Design methodology and experimental verification used to

DESIGN METHODOLOGY AND EXPERIMENTAL VERIFICATION USED TO OPTIMIZE LIQUID OVERFEEDING

EFFECTS ACHIEVED WITH HEAT EXCHANGER ACCUMULATORS

by

Craig Willoughby Wood

A project submitted in partial fulfilment of the

requirements for the degree of

MAGISTER INGENERIAE

in

MECHANICAL AND MANUFACTURING ENGINEERING

at the

FACULTY OF ENGINEERING

of the

RAND AFRIKAANS UNIVERSITY

JULY 1999

Supervisor : Professor Josua P. Meyer

Work hard!

But give the glory to the Father above;

For all good gifts come from His hand as tokens of His love.

Gustafson

Abstract

This study involves the mathematical modeling and experimental verification of a

heat exchanger accumulator. The study was initiated with a literature survey which,

according to the author, revealed that there was no published material that described

how heat exchanger accumulators are designed to ensure that they are correctly sized

according to the operating system and conditions. The heat exchange process that

takes place within the heat accumulator was studied and a mathematical model of a

heat exchanger accumulator developed. This model was used to develop a universal

design procedure that correctly sized the heat exchanger accumulator according to

various requirements identified by the author. The model was then verified by

conducting experimental tests and it was concluded that the model could be used to

design heat exchanger accumulators.

Keywords

heat exchanger accumulator

design experimental verification

liquid overfeeding refrigerant 22

Acknowledgements

I would like to thank Mr. Phillip Nel of York-Miac, South Africa for the donation of

the small air conditioning system used for the experimental section of this work.

Gratitude is extended to ESKOM and the Foundation for Research Development for

financial assistance.

I am tremendously grateful to Professor Meyer for his continuos support, assistance

and advice. His guidance has been of great value and I am exceptionally grateful for

the opportunities he gave me to present my work at the Eurotherm No 59 Conference

held in Nancy France, the 1998 International Mechanical Engineering Congress and

Exposition held in Anaheim, California, U.S.A, the 1999 Domestic Use of Electrical

Energy Conference held in Cape Town, R.S.A, the 1999 International Mechanical

Engineering Congress and Exposition held in Nashville, Tennessee, U.S.A and the

2000 South African Conference on Applied Mechanics held in Durban, R.S.A.

Many thanks go to Mr. Karl Holm whose contributions throughout the practical

section of this project have been invaluable.

A very special thank-you goes out to Kirsten de Villiers for her never-ending love,

support and encouragement.

ii

Table of Contents

Abstract i

Keywords i

Acknowledgements ii

Table of Contents iii

List of Figures xi

List of Tables xiv

Introduction 1

Heat Exchanger Accumulators 5

Mathematical Model 8

Application of Design Method 17

Experimental Verification 20

Discussion of Results 24

Conclusion 26

Nomenclature 28

References 31

iii

APPENDIX A : PREDICTION AND VERIFICATION OF HEAT TRANSFER

COEFFICIENTS OF REFRIGERANTS DURING EVAPORATION A-1

A.1 Introduction A-1

A.2 Implementation A-4

A.3 Comparison and Conclusion A-10

A.4 Nomenclature A-12

A.5 References A-14

APPENDIX B : DERIVATION OF A FORMULA TO CALCULATE THE LENGTH OF

THE COIL IN THE HEAT EXCHANGE ACCUMULATOR B-1

B.1 Introduction B-1

B.2 Theoretical Background B-1

B.3 Derivation B-4

B.4 Conclusion B-5

B.5 Nomenclature B-6

B.6 References B-8

iv

APPENDIX C : INTERPRETATION OF COMPRESSOR CURVES USING

ISENTROPIC AND VOLUMETRIC EFFICIENCIES C-1

C.1 Introduction C-1

C.2 Theoretical Background C-1

C.3 Graphs C-8

C.4 Verification of Equations C-12

C.5 Conclusion C-13

C.6 Nomenclature C-14

C.7 References C-14

APPENDIX D : DETERMINATION OF LOCAL HEAT TRANSFER COEFFICIENTS

WITHIN THE HEAT EXCHANGE ACCUMULATOR D-1

D.1 Introduction D-1

D.2 Theoretical Background D-2

D.3 Simulation D-4

D.4 Discussion of Results D-17

D.5 Conclusion D-21

D.6 Nomenclature D-22

D.7 References D-25

v

APPENDIX E : DERIVATION OF AN EQUATION THAT DETERMINES THE

REFRIGERANT MASS FLOW RATE FOR AN ACCUMULATOR HEAT EXCHANGER AT

A SPECIFIED RANGE OF AMBIENT CONDITIONS E-1

E.1 Introduction E-1

E.2 Derivation of a general equation for refrigerant mass flow E-2

E.3 Equation Accuracy E-4

E.4 Alternative Verification Method E-5

E.5 Discussion of Results E-9

E.6 Nomenclature E-10

E.7 References E- 1 1

APPENDIX F : DERIVATION OF AN EQUATION THAT DETERMINES THE

ENTHALPY DIFFERENCE IN THE HEAT EXCHANGER ACCUMULATOR FOR A

SPECIFIED RANGE OF AMBIENT CONDITIONS F-1

F.1 Introduction F-1

F.2 Theoretical Background F-1

F.3 Derivation of a general equation for the enthalpy difference F-2

F.4 Equation Accuracy F-4

F.5 Discussion of Results F-4

F.6 Nomenclature F-5

F.7 References F-5

vi

APPENDIX G : MATHEMATICAL MODELLING OF HEAT TRANSFER WITHIN

THE HEAT EXCHANGE ACCUMULATOR WITH THE AIM OF DETERMINING THE

REQUIRED COIL LENGTH G-1

G.1 Introduction G-1

G.2 Theoretical Background G-2

G.3 Simulation G-5

G.4 Interpretation of Results G-9

G.5 Conclusion G-11

G.6 Nomenclature G-12

G.7 References G-14

APPENDIX H : MATHEMATICAL SIZING OF HEAT EXCHANGE ACCUMULATOR .. H-1

H.1 Introduction H-1

H.2 Evaluation of previous design method H-1

H.3 New Accumulator Design Process H-2

H.4 Design H-5

H.5 Heat Transfer Coefficients H-6

H.6 Heat Exchange Accumulator Size H-10

H.7 Conclusion H-11

H.8 Nomenclature H-11

H.9 References H-13

vii

APPENDIX I : SIZING OF A HEAT EXCHANGE ACCUMULATOR FOR A SMALL

AIR CONDITIONING SYSTEM

I.1 Introduction I-1

1.2 Practical system I-1

1.3 Heat exchange accumulator design 1-3

1.4 Conclusion 1-7

1.5 Nomenclature 1-7

1.6 References 1-8

APPENDIX J : INVESTIGATION OF THE INFLUENCE OF VARYING AMBIENT

TEMPERATURES ON COIL LENGTH J-1

J.1 Introduction J- 1

J.2 Investigation J-1

J.3 Conclusion J-5

J.4 Nomenclature J-6

J.5 References J-7

APPENDIX K : EXPERIMENTAL TESTING AND DATA MANIPULATION

PROCEDURE K-1

K.1 Introduction K-1

K.2 Experimental Set-up K-1

viii

K.3 Experimental Procedure K-2

K.3.1 Charging the System K-2

K.3.2 Experimental Data Equipment K-3

K3.3 Experimental Results and Data Manipulation K-5

K.4 Application Example K-10

K.5 Conclusion K-11

K.6 Nomenclature K-11

K.7 References K-12

APPENDIX L : INITIAL EXPERIMENTAL TESTING AND VERIFICATION OF

RESULTS L-1

L.1 Introduction L-1

L.2 Experimental Method L-1

L.2.1 Test 1 — Baseline test at low fan speed L-1

L.2.2 Test 2 — Baseline test at high fan speed L-3

L.2.3 Test 3 — Accumulator test at low fan speed L-3

L.2.4 Test 4 — Accumulator test at high fan speed L-4

L.3 Experimental Results L-4

L.3.1 Test 1— Baseline test at low fan speed L-4

L.3.2 Test 2 — Baseline test at high fan speed L-6

L. 3.3 Test 3 — Accumulator test at low fan speed L-7

L.3.4 Test 4 — Accumulator test at high fan speed L-8

L.4 Verification of Baseline Test Results L-9

L.5 Discussion of Results L-10

ix

L.6 Conclusion L-16

L.7 Nomenclature L-17

L.8 References L-18

APPENDIX M : LIQUID OVERFEEDING EXPERIMENTAL TESTING AND

ANALYSIS OF RESULTS M-1

M.1 Introduction M-1

M.2 Liquid Overfeeding M-1

M.3 Experimental Method M-2

M3.1 Test 1 - Baseline test at high fan speed M-2

M 3.2 Test 2 — Accumulator test at high fan speed M-4

M3.3 Test 3 — Liquid overfeeding test at high fan speed M-4

M.4 Experimental Results M-5

M4.1 Test 1 — Baseline test at high fan speed M-5

M4.2 Test 2 — Accumulator test at high fan speed M-6

M4.3 Test 3 — Liquid overfeeding test at high fan speed M-7

M.5 Discussion of Results M-8

M.6 Conclusion M-13

M.7 Nomenclature M-14

M.8 References M-15

List of Figures

Figure 1 Temperature — entropy diagram and heat exchanger accumulator 8

Figure 2 Heat transfer coefficients calculated using the Jung and

Radermacher (1991) equation (for qualities x < 1) and the Dittus-

Boelter equation (for qualities x 1) for a range of coil lengths 11

Figure 3 Critical diameters of the heat exchanger accumulator 15

Figure 4 Schematic diagram of experimental set-up with measuring points 20

Figure 5 Influence of the heat exchanger accumulator on the experimental

system 23

Figure A-1 Chart comparing Jung's predicted/measured values and the

values calculated using Jung's correlation A-10

Figure B-1 Temperature — entropy diagram and heat exchange accumulator B-1

Figure C-1 Temperature — Entropy diagram for vapour-compression cycle C-3

Figure C-2 Tecumseh AJ5515F capacity curve in SI units at 50Hz, 220V C-8

Figure C-3 Tecumseh AJ5515F mass flow curve in SI units at 50Hz, 220V C-9

Figure C-4 Tecumseh AJ5515F compressor power curve in SI units at 50Hz,

220V C-9

xi

Figure C-5

Graph showing isentropic efficiency versus compression ratio for

Tecumseh AJ5515F compressor at 50Hz, 220V C-10

Figure C-6 Graph showing volumetric efficiency versus compression ratio

for Tecumseh AJ5515F compressor at 50Hz, 220V C-10

Figure D-1

Figure D-2

Figure D-3

Figure D-4

Figure D-5

Figure D-6

Figure D-7

Figure D-8

Figure D-9

Figure D-10

Temperature-entropy diagram of ideal process D-4

Figure illustrating critical diameters D-7

Figure illustrating average diameter of coil D-7

Figure illustrating coil-winding diameter with respect to heat

exchange accumulator diameter where D = DHXA D-9

Graph showing heat transfer coefficients as a function of quality

for a heat exchange accumulator inner diameter of 0.03m D-12









Graph illustrating relationship between Jung and Radermacher

and Dittus-Boelter (DB) methods of calculation D-20

xii

Figure E-1 Graph illustrating density of R-22 at compressor inlet (35°C) for

evaporating temperatures ranging from -12°C to 12°C E-6

Figure F-1

Temperature — entropy diagram and heat exchange accumulator. F-1

Figure F-2

Graph illustrating the enthalpy difference (hl - h8) for

evaporating temperatures ranging from -12°C to 12°C F-3

Figure G-1

Temperature — entropy diagram and heat exchange accumulator..... G-2

Figure G-2

Graph illustrating the relationship between the coil length and

accumulator diameter G-9

Figure H-1

Figure illustrating heat exchange accumulator with solid centre H-2

Figure H-2 Temperature — entropy diagram and heat exchange accumulator H-2

Figure H-3

Figure illustrating critical diameters H-4

Figure H-4

Outer heat transfer coefficients at A.R.I. conditions H-9

Figure I-1

Diagram of air conditioner used for practical tests 1-2

Figure 1-2

Figure illustrating critical diameters 1-3

Figure K-1 Schematic diagram of experimental set-up with measuring points....K-1

List of Tables

Table 1 Mass flow rate coefficients 13

Table 2 Technical data of experimental air conditioning unit 17

Table 3 Physical accumulator dimensions as determined by the design

procedure 17

Table 4 Calculated results for application example 18

Table 5 Comparison of the baseline experimental results to that of the

steady-state model of the high-pressure side of a unitary air

conditioning unit and to the results obtained using HPSIM. 22

Table A-1 Summary of heat transfer coefficient correlation by Jung et al A-3

Table A-2 Table of calculated local and average heat transfer coefficients

for R-22 using Jung's correlation A-5


for R-143a using Jung's correlation A-6




for R-141b using Jung's correlation A-8



Table A-7 Table showing average and mean deviation of local and average

calculated heat transfer coefficients from Jung's prediction A-11

xiv

Table B-1 Summary of heat transfer coefficient correlation by Jung et al B-4

Table C-1 Tables showing conversion of data from 60Hz to 50Hz and to SI

units. C-2

Table C-2 Tables showing Tecumseh AJ5515F data for various evaporating

and condensing temperatures C-4

Table C-3 Tables showing enthalpy values and calculated values for the

Tecumseh AJ5515F compressor at various evaporating and

condensing temperatures C-5

Table C-4 Tables showing calculated values for the Tecumseh AJ5515F

compressor at various evaporating and condensing temperatures C-7

Table C-5 Curve-fitting coefficients for isentropic efficiency C-11

Table C-6 Curve-fitting coefficients for volumetric efficiency C-11

Table C-7 Table illustrating accuracy of isentropic efficiency equation. C-12

Table C-8 Table illustrating accuracy of volumetric efficiency equation C-13

Table D-1 Summary of heat transfer coefficient correlation by Jung and

Radermacher D-3

Table D-2 Table of initial known values required for the simulation D-5

Table D-3 Jung and Radermacher method used to calculate heat transfer

coefficients for an internal heat exchange accumulator diameter

of 0.03m and a coil length of 100m D-11

xv

Table D-4 Jung and Radermacher heat transfer coefficients for various

lengths and a heat exchange accumulator inner diameter of 0.03m D-12









Table D-9 Table of calculated heat transfer coefficients for various internal

heat exchange accumulator diameters using the Dittus-Boelter

equation D-17

Table D-10 Table illustrating relationship between Jung and Radermacher

and Dittus-Boelter (DB) methods of calculation D-20

Table E-1 Table illustrating matrices [A] and [B] E-3

Table E-2 Table shown coefficients for mass flow rate calculations E-3

Table E-3 Table illustrating accuracy of Equation E-1 when used to

determine mass flow rate E-4

Table E-4 Table illustrating matrices [A],[B] and [X] for volumetric

efficiency E-7

Table E-5 Table shown coefficients for mass flow rate calculations E-7

xvi

Table E-6 Table illustrating accuracy of Equation E-1 when used to

determine volumetric efficiency E-8

Table E-7 Table showing alternative verification method E-9

Table F-1 Table illustrating enthalpies F-3

Table G-1 Table showing thermodynamic properties of R-22 at A.R.I.

conditions and other input variables G-6

Table G-2 Preliminary calculations of variables not dependent on DHXA G-7

Table G-3 Calculation of variables dependent on DHXA G-8

Table H-1 Tables illustrating basic refrigerant properties at A.R.I.

conditions H-7

Table H-2 Table illustrating Jung and Radermacher calculation procedure

for a coil length of 0.1m H-8

Table H-3 Heat transfer coefficients as calculated by the Dittus-Boelter

Equation H-9

Table I-1 Air conditioner specifications I-1

Table 1-2 Critical lengths and diameters relating to Figure I-1 1-2

Table 1-3 Table illustrating accumulator dimensions 1-4

xvii

Table 1-4 Refrigerant R-22 properties at an evaporating temperature of 7°C

and a condensing temperature of 50°C 1-5

Table 1-5 Dittus Boelter heat transfer coefficients 1-6

Table J-1 Refrigerant R-22 properties at an evaporating temperature of -

3°C and a condensing temperature of 60°C J-2

Table J-2 Dittus Boelter heat transfer coefficients J-3

Table J-3 Refrigerant R-22 properties at an evaporating temperature of -

3°C and a condensing temperature of 60°C J-4

Table J-4 Dittus Boelter heat transfer coefficients J-5

Table K-1 Table showing experimental results and their manipulation

according to the method discussed in this Appendix K-10

Table L-1 Table showing measured properties and symbols under which the

quantity was recorded L-2

Table L-2 Extra measurements and corresponding symbols taken with

accumulator added to baseline system L-4

Table L-3 Experimental averages and calculations for Test 1 — Baseline test

at low fan speed L-5

Table L-4 Experimental averages and calculations for Test 2 — Baseline test

at high fan speed L-6

xviii

Table L-5 Experimental averages and calculations for Test 3 — Accumulator

test at low fan speed L-7

Table L-6 Experimental averages and calculations for Test 4 — Accumulator

test at high fan speed L-8

Table L-7 Table showing the comparison of the low fan speed experimental

results to that of the steady-state model of the high-pressure side

of a unitary air conditioning unit and to the results obtained using

HP SIM L-9

Table L-8 Table showing the comparison of the high fan speed

experimental results to that of the steady-state model of the high-

pressure side of a unitary air conditioning unit and to the results

obtained using HPSIM. L-10

Table L-9 Comparison of baseline and accumulator systems at the low fan

speed setting. L-1 1

Table L-10 Comparison of baseline and accumulator systems at the high fan

speed setting L-11

Table M-1 Table showing measured properties and symbols under which the

quantity was recorded M-3

Table M-2 Extra measurements and corresponding symbols taken with

accumulator added to baseline system M-4

Table M-3 Experimental averages and calculations for Test 1 — Baseline test

at high fan speed M-5

xix

Table M-4 Experimental averages and calculations for Test 2 — Accumulator

without liquid overfeeding and at high fan speed M-6

Table M-5 Experimental averages and calculations for Test 3 — Accumulator

with liquid overfeeding operation and at high fan speed M-7

Table M-6 Comparison of the accumulator system with/without LOF in

relation to the baseline system at the high fan speed setting. M-8

xx

Introduction

Based upon 1985 rates of consumption, world reserves of fossil fuels such as

natural gas have been estimated to last another 60-170 years, petroleum will last 35-

110 years and coal will be available for 230-1 700 years (A.R.I. 1999). The first

figure listed for each fuel type represents the "economically" recoverable number of

years which depends upon the current market price and existing technologies, while

the second figure, "total known" recoverable is affected by the continuing search for

new energy sources. These figures are indicative of world reserves but will change

with changing global conditions.

If every inhabitant of the earth were to reach the U.S. level of energy use (348

GJ/person/year), annual world energy consumption would increase five times to 1 751

EJ'. Using this extreme scenario, known oil reserves would be exhausted in six years.

Although such an increase is not realistic, continuing population growth will be

accompanied by increased energy consumption.

A survey completed in the early 1930's indicated that the world population

was just two billion; today it is about five billion, two an a half times that. Since 1930,

world annual energy consumption has increased by more than a factor of six, from

52.75 EJ to 337.6 EJ in 1987. Since 1950, world population has been doubling in

forty years or less. Demographers predict that population growth will not end before

the next century, reaching 10 billion sometime in the next century.

1 lEJ= 10 18J

1

It is reported that in some countries more than 30% of their national budget is

devoted to energy development. As energy costs rise there will be an increasing

demand for operationally inexpensive cooling systems. With increasing electricity

rates, there is motivation to assess whether improved cooling technology can reduce

energy consumption.

Refrigeration including both refrigeration and air-conditioning for homes,

businesses and industry, as well as heat pumps is a leading use of electric power in the

United States. The Electric Power Research Institute estimates that vapor compression

refrigeration systems consume 23 percent of all electric energy. If one does not

consider the gasoline burned to run automobile air conditioners, it is clear that

improving the efficiency of the venerable (100-year-old) vapor compression cooling

technology has the potential for substantial savings in energy conservation.

Several manufacturers of cooling systems have indicated that one of the

largest problems in this regard is the lack of good but inexpensive heat exchanger

design methods (Turner and Chen 1987). Criteria for general heat exchanger design

and fabrication techniques would benefit the entire industry.

The efficiency of the vapour compression cycle must be substantially

improved as it forms the heart of the vast majority of modern cooling equipment.

Most residential and mobile air-conditioning and refrigeration systems are direct

expansion units, that have protection to prevent liquid slugging in the compressor. By

utilising about 85% of the evaporator capacity for cooling and the remaining 15% for

superheating the refrigerant, the compressor can be protected from receiving liquid

2

refrigerant. This practice results in excessive evaporator volume (Mei et al. 1993).

Full use of the evaporator provides higher cooling capacity and better

dehumidification in residential applications. A system that utilises 100% of the

evaporator (flooded evaporator) is known as a liquid overfeeding system and has been

successfully used on ammonia refrigeration systems for many years. In these systems

excess liquid is forced mechanically or by gas pressure through organised-flow

evaporators, separated from the vapour and then returned to the evaporators. The

liquid overfeed system is however too complicated to be used in small air

conditioners and heat pumps (Mei et al. 1996).

The liquid overfeeding operation has however been applied to small air

conditioning systems in recent years. This has been achieved using a heat exchange

accumulator. Heat exchanger accumulator patents date back to the 1970's. Since then

many forms and variants have been investigated (Ecker 1980, Schumacher 1976).

Probably the most successful and latest version is that of Mei and Chen (1993).

Despite these recent developments and achievements the authors could not find any

documented mathematical process, model or design procedure that described how the

accumulators have been sized with respect to their relevant operating systems. There

was also no evidence of any equations that accurately and sufficiently describe the

heat exchange process that takes place within the heat exchanger accumulator.

An intense literature survey conducted by the author indicated that there were

several papers dealing with the implementation and effects of heat exchange

accumulators on systems that ranged from an off the shelf window air conditioner

(Mei et al. 1996) to mobile (Mei et al 1994) and military air conditioners (Mei et al.

3

1995). However, none of these studies mentioned how the heat exchanger

accumulator was designed with respect to the system into which it was to be

implemented. Heat exchanger accumulator design seemed to be an experimental trial

and error procedure with each design improving with experience gained.

It is the aim of this study to mathematically model and experimentally verify

the basic heat exchange process that takes place within heat exchanger accumulators.

The outline of the paper is: heat exchange accumulators are briefly described,

the mathematical modeling of the system follows in which the heat transfer equations

are derived. A universal design procedure is then developed, the experimental results

presented and discussed and finally, the conclusions drawn.

4

Heat Exchanger Accumulators

A heat exchanger-accumulator is placed in a system to provide a heat

exchange relationship between hot liquid refrigerant discharged from the condenser

and a relatively cool mixture of liquid and vaporous refrigerant discharged from the

evaporator. This heat exchange relationship substantially sub-cools the hot liquid

refrigerant and provides a liquid overfeeding operation through the evaporator for

effectively using 100% of the evaporator for cooling purposes.

A basic air conditioning system requires the compressor to be protected from

liquid slugging effects, which can significantly detract from the integrity of the

compressor. Efforts to ensure that essentially only vaporous refrigerant, (preferably

saturated vaporous refrigerant), is introduced in to the compressor is accomplished by

appropriately sizing the evaporators. This is achieved by providing a dry coil region,

which, theoretically, is free of liquid refrigerant and corresponds to about 10-15% of

the evaporator coil volume. This ensures that essentially all of the liquid refrigerant is

evaporated in the evaporator. This dry coil region does not provide for any

meaningful cooling of the heat exchange medium passing through the evaporator and

thus adversely affects the overall system efficiency of the air conditioning system. It

also adds to the weight and cost of the evaporator.

The use of suction liquid line heat exchangers causes the vaporous refrigerant

in the suction line to be superheated. Such superheating of the gaseous refrigerant

directly affects the temperature of the vaporous refrigerant discharged from the

compressor and requires that the compressor provide additional work for compressing

5

the vaporous refrigerant to the pressure necessary for effecting the condensation

thereof in the condenser. The heat exchanger accumulator allows the dry coil region

to be removed from the evaporator and ensures that the vaporous refrigerant is then

superheated in the heat exchanger accumulator. The compressor exit temperature is

then not adversely affected. The principal aims (Mei and Chen 1993) of the heat

exchanger accumulator are;

To provide an improved air conditioning system having a system efficiency

higher than that attainable with previously known air conditioning systems when

using the same - or a less efficient refrigerant.

To provide the system with a liquid overfeeding operation which replaces the

previously utilised direct expansion operation. This increases the cooling capacity of

the system by eliminating the need for dry coil regions in the evaporator.

To pass hot liquid refrigerant from the condenser in a heat exchange

relationship with a relatively cool mixture of liquid and vaporous refrigerant

discharged from the evaporator so as to substantially sub-cool the liquid refrigerant

from the condenser. This ensures that little or no vaporisation of the refrigerant occurs

across the expansion device and provides the evaporator with a relatively cool stream

of liquid refrigerant in a liquid overfeeding arrangement. As a result, a substantial

portion of the liquid refrigerant is not evaporated in the evaporator and is

subsequently used to effect the sub-cooling of the hot liquid refrigerant discharge

from the condenser.

6

To provide a heat exchanger accumulator assembly in which the mixture of

liquid and vaporous refrigerant discharged from the evaporator is used in heat

exchange relationship with hot refrigerant from the condenser in order to sub-cool the

hot refrigerant, while evaporating the liquid refrigerant in the mixture thus ensuring

that the refrigerant from the mixture is conveyed to the compressor as saturated vapor.

To provide a system that when compared to direct expansion systems,

provides a substantial reduction in the compressor discharge pressure, and power

consumption and provides an increase in suction pressure, an improvement in the

compressor volumetric efficiency and a relatively fast cooling response time during

start-up.

With these aims in mind a basic mathematical model of the heat exchanger

accumulator model may be developed.

7

T

S

Mathematical Model

Due to the complexity of heat exchange certain assumptions are made in all

heat transfer problems. As this is a basic attempt at modelling the heat exchange

process that takes place within the heat exchanger accumulator, this model will deal

with the process drawn on the T-s diagram in Figure 1. The heat exchanger

accumulator is also shown.

Figure 1

Temperature — entropy diagram and heat exchanger accumulator

When one analyses the heat exchange process that takes place within the

accumulator, there are several factors that determine the heat transferred. These

factors vary from the tube material to surface area available for heat exchange. In the

heat exchanger accumulator, the greatest influence on all these factors is the length of

the coil as this determines the surface area available for heat transfer. It also

determines the amount of superheat. From heat exchanger theory the heat transfer

may be calculated using

Q = U•A•LMTD (1)

8

Where the logarithmic arithmetic mean temperature difference (Holman 1992)

may be defined as

LMTD = (T5 — T1 — (r4 — T8 )

ln[(T5 — T1)/(T4 T8 (2)

From the T-s diagram (Figure 1) it follows that the heat exchanged within the

heat exchange accumulator is equal to

Q = —h 8 )= m(h 4 —h 5 )

(3)

The overall heat transfer by combined conduction and convection may be

expressed in terms of the overall heat transfer coefficient. The overall heat transfer

coefficient based on the inside tube is defined as

= 1

1 + A. •14)./D i ) ± Ai 1

(4) h i 2•7-c•k•L A. h.

The inside heat transfer coefficient in the above equations applies to the liquid

refrigerant flowing from the condenser and may be calculated using the following

form of the Dittus-Boelter equation,

h • Nu d =

D = 0.023 • Red. ' • Pr" (5 )

A change in ambient conditions will cause a change in operating pressures and

temperatures. If the quality of the refrigerant flowing from the evaporator is equal to,

or greater than unity (i.e. single-phase gaseous flow), h o will be calculated using the

9

Dittus-Boelter equation. If the quality is less than unity (i.e. two-phase flow) the Jung

and Radermacher (1991) equation may be used.

h tp = h nb, + h cee = N • h sa + F - h i, (6)

Ideally the value of the local heat transfer coefficient predicted by Jung and

Radermacher at high qualities should tend toward the value predicted by the Dittus-

Boelter equation. Investigations (Appendix A)(Wood and Meyer 1998) that tested a

wide range of accumulator hydraulic diameters and coil lengths show that this is not

true and that there is no fixed relationship between the two methods of calculation

(Appendix D). Figure 2 illustrates one such case where a hydraulic diameter of 0.03m

was assumed and the coil length varied between 0.1 and 100m. Results show that

there is a large deviation between the heat transfer coefficients given by the Jung and

Radermacher equation at high qualities and the Dittus-Boelter equation at a quality of

x = 1.

10

0.1

_.__ 0.2

)4 0.5

1.0

•

2.0

, 5.0

10.0

50.0

100.0

Dittus Boelter

10000

8713

1000 .c

179

I I I I I 1 I 4 I 4

0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

Quality

100 0.00 1.10

Coil Length (m]

Figure 2

Heat transfer coefficients calculated using the Jung and Radermacher (1991) equation

(for qualities x < 1) and the Dittus-Boelter equation (for qualities x 1) for a range of

coil lengths

A survey (Wood and Meyer 1998) revealed that there is very little

evaporation theory between qualities of 0.9 and 1. Therefore, for purpose of design,

the worst case scenario, i.e. minimum heat transfer coefficient will be considered

(Appendix D). Therefore, the Dittus-Boelter equation was used to determine the

values of the heat transfer coefficient.

Substituting equation (2) to (5) into (1) (Appendix B), basing the overall heat

transfer coefficient on the inside of the tube and solving for the length (L) yields

L = m(h

' -h

8) [ 1

+ ln(D

°/D

")

+ 1

TC • LMTD 1-1 ; - D i 2.k h. • D. (7)

11

which gives L in terms of the heat transfer coefficient based on the inside area of the

coil.

Any practical air conditioning system operates at a range of ambient

temperatures. Varying ambient temperatures will cause variations in operating

pressures and temperatures, which in turn cause other system variables such as

refrigerant mass flow to vary. Any good design must consider these variations. A

variation in mass flow rate with a variation in operating conditions may be modeled as

follows.

An equation that predicted the refrigerant mass flow rate at a specified range

of evaporating and condensing temperatures was derived in Appendix E. This

equation was based on the compressor (Tecumseh AJ5515) used for the experimental

verification of the results (Appendix C). According to the A.R.I specification 540P-

D4 (1990), variables such as the refrigerant mass flow rate and efficiencies (isentropic

or volumetric) may be expressed by a single equation that is a function of evaporating

and condensing temperatures. The equation is

x = C o + C I TE + C 2 Tc C3 TE2 C4 TE Tc

C s Tc2 C6 TE3 C 7 TcTE2 C8 TE Tc2 C9 T (8)

where x is the required variable (refrigerant mass flow rate or efficiency). The

coefficients are determined by solving a system of linear equations. Equation (8) can

be expressed by the matrices, [A]•[X]=[B]. Matrix A represents the range of

condensing and evaporating temperatures and their higher order values and products.

In this case, evaporating temperatures varying from —12°C to 12°C and condensing

12

temperatures ranging from 43°C to 66°C were considered. The refrigerant mass flow

rates (determined from compressor curves) corresponding to the respective

evaporating and condensing temperatures, formed matrix B which then allowed the

system to be solved using matrix algebra (method of least squares). After solving, the

resulting matrix was matrix X which represented constants Co —C9. Once solved the

coefficients in matrix X were,

Table 1

Mass flow rate coefficients

Co 2.23E-02 C5 3.79E-07

C1 8.75E-04 C6 -3.53E-10

C2 - 1.62E-04 C7 1.56E-09

C3 -8.17E-08 Cs -1.66E-07

C4 1.19E-05 C9 -2.28E-09

Substituting these constants into equation (8), gives an equation that

determines the mass flow rate (m) at any given evaporating or condensing

temperature, within the above-mentioned range. With the constants given in Table 1

substituted into equation (8), the error of the equation, when compared to the

manufacturers data, is 0.24% (Appendix E).

Similarly, as the evaporating and condensing temperatures vary, so the

enthalpy difference across the heat exchange accumulator will vary. The enthalpy

difference determines the amount of heat exchanged within the accumulator and

affects the length of the coil according to equation (7). An equation that determines

these enthalpies at all conditions is therefore required for a complete mathematical

model of the heat exchange process.

13

The enthalpies corresponding to points 1 and 8 in Figure 1 are only a function

of the evaporating temperature and refrigerant used. Evaporating temperatures

ranging from —12°C to 12°C and the corresponding enthalpies were plotted and a

curve fit applied (Appendix F). The curve fit yielded the following equation for R-22

h1 —118 = -0.0018 T E2 - 0.6049 TE + 24.185 (9)

The equation has a correlation coefficient of 0.999. The enthalpy difference

across the evaporator is now defined for a range of evaporating temperatures.

An ideal heat exchanger accumulator has two optimum operating conditions

(Appendix G, Appendix H). These conditions are; firstly, a minimum refrigerant

velocity over the coil within the accumulator, to ensure that no liquid refrigerant

remains in suspension and secondly, maximum heat transfer must take place within

the accumulator. Maximum heat transfer requires maximum refrigerant velocity over

the coil within the accumulator. These two factor directly oppose one another and a

compromise situation must be found. It must also be mentioned that when the

refrigerant velocity is slowed down sufficiently to ensure that no liquid refrigerant is

held in suspension, a special mechanism that ensures that oil is transported to the

compressor must be devised.

A logical starting point for the design would be to use the refrigerant velocity

through the dry coil region of the evaporator and use this as the initial design velocity

within the accumulator (Appendix H, Appendix I). In order to maintain this velocity

through the accumulator, the hydraulic diameter needs to be determined. Figure 3

shows the critical dimensions of the heat exchanger accumulator used in this study.

14

Figure 3

Critical diameters of the heat exchanger accumulator

Assuming that the outer diameters of the coils touch, and that there is coil

throughout the vertical height of the heat exchange accumulator, the varying cross-

sectional area of the coil (shown in Figure 3) may be simplified by integrating the

cross-sectional area of the coil, to get an average diameter (DAc) for the entire vertical

height of the coil. Once simplified

D _ Doc AC — 4

(10)

The hydraulic diameter (D H) (Appendix H) may then be expressed as

D 2 —4.D w • D Ac — D 211)(A,

D u = D +2.D w + D

15

Let DHXAo and DmAi be equal distances from D. This ensures that the coil is

in the center of the accumulator chamber. If the distance (DxxA0 - Dw) is called z, then

(D, - D mcki) is also equal to z. Thus,

D HxA. = D w +z

D =D w —z

Substituting (12) into (11) yields

D H =Z —D Ac

Rearranging gives

z=D H +D Ac

It is important to note that equation (14) is only a function of the hydraulic and

coil diameter and not a function of the coil-winding diameter. This is expected

because a certain hydraulic diameter (flow area) is required, irrespective of the coil-

winding diameter. The strength of this design process is that the heat exchange

accumulator is designed around the coil-winding diameter. This has many advantages,

for example, different systems will have different diameter tubes in the evaporator

and this design process facilitates these variations. Certain tube diameters have

minimum practical diameters into which they can be coiled without the use of special

equipment, meaning that this calculation procedure may be used after a coil-winding

diameter has been selected. The coil-winding diameter is a manufacturing limit and

by starting here eliminates backtracking or redesign after manufacture.

16

Application of Design Method

A small off-the-shelf window air conditioning unit was obtained for the

experimental section of this work. The unit had the following characteristics;

Table 2

Technical data of experimental air conditioning unit

Compressor Tecumseh AJ5515E

Model Mech Air WP157E

Cooling Capacity 3780 W

Heating Capacity 2850 W

Refrigerant Charge 0.83 kg R-22

Electrical Specifications 220 V, 50 Hz, 8.5 A

In this case, the air conditioner had a 9.5 mm OD (8.1 mm ID) diameter

condenser tube. A coil-winding diameter of 100 mm was chosen as this tube may be

bent into a 100 mm coil without severe distortion taking place. As stated, the

accumulator will be designed to have the same hydraulic diameter as the original

system, in this case 8.11 mm. Substituting these diameters into equations (10) to (14)

yields the dimensions given in Table 3 (Appendix I).

Table 3

Physical accumulator dimensions as determined by the design procedure

D,, 100 mm

DAC 6.24 mm

z 17.5 mm

DlixA0 118 mm

DFIxAi 82.5 mm

The majority of air conditioners operate approximately at an evaporating

temperature of 7 °C and a condensing temperature of 50 °C. These operating

17

conditions, along with the Dittus-Boelter equation were used to calculate the

enthalpies at the respective points, refrigerant mass flow rate and heat transfer

coefficients. These values are shown in Table 4 (Appendix I).

Table 4

Calculated results for application example

Property Symbol Value

Evaporating temperature TE 7 °C

Condensing temperature Tc 50 °C

Enthalpy at point 1 h1 416.8 Idle

Enthalpy at point 8 h8 409 kJ-kg-1

Inner heat transfer coefficient h1 1392 W.m-2.K-1

Outer heat transfer coefficient ho 351 W.r11-2.1C 1

Refrigerant mass flow rate m 0.2218 kg . .s-1

Substituting all known variables into equation (7) yields an accumulator coil

length of 0.762 m (Appendix I). The height of the heat exchanger accumulator may

now be calculated as the coil winding diameter along with the coil length are known.

All other accumulator dimensions are known and the accumulator may be

manufactured as it is correctly sized according to the operating system and conditions.

The calculated coil length is valid for an evaporating temperature of 7 °C and

a condensing temperature of 50 °C. Although these are the approximated conditions

the system is most likely to operate under, it is impractical to assume that the system

will always operate at these conditions. In practice, these temperatures will vary and

thus, the required length of the accumulator coil will change. A 10 °C increase and

decrease in ambient temperatures was investigated (Appendix J). These two extreme

18

cases had evaporating temperatures of —3 °C and 17 °C with respective condensing

temperatures being 40 °C and 50 °C.

Results indicated that a 10 °C increase in each of the evaporating and

condensing temperatures caused a 3 % (23 mm) increase in the required coil length

while a 10 °C decrease in each of the evaporating and condensing temperatures

caused a 2 % (17 mm) decrease in the required coil length (Appendix J).

19

T

Evaporator

Environmental Chamber

Experimental Verification

A schematic diagram of the system including measurement points is shown in

Figure 4. All temperature readings were taken with K-type thermocouples that were

calibrated to accuracy's of ± 0.2 °C. Refrigerant pressures were measured on either

side of the compressor with pressure gauges having a 0.2 % average error on the full-

scale reading. The power consumed by the system was measured with a wattmeter

having a 1 % error (Appendix K).

Figure 4

Schematic diagram of experimental set-up with measuring points.


T

Condenser

T

Capillary Tube

_L 0 T

Accumulator

T -1—

Compressor

T

Watt Meter

Thermocouple OO Sight Glass 0 Pressure Gauge

20

The baseline system (no accumulator) was switched on and the environmental

chamber set for evaporator and condenser ambient temperatures of 25 °C. The

humidity ratio of the air at the evaporator inlet was set between 50 and 60 %. The air

mass flow rates were 0.12 kg/s over the evaporator and 0.36 kg/s over the condenser

(Appendix K). Once all the set-up procedures were completed the system was allowed

to run for a minimum period of an hour to allow it to stabilise in an attempt to reach

steady state conditions.

Readings were taken three times at three different twenty-minute intervals.

Each set of three readings was averaged to give an experimental average at each

twenty-minute interval. One test comprised three different sets of three readings

(taken over a 40-minute period). Three different tests, all at the same ambient

conditions, were completed on three different days. This gave three baseline test

results.

The accumulator was added and the last 15 % of the evaporator removed. No

other modifications where made to the system. The experimental process was then

repeated under the same conditions used for the baseline test.

The baseline tests were verified using a steady-state mathematical model for

the high-pressure side of a unitary air conditioning unit (Petit and Meyer, 1999). This

verification comprised a three-way comparison in which the experimental results were

compared to results obtained from this mathematical model and to those of a

simulation program, HPSIM (ENERFLOW Technologies 1994) that predicts the

performance of air-conditioners and heat pumps that operate on the vapor-

21

compression cycle. Table 5 shows the comparison of the results (Appendix L). Exp

represents the experimental data, Model, the data derived from the above-mentioned

model and HPSIM, the data from the simulation program. % devl and % dev 2

respectively represent the deviation of the model from the experimental results and

the deviation of the simulation program from the experimental results.

Table 5

Comparison of the baseline experimental results to that of the steady-state model of

the high-pressure side of a unitary air conditioning unit and to the results obtained

using HPSIM.

Exp. Model HPSIM % devl % dev2

m [kg/s] 0.0175 0.0194 0.020297 -11.36 -16.59 p [kW] 1.41 1.36 1.22 3.30 13.25

QE [kW] 3.73 4.18 3.6 -12.51 2.91 Qc [kW] 5.04 5.54 4.82 -9.96 4.26

COPCooling 2.64 3.07 2.95 -16.31 -11.83 COPHeaung 3.58 4.07 3.95 -13.71 -10.34

It can be concluded that all deviations are within an acceptable range thus

indicating that the experimental measurements should be correct when evaluating the

performance of the baseline system (Appendix L).

Measurements taken on the evaporator tubes during baseline testing

determined that 15 % of the evaporator area was used for superheating the refrigerant.

Therefore the evaporator size was reduced by 15 % for experiments with the heat

exchange accumulator (Appendix M).

The measurements in Figure 5 show how the heat exchanger accumulator

affects the air conditioning system. It shows how the condensing pressure (pc),

22

evaporating pressure (pE), pressure ratio (pc/pE), compressor isentropic efficiency (M),

refrigerant mass flow (m), compressor power consumption (P), cooling capacity (QE),

heat exchanged over the condenser (Qc) and coefficient of performance (COP) are

affected by the addition of the heat exchanger accumulator. The percentage difference

is the difference between the baseline operating conditions and the operating

conditions with the heat exchanger accumulator added to the system.

Figure 5

Influence of the heat exchanger accumulator on the experimental system

8%

7%

6%

5%

W 4°/ co . MI

3% a9

e % 2

0-

1%

0% Pc/PE P

-1%

Pc PE m ■ II E • C COP

-2%

23

Discussion of Results

All results discussed are shown in detail in Appendix M. The liquid

overfeeding operation has a very small influence on the condensing pressure. The

small increase of 0.4 % (7.4 kPa) is reasonable, as it shows that the compressor exit

temperature has a very small increase when the heat exchanger accumulator is added.

The evaporating pressure has a desirable increase of 2.1 % (10.6 kPa), meaning a

reduction in the work required by the system. The addition of the accumulator reduces

the pressure ratio by 1.7 % resulting in less work and longer compressor life.

The liquid overfeeding operation has a better compressor isentropic efficiency

than the baseline operation. This is due to the reduced pressure ratio caused by the

addition of the heat exchanger accumulator. According to the mass flow rates

obtained from the compressor curves, there is a general increase in refrigerant mass

flow rate when the accumulator is added. A 4 % (0.7 g/s) increase is obtained with the

liquid overfeeding operation. The increase in refrigerant mass flow rate is attributed to

the higher evaporating temperature, lower pressure ratio and increase in compressor

isentropic efficiency.

The liquid overfeeding operation decreases the power consumed by the

compressor when compared to the baseline operation. Although the decrease is quite

small 1 % (11 W), it is still favourable especially when one considers that all the other

benefits are obtained at no extra expense.

24

The addition of the heat exchanger accumulator increases the cooling capacity.

The increase of 6.5 % (180 W) is directly related to the fact that the refrigerant is sub-

cooled in the heat exchanger accumulator before entering the evaporator. Effectively

the evaporator in the liquid overfeeding system improves the cooling capacity when

compared to the baseline case that has a 15 % larger evaporator.

The addition of the heat exchanger accumulator results in an increase in heat

exchanged over the condenser by 3.7 % (118.5 W).

The COP increases from 2.4 for baseline operation to 2.6 for the liquid

overfeeding operation, an increase of 7.5 %. The increase in COP is consistent with

that obtained by Mei and Chen (1996). This means that the mathematical model and

design process is a very good representation of the heat exchange process.

25

Conclusion

With the help of common mathematical and engineering equations the basic

heat exchange process that takes place within heat exchanger accumulators was

studied and a mathematical model of this basic heat transfer process developed. The

model was used to develop a heat exchanger accumulator design process. The design

process correctly sizes the heat exchanger accumulator according to the operating

system and conditions and is valid for any vapor compression cycle. The data

obtained from a small air conditioning system, used for experimental verification of

the results, was then used in the design process and a heat exchanger-accumulator

manufactured for this system.

Results show that the addition of the heat exchanger accumulator results in a

liquid overfeeding operation that replaces the previously utilised direct expansion

operation. It provides an improved air conditioning system that has a 7.5 % increase

in coefficient of performance and a 4.4% increase in refrigerant mass flow rate. A

pressure ratio reduction has a positive effect on the compressor performance and life

span.

Liquid overfeeding increases the cooling capacity of the system by 6.5 %.

When compared to direct expansion systems, this basic heat exchanger accumulator

provides a reduction in cycling losses and power consumption, an increase in suction

pressure and an improvement in isentropic compressor efficiency.

26

Removing the dry coil region means that manufacturers can fit evaporators

that are up to 15 % smaller, assisting in decreasing the physical size of the unit whilst

still increasing the system's COP. The cost saving could possibly cover the capital

cost of the accumulator. It is therefore recommended that further research be

conducted to minimize the manufacturing cost of heat exchanger accumulators.

Although the results obtained in this study are encouraging, further

development of the mathematical model, design process and especially laboratory

testing need to be completed to embrace the widest possible range of operating

conditions. However the mathematical model and design process developed in this

work are a successful and important first step in solving a difficult problem.

27

Nomenclature

A = heat transfer area (m 2)

C = coefficients in equation (8)

Cp = specific heat (J.kg - 1.K-1 )

D = tube diameter (m)

h = enthalpy (kJ.kg-1 ) or heat transfer coefficient (W.m -2 -K-1 )

h, = heat transfer coefficient on inside of the tube (W.m -2-K-1 )

ho = heat transfer coefficient on outside of the tube (w•m.-2•K-1)

hsa = pool boiling heat transfer coefficient obtained by Stephan and

Abdelsalam (1980) (W.m -2 .K-)

ID = inner diameter (m)

thermal conductivity (W.m - 1 .K-1)

tube length (m)

LMTD = logarithmic arithmetic mean temperature difference (K)

mass flow rate (kg.s -1 )

OD = outer diameter (m)

power consumption (W)

pressure (kPa)

heat transfer (W)

entropy (kJ•kg -1 •K-1 )

temperature (K)

overall heat transfer coefficient (W.m -2 •K-1 )

variable (refrigerant mass flow (kg•s 1 ) or efficiency)

D, — DEmAi (m)

28

Greek letters

It = pi

11 = viscosity (Pa•s)

isentropic efficiency (%)

Dimensionless Numbers

COP = coefficient of performance

heat transfer enhancement factor

factor due to nucleate boiling

Nusselt number, (h•D)/k

Prandtl number, (Cp•}1)/k

Reynolds number, (G-D/ t)

Subscripts

AC = average coil

condenser

cold fluid

cec = convective evaporation contribution

diameter

evaporator

hydraulic

heat exchanger accumulator

inner

liquid only

nucleate boiling contribution

Nu =

Pr =

Re =

HXA =

lo =

nbc =

29

OC = outer coil

o = outer

tp = two-phase

w = coil winding

30

References

Air conditioning and Refrigeration Institute. 1990. A.R.I. Specification 540-D4. Air

conditioning and Refrigeration Institute, 1501 Wilson Boulevard, Arlington,

Virginia 22209, U.S.A.

A.R.I. 1999, Air conditioning and Refrigeration Institute Web Site, www.ari.org .

Ecker A.L. 1980. Heat exchanger-accumulator. United States Patent 4 217 765,

August 19 1980.

ENERFLOW Technologies 1994. HPSIM Version 1.0. University of Potchestroom,

South Africa.

Holman J.P. 1992. Heat Transfer. (7 th Ed) London: McGraw-Hill pp. 551-552.

Jung D.S., Radermacher R. 1991. Prediction of heat transfer coefficients of various

refrigerants during evaporation. ASHRAE Transactions Vol. 97, No. 2, 48-53.

Mei V.C., Chen F.C. 1993. Liquid overfeeding air conditioning system and method.

United States Patent 5 245 833, September 21 1993.

Mei V.C., Chen, F.C., HuangFu, E.P. 1993 A recuperative air conditioning cycle.

AES-Vol. 29 Heat Pump and Refrigeration Systems Design, Analysis and

Applications, A.S.M.E. pp.19 —26.

Mei V.C., Chen, F.C., Sullivan, R.A. 1994. Experimental Study of a Liquid

Overfeeding Mobile Air Conditioning System. ASHRAE Transactions Vol.

100, No. 2, pp. 653-656.

Mei V.C., Chen, F.C., Fang, C. 1995. Liquid Overfeeding Military Air Conditioner.

Proceedings of the intersociety energy conversion engineering conference,

Vol. 3, pp. 29-34.

31

Mei V.C., Chen, F.C., Chen, T.D., Jennings, L.W. 1996. Experimental study of a

liquid overfeeding window air conditioner. ASHRAE Transactions, Vol. 102,

No. 1, pp. 63-67.

Petit P., Meyer J.P. 1999. A steady state model for the high-pressure side of a unitary

air conditioning unit. MEng. Dissertation, Rand Afrikaans University, South

Africa.

Schumacher E.W. 1976. Combination liquid trapping suction accumulator and

evaporator pressure regulator device including a capillary cartridge and heat

exchanger. United States Patent 3 955 375, May 11 1976.

Stephan K., Abdelsalam M. 1980. Heat transfer correlation's for natural convection

boiling. International Journal of Heat and Mass Transfer, Vol. 23, pp. 73-87.

Turner R.H., Chen F.C. 1987. Research requirements in the evaporative cooling field.

ASHRAE Transactions, Vol. 93, No. 1, pp. 185-196.

Wood C.W., Meyer J.P. 1998. A mathematical analysis of accumulator heat

exchangers to achieve liquid overfeeding effects in small air conditioning

systems. Proceedings of the ASME Advanced Energy Systems Division, AES-

Vol. 38, pp. 409-413.

32

Appendix A

Appendix A: Prediction and verification of heat transfer

coefficients of refrigerants during evaporation.

A.1 Introduction

The aim of this section of work is to verify the calculation method of Jung so that

this method may be implemented in this study.

At many institutions extensive research is being undertaken to replace fully

halogenated chlorofluorocarbons (CFCs) as they are directly and partially

responsible for the destruction of the ozone layer and contribute to global

warming. In accordance with the Montreal Protocol new ozone-safe fluids such

as R-134a, R-134, R-141b, R-142b, R-143a, R-123 and R-124 have been

developed. In utilizing these new refrigerants, modifications in the vapor-

compression cycle are needed due to the expected changes in the physical

properties of the new fluids.

When designing heat exchangers one of the major concerns is the determination

of the heat transfer coefficient which is greatly affected by the physical properties

of the working fluids. As part of the global effort to speed up the process of

replacing the ozone-depleting substances, the prediction of heat transfer

coefficients of fluids with proper correlation's is needed for design engineers

while experimental investigations are being carried out. In 1991 Jung and

Radermacher l predicted and compared the evaporation heat transfer coefficients

of prospective substitutes with base fluids of R-12, R-22, R-114 and R-11. To

A-1

Appendix A

accomplish this objective, the correlation's that were developed by Jung et al.

(19882, 19893) were used to calculate the heat transfer coefficients. The results

obtained by Jung indicated that nucleate boiling is fully suppressed at qualities

greater than 20% for all pure refrigerants studied. Two distinct heat transfer

regions existed in annular flow, which were observed at qualities greater than

10%. In the partial boiling region heat transfer coefficients were observed to be

strongly influenced by heat flux while in the convective evaporation region the

heat transfer coefficients were independent of heat flux. Thus, in the convective

region heat transfer coefficients at various heat fluxes merged into a single line,

depending only upon flow parameters such as quality. Furthermore, heat transfer

coefficients in the convective region increase in proportion to quality. These

results support Chen's supposition4 that two-phase heat transfer coefficients may

be predicted by superimposing the two contributions. The final correlation for

pure refrigerants became:

h 1, = h nbc + h. = Nh. + M I.

where;

A-2

N = (4048). XV 2 .130 133

for X t, 1

N = 2.0 — (0.0 • X: 28 • B0 -°33

for 1 < 5

0.745 )0.581

hsa = 207 k q • b • d p v )0.533

b • d k i • Tsa, p i

where

b • d = 0.014613 cr[ 2

1.5

8(P1 Pv ) with a contact angle of = 35°

1.85

F = 2.37(0.29 + 1 X tt

0.9 ( )0.5 )0.1

X 1 - X p v

= tt x ) p i j_t v

lc, (G(1 — x)D y 8 (Colli )0.4 h 10 = 0.023 D lc,

Appendix A

Table A-1 Summary of heat transfer coefficient correlation by Jung et al. 3

Jung's results obtained heat transfer coefficients with a mean deviation of 7.2%

based on experimental data obtained with R-22, R-12, R-152a and R-114.

Comparing it with more experimental data for R-11 and R-134a further validated

the correlation. The prediction was based on the assumption that the evaporator

coil was a straight tube with an inner diameter of 8mm and a length of 7.96m.

A-3

Appendix A

A.2 Implementation

Table A-2 to Table A-6 show the local and average heat transfer coefficients for

refrigerants R-22, R-143a, R-114, R-11 and R-141b which were calculated using

Jung's correlation on a commercially available spread sheet program. These

refrigerants were randomly selected for the purpose of verifying that the

calculated results were in agreement with the predictions/measurements of Jung.

The heat transfer coefficients were calculated at an evaporating temperature of

0°C, a cooling capacity of 4kW and a heat flux of 20kWm 2. The average heat

transfer coefficients where calculated by integrating the line functions and

dividing by the quality range i.e.

h ave -= 1/(X maa — X mia max

h mi.

A-4

Appendix A

Calculation of Local and Average Heat Transfer Coefficiens for R22 using Jung's Correlation

Temp. Pressure Density Enthalpy Cp Viscosity Therm Con

[° C] [kPa] [kg/m3] [kJ/kg] [kJ/kg.K] [micropoise] [W/(m.K)]

0 497.7 1279 44.4 1.153 2205 0.1034 Liquid

0 497.7 21.11 250.9 0.681 117.2 1.00E-02 Vapour

Constants

Surface Tension (m.lim 21 11.79

Heat Transfer (W] 4000

Refrig. Mass flow (kg/s] 0.02546

Tube Inner Diam (m] 0.008

Tube Length (m] 7.96

Gravity (m/s 2J 9.81

Preliminary Calculations Beta = 35

A s (m 2] 2.001E-01 mu, (Pa.sJ 2.205E-04

A, (m 21 5.027E-05 mu, (Pa.sJ 1.172E-05

q (w/m 21 1.999E+04 Bo 1.912E-04

G (kg/(s.m 2) 5.065E+02 Pr, 2.459E+00

h fg (j/kg] 2.065E+05 bd (m] 7.064E-04

s (Wm] 1.179E-02 h 88 (W/(m 2 K) 2.691E+03

Tsat [K] 2.732E+02

Local Heat Transfer Coefficients [Wm" 2 K-1]

x Xff N1 1N5 N F h,0 h,p Integration

0.1 1.24473 0.33206 0.41322 0.41322 2.5569 1009.8463 3693.9990

0.15 0.82083 0.19981 0.21701 0.19981 3.3609 964.7092 3779.9921 186.8498

0.2 0.59994 0.13631 0.05344 0.13631 4.1934 919.0376 4220.6977 200.0172

0.25 0.46309 0.09939 -0.09292 0.09939 5.0752 872.7911 4697.0070 222.9426

0.3 0.36935 0.07542 -0.22975 0.07542 6.0255 825.9233 5179.5257 246.9133

0.35 0.30076 0.05870 -0.36177 0.05870 7.0653 778.3805 5657.4880 270.9253

0.4 0.24816 0.04643 -0.49236 0.04643 8.2201 730.0999 6126.4030 294.5973

0.45 0.20639 0.03708 -0.62437 0.03708 9.5218 681.0068 6584.1938 317.7649

0.5 0.17229 0.02975 -0.76049 0.02975 11.0136 631.0115 7029.7405 340.3484

0.55 0.14382 0.02387 -0.90368 0.02387 12.7551 580.0044 7462.2365 362.2994

0.6 0.11961 0.01906 -1.05747 0.01906 14.8330 527.8485 7880.8393 383.5769

0.65 0.09870 0.01508 -1.22653 0.01508 17.3786 474.3684 8284.4086 404.1312

0.7 0.08037 0.01173 -1.41756 0.01173 20.6033 419.3323 8671.2075 423.8904

0.75 0.06410 0.00890 -1.64100 0.00890 24.8729 362.4209 9038.4254 442.7408

0.8 0.04948 0.00649 -1.91476 0.00649 30.8862 303.1693 9381.2281 460.4913

0.85 0.03616 0.00443 -2.27391 0.00443 40.1862 240.8431 9690.4861 476.7929

0.9 0.02385 0.00266 -2.80237 0.00266 57.0781 174.1251 9945.9016 490.9097

0.95 0.01217 0.00117 -3.79739 0.00117 100.8039 100.0086 10084.4109 500.7578

Average 7078.2328 7089.3521

Table A-2 Table of calculated local and average heat transfer coefficients for R-22 using Jung's correlation

A-5

Appendix A

Calculation of Local and Average Heat Transfer Coefficients for R143a using Jung's Correlation

Temp Pressure Density Enthalpy Cp Viscosity Therm Con

(° C] [kPa] (kg/m3] [kJ/kg] [kJ/kg.K] [micropoise] [W/(m.K)]

0 620.7 1021 54.5 1.451 1621 8.50E-02 Liquid

0 620.7 26.65 247.1 0.9798 107.9 1.27E-02 Vapour

Constants

Surface Tension IMJ/m 21 8.18

Heat Transfer 1141 4000



Tube Length (ml 7.96

Gravity (m/s 2J 9.81


A, (m 2J 2.0006E-01 mu, (Pa.sJ 1.6210E-04

A, lm21 5.0265E-05 mu, (Pa.$) 1.0790E-05

q [Wm 2] 1.9994E+04 Bo 1.6566E-04

G fkg/(s.m 2 ) 6.2667E+02 Pr, 2.7675E+00

h ,. (j/kg] 1.9260E+05 bd (ml 6.6177E-04

s pl/mj 8.1800E-03 h „„IIN/(m 2 K) 3.6179E+03

Tsat pcI 2.7315E+02

Local Heat Transfer Coefficients (Wm -2 K-1 .1

x Xu N1 1N5 N F h,0 hip Integration

0.1 1.53049 0.36345 0.42997 0.42997 2.2555 1319.8083 4532.3364

0.15 1.00927 0.21869 0.23584 0.23584 2.9249 1260.8168 4540.9971 226.8333

0.2 0.73768 0.14919 0.07399 0.14919 3.6193 1201.1268 4887.0039 235.7000

0.25 0.56940 0.10878 -0.07082 0.10878 4.3557 1140.6854 5362.0440 256.2262

0.3 0.45414 0.08255 -0.20621 0.08255 5.1500 1079.4320 5857.7406 280.4946

0.35 0.36980 0.06425 -0.33684 0.06425 6.0197 1017.2965 6356.3152 305.3514

0.4 0.30514 0.05082 -0.46605 0.05082 6.9860 954.1966 6849.8823 330.1549

0.45 0.25377 0.04059 -0.59666 0.04059 8.0757 890.0348 7334.5273 354.6102

0.5 0.21184 0.03256 -0.73135 0.03256 9.3250 824.6940 7808.0422 378.5642

0.55 0.17684 0.02612 -0.87302 0.02612 10.7838 758.0308 8268.9185 401.9240

0.6 0.14707 0.02086 -1.02519 0.02086 12.5247 689.8662 8715.8146 424.6183

0.65 0.12135 0.01650 -1.19247 0.01650 14.6579 619.9709 9147.1890 446.5751

0.7 0.09882 0.01284 -1.38149 0.01284 17.3608 548.0420 9560.9259 467.7029

0.75 0.07881 0.00975 -1.60257 0.00975 20.9401 473.6623 9953.7850 487.8678

0.8 0.06084 0.00711 -1.87344 0.00711 25.9818 396.2241 10320.3412 506.8532

0.85 0.04446 0.00485 -2.22879 0.00485 33.7803 314.7675 10650.4803 524.2705

0.9 0.02932 0.00292 -2.75167 0.00292 47.9468 227.5710 10921.8497 539.3083

0.95 0.01497 0.00128 -3.73619 0.00128 84.6220 130.7052 11065.1876 549.6759

Average 7896.2989 7902.0364

Table A-3 Table of calculated local and average heat transfer coefficients for R- 143a using Jung's correlation

A-6

Appendix A

Calculation of Local and Average Heat Transfer Coefficients for R114 using Jung's Correlation


r C] [kPa] [kg/m3] [kJ/kg] [kJ/kg.K] [micropoise] [W/(m.K)]

0 85.83 1530 38 0.9451 4763 6.86E-02 Liquid

0 85.83 6.727 176.5 0.663 103.1 9.50E-03 Vapour

Constants

Surface Tension linJ/m 2.1 13.65

Heat Transfer 1141 4000



Tube Length (MI 7.96

Gravity (Ms 2] 9.81


A s (m 2] 2.0006E-01 mu, (Pa.s] 4.7630E-04

A s lm 21 5.0265E-05 mu, 112a.s] 1.0310E-05

q Etv/m 2] 1.9994E+04 Bo 1.7398E-04

G fkg/(s.m 2) 8.2979E+02 Pr, 6.5620E+00

h ,, (]/kg] 1.3850E+05 bd [m] 6.9068E-04

s 1N/ml 1.3650E-02 haW/(m 2 K) 1.9073E+03

Tsat pq 2.7315E+02

Local Heat Transfer Coefficients (Wm " 2K"']

x X,, N1 1N5 N F h,0 hip Integration

0.1 0.70282 0.14864 0.07902 0.14864 3.7446 795.2679 3261.4683

0.15 0.46347 0.08944 -0.15851 0.08944 5.0720 759.7218 4023.9302 182.1350

0.2 0.33875 0.06102 -0.35653 0.06102 6.4408 723.7548 4777.9502 220.0470

0.25 0.26148 0.04449 -0.53371 0.04449 7.8870 687.3350 5505.8323 257.0946

0.3 0.20855 0.03376 -0.69936 0.03376 9.4428 650.4260 6206.2199 292.8013

0.35 0.16982 0.02628 -0.85919 0.02628 11.1431 612.9854 6880.6571 327.1719

0.4 0.14012 0.02078 -1.01729 0.02078 13.0292 574.9637 7530.9854 360.2911

0.45 0.11654 0.01660 -1.17709 0.01660 15.1539 536.3022 8158.7363 392.2430

0.5 0.09728 0.01332 -1.34189 0.01332 17.5871 496.9303 8764.9816 423.0929

0.55 0.08121 0.01068 -1.51523 0.01068 20.4262 456.7615 9350.2812 452.8816

0.6 0.06754 0.00853 -1.70141 0.00853 23.8120 415.6880 9914.6205 481.6225

0.65 0.05573 0.00675 -1.90608 0.00675 27.9583 373.5716 10457.2798 509.2975

0.7 0.04538 0.00525 -2.13735 0.00525 33.2088 330.2299 10976.5706 535.8463

0.75 0.03619 0.00399 -2.40784 0.00399 40.1585 285.4115 11469.2953 561.1466

0.8 0.02794 0.00291 -2.73926 0.00291 49.9436 238.7500 11929.5776 584.9718

0.85 0.02042 0.00198 -3.17405 0.00198 65.0729 189.6673 12345.9883 606.8891

0.9 0.01347 0.00119 -3.81381 0.00119 92.5464 137.1259 12692.7796 625.9692

0.95 0.00687 0.00053 -5.01839 0.00053 163.6465 78.7581 12889.4977 639.5569

Average 8729.8140 8768.3041


A-7

Appendix A

Calculation of Local and Average Heat Transfer Coefficients for R141b using Jung's Correlation


[° C] [kPal [kg/m3] [kJ/kg] [kJ/kg.K] [micropoise] [W/(m.K))

0 28.16 1280 43.5 1.118 5597 0.1054 Liquid

0 28.16 1.47 281.1 0.7202 87.7 8.63E-03 Vapour

Constants

Surface Tension [mJ/m 2) 24.55

Heat Transfer (INI 4000

Refrig. Mass flow 11(g/s] 0.02114

Tube Inner Dlam (m] 0.008

Tube Length MI] 7.96

Gravity (m/s 2] 9.81


A, (m 2] 2.0006E-01 mu, (Pa.s] 5.5970E-04

A, frn 2] 5.0265E-05 mu, (Pa.s] 8.7700E-06

q (w/m 2] 1.9994E+04 Bo 2.0009E-04

G Ikes.m 2) 4.2057E+02 Pr, 5.9369E+00

h k 11/kg] 2.3760E+05 bd Em] 1.0110E-03

s[Wm] 2.4550E-02 h sa fIN/(m 2 K) 8.3919E+02

Tsat pg 2.7315E+02 h se pil//(m 2 K)]

I

Local Heat Transfer Coefficients fWm -2 K -1]

x X,, N1 1N5 N F h,0 h4, Integration

0.1 0.37099 0.07985 -0.19368 0.07985 6.0049 599.0608 3664.3218

0.15 0.24465 0.04805 -0.46492 0.04805 8.3136 572.2846 4798.0635 211.5596

0.2 0.17881 0.03278 -0.69106 0.03278 10.6873 545.1913 5854.1353 266.3050

0.25 0.13803 0.02390 -0.89339 0.02390 13.1908 517.7569 6849.6934 317.5957

0.3 0.11009 0.01814 -1.08256 0.01814 15.8811 489.9540 7796.2186 366.1478

0.35 0.08964 0.01412 -1.26507 0.01412 18.8187 461.7507 8701.3748 412.4398

0.4 0.07397 0.01116 -1.44562 0.01.116 22.0753 433.1097 9570.3877 456.7941

0.45 0.06152 0.00892 -1.62811 0.00892 25.7418 403.9867 10406.8292 499.4304

0.5 0.05135 0.00715 -1.81629 0.00715 29.9391 374.3285 11213.0493 540.4970

0.55 0.04287 0.00574 -2.01424 0.00574 34.8347 344.0701 11990.3933 580.0861

0.6 0.03565 0.00458 -2.22685 0.00458 40.6713 313.1302 12739.2617 618.2414

0.65 0.02942 0.00362 -2.46057 0.00362 47.8172 281.4047 13459.0196 654.9570

0.7 0.02395 0.00282 -2.72468 0.00282 56.8642 248.7562 14147.6975 690.1679

0.75 0.01910 0.00214 -3.03357 0.00214 68.8365 214.9953 14801.3203 723.7254

0.8 0.01475 0.00156 -3.41204 0.00156 85.6905 179.8460 15412.4087 755.3432

0.85 0.01078 0.00106 -3.90854 0.00106 111.7453 142.8729 15966.2688 784.4669

0.9 0.00711 0.00064 -4.63913 0.00064 159.0513 103.2944 16429.6475 809.8979

0.95 0.00363 0.00028 -6.01471 0.00028 281.4597 59.3271 16698.4147 828.2016

Average 11138.8059 11195.1257

Table A-5 Table of calculated local and average heat transfer coefficients for R- 141b using Jung's correlation

A-8

Appendix A

Calculation of Local and Average Heat Transfer Coefficients for R11 using Jung's Correlation


[° C] [kPa] [kg/m3] [kJ/1<g] [kJ/kg.K] [micropoise] [W/(m.K)]

0 40.41 1532 33.2 0.8494 5338 9.50E-02 Liquid

0 40.41 2.49 222.3 0.5508 98.93 7.41E-03 Vapour

Constants

Surface Tension IMJ/m 2] 20.96

Heat Transfer pm 4000

Refrig. Mass flow (Ws] 0.02591

Tube Inner Dim [m] 0.008

Tube Length I'm] 7.96

Gravity (m/s 2] 9.81


A. IM 2] 2.0006E-01 mu, (12a.s] 5.3380E-04

A, (m 2] 5.0265E-05 mu, Pa.s] 9.8930E-06

q fw/m 2] 1.9994E+04 Bo 2.0512E-04

G fkg/(s.m 2) 5.1546E+02 Pr, 4.7752E+00

h 4, 11/kg] 1.8910E+05 bd fm] 8.5412E-04

s EN/m] 2.0960E-02 h ..(W/(m 2 K) 9.2942E+02

Tsat pq 2.7315E+02

Local Heat Transfer Coefficients (Wm" 2 K°]

x X,, N1 1N5 N F h,0 h,,, Integration

0.1 0.43400 0.09944 -0.08226 0.09944 5.3289 604.5780 3314.1822

0.15 0.28620 0.05984 -0.33973 0.05984 7.3453 577.5552 4297.9541 190.3034

0.2 0.20918 0.04082 -0.55438 0.04082 9.4198 550.2123 5220.8012 237.9689

0.25 0.16147 0.02976 -0.74644 0.02976 11.6083 522.5253 6093.3085 282.8527

0.3 0.12878 0.02259 -0.92600 0.02259 13.9607 494.4664 6924.0923 325.4350

0.35 0.10487 0.01758 -1.09925 0.01758 16.5298 466.0033 7719.2633 366.0839

0.4 0.08653 0.01390 -1.27062 0.01390 19.3782 437.0985 8483.1036 405.0592

0.45 0.07196 0.01110 -1.44384 0.01110 22.5855 407.7073 9218.5800 442.5421

0.5 0.06007 0.00891 -1.62247 0.00891 26.2573 377.7760 9927.6532 478.6558

0.55 0.05015 0.00715 -1.81037 0.00715 30.5403 347.2389 10611.4364 513.4772

0.6 0.04171 0.00571 -2.01218 0.00571 35.6469 316.0140 11270.2319 547.0417

0.65 0.03441 0.00451 -2.23403 0.00451 41.8993 283.9964 11903.4420 579.3418

0.7 0.02802 0.00351 -2.48472 0.00351 49.8155 251.0472 12509.2995 610.3185

0.75 0.02235 0.00267 -2.77793 0.00267 60.2916 216.9753 13084.2712 639.8393

0.8 0.01725 0.00194 -3.13717 0.00194 75.0399 181.5024 13621.7327 667.6501

0.85 0.01261 0.00133 -3.60846 0.00133 97.8402 144.1887 14108.6883 693.2605

0.9 0.00831 0.00080 -4.30194 0.00080 139.2384 104.2457 14515.7481 715.6109

0.95 0.00424 0.00035 -5.60766 0.00035 246.3627 59.8735 14750.9110 731.6665

Average 9865.2611 9914.2443


A-9

Appendix A

A.3 Comparison and Con clusion

Figure A-1 compares the calculated heat transfer coefficients to those of Jung

under the same conditions. The average and mean deviations are given in Table

A-7 from which it may be concluded that the spread sheet program gives the

correct answers within a maximum error of 5.7%.

Evap Tenix O'C Cooing Capacibi: 46/1/ Rut Flux alMtri

1E003 . • --&-- R22 al c

x-- - R221rg

R1433 Gic --&--

-.0-. R.1433Arg

NI('

--&-- Rll4 laic

- - El- R1143trg - - --*-- Rll Cac

- - *- - R11 .1.rg '

—&-- R143bC.dc •

- - & - - 8141b lug •

Hea

t Tra

nsfe

0 0 0 I

•

.o...

. •

•

.

' .

• ,.„

I I

0 al 02 0.3 0.4 0.5 0.6 0.7 0.8 139 1

Clidity

Figure A-1 Chart comparing Jung's predicted/measured values and the values calculated using Jung's correlation

A-10

Appendix A

Deviation % Quality I Ca/c. Integrat.1 Jung Integrat. Mean Ave

R 22 0.1 3694.00 3437.13 7.47 7.47 0.2 4220.70 395.73 4065.87 375.15 3.81 3.81 0.4 6126.40 1034.71 5772.45 983.83 6.13 6.13 0.6 7880.84 1400.72 7479.04 1325.15 5.37 5.37 0.8 9381.23 1726.21 8916.16 1639.52 5.22 5.22 0 . 9 9945.90 966.36 9365.27 914.07 6.20 6.20

Ave. h tp 6874.84 6904.67 6505.99 6547.15 5.70 5.70

- R143a

0.1 4532.34 4514.97 0.38 0.38 0.2 4887.00 470.97 4694.61 460.48 4.10 4.10 0.4 6849.88 1173.69 6580.84 1127.55 4.09 4.09 0.6 8715.81 1556.57 8287.43 1486.83 5.17 5.17 0.8 10320.34 1903.62 9814.37 1810.18 5.16 5.16 0 . 9 10921.85 1062.11 10353.29 1008.38 5.49 5.49

Ave. h tp 7704.54 7708.69 7374.25 7366.77 4.06 4.06

R 114 0.1 3261.47 3437.13 5.11 -5.11 0.2 4777.95 401.97 4694.61 406.59 1.78 1.78 0.4 7530.99 1230.89 7479.04 1217.37 0.69 0.69 0.6 9914.62 1744.56 9814.37 1729.34 1.02 1.02 0.8 11929.58 2184.42 11880.24 2169.46 0.42 0.42 0 . 9 12692.78 1231.12 12688.62 1228.44 0.03 0.03

Ave. h tp 8351.23 8491.20 8332.34 8439.00 1.51 -0.20

' R141b 0.1 3664.32 3437.13 6.61 6.61 0.2 5854.14 475.92 5592.81 451.50 4.67 4.67 0.4 9570.39 1542.45 9275.45 1486.83 3.18 3.18 0.6 12739.26 2230.96 12329.34 2160.48 3.32 3.32 0.8 15412.41 2815.17 14934.13 2726.35 3.20 3.20 0 . 9 16429.65 1592.10 15742.51 1533.83 4.36 4.36

Ave. h tp 10611.69 10820.76 10218.56 10448.73 4.23 4.23

R 11 0.1 3314.182 3257.48 1.74 1.74 0.2 5220.801 426.7492 5143.71 420.0595 1.50 1.50 0.4 8483.104 1370.39 8556.88 1370.059 0.86 -0.86 0.6 11270.23 1975.334 11341.32 1989.82 0.63 -0.63 0.8 13621.73 2489.196 13676.65 2501.797 0.40 -0.40 0 . 9 14515.75 1406.874 14574.85 1412.575 0.41 -0.41

Ave. h tp 9404.30 9585.68 9425.15 9617.89 0.92 0.16

Table A-7 Table showing average and mean deviation of local and average calculated heat transfer coefficients from Jung's prediction

A-11

Appendix A

A.4 Nomenclature

AS surface area

Ac cross-sectional area

b Laplace constant [m]

Cp specific heat [J.kg -I .K-1 ]

tube diameter [m]

d equilibrium break-off diameter [m]

F heat transfer enhancement factor

mass flux [kg.m-2 .s-1 ]

Gg gravitational force [tn-s -2 ]

heat transfer coefficient [W.m -2 .K-I ] or enthalpy [Ole]

hfg latent heat of vaporisation [k.1-1cg -1 ]

hsa pool boiling heat transfer coefficient obtained by Stephan and

Abdelsalam 5 [W.m-2 .K-I ]

k thermal conductivity [W.m -i .K-1 ]

tube length [m]

m mass flow rate [kg•s -1 ]


pressure [kPa]

heat flux [W.m -2 ]

s surface tension [N.m -1 ]

T temperature [K]

x quality

A-12

Appendix A

Greek letters

contact angle [ 0 ]

p density [kg.m-3 ]

a surface tension [N.m -1 ]

viscosity [Pa.s]


Bo boiling number, q/(G.hfg)

Pr Prandtl number of liquid, (Cp-µ)/k

Re Reynolds number, (G-D/11)

Xtt Martinelli's parameter

Subscripts

cal calculated

cec convective evaporation contribution

exp experimentally determined

1 liquid

lo liquid only

nbc nucleate boiling contribution

sat saturation

tp two-phase

v vapour

A-13

Appendix A

A.5 References

1 Jung, D.S., Radermacher, R. Prediction of heat transfer coefficients of various

refrigerants during evaporation ASHRAE Transactions Vol. 97, No. 2 (1991) 48-

53

2 Jung, D.S. Mixture effects on horizontal convective boiling heat transfer Ph.D.

thesis, Department of Mechanical Engineering, University of Maryland (1988)

3 Jung, D.S., McLinden, M., Radermacher, R, Didion, D. A study of flow

boiling heat transfer with refrigerant mixtures International Journal of Heat and

Mass Transfer, Vol. 32, No. 9 (1989) 1751-1764

4 Chen, J.C. Correlation for boiling heat transfer to saturated fluids in convective

flow Ind. Eng. Chem. Process Design Develop. Vol. 5, No. 3 (1966)

5 Stephan, K., Abdelsalam, M. Heat transfer correlation's for natural convection

boiling International Journal of Heat and Mass Transfer, Vol. 23 (1980) 73-87

A-14

Appendix B

Appendix B

Appendix B : Derivation of a formula to calculate the

length of the coil in the heat exchange accumulator

B.1 Introduction

In order to obtain the correct size of the accumulator, the process must be

modeled mathematically. The length of the coil that supplies the heat necessary

to superheat the gaseous refrigerant is critical for both the superheat and

subcooling processes. Using basic mathematical and engineering equations an

equation for the length of the coil will be derived.

B.2 Theoretical Background

The Temperature-Entropy diagram of the entire ideal process is drawn below,

T

s

Figure B-1 Temperature — entropy diagram and heat exchange accumulator.

From double pipe heat exchanger theory the heat transfer may be calculated

using

B-1

Appendix B

Q = U•A•LMTD Equation B-1

Assuming that the fluid specific heats do not vary with temperature and the

average heat transfer coefficients are constant throughout the heat exchanger, the

logarithmic arithmetic mean temperature difference ) may be defined as

LMTD = (T

5 — T1 )— (T4 1.8

ln[(T5 — T1 )/(T4 — T8 )A Equation B-2

From the T-s diagram it follows that the heat exchanged within the heat

exchanger accumulator is equal to

Q = —h 8 ). m(h 4 —h 5 )

Equation B-3


expressed in terms of the overall heat transfer coefficient. The value of U is

governed in many cases by only one of the convection heat transfer coefficients.

The conduction resistance is generally small when compared with the convection

resistance's. If one value of h is markedly lower than the other value, it will tend

to dominate the equation for U 1 . The overall heat transfer coefficient may based

on either the inside or outside area of the tube and is at the discretion of the

designer. When based on the inside area, U is defined as

= 1

1 ± ln(rjr, ) ± A, 1 Equation B-4 h, 2itkL A. h o

and if the overall heat transfer coefficient is based on the outside area of the tube

U becomes

B-2

Appendix B

Uo = 1

(

A. 1 + A. ln(r./ri ) + 1 Equation B-5 A i h i 2tkL ho

hi in the above equations applies to single phase flow and may thus be calculated

using the following form of the Dittus-Boelter equation,

Nu d = Ill = 0.023 Red. ' Prn k

where Re = pVD , pr . Cd-1, , V _ 4m

11 k ' prED 2

n = 0.3 for cooling of the fluid

and 0.4 for heating of the fluid

Equation B-6

If the quality of the gaseous refrigerant on the outside of the coil is equal to, or

greater than unity (i.e. single-phase flow), h o may be calculated from the Dittus-

Boelter equation. If the quality is less than unity (i.e. multiple phase flow) the

Jung and Radermacher equation 2 may be used.

h tp = h nbc + h cec = Nh sa + Fh lo Equation B-7

where

B-3

N = (4048)• X1; 22 • Bo 133

N = 2.0 — (0.1) - X -„°.28 • Bo -°33

(

h sa = 207

for X„ 1

for 1<X„ 0.745 )0.581

b • d • Tsat ) 12` • (Pr, )0333

Pi

k, q•b•d

where i0.5

b d 0.01460[ 26

with a contact angle of [3 = 35 ° 8(131 Pv

0.85

X„ I-L v

= 0.023 1(1 ( G(1 — x)D )

0.8 (Cp1111

k,

)0.4

D p.,

F = 2.37[0.29+ 1 X„

1 — x ( ) p, 1-1 1 09( ) 0.5 ( ) 0.1

Appendix B

Table B-1 Summary of heat transfer coefficient correlation by Jung et al. 2

B.3 Derivation

Substituting Equation B-2 to Equation B-6 into Equation B-1 and basing the

overall heat transfer coefficient on the inside of the tube yields

m(h, 1

A, • LMTD 1 + A, ln(r./r,) A. 1

h, 27ckL A. h.

m(h, — h 8 ) . A, LMTD 1 A, ln(r./r,) ± A, 1

h, 2rckL A. h.

1 A. ln(r /r.) A. 1

LMTD (h, 2itkL A. h.

m(h, — h 8 ) A.

B-4

Appendix B

LMTD = 1 + ln(ro /ri ) + 1

m(h, — h 8 ) Ai h, 2itkL A o h.

LMTD 1 + 10. /D ; ) 1

— h 8 ) TED i Lh i 2rckL rcD o Lh o

Therefore

M(h i -h 8 )[ 1 + 111(3 0 /D 1 ) ± 1

TC • LMTD h i D, 2k h o D o Equation B-8

which gives L in terms of the heat transfer coefficient based on the inside area of

the coil. When the overall heat transfer coefficient is based on the outside area of

the coil, the exact same equation is obtained. This is expected, as the length of

the coil is a constant. The term (h1-h8) may be replaced by (h 4-h5) according to

Equation B-3. However the term (h 1 -h8) is preferred since most compressor

manufacturers recommend a superheat of about 10°C.

B.4 Conclusion

Equation B-8 gives the length of the coil inside the heat exchange accumulator in

terms of; mass flow rate, enthalpies, logarithmic mean temperature difference,

coil diameters, thermal conductivity's and heat transfer coefficients. These

quantities are all known or otherwise may be calculated. The length of the coil

may now be determined with the help of this equation.

B-5

Appendix B

B.5 Nomenclature

A cross sectional area [m 2]


Cp specific heat [J•kg - 1•1(-1 ]

tube diameter [m]



mass flux [kg.m-2 .s-1 ]

g gravitational force [m.s -2]

h enthalpy [kJ-kg-1 ]

hi heat transfer coefficient on inside of the tube [w.m-2.K-i]

h0 heat transfer coefficient on outside of the tube [Wm 2 •K" 1 ]


Abdelsalam 3

k thermal conductivity [Wm -1 .1(-1 ]

tube length [m]

LMTD logarithmic arithmetic mean temperature difference [K]

m mass flow rate [kg-s -1 ]


Q heat flux [W]

q heat flux per unit area [Wm -2 ]

r radius [m]

T temperature [K]

overall heat transfer coefficient [Wm -2 .K-1 ]

B-6

Appendix B

velocity [m.s-1 ]

quality

Greek letters

13 contact angle [ 0]

TC Pi

p density [kg.m-3 ]

cy surface tension [N.m-I ]

1-1 viscosity [Pa•s]


Bo boiling number, q/(G•hfg)

Nu Nusselt number, (h•d)/k

Pr Prandtl number, (Cp•O/k

Re Reynolds number, (G•D/0


Subscripts

c cold fluid

cal calculated



h hot fluid

1 liquid

B-7

Appendix B

to liquid only


sat saturation

tp two-phase

v vapour

Superscripts

n exponent used in Dittus-Boelter equation

B.6 References

1 Holman, J.P. Heat Transfer (7 th Ed) McGraw-Hill (1992)

2 Jung, D.S., Radermacher, R. Prediction of heat transfer coefficients of

various refrigerants during evaporation ASHRAE Transactions Vol. 97, No. 2

(1991) 48-53

3 Stephan, K., Abdelsalam, M. Heat transfer correlations for natual

convection boiling International Journal of Heat and Mass Transfer, Vol. 23

(1980) 73-87

B-8

Appendix C

Appendix C : Interpretation of Compressor Curves using

Isentropic and Volumetric Efficiencies

C.1 Introduction

This Appendix converts the existing compressor curves into formats that may be

effectively used for this project.

The compressor that was used in all the experimental tests was a Tecumseh

AJ5515E. The compressor performance curves obtained from the compressor

manufacturers where all given with a constant final superheat temperature of

35°C. The compressor performance curves assume a liquid subcooling value of

8.33°C, which may not be valid for the heat exchange accumulator. The curves

are given in terms of an electrical current frequency of 60Hz, which is used in the

United States and other countries. South Africa uses a frequency of 50Hz.

Modifications to these performance curves are therefore necessary. These

modifications may be achieved with the help of isentropic and volumetric

efficiencies.

C.2 Theoretical Background

The compressor performance curves give the capacity, mass flow rate, input

power and current in terms of evaporating and condensing temperatures. In order

to convert the electrical current frequency to 50Hz, the data is multiplied by a

factor of 0.833 (50/60). The converted values are given in Table C-1.

C-1

Appendix C

Tecumseh AJ5515F Compressor

Refrigerant R22 Motor Type PSC Gas leaving Evaporator Superheated to 95°F Volts-Hz-Phase 230/208/60/1 Gas Entering Compressor 95°F Volts [Tested at] 230 Liquid Subcooled 15°F Run Capacitor [M fd] 20 Room Ambient 95°F Forced Air Over Compressor Yes

Ca pacity [BTU/h] Cond. Temp

°F

60Hz 50Hz Evaporating lTemperature

32 53 32 53

110 13200 20000 11000.00 16666.67 13 0 11000 17600 9166.67 14666.67 140 10000 16200 8333.33 13500.00 150 9000 15000 7500.00 12500.00

Mass Flow [lbs/h] Cond Temp

°F

60Hz 50Hz Evaporating iTemperature

32 53 32 53

110 150 270 125.00 225.00 130 135 250 112.50 208.33 140 127.5 2375 106.25 197.92 150 120 225 100.00 187.50

Input Power [W]

Cond. Temp.

°F

60Hz Evaporating Temperature

32 35 40 45 50 53

110 1410 1455 1520 1570 1600 1610 130 1550 1615 1715 1810 1860 1890 140 1600 1705 1830 1935 2020 2055 150 1695 1795 1950 2080 2185 2230

Capa city [kW] Cond. Temp.

°C


0.00 1.67 4.44 7.22 10.00 11.67

43.33 3.224 3.46 3.86 4.25 4.65 4.885 54.44 2.687 2.92 3.30 3.68 4.07 4.299 60.00 2.443 2.66 3.02 3.38 3.74 3.957 65.56 2.198 2.41 2.76 3.11 3.45 3.664

Mass Flow [kg/s] Cond. Temp.

°C


0.00 1.67 4.44 7.22 10.00 11.67

43.33 0.01575 0.01755 0.02055 0.02355 0.02655 0.02835 54.44 0.01418 0.01590 0.01878 0.02165 0.02453 0.02625 60.00 0.01339 0.01504 0.01779 0.02054 0.02329 0.02494 65.56 0.01260 0.01418 0.01680 0.01943 0.02205 0.02363

Input Power [W] Cond. Temp.

°C


0.00 1.67 4.44 7.22 10.00 11.67

43 . 33 1175.00 1212.50 1266.67 1308.33 1333.33 1341.67

54 .44 1291.67 1345.83 1429.17 150833 1550.00 1575.00 60.00 133333 1420.83 1525.00 1612.50 168333 1712.50 65.56 1412.50 1495.83 1625.00 1733.33 1820.83 1858.33

Table C-1 Tables showing conversion of data from 60Hz to 50Hz and to SI units.

C-2

Appendix C

Figure C-1 Temperature — Entropy diagram for vapour-compression cycle.

Isentropic Efficiency

From Figure C-1, it follows that

Wideal = m(h2' — hl)

Equation C-1

where the enthalpy at point 1 is obtained using the REFPROP I database and the

method that follows. The evaporating temperature (and the fact that the quality at

point 8 is 100% - vapour only) is used to determine the evaporating pressure,

which in turn is used along with the temperature at point 1 (evaporating

temperature plus 11.11°C) to obtain the properties at point 1. Once the enthalpy

at point 1 is known, the related entropy may be determined. Point 2' has the

same entropy as point 1 (isentropic process) and the pressure at point 2' may be

found by determining the pressure at point 3 from the condensing temperature

and the fact that the quality at point 3 is 100% (vapour only).

C-3

Appendix C

Capacity [W] Cond. T Evaporating Temperature

°C -11.67 -5 0 5 7.22 11.67

43 . 33 1563.00 2512.35 3224.00 3935.65 4251.63 4885.00 54.44 1075.00 1996.34 2687.00 3377.66 3684.31 4299.00 60.00 929.00 1794.33 2443.00 3091.67 3379.68 3957.00 65.56 732.00 1569.89 2198.00 2826.11 3104.99 3664.00

Input Power [W] Cond. T Evaporating Temperature

°C -11.67 -5 0 5 7.22 11.67

43 . 33 760.00 1025.00 1175.00 1275.00 1308.33 1341.67 54.44 700.00 1080.00 1291.67 1429.17 1508.33 1575.00 60.00 570.00 1060.00 1333.33 1541.67 1612.50 1712.50 65.56 570.00 1110.00 1412.50 1645.83 1733.33 1858.33

Mass Flow [kg/s] Cond. T Evaporating Temperature

°C -11.67 -5 0 5 7.22 11.67

43 . 33 0.00315 0.01035 0.01575 0.02115 0.02355 0.02835 54.44 0.00210 0.00900 0.01418 0.01935 0.02165 0.02625 60.00 0.00184 0.00844 0.01339 0.01834 0.02053 0.02494 65.56 0.00158 0.00788 0.01260 0.01732 0.01942 0.02363

Table C-2 Tables showing Tecumseh AJ5515F data for various evaporating

and condensing temperatures

The actual work may be taken as the compressor input power. This is obtained

from the compressor manufacturer's tables shown in Table C-2. The isentropic

efficiency is defined as

'ideal

i = 'actual actual

Equation C-2

Table C-3 illustrates the calculation of isentropic efficiency as discussed, for

various evaporating and condensing temperatures.

C-4

Appendix C

Point 1

T [°C] h [kJ/kg] s [kJ/kgK] p[kg/m1

-0.56 409.1 1.801 13.66 6.11 412 1.79 17.04 11.11 414.1 1.783 19.99 16.11 416.1 1.776 23.31 18.33 416.9 1.773 24.92 22.78 418.6 1.767 28.41

Point 8 T [°C] P [kPa] h jkJ/kg]

-11.67 334 401.9 -5 421.5 404.6 0 497.7 406.5 5 584 408.3

7.22 625.7 409.1 11.67 716 410.6

Point 3 T [°C] P [kPa]

43.33 1666 54.44 2154 60.00 2434 65.56 2739

Point 2' s [kJ/kgicl 1.801 1.79 1.783 1.776 1.773 1.767 h [kJ/kg] Evap T °C -11.67 -5 0 5 7.22 11.67 P [kPa] Gond T °C

1666 43.33 452.6 448.7 446.3 443.8 442.8 440.7 2154 54.44 492.2 456.2 453.7 451.1 450 447.9 2434 60.00 496.6 459.8 457.2 454.6 453.5 451.3 2739 65.56 500.8 463.4 460.7 458.1 456.9 454.7

Ideal Work

Evap T °C -11.67 -5 0 5 7.22 11.67 Cond T °C

43.33 137.025 379.902 507.150 585.812 609.825 626.535 54.44 174.510 397.865 561.330 677.198 716.468 769.125 60.00 160.781 403.380 577.001 705.939 751.517 815.456 65.56 144.428 404.844 587.160 727.593 776.838 852.862

Isentropic Efficiency

Evap T °C -11.67 -5 0 5 7.22 11.67

Cond T °C

43.33 0.18030 0.37064 0.43162 0.45946 0.46611 0.46698 54.44 0.24930 0.36839 0.43458 0.47384 0.47501 0.48833 60.00 0.28207 0.38055 0.43275 0.45791 0.46606 0.47618 65.56 0.25338 0.36472 0.41569 0.44208 0.44818 0.45894

Table C-3 Tables showing enthalpy values and calculated values for the

Tecumseh AJ5515F compressor at various evaporating and condensing

temperatures

C-5

Appendix C

Volumetric Efficiency

The ideal mass flow rate is defined as

mideal = PlQideal Equation C-3

where Qideal is the compressor volumetric displacement specified by the

compressor manufacturers as 4.545 m 311 1 at a reciprocating speed of 2900 rpm

and a frequency of 50 Hz. The inlet density (point 1 in Figure C-1) may be

determined using the final superheat temperature and pressure that are known.

The actual mass flow is obtained from the compressor curves supplied by the

manufacturers.

The volumetric efficiency may then be defined as

11v = M actual Equation C-4 M ideal

Table C-4 illustrates the calculation of volumetric efficiency as discussed, for

various evaporating and condensing temperatures.

C-6

Appendix C

Pressure Ratio

Evap T °C -11.67 -5 0 5 7.22 11.67 Cond T °C

43.33 4.98802 3.95255 3.34740 2.85274 2.66262 2.32682 54.44 6.44910 5.11032 4.32791 3.68836 3.44254 3.00838 60.00 7.28743 5.77461 4.89050 4.16781 3.89004 3.39944 65.56 8.20060 6.49822 5.50332 4.69007 4.37750 3.82542

Ideal Mass Flow

Evap T °C -11.67 -5 0 5 7.22 11.67 Cond T °C

43.33 0.01725 0.02151 0.02524 0.02943 0.03146 0.03587 54.44 0.01725 0.02151 0.02524 0.02943 0.03146 0.03587 60.00 0.01725 0.02151 0.02524 0.02943 0.03146 0.03587 65.56 0.01725 0.02151 0.02524 0.02943 0.03146 0.03587

Volumetric Efficiency

Evap T °C -11.67 -5 0 5 7.22 11.67 Cond T °C

43.33 0.18265 0.48118 0.62407 0.71863 0.74839 0.79041 54.44 0.12177 0.41842 0.56167 0.65747 0.68800 0.73186 60.00 0.10655 0.39227 0.53046 0.62306 0.65265 0.69526 65.56 0.09133 0.36612 0.49926 0.58866 0.61729 0.65867

Table C-4 Tables showing calculated values for the Tecumseh AJ5515F

compressor at various evaporating and condensing temperatures

C-7

Appendix C

C.3 Graphs

The following graphs may now be drawn at 50Hz in SI units;

Capacity as a function of evaporating and condensing temperatures,

Mass flow rate as a function of evaporating and condensing temperatures,

Compressor work as a function of evaporating and condensing temperatures,

Current as a function of evaporating and condensing temperatures,

Isentropic efficiency as a function of pressure ratio.

Volumetric efficiency as a function of pressure ratio.

The tables along with these graphs follow.

5.000

4.750

4.500 _■111111 4.250

4.000

Condensing Temperature rC] _... -s- 4133 -e- 54A4 —a— EOM -e- 65.%

3.750

.....

Je Z., 3.500 3 co 0- 3.250 (a Li

3.000

2.750

2.500

2.250

2.000 -0

_..miiiiiiiiiiiIIIIIIIIIIIIIIIIIIIII

0111111111111111111111111 11111111111111111111.— __aggill1=11111111111111111111111w—__iai. .

_,.../0111111111111111111111.1.1°—/111111111111111111111111111111.— ,_....digigillppllIllPlIlliIlliP .

=11111111111.11."--.■11111111111111111111111111111111111111111111°."-.

11111.111111111.11111"..--

50 0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50 8.50 9.50

Evaporating Temperature ['C] 10.50 11.50

Figure C-2 Tecumseh AJ5515F capacity curve in SI units at 50Hz, 220V

C-8

Appendix C

Zr, -1C 0

113 re

o u to to A 2

0.0300

0.0290

00283

0.0270

0.0260

0.CQ50

o.ce4o

0.0230

0.0220

0.0210

0.0200

aose

ama-.1

0.0170

0.0160

0.0150

0.0140

00130

0.0120 .

Condensing Temperature rC]

-0- 4333 -e- 54.44 -6- 60.03 -0- 6556 _

-

. :

' i f i I I I 1 -0.93

I 0.93

' i 1.50

i

250 3.50 4.93 550 650 7.93

Evaporating Temperature ["C]

8.50 9.93 1030 11.93

Figure C-3 Tecumseh AJ5515F mass flow curve in SI units at 50Hz, 220V

1900

1850

1800

"

'

1750 -r Condensing Temperature rC

1700

1650

H4. -- 41 -e- 33 54.44 -a- 6200 -0- 65.56 •

1600 '

41 1550

0 1500

S. 1450 o *5 1400

1350

1300

1250

1200

1150

-0

'

'

.---------•

- 1 50 0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50

Evaporating Temperature ['C]

8.50 9.50 10.50 11.50

Figure C-4 Tecumseh AJ5515F compressor power curve in SI units at 50Hz, 220V

C-9

Appendix C

050

.

0.45 -

Condensing Temperature

° 0 0.40

C 13

7.5 E 035.

-a-43.33 -9- 54.44

-6-60.00 -*- 6595

C

' ' ' ' ' • ' ' ' ....... ; ; i 1 1 I i 1 2.0 2.5 3.0 3.5 4.0 4.5 50 55 60 6.5 7.0 7.5 60 85

Compression Ratio

Figure C-5 Graph showing isentropic efficiency versus compression ratio for

Tecumseh AJ55 15F compressor at 50Hz, 220V

0.80

0.70 „ Condensing Temperature [ ° C]

0.60 >.■ 0 C a)

• -0- 43.33 -e- 54.44 -8- E01:0

.65.%

..- 0 50 9

E u.i u 0.40 L Q1 E 0.30 7 o >

020

0.10

0.00

.

,

' 1 20 2.5 3.0 35 4.0

I

4.5 5.0 5.5 6.0

Compression Ratio

f I i I

6.5 7.0 7.5 8.0 85

Figure C-6 Graph showing volumetric efficiency versus compression ratio for

Tecumseh AJ5515F compressor at 50Hz, 220V

C-10

Appendix C

Curve fits for the isentropic and volumetric efficiencies where completed on a

scientific graphing program. This was done so that the isentropic and volumetric

efficiencies could be calculated at any compression ratio or stipulated

evaporating temperature. The results are shown in Table C-5 and Table C-6

respectively where x represents the compression ratio and b the coefficient for

the relevant equation and condensing temperature. The accuracy of the curve fit

is indicated by the correlation coefficient (defined as the covariance divided by

the product of the sample standard deviations). In other words, the closer the

correlation coefficient to unity, the more accurate the curve fit.

Cond. T. emp

1°C1

i i = b[3]x3 + b[2]x2 + b[l]x + MO] Correlation Coefficient

13131 13121 bill b[O]

43.33 -0.0025 -0.0181 0.1279 0.2953 0.9999 54.44 0.0047 -0.0779 0.3405 0.0406 0.9991 60.00 0.0015 -0.031 0.1504 0.2651 0.9996 65.56 0.0005 -0.0163 0.093 0.3129 0.9998

Table C-5 Curve-fitting coefficients for isentropic efficiency

Cond. Temp.

1°C]

i. = 13131x3 + b[2]x2 + b[l]x + 13101 Correlation Coefficient

b[3] b[2] bill b[O]

43.33 0.0056 -0.0994 0.2654 0.641 0.99999 54.44 0.0025 -0.0569 0.1879 0.6143 0.99999 60.00 0.0016 -0.0426 0.1576 0.5876 0.99999 65.56 0.0011 -0.0321 0.1324 0.5609 0.99999

Table C-6 Curve-fitting coefficients for volumetric efficiency.

C-11

Appendix C

C.4 Verification of Equations

The isentropic and volumetric efficiency equations that where derived in the

previous section need to be verified before they may be used. The equations are

used to calculate the efficiencies, which are then compared to the actual values.

The average and mean deviations are also calculated and shown in Table C-7 and

Table C-8.

Cond T pc]

Pressure Ratio

Expected

1 I

Calculated

ri I

Ave. Deviation

Mean Deviation

43.33 4.988 0.180 0.173 -4.228 4.228 43.33 3.953 0.371 0.364 -1.875 1.875 43.33 3.347 0.432 0.427 -1.104 1.104 43.33 2.853 0.459 0.455 -1.009 1.009 43.33 2.663 0.466 0.460 -1.239 1.239 43.33 2.327 0.467 0.463 -0.765 0.765

54.44 6.449 0.249 0.257 3.185 3.185 54.44 5.110 0.368 0.374 1.394 1.394 54.44 4.328 0.435 0.436 0.357 0.357 54.44 3.688 0.474 0.473 -0.269 0.269 54.44 3.443 0.475 0.481 1.332 1.332 54.44 3.008 0.488 0.488 -0.089 0.089

60.00 7.287 0.282 0.295 4.704 4.704 60.00 5.775 0.381 0.389 2.146 2.146 60.00 4.890 0.433 0.435 0.439 0.439 60.00 4.168 0.458 0.462 0.904 0.904 60.00 3.890 0.466 0.469 0.708 0.708 60.00 3.399 0.476 0.477 0.185 0.185

65.56 8.201 0.253 0.255 0.689 0.689 65.56 6.498 0.365 0.366 0.387 0.387 65.56 5.503 0.416 0.414 -0.316 0.316 65.56 4.690 0.442 0.442 0.007 0.007 65.56 4.377 0.448 0.450 0.318 0.318 65.56 3.825 0.459 0.458 -0.178 0.178

A verage 0.237 1.159

Table C-7 Table illustrating accuracy of isentropic efficiency equation

C-12

Appendix C

Cond T pc]

Pressure Ratio

Expected

1v

Calcula

1, I Ave.

Deviation Mean '

Deviation

43.33 4.988 0.183 0.187 2.212 2.212 43.33 3.953 0.481 0.483 0.361 0.361 43.33 3.347 0.624 0.626 0.254 0.254 43.33 2.853 0.719 0.719 0.079 0.079 43.33 2.663 0.748 0.749 0.038 0.038 43.33 2.327 0.790 0.791 0.066 0.066

54.44 6.449 0.122 0.130 6.861 6.861 54.44 5.110 0.418 0.422 0.906 0.906 54.44 4.328 0.562 0.564 0.486 0.486 54.44 3.688 0.657 0.659 0.190 0.190 54.44 3.443 0.688 0.689 0.119 0.119 54.44 3.008 0.732 0.733 0.112 0.112

60.00 7.287 0.107 0.093 -12.739 12.739 60.00 5.775 0.392 0.385 -1.795 1.795 60.00 4.890 0.530 0.527 -0.724 0.724 60.00 4.168 0.623 0.620 -0.445 0.445 60.00 3.890 0.653 0.650 -0.373 0.373 60.00 3.399 0.695 0.694 -0.194 0.194

65.56 8.201 0.091 0.095 3.560 3.560 65.56 6.498 0.366 0.368 0.410 0.410 65.56 5.503 0.499 0.501 0.286 0.286 65.56 4.690 0.589 0.589 0.100 0.100 65.56 4.377 0.617 0.618 0.056 0.056 65.56 3.825 0.659 0.659 0.083 0.083

A verage -0.004 1.352

Table C-8 Table illustrating accuracy of volumetric efficiency equation

C.5 Conclusion

Figure C-2 through Figure C-6 illustrate the compressor's characteristic graphs in

S.I. units at 50 Hz. The equations representing isentropic and volumetric

efficiency (illustrated in Table C-5 and Table C-6) give accurate representations

of the respective efficiencies.

C-13

Appendix C

C.6 Nomenclature

h enthaply [kJ.kg-1 ]

Q volumetric displacement [m 3 •h-1 ]

m mass flow rate [kg.s -1 ]

P pressure [kPa]

s entropy [kJ.kg -1 .K-1 ]

T temperature [K]

W work [J]

Greek letters

rl efficiency

p density [kg.m-3]

Subscripts

i isentropic

v volumetric

ideal ideal quantities

actual real quantities

C.7 References

Gallager, J., McLinden, M., Morrison, G., Huber, M. NIST Thermodynamic

Properties of Refrigerant Mixtures, Version 4.01 Thermophysics Division,

Chemical Science and Technology Laboratory, National Institute of Standards

and Technology, Gaithersburg, MD 20899 (1993)

C-14

Appendix D

Appendix D

Appendix D: Determination of local heat transfer

coefficients within the heat exchange accumulator

D.1 Introduction

In order to model the system using basic heat transfer equations the amount of

heat exchanged within the heat exchange accumulator must be calculated. This

heat transfer is dependent on the quality of the refrigerant within the

accumulator. Should the quality of the refrigerant entering the accumulator be

less than unity, the method of Jung and Radermacher l shall be used to calculate

the local heat transfer coefficients. On the other hand, should the quality of the

refrigerant entering the accumulator be equal to or greater than unity, the Dittus-

Boelter2 equation will be employed to calculate the local heat transfer

coefficients. Ideally the value of the local heat transfer coefficient predicted by

Jung and Radermacher at high qualities should tend toward the value predicted

by the Dittus-Boelter equation.

The aim of this section of work is to investigate the relationship between the

values of the local heat transfer coefficients as determined by the method of Jung

and Radermacher at high qualities and the Dittus-Boelter equation at a quality of

one.

D-1

Appendix D

D.2 Theoretical Background

Dittus-Boelter

The Dittus-Boelter equation 2 is given as

111) Nu d = H = 0.023•Re a'•Pr n

Equation D-1

4m 2 where Re =

pVDH , Pr = C P , V =

1-t pTcD H

n = {0.3 for cooling of the fluid


This equation is only valid for single-phase fluids.

Jung and Radermacher Equation

The Jung and Radermacher equation' is discussed in detail in Appendix A. The

equation was given as

h tp= h nbc h cec Nh sa Fh lo Equation D-2

where

D-2

N = (4048)• X1;22 • Bo' .33 for X t, 1

N = 2.0 — (0.1). X: .28 • Bo-°33 for 1 < X tt 5

k q 0.745 ) 0.581

h— 207 - b

p )

Pr 0 . 533 sa b • d k 1 • Tsa, PI

1

where

1.5

b • d = 0.014613[ 2a

g(p i - Pv ) with a contact angle of p = 35°

0.85

F = 2.37(0.29 + 1 X tt

0.5 )0.1

x tt = 1 — X ) 119 p, )

0.8

h 10 = 0.023 kl (0— x)D) (C o • [1 1

D µ1 k1

Appendix D

Table D-1 Summary of heat transfer coefficient correlation by Jung and

Radermacher l

The down fall of this method in this work is that Jung and Radermacher state that

their equation is only valid between the qualities of 0.1 and 0.9 1 .

D-3

5 4AL ■ Ant TA

S

Appendix D

D.3 Simulation

In order to compare the heat transfer coefficients, a set of common conditions

must be specified in order to obtain coefficients that may be compared. The

refrigerant R22 was chosen to operate in a small air conditioning system at

standard ARI conditions. This represents a condensing temperature of 54.44°C

and an evaporating temperature of 7.22°C. The compressor that was chosen to be

used in the simulation was a Tecumseh AJ5515E whose properties are shown in

Appendix C. The simulation was completed on an ideal process i.e. no pressure

losses. The process is shown on a temperature-entropy diagram below.

Figure D-1 Temperature-entropy diagram of ideal process

The compressor manufacturers curves stipulate the capacity of the system, mass

flow rate and amount of superheat. Once the condensing and evaporating

temperatures have been established, the respective enthalpies, entropies,

temperatures and pressures of the points illustrated on the temperature-entropy

diagram may be determined using a database such as REFPROP 3 . The refrigerant

density, viscosity, thermal conductivity and specific heat at constant pressure

D-4

416.9 1 1.773 18.33 625.7 450 2 1.773 87.32 2154

418.7 3 2154 54.44 1.682 268 4 2154 54.44 1.222

260.2 5 1.198 48.8 2154 260.2 6 7.22 1.215 625.7 208.4 7 7.22 1.03 625.7 409.1 8 625.7 1.746 7.22

h [kJ/kg]

s (kJ/(kg.K))

P L (k Pa)

T pc]

Appendix D

values may be determined at the respective evaporating and condensing

temperatures. The results of these procedures are illustrated in Table D-2.

Constants

Refrigerant Compressor Type Evap Temp [°C] Cond Temp [°C] Mass Flow Rate[kg/s]

R 22 Tecumseh AJ5515E 7.22 54.44 0.02164747

Critical Temperatures

Coil Inlet Temp [°C] 54.44 Coil Exit Temp [°C] 48.8 HXA Inlet Temp [°C] 7.22

HXA Exit Temp [°C] 18.33

Other Input Values

plc [m] 0.00811

Doc Eml 0.009525

DH)(A [m] 0.2

k [W/(mK)] (Cu 50°C) 383

Vapour R22 Properties at 7.22°C

Density [kg/m 3] 26.38 Viscosity [kg/(ms)] 1.21E-05 Cp [J/(kgK)] 706.1 Thermal Cond. [Wm -1 K-1 ] 1.04E-02

Liquid R22 Properties at 54.44°C

Density [kg/m 3] 1058

Viscosity [kg/(ms)] 1.26E-04

Cp [J/(kgK)] 1426

Thermal Cond. [Wm -1 K-1 ] 7.12E-02

Table D-2 Table of initial known values required for the simulation

Two modifications to the Jung and Radermacher method described in Appendix

A are made in order to adapt the method for use with the heat exchange

accumulator. The coil length has a direct influence on the heat flux. A change in

length changes the surface area available for heat exchange i.e.

D-5

Appendix D

AS = n-Dcoii.Lcoii and therefore q = Q/A, Equation D-3

Thus the surface area is, in this case, not only dependent on the coil diameter but

also on the coil length. The second modification is made to the cross-sectional

area available for the gaseous refrigerant's mass flow through the accumulator.

The mass flux is dependent on the internal cross-sectional area of the heat

exchange accumulator (in this case there is a coil that decreases the area available

for the mass flow). The inner diameter available for the vapour to pass though is

known as the hydraulic diameter defined as

D = 4A

F H p Equation D-4

Referring to Figure D-2 the hydraulic diameter for the heat exchange

accumulator is

D = 4[A

' + A

2]

H p Equation D-5

D-6

Appendix D

Figure D-2 Figure illustrating critical diameters.

Al and A2 will vary at different vertical heights in the heat exchange accumulator

due to the cross-sectional profile of the coil. This profile' is illustrated in Figure

D-3 a.

Figure D-3 Figure illustrating average diameter of coil.

Assuming that the outer diameters of the coils touch (Figure D-3b) and that there

is coil throughout the vertical height of the heat exchange accumulator, the

D-7

Appendix D

problem of this varying area may be overcome by calculating the average cross-

sectional area. This is obtained by integrating the cross-sectional area of the coil

to get an average diameter (D AC) for the entire vertical height of the coil.

Referring to Figure D-3c, the average radius of the coil is given by

x1139X 1 Sr dr = Ac

x max — X mm xm. X max — X

where A c = , therefore 2

2 nr rOC OC TED OC giving D AC = TED OC rAC = n 2(D oc — 0) 4 8 4

Equation D-6

Referring to Figure D-2 and substituting the relevant variables into Equation D-5

the hydraulic diameter then becomes

4{ D =

—D AC )274D 2Fixik — ± D Ac )2 11 HXA +IDW D Ac )4- w —DAC

)]

Resulting in

2 D FD,A — 4 • D Ac H D + 2 .D w

Equation D-7

The choice of the coil-winding diameter (D, in Figure D-2) is complex due to

practical limitations at small diameters i.e. it is not practically possible to coil a

9.525mm outer diameter pipe into a winding diameter of 30mm (taken from pipe

i When piping is bent to form a coil the cross-section normally distorts to an oval shape. For the purpose of this work a circular cross-section will be assumed.

1 rAC

n

D-8

Appendix D

centre to centre), without severe distortion of the pipe taking place. For the

purpose of this theoretical simulation it will be assumed that the coil-winding

diameter will be 50% of the heat exchange accumulator diameter with the centre

of the accumulator and coil windings coinciding (Figure D-4). Although this is

not always practically possible this assumption is made in order to complete the

simulation. This is an aspect that is researched in the appendices that follow in an

attempt to find the optimum coil-winding to accumulator diameter ratio.

Figure D-4 Figure illustrating coil-winding diameter with respect to heat

exchange accumulator diameter where D = DHXA

When the coil-winding diameter (D w) is equal to 0.5DHxA, then

D MCA

2

D H = - 2 • D HxA • D AC

D + D HXA HXA

therefore

D-9

Appendix D

D H 2D

FIXA — • D Ac 2

Equation D-8

DAC may be written in terms of the coil outer diameter, Doc, as in Equation D-6

D — DH

oc Equation D-9 2

Therefore the cross-sectional area available for gaseous refrigerant to flow

through is given by

A c = 4 .D2H =16

(13 Hxik — % • Doc )2 Equation D-10

Other Variables

Once the evaporating temperature is known, the other evaporating refrigerant

properties (pressure, density, enthalpy, specific heat at constant pressure, viscosity

and thermal conductivity) may be determined using a program such as REFPROP 3 .

The mass flow is given in the compressor curves and the heat transfer may then be

calculated using Q = m(hi-h8). A 3/8" outer diameter pipe was measured at the

condenser exit on a small air conditioning system that was used in the practical set-up.

This translates to an inner coil diameter of 8.11mm and a outer coil diameter of

9.525mm. All the above-mentioned values may now be inserted into the computer

program (Appendix A) adapted for the Jung and Radermacher method with a heat

exchange accumulator (Table D-3).

D-10

x„ N1 1N5 h lo F N x Integration h Local Heat Transfer Coefficients 11N/m 2 .KJ

Appendix D

Temperature Pressure Density tnthalpy Cp Viscosity Therm Conti [ °C] [k Pa] [kg/m') [kJ/kg] [kJ/kg.K] [micropoise] [VV/(m.K)]

(.22 525.1 1255 52.8 1.1 /3 2053 9.895-U2 Liquid (.22 625.1 25.38 253.5 U./051 120.9 1.114E-02 Vapour

Constants Preliminary Calculations II = 35

Surface Tension linJ.m -2 ] 11.79 D tap IMI 0.03 As lin ‘1 2.5478E+00 mu, (Pa.sJ 2.0530E -04

Heat Transfer AV] 168.850 D 5 I'M] 0.00748 A c im ‘,1 4.4404E-05 mu„ (Pa.$) 1.2090E -05

Refrig. Mass flow lkg.s -1 ] 0.0216 D. I'm] 0.015 el [Yam 'I 6.6272E+01 Bo 6.7732E -07

Coil Inner Diameter lin] 0.00811 D. lin] 0.00752 G Presm ' )) 4.8751E+02 Pr, 2.4354E+00

Coil Outer Diameter I'm] 0.009525 h 4, a/kg] 2.0070E+05 bc I linl 7.1474E -04

Coil Length (ml 100 s (Wm] 1.1790E -02 h 44 (Wm 2 .K] 4.2339E+01

Gravity lin.s- 2 ] 9.81 Tsat IK] 2.8037E+02

=12NMEMIUMMNUMMEMMI2MINI MW=MINUALIMI MUMIMMIUM ILL=MINLMMEMIIMMMUSIMIll ME2=EIMUMWSZUSIiIMMILIMMII MEM12=1112:161=1Mii11

MINIMMIUMMMUSilif==ililiSIMMUI IM=MMEMIMM MILIIMMI ZMINWRIIMUMMUMUOMIMIUMMIMaIMIIM.IIMM

MELLMEMUIEMMWMA =MML211MM2UMMWMA2=11MiaMM M2kMEMSMIRM=WW=M12 111M MULIMIll IM=MMUMAMIUMSki laUMMULMMINUMMIMI=M1 MUL=MM2E=MMEAMMZMWI NIUMINI MINIMUAM MEWMEM112iii =MMU=MMIUMMlialMilIMLWMMIIUMMall MMIMINEWMAMINJ UNIMMIMMMWMIIIMMNiiW

MII=IIIMMUIIIIMMIMUIMMMIIIMLZSMIMUMMIMILMIIMQ:MMIMMUM IIMNIIMIL=1111=1:MUIMWMIIMMISMMIUMI IMMMM

Average 613526 6116.556

Table D-3 Jung and Radermacher method used to calculate heat transfer

coefficients for an internal heat exchange accumulator diameter of 0.03m and a

coil length of 100m

The coil length and a heat exchange accumulator diameter are then varied and the

respective heat transfer coefficients calculated. Table D-4 to Table D-8 shows the

calculated heat transfer coefficients for a variety of coil lengths and accumulator

inlet qualities using the Jung and Radermacher method. In each case the

accumulator inner diameter is held constant (the chosen diameters range from

0.03m to 0.3m). Although a heat exchange accumulator diameter of 0.03m is

very impractical the results were calculated to show that the expected Jung and

Radermacher trend is observed when the accumulator diameters are small. Figure

D-11

Appendix D

D-5 to Figure D-9 illustrates the heat transfer coefficients as a function of quality

for the respective internal heat exchange accumulator diameters.

DiixA [m] E"fiiii

C) [WI .

0.030

01" 36272:15 .

0.030

"0:2 "531 36075"13254t430

0.030

'0.5 0.030

1 ..0 .

6627.215

0.030

270 -3313.608-

0.030

5.07 -1325:443 ..

0.030

-10707 662:722

0.030

50.0 7132:544"

0.030 100:0

361272

0:1 00 . -9529357 -5504403 295T5417 -MS:4W -1783:609- 13887684 -1733341.7 71936:193- '201'3702 - 770:150- --0861:267. -48287216" -5274 .386- 730239247 7295975417 -2087816- 7203575207 729341-3457 -2934T302-

"*U00 . 7707250-

-3212307 ' 77435:49-749217095-

-4764330- -3704:620- 417487933-

-3533007- 74625.991-7399

-3490:038- 73475:0007 -3473:65'17 9 8 075247

-3472150- -39797940--S97991-8-

-3472:82C 2 473 . 3 9327f6-47--3

07300 7703479- 751767603- 459071657 744967663- -4-4717432-44637609- -4-4-6-27365- 443179127 74431-.905- 7707350- 6933772' 75479:177-50-2275687 4923.1204922:775- 74922-7627 -49-497974 4930.17i 40247089

07400-7 6979745- -5305:232-544470377 53667652- -537079937 753667177` -53657411- --53-65:138-- -533571287 07450- --7030-701- -31-4-27249- 7585378307 753077931-75795.4567-579T76TO 579 0.993 73790778 0 57907772 77075007- 772357-12-- 64327832- 7625174177 -621-47619- -62047587 -6201-75017 76201701977-6207835- -6200:829-

0 .5 0 7425.67 6822-130--76636:51 .. • . • :1 . • . • 0.800 -76-3-878-3-715682-2- -7008.575- 6 98 4.990-76978:571-61j76759-4-7-6073728-07-6976.168-6976.1 -07650 7365T29--7484.045-7366:787--7 ... • . . , . , . . . 3-41:1507

-0.700 8097.70 7800.968 7709706 -769571918 -7391.234 -76901017- 7689.824 7689.755 7639.752 -70-.7507- -33297347 -61047168- 780347912 80237898 783207895- 7801979727 -3019:8257 -30197772- -8019-770 -

0.800 8552.85 -3338.665 783387166- 73330;137" 8327:947 . 8327:274' 8327.167" 8327.129 8327.127 0.850- 73757357 -8-6457847- 76611739877-660579197 7666474167 7660379667 7660376937 766037867- "36037666- 0.900 6924.72 8857.320 -8336759T 8333:295" -88327396 -883271207 -8832:076 8832.060- "83327059 -

7-079507-3996527 7896676517 789577725- 7895672747 7895578787 78955757- -8955:737- 8955:730.78955:730 0.590 8720.63- 87157785 87147295 8714.058 8713.9947 '-87131974 8713.971 8713:970 8713.969

Table D-4 Jung and Radermacher heat transfer coefficients for various lengths

and a heat exchange accumulator inner diameter of 0.03m

Figure D-5 Graph showing heat transfer coefficients as a function of quality for

a heat exchange accumulator inner diameter of 0.03m

D-12

10 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

Quality

Coll Length [m]

X 0.1

0.2

•

0.5

1.0

,2.0

, 5.0

▪

50.0

DMus Boelter

100000

10000

1000 .c

100

54.670

0

Appendix D

DFixA [M] 0.05 0.05 01

331-36-076

0.05

0.5 -13254743V

0.05

1.0 -662772W

0.05

270 --53137608-

0.05

570 -13257-443-

0.05

10.0 6627722-

0.05

5070 -13275-4-4--

0.05

100.0 -66172-

E[m] -Q-[WI-

071 86272716-

0:400- 10037.46 6124.520 '26347102" -1602:823 '052:652 5657231 -454.045- -430:070 4'52.703 0:150- 47747:43 13565685 "3056561 - T M4. 750 026:060 788.767- 166.403 758:546" 758:249.._ 0100 -.32053:10 -0636 . 558- 2465148 1324.748 1013.817- 048. 466 -002:077 .807:556- -807:353-

--0150. 24409.182 7400.550 -2174:585 4339 . 080 t T13. 275 -1043:544- 4052.454 Ton . 5at -1026.353 0:300..- -1688007- 5065452- 1020421 1360359 1.247. 344- ""1464:400- 1155.064 1.152.064 -11 52. 872-

-0735-0--- -150-T6-13-50-3•5:525- 19477159- -14557006 1322:002- 12607008 -T2747558- -f2727023 -T271:936- 07400 12505745 -43657063-10207301-1551:600-1425:606-7303. 3 1 -13687140-1566.103- -1"356124- -07450" 10216755 -38757667 10227720 1612:469---15277676 -15017661-1-4077724- 14067240- 14067404 .`0"500" -650504-3500750810447318 -1606:415-1627:554- 1606:664 -160-5565-1-6027f81- 160271"37-

0.550" 7546.67 -5234. 51"1"- .T978:728 4770.044 1724.605 -1707:661 1705:108 1.704.240- J704144- 01.600- -6264. 70. 3024.430 '2021:600- -1862147- -1-816749 - 1606360- "1805241- -4 602:485- "18027456 0:650" 5442.05 2663102- "20701462-1044;025 4000.657 '1800:061 4607:578 1.606 .770 .1806756- 0:700 -4746:47 2750.000' "2121:787- 2021614 1906:849- -1086:647- -1087:308- -1086:844- -1986:824- 0:750. 4166.05 -2642:051- 14747505- ""2100:006- 10707607- -2073:450- 1072:457- --2072t103"" -2072:000-

--T800-- 3678730- 1567145-2226.179 1171:657- 11577048- 21527403 1151:769-21517510- 11517501- 07650 -5264758--2566:061--22737046-2236:668 2226 . 7-65"2 223 . 676-2225. 1 8 4-2223T0-08-222'300T- -n00- 200610 -2452:623-2312761422007315- 218217236 -226273a- 2262:089- 2281:963 22617059- -0:950 - -1680762- 236071522527:10 7 -23177590- -231470-14-23r4:001-23-137060- -2315-043- 151'57011-

0000" 2206.40 2263.727 .2255650 2252.047" 2251.:6. 1.0 2254:476- 2251 .454 2251 .447 2254.447-





D-13

544.937

13.448

,0.1

0.2

3 , 0.5

1.0

-e- 2.0

, 5.0

▪

10.0

50.0

•

100.0

_y_ Dittos Boelter

10

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10

Quality

100000

10000

1000

100

Coil Length [m]

Appendix D

Dm% [M] 0.1 071-----072

--662727f5-13-f3670"8-T3254.43T-652T.215

0.1 0.1 0.5

0.1 1. •

0.1 .0

0.1 5. •

13257443-662772.2

0.1 1 07Cr"--5070---16070--

0.1 0.1

L [m) --0-1W1-- 331"37668- 1327544 567272--

071'0 0" -12344. 078 7064:97 -31.28 :292 1860. 518 • "10301022 . 472. 628 276.455 IT 0 .915" .9621 4 . 071 50" -34871165 95207. 1 1 "I 7212 . am 4831 .462 - 1450:656 410:848- -245486- -166536- -184:325- -0:200" 237994.74 65041:74 11647775 31871190 -10617625 "172.272 259:459 210.244" 217.739" 0:250 173624.55 47515.76 '8729:347 2560.880 870:201 -361.976" 270/15 '250:395" 249.208

-07500" 111846:10 36147.78 "6714:477 2013:505 -757.346 -364.847 302:425- 260.173 279:341-- --Tam- 16270611 26224792 -51167534 16737379- 6807119- -37476-42- -3167059- 308740- ...308:092- 0-400 813107326 22416768 -4207:276--T4157596--6207073---3-6873-44- -3407916 -336267 155 . 705- -07450-- 650467562 -17906755--15267002 -12247712- -5977294- --4047321-3717634- -1627604- -3627284" --07500-522607801 f451572120267650-710707772 5767413 421:623 -307:002- -3687226- -1877697-

0:550- "42041603 -11'762:25- -24467817 - -087:642 563.813 439:637- 419 ..665' "4127644" 412:580- 0:606 33683.899 .9500746 -2062:526" 879:625 557:134 457:947 442:171- -436:550- --436:340-

""0:650 . 26756.73 7626;51 -17457403- -6091770 554.692"' 476.230 463:762-4597314- --45971"48- "0:700' 20948.654 -6060795 -1 482:042 ." "753:825 -555.207- 404:236 484:525"461 :064 . -480.934 -0:750-- 16033:612 4735:90- -1261:257--7087647---557:091 511.655 "5047286-501 7659- -5017561-

--T800 "T18457977 -1608731- T0747704- 6717769- -5617918- -528.-132 522:758- -5207843- -520:771- 07650 626470590 -26-44757- - 157050 6417070-556 . 139- -5417690- -519425-5387118-5587059- 0.9005201.2265" -181974- -7707717- -6T473T5- -5697222-- -5557353- -553:146- -5527161--5527132 -07050 -266676764 -71-118:62- -6607163---56r.347- 5677405- 5617100- 5507419- 5607071- -5607660 -

0:996 ....- 879.0554' 616M- 581 .270 "5491102 -5467151 545.154 -544.096- .-5447930- -5447037-





D-14

0.90 1.00 1.10

1 i i i i I i i i 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Quality

- Coil Length [nil

3.610

10000000

1000000

100000

10000

1000

100

10

0.1

▪

0.2

•

0.5

▪

1.0

-o- 2.0

5.0

10.0

50.0

100.0

DMus Boelter

Appendix D

D H [In]

L imi ---071W1--

0.2 --t1.1

-66-27272-

0.2 072-

7331367075

0.2

1325474307

0.2 T-0

0.2 270-

0.2 -5:0-

0.2 7-1-0.13-

6527722

0.2 50.0

1327544-

0.2 100707

-6-67272- 66277215 33137608 13257443

1 3-1-5371---766774-0- 3707.04 ; . • 1 I . . • . a- 0 .1 00 -07150-7 720200'2775 -55075275- -98657751- -259-8-T-69- -73967590-- -T3707473- 41271-01-- -707-453-- -577653- --07200-- T37807870- 37574677- -6740754- -18438773- -50727428 9-617446 -3077650- -7747556- -557860- -07250-- 100465276- -2740021 497219737-773470771 3724760--7277135- -2507-470--- 807-451 -74124--

0.300 762564.4 720795409- 37376. 40 1024532 -2552:469- .577 .770 - 2167020- -7677061- ' . 7527237 -7 ' 7- 0.350-- ' 593539.0 161879.27 29116.65- 6002752 2246.248 475:530 194.26077 7-9105 - - 95 144- 77-0:400-7 -46940357 1 . 28067:0.0.. 2305570... -6356722 1003.222 402:887- '180 . 182 .. .00.793 - -797524- -"' 0.450-7 - 374976.5 102304:6118440779- 5103.38 1467.2457 348.903 171.0457 -107.6447 ' 105272-- -70:500-7 -3005525- 7-82f Of '79- -T482'271'47 -4122722- -12-05129- '7-3077940 '165.255 11-4. sof 112:48-8- --- 07550---- 724138778- -6095729 -11920727-3336727- --99-670-3-9---2767270- ----1-61 - 601- 1207905- 1197469- 7-0500- 71928095 - -52656740- -055052- -2595:22- -6267258- -251:433 1'607015- 127.427 1267205 -07650 752537.6 4 16-8-272- -7 ; .1 1.740 159.432 133.655 132.691 -07700 - 118757:5- 32477"31-- 594077x- -59-40771-- -17207-42 569.-857-- 215:"986- 1'597707- 139545- --73876-65--- 07750 9015972- -2215-84797- 4547:52- 1'344.-93- 4717814 1607570-1-4573-45-----14-47776-- 2037277 -07500- -6-578-4:3 1043776 -3350752 1-02-5735- 3587719 1927914 1517774 1507674-- - 507258- -77 0:8507- 7-4493074 12362:04 134512 752718 3177874- 184.297- -1637054- 155:481 -7 -1557197-

0160 2710 T757 7504.39 -1477:05 518749 2577154' 176.778 153:996--- -159143977 -1597268- 0:950 • 0

..9

.9

.0-

1202274- 2Ci93. 4

3305. 06 04798

741:60' -25T .79'

31'950 182790

7204:555- 164.116 .

169.170 '158.339

10.543 157.420

i 61. 55777 -157:093-

T617462- ' 157:051 --

...........





D-15

Appendix D

DH [m]

Clair -0-1Vfl1

0.3

-0. f'

0.3

012

0.3

-075-

0.3

170

0.3

2.0

0.3

5.0.

0.3

'10.0- 0.3

-50.0

0.3

-100.0

162 .150 3 . • • .. . 1 : • • . 66.272

0.160- -135-10.8-7907. - 3684777---2231741- 12-77.622- 601.663- 33575-87 457'80- 6Z974

0450 --5363T3-1-71-46-21537-1-282-356.20-71-54-4764-19-52-47287-352477T8- 9807205- ---73T45- 39-7213

0200 3858710 997485.8- 178991 -19 48820. 2417.826 681.973 63.182 40.034-

07250- 266776-472-72735-67513-082-41-f -3-66-10768- - 73-475w 1-77676314 5-107333 -597-141-- 427263

0100- 2024461 -8 . -551952:1 00062:40 72703673-6 7400.152 1360:770 400.266 57.898 45090-

0:350 . 1575875.7 420604.0 77114.54 21055:63 5772:710 1 -0727196- -324.842 58.158 46:187

0400 1246314.2 -330814:0 61006:01 16687:67- 4579.292 8617354 270:066 50:285 51 .:400

0.450 9053508 271307:5 48736.10 - 13324.81 3870.734 701.407 220.280 80045 54.646

0.500- -798533:1 217742.3 -30112.52 -10703.65 -2058.665 576.618 197:062 62.936 57:884--

0.550 640636:9 1 . 746062- 51302.62 8801.70 2388.402 477.301 173:471 85.130 617077-

01600 ----0150-

_511543:8 ... -40-470777-

-139533.7 --f10-3-827-41-065-878-27

250887344 -6685031 -54-627267-

1 .022.663 1637:377

306.683 33872257

153.086- 1387244-

67.442 ---697607-

647205- --17247--

--Y700-----3T50-6.6- *850296 '15474.204 426971 .90 1214.401- 274.661 125.4-40- -72.175- 70:182

-07750- 2300647-4-852281 11762116 3258.424- 941-7280- -2287304 -- 1-479-14- -747494- -7270-62--

07600- 1743381- 4758175 8598702 2399.000 768.723--1-667657 106.1 9---767708-7-75-1-04-

-0 .8 50- -1160-5777-3-24871 5892. • Il• ; