fraction

xiv
p. = exponent in equation (83)

Y

= isentropic index

a - liquid layer (frost) thickness or Stefan Baltzman constant

e - surface emissivity

H

= electric motor effiiency

n = mechanical efficiency of compressor

n = polytropic efficiency of compressor

1} = volumetric efficiency of compressor

)i - absolute viscosity

p = density

X = skin friction factor

({> - correction factor for two-phase pressure drop

<t> = fin efficiency

Subscripts:

a = air, a,d refers to dry air

e = exit

f = frost or fin

1 = inlet

L = liquid

m - mean value

P = constant pressure process

r = refrigerant

s = constant entropy process

t - total value

V = vapor

v = constant volume process

w = water

1 to 13 = refrigerant key locations in a heat pump, as per figure A, unless

otherwise explained in the text

XV

1 . INTRODUCTION

Among equipment providing thermal comfort for indoor spaces, the heat pump has

gained in recent years substantial popularity for residential applications.

The heat pump is unique since it is the only device, which can provide both

heating and cooling. Heat pumps have become very competitive economically and

are considered to be a very good investment by homeowners.

A heat pump works on the vapor compression cycle principle. The most

important heat piunp components are two heat exchangers, a compressor and an expansion device. The heat pump thermodynamic cycle c^n be explained by

analysing the processes that the refrigerant undergoes in these four components. The most convenient diagram for such an explanation and performance

analysis is that of a pressure vs. enthalpy coordinate system, as shown in

figure 1. The compressor receives low pressure and temperature refrigerant at

state 1 and compresses it to a high pressure. This compression process is

associated with an increase of refrigerant temperature. At state 2, the high

pressure and high temperature vapor enters the condenser. The refrigerant

passing through the condenser rejects heat to the high temperature reservoir

and changes, usually to a subcooled liquid at state 3. Then, the refrigerant

flows through the expansion device undergoing a drop in pressure and temperature. Finally, the low pressure, low temperature, and low quality refrigerant

at state 4 enters the evaporator, where it picks up heat from the low temperature reservoir, reaching a superheated (or high quality) vapor state 1 at the

evaporator exit. In the explanation above, the low and high temperature

reservoirs are the indoor and the outdoor environment, when the heat pump is

operating in the cooling mode.

Besides the compressor, two heat exchangers, and the expansion device, there

are, for practical reasons, many other components in an actual heat pump

system. For modeling consideration, the most important are: tubes connecting

basic elements, 4-way valve enabling refrigerant flow reversal in the unit to

operate in the heating or cooling mode, and an accumulator (not used in all

systems), which acts as a protective device for the compressor by storing excess refrigerant during part lo&d operation and preventing liquid

refrigerant from entering the compressor.

There are many concepts and designs of heat pump components, however, certain

types are predominant. A reciprocating hermetic compressor is usually used

for vapor compression in small systems. Heat exchangers are usually in the

form of staggered tubes with closely packed wavy fins (spine-fins or bristlefins are sometimes used). There are basically two types of expansion devices

in application today. Constant flow area restrictors prevail in small capacity units such as household refrigerators, window-type air conditioners, and

central residential air conditioners and heat pumps. Larger, more expensive

residential units and commercial units are usually equipped with a variable

flow area device called a thermostatic expansion valve (TXV)

.

All the above mentioned components make up an actual vapor compression system.

Configuration of such a system and the thermodynamic cycle are illustrated in

figure 2 and figure 3, respectively. Refrigerant states in figure 3 correspond to particular locations in the system marked in figure 2, which

are:
'2.3

CONDENSER

X

THROnilNG

VALVE

EVAPORATOR

'4.1

COMPRESSOR ^].2

W = WORK TRANSFER

= HEAT TRANSFER

^

ENTHAIJ»Y

Figure 1. Oversimplified thermodynamic cycle of a heat pump.
4-WAY VALVE OUTDOOR COIL

Note: 1. Refrigerant flow direction is marked for cooling operation.

2. Numbers 5 and 6 situated in the compressor correspond to

refrigerant state before and after the compression process,

Figure 2. Schematic of a heat pump.
1 - evaporator exit, suction pipe inlet

2 - suction pipe outlet, low pressure 4-way valve inlet

3 - low pressure 4-way valve exit, compressor enclosure inlet

4 - inside compressor enclosure

5 - compressor cylinder at suction

6 - compressor cylinder at discharge

7 - discharge manifold

8 - compressor enclosure exit, high pressure 4-way valve inlet

9 - high pressure 4-way valve exit, discharge pipe inlet

10 - discharge pipe outlet, condenser inlet

11 - condenser outlet, liquid line inlet

12 - liquid line outlet, expansion device inlet

13 - evaporator inlet

In the heat pumping process refrigerant is the carrier of heat from a low

temperature reservoir to a high temperature reservoir. There are many kinds

of refrigerants of different properties available and they are being used

depending on the application. For residential air-to-air heat pumps, refrigerant 22 has been generally accepted as the most advantageous. However, in

recent years interest has intensified in non-azeotropic binary mixtures as potential working fluids in heat pumps. Gliding evaporation/condensation

temperatures and the possibility of heat pump capacity control via mixture

composition shift are often cited as factors giving mixtures a theoretical

performance edge over single component refrigerants.

The objective of this study is the development of a mathematical model of an air-to-air heat pump working with a non-azeotropic mixture as the refrigerant

in order to be able to investigate performance potentials of mixtures. The

type of heat pump considered here is the one most commonly commercially

available with a reciprocating hermetic compressor, fin-tube heat exchangers

and a constant flow area expansion device. The mixture considered in this

study consists of refrigerants 13B1 and 152a.
k

CO

ENTHALPY

Figure 3. Thermodynamic cycle realized by a heat pump (for number location

refer to figure 2)

.

2. GUIDELINES FOR MODEL DEVELOPMENT

Before beginning the modeling effort, general guidelines for model development

have to be established. These guidelines should evolve from future model

applications as they are broadly perceived today. It is understood that the

model is planned to be used for parametric studies by different users, applied

to different hardware and possibly charged with different non-azeotropic

refrigerants* The model should help prospective users to evaluate potential

benefits of non-azeotropic mixtures, as applied to heat pumps, resulting from

changing refrigerant temperature during evaporation/condensation and change

of mixture composition which influences heat pump capacity.

It has been stated already that a heat pump equipped with a reciprocating

compressor, compact staggered tube and flat fin heat exchangers, and a constant flow area expansion device will be modeled. This choice has been

made since, in addition to the fact that components of this design type are most commonly encountered, results of initial research indicated a possibility

of inherent to the system capacity modulation in systems employing a capillary

tube [1].

The model should be a first principle one. Regression analysis curve fits

should be avoided so the program could be applied to simulate systems of

different characteristics, size and performance level. Modular structure of

the program should allow for later model upgrades on the local basis. Since

heat exchangers and changing refrigerant mixture temperatures during change of

phase are going to be investigated, a tube-by-tube approach to modeling of an

evaporator and condenser was adapted. Finally, an appropriate equation of

state is desirable that could be universally used for accurate predictions of

thermodynamic properties for a variety of possible non-azeotropic mixtures.

During the past, a heat pump modeling effort has been underway at NBS [2,3].

The latest model [3] fulfills the basic postulates of the guidelines and is

adopted here for expansion to the simulation model of a heat pump charged with

a non-azeotropic mixture.

3. EVALUATION OF THERMODYNAMIC AND TRANSPORT PROPERTIES OF A NONAZEOTROPIC

MIXTURE, R13B1/R152a

The refrigerant mixture, R13Bl/RlS2a, discussed in this chapter showed

promising performance in experiments performed by Cooper [1] . The choice of

this mixture for development of this heat pump model does not mean this

mixture to be optimum and precludes other mixtures to be more suitable for

heat pump application.

3.1. Evaluation of Thermodynamic Properties

Evaluation of thermodynamic properties for a non-azeotropic mixture represents

an additional complication as compared to single component refrigerants. The

employed equation of state has to be able to provide predictions for a broad

range of compositions that the circulating mixture may have during heat pump

operation. This range of possible compositions is even further expanded by

the fact that in the two-phase region, saturated liquid and saturated vapor in

equilibrium have different compositions.

Connon and Drew [4] presented application of Redlich-Kwong-Soave (R-K-S)

equation to generate R13B1/R152a mixture thermodynamic data. The R-K-S equation successfully generated all vapor thermodynamic information, however,

prediction of liquid density of the mixture was based on densities of pure

components and application of a mixing rule, since the R-E-S equation did not

provide the desired accuracy.

It has been shown by Morrison et al . [5] that it is possible to describe both

the liquid and the vapor properties of pure-refrigerants as well as refrigerant mixtures with a single equation of state. They have shown that this

approach has a significant advantage over the traditional methods, that of

using a vapor equation of state and a library of liquid properties. This

advantage is that it will accurately predict property values in the region

near or above the critical point of either of the binary components [6]

Because of this advantage, Morrison's equation was adopted in this modeling

effort. The basic features of this equation are given below, though for full

review, the source report is recommended [5]. The equation of state has the

following form:

Pv ^ 1 + V + v^ - v^ a RT (1 - y)3 RT(v + b)

(1)

where y = —

4v

For single component refrigerants, parameters a and b can be determined by

second degree polynomials:

a = a^ + aj^T + ajT^ (2)

b = bQ + bjT + b^T^ (3)

9

I
;;re a.Q, a.-,, a.^, ^q, bi, and b2 are constants which are based on empirical

ita for a given refrigerant. For mixtures, these parameters may be

etermined by:

a = w|aj + 2wjWjjaj jj + Wj|ajj (4)

b = w|bj + 2wjWjjbj jj + Wj|bjj (5)

Parameters aj, ^jj, bj, and bjj are for pure refrigerants and are obtained by

equations (2) and (3).

Remaining parameters are:

f J jj = d - cT (6c) (c and d constants are obtained from mixture measurements to allow for the

interactions of the different molecular

species.)

Wj,Wjj = molar composition of the mixture, fraction of I and II

components, respectively.

Numerical values of the above explained constants are given in Table 1 for

refrigerants R13B1 and R152a.

Having defined the mixture thermodynamic state, by specifying temperature,

pressure and mixture composition, in order to evaluate other state thermodynamic properties it is essential to determine if the mixture is liquid,

vapor, or two-phase. In the latter case, evaluation of the compositions of

liquid and vapor in equilibrium is also required.

The starting point to this calculation procedure is pure component analysis

to determine saturation pressure for a given temperature. Since equation (1)

also contains molar volume, an iterative process is mandatory for both the

liquid and vapor phases. The criteria for verifying that the saturation

pressure and molar volume guesses are correct is the equality of the Gibbs

free energy and pressure of the two phases. The logic of this procedure is

illustrated in the flow diagram in figure 4, and Gibbs free energy is

calculated by the equation:

G = gP8(p*,T) + RT In ^^ + (pv - RT) - -^ In v_+_b

p*v b V

+ 4RTy + RTy ^^j ^-y (v-y)2

where G^^ = perfect gas Gibbs free energy

p* = equilibrium vapor pressure of the pure liquid at

temperature T

10
Table 1. Equation of State Constants for Refrigerants R13B1 and R152a

R13B1 R152a

•o 25.4145 27.39273

'1 -0.063368 -0.059421169

"2 4.140051 E-5 3.3176956 E-5

"o 0.1353977 0.1239878

"l -1.50409 E-4 -1.445514 E-4

"2 -1.354434 E-7 -1.9022281 E-8

c -2.241 E-4

d 0.1466

11
/input t/

Estimate

Psat. VV. VL

Using: T. Psat

& eq. of state

Calculate: VV, VL

Calculate:

Gibbs free energy

for liquid (GL) &

vapor (GV)

Print:

Psat. VV. VL,

Figure 4. Flow chart for calculating the saturation pressure of single

component refrigerant

12
The evaluation of compositions of the liquid and vapor phases in equilibrium

follows the rule that phase equilibrium in mixtures is defined by equality of

pressure, temperature and the chemical potential between phases of each of the

species in the mixture. Determination of the equilibrium composition is a rather lengthy procedure and it is not practical to use a full algorithm in a large vapor compression cycle simulation program where property values are requested on the order of hundred of thousands of times. For this reason,

equation of state was used to generate sufficient data to create a polynomial

spline where saturated liquid and saturated vapor compositions are functions

of temperature, pressure and saturation pressures of pure components at mixture temperature. Generation of polynomial splines is discussed in [7] and

[8]. The following equations were obtained for R13B1/R152a mixture:

RP=P1_J^P_

PI - P2

SI

S2

S3

S

Zl

Z2

Z3

Z

XL

12.58741 - 0.06465226 * TK 9.56391 * 10"^ * TK^

-48.9799 - 0.289414 * TK - 4.504945 * lO""* * TK^

47.7509 - 0.273993 * TK + 4.14487 * 10"'* * TK^

SI + S2 * RP + S3 * RP^

-0.34065414 - 3.337532 * 10"^ * TK + 9.66115 * 10~^ * TK^

-10.3139754 + 0.0653856 * TK - 9.9899162 * 10~^ * TK^

10.035917 - 0.05527259 * TK + 7.6821554 * lO"*'' * TK^

1 + Zl * (RP - 1) + Z2 * (RP^ - 1) + Z3 * (RP^ - 1)

(1 + S) * RP

(1 + S * RP)

(8)

XV = XL * Z

where

(9)

TK = mixture temperature (K)

P = mixture pressure (std atm)

PI = saturation pressure of pure R13B1 at temperature TK (std

atm)

P2 = saturation pressure of pure Rl52a at temperature TK (std

atm)

XL = molar composition of liquid phase (fraction of R152a)

XV = molar composition of vapor phase (fraction R152a)

Knowing saturated liquid and vapor compositions and overall mixture

canposition, evaluation of mixture quality, XQ, is readily available

XQ = XL - XM

XL - XV

where XM = mixture molar composition (fraction of R152a)

(10)

13
Phase equilibriuin compositions calculated by the spline agree to the third

decimal point with compositions obtained using the equation of state.

Equation of state does not provide us directly with information about the

bubble point or dew point. However, the bubble point for a mixture of given

composition and pressure can be found by iteration using the criteria that, at

bubble point the liquid composition (XL) is equal to a known mixture composition (XM) . The solution logic is illustrated in the flow diagram of Figure 5,

where the parameters are graphed in the phase diagram of Figure 6. Similar

logic is used for calculating the dew point temperature; in this case,

searching for the Unique temperature at which the saturated vapor composition

equals to composition of the mixture.

Evaluation of molar enthalpy is straight forward:

h = hPS + a'^TK - ab'TK - ab ^^ v + b ab'T - ab

b(v + b)

+ 8RTv(8v - b) (^, _ ^,j.^

(4v - b)3

(11)

where prime denotes a temperature derivative.

The molar enthalpy of a perfect gas of a mixture, h^^, is the integral of a linear weighting of the heat capacities of the component perfect gases.

T T

hP8 = / cpdt = / (wjCpj + WjjCpjj)dT (12)

^ref -40F

where Cpj and Cpjx are perfect gas heat capacities of the respective

components, functions of temperature, whose coefficients are determined

empirically.

Cpj = Cj(l) + Cj(2) • T + Cj(3) T^ (13)

Cpjj = Cjj(l) + Cjj(2) • T+ Cjj(3) • T^ (14)

Specific entropy can be calculated by the following expression:

m -rf

-40

Cvi

i^dT + R In

Wn V*

I

- AS{S (vj, -40°C)

r ^v

Wtt / —— dT + R In ^ AS?f (Vtt, " " y T Wtt . V* II II

^^ II

40

40 °C)

+ AsP8(v.T) (15)

14
/Input: /

Guess:

Tbub=T

For: T

Calculate: PI & P2

Calculate: liquid &

vapor comp. (XL&XV)

which are in equilibrium

at T & P

'bub='''

Print: Tbub

Adjust T

XL = 1

XL =

Figure 5. Flow chart for calculating the bubble point temperature of a non- azeotropic binary mixture.

15
UJ

QC3

h-

<

HI

fOL

UJ sat,

I

Vapor region

Liquid region

^sat,ll

XV XIM 1.0

Figure 6. Temperature- composition diagram for a non-azeotropic binary mixture

16
where:

Vj and Vjj are reference state (-40°C) molar volumes of liquid for each of the

pure components, ASi^ and AS^I are the differences of entropy between the

perfect and the real gas having a molar volume of saturated pure component

liquid I and II, respectively, at the reference temperature (-40°C) , AS^^ is

the difference of entropy between perfect and real mixture of the actual molar

volume V and at the actual mixture temperature T.

In either case, AS^^ can be evaluated by the equation (16) with v put to Vj or Vjj, if pure components are considered.

AsPS - a'b - ab' , v + b ^ ab' _ Rb(16v - 3b)

b' V b(v+b) (4v-b)2

_ 8RTbv(8v - b)

(4v - b)^

(16)

Application of the equation of state requires estimated values of the

following pure component properties at saturation as function of temperature;

pressure, molar volume of vapor, and molar volume of liquid. Correlations to

provide these guesses are given below:

3

P = exp J^ a(I) • T^ I (17) 1=1

^V

^L

3 = J] b(I) ' T^ /P (18) 1=1

3

X; c(I) • T^ ^ (19) 1=1

where P = saturation pressure

T = temperature

Vy = molar volume of saturated vapor

Vr = molar volume of saturated liquid

The equation coefficients a(I), b(I), c(I) for refrigerants 13B1 and 152a are given in Table 2 along with applicable units of refrigerant state property

parameters.

17
Table 2. Coefficients to be Used in Equations (17), (18) and (19)

Coefficient R13B1 R152a

a(l) 1. 00522 804E+1 1.06410518E+1

a(2) -2.2045632E+3 -2.6428994E+3

a(3) 9.6365313E+3 4.6087585E+2

b(l) -5.05060051E-2 2.18192 958E-2

b(2) 1.11455764E-3 5.416820778E-4

b(3) -2.56392871E-6 -1.24731336E-6

c(l) 2.749422E-1 1. 0236887 15E-1

c(2) 1.70256 9E-3 -4.0752759E-4

c(3) 3. 7 100 83 13 E-6 lo0409447E-6

Applicable units of the state parameter in equations (17), (18) and (19) are

pressure - std. atm

temperature - °K

molar volume - L/mol

18
3 .2 Evaluation of Transport Properties

In addition to the thermodynamic state equation, algorithms have to be used to

calculate thermal conductivity and absolute viscosity of the liquid and vapor.

These algorithms consist of curve-fitted correlations for the prediction of

properties of pure conponents, and of some kind of a mixing rule. Reid,

Prausnitz and Sherwood [9] gave a comprehensive review of mixing rules that

could be used depending on mixture component characteristics and component

property data availability. Following their recommendation, appropriate cor- relations were selected and are listed below along with the correlations used

for evaluation of the transport properties of pure components. Correlations

for property calculations are given here as presented in the referenced documents. However, for use in the mixing rule they were converted to common

dimensions.

Liquid Thermal Conductivity, k

(The Filippov Equation is used. The error should not exceed 4% [9].)

k = kl + (k2 - kl) * XW * (0.72 * XW + 0.28) (20)

where: kl, k2 = thermal conductivity of the pure components of R13B1 and

RlS2a, respectively,

kl = 0.35 - 1.5 10""* • TF (Btu/h ft F) [8]

k2 = 0.11650 - 0.000497 • TC (w/m • K) [8]

TC = temperature (C)

TF = temperature (F)

XW = weight composition (fraction of R152a)

Vapor Thermal Conductivity, k

(The Wassiljewa Equation is used with the Lindsay and Bromley Modification.

The error rarely exceeds 5% [9] .)

t = (1 - XM) ' kl ^ XM • k2 (21)

(1 - XM) • Ajj + XM • A^2 (1 - XM) • A21 + XM • A22

where: kl, k2 = thermal conductivity of the pure components of R13B1 and

R152a, respectively.

kl = 8.2982 * 10"^ - 5.1971 * 10~^ * TK + 1.8413 * lO"*^ TK^

[w/m -K] [8] _ k2 = -8.357 * 10 ^ + 6.32 * 10 ^ • TK + 4.257 * 10 ^ * TK^

[w/m • K] [9]

Aj^j = 0.25

f,

,0.75 \0.5 2

TK + S11

TK + Sj^

fij,H2 ~ absolute viscosity of the pure components, R13B1 and R152a,

respectively.

Mj,M2 = molecular weight of the pure components, R13B1 and R152a,

respectively.

TK = absolute temperature (K)

19
Si = 1.5 • T^i

Tt. = normal boiling point of 'i' component (K)

S^ = 0.73 * (S^ • Sj)®'^

XM = composition (mole fraction of RlS2a)

Liqnid Absolute Viscosity, u

(The Lobe correlation is used. The prediction error should be less than 15%,

19].)

^m

(22)

Vjjj = mixture specific volume

0]^,02 = volume fraction of the pure components, R13B1 and R152a,

respectively.

Yi»Y2 - kinematic viscosity of the pure components, R13B1 and R152a,

respectively, (obtained, as shown below, through evaluation of

the absolute j/^cosities. |ij and ^2) , = (e 4.22529 + VIO.gWTX) » ^^-3^ ^ (^ • s/m^) [10]

l\ = (e-4. 28224 + 753.013/TC) » ^^-Z ^^

. ,/„2) j^o]

a! = 1.7 In

^ ^

T^l

0.5

o! = 0.27 In

^ + (1.3 * In ^) ^ Yi Yi

TK = temperature (K)

Vapor Absolute Viscosity, u

(The equation derived from the vigorous kinetic theory of Chapman-Ensbog is

used. The error seldom exceeds 4% [9].)

(1 - XM)(ii XMI12

(1 - XM) + XM • 12 + (1 - XM)l02i

(23)

where

'12

3^0 (5)

K'*ai

0.25

20
XM = composition (mole fraction of R152a)

)i|, ^2 ^ absolute viscosity of the pure components, R13B1 and R152a,

respectively.

jij = 0.67329 * 10"^ + 7.60593 + 10"^ * TK - 2.81108 * 10"^ TK^ +

3.47410 10"^^ TK^ (N • s/m^) [9]

H, = 3.205 10"^ '^-^ (N • s/m^) [11]

k2 = thermal conductivity of pure R152a vapor (w/m ' K)

^1'

^ ~ molecular weight of the pure components, R13B1 and R152a,

respectively.

FE = 0.115 + 0.354 -^^

R

Cpjj = specific heat at constant pressure of R152a vapor.

Cpjj = -7.33704 + 0.093438 TK - 3.61094 * 10~^ TK^ + 4.80449 * 10"'' * TK^

kg K

21

4. OPERATION OF A HEAT PUMP WITH A CONSTANT FLOW AREA EXPANSION DEVICE

In a heat pump with a capillary tube, vapor superheat at the compressor inlet

will vary with changing operating conditions. As a matter of fact, no single

refrigerant parameter stays constant when indoor or outdoor air conditions are altered and the system seeks equilibrium under new conditions. To understand

the phenomena that cause refrigerant state changes, consider a heat pump

working in the cooling mode at constant indoor air conditions subjected to a step increase of the outdoor temperature. For the purpose of the analysis, it

is assumed that the overall heat transfer coefficient for both heat exchangers

does not vary. It is also assumed, as a first approximation, that the latent

heat of evaporation, if , is constant under the conditions discussed.

A step increase in the outdoor air temperature first affects the performance

of the condenser. Since the condenser environmental temperature increases,

the mean temperature difference between the air and the refrigerant decreases.

Less heat is rejected by the refrigerant to the air and a smaller enthalpy

change is realized in the coil. Consecutively, higher enthalpy, less subcooled liquid refrigerant enters the capillary tube. The capillary tube is

sensitive to the amount of subcooling and with less subcooling the mass flow

rate through the capillary tube decreases. Since the compressor capacity

stays unchanged, pressure builds up in the condenser. Thus point 11 on the

p - h diagram (figure 3) moves in the direction of higher enthalpy and higher

pressure.

The environment of the evaporator was not altered. However, refrigerant

parameters in the evaporator change in response to the change of refrigerant

state at location 11 as well as to the change in refrigerant mass flow rate.

For pressure drop considerations, as a first spproximation, the liquid line,

the capillary tube, and the evaporator are viewed as one tube, in which a given flow experiences a certain pressure drop. As pressure of the refrigerant at location 11 increases, it pulls up the refrigerant pressure in the

evaporator. Conflicting phenomena affect the change of refrigerant enthalpy

at point 1. Increased enthalpy at point 11 and reduced refrigerant mass flow

rate work against the impact of the smaller temperature difference between the

air and the refrigerant causing refrigerant enthalpy to slightly decrease.

The significance of the change of the refrigerant state at location 1 is a move towards smaller vapor specific volume. Since the compressor, as a first

approximation, is a constant intake volume piunp, increase in gas density

results in a higher mass flow rate.

The indicated phenomena will balance themselves further until the refrigerant

in the key locations of the system acquires the thermodynamic states that

satisfy simultaneously the equilibrium of all the heat pump components. Since

under steady-state operation, the refrigerant mass flow rate through the

compressor and the capillary tube have to match, the pressure in the condenser

will rise to an appropriate level. Again, higher pressure in the condenser

implies some increase of pressure (and saturation temperature) in the evaporator. The smaller temperature difference between the indoor air and the

refrigerant, and higher refrigerant mass flow rate result in a smaller

refrigerant enthalpy increase in the evaporator. Tbe refrigerant state at

point 1 with respect to point 11 is determined by this enthalpy change and the

appropriate pressure drop. Finally, when steady^state conditions are reached

the following changes in refrigerant thermodynamic states can be noted:

23
higher refrigerant pressure in the condenser, higher refrigerant pressure in

the evaporator, less superheat at the evaporator exit, and less refrigerant

liquid subcooling at the condenser exit. The change of saturation temperature

in the condenser corresponds approximately to the change in the outdoor air

temperature. The change of pressure in the evaporator is a fraction (approximately 15 percent) of the pressure change in the condenser. Though the

refrigerant is circulated in the system at a higher mass flow rate, the

capacity of the heat pump is decreased due to the smaller refrigerant enthalpy

change in the evaporator. The efficiency also drops since, in addition to a smaller cooling effect, the energy input to the compression process increases

due to the higher refrigerant mass flow rate and the higher compression rate.

A decrease of the outdoor air temperature would result in the opposite trends.

The change of refrigerant parameters is illustrated in figure 7, where results

of three tests of a heat pump charged with refrigerant 22 are plotted on the

pressure-enthalpy diagram (the plot is based on measured condenser and

evaporator pressures and temperatures only) . In these tests, the indoor air

conditions were held constant while the outdoor air dry bulb temperature was

changed producing modifications of the thermodynamic cycle.

For the heating mode operation, refrigerant flow is reversed by the action of

the four-way valve. The flow direction of the refrigerant in the system is

the opposite to that in the cooling mode, with the exception of the compressor. The indoor coil becomes the condenser while the outdoor coil serves as the evaporator. It is worthwhile to note the effect this change has on the

system. Since pressures in heat pump heat exchangers are functions of environment temperatures, the pressure in the evaporator is now much lower than

during cooling operation. Consequently, the density of the refrigerant at the

evaporator exit is smaller and less refrigeant is being pumped by the compressor. Also note that an indoor coil is usually much smaller than an outdoor

coil. The need for dehumidif ication is the primary reason. The indoor coil

working as a condenser cannot condense and hold as much refrigerant as the

outdoor coil during cooling operation. In heat pumps equipped with a capillary tube the excess of liquid refrigerant is stored in an accumulator.

A schematic of an accumulator is given in figure 8. The accumulator is a closed container with two tubes. The longer bent tube has a small diameter

hole on the bottom side, and is connected to the compressor. The other

connects the tank with the evaporator exit.

If superheated vapor leaves the evaporator, only vapor is contained in the

accumulator and no special function is fulfilled by the accumulator. If wet

vapor enters the accumulator, liquid droplets accumulate on the bottom of the

tank, while saturated vapor enters the tube leading towards the compressor.

Some liquid refrigerant enters the vapor stream through the hole in the tube,

driven by the static pressure difference in the liquid-vapor stream interface.

It should be noted that during steady^state operation with liquid in the

accumulator, qualities of the vapor entering and leaving the accumulator must

be equal.

In a heat pump charged with a non-azeotropic mixture, incomplete evaporation

in the evaporator and collection of liquid refrigerant in the accumulator

affect the actual mixture circulating composition. As shown on the temperature-composition diagram (figure 6) the liquid and vapor phases in

24
CO

enthalpy (kj/kg)

0.0 58.1 116.3 174.4 23E.6 390.7 348.9

6.500-

6.000-

5.500-

5.000-

4.500-

4 .000-

3.500-

^—1-^

Outdoor dry bulb temperature:

40.6°C (105°F) 35.0°C (95"F)

Indoor dry bulb temperature: 26.7°C (eO°F) Indoor wet bulb temperature: I9.4°C (67^F)

I

I

I

i

I

I

15.339

14.839

14.339

13.839

cd

P-> 13.339 .H

12.839

12.338

0.0 25.0 50.0 75.0 100.0 125.0 150.0

enthalpy (Btu/lb)

Figure 7. Simplified thermodynamic cycles realized by a heat pump charged with

refrigerant 22 in the cooling mode at different outdoor

temperatures.

25
FROM EVAPORATOR TO COMPRESSOR

SMALL DIAMETER HOLE

Figure 8. Schematic of an accumtilator.

26
equilibrium at a given temperature and pressure have different conpositions,

the liquid being richer in less volatile component. Consequently, with the

first liquid drop stored in the accumulator, circulating mixture composition

becomes richer in the lower boiling point refrigerant. This composition shift

increases with the increase of accumulated liquid.

27

5. MODELING OF A HEAT PUIUP

5.1. The Logic of a Model of a Heat PTunp Charged with a Non-Azeotropic

Refrigerant Mixture

During heat pump operation, refrigerant parameters at any location are established at a level which satisfies the respective components of the system.

There is a one-to-one relationship between working medium parameters and the

operating conditions, i.e., for given outdoor and indoor air conditions, there

is just one set of refrigerant parameters at any location within the system

which satisfy steady state operation. This unique set of refrigerant parameters has to be determined by the heat pump simulation program in an iterative process.

In order to set up a heat pump iteration process (Fig. 9), balances taking

place Cii.Ting steady state operation have to be recognized. From the fact that

a thermodynamic cycle is a closed loop, an analysis of a heat pump cycle on a pressure-enthalpy diagram allows the statement of two balances:

- Enthalpy Balance

The net refrigerant enthalpy change in all component s of the

system has to equal zero.

- Pressure Balance

This balance implies that the increase of refrigerant pressure

during the compression process has to be equal to the total pressure

drop during the other processes forming the cycle. As pressure drop

and mass flow rate are strictly related, this balance may be

restated that pressure drop through each component has to be such

that the mass flow rate in each component is the same.

The enthalpy balance and pressure balance can be supplemented by two

additional balances resulting from the law of mass conservation, as expressed

by the following equations;

51 ^ '^<" =

(24)

¥

5- / p.dV = Dt

^

V

where p = mean density of the mixture

p, = mean density of 'i' compone

V = system internal volume

(25)

29
(^ start ^

'input: Heat pump data

Operating conditions

Compressor suction pressure Compressor head pressure Vapor superheat at compressor Intet Refrigerant charge

Composition of charged refrigerant

Circulating composition

Cl5Z)

Figure 9. Overall logic of a program simulating performance of a heat pump

employing a constant flow area expansion device and charged with a nojL-azeotropic binary refrigerant mixture.

30
Equation (24) implies, that the amount of working medium in the system is the same at all times, for any operating conditions. Equation (25) states the same conservation principle for each of the mixture components. Though for a binary mixture the last equation provides us with two balances, we can actually use only one of them with conjunction with equation (24).

It should be noted that the first three balances are sufficient to set up the

logic of a simulation program of a heat pump charged with a single component

refrigerant. These three balances were utilized in [3] allowing for iteration

of the refrigerant thermodynamic states at key system locations without

imposed restrictions on the refrigerant state anywhere in the system. In a heat pump charged with a non-azeotropic binary mixture, the circulating composition may change if some liquid refrigerant is collected in the accumulator.

The actual composition of the circulating mixture has to be evaluated during

simulation. Since this change of composition represents an additional degree

of freedom, an additional equation (equation (25)) is used in the solution

logic.

The logic of the program is based on these four balances. It provides means

for calculation of vapor superheat (quality) at the compressor can inlet and

allows for heat pump simulation at the imposed operating conditions. Explanation of the logic, for sake of clarity, is done considering only four main

components of a heat pump, i.e., a compressor, a condenser, a capillary tube,

and an evaporator.

The required input consists of outdoor and indoor conditions, heat pump data

and composition of the charged and circulating mixture. The simulation process begins with estimated refrigerant pressure and vapor superheat at the

compressor inlet, and the compressor discharge pressure. Using these data,

the compressor performance is simulated yielding the refrigerant mass flow

rate. Next, the condenser and the capillary tube are simulated and a mass

flow balance is sought by comparing the refrigerant mass flow rates through

the compresf^or and capillary tube. If the ccanpared mass flows are not equal,

simulation of the compresor, the condenser, and the capillary tube is redone

with an unchanged refrigerant state at the compressor can inlet and a modified

estimate of compressor discharge pressure. Increasing this pressure reduces

refrigerant mass flow rate through the compressor. Then the condenser works

with this smaller mass flow rate and at a higher saturation temperature.

Consequently, refrigerant reaching the expansion device inlet is at a higher

pressure and has more subcooling. Both factors promote greater mass flow rate

through the capillary tube. Thus, increase in the discharge pressure has a clear and opposite impact on mass flow rates through the compressor and

through the capillary tube and the appropriate discharge pressure can be found

for which mass flow balance exists.

Once mass flow balance is reached, simulation of the evaporator is performed

with the known refrigerant state at the evaporator exit and the refrigerant

mass flow rate. Since the thermodynamic process in a capillary tube may be

viewed as adiabatic, refrigerant enthalpy at the evaporator inlet should be

equal to the enthalpy at the condenser outlet. If these enthalpies are not

equal (energy balance is not reached), a new calculation starts from the

beginning with a modified estimate of the refrigerant pressure at the compressor can inlet. From the condenser operation point of view, a change in

compressor suction pressure induces a change in the refrigerant mass flow rate

31
and a modification of the condenser saturation temperature resulting from the

system flow balance search. These two changes have opposite effects on refrigerant enthalpy at the condenser exit, leaving it only slightly altered.

On the other hand, the same change of ccmpressor suction pressure has a strong

effect on the refrigerant enthalpy at the evaporator inlet due to a change in

the evaporator saturation temperature and refrigerant mass flow rate, both

working to change the enthalpy in the same direction. Thus an appropriate

suction pressure at the compressor inlet can always be found when an energy

balance exists.

Once energy and pressure balances are established, two out of four refrigerant

parameters estimated at the outset are determined. However, these two parameters, compressor suction and discharge pressures, were obtained for imposed

refrigerant superheat (quality) at compressor can inlet and assumed circulating composition which still have to be verified. For refrigerant superheat

(quality) verification, the refrigerant mass inventory is made. It is based

on refrigerant states in the system which are found to satisfy energy and

pressure balances with assumed vapor superheat at the compressor can inlet.

The amount of refrigerant obtained from mass inventory calculations is com- pared to the actual refrigerant mass input (known design parameter). If the

amount of refrigerant calculated is smaller than refrigerant input into the

heat pnmp, the superheat (quality) estimate has to be decreased and all

calculations have to be repeated from the outset.

Once, in addition to satisfied pressure and energy balances, the refrigerant

superheat (quality) at the compressor can inlet is verified by means of mixture mass inventory, the ultimate verification of iterated refrigerant states

has to be done by checking if the circulating mixture composition for which

all results were obtained is in fact the actual circulation composition. This

is done by performing a mass inventory of one of the mixture components. It

should be mentioned that a composition shift of circulating mixture can occur only as a result of accumulation somewhere in the system of some of the

mixture of composition different from the original, i.e., accumulation of

liquid in the accumulator. If such accumulation does not take place (refrigerant entering the conpressor is a superheated vapor) the circulation composition equals the original composition of the charged refrigerant. If

refrigerant entering the compressor has quality less than 1, the program has

to proceed with mass inventory for one mixture component. This mass inventory

is based on refrigerant states in the system which are found to satisfy

enthalpy and pressure balances, and for which the total mass of refrigerant in the

system is conserved. If the amount of calculated mixture component is not

equal to the original amount charged into the system, the estimate of

composition of the circulating refrigerant has to be adjusted and all calculations have to be repeated from the outset. The solution logic described, here

is presented graphically in figure 9. The actual implementation of thi ogic

in the main program of the model is presented in Appendix D.

32
5 .2 Modeling of a Reciprocating. Hermetic Compressor

5.2.1 Compressor Operation

The compressor is mechanically the most complex component of a heat pump. A

reciprocating, hermetic compressor is most commonly used in heat pump systems.

A schematic of this type of compressor is shown in figure 10. The compressor

consists of a shell containing an electric motor, a cylinder/piston assembly

with valves and manifolds and tubes. The electric motor is coupled to the

compressor eccentric. Lubricating oil is collected on the bottom of the can and is in free contact with the refrigerant.

Flow of the refrigerant is from location 3 to location 8, as marked in figure

10. Low pressure refrigerant enters the compressor can and is directed

towards the electric motor to cool motor windings. The enthalpy of the

refrigerant changes due to this and other heat transfer with other surrounding

surfaces, namely, the ccMpressor can, manifolds, the discharge tube and the

cylinder body. Then the refrigerant at state 4 undergoes the process in the

cylinder, which in case of positive displacement compressors consists of:

expansion through the suction valve and mixing the residual gas, compression,

expansion through the discharge valve, and re-expansion of residual gas. The

compressed, high temperature and high pressure refrigerant vapor leaves the

compressor through the discharge manifold and discharge line after giving up

some heat to the low pressure refrigerant at state 4.

The numbers marked in figure 10 identify key compressor locations and the

corresponding refrigerant states. Even during steady state operation refrigerant parameters in the compressor can are not steady, since pressure changes

in a series of rapid pulses. This pulsation is initiated by the periodic

compression and suction processes and valve behavior. Because a certain

pressure difference is needed for valve opening, the pressure in the cylinder

at the end of ccanpression is considerably above the discharge manifold pressure. Similarly, pressure during intake falls below suction manifold pressure. Particularly strong pressure peaks are observed in case of spring

equipped valves. These pressure differences vary from compressor to compressor because of valve and manifold design, but also vary for the same canpressor with compressor speed, compression pressure ratio, refrigerant, and mass

flow rate.

Since processes taking place in a compressor are dynamic in nature, the most

correct way of modeling a compressor would require dynamic simulation of valve

motion, cylinder-manifold presstire interaction, and cylinder heat trr.nsfer.

Such models exist and are described in [12], [13], and [14], However, these

models usually require some very detailed experimental data or design information, not necessarily readily available for the prospective user of a heat

pump simulation program. That is why a relatively simpl,:5r approach to

compressor modeling was takan in this study.

5.2.2 Theory and Governing Relations

Several assumptions are made for model formulation. The basic assumption is

that the highly dynamic process in the compressor results in steady gas parameters throughout the can. The pressure and temperature in the cylinder and

in suction and discharge manifolds are assumed to have constant values.

33
LUBRICATING OIL

MOTOR/

COMPRESSOR

CAN

DISCHARGE LINE

Note: Numbers 5 and 6 situated in the compressor correspond to the

refrigerant state before and after the compression process.

Figure 10. Schematic of a hermetic compressor.

34
The refrigerant is considered to have uniform thermodynamic properties

throughout the space assigned to the particular location. Refrigerant flow

through the compressor is assumed to be one-dimensional, so one-dimensional

steady flow equations can be used. Though the model does not simulate valve

dynamic behavior, it allows for valve representation by a steady difference

between manifold and cylinder pressures.

In order to derive equations governing compressor balances, the thermodynamic

irreversibilities taking place in the hermetically sealed compressor have to

be identified. These losses can be put into four categories:

1. Those associated with incomplete conversion of electric energy into

a mechanical energy available for vapor compression.

2. Those associated with the non-isentropic conversion process inside

the cylinder.

3. Those due to heat transfer at the different locations.

4. Those due to pressure drop at the different locations.

All of these losses contribute to the overall compressor efficiency and have

to be considered in the modeling effort.

Conversion of Electrical to Mechanical Energy

Electric energy is supplied to an electric motor to be converted into

mechanical energy. This conversion has losses due to windage, friction, winding

resistance, and hysteresis, which are accounted for by a motor efficiency, i\ . By definition

where E = electric power input

W- = mechanical power output

Electric motor efficiency, ti\ , depends on load and is customarily given as a function of the fraction of actual mechanical power output to the maximum

power output. In heat pumps with power requirements below 5 hp, single phase

electric motors are usually used. They are permanent split-capacitor or capacitor-start capacitor-run types. A typical efficiency versus load curve

for a permanent split-capacitor 2 pole electric motor is shown in figure 11

[151.

The electric motor is coupled to the compressor eccentric. Moving compressor

parts experience friction and a power loss accounted for by the compressor

mechanical efficiency, r\ . By definition

^m = r

^^'^^

35
1.0

.2 -

LOAD (FRACTION)

Figure 11. Typical speed (RPM) versus load curve for a permanent splitcapacitor 2 pole electrical motor [15]

36
where W = mechanical power available for compression

c A common value of compressor mechanical efficiency falls in range of 0.95 to

0.98.

Compression Process

A simplified indicator diagram is shown in figure 12. It shows idealized

constant suction and discharge pressures in a cylinder. In modeling the

cylinder process, both compression and re-expansion processes are assumed to

be polytropic with the same polytropic index, n, following the equation [16]:

P • v° = const (28)

where n = polytropic index

P = pressure

v = refrigerant vapor specific volume

Since constant pressure and temperature are assumed during the discharge

process, this implies no change in specific volume between points C and D

(figure 12); consequently, the compression and re-expansion polytropic curves

will coincide. This further means, that the net work required for compression

of the residual gas is zero.

The refrigerant enthalpy increase during polytropic compression, ig - i^

(refer to figure 3), can be evaluated by the equation derived from the expressions for isentropic and polytropic work of compression at the same compression ratio. Equating these expressions results in the equation:

n - 1 Pz

/ 6 \ ^

i - i = (i - i )iZI ll5__ (29)

where i- = refrigerant enthalpy before compression

ig = refrigerant enthalpy after compression

ig = refrigerant enthalpy after isentropic compression, ''^^ined by

pressure pg and entropy s^

n. = polytropic index

Pc = suction pressure

Pg = discharge pressure

y = isentropic index

The isentropic index, y, and the polytropic index, n, are related by the

polytropic efficiency of the compressor:

Y - 1 n„ =

P n - 1 ^^ (30)

37
PRESSURE

DISCHARGE

MANIFOLD

PRESSURE

A - B SUCTION

B - C COMPRESSION

C - D DISCHARGE

D - A RE-EXPANSION

SUCTION

MANIFOLD

PRESSURE

CYLINDER VOLUME

Figure 12. Simplified indicator diagram for a reciprocating compressor,

38
The isentropic index, y, equals the ratio of specific heats, as in the

following formula:

Y =^ (31)

Cv

where Cp = specific heat at constant pressure

Cv = specific heat at constant volume

The specific heats of ideal gases are constant, thus the isentropic index of an ideal gas is also constant. For real gases such as refrigerant vapors,

specific heats vary along the compression path. To accommodate this fact, the

isentropic index can be evaluated by taking the average of the respective

specific heat ratios at points 5 and 6s.

The refrigerant enthalpy increase during polytropic compression could also be

calculated using the isentropic efficiency and enthalpy increase during isentropic compression at the same ccmpression ratio. However, isentropic efficiency is sensitive to the compression ratio while polytropic efficiency is

more consistent from one application to another and provides a more consistent

representation of average compressor performance [17] . The imperfection of

using isentropic efficiency may be traced to the general thermodynamic relation:

(asjp

= T

(32)

where i = enthalpy

P = pressure

s = entropy

T = temperature

which requires pressure lines to diverge on a Mollier chart.

Hie refrigerant mass flow rate pumped by a compressor can be calculated by the

following formula:

„ _ 60 RPM Vs „ /„v

""r ; ^v ^33)

where m^. = refrigerant mass flow rate

RPM = compressor speed (revolutions per minute)

Vs = compressor displacement per revolution

V- = refrigerant specific volume in the cylinder before compression

Tj = volumetric efficiency

The RPM of a compressor is equal to that of an electric motor and is a function of load on the motor. A typical speed (RPM) versus load curve for a permanent split-capacitor 2-pole electric motor is shown in figure 13.

39
3800

3600 B

3400 -

3200

3000

2800 J L 1

0.2 0.4 0.6 0.8 1.0

LOAD (FRACTION)

Figure 13. Typical efficiency versus load curve for a permanent splitcapacitor 2 pole electric motor [15]

.

40
With assTunptions stated so far for the compression and re-expansion processes,

the following formula for volumetric efficiency of a compressor can be

derived [16]:

n. = c, [1 - c. m- ]

(34)

where C = correction factor for leakage from the piston, valves and for

the throttling effect, assumed to be 0.96, [18]

C^ = clearance volume, fraction of displacement

Heat Transfer Relations

Electrical energy supplied to an electric motor is in part transferred to the

refrigerant and in part is dissipated to the comprs^ssor environment. This

compressor heat balance can be expressed by the following equation:

E + m^ (ig - ig) - Q^^ = (35)

where E = electric energy input

ig , ig = refrigerant enthalpy at respective locations (refer to

figure 10)

Q

m = refrigerant mass flow rate

P A = rate of heat rejected to ambient air

Reference is made to figure 10, where key locations of refrigerant in the

hermetic compressor are marked. In order to solve the compressor heat balance

represented by equation (35), the following heat transfer losses are considered in the compressor model:

1. Heat transfer between the compressor can and ambient air, Qp .

2. Heat transfer between the refrigerant in the compressor can and the

compressor can, Q^ p

3. Heat transfer between the inlet refrigerant and the suction manifold

and valve, Q^ c

4. Heat transfer between the discharge refrigerant and the discharge

valve and manifold, Qg •j

5. Heat transfer between the refrigerant in the compressor can and the

refrigerant in the discharge line, Q.^ g

The heat transfer between the compressor can and ambient air (item 1) is

governed by free convection and radiation. Respetive heat transfer

coefficients, h„ and h_, are calculated by the following equations [19]:

h^ = 0.18(T^ - T )^-^^ (Btu/(h • ft^ • F)) (36)

41
(T_ + 459.67)^ - (T, + 459.67)^ . -, hy = <y • 8

• —

S

^ ^ (Btu/(h • ft*^ • F)) (37)

where T^^ = ambient air temperature (F)

T^ = compressor shell temperature (F)

ff = 0.1714 X 10"^ Sis = Stefan-Boltzman constant

h • ft • R^

e = surface emissivity (e = 0.9 is used)

The heat transfer rate between the compressor shell and the ambient air, Qq ^

can be calculated by the equation:

^.A = CQc,A • ^K "

^r> • <Te - T^) (38)

where CQf« & ~ heat transfer parameter

The heat transfer inside the compressor shell between the shell and

refrigerant vapor (item 2) is governed by forced convection, for which the

non-dimensional heat transfer parametric expression in terms of Nusselt,

Reynolds, and Prandtl numbers is in the form [20]:

Nu « Re^-^ • Pr®-333 ^39)

where Nu = , ^ = Nusselt Number

Pr = n ' Cp = Prandtl Number

Re = ^ ' ^ = Reynolds Number

m

G = — = refrigerant mass flux

A

L = characteristic length

k = refrigerant thermal conductivity

(1 = refrigerant dynamic viscosity

Using equation (39) the forced convection heat transfer coefficient, h, can be

expressed as:

h = C

• m

^-8 • ^0.666 . cpO.333 . ^^^-0.467 (40)

where C = constant of proportionality, a function of wetted surface

geometry

42
Combining equations (36) and (40) yields the following expression for heat

transfer rate between the compressor can and refrigerant:

Q4,C

= C

• Ai^• mj.0-8 • k^O.ee? . CP4O.333 . ^^-0.467 ^j^ _ ^^j (41)

or

Q4 C = CQ4 c

• n»/*^ • ^4®-^^'' • Cv4^^'^^^ • M"®-'*^'' (T4 - Tp) (42)

where CCb r = heat transfer parameter

Obviously, heat transfer rates Q^ ^ and Q4 q are equal. Derivations of

equations for the heat transfer ra'tes between the inlet refrigerant and the

suction manifold and valve, Q4 ., and between the discharge refrigerant manifold valve, Qg .7, are similar to the derivation just performed for Q4 q, since

in these two cases heat transfer is also by forced convection. Resulfing

expressions for these heat transfer rates are:

Q4.5 = «i4,5 • -r'-'

• ^4^50.666 . cp4^50.333 . ,,3-0.467 (43)

(Tg - T4)

^,7 = ^6,7 ' »r^-^ • ^6,7^*^^^ * ^^4,5^'^^^ ' ^,1'^'^^'^ ^^4)

(T7 - T4)

The heat transfer between the refrigerant in the compressor can and the

refrigerant in the discharge line (item 5) is modeled as forced convection

heat transfer between the fluids separated by a barrier non-resistant to heat

flow. Assuming that the temperature of refrigerant in the shell does not

change (as a result of other heat transfers in the can and mixing) and

applying the logarithmic mean temperature difference, the following expression

for heat transfer rate Q.^ » can be derived [2]:

Q7 = CQ7 8

• »r®*^ /^ , (T7 - To)/ln 1^ " l^ (45) '»» /*» r a2 + a3 ' ** Tg - T4

where al = (CP4 • Cpy^g)® '^^^(14 ' 17^3)®*^^'

«j = „ 0.467 . p- 0.333 . v 0.667 " ^^4 ^^7,8 '^7,8

., _ „ 0.467 . p_ 0.333 . ^ 0.667 a3 - 117 8 CP4 1:4

Subscripts 3 through 8 refer to refrigerant key locations in the compressor in

figure 10. If the subscripts are separated by a comma, the average value is

implied.

The heat transfer to/from the flowing refrigerant changes the refrigerant

enthalpy according to the equation:

Q = m^. • Ai (46)

where Ai = refrigerant enthalpy change

43
Combining equations (43), (44), (45), and (46) yields the following

expressions for the refrigerant enthalpy change during flow between respective

locations of the compressor:

i, - i. = CQ. , • k. 0.667 . cp. 0.333(T _ t.)/ (47) 5 M - ^«4.5 M,5 ^1*4,5 ^^6

•r H,5^

/„ 0.2 . „ 0.467^

^6- h

- CQ6,7 • kg. 7^-^^^ • CP6,7®'^^^<T7 - T4)/ (48)

/_ 0.2 . „ 0.466x

^"r f^6,7 ^

7 - ^8 = CQ6,7 ;^-^(T7 - Ts)/(mJ>'^ In hjLlA (49) T8-T4

where al, a2, a3 are as in equation (45)

The derived heat transfer relations contain heat transfer parameters CQ^ ^,

CQ4 5, CQg n, and CQ^ g. These parameters are primarily functions of heat

transfer surface geometry and have to be found empirically. If required

laboratoiy test data for a given compressor are not available, typical

compressor test data can be used. A large number of experimental compressor

measurements have been published. The summary of these data and a list of

references can be found in [21].

Pressure Drop Relations

Total pressure drop AP^ ^ experienced by a flowing fluid results from pressure

drops due to friction, momentum change, and gravity, i.e.,

^tot = ^friction + ^Paccel "^ ^^gravity <50)

Pressure drop due to gravity in the hermetic compressor may be disregarded

based on an order of magnitude analysis. On the same grounds, pressure drop

of the flowing refrigerant between certain compressor locations may be

attributed to either dynamic effect or viscous effect.

Pressure drop due to the dynamic effect, AP„„„_,, is proportional to velocity

head, i.e.,

^accel - P

• V^ ^51)

which can be written, using the continuity equation:

^^accel = CP • m^2/p (52)

where CP = pressure drop parameter

m^ = refrigerant mass flow rate

V = refrigerant velocity

p = refrigerant density

44
The relation for the pressure drop due to the viscous effect, ^friction' ^^^

be derived from the classical Fanning equation for pressure drop in a tube:

APf^4^^i«„ = 2f • p

• V^ • L/D (53) triction '^ where f = friction factor

D = tube diameter

L = tube length

The friction factor, f, in the equation above is approximately proportional to

the Reynolds number to the -0.2 power for the Reynolds number greater than

2000 [22], Considering this and applying the equation of continuity, equation

(53) becomes:

AP* . ^. = CP • u®-^ • m ®*^/p (54) friction ^* K r '^ ^'^^'

The pressure drop of the refrigerant in the compressor can is modeled by

evaluating individual pressure drops between refrigerant key locations indicated in figure 10. Based on equations (52) and (54), and attributing pressure drop between particular compressor locations either to the viscous or friction effect, the following pressure drop relations are proposed:

Pg - P^ = CPo A ' TMr '^3 4 ^°^ ^^® compressor (55) can inlet

P^ - Pj = CP4 5

• vijP'/p^

5 for the suction (56)

manifold and valve

Pg - P^ = CPg ^

• mj-^/pg

7

for the discharge (57)

valve and manifold

P7 - Pg = CP7 g

• m^}'^ ' n^ s^'^^h 8 ^°^ ^^^ discharge line (58)

Pressure drop parameters CPo a, CPm s, CPg ^, and CP^ have to be found

experimentally for a given compressor or can be calculated using test data for

a similar compressor. For sources of such data, refer to [21].

Equations derived in this section are used in a compressor subroutine, COMPRE,

described in Appendix E. These equations make it possible to carry out an energy balance of a hermetic compressor using an iterative process for electrical energy input, for heat lost to the ambient air, and for refrigerant

parameters in compressor key locations. The variety of designs of refrigerant

flow passages in the compressor caused the modeling of pressure drop and heat

transfer to be done in an approximate manner in this general compressor model.

In spite of several assumptions that were made to simplify the modeling process and reduce computing time, the model still retains sufficient details of

the underlying physical principles to allow designers to determine which

specific changes in the compressor design will lead to increased efficiency of

the compressor and the heat pump system.

45

5.3 Modeling of a Constant Flow Area Expansion Device

A constant flow area expansion device, as used in heating/air conditioning

systems, is commonly called a capillary tube or a refrigerant flow restrictor.

Usually it is a small bore tube of length as short as one-half inch up to a few feet, connecting the outlet of the condenser (or a liquid line) to the

inlet of the evaporator. The main task of the constant flow area expansion

device is to maintain the minimum pressure at the condenser at which all the

flowing refrigerant can condense. Many researchers have investigated flow of

a single component refrigerant through a capillary tube and a bibliography on

the subject can be found in [15].

There is no experimental data known to the authors which would refer to the

flow of a non-azeotropic mixture through a capillary tube or orifice. Because

of lack of data, single component refrigerant flow experience has been extrapolated to the non-azeotropic binary situation and the model developed

accordingly.

5.3.1 Available Capillary Tube Performance Data

The capillary tube is a traditionally accepted name for a constant flow area expansion device used in heat pump systems. This name is inadequate and

misleading since for tube diameters in the neighborhood of 1/16 of an inch,

capillary forces are negligible. The pressure drop consists primarily of:

- the loss due to sudden contraction at the entrance

- the loss due to flow in the tube - the loss due to sudden enlargement at the exit to the evaporator

The flow of refrigerant through a constant bore tube is more complex than the

geometric simplicity of the device would first indicate. The pressure and

temperature distribution along a typical capillary tube is shown in figure 14.

Bolstad and Jordan's description of the flow is as follows:

At the entrance to the tube, section 0-1, there is a slight pressure drop

which was usually unreadable on the gages. From point 1 to point 2 the

pressure drop is linear. In the portion of the tube 0-1-2 the refrigerant is entirely in the liquid state and at point 2 the first bubble of

vapor forms. From point 2 to the end of the tube the pressure drop is

not linear, the pressure drop per unit length increasing as the end of

the tube is approached. For this portion of the tube, both the saturated

liquid and saturated vapor phases are present, the percent and volume of

vapor increasing in the direction of flow . . .

With a saturation temperature scale corresponding to the pressure

scale superimposed along the vertical axis, it is possible to plot the

observed temperatures in a more meaningful way than if a uniform temperature scale were used. The temperature is constant for the first portion

of the tube 0-1-2. At point 2, the pressure has dropped to the saturation pressure corresponding to this temperature. Further pressure drop

beyond point 2 is accompained by a corresponding drop in temperature, the

47
CONDENSER CAPILLARY TUBE EVAPORATOR

DISTANCE FROM CAPILLARY INLET

Figure 14. Pressure and temperature distribution along typical capillary tube

[231.

48
temperature being saturation temperature corresponding to the pressure.

As a consequence, the pressure and temperature lines coincide from point

2 to the end of the tube [23]

.

The point of the tube where the first bubble forms is called a bubble point or

a flash point. The pressure at the point is called the flash pressure.

Bolstad also presented an analytical method of solution for adiabatic flow

through the capillary based on the Fanno flow theory.

Mikol [24] performed a capillary tube investigation from which his conclusions

can be summarized as follows:

- Fluid flow through small bore tubes conforms to continuous flow as established for large bore tubes and pipes.

- The friction factor correlation of Moody and any others consistent

with Moody's correlation [25] is applicable to single-phase flow in

small bore tubes.

- The phenomena of metastability, persistance of the liquid state at

pressures less than the saturation pressure corresponding to its

local temperature, has been found to occur.

- The phenomenon of choked flow in two-phase flow occurs in the same way and for the same reasons as in the case of gaseous flow. Sonic

velocity occurs at the tube exit.

One of Mikol ' s findings, existence of superheated liquid in a small portion of

a tube, was not observed by Bolstad and Jordan [23]. However, it was reported

by Cooper et al. [26] and Rezk [27]. Investigators have found that delayed

evaporation is affected by initial disturbances and flow agitation, but there

is not enough data in the current literature to assess all the factors promoting or eliminating this phenomena and making it possible to consider

metastability in a capillary tube model at this time.

The pressure and temperature distributions along a capillary tube as shown in

figure 14 occur at design operating conditions of a long (a few feet) capillary. Part of the capillary is filled with flowing liquid, while two-phase

flow exists in the other part. However, there are also other possible modes

of operation, i.e., with only two-phase flow in the capillary (the case of

incomplete condensation in the condenser) or with only liquid flow (the case

of short restrictor). All these cases are observed in practice and have to be

simulated by a general model of the constant flow area expansion device.

Based on the experimental evidence and the theory of large tube fluid

mechanics, the following assumptions were used for model formulation:

1. The capillary tube is straight, horizontal, and has a constant inner

diameter.

2. Flow in the capillary is one-dimensional and homogeneous.

3. Flow in the capillary is adiabatic.

49
4. Flow resistance in the capillary tube can be subdivided into

a. Resistance due to the entrance effect

b. resistance due to flow in a tube which consists, in the general

case, of single-phase liquid flow resistance from the entrance

to the flash point, and two-phase mixture flow resistance in the

rest of the tube. The existence of the delayed evaporation

phenomena is neglected. Resistance due to the exit effect is

neglected as meaningless for a choked flow and insignificant for

a non-choked flow [23].

5. Choked flow phenomenon for two-phase flow of a non-azeotropic

mixture is governed by the same laws as for single-phase flow of a single component fluid and can be modeled accordingly.

5.3.2 Available Short Tube Restrictor Performance Data

An experimental study on the flow of refrigerant 12 through short tubes was

performed by Pasqua [28]. From his visual observations he found that the

refrigerant flowed through the restrictor in the form of a metastable liquid

core surrounded by a vapor annulus. Based on his experiment, Pasqua also

determined flow characteristics of subcooled and saturated liquid through a short tube restrictor. A study of short tube restrictors applied to

refrigerant 22 was performed by Mei [29]. He tested five restrictors of a length/diameter rations from 7.5 to 11.9. He confirmed occurrence of firststage choking but reported that second-stage choking did not take place at

conditions obtainable in his test facility. Mei provided two correlations for

evaluation of refrigerant mass flow rate which, however, are limited to the

tested refrigerant 22.

As experimentally obtained information available in the literature is not

sufficient for a development of a general simulation model of a short

restrictor applicable to different refrigerants, such models have to be

developed using fundamental equilibrium fluid mechanics. Using this approach,

the analysis and basic assumptions made in the previous section regarding a capillary tube would apply to a short tube.

5.3.3 Critical Flow

Refrigerant mass flow rate through a given flow restrictor will depend on the

inlet refrigerant state and on the pressure that will be established at the

tube outlet. This pressure may equal the evaporator pressure or may have a higher value if the flow is choked. Since pressure at the tube exit

is one of the parameters affecting the flow, it has to be known for accurate

refrigerant mass flow rate prediction.

The assumption that the flow in the flow restrictor is one-dimensional and

homogeneous enables the two-phase flow in the tube to be treated as single-phase flow with uniform properties at any cross-section of the flow and

allows use of the single-phase, one-dimensional form of the governing equations as presented in figure 15, 16 and 17.

50
pAV ^

I PAV + -^ ( PAVldL

I O L k dL

CONTINUITY EQUATION: d(pV] =

Figure 15. Mass balance for an element of fluid in one-dimensional steady

flow in a constant area duct.

PA

1

1

-af-' —

r

PA + ^1^ |PA)dL

pAv2 PAV^ +4T-(pAV2)dL

L -^^

• dL -

MOMENTUM EQUATION: AdP + pAVdV + rSdL =

Figure 16. Momentum balance for an element of fluid in one-dimensional steady

flow in a horizontal, constant area duct.

51
Q = W = \ /

2 i pVA(u + y + p-1 j *^«

V^ P pVAtu+l +|-)+-|Yl^VA(u + -y +^l)tlL^^

dL —^"

ENERGY EQUATION: = d(i + y- = '^T='o

Figure 17. Energy balance for an element of fluid in one-dimensional

adiabatic, steady flow in a horizontal, constant area duct.

a.

_i

SUBSONIC FLOW

SUPERSONIC FLOW

ENTROPY

Figure 18. Fanno line.

52
Adiabatic flow through a capillary tube is a classical example of so called

Fanno flow*, adiabatic flow with friction in a constant area duct. The energy

equation for such flow has the form:

di + V • dV = or 1^=1+ V^/2 = const (59)

which, when combined with the equation of continuity yields:

2

i„ = i + ^ • v^/2 = i + G^ • -P-Il (60)

" A

where A = tube cross-sectional area

G = —^ , refrigerant mass flux

i = refrigerant enthalpy

i = refrigerant stagnation enthalpy

ffl = refrigerant mass flow rate

V = flow velocity

V = refrigerant specific voltme

Graphical representation of equation (60) on the enthalpy-entropy diagram, as shown in figure 18, is called a Fanno line. Fanno flow, as an irreversible

adiabatic process, can sequentially exist only in the direction of increasing

entropy. The upper branch of the Fanno line corresponds to subsonic,

accelerating flow while the lower branch is the supersonic, decelerating flow.

Both flows tend towards point C where the sonic velocity is reached.

The Fanno line implies that fluid cannot reach the velocity of sound inside a constant area duct, because, if this happened, further flow in the duct would

have to be associated with a decrease of entropy (figure 18), and that would

be in violation of the Second Law of Thermodynamics. Thus, the only location

of a tube at which sonic velocity can be reached is the tube exit, and choking

will never occur inside the capillary regardless of external outlet pressure.

5.3.4 Model Formulation

Refrigerant flow from the liquid line into the capillary tube experiences a pressure drop due to sudden contraction. This pressure drop consists of an acceleration loss and entrance friction loss and is usually expressed by a decrease in the Bernoulli head and a contraction coefficient referred to the

kinetic energy of the flow in the section of smaller flow area:

"0,1 ^ 2

Subscripts in eq. (61) refer to sections shown in figure 14. Combining with

the equation of continuity, the above can be rearranged to:

53
P(j - P^ = AP = (1 + K)po 1

• ^ (62)

The contraction coefficient, K, given in the literature is strictly empirical

and is represented as a function of the contraction area ratio. Several

sources are in disagreement about its value. The value of K = 0.15, used here

is from a derivation based on Kays' general formula [30]. It was calculated

for a normal range of contraction area ratios for capillary tubes with

slightly beveled entrances.

The equation of motion for steady flow in a constant cross-section area pipe

has the following form:

p-A-V-dV+A-dP+T-S-dL=0 (63)

The skin friction coefficient, t, can be expressed in terms of the friction

coefficient, f, and the velocity head:

-c = i f • p

' v^ (64)

The flow velocity term, V, can be eliminated by means of the equation of

continuity:

d(V • p) = (65)

Substituting and rearranging, the equation of motion assumes the following

form:

P. ^ 1 L. + 1 & I

dp + 2. / f

• dL + In —^li— =0 (66) ^ L^ Pi + 1

As discussed before, flow in a capillary tube, in the general case, can be

subdivided into two parts separated by a flash point: the liquid flow part

and the two-phase mixture part. The same equation will be applicable for both

flows though in the case of liquid flow, it can be simplified on grounds of

incompressibility. In fact, it reduces to the Fanning pressure drop formula

in the following form:

AP = 2f • g2 ' L (67)

where the friction factor, f, can be evaluated by the empirical formula:

f = 0.046 • Re~®-^ (68)

for the Reynolds number. Re, greater than 2000 [22]

.

For the two-phase mixture flow, equation (66) has to be solved in its full

form. This was done by Whitesel [31,32] for refrigerants 12 and 22 , but with

significant oversimplified approximations for the refrigerant properties. In

54
solving equation (42), difficulty arises with evaluating the first term

because it depends directly on the pressure-density relation along the path of

flow. However, the relation can be obtained by considering the adiabatic flow

case. The specific volume at a given pressure can be expressed in terms of

the property values for saturated liquid and vapor and in terms of quality:

V = Vl + x(Vy - Vl)

where v = specific volume

X = quality

Subscripts L and V are for liquid and vapor, respectively

(69)

The quality of the flow in the Fanno path can be found as explained in

Appendix C. Thus integration of refrigerant density over a given pressure

interval can be done numerically. Still another problem is faced in

evaluating the second term of equation (66), which includes a two-phase

friction factor as a function of tube length. Erth [33] made an effort to

correlate two-phase average friction factor in a capillary tube for

refrigerant 12 and refrigerant 22. His regression analysis, based on four

sets of data from four different experiments, yielded the following

correlation for a two-phase flow mean friction factor, f^, as a function of

the inlet conditions only:

f„ = ^-^ exp [(1 - x^^-^^)/2A]

Re" '5

(70)

where x. = quality of refrigerant entering capillary tube

Re = ^L + ^i <t^V " ^^L^ (71)

Using this mean friction factor, f^^, equation (66) may be written for the twophase portion of the flow in the following form:

0.5

m^ = A

- / p dP

P2

^f. (L3 - Lj) + In (P2/P3)

(72)

where the numbers used as subscripts denote location consistent with

figure 14.

A subroutine, CAPIL, modeling a constant flow area expansion device is based

on the equations presented above. These equations have to be solved in a highly iterative process since choking pressure, friction factor, fraction of

capillary tube length with liquid and two-phase flow, and the velocity head

used to correct enthalpy are functions of refrigerant mass flow rate which has

to be determined. Additional information about the subroutine CAPIL is given

in Appendix F.

55
5 .4 Modeling of an Evaporator and a Condenser

5.4.1 Modeling Methodology

There are two heat exchangers in a heat pump: an indoor coil and an outdoor

coil. Both coils are made in a similar way and both serve as an evaporator or condenser depending on the heat pump operation mode. A schematic of a typical

heat pump heat exchanger is shown in figure 19. It consists of a set of

finned tubes connected in a specifically designed circuit configuration. The

refrigerant flows through the tubing while air flows over the outside of the

coil. Various schemes of circuiting the tubes together can be used. An

example of the coil circuitry is illustrated in figure 20.

The tube-by-tube modeling technique is applied here to model the coil. This

technique depends on imaginary isolation of one tube with appropriate fin

surfaces from the coil assembly and calculating the performance independently.

The heat transfer to and from a tube is calculated with the aid of the heat

exchanger cross-flow theory. Input for calculations consists of finned tube

design data, refrigerant and air mass flow rates, and inlet refrigerant and

air thermodynamics states. These are uniquely evaluated by the model for each

particular tube. Performance calculations are conducted for each tube independently in proper sequence and their summation results in total coil

capacity.

In order to perform heat transfer calculations, four surfaces associated with

the tubes must be defined. Following Carrier and Anderson [34], it was

assumed that the fin area served by each tube is equivalent in performance to

a circular-plate fin of equal area. Thus a single tube is considered with a circular fin of diameter, D^, as shown in figure 21.

5.4.2 Heat Transfer Rate for a Tube in a Cross-Flow Arrangement

Usually a heat pump coil employs some form of cross-flow arrangement. If a separate tube is considered, the problem is one of pure cross flow. Fortunately, this kind of arrangement has received much attention in theoretical

investigations. According to the general heat transfer equation:

Q = U • Aj^ • AT (73)

where At = heat transfer surface area U = overall coefficient of heat transfer

AT = temperature difference

In the case of a pure cross-flow arrangement with changing temperatures of both

fluids during heat exchange, the following equation for mean temperature

difference between fluids applies [16]:

^T = 4 ~ ^1 (74)

Ti - T2

In

t - t 2 1

<^2 - h Ti - tj

56
REFRIGERANT

REFRIGERANT

REFRIGERANT

Figure 19. Schematic of a heat pump heat exchanger.

57
f

SUBCOOLED LIQUID OR LOW

QUALITY VAPOR SIDE MANIFOLD

1

25 3 17 1 2

1

16

15 r

1 26

57 1 58

32 14 1 56 1 59

33 13 1 24 1 27 34

66

44

76

55 . 1

, 29

28

i 65 1

I 75 1 |~23 —i 54 I 601 ^^64 1

I 4

35

! 36

43

12

1 45 22

21

53

52

30

31

61 96 J~46* I 77 62

97 5 67 1' 47 78 20 84 63 94 98 6 68 1 42 1 48 no 1 19 85 95 93 99 7 37 1 74 1 49 liii 1 51 > 86 Il26 1 92 MOO I 8 1 69 1106 1 18 1 79 1 83 87 Il25 1 90

1 101 1 9 1 38 1107 1 50 1 80 1 114 1 88 1124 1 89

1 102 1 10 1 39 1108 1 82 1 81 1 115 Il20 1123 |121

1 70 1 41 1 40 1109 1113 1112 1 116 1119 1122

1 71 1 73 1 72 1118

1 103 1105 1104 1117

t t t t t t t t t t

I SUPERHEATED VAPOR SIDE MAINIFOLD

I REFRIGERANT FLOW DIRECTION IN CONDENSER

Numbers in the figure represent a location of the particular tube counting

them left to right in each depth row starting with the row facing the incoming

air.

Figure 20. Example of coil circuitry.

58
.2(J-J2)0-5

TV

Figure 21. Approximation method for treating a rectangnlar-plate fin of

uniform thickness in terms of a flat circular-plate fin of

equal area.

59
where T = temperature of one fluid

t = temperature of another fluid

AT = mean temperature difference

subscripts 1 and 2 refer to tube inlet (upstream) and outlet

(downstream) conditions, respectively.

The heat exchanged with the fluid can be calculated by the equation:

Q = m • (i2 - ij)

or

Q = m • Cp • (T2 - Tj) (75)

where Cp = average specific heat of fluid at constant pressure

i = enthalpy

m = mass flow rate

Looking at any vapor compression cycle P-h or T-s diagram, it can be realized

that both single-phase and two-phase refrigerant flow usually exists in a given heat exchanger. Also, both flow patterns can actually exist in one

tube. That means that the rate of change of temperature of refrigerant

flowing in the tube will not be uniform over tube length. Not only the mean

temperature between fluids is affected by the flow pattern inside the tube but

also the refrigerant pressure drop.

Equations presented below, derived from equations (73), (74), and (75), allow

for detailed consideration of these problems. The heat transfer rate for each

mentioned flow condition can be calculated as follows:

- single-phase or two-phase flow only, refrigerant is superheated,

subcooled or in two-phase at both inlet and outlet

Q = Cpr • m.(T, . - T^ Jd - exp(- ^^-L^{1 - exp( "^ ' ^

))))(76) ^ ^'^ a,i cp^ . „^ Cp^ . „^

- superheated vapor at tube inlet, two-phase at the tube outlet

^ = »r<ir,i - ^r,V> ^ ^p, * '"r * <T,,v " \,0 <77)

(1 - ^^^

Cp m,(l-Zv)

^^ _ ^^p^_ JL:_^)))

CPj. . m^. Cp^ . m^^

where Zy = fraction of the tube length in the superheated region which can

be calculated by the equation:

60
-Cp • m • ln(l ^-^ ^-^ ) ^r r ^"^^ Ct) (T . - T ) Zy = (78)

U . Art Cp^ • m^(l- exp(--—5-))

- two-phase at tube inlet, subcooled liquid at the tube outlet

Cp„ . m-d - Zfn)

r X i,L. a,i Cp „

(1 - exp(- -5-^-^)))) + in_(i_ i - i. t) (79)

*^a a

where Z^_ = fraction of the tube length in the two-phase region which can

be calculated by the equation:

Z

-Cpj. • nij. • ln(l - —^iti ll^ ) ^ CPr^Tj i - Ta,i)

tP U . A.

Cpa -mad - exp(- - ° ))

CPa ""a In equations (76) through (79) the following nomenclature was used:

A = total exterior surface area associated with the tube wetted by air

Cp„ = air specific heat at constant pressure

Cp = refrigerant specific heat at constant pressure (in the two-phase

region the specific heat is assumed to be a ratio of enthalpy change

to temperature change, i.e., Cp^. = Aij./ATj.)

ij. £ = refrigerant enthalpy at the tube inlet

ij. T = enthalpy of refrigerant saturated liquid

ij.'y = enthalpy of refrigerant saturated vapor

in„ = air mass flow rate associated with the tube

tHj. = refrigerant mass flow rate in the tube

Tj^ £ = air temperature upstream of the tube

Tj.' £ = refrigerant temperature at tube inlet

Tj T = refrigerant bubble-point temperature

'U = overall tube heat transfer coefficient

5.4.3 Refrigerant and Air Mass Flow Rates Associated with a Tube

Refrigerant Mass Flow Rate

During flow through a heat pump heat exchanger, the refrigerant undergoes a change of phase in the course of evaporation or condensation. The change of

phase is associated with a dramatic change of density which affects the

61
velocity and pressure drop of the working fluid. In order to prevent a higli

pressure drop, tubes in some heat pump coils are connected to form branched

circuits. An example of such coil circuitry is shown in figure 20.

Refrigerant flow direction marked in figure 20 is for the coil working as a condenser. Superheated vapor enters the vapor side manifold and is

distributed into 10 tubes. On its flow path, refrigerant merges several times

and finally merges in the liquid manifold to enter the liquid line. For the

coil operating as an evaporator, the direction of flow is opposite to that

marked in the figure. Low quality refrigerant enters the coil and the flow is

subdivided into three circuits. On its way through the coil the refrigerant

evaporates and splits several times on its way towards the exit where it is

finally collected into one larger diameter vapor line. The mass flow rates

through the particular circuits of the coil are self adjusting so the pressure

at merging (splitting) tubes is the same.

To perform a simulation of a coil by the tube-by-tube method, refrigerant mass

flow rate for each tube has to be known. Since total refrigerant mass flow

rate supplied to the coil is known, the problem reduces to the determination

of refrigerant distribution. This could be determined by the model itself,

however, at expense of going through iterative calcuations. Another approach

was tried to determine refrigerant flow distribution. Since most of the coil

total pressure drop may be expected to result from superheat vapor and twophase flow, it was assumed that the refrigerant flow is uniformly distributed

among tubes connected to the vapor side manifold and that mass flow rates in

other tubes may be found by following the refrigerant path with direction of

flow as marked in figure 20. Ihe resulting distribution was checked by examining calculated refrigerant (R22) pressures at the ends of circuit branches.

These pressures should be equal if the assumed distribution is correct. Tbe

maximum pressure discrepancy found was equal to 0.3 psi which represented less

than a 0.2*'F variation in the saturation temperature of refrigerant 22 between

merging tubes. This was considered satisfactory and the method was adopted

for determining refrigerant mass flow rate distribution in a coil.

Air Mass Flow Rate

Air mass flow rate was assiuned to be distributed uniformly over the whole coil

face regardless of the coil and fan respective locations, so each tube in

particular depth row was associated with the same air mass flow.

The temperature of the inlet air for a given tube was assumed to be equal to

the temperature of air exiting from the upstream tube and not to be affected

by mixing with air leaving neighboring tubes.

5.4.4 Overall Heat Transfer Coefficient for a Dry Finned Tube

Dry finned tube analysis is applicable to a condenser and also to an

evaporator if no dehumidif ication takes place. The overall heat transfer

coefficient, U, for a dry finned tube can be derived by summing the individual

resistances between the refrigerant and the air, [16]:

62
+ + _*2iE.

A^ _k« Af

- 1

(81)

vhere Af = fin surface area A = total exterior surface area exposed to air

A„ i = pipe inside surface area

p, 1 ^ ^ A„ _ = pipe mean surface area

h„ ^ = convection heat transfer coefficient at the exterior surface

c . o

h. = inside tube convection heat transfer coefficient

k = thermal conductivity of pipe material

X = thickness of pipe wall

Tf - T

<^ = —Ltl a fin efficiency

Tf,b - Ta

T = air temperature

T* V = fin base temperature

Tf'ju = mean fin temperature

The second term of equation (81) can be evaluated if the heat exchanger

material and geometry are known. Terms 1 and 3, which refer to the inside and

outside convection resistance respectively, required considerably more

analysis to establish the proper algorithm for determining the heat transfer

coefficient.

5.4.5 Forced Convection Heat Transfer Inside a Tube

Analyzing the problem for both an evaporator and a condenser, the following

modes of forced convection are encountered:

- single-phase forced convection - two-phase forced convection with condensation

- two-phase forced convection with evaporation

The physics of these phenomena are very much different and forced convection

in each mode have to be considered separately.

Single-Phase Forced Convection

Single-phase forced convection takes place in a condenser, at the entrance

section where the superheated vapor is being cooled, and at the exit section

where a subcooled liquid is being cooled. It is also applicable in the

evaporator, as the superheated vapor passes through the exit tubes. The non- dimensional heat transfer parameter describing this phenomena, Nusselt number,

is related to the non-dimensional Reynolds and Prandtl numbers in the

following form [19]:

Nu = 0.023 • Re®-^ ' Pr** (82)

63
where Nu =

' = Nusselt Number

Pr = \^ • Cp = prandtl Number

k

Re = s. H = Reynolds Number

a = 0.3 for cooling; 0.4 for heating

Cp = specific heat at constant pressure

D = inside diameter of a tube

G = refrigerant mass flux

h = convection heat transfer coefficient

k = refrigerant thermal conductivity

\i = refrigerant absolute viscosity

Two-Phase Forced Convection with Condensation

The predominant flow pattern during condensation in a heat pump condenser is

annular flow with liquid refrigerant flowing on the pipe wall and vapor

refrigerant flowing in the core. To the author's knowledge there are no data

or correlations available in the literature on the forced convection condensation heat transfer coefficient of non-azeotropic mixtures flowing inside a tube. The only option left here is to use one of the correlations developed

for condensing heat transfer coefficient for single component refrigerant.

The the correlation proposed by Traviss, Baron and Rohsenow [35] was chosen as

the most theoretically derived, thus having most chances to provide reasonable

predictions for other than the tested refrigerants 12 and 22. The correlation

proposed in [35] and adopted in this modeling effort without modification is

expected to overpredict condensing heat transfer coefficient for binary

mixtures.

The theoretical background for the Traviss et al. correlation is as follows:

the von Earman universal velocity distribution in the condensate film was assumed

(like on a flat plate), pressure was calculated using the Lockhart-Matinelli

method [22], and the momentum and heat transfer analogy was applied. The proposed

correlation has the following form:

Rer®*^ . Pri . FlP , , Nu = —^ *^ (83)

F2

where Nu = h • D

h = condensation heat transfer coefficient

D = tube inside diameter

kf = thermal conductivity of liquid refrigerant

64
Re, = G(l - ^)D

G = refrigerant mass flux

X = quality

]ij^ = liquid refrigerant absolute viscosity

Pr, _ t^L CPl

ki

p = 1 for Fl 1 1, p = 1.15 for Fl > 1

Fl and F2 in equation (83) are dimensionless parameters expressed as follows:

Fl = 0.15 (X^^"l + 2.85 Xtt®-524)

F2 = 0.707 • PrL * Rbl^*^ for Rol < 50

F2 = 5 • Pr^ + 5 • ln(l + PrL( 0.09636 * ReL^'^^^-1)) for 50 < ReL < 1125

F2 = 5 • PrL + 5 • ln(l + Prj^) + 2.5 * ln(0. 00313 * Re

for Re, < 1125

0.812

Parameter, X^^, formulated by Lockhart-Martinelli [22] with the assumption of no radial pressure gradient and a smooth pipe, has the following form:

0.9 „ 0.5 ,, 0.1

-"KH") (^) (84)

Parameter X^^ is inversely proportional to flow quality and refers to

turbulent vapor and turbulent liquid flow. Physically it is equal to the

square root of the ratio of the frictional pressure drop of the liquid phase

to the frictional pressure drop of the vapor phase if each of these phases was

flowing alone in the tube, i.e.,:

Xtt

VdL/L

"10.5

dP

dL

(85)

Equation (83) is applicable where conditions for annular condensation in a tube exists. Such conditions may be assumed to exist for flow qualities

ranging from 0.1 to 0.9. At qualities larger than 0.9, the whole tube inner

surface is not covered by a liquid film and part of the heat transfer is just

that of single-phase convection. At qualities less than 0.1, flow was

observed to be in the slug regime [35]. It is assumed, that in the quality

range 0.0 to 0.1 and 0.9 to 1.0, the heat transfer coefficient changes

linearly from a two-phase flow value to a single-phtse flow value and is

calculated using linear interpolation between values obtained from equations

(82) and (83).

65
Two-Phase Forced Convection with Evaporation

Refrigerant enters an evaporator from an expansion device at a quality of

about 20 percent and forms an annular flow instantly. The quality increases

with the proceeding flow and the annular flow pattern is maintained until the

quality reaches about 0.90, at which point refrigerant vapor has enough kinetic energy to gradually destroy the liquid layer and patches of dry wall appear.

Many experiments were performed and correlations published for calculating the

forced convection evaporative heat transfer coefficient for R12 and R22,

however, no data are available in the literature on non-azeotropic mixtures.

Simultaneous to the development of this model, evaporative heat transfer

coefficient measurements were performed at NBS on mixtures of R13B1/R152a at a variety of compositions. The results of preliminary tests with heat balances

within 10% were correlated for use in this model in the following form:

^^ev,m = ^ * 3.22 X,,-0-3 (86)

where h = evaporative heat transfer coefficient of the refrigerant

mixture

h = forced convection heat transfer coefficient of the liquid film

calculated by equation (82) for liquid flow rate equal to twophase refrigerant flow rate in the tube.

X^^ = Lockhart-Martinelli parameter, equation (84)

It is important to note that all liquid and vapor properties used in X^.

parameter have to be evaluated for liquid and vapor phases being in equilibrium based on mixture temperature, pressure and composition of mixture in the

tube.

Predictions of the above correlation agree within accuracy of + 10% for 50

percent of experimental data, + 20% for 89% of data, and within +31% for all

data. This correlation is applicable for annual flow at qualities from 10% to

90%.

5.4.6 Forced Convection Heat Transfer at the Air-side of a Flat-Finned Tube

In order to evaluate the forced convection heat transfer outside a flat-finned

tube (term 4 of equation (81)), the total exterior surface area, A , the fin

area, A^, the air-side heat transfer coefficient, h , and fin efficiency, , have to be known.

From the number of air-side heat transfer correlations available in the

literature, the one proposed by Briggs and Young [36] is most applicable here.

TTiis correlation was developed after extensive tests on 18 tube banks of

different fin geometry. A regression analysis of the test data for the air

Reynolds number range from 1000 to 20000 yielded the following equation:

Nu = ^<^>Q • ^Q = 0.134 • Re/-681 • Pr^O.333 . /z\0.2 . /z\0.1134 (g?)

where D = outside tube di»ineter

h„ „ - air-side mean convective heat transfer coefficient for dry air

c,o

66
k = air thermal conductivity

Pr = Jia-J—Ea^ Prandtl nTunber

^a

Re„ = _Mx_L_o^ Reynolds number

a M

*^a

G«»,, = air mass flux at minimum cross section

max

t = fin thickness

y = fin height

z = distance between adjacent fins

The geometric parameters affecting the heat transfer are illustrated in figure

22. The accuracy of equation (87) was further verified by Jones and Russell

[37].

The addition of fins to the tubes greatly increases the outer heat transfer

area but at the expense of decreasing the mean temperature difference between

the surface and the air stream. The parameter, fin efficiency, 4> , is used to

rate the thermal effectiveness of a fin. As mentioned in Section 5.4.1, it is

assumed in this study for heat transfer analysis, that each tube is served by

a circular-plate fin of equilivalent surface area, as in figure 21. Gardner

[38] solved the differential equation for describing the temperature distribution in a circular fin and presented fin efficiency curves in t^ms of two

parameters.

D„/D, and y ^^_

0.5

(88)

The theoretical results are correlated well by the following equation (see

also figure 23) [2]:

8 n n 2 , I, 0.5 i-1 ^^ 1,1 '^ ' ^ D^ ^ ' ^ D^ kj . t

where h = air-side convective heat transfer coefficient

kf = fin material thermal conductivity

The geometric parameters are indicated in figure 22. The coefficients, A^^ £, are given in Table 3.

5.4.7 Overall Heat Transfer Coefficient for a Wet Finned Tube

Wet finned tube analysis is applicable to an evaporator when its temperature

is below the dew point temperature of ambient air. In such a case, moisture

is being removed from an air stream and is transferred to the evaporator

external surface. If the evaporator temperature is above 32"?, a water film

flows down the fin under force of gravity. If the exterior evaporator

temperature is below 32'*F, frost is accumulated.

67
"0

-

Dt

-

y =

t =

z =

TUBE OUTSIDE DIAiETER

FIN TIP DIAMETER

FIN HEIGHT

FIN THICKNESS

DISTANCE BETWEEN ADJACENT FINS

Figure 22. Cross section of a flat-finned tube indicating parameters which

affect the air-side heat transfer coefficient.

68
>•o

1.0

0.8

0.6

0.4

0.2

\ — EXACT THEORY \ • EQUATION [89]

\\\ Dt ^k "•

\R^^::i= ''----^ :5^

*

1

2h

.0.5

k^t

Figure 23

Efficiency for a circular^plate fin of uniform thickness.

Comparison of exact theory results with those obtained by

equation (89).

69
Table 3. Coefficients to be Used in Correlation for Fin Efficiency (Equation

(89)).

i Al,i ^2.1 ^3,i

1 1.0 0.0 0.0

2 -0.22920E-01 -0.13755E+00 0.20130E-01

3 0.16106 E+00 0.81890E-01 -0.1 1440E-01

4 -0.64975E+00 -0.55500E-01 -0.28753E-01

5 0.53 491 E+00 0.18040E-01 0.42477E-01

6 -0.1 92 86 E+00 0.36494E-03 -0.20335E-01

7 0.32564E-01 -0.10660E-02 0.40947E-02

8 -0.20972E-02 0.12410E-03 -0.29673E-03

70
Considering the heat transfer from the refrigerant to the air, one can

realize that the dehumidif ication process will alter the heat transfer situation on the external surface of the finned tube, while other processes in the

tube and refrigerant stay unaffected and are governed by relations already

proposed in previous sections. Thus only processes connected with

dehumidif ication need to be discussed.

The heat transfer rate between the air stream and the water surface is

described by the following equation:

dQ = <^,o<Ta - V ^ Vo<^a " %>ifg,w)dAo (90)

The first term accounts for sensible heat transfer and the second term

accounts for latent heat transfer. For air at atmospheric pressure the Lewis

number,

Le = ^^'° , (91)

is close to 1 [16]. Therefore, equation (90) assumes the following form for a tube

with flat fins:

dQ = h^(l - ^(1 -4>)){T^ - T^)dAo (92)

^o

where h = h_(l + ^f«,w<Wa w ) ^ c CO Cp„(T, - T„)

*^a a w

Symbols used in equations (90), (91) and (92) denote:

Af = fin area A = total external area

Cp_ = specific heat of air

h = air-side forced convection heat transfer for wet air

h = air-side forced convection heat transfer coefficient for dry air

hn . = air-side mass transfer coefficient D,o

latent heat of condensation for water (frost sublimation)

1" = temperature of liquid water (frost)

Q = heat transfer rate

Wg = humidity ratio of air w = humidity ratio of saturated air at T temperature

^ = _Wtm a ^^^ efficiency

w, D a

T ju = mean temperature of water film (frost)

T^\ = temperature of water film (frost) at fin base

71
The one-dimensional heat conduction across the condensate (frost) film can be

expressed by the equation:

dQ = hL • ATl • dA^ (93)

kwhere h* == -^ , heat transfer coefficient for the condensate (frost) film ^ 8

= thermal conductivity of water (frost) - thickness of condensate (frost) film (for evaluation of water

and frost properties see Appendix B)

ATj^ = temperature difference across the condensate (frost) film

Using equations (92) and (93) and referring to equation (81), the following

relation for overall heat transfer coefficient for a wet finned tube can be

derived.

U = + ^o^P + 1- + h.A„ . A_ ^k^ h, i-„ „(w„ - w„) Af

a a w o

-1

(94)

where symbols used are defined as in equations (81) and (92).

In the above formulation of the overall heat transfer coefficient, it is

assumed that the temperature difference across the liquid film (frost) is

uniform. The calculated value for wet fin efficiency is affected by the

change of the air-side heat transfer coefficient caused by the air passage

geometry alteration by liquid (frost) accumulation, and by the released

latent heat of condensation (sublimation). The effect of water (frost) con- ductance on fin efficiency is neglected. In summary, the heat transfer phenomena that occurs during dehumidif ication on the air-side may be itemized as follows:

(1) the layer of wet (frost) offers additional heat flow resistance

(2) the air-side heat transfer resistance is decreased due to effect of

condensation.

(3) the air-side heat transfer coefficient, h_, has an increased value

c since it is sensitive to external surface geometry and the Reynolds

number (see equation (87)).

(4) fin efficiency decreases as h is increased (see figure

23).

(5) the cross sectional area of the air flow passage between the fins

has decreased, decreasing the flow rate.

In order to evaluate water (frost) layer thickness, consider the mass transfer

equation:

%,d • d^a = - ^D,o<^a - V^A^ <^5)

72
For the Levis number equal to 1 equation (95) assumes the following form:

«a,d • dw, = - ^(w^ - w^) • dA^ {96)

The change in the air humidity ratio can be calculated by integrating equation

{96), which yields:

w

~ ^c,o • A,

.,e = -a.i - (-a,i " w,)(l " exp

, --" " ) (97)

The rate of moisture removal per unit area, R, can now be calculated:

R = ">a.d<^a.i - ^a.e)/Ao (98)

where °a d ~ "lass flow rate of dry air

w^ g = humidity ratio of air at tube row exit

w-*i = humidity ratio of air at tube row inlet

If the evaporator temperature is below the freezing point, moisture removed

from the air stream accumulates on the evaporator external surface in the form

of frost. Its thickness, b^, can be evaluated by integrating the rate of

moisture removal with respect to time, i.e.,:

t 8« = / B_ dt {99)

Pf

where t = time

R = rate of moisture removal per unit area

&£ = frost layer thickness

P£ = frost density

In case of evaporator temperature above 32**F, condensate flows down on the

fin. Assuming no air drag on the liquid layer, its local velocity is

expressed by the closed solution of the Navier-Stokes equation for a viscous

flow on a vertical wall [39]:

2 2

^ 2n o

where V, = local liquid layer velocity

p = liquid density

g = gravitational acceleration

y

= distance from the wall

6 = liquid layer thickness

(1 = liquid absolute viscosity

Applying to the liquid film the continuity equation:

73
in(z) = p / V^ dy (101)

o

and assuming uniform condensation rate on the fin (i.e., m(z) = m * z/h,

where: m(z) = mass flow rate of condensate at elevation z, m = water condensation rate by a fin of height h), the average condensate layer thickness can

be obtained by integrating a local layer thickness over the fin height and

dividing the obtained expression by the height. The resulting expression is:

8f = 1.082

-il/3

t^w > R'

.8 • Pw^

(102)

where g = gravitational acceleration

R' = condensation rate per unit width of a fin

|ijj = water dynamic viscosity

p^ = water density

5.4.8 Pressure Drop in a Tube

As expressed by equation (50), the total pressure drop experienced by a flowing fluid results from pressure drops due to friction, momentum change,

and gravity. In an actual heat pump heat exchanger, pressure drop due to

gravity effect is very small and may be neglected. Only pressure drop due to

friction and due to momentum change will be considered for the

different flow patterns in a tube.

Single-Phase Flow

Frictional pressure drop for a single-phase turbulent flow in a tube can be

calculated by the Fanning equation with the Fanning friction factor, equations

(67) and (68):

AP = 2f > g2 . L (103)

D • p

f = 0.046 Re"®-^ (for Re > 2000, [22]) (104)

Pressure drop due to momentum change can be calculated by the following

equation:

dP = _ g2 dv (105)

dL dL

where G = refrigerant mass flux

L = tube length

V = refrigerant specific volume

Two-Phase Flow with Condensation

The frictional pressure drop for two-phase flow with condensation can be

calculated by the method proposed by Lockhart and Hartinelli [22]. They

74
performed a semi-empirical study of adiabatic two-phase flow with air and

different liquids including benzene, kerosene, water, and various oils in

tubes varying in diameter from 0.586 to 1.017 inch. They related the pressure

drop of two-phase flow to the pressure drop of the liquid portion of the flow

flowing alone in the pipe, by a dimensionless parameter X^^, i.e.,:

^= f(XtP =(D or AP^p = APl-cD (106)

J-/

where AP, = frictional pressure drop of the liquid portion of two-phase

flow flowing alone in the tube

AP^ = frictional pressure drop of two-phase flow

(J> = correction factor for two-phase pressure drop

X^^ = as given by equation (84)

The pressure drop, AP,, is calculated by the singlo-phase pressure drop

relation with the liquid Reynolds number and friction factor calculated as follows:

tp,L

^ (1 - x)G (107)

ftp,L = 0-046 • Retp^L

®*^

^^°' »«tp,L > ^000) (108)

where f. , = friction factor for the liquid portion of two-phase flow

flowing alone in the pipe

Re^ T = Reynolds number for the two-phase liquid portion flowing

alone in the pipe

X = quality

(It = liquid dynamic viscosity

A correction factor for two-phase pressure drop, ^, was correlated by the

following equation:

i=l

^ (109)

where A^ = -0.418956

A2 = 1.47330

A3 = 0.6685 83

A^ = -0.321168

A5 = 0.0408167

Combining equations (106), (107), (108), and (109), the two-phase pressure

drop equation assumes the form:

AP^p = 2 f^p L

• G^d - x)2 L • <I) /(D • Pl) (110)

The pressure drop due to momentum change for separated two-phase flow can be

estimated by the following equation:

75
dL dL a ( 1 - a)

where x = quality

Vy = specific volume of liquid

Vy = specific volume of vapor

a = void fraction

Void fraction^ a, percent of tube filled with vapor, was shown by Lockhart and

Martinelli to be a function of X^^^ under any flow conditions for separated

flow with both phases turbulent^ Wallis [40] correlated their results in the

following form:

fi s -0.378

a = (1 + X^^^"^) (112)

This expression was found to correlate well with data presented in [22] for

values of X^^ <_ 10. For X^^ greater than 10, another curve fitted formula is

used:

a = 0.823 - 0.157 » la X^^ (113)

Two-Phase Flow With Evaporation

The Lockhart-Martinelli method for pressure drop calculation of two-phase flow

is widely used for adiabatic and condensing flows of single component refrigerants. However, it does not yield accurate prediction for evaporative flow.

Instead of the Lockhart-Martinelli correlation, Anderson, Rich and Geary [41]

recommended a method proposed by Pierre [42]. In order to evaluate the

accuracy of this correlation for the R13B1/R152a mixture, pressure drop predictions were compared with laboratory data of evaporator tests performed in

NBS environmental chambers. It was found that this correlation underpredicted

pressure drop by about 40 percent in a consistent manner. Until pressure drop

of non-azeotropic mixtures is fully investigated Pierre's correlation will be

used for calculation of pressure drop with a correction factor of 1.4.

Tbe correlation of Pierre based on experiments with refrigerants 12 and 22 has the

following form:

AP = (f L + 42)g2 . (J14J

D

„ m

in

where D = inner tube diameter

D = tube length

f = friction factor (calculated by equation (115))

Xjjj = mean quality

Ax = quality change

""^m ~ ^L ^ -^m^^V ~

^L^ ' "^®^^ specific volume

The friction factor to be used in equation (114) was correlated by Pierre from

his experimental data by the following empirical equation valid for Re/Kf > 1:

76
0.25

f = 0.0185(Kf/Re) (115)

J * if c

* Ax

^here K^ = ^^'*—

, boiling number

Re = — — , Reynolds number

J = mechanical equivalent of heat

The correlation proposed by Pierre is in the conventional format for the

single pressure drop formula. The first term of equation (114) is for frictional pressure drop while the second is for pressure drop due to change of

momentum. The formula for the friction factor contains the Reynolds number

divided by the boiling number, making the friction factor sensitive to vapor

generation rate at the vapor-liquid interface.

5.5 Modeling of Additional Heat Pump Components

In the previous sections, modeling of the main heat pump components has been

discussed. The analysis included a compressor, a constant flow area expansion

device, a condenser, and an evaporator. Additional components that have to be

considered for a more accurate heat pump performance prediction by the model

are: the vapor suction and discharge lines, the liquid line, and the four-way

valve. Their modeling is briefly explained below.

Vapor Lines

A suction line connects the evaporator with the compressor. A compressor and

a condenser are connected by a discharge line. Usually, single-phase flow

exists in the vapor lines in the form of either saturated or superheated

vapor. Heat transfer rates between the refrigerant vapor flowing in the

vapor lines and ambient air can be calculated by a general heat transfer

equation for a circular duct with insulation [19]. Single-phase forced

convection is assumed inside the tube (equation (82)) and free convection is

assumed outside the tube. The following equation is used for calculation of

the free convection heat transfer coefficient for a horizontal tube [43]:

h = 0.27 (41)®-^^ (116)

Do

for Grashof numbers from 10^ to 10^.

where AT = temperature difference between tube wall and air

D^ = tube outside diameter

Pressure drop in vapor lines can be calculated by the single-phase pressure

drop equation (67).

77
Liquid Line

A liquid line connects the evaporator and tlie condenser. This line is filled

with a soboooled liquid or low quality two-phase flow. The pressure drop can

be calculated by equations (67) or (108), depending on the flow pattern. Heat

loss from the liquid line to the ambient air is neglected.

Four-Way Valve

The main function of a four-way valve is to direct refrigerant flow from the

compressor to the indoor or outdoor coil depending on the mode of operation

(heating or cooling). The side effects of flow through a four-way valve are changes in the refrigerant thermodynamic state due to the pressure drop and

heat exchange. Assuming for simplicity an adiabatic exterior wall, all heat

lost by the discharge refrigerant is gained by the suction refrigerant. The

heat transfer rate and refrigerant pressure drop in the valve can be evaluated

by formulas similar to equations (45) and (55), respectively. Heat transfer

and pressure drop parameters in these formulas have to be found using a subroutine VALPAR and a four-way valve (heat pump) one test data as explained

in Appendix E.

Accumulator

Simplified schematic of an accumulator is shown in Figure 8. It is assumed

that refrigerant experiences no pressure drop while flowing through the

accumulator, and the accumulator is adiabatic. With these assumptions the

refrigerant state at the accumulator inlet is equal to the state at the outlet

during steady-state operation. The main purpose of the simulation of the

accumulator is the calculation of mass of refrigerant contained in it. If

superheated vapor is entering the accumulator, the accumulator is filled with

vapor and calculation is straight forward. If wet vapor is entering the

accumulator, refrigerant liquid is collected in it and the liquid level has to

be evaluated. The liquid level is found by evaluating the hydrostatic pressure that along with the dynamic pressure exerted at the oil return hole would

cause refrigerant liquid to flow through the hole at the rate that would

change saturated vapor in the accumulator tube into a wet vapor of the inlet

vapor quality.

The basic equations used in the accumulator subroutine, WACCJUM, are:

m(l - x) = A • K 2 • AP • Pl (117)

T

AP = H • Pl • g + 0.5 ( ^ ' '"

) Vy (118)

where E = orifice flow coefficient assumed K = 0.585 [44])

A = tube cross section area H = liquid refrigerant level in the accumulator

g = gravitational acceleration

m = refrigerant mass flow rate throught the accumulator

Ap = pressure drop through the oil return hole

Vy = specific volume of vapor

X = refrigerant quality

Pi = liquid density

78
Equation (117) is the orifice equation applied to the oil return hole. In

equation (118) the first term represents the hydrostatic pressure while the

second term expresses the dynamic pressure exerted at the hole (velocity of

the liquid is neglected)

Some accumulators have two holes in the accumulator suction line. In addition

to the regular oil return hole at the bottom of the suction line, they have

another hole located some distance (approximately 1.5 inch) above. The

accumulator subroutine is capable of simulating both types of accxunulators.

In either case the subroutine is solving for the liquid level, H, using

equations (117) and (118).

5 »6 Refrigerant Mass Inventory in a Heat Pump

The mass, M, of a substance occupying a known volume, V, may be determined by:

M = / p

• dV (119)

V

where p = local density

In reality, the mass of refrigerant in the system can be found by estimating

the masses of the refrigerant in each system component and adding them up.

For this purpose, equation (119) can be written in the form:

M=2]Mj (120)

Mi=Vi*P„.,i

where Mj = mass of refrigerant in particular component i

Vj = internal volume of component i

pg^ £ = mean fluid density in component i

In order to make mass inventory of individual mixture components, the

following equation can be applied with the known mixture weight composition, XW,

of the considered refrigerant:

M^

J = Mj * ^

<^21)

where ^i I ~ I'&ss of refrigerant 'I' in heat pump component, 'i'

The heat pump components taken into account in the mass inventory calculations

are shown in figure 24. The refrigerant phase in each of the components as indicated in the figure, is based on the following considerations:

Discharge line - receives and is filled with superheated vapor from the

compressor.

Condenser - receives superheated vapor from a discharge line. In the course of passage through the condenser tubes, vapor temperature is

brought to the dew point temperature. Starting at this point, a thin

condensed liquid layer forms on the tube walls. Depending on the mass flux, this liquid film may be swept and entrained within the

vapor as a mist forming a dispersed flow. With more condensed vapor,

79
DISCHARGE LINE SUCTION LINE VAPOR PHASE OR HIGH QUALITY TWO-PHASE

CONDENSER

VAPOR PHASE, TWO-PHASE AND

LIQUID PHASE

LIQUID PHASE OR LOW

QUALITY TWO-PHASE

Figure 24. Refrigerant phase in the heat pump components

80
the velocity of vapor decreases, a permanent liquid film is formed on

the wall, and the flow proceeds farther as the annular or semiannular

flow. The quality decreases and the flow slows down in the direction

of flow. Gravity forces result in a stratifying effect and the

liquid flowing in the bottom of the tube periodically wets the upper

tube wall (slug flow). If full condensation is reached, there will

be subcooled liquid at the condenser exit.

Thus there are four two-phase flow patterns in the condenser, i.e.,

dispersed flow, annular flow, semi-annular flow, and slug flow as identified by Traviss and Rohsenow [45]. Soliman and Azer [46] identified nine

flow regimes, however, five of them may be considered as transition

regimes and can be put into the above basic four categories. The effect

of return bends connecting condenser tubes was investigated in [47] . It

was found that this effect is insignificant and that the annular flow

pattern 'recovers' almost immediately in a tube after a return bend.

Liquid line - receives refrigerant from a condenser and delivers it to an expansion device. Entering the expansion device at the end of the liquid

line, the flow experiences a sudden contraction. The entrance pressure

drop depends upon the mass flow rate and the fluid density. This, along

with the capillary tube sensitivity to the amount of subcooling, provides

a flow controlling mechanism for the system. It is common practice to

design a capillary tube so the refrigerant mass flow rate through it

would balance with the mass flow rate through the compressor when a liquid seal exists at the capillary tube entrance. Temporary existence

of vapor at the capillary tube would decrease the mass flow rate and

build up the pressure. This would provide better conditions for condensation in the condenser and thus cause a return to a subcooled liquid or very low quality two-phase flow in the liquid line.

Expansion device - due to its small internal volume it may be disregarded

for mass inventory purposes.

Evaporator - receives refrigerant from a capillary tube in the form of

homogeneous flow of about 20 percent quality, at sonic or close to sonic

velocity. This flow experiences a sudden deceleration and is assumed to

form an annular or semi-annular flow very quickly having a void fraction

about 0.8 [48]. The liquid phase flows along the tube in the form of an annulus and the vapor phase flows in the core. This type of flow prevails in most of the evaporator. With increasing quality, the velocity

of the vapor increases and becomes eventually high enough to entrain

small liquid drops and tear the liquid film apart. This results in a mist flow at qualities close to 1. Finally, the flow may reach the

evaporator exit in a superheated vapor state.

Suction line - receives refrigerant from the evaporator as a mist flow or superheated vapor flow and the same flow pattern exists at the exit.

Accumulator - receives the refrigerant from a suction line after some heat is added in the four-way valve. Superheated, saturated or wet vapor

may be expected. With wet vapor entering, liquid will be accumulated on

the accumulator sxmip.

81
Compressor can - receives refrigerant from the accumulator as a saturated

or superheated vapor which is further superheated due to heat transfer

from an electric motor, discharge line, and compressor cylinder body.

According to the above analysis, refrigerant in the compressor can, suction

line, and discharge line is in (or close to) a homogeneous vapor state. In

the liquid line, homogeneous liquid flow or two-phase flow exists but in a state so close to saturation that for simplicity of mass inventory no slip is

assumed and the flow is considered to be homogeneous. The mass of refrigerant

in these components can be then calculated straight forward in a similar

manner since refrigerant densities in the components described above will be

known as a result of the simulation program iteration process.

In order to calculate the mass of refrigerant in the accumulator, it is

necessary to determine the portion of the internal volume filled with liquid.

Once this is found, total refrigerant mass in the accumulator can be calculated based on refrigerant state parameters.

In the case of both coils, the refrigerant flow is partly homogeneous,

however, in most of the coil some type of annular flow prevails. For a separated flow regime, like an annular flow, density of the flowing fluid

is determined from vapor and liquid densities and the fractions of tube volume

occupied by the liquid and vapor phase:

^_ , PL • Vl ^ PY • Vy

, ^^(1 . ., + p^ . „ (122,

^t

where H = mass

V "= occupied volume

p = density

a = ¥y/V^, void fraction

subscripts refer to:

L = liquid phase

m = mean value

t = total value

V = vapor phase

It should be pointed out that for a two-phase flow of a given quality, mean

density depends not only on the thermodynamic parameters affecting densities

of the liquid and vapor, but also on the ratio of mean velocities of the vapor

and liquid referred to often as the slip ratio. This can easily be noticed by

examining the equation for the void fraction, which can be derived,

considering mass flow rates of each phase:

. (123) a = ±

1 + 1 - X XV PV

^ VlPl

where V = velocity

82
Calculation of the void fraction has received much less attention than the

calculation of heat transfer or pressure drop, although all three of these

quantities are undoubtedly inter-related. The most often referenced method for

void fraction calculation is that of Lockhart and Martinelli [22] based on

their experimental void fraction data reported along with pressure drop

results. They correlated void fraction with the dimensionless parameter, X^^.

Their experiment dealt with adiabatic flow, however, in the conclusions of

their paper they suggested that their pressure drop correlation could be used

for prediction of pressure drop during evaporation and condensation as well.

On similar grounds, their void fraction data should be applicable beyond the

adiabatic case.

There is another, earlier, method available for void fraction calculation by

Martinelli and Nelson [49], derived with the same assiunptions for water/steam

evaporating flow. The method is similar to the Lockhart-Martinelli method so the Lockhart-Martinelli method was used in this study for calculation of the

void fraction in both the evaporator and the condenser coils.

Correlations for void fraction based on [22] have already been given in

section 5.4.8 (equations (112) and (113)).

o = (1 + x^^®-^)"®-^''^ for X^^ <. 10 (124)

a = 0.823 - 0.157 In X^^ X^^ > 10 (125)

The parameter X.^, as defined by equation (84), is a function of flow quality,

specific volume, and the viscosities of the liquid and vapor, and is not

sensitive to the mass flux which in turn affects the slip ratio.

Experimental data of Staub and Zuber [48] for evaporating refrigerant 22

indicate that void fraction increases with increased mass flow rate. Comparison of their data with the void fraction predicted by the Martinelli-Nelson

method showed a discrepancy which may lead to underestimation of the two-phase

flow mean density by as much as 300 percent. (Note that a small difference in

void fraction results in a large error in mean density prediction as density

of the vapor and liquid are vastly different.) The results of Staub and Zuber

also indicate that approximate agreement with the Martinelli-Nelson could be

obtained at high mass fluxes, more than five times higher than those observed

in usual heat pump evaporators.

In discussing the accuracy of a refrigerant mass prediction method, it should

be noted that it also depends upon an accurate measurement of the internal

volume of the system. Internal volume can be easy calculated for straight

pipes. For valves, bends, etc., it can only be approximated.

Mass inventory of a heat pump system, as explained in Section 5.1, is intended

to be used for iteration of refrigerant superheat at the compressor can inlet.

The discussions above indicated that mass inventory calculations may have errors from two different sources. These sources are: inaccurate density

prediction in the two-phase region, and inaccurate internal volume measurement. However, effect of these inaccuracies can be diminished since the

program does not really need prediction of the absolute value of refrigerant mass in the system, but rather requires sensitivity in relative mass predictions in a heat pump with changes of operating conditions. This requirement

83
should be satisfied by the Lockhart-Martinelli method and very precise

knowledge of the internal volume should not be that important. Since the

refrigerant vapor superheat at the ccanpressor can inlet is known at the

cooling design operating mode at conditions (usually: outdoor temperature

95®F, indoor dry bulb temperature 80"F, and wet bulb 67°F) and does not have

to be iterated for solution, refrigerant mass in the system can be calculated

at this operating condition. This calculated mass of refrigerant may then be

used as input data for refrigerant vapor superheat/quality iteration at other

outdoor or indoor air conditions at which heat pump simulation results are required.

84
6. MODEL VERIFICATION

A verification of the computer model has been done by comparison of computer

predictions with performance data obtained from laboratory tests conducted in

NBS environmental chambers. In this stage of model development, laboratory

data were available on one heat pump tested at two cooling and two heating

standard rating operating conditions [SO].

The sequence for running laboratory tests was as follows:

1. DoE cooling test A, T ^ = 950F

indoor conditions: 80®F DB, 67 'F WB

refrigerant charge adjusted to obtain 10® superheat at evaporator

outlet

2. DoE cooling test B, T^^ = 82 ^F

indoor conditions: 80*F, 67*F WB

3. DoE high temperature heating test

outdoor conditions: 47 ^F DB, 43 ^F WB

indoor temperature: 70'*F

4. DoE low temperature heating test

outdoor conditions: 17»F DB, IS'F WB

indoor temperature: 70*F

The laboratory data of DoE cooling Test A were used first to obtain compressor

and four-way valve parameters as explained in Appendix E. Then computer model runs were started with simulation of performance at DoE cooling test A conditions with the appropriate imposed superheat at compressor can inlet tliat

resulted in lO^F superheat at evaporator inlet as observed during laboratory

test at this operating condition. Along with the performance results,

refrigerant charge at the imposed superheat was obtained. This charge was

then included in a heat pump data file to be used for iteration of superheat/

quality of vapor at compressor can inlet, and composition of the circulating

refrigerant at other operating conditions.

The laboratory and simulation results are given in Table 3 for the cooling

mode and in Table 4 for heating operation.

During cooling operation no liquid was collected in the accumulator and the

composition of the mixture did not change. In the heating mode refrigerant

liquid was collected and a shift of composition of the circulating mixture

occured.

For both the cooling and heating modes, agreement between the results is very

good, in fact, better than could be expected taking into account the number of

simplifications used in the model, even the model is complex. It is not

implied that this type of agreement can be obtained for every heat pump.

It is believed that the accuracy of prediction stems partially from the effective cancellation of different simulation approximations, and this may not

necessarily occur in simulation of every heat pump. However, the model

85
proved to provide physically consistent predictions including evaluation of

refrigerant superheat /quality at the compressor can inlet and the circulating

composition. Validation of this model with test data at other heat pumps

charged with different mixtures, when available, would further increase

confidence in the model.

Since two-phase heat transfer and pressure drop of non~azeotropic mixtures

have not been fully presented in the literature and appropriate correlations

are not available, the evaporative and condensation heat transfer coefficients

and respective pressure drops are calculated in the model by formulas that may

provide approximate values of the parameters in question. To evaluate the

impact of possible approximate prediction on the final results, a few

simulation runs were performed in which the specific parameter calculated

within the program was altered by a preset factor. Change of calculated

system capacity and COP as compared to performance obtained with unaltered

parameter describes sensitivity of the model on this particular parameter.

The following results were obtained. Increase of the evaporative heat

transfer coefficient by 50% resulted in 2.5% increase of system capacity and

1.8% of system COP. Decrease of the evaporative heat transfer coefficient by

50% caused reduction in capacity and COP by 6.9% and 5.4%, respectively.

Increase in the condensation heat transfer coefficient by 50% increased

capacity by 0.6% and COP by 1.1%. The same reduction in the condensation heat

transfer coefficient caused reduction of system capacity by 2%, and reduction

of COP by 3.1%.

Similar comparison was done for the evaporative and condensation pressure

drops. Sensitivity of the final performance predictions was much smaller. In

either considered case a change in pressure drop by 50% did not affect system

capacity or COP by more than 1%.

Comparison numbers given above were obtained at indoor and outdoor air

conditions specified for DoE cooling Test A. These findings should still

apply for other operating conditions. S<»newhat different results could be

obtained simulating different systems.

86
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88
7. SUMMARY AND CONCLUSIONS

This report describes a model of a heat pump equipped with a constant flow

area expansion device and operating with a non-azeotropic binary mixture

refrigerant.

The model is able to simulate performance of a heat pump at imposed operating

conditions without restriction on the refrigerant thermodynamic state at any

point of the system. The simulation power includes simulation of the circulating mixture composition shift resulting from incomplete evaporation and

accumulation of liquid refrigerant in the accumulator.

The model has a modular structure", it consists of independent models of heat

pump components linked together by appropriate logic iterating refrigerant

thermodynamic states in thirteen key locations of a heat pump thermodynamic

cycle. Heat pump system component models were developed with emphasis on

description of processes by fundamental heat transfer and pressure drop equations, and equation of state relationships among material properties. In the

compressor model several refrigerant locations were identified and processes

taking place between them accounted for all significant heat and pressure

losses. Evaporator and condenser models were developed on a tube-by-tube

basis where performance of each coil tube is computed separately by considering the cross-flow heat transfer with the external air-stream and the appropriate heat and mass transfer relationship. A constant flow area expansion

device model was formulated with the aid of the Fanno flow theory.

The model utilizes an equation of state which is applicable for both liquid

and vapor phases. Unlike the usual practice of using separate pressuresaturation temperature and liquid density-saturation temperature correlations

with P-V-T relationship, one P-V-T relationship and physical equilibrium

criteria are used in this project in establishing saturation state parameters

and properties.

Since two-phase heat transfer and pressure drop of non-azeotropic mixtures

have not been fully presented in the literature and appropriate correlations

for their evaluation are not available, the evaporative and condensation heat

transfer coefficients and respective pressure drops are calculated in the

model by formulas either derived from a single component flow experiments or

at best from limited experiments of one mixture only. There is certainly a need of research in these areas and this model should be updated when our knowledge about these phenomena is advanced.

The model was validated by comparing its performance predictions with

laboratory test results of one heat pump charged with R13B1/R152a mixture at

two cooling and heating operating conditions. The data presented in this

report, established our confidence in the model. The choice of R13B1/R152a

for development and verification of this model does not mean recommendation of

this mixture as an optimum and precludes other mixtures to be more suitable

for heat pump application.

This report is intended for research and development engineers to provide a tool for evaluation of the potential of non-azeotropic binary mixtures in heat

89
pumps. The User's Manual of the developed program, HFBI, is included in the

Appendix Section to enable readers to prepare input data for other heat pumps

and to run the program even without detailed knowledge of the main section of

this report. An example run and a listing of the program are also included.

HPBI program is applicable to the standard split residential system. It is>

however, limited in the form presented here to the R13B1/R152a mixture due to

a saturated refrigerant property spline which was incorporated in the program

to decrease required computing time. Once a more efficient scheme is developed

to use the equation of state directly, the spline will be removed along with

present model limitations.

The current version of the model can be used to evaluate performance of a heat

pump charged with R13B1/R152a mixture at different operating conditions and

different mixture compositions. It is intended to be used, after slight

modification, to predict the possible potentials of mixtures working in modified thermodynamic cycles. The computing time required by the program will

vary with the size of the heat exchangers and the accuracy of estimated

refrigerant parameters given as inputs. On the average, HFBI program run on

Sperry 1100/82 computer requires 10 minutes of CPU time to converge with

iteration of superheat, and about 40 minutes to converge iterating refrigerant

quality at the compressor can inlet and the circulating mixture composition.

90
8. REFERENCES

1. Cooper, W.D., The Use of Mixed Refrigerants in Air-to-Air Heat Pumps,

ASHRAE Transaction, Vol. 88, 1982.

2. Chi, J., A Computer Model HTPUMP for Simulation of Heat Pump Steady-State

Performance, National Bureau of Standards, Internal Report, Washington,

D.C., 1979.

3. Domanski, P., and Didion, D., Computer Modeling of the Vapor Compression

Cycle with Constant Flow Area Expansion Device, National Bureau of

Standards, Building Science Series 155, Washington, D.C. , May 1983.

4. Cannon, H.A., and Drew D.W., Estimation and Application of Thermodynamic

Properties for a Non-Azeotropic Refrigerant Mixture, IIR Meeting of

Commissions Bl, B2, El and E2, Essen, West Germany, September 1981.

5. Morrison, G., Francis, G., and Bland, T., An Equation of State for

Refrigerant Mixtures, Report to EPRI, National Bureau of Standards, March

1983.

6. Morrison, G., The Importance of Including the Liquid Phase in Equation

of State for Non-Azeotropic Refrigerant Mixtures, ASHRAE Transactions, Vol. 91, Part 1, 1985.

7. Baker, G.A., Gammel, J.L., and Wils, J.G., Journal of Mathematical

Analysis Application, Vol. 2, p. 405, 1961.

8. Baker, G.A., Advances in Theoretical Physics, Brueokner, K,A., ed..

Academic Press, New Tork, 1965.

9. Reid, R.C., Prausnitz, J.M., and Sherwood T.K., The Properties of Gases

and Liquids, McGraw-Hill Book Company, New York, 1977.

10. Thermophysical Properties of Refrigerants, American Society of Heating,

Refrigerating and Air Conditioning Engineers, Inc., Atlanta, Georgia,

1976.

11. Afshar, R., and Saxena, S.C., International Journal of Thermophysics,

Vol. 1, 1980.

12. Proceedings of the 1976 Purdue Compressor Technology Conference, Purdue

Research Foundation, 1978.

13. Proceedings of the 1978 Purdue Compressor Technology Conference, Purdue

Research Foundation, 1978.

14. Proceedings of the 1980 Purdue Compressor Technology Conference, Purdue

Research Foundation, 1980.

15. American Society of Heating, Refrigerating and Air Conditioning

Engineers, ASHRAE Guide and Data Book, Equipment Volume, New Tork, 1983.

91
xo. Threlkeld, J.L. , Thermal Environmental Engineering, Prentice-Hall, Inc.,

New Jersey, 1970.

17. Schultz, J.M. , The Polytropic Efficiency of Centrifugal Compressors, ASME

Transactions , Journal of Engineering for Power, Vol. 84, January 1962.

18. Hirsch, S.R. , On the Relation of Compressor Theory to Performance, ASHRAE

Journal . July 1973.

19. American Society of Heating, Ref rigeranting and Air Conditioning

Engineers, Inc., ASHRAE Handbook, Fundamentals Volume, New York, 1985.

20. Colburn, A. P., A Method of Correlating Forced Convection Heat Transfer

Data and a Comparison with Fluid Friction, AIChE Transactions , Vol. 29,

p. 174, 1930.

21. Hiller, C.C. and Glickman, L.R. , Improving Heat Pump Performance via

Capacity Control - Analysis and Test, Report No. 24525-96, Heat Transfer

Laboratory, Massachusetts Institute of Technology, Cambridge,

Massachusetts, 1976.

22. Lockhart, R.W. , and Martinelli, R.C, Chemical Engineering Progress, Vol.

45, pg. 39, 1949.

23. Bolstad, M.M. and Jordan, R.C, Theory and Use of the Capillary Tube

Expansion Device, Refrigeration Engineering , Vol. 56, No. 6, pg. 519,

December 1948.

24. Mikol, E.P. , Adiabatic Single and Two-Phase Flow in Small Bore Tubes,

ASHRAE Journal . Vol. 5, No, 11, November 1963.

25. Moody, L.F., Friction Factors for Pipe Flows, ASME Transactions , Vol. 66,

No. 8, pg. 671, November 1944.

26. Cooper, L. , Chu, C.K., and Brosken, W.R. , Simple Selection Method for

Capillaries Derived from Physical Flow Conditions, Refrigeration

Engineering , Vol. 65, No. 7, pg. 37, July 1957.

27. Rezk, A.M.A. , Investigation on Flow of R12 Through Capillary Tubes, Paper

presented on XV International Congress of Refrigeration, Venezia,

September 23-29, 1979.

28. Pasqua, P.F., Metastable Flow of Freon-12, Refrigerating Engineering , Vol. 61, No. 10, 1953.

29. Mei, V.C, Short-Tube Refrigerant Flow Restrictors, ASHRAE Transactions . Vol. 88, Pt. 2, 1982.

30. Kays, W.M. , Loss Coefficient for Abrupt Changes in Flow Cross Section

with Low Reynolds Number Flow in Single and Multiple-Tube Systems, ASME

Transactions . Vol. 72, No. 8, pg. 1067, November 1950.

31. Whitesel, H.A. , Capillary Two-Phase Flow, Refrigerating Engineering , Vol.

65, No. 4, pg. 49, April 1957.

92
32. Whitesel, H.A., Capillary Two-Phase Flow, Part II, Refrigerating

Engineering . Vol. 65, No. 9, pg. 35, September 1957.

33. Ertli, R.A., Two-Phase Flow in Refrigeration Capillary Tubes: Analysis

and Prediction, Ph.D. Thesis, Purdue University, January 1970.

34. Carrier, W.H. and Anderson, S.W., The Resistance to Heat Flow Through

Finned Tubing, ASHVE Transactions . Vol. 50, 1944.

35. Traviss, D.P., Baron, A.B., and Rohsenow, W.M., Forced-Convection

Condensation Inside Tubes, Technical Report No. 72591-74, Massachusetts

Institute of Technology, Cambridge, Massachusetts, 1971.

36. Briggs, D.E. and Toung, E.H., Convection Heat Transfer and Pressure Drop

of Air Flowing Across Triangular Pitch Banks of Finned Tubes, 5th

AICHE/ASME National Heat Transfer Conference, Houston, Texas, 1962.

37. Jones, T.V. and Russell, C.B.B., Heat Transfer Distribution on Annular

Fins, AIAA-ASME Thermophysics Heat Transfer Conference, Palo Alto,

California, May 1978, ASME Paper No. 78-HT-30.

38. Gardner, K.A., Efficiency of Extended Surface, ASME Transactions . Vol.

67, 1945.

39. Bird, R.B., Steward, W.E., and Lightfoot, E.N., Transport Phenomena, John

Wiley and Sons, Inc., 1980.

40. Wallis, G.B. , One-Dimensional Two-Phase Flow, McGraw-Hill, 1969.

41. Anderson, S.W., Rich, D.C., and Geary, D.F., Evaporation of Refrigerant

22 in a Horizontal 3/4 - in. CD Tube, ASHRAE Transactions . Vol, 72,

1966.

42. Pierre, B., Flow Resistance with Boiling Refrigerants, ASHRAE Journal , September 1964.

43. McAdams, W.H., Heat Transmission, McGraw-Hill, Inc., New York, New York,

1954.

44. Fox, R.W., McDonald, A.T., Introduction to Fluid Mechanics, J. Wiley and

Sons, 1978.

45. Traviss, D.P. and Rohsenow, W.M., Flow Regimes in Horizontal Two-Phase

Flow with Condensation, ASHRAE Transactions . Vol. 79, Part 2, pg. 31,

1973.

46. Soliman, H.M. and Azer, N.Z., Flow Patterns During Condensation Inside a Horizontal Tube, ASHRAE Transactions . Vol. 77, Part 1, pg. 210, 1971.

47. Traviss, D.P., and Rohsenow, W.M., The Influence of Return Bends on Downstream Pressure Drop and Condensation Heat Transfer in Tubes, Heat

Transfer Laboratory, Massachusetts Institute of Technology, Cambridge,

Massachusetts, 1971.

93
48. Staub, F.W. and Zuber, N. , Void Fraction Profiles, Flow Mechanisms, and

Heat Transfer Coefficients for Refrigerant 22 Evaporating in a Vertical

Tube, ASHRAE Transactions . Vol. 72, 1966.

49. Martinelli, R.C. and Nelson, D.B. , Prediction of Pressure Drop During

Forced Circulation Boiling of Water, ASME Transactions , No. 6.

50. Federal Register, Part III, Test Procedures for Central Air Conditioners,

Including Heat Pumps, Vol. 44, No. 249, p. 76708, December 27, 1979.

51. Biguris, G. and Wenzel, L.A. , Industrial Engineering Chemical

Fundamentals, Vol. 9, No. 1, 1970.

52. International Critical Tables, McGraw-Hill Book Co., pg. 216, New York,

1929.

94
APPENDIX A. CALCULATION OF PROPERTIES OF MOIST AIR

For the selection of moist air property equations, it was assumed that air dry

bulb temperature, T, relative humidity, RH, and pressure would be known, and

the properties that would be the output were: humidity ratio, specific heat

at constant pressure, gas constant, dynamic viscosity, and thermal conductivity. Presented here are the psychometric equations in their fundamental

form. They are derived assuming moist air to be a mixture of two independent

perfect gases, so that the perfect gas equation of state and Dalton's rule can

be applied. The transport properties, dynamic viscosity, and thermal conductivity of air are assumed to be negligibly affected by the moisture content.

Correlations for these two properties were based on dry air data.

Relations of this appendix were applied in air properties subroutine AIRPR.

The humidity ratio is determined by [16]:

w = 0.622 PSAT/(PATM - RH • PSAT) (Al)

where PATM = atmospheric pressure

PSAT = saturation pressure of water vapor at temperature T

w = humidity ratio (lb water/lb dry air)

RH = relative humidity (-)

The saturated water vapor pressure, PSAT (psi) , is calculated by the

polynominal approximation [2]

For T > 32°F

PSAT = exp(19.504 - 10.431z - 0.2755z2 + 0.03940z^)

For 32 < to < 180^F

PSAT = exp(13.4353 - 5.0988z - 1.6B96z'^ + 0.17829z^)

For T 1 180°F

PSAT = exp(16.8255 - 14.213z + 7.5568z^ - 4.01506z^ + 0.17692z'*)

where z = -^^^— (A2)

460 + T

The specific heat at constant pressure is [16]

Cp = (Cp^j^y + 0.444)/(l + w) (A3)

where Cp = specific heat at constant pressure of moist air

(Btu/(lb moist air * F))

Cp^ = specific heat at constant pressure of dry air (Btu/(lb * F)) w = humidity ratio (lb water/lb dry air)

The specific heat at constant pressure of dry air is approximated by the

following polynominal [2]

Cp^ = 0.247 8786 - 0.4204563 * lO"^ * TO + 0.567857 * lO"'' (A4)

• TR^ - 0.14936056 TR^

95
where TR = T + 460°F is the dry bulb air temperature on the Rankine scale

The gas constant is [16]

R = (53.34 + 85.76 • w) /(I + w) (A5)

where R = moist air gas constant —^

'-—=^

lb R

w = humidity ratio (lb water/lb dry air)

The dynamic viscosity and thermal conductivity values are obtained from the

respective equations [2]:

ji = 5.5029 • 10"^ + 8.7157 * lO"^ TR -2.9464 * 10~^TR^

+ 6.25 • lO'^^TR^ (A6)

k = -2.853 • 10""* + 3.268 ' 10~^ IR -8.253 * 10~^TR^

1,239 • lO'^^TR^ (A7)

where k = moist air thermal conductivity (Btu/(h * F * ft))

TR = 460 + T = dry bulb air temperature on the Rankine scale (R)

96
APPENDIX B. CALCULATION OF WATER AND FROST PROPERTIES

The equations presented below are for calculation of the properties of water

and frost deposited on a heat pump evaporator outer surface. These properties, for specific conditions, are either solely a function of temperature or can be assumed to be constant. The equations below are used in the ^ater and

frost properties subroutine, WATPR.

Hie following fourth degree polynomial expression is used for calculating

water density, conductivity, dynamic viscosity and latent heat of

condensation [2]

PROP = ^ A(I) • T^ - 1 (Bl)

1=1

where A(I) = five constants per calculated property

PROP = calculated property

T - water temperature (F)

Constants A(I) for each property are given in Table Bl. The specific heat of

water at constant pressure is assumed to be independent of temperature and to

have a constant value of Cp = 1—st5

lb • F

The density of frost, as proposed in [51], is calculated by the following

equation:

Pf = expCbi + b2 * (TV - TP)

)

(B2)

where bl = 11.9521 + 0^02422 TPR + 35.5498 WA -9.1742 • 10""^ VA + 3.1138 • 10 ^ VA • TPR - 0.03838

b2 = 13.1606 - 0.02133 TPR -81.955 WA/32.018 - TP

TP = tube temperature (F)

TPR = TP + 460. tube temperature (R)

IW = water (frost) temperature (F)

¥A = air humidity ratio

VA = air velocity (ft/sec)

pf = density of frost (Ib/ft^)

The frost conductivity, as proposed in [52], is calculated by the equation:

kj = 0.012138 + 3.8909 10"^ * p^ + 5.1409 10"^ ' Pf (B3)

where k^ ~ frost conductivity (Btu/(h * F * ft))

pf = frost density (Ib/ft^)

Frost heat of sublimation, ^g^j^j^^ &i^& frost specific heat C^, are assumed to

have the following constant values [52]:

*^SDBL " 1219.0 Btu/lb

Cf = 0.46 Btu/(lb • F)

97
Table Bl . Water Property Evaluation Constants wbich are Used in Equation (Bl)

Calculated

Property

A(I)

Density

Ib/ft^

Dynamic

viscosity

lb/(h • ft)

Thermal

conductivity

Btu/(h • F • ft)

Latent heat

of condensation

Btu/lb

A(l) 0.11647 E+03 0.79422 E+03 -0.27694 0.31514 E+04

A(2) -0.40054 0.47589 E+01 0.45215 E-03 0.13714 E+02

A(3) 0.10815 E-02 0.10622 E-01 0.49008 E-05 0.35945 E-01

A(4) 0.12387 E-05 0.10416 E-04 0.88613 E-08 0.43525 E-04

A(5) 0.49002 E-09 0.37690 E-08 0.41387 E-11 0.19695 E-07

98
APPENDIX C. CALCULATION OF CRITICAL PRESSURE FOR TWO-PHASE FANNO FLOW

OF A NON-AZEOIROPIC MIXTURE

In this appendix, the procedure is explained for calculation of critical

pressure of a flow if mass flow rate and stagnation enthalpy are given. The

procedure focuses on the fact that Fanno flow assumes maximum entropy at the

flow critical pressure. Hence, the point of maximum entropy on the Fanno line

is being sought and once determined, the choking pressure is found.

Ihe entropy of two-phase flow is calculated by the equation:

8=8^+ x(Sy - 8^) (CI)

where s = entropy

X = quality

subscripts L and V refer to liquid and vapor phase, respectively,

being in equilibrium

The quality for Fanno flow can be found us-'"" the energy equation:

Iq = i + ^ • v^ (C2)

where G = mass flux

i = enthalpy

i^ = stagnation enthalpy

v = specific volume

IVo-phase specific enthalpy and specific volume are:

i = 11 + x(iy - i^) (C3)

V = Vl + x(vy - Vl) (C4)

Substituting and rearranging, the following quadratic equation can be

obtained [23]

x2+x-b+c=0 (C5)

where b =

- 2 (vy - Vl) . Vl . G^ + iy - JL

G^Cvy - Vl)^

,= iiikHiol , ^ 2

2 " *L 2 J (Vy - Vl)^

It should be noticed that saturated volumes of liquid and vapor and respective

enthalpies are uniquely defined at a given pressure for a single component

refrigerant. In such situation, refrigerant quality for a given Fanno flow can be calculated explicitly. When a non-azeotropic mixture is used, saturated liquid and vapor properties needed for evaluation of the quality are function of the quality thus an iterative procedure has to be used as shown

99
in the figure CI. Once the mixture quality (thus also temperature) at the

Fanno flow at a given pressure is known, entropies of the saturated liquid and

vapor are readily available and the flow entropy can be evaluated by equation

CI.

The above described equations and procedures are applied in a double precision

function, DFANNO, The Secant Method is used to provide the solution.

100
u

c

3

V)

111

C START ^

INPUT PRESSURE

I

GUESS TEMPERATURE

I CALCULATE XQ

I

[ CALCULATE Vy, V|., ly, i|.

I CALCULATE XQQ I

Figure CI.

XQ - quality calculated by equation of state

XQQ - quality calculated by equation C5

Logic to evaluate the quality of the Fanno flow at a given

pressure for a non-azeotropic mixture.

101

APPENDIX D. IHE LOGIC FOR THE MAIN PROGRAM, BMAIN

The principle of the logic for the heat pump model has been explained in

section 5.1. It is based on four balances:

- enthalpy balance

- pressure balance

- mass balance of non-azeotropic mixture

- mass balance of one of the mixture ccmponents

The enthalpy balance and pressure (mass flow rate) balance are interdependent

and have to be found in a simultaneous iteration process. Their solution

provides refrigerant properties in the system which are required for mass

inventory calculations. The balances are performed in the manner as shown in

figure Dl, which presents the logic developed during this study and contained

in the main program, BMAIN.

The objective of the logic is to iterate refrigerant states at key locations

of a heat pump for given outdoor and indoor conditions. Ihe addresses of the

key locations used in the program BMAIN are consistent with those marked in

figures 2 and Dl

:

1 - evaporator exit, suction tube inlet

2 - suction tube outlet, low pressure four-way valve inlet

3 - low pressure four-way valve exit, compressor can inlet

4 - inside compressor can

5 - compressor cylinder during suction stroke

6 - compressor cylinder during discharge

7 - discharge manifold

8 - compressor can exit, high pressure four-way valve inlet

9 - high pressure four-way valve exit, discharge tube inlet

10 - discharge tube outlet, condenser inlet

11 - condenser outlet, liquid line inlet

12 - liquid outlet, expansion device outlet

13 - evaporator inlet

The thermodynamic processes shown in figure Dl are covered by five subroutines: COMPRE, CONDHX, BLINE, CAPIL, and EVAPHX. The iteration process

starts with an estimated refrigerant pressure, superheat or quality at the

compressor can inlet, and an estimated compressor discharge pressure (points 3

and 6). From these data, the compressor simulation subroutine COMPRE computes

the refrigerant mass flow rate through the compressor and refrigerant parameters from point 1 to 10. The condenser and liquid line subroutines CONDHX

and BLINE are called next to perform calculations which yield refrigerant

states at point 11 and 12. Subsequently, the expansion device simulation

program, CAPIL computes refrigerant mass flow rate through the flow restrictor. At this point, the mass flow rate through the compressor, RMASS, and mass flow rate through the expansion device, XMASS, are compared and mass flow

balance is sought. This is done by resuming calculations by COMPRE, CONDHX,

BLINE, and CAPIL, holding constant refrigerant parameters at the compressor

can inlet (point 3) and adjusting refrigerant saturation temperature at discharge (point 6) until an appropriate saturation temperature at point 6 is

found at which RMASS and XMASS are equal.

103
The evaporator performance simulation routine, EVAPHX, was chosen in this

logic to be run after the mass flow balance between the compressor and expansion device has been found. (EVAPHX requires the most ccmputing time of all

the subroutines.) Evaporator simulation requires input of refrigerant mass

flow rate and refrigerant state at the evaporator inlet. The refrigerant

enthalpy at the evaporator inlet, H13, is equal to that at point 11, Hll,

since the thermodynamic processes in the liquid line and flow restrictor are adiabatic. The refrigerant pressure at evaporator inlet, P13, is unknown and

has to be guessed based on the known pressure at location 1 and the pressure

drop across the evaporator (if known from the previous simulation of the

evaporator) . The output from EVAPHX is pressure and enthalpy at evaporator

outlet, PIE and HIE, respectively. If the pressure PIE is not equal within

imposed tolerance to PI, pressure P13 has to be adjusted and evaporator simulation repeated. After the condition of equal PIE and PI pressures is satisfied, the refrigerant enthalpy at the evaporator outlet obtained from evaporator simulation, HIE, and enthalpy HI are compared. If these enthalpies are not equal, the refrigerant saturation temperature at the compressor can inlet

is adjusted and all calculations repeat.

Once an enthalpy balance and mass flow balance are established, two out of

four refrigerant parameters estimated at the outset are temporarily obtained.

To verify the third estimated parameter, i.e., the refrigerant vapor superheat

at the compressor can inlet, the refrigerant mass inventory in the system is

used. Each time the mass inventory is performed, it provides a result based

on refrigerant states in the system found after solving enthalpy and pressure

balances with the assumed vapor superheat (quality) at points 3 and refrigerant mixture composition. If the amount of refrigerant obtained from the mass inventory calculations is less than the refrigerant in the system, the

superheat (quality) estimate has to be decreased and all calculations have to

be repeated from the beginning.

After the refrigerant mixture mass inventory agrees with mass of charged

refrigerant, the mass inventory of one of the mixture components is made. If,

based on this inventory, calculated circulating mixture composition is not

equal (within imposed tolerance) to circulating composition estimated for use

for simulation calculations, new estimate for the circulating composition is

computed and all the calculations have to be repeated from the outset. If

the equality between the estimated and calculated compositions is obtained,

the iteration process is ended and the results are printed.

In the course of the computing process, the main program gathers information

about the heat pump components' performance, updated at each iteration loop,

and applies them to anticipate changes of some parameters caused by a change

in some state property. This allows for the iteration process to converge

faster with each iteration loop. The Secant Method is used in the solution of

the two most internal loops and the external loop of the main program. The

Binary Search Method was applied to the mixture mass inventory loop due to

highly non-linear characteristic of the accumulator.

104
r start J

f Input r*frlgarant data

Input heat pump daaign data

Input outdoor and Indoor air conditions

Input TG3, TSUP3, X3, TG6 (guasaes))

Composition of charged refrigerant

Composition of circulating refrigerant/ (guess)

COMPRE

CONDHX

~~T~

BLINE T

CAPIL

yes

yes

Adjust TG3

Adjust TSUP3

or X3

Adjust XW —

,

yes

/ Print results /

d^

Symb 1 s :

HI - refrig. enthalpy at evaporator outlet calculated by COMPRE

HIE - refrig. enthalpy at evaporator outlet caluclated by EVAPHX

H12 - refrig. enthalpy at point 12 H13 - refrig. enthalpy at point 13 PI - refrig. pressure at evaporator outlet calculated by COMPRE PIE - refrig. pressure at evaporator outlet calculated by EVAPHX REFIN - mass of refrig. charged into a machine RMASS - refrig. mass flow rate through a compressor

TG3 - refrig. dew point temp, at point 3 TG6 - refrig. dew point temp, at point 6 TMASS - total mass of refrig. calculated by inventory program

TSUP3 - refrig. superheat at point 3 XMASS - refrig. mass flow rate thronth an expansion device XW - circulating refrigerant mixture composition used for the calculations XWC - circulating refrigerant mixture composition resulting from the component refrigerant mass inventory

X3 - refrig. quality at point 3

BIMASS - calculates mass of refrigerant in a coil

Input: refrig. state at each coil tube end Output: mass of refrig. in a coil

BLIhfE - calculates pressure drop in a liquid line

Input: RMASS and refrig. state at point 11 Output: refrig. state at point 12 BPMASS - Calculates mass of refrig. in a tube Input: refrig. state at tube ends

Output: mass of refrig. in a tube CAPIL - calculates performance of an expansion device

Input: refrig state at point 12 and pressure at point 13 Output: XMASS

COfCPRE - calculates performance of a compressor with a 4-way valve

and tubing connecting eompresor with both coils

Input; refrig. state at point 3 and pressure at point 6 Output: RMASS and refrig. state at points 1 through 10 CONDHX - calculates performance of a condenser

Input: RMASS and refrig. state at point 10 Output: refrig. state at point 11 EVAPHX - calculates performance of an evaporator

Input: RMASS and refrig. state at point 13 Output: refrig. state at point 1 IVACCUM - calculates mass of refrigerant in an accumulator

Input: refrig. state in an accumulator

Output: mass of refrig. in an accumulator and mean refrig compos i t ion

Figure Dl . Overall logic of the program HPBI,

105

APPENDIX E. COMPRESSOR SIMULATION SUBROUTINE, COMPRE

Refer to figure 2 where the configuration of the main heat pump components is

shown. It was decided to include in one subroutine called COMPRE all

refrigerant processes from point 1 to point 10. The refrigerant path covered

by this subroutine consists of:

flow through a suction tube 1-2 and discharge tube 9-10 - flow through a reversing valve on suction side 2-3 and discharge

side 8-9

- flow through a compressor 3-8

Input data to COMPRE is detailed in comment statements inserted in the

program. Basically they consists of:

- connecting tubing design data

- compressor design and performance parameters

- four-way valve performance parameters

- refrigerant state at the compressor can inlet (point 3) - refrigerant pressure after compressor (point 6)

The design input data are explained in Table HS . The compressor performance

parameters include:

Ti- = electric motor efficiency versus load

RPM = electric motor speed (RPM) versus load

Tljjj = compressor mechanical efficiency

Cg = compressor effective clearance

T] = compressor polytropic efficiency

CPC34, CPC45, CPC67, CPC78 = pressure drop parameters

CQC4C, CQCCOA, CQC45, CQC67, CQC78 = heat transfer parameters

One of the parameters, the compressor mechanical efficiency, r\ , is assumed

here to be constant and equal to 0.96. The rest of the parameters can be

calculated by means of subroutine COMPAR using compressor test data. The

efficiency, r\^, and RPM as functions of mechanical load are both part of

typical electric motor characteristic for its class (see figures 11 and 13) . Coefficients describing these curves are required as an input to COMPAR. In

the course of calculations, new coefficients are computed which retain the

shape of the characteristic curves, although changes in absolute values of

efficiency, ti^, and RPM do occur according to test data supplied. The rest of

the parameters (compressor effective clearance, compressor polytropic efficiency, five heat transfer parameters, and four pressure drop parameters) are calculated by COMPAR using relations presented in section 5.2.2.

Subroutine COMPAR is incorporated in the general program HPBI and is called by

the main program, BMAIN. It is executed by running the HPBI program with

appropriate run control data input as explained in Appendix H.

Four-way valve performance parameters are the pressure drop parameter and

heat transfer parameter. These parameters are calculated by subroutine VALVPA

using four-way valve test data. Similar to the compressor case, VALVPA is a part of the program HPBI and can be accessed by executing it with appropriate

run control input data (refer to Appendix H)

.

107
Organization of COMPRE may be followed by examining the program listing with,

inserted comment statements. Based on a known refrigerant state at the can

inlet (point 3), refrigerant parameters at the suction valve (point 5) are estimated and since the compression pressure is given, the compression process

can be ccmputed. Using the refrigerant mass flow rate from this computation

and applying equations given in section 5.2.2, enthalpy and pressure balances

are conducted. If balance is not reached, the estimate of the refrigerant

state at the suction valve, point 5, is adjusted. Calculations are repeated

until balances are satisfied.

Once refrigerant states at compressor stations 3 to 8 and the mass flow rate

are known, the properties for other refrigerant paths are computed. Simulation of the four-way valve and tubes are done by routines MVAL4 and PIPE,

respectively.

The output from subroutine (X)MPRE is detailed in the program comment

statements and consists of refrigerant thermodynamic properties for points 1 to 10, refrigerant mass flow rate, compressor RPM, energy consumption rate,

electric motor efficiency, compression efficiency, and volumetric efficiency.

108
APPENDIX F. CONSTANT FLOW AREA EXPANSION DEVICE SUBROUTINE, CAPIL

The purpose of the capillary tube simulation subroutine is to calculate the

refrigerant mass flow rate when the capillary dimensions, refrigerant inlet

state, and pressure in the evaporator are given. Depending on the above

input, there are several possible capillary tube operation modes. For

example, the refrigerant can be either a single -or a two-phase state prior to

the tube entrance. If there is a two-phase mixture at the inlet (a highly

undesirable but possible condition under very low load operating conditions),

two-phase flow will exist along the whole tube length.

For a subcooled liquid at the inlet, there are three flow alternatives:

- liquid flow only along the whole tube length

- liquid flow in the first portion of the tube and two-phase flow in

the latter portion of the tube - two-phase flow only along the whole tube length

Each of the above flow situations can exist with or without choking condition

at the tube exit. The capillary tube simulation routine, CAPIL can distinguish among all of the above operational modes. During the course of the

calculations, the refrigerant critical pressure is found by routine CHOKE

using a binary search iteration method. Then equations (62), (67), and (72) are used to compute the refrigerant mass flow rate. The densitj^pressure

integral in equation (72) is evaluated by routine SIMP based on Simpson's

rule. An iteration solution is required to obtain the final simulation result

since choking pressure, friction factor, fractions of tube length with liquid

and two-phase flow, and the velocity head used to correct enthalpy are functions of refrigerant mass flow rate which has to be found. The Secant Method

is used in the iteration for the final CAPIL solution. The logic of the

routine CAPIL is presented in figure Fl . The input and output data are listed

in comment statements in this routine.

109
( tT«W ')

MFMSCBANT GOMHtSmH

EXPANSION KVKE LBNTO I MUD ML

WEPtK. ENTNM?Y MPME TNK ERnUNR

MFMC MCSSHNC MFMK TME ENTHMGE

KFWfi. PRESSWE IN EVfti»tRAT8N WESSEfi KFRM. HMS FUW MTE

Fme ALL REFNNL STATE PARAMETEK

lEFIWE E)VANSiaN KVICE ENTRANCE

|ll«Hltfat MMI

m

ASSIfiN REFRK. SAT. nKSSURE

AT TURE RUTLCT

fINfl MASS FLOW RATE HI

^ |2-^»t at IsMl ^ 1

ill = iUESStD'ilE^ kkti

NC IWOVE FLBW 'S-^.

CHOKED ?

YES

NO

fYES

"^r

FWD PFLASM PFLASM = n|

—^r __^

FWRNXIT

l»1

CALC. LEN6TN OF T1»E

WtTN SURCOOLER LMUIR RNO LEN6TN OF TURE

WITH 2n(ASE aiRf

i-wla$r:

PEXIT = refrigerant pressure at expansion device exit PFLASH = refrigerant flash pressure

PO = refrigerant pressure before expansion device inlet

PI = refrigerant pressure in expansion inlet X = refrigerant quality before expansion device inlet

YES

12-fiMM

to ttttiiktl

ARNISTII1

CALC. REFRIfi. MASS FLOW RATE M2

FOR 2-PHASE PORTION OF TURE

Figure Fl. Logic of a constant flow area expansion device simulation program.

CAPIL

110
APPENDIX G. EVAPORATOR AND CONDENSER SIMULATION SUBROUTINES, EVAPBX AND CONDHX

The tube-by-tube approach to coil simulation has been explained in section 5.4

where applicable heat, mass, and momentum transfer equations have also been

presented. Though the evaporator and condenser simulation programs require

somewhat different heat transfer relations, their logic is the same as shown

in figure Gl.

The input to coil simulation program are coil design data, refrigerant flow

distribution sequence, and air and refrigerant inlet conditions. During the

first bank of tubes' performance calculations, the air parameters upstream of

each tube row are estimated. The program then computes the heat transer rate

and pressure drop tube-by-tube from the inlet to the exit of the coil. Mean

refrigerant properties in each tube are used to calculate heat transfer rates

and pressure drops applying equations described in section 5.4. An iterative

procedure is used for each tube since only refrigerant conditions at tube

inlet are known when the calculations begin, and initially the average refrigerant properties in a tube have to be assumed to be those at the inlet conditions. Upstream air temperature and humidity ratio may not be accurately

known at the time tube performance is being calculated, so a second iterative

loop is used to update air-side data after each loop. It should be realized

that, while in the condenser case, update of air-side data means update of air

temperature and humidity ratio; for the evaporator it also includes liquid

(frost) layer thickness. When refrigerant enthalpy values at the coil exit

obtained from two consecutive loops are within the imposed tolerance, the

calculations of coil performance are completed and results printed.

Both the evaporator coil simulation model EVAFHX and condenser coil simulation

model C(^DHX comply with the logic and equations previously described. Input

and output data for these programs are detailed in comment statements at the

beginning of each subroutine. Other inserted comment statements along with

the flow chart (figure 61) facilitate the understanding of both program's

organization.

in
( START ") I

MPUT:

COIL GEOMHRY

KFRI6ERANT FLOW DISTRIBUTION^ AM INLET CONDITIONS KFRIGERANT INLET CONDITIONS i FRBERANT COIIPOSITION

ESTIMATE AIR PARAMETERS HPSTREAM EACH TUBE

SELECT^1TUBE FOR CALCULATIONS

ESTNIATE MEAN REFRIG PROPERTIES IN A TUBE

refrigerant enthalpy at tube end obtained from present

calculation loop

refrigerant enthalpy at tube end obtained from previous

calculation loop

refrigerant enthalpy at coil exit obtained from present

calculation loop

refrigerant enthalpy at coil exit obtained from previous

calculation loop

Figure Gl. Flow chart for coil performance simulation programs

112
APPENDIX H. PROGRAM USER'S GUIDE

HI. General Information

The simulation program of a heat pump charged with a non-azeotropic binary

mixture, HPBI, is written in Fortran 77 and makes use of standard Fortran

mathematical functions. It is built around the main program, BMAIN, and 65

subprograms for heat pump component simulation, and heat transfer, fluid

mechanics, and fluid property calculation. Relations used in the heat pump

component simulation subprograms, fluid mechanics, heat transfer and refrigerant property routines are described in the main text of this report.

Equations used in moist air, water and frost property routines are described

in Appendices A and B.

Tables HI, H2, and H3 list, by categories, all programs used in the heat pump

model. Short descriptions of applications are stated in the tables for each

program. A listing of all programs is given in Appendix J. A detailed

description with specification of input and output parameters is given in the

comment statements at the beginning of each program. Comment statements are also located within routines to facilitate understanding of the program

organization. Organization of principal program modules is explained in

Appendices D, E, F and G.

H2 . Input and Output Data Coding

There are five categories of input values for the HPBI runs, namely:

- refrigerant constants

- heat pump data

- run controlling data

- indoor and outdoor air conditions

- refrigerant parameters

H2.1 Refrigerant Constants

Refrigerant constants for evaluation of thermodynamic properties are read into

the program by subroutine BCONST from a disc file. File 7 is used in the

program for input of these data. Table H4 presents a proper format of

refrigerant data file. Comment statements inserted into subroutine BCONST

help to identify specific constants.

Refrigerant constants for evaluation of transport properties are contained in

function VISCON. Input of these data is not organized through reading of a data file since transport property constants may not have the same format for

all mixtures. This may be due to different availability of data as well

as different data possibly required by other kinds of mixing rules that could

be more applicable for the new mixtures under consideration. Thus, if a new mixture is to be examined, function VISCON has to be redone from the source element.

H2.2 Heat Pump Data

Heat pump data are read into the program by the main program, BMAIN, from a disc file. File 8 is used in the program for input of heat pump data. Coding

113
of these data is described in Table H5 which includes Fortran symbols with

their explanation. An example of a heat piunp data file is given in Table H6

.

Heat pump data include information about each modeled component, i.e., com- pressor, condenser, expansion device, evaporator, accumu.lator, four-way valve,

vapor line and liquid line. All components with the exception of the compressor and the four-way valve are described by design data only (dimensions,

material properties, coil circuitry, etc.). The compressor and the four-way

valve simulation also require performance parameters which are derived from

test information using subroutines COMPAR and VALVPA, respectively, included

in this report (see Appendix E) . The subroutines are run by executing the

HPBI program and providing appropriate run controlling data, as explained

below in this appendix. Heat pump data also include the amount of refrigerant

charge. This input is used in simulation runs in which iteration of refrigerant superheat (quality) at the compressor can inlet is required. For determining this input value refer to Oiapter 5.6.

H2.3 Run Controlling Data, Indoor and Outdoor Air Conditions, Refrigerant

Parameters and Output Data

This category of input data have to be contained in a runstream file or are read from a terminal if simulation run is executed in the interactive mode.

They are clearly requested by the program and responses have to be given in a Fortran free format.

The sequence of requests depends on the response to the first request given by

the program to determine which one of three possible tasks the user wants the

program to perform, i.e.,

1. evaluation of compressor parameters

2. evaluation of four-way valve parameters

3. simulation of heat pump performance

Evaluation of compressor parameters and evaluation of four-way valve

parameters has to be done once to generate performance parameters of these

components needed as input for simulation of performance of a heat pump

sy s t em

.

Evaluation of Compressor Parameters

The following is the sequence of program requests and explanation of reponses

for evaluation of compressor parameters:

1. Request: COMPRESSOR PARAMETER (1), FOUR-WAY VALVE PARAMETERS (2)

OR HEAT PUMP PERFORMANCE (3)

Response: 1

2. Request: DETERMINE COMPRESSOR PERFORMANCE PARAMETERS

ENTER: FOR PARTIAL TEST DATA OR 1 FOR FULL TEST DATA = Response: as explained in the request. Most likely user will not

have detailed compressor test data. Assume then that

response is

114
3. Request: ENTER: ELEFUL, ELEIPT, RPMCP. SWPVOL, RMASS, TOA = Response: ELEFUL = compressor motor energy input rate at max. rated

load (kW)

ELEIPT = compressor motor energy input rate at test

conditions (kW)

RPMCP = compressor number of revolution per minute at

test (1/min), enter if not measured.

SWPVOL = total compressor displacement volume per

revolution ( in ) RMASS = refrigerant mass flow rate at test conditions

(Ib/h)

TOA = ambient air temperature (F)

4. Request: WEIGHT COMPOSITION OF MIXTURE IN FRACTION OF MORE

VOLATILE COMPONENT, XW = Response: weight ccnnposition (decimal fraction)

5. Request: ENTER: T3 , P3 = Response: T3 = refrigerant temperature at compressor can inlet (F)

P3 = refrigerant pressure at compressor can inlet (psia)

6. Request: ENTER: T8, P8 = Response: T8 = refrigerant temperature at compressor can inlet (F)

P8 = refrigerant pressure at compressor can inlet (psia)

At this point, the program will evaluate refrigerant state at key compressor

locations and compressor parameters. Output symbols are explained in the

comment statements in the beginning of subroutine COMPAR. Note, that evaluation of compressor parameters requires information on standard electric motor

characteric (motor efficiency vs. load and RPM vs. load) that should be con- tained in the mass storage data file in lines 2, 3, 4, 5 and 6 as explained in

Table H5 . This file should be assigned to nimber 8 for program execution.

Evaluation of Four-Way Valve Parameters

The following is the sequence of program requests and explanation of responses

for evaluation of four-way valve parameters.

1. Request: COMPRESSOR PARAMETER (1), FOUR-WAY VALVE PARAMETRS (2) OR

HEAT PUMP PERFORMANCE (3)

Response: 2

2. Request: EVALUATION OF FOUR-WAY VALVE PARAMETERS, ENTER: T2, P2,

T3, P3 = Response: T2 = refrigerant temperature at valve low pressure inlet

(F)

P2 = refrigerant pressure at valve low pressure inlet

(psia)

T3 = refrigerant temperature at valve low pressure outlet

(F)

P3 = refrigerant pressure at valve low pressure outlet

(psia)

115
3. Request: ENTER: T8, P8, T9, P9 = Response: T8 = refrigerant temperature at valve high pressure inlet

(F)

PS = refrigerant pressure at valve high pressure inlet

(psia)

T9 = refrigerant temperature at valve high pressure

outlet (F)

P9 = refrigerant pressure at valve high pressure outlet

(psia)

4. Request: ENTER: RMASS, XW = Response: RMASS = refrigerant mass flow rate at test conditions

(Ib/h)

XW = refrigerant weight composition (decimal fraction

of the more volatile component)

At this point, the program will evaluate the four-way valve pressure drop

parameter, CPD, and heat transfer parameter, CQ. (All output symbols are explained in the comment statements in the beginning of subroutine VALVPA.)

Parameters CPD and CQ are to be included in heat ptunp data file in line 10 as explained in Table H5

.

Simulation of Heat Pump Performance

Simulation of heat pump performance is the ultimate purpose of the program

HPBI. Once the heat pump data file is completed with the compressor and fourway valve performance parameters, simulation runs of heat pump performance can

be conducted for a full range of operating conditions in the heating and

cooling mode.

The following is the sequence of program requests and explanation of responses

for the heat pump performance simulation run:

1. Request: COMPRESSOR PARAMETERS (1), FOUR-WAY VALVE PARAMETERS (2)

OR HEAT PUMP PERFORMANCE (3)

Response : 3

2. Request: ANSWER 1 FOR YES OR FOR NO

DO YOU WANT ANY INPUT DATA PRINTED? LPF = Response: for no input data print

or 1 for input data printout (request for specification of

desired data will follow)

3. Request: OUTDOOR AND INDOOR AIR CONDITIONS, POA, TOA, RHOA, PRA,

TRA, RHRA = ? Response: POA = outside air pressure (psia)

TOA = outside air temperature (F)

RHOA = outside air relative humidity (decimal fraction)

PRA = indoor air pressure (psia)

TRA = indoor air temperature (F)

RHRA = indoor air relative humidity (decimal fraction)

4. Request: NSYS = 1 FOR HEATING, NSYS = 2 FOR COOLING, NSYS = ? Response: as explained in the request

116
5. Request: IS ITERATION OF SUPERHEAT/ QUALITY REQUESTED?

ITER = FOR NO, ITER = 1 FOR YES, ITER = ? Response: as explained in the request

6. Request: IS ITERATION OF CIRCULATING COMPOSITION REQUESTED?

ITERXW = FOR NO, ITERXW = 1 FOR YES, ITERXW?

Response: as explained in the request

7. Request: COMPOSITION OF CHARGED REFRIGERANT = (WEIGHT FRACTION OF MORE VOLATILE COMPONENT)

Response: as explained in the request (decimal fraction)

8. Request: COMPOSITION OF CIRCULATING REFRIGERANT = (WEIGHT FRACTION OF MORE VOLATILE COMPONENT)

Response: as explained in the request (decimal fraction)

9. Request: REFRIGERANT STATE ESTIMATES: TG3, X3, TSUP3 , TG6

Response: TG3 = dew point temperature of refrigerant at the

compressor can inlet (F)

X3 = refrigerant quality at the compressor can inlet

(decimal fraction)

TSUP3 = refrigerant superheat at the compressor can inlet

(F)

TG6 = dew point temperature of refrigerant vapor in

compressor cylinder after compression

(all above values are estimates, subject to iteration)

At this point, the program starts to iterate the refrigerant thermodynamic

states at heat pump key locations following the logic explained in Appendix D.

Once a solution is obtained the results are printed in the format shown in a printout of an example run (Appendix I)

.

The output data consist of refrigerant thermodynamic states at 13 key heat

pump locations, identified on figure 4, along with results describing the heat

pump performance. Symbols used for output data have the following meaning:

T,P,H, S,X refrigerant temperature (F), pressure (psia), enthalpy

(Btu/lb), entropy, (Btu/(lb * F) , quality (decimal

fraction)

COP coefficient of performance (-)

ELUSE total heat pump energy consumption rate (kW)

QLOAD net capacity of the heat pump (Btu/h)

RMASS refrigerant mass flow rate (Ib/h)

TMASS refrigerant charge (lb)

TG3 refrigerant dew point temperature at compressor can

inlet

117
TG6 refrigerant dew point temperature at compressor delivery

valve (F)

TSUP3 refrigerant superheat at compressor can inlet (F)

The last three output data TG3 , TG6, and TSUP3 are final values iterated from

T&3, TCf6, and TSUP3 supplied as estimated input values.

It should be noted that the program prints the above results every time the

enthalpy loop and pressure loop are closed, and proceeds with further calculations until the mass inventories of the mixture and one of mixture components

are satisfied. The final results in the printout are the requested heat pump

performance data at the imposed operating conditions.

118
Table HI. Refrigerant Property Single Precision Functions and Subroutines

NAME

BUBPRE

BUBTEM

DEWPRE

DEWTEM

EBUBPR

EBUBTE

ENTROP

ENTR02

EQPAR

ESVOL

FGIBBS

HCVCP

HPAR

HPIN

HPPROP

PXQIN

PXQIN2

QLITY

SATCOM

SPIN

SAILIB

TPPROP

TXQIN

PURPOSE

Calculate bubble point pressure from a given composition and

temperature.

Calculate bubble point temperature from a given composition and

pressure.

Calculate dew point pressure from a given composition and

temperature.

Calculate dew point temperature from a given composition and

pressure

.

Estimate bubble point pressure from a given composition

and temperature.

Estimate bubble point temperature from a given composition

and pressure.

Calculate specific entropy of refrigerant being in a single

phase from given composition, temperature and specific volume.

Calculate specific entropy from given composition, temperature

and pressure.

Calculate parameters for the equation of state.

Estimate specific volume of liquid or vapor from given

composition, temperature and pressure

Calculate Gibbs free energy

Calculate enthalpy, specific heat at constant volume and

specific heat at constant pressure from given composition,

temperature, and specific volume.

Calculate parameters for calculation of specific enthalpy,

specific heat at constant volume, specific heat at constant

pressure and specific entropy.

Calculate temperature from given composition, enthalpy and

pressure

.

Calculate thermodynamic and transport properties from given

composition, pressure and enthalpy.

Calculate temperature of two-phase refrigerant from given

composition, pressure and quality.

Calculate temperature and enthalpy of two-phase refrigerant

from given conposition, pressure and quality.

Calculate quality of R13B1/R152a mixture from given

composition, temperature and pressure.

Calculate pressure, specific volume of liquid and specific

volume of vapor of mixture pure components at saturation from

given temperature.

Calculate temperature from given composition, entropy, and

pressure

.

Estimate saturation pressure, specific volume of liquid and

specific volume of vapor at given temperature for pure components,

Calculate specific enthalpy, specific volume and quality from

given composition, temperature and pressure.

Calculate pressure of two phase refrigerant from given

composition, temperature, and quality.

119
TXQIN2 Calculate pressure and specific enthalpy of two-phase

refrigerant from given composition, temperature and quality.

VISCON Calculate absolute viscosity and thermal conductivity of liquid

or vapor and specific heat of saturated liquid of R13Bl/RlS2a

mixture from given composition and temperature.

VOLITl Calculate specific volume from given composition, temperature

and pressure.

120
Table H2 . Refrigerant Property Double Precision Function and Subroutines

NAME PURPOSE

DBUBTE as BUBTEM (Table HI)

DDEWTE as DEWTEM (Table HI)

DENTRO as ENTROP (Table HI)

DH Calculate specific enthalpy from given composition,

and specific volume.

temperature

DQLIXy as QLITY (Table HI)

DVOLl as VOLITl (Table HI)

121
Table H3 . Functions and Subroutines for Heat P\unp Component Simulation, Heat

Transfer and Fluid Mechanics Calculations

NAME PURPOSE

AIRHT Calculate finned tube air-side heat transfer coefficient.

AIRPR Calculate air properties.

BCONST Read refrigerant constants for equation of state.

BIMASS Calculate mass of refrigerant in a coil.

BLINE Calculate frictional pressure drop in a liquid line.

BMAIN Main program, solution logic contained.

BPMASS Calculate mass of refrigerant in a tube.

BSIMP Integrate numerically using Simpson's 1/3 Rule.

CAPIL Simulate performance of a constant flow area expansion device.

CHOKE Calculate the thermodynamic critical pressure for a non- azeotropic mixture in two-phase Fanno flow.

COMPAR Evaluate compressor parameters.

COMPRE Simulate compressor performance.

CONDHX Simulate condenser performance.

DDENFA Calculate refrigerant density for two-phase Fanno flow (double

precision)

DFANNO Calculate refrigerant entropy for two-phase Fanno flow (double

precision)

DPDYNl Calculate dynamic pressure drop for a single-phase flow in a tube.

DPDYN2 Calculate dynamic pressure drop for a two-phase flow in a tube,

EVAPHX Simulate evaporator performance.

EVDP Calculate frictional evaporation pressure drop.

FINEFF Calculate fin efficiency.

FEELIQ Calculate Lockhart-Martinelli correction factor for two-phase

pressure drop.

HTCCON Calculate condensation heat transfer coefficient.

HTCEV Calculate evaporation heat transfer coefficient.

HXCODE Determine refrigerant and air flow distribution in a tube.

MVAL4 Simulate four-way valve performance.

OVLHTC Calculate overall heat transfer coefficient for a dry finned

tube

OVLWET Calculate overall heat transfer coefficient for a wet finned

tube

PFLASH Calculate flashing pressure and temperature for a Fanno flow.

PIPE Simulate flow through a tube.

SPHDPl Calculate frictional single-phase pressure drop in a tube.

SPHTC Calculate single-phase heat tranfer coefficient in a tube.

VALVPA Calculate four-way valve parameters.

WACCUM Calculate mass of refrigerant in accumulator.

WATPR Calculate water properties.

122
Table H4 . Data File Containing Constants for Evaluation of Thermodynamic

Properties of R13B1/R152a Mixture

1 25.4145,-0. 063368,4. 1 40051 E-05

2 0. 1353977, -1 . 50409E-04, -1 . 354434E-07

3 27.392729669, -0.059421 1671 ,3. 317695607E-5

4 0. 1239878, -1 . 44551 4007E-4 , -1 . 90223806E-8

5 0. 1466, -2. 241E-04

6 J48.93,66.05

7 340.15,386.65

® 10. 0522804 , -2204 . 5632, 9636 . 531

9 -0. 05060051 , 1 . 1455764E-03, -2. 56392871E-06

0.2749422, -1 . 702569E-03, 3. 71 00831 3E- 06

11 10, 6410518, -264 2. 8994,460. 87585

12 0,0218192958, 5 . 4 1 6820778E-04, -1 , 24731 336E- 06

13 0, 1023688715, -4 . 0752759E-04, 1 .0409447E-06

10

123
Line 1

Line 2

Line 3

Line 4

Line 5

Line 6

Line 7

Table H5 . Heat Pump Input Data Code to Program HPBI

All input data are in FORTRAN free field input format with data values on the same line separated by commas.

ATITLE

ATITLE = title, maximum 80 characters

EMETA(I), I = 1,5

EMETA(I) = compressor motor effiiency in fraction at fraction of

full load specified by EMOPT(I) , I = 1,5 (-)

EMETA(I), I = 6,11

EMETA(I) = compressor motor efficiency in fraction at fraction of

full load specified by EMOPT(I), I = 6,11 (-)

EMOPT(I), I = 1,5

EMOPT(I) = compressor motor full load fraction (decimal fraction)

EMOPT(I). I = 6,11

EMOPT(I) = compressor motor full load fraction (decimal fraction)

EMRPM(I), I = 1,6

EMRPM(I) = coefficient for compressor motor RPM calculations (-)

ELEFUL, SWPVOL, ETAPLY, CLREFF

ELEFUL = compressor motor energy input rate at max. rated load (kW)

SWPVOL = compressor displacement volume per revolution ( in ) ETALPY = compressor polytropic efficiency (-)

CLREFF = compressor clearance volume as fraction of displacement

volume (-)

Line 8 : CPC34, CPC45, CPC67, CPC78

CPC34 = pressure drop parameter at compressor can inlet

(dbf • h^)/(lb • in^ - ft^))

CPC45 = pressure drop parameter at compressor suction valve

(dbf • h^)/(lb • in^ • ft^))

CPC67 = pressure drop parameter at compressor discharge valve

(dbf • h2)/(lb • in^ • ft^))

CPC78 = pressure drop parameter at compressor can exit

(dbf • h^-^)/(lb • in^ • ft^*^))

Line 9 : CQC4C, CQCCOA. 0QC45, CQC67, CQC78

CQC4C = parameter for compressor can wall - refrigerant vapor heat

transfer (ft®"^)

CQCCOA = parameter for compressor can - ambient air heat transfer

(Btu/h • F^-^^^)

2 CQC45 = suction valve heat transfer parameter (ft • ) A O CQC67 = discharge valve heat transfer parameter (ft ) CQC78 = heat transfer parameter at can exit iit^'^)

Line 10 : CQ, CPDR, VCAN, REFIN

2 CQ = parameter for 4-way valve heat transfer (ft ) CPDR = pressure drop parameter for a 4-way valve (lbf*h /(lb*in *ft ) VCAN = volume of compressor can filled by liquid ( f t ) REFIN = refrigerant charge (lb)

Line 11 : AHGT, DACC, DHOLE(l), DH0LE(2), DTUBE, HDIS

AHGT = distance between accumulator top and oil return hole (ft)

DACC = inner diameter of accumulator (ft)

DHOLE(l) = diameter of oil return hole (ft)

DH0LE(2) = diameter of upper hole in accumulator tube (ft)

124
Line 12;

Line 13

Line 14

Line 15:

DTTJBE = diameter of accumulator tube (ft)

HDIS = vertical distance between holes in accumulator tube (ft)

NDEP(l). NROW(l)

NDEP(l) = number of indoor coil tube depth rows (-)

NROW(l) = number of tubes per indoor coil depth row (-)

Did), D0(1), DT(1), RPCH(l). DPCH(l), WIDTH(l)

Did) = inner diameter of indoor coil tubes (in)

DOd) = outer diameter of indoor coil tubes (in)

DT(1) = indoor coil fin tip diameter (in) (refer to figure 21)

RPCHd) = pitch between tubes of the same depth row in indoor coil

(in)

DPCHd) = pitch for indoor coil tube depth rows (in)

WIDTP9H(1) = indoor coil width (equal tube length) (in)

FPCH(l), FTK(l), FMKd), TMK(l). AMAS(l)

FPCH(l) = indoor coil fin pitch (in)

FTK(l) = indoor coil fin thickness (in)

FMK(l) = indoor coil fin material thermal conductivity

(Btu/(ft • h • F))

TMK(l) = indoor coil tube material thermal conductivity

(Btu/ft • h • F))

AMASd) = air mass flow rate through indoor coil (Ib/h)

CONST(l), CPOWd), ANGLE (1)

CONST(l) = constant for air side heat transfer correlation for

indoor coil equal to 0.134 (-)

CPOW(l) = constant for air side heat transfer correlation for

indoor coil equal to 0.681 (-)

ANGLE(l) = angle between indoor coil face and air streamlines (rad)

E IDFAN

EIDFAN = indoor fan energy input rate (kW)

NREPTI

NREPTI = number of repeating sections in indoor coil (-)

NTlBEd,!) I = 1.5

NTDBE(1,1) = number of tubes in first row in each section of indoor

coil (-)

NTDBE(1,2) = number of tubes in second row in each section of

indoor coil (-)

NTUBE(1,3) = number of tubes in third row in each section of indoor

coil (-)

NTUBE (1,4) = number of tubes in fourth row in each section of

indoor coil (-)

NTDBE(1,5) = number of tubes in fifth row in each section of

indoor coil (-)

Line 19 : IFR0M(1,I), I = 1,10

IFR0M(1,1) = number of tube of indoor coil from which tube 1 receives refrigerant when indoor coil works as evaporator (-)

IFR0M(1,2) = number of tube of indoor coil from which tube 2

receives refrigerant when indoor coil works as evaporator (-)

IFR0M(1.3) = IFR0M(1,9) = IFROMd.lO) = number of tube of indoor coil from which tube 10

receives refrigerant when indoor coil works as evaporator (-)

Line 16

Line 17

Line 18

125
Line 21

Line 22

Line 23

Line 24

Line 25

Line 26

Line 27

Line 28

Line 29

Line 30

Line 31

Line 32

Line 33

Line 20 ; IFR0M(1,I), I = 11,20

IFROMd,!) = number of tube of indoor coil from which tube I receives refrigerant when indoor coil works as evaporator (-)

IFROMd, I), I = 21,30

IFROMd, I), I = 31,40

IFROMd, I), I = 41,50

IFROMd, I), I = 51,60

IFROMd, I), I = 61,70

IFROMd,!), I = 71,80

IFROMd, I), I = 81,90

IFROMd,!), I = 91,100

IFROMd, I), I = 101,110

IFROMd,!), I = 111,120

IFROMd,!), I = 121,130

!FR0M(1,!) = number of tube of indoor coil from which tube I receives

refrigerant when indoor coil works as evaporator (-)

NDEP(2), NR0W(2)

NDEP(2) = number of outdoor coil tube row depths (-)

NR0W(2) = number of tubes per outdoor coil depth row (-)

D!(2), D0(2), DT(2), RPCH(2), DPCH(2), WIDTH(2)

D!(2) = inner diameter of outdoor coil tubes (in)

D0(2) = outer diameter of outdoor coil tubes (in)

DT(2) = outdoor coil fin tip diameter (in) (refer to figure 21)

RPCH(2) = pitch between tubes of the same depth in outdoor coil

(in)

DPCH(2) = pitch between tube depth rows for outdoor coil (in)

W!DTH(2) = outdoor coil width (equal tube length) (in)

Line 34 ; FPCH(2), FTK(2), FMK(2) , TMK(2) , AMAS(2)

FPCH(2) = outdoor coil fin pitch (in)

FTK(2) = outdoor coil fin thickness (in)

FMK(2) = outdoor coil fin material thermal conductivity

(Btu/(ft • h • F))

TMK(2) = outdoor coil tube material thermal conductivity

(Btu/(ft • h • F))

AMAS(2) = air mass flow rate through outdoor coil (Ib/h)

Line 35 ; C0NST(2), CP0W(2), ANGLE(2)

C0NST(2) = constant for air side heat transfer correlation for

outdoor coil equal to 0.134 (-)

CP0W(2) = constant for air side heat transfer correlation for

outdoor coil equal to 0.681 (-)

ANGLE(2) = angle between outdoor coil face and air streamlines

(rad)

Line 36 ; E IDFAN

EIDFAN = outdoor fan energy input rate (kW)

Line 37 ; NREPTO

NREPTO = number of repeating sections in outdoor coil (-)

Line 38 ; NTIBE(2,I). I = 1.5

NTUBE(2,1) = number of tubes in first row in each section of

outdoor coil (-)

NTUBE(2,2) = number of tubes in second row in each section of

outdoor coil (-)

NTUBE(2,3) = number of tubes in third row in each section of

outdoor coil (-)

126
NTDBE(2,4) = number of tubes in fourth row in each section of

outdoor coil (-)

NTDBE(2,5) = number of tubes in fifth row in each section of

outdoor coil (-)

Line 3 9 : IFR0M(2,I), I = 1,10

IFR0M(2,1) = number of tube of outdoor coil from which tube 1 receives refrigerant when outdoor coil works as evaporator (-)

IFR0M(2,2) = number of tube of outdoor coil from which tube 2

receives refrigerant when outdoor coil works as evaporator (-)

IFROM(2,3) =

Line 41:

Line 42:

Line 43:

Line 44:

Line 45:

Line 46:

Line 47:

Line 48:

Line 49:

Line 50:

Line 51:

IFROM(2,9) = IFROM(2,10) = number of tube of outdoor coil from which tube 10

receives refrigerant when outdoor coil works as evaporator (-)

Line 40 : IFR0M(2,I), I = 11,20

= nvimber of tube of outdoor coil from which tube I receives refrigerant when outdoor coil works as evaporator (-)

, I = 21,30

, I = 31.40

I = 41,50

, I = 51,60

I = 61,70

I = 71,80

I = 81,90

I = 91,100

I = 101,110

I = 111,120

I = 121,130

= niimber of tube of outdoor coil from which tube I receives refrigerant when outdoor coil works as evaporator (-)

Line 52 : CAPIDl, CAPLl, NCPLl, CAPID2, CAPL2, NCPL2

CAPIDl = inner diameter of cooling operation expansion device (in)

CAPLl = length of cooling operation expansion device (in)

NCPLl = number of cooling operation expansion devices (-)

CAPID2 = inner diameter of heating operation expansion device (in)

CAPL2 = length of heating operation expansion device (in)

NCPL2 - number of heating operation expansion devices (-)

Line 53 : YL, YD, YKl , YDl, YK2, YD2

YL = length of compressor-outdoor coil tubing (in)

YD, inner diameter of compressor-outdoor coil tubing (in)

YKl = thermal conductivity of compressor-outdoor coil tubing

material (Btu/(ft * h ' F))

YDl = outer diameter of compressor-outdoor coil tubing (in)

YK2 = thermal conductivity of compressor-outdoor coil tubing

insulation (Btu/(ft * h * F))

YD2 = outer diameter of compressor-outdoor coil tubing insulation

(Btu/(ft • h • F))

IFR0M(2,I)

IFR0M(2,I)

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

IFR0M(2,I),

127
Line 54 : RL. RD, RKl, RDl, RK2, RD2

RL = length of compressor- indoor coil tubing (in)

RD = inner diameter of compressor-indoor coil tubing (in)

REl = thermal conductivity of compressor-indoor coil tubing

material (Btu/(ft • h • F))

RDl = outdoor diameter of compressor-indoor coil tubing (in)

RK2 = thermal conductivity of compressor-indoor coil tubing

insulation (Btu/(ft * h • F))

RD2 = outer diameter of compressor-outdoor coil tubing insulation

(Btu/(ft • h • F))

Line 55 : RYL, RYD

RYL = liquid line length (in)

RYD = liquid line diameter (in)

Note on coil input data:

The coil depth is in the direction perpendicular to a coil surface facing the

incoming air. Lines 19-31 and 39-51: tubes are numbered consecutively from

the first tube in the first row (facing incoming air) to the last tube in the

last row. Enter (zero), if considered tube receives refrigerant from coil

inlet port*, enter 999, if the tube is nonexistent.

128
Table H6 . Example of a Heat Pump Data File

1 ***SYST4 WITH ACCUM., 13B1/152A 6-22-84**«

2 3.9,3.64,0.706,0.06315

3 0. 2076, 0. 34 90, 0. oGG5, 0. 6803, 0. 72CS

4 0.7523,0.7712,0.7821 ,0.7900,0. 7929, 0. 7940

5 0.05,0.1,0.2,0.3,0.4

6 0.5, 0. 6, 0. 7,0. 8,0. 9, 1 .0

7 3578 , -36. 01 , -39. 0558, 22. 2747, -40. 971 2, 14 . 7620

8 5.266E-7, 1 . 504E-5, 3. 603E-4, 1 . 173E-4

9 10. 16,5. 279, 0.2060,0.2027, 2. 893

10 0, 968,4. 47E-5,0. 104, 5.082

11 0.92,0.42, 0. 0029, 0. 0033,0. 0625, 0. 27

12 4,36

13 0.31 1 ,0. 375, 1 . 056, 1,0.875, 18.

14 0.068,0.008, 1 18. ,223. ,5000.

15 0. 134,0. 681 , 1 . 13

16 0.485

17 2

18 18,18,18,18,0

19 2,3,4,5,6,7,69,9,10,11

20 12,13,14,33,0,15,16,17,1,19

21 20,21,22,23,24,8,26,27,28,29

22 30,31,51,35,53,18,38,39,40,41

23 42,61,25,45,46,47,48,49,68,32

24 52,34,71,36,37,55,56,57,58,59

25 43,44,62,63,64,65,66,50,70,52

26 72, 54, 999, 999, 999, 999, 999, 999, 999, 999

27 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

28 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

29 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

30 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

31 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

32 3,20

33 0.31 1 ,0.375, 1 .338, 1 . 25, 1 . 1 25, 40.

34 0. 075,0. 008, 1 18. , 223. , 10700.

35 0.134,0.681,1.52

36 0.380

37 1 36 20,20,20,0,0

39 21,1,2,3,6,7,8,48,0,9

40 12,10,33,13,14,15,18,19,20,40

41 41,43,44,44,24,46,28,49,50,11

42 11,52,34,55,56,54,36,58,59,60

43 42,22,23,45,27,25,26,47,29,30

44 31,51,32,53,35,57,37,37,38,39

45 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

46 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

47 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

48 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

49 999, 999, 999, 999, 999, 999, 999, 999, 999, 999

50 999, 99S, 999, 999, 999, 999, 999, 999, 999, 999

51 999, 999, 999 . 999, 999, 999, 999, 999, 999, 999

52 0.08202,0.5,1,0.09,0.5,1

53 192, ,0,68,223. ,0.75,0.05, 1 .5

54 36. , 0, 68,223, ,0.75,0. ,0.

55 312. ,0,249

129

APPENDIX I. EXAMPLE OF RUN OF THE PROGRAM HPBI

The following is a computer printout for a HPBI run in which performance of a heat pTunp in the heating mode was simulated. Input for this run was as follows:

- refrigerant data - as shown in Table H4 - heat pump data - as shown in Table H6 - run controlling data, operating conditions, estimated refrigerant

parameters - as shown on the printout (lines 4-36).

The results of this run are included in Table 5.

The solution was iterated in two loops iterating composition of the

circulating refrigerant (lines 39-2592 and 2593-4762). The second loop

required eight internal loops in which the total refrigerant mass conservation

was sought (TMASS = REFIN) . The run required 33 minutes of CPU on a Sperry

1100/82 computer.

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APPENDIX J. LISTING OF THE PROGRAM, HPBI

The following is a complete listing of the program HPBI. All source elements

of the program are listed in alphabetical order. For fast reference, the

reader can review Tables HI, H2 and H3 , which contain name lists of all

functions and subroutines with a short statement of their purpose.

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NBS-114A (REV. 2-BC) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBS/TN-1218

2. Performing Organ. Report No. 3. Publication Date

January 1986

4. TITLE AND SUBTITLE

MODELING OF A HEAT PUMP CHARGED WITH A NON-AZEOTROPIC REFRIGERANT MIXTURE

5. AUTHOR(S)

Piotr Domanski

6. PERFORMING ORGANIZATION (if joint or other thon NBS. see instructions)

National Bureau of Standards

Department of Commerce

Gaithersburg, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

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

Electric Power Research Institute

3412 Hi 11 view Avenue

P.O. Box 10412

Palo Alto, California 94303

10. SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, PIPS Software Summary, is attached.

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

bibliography or literature survey, mention it here)

An analysis of the vapor canpression cycle and the main components of an airto-air heat pump charged with a binary non-azeotropic mixture has been perfonned for

steady-state operation. The general heat pump simulation model HPRI has been foniiu- lated which is based on independent, analytical models of system components and the logic linking them together. The logic of the program requires an iterative solution

of refrigerant pressure and enthalpy balances, and refrigerant mixture and individual

mixture component mass inventories.

The modeling effort emphasis was on the local thennodynanic phenanena which were described by fundamental heat transfer equations and equation of state relationships

among material properties. In the ccmpressor model several refrigerant locations were identified and the processes taking place between these locations accounted for

all significant heat and pressure losses. Evaporator and condenser models were developed on a tube-by-tube basis where performance of each coil tube is canputed

separately by considering the cross-flow heat transfer with the external air stream

and the appropriate heat and mass transfer relationships. A capillary tube model was formulated with the aid of Fanno flow theory. Equation of state for mixtures is described and equation constants for R13B1/R152a mixture are given. The developed heat pump model was validated by checking computer results against

laboratory tests data of one heat pump at two cooling and two heating rating points.

Program HPBI can be used to evaluate potentials of non-azeotropic mixtures

working in a heat pump. User's Manual and listing of the program is included in the report.

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

air conditioner; capillary tube; coil; compressor; condenser; expansion device; heat

pump; modeling; mixture; non-azeotropic refrigerant; vapor modeling cycle

13- AVAILABILITY

[V] Unlimited

lJ For Official Distribution, Do Not Release to NTIS

[\n Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

QJ] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

391

15. Price

USCOMM-DC «043-PeO


I
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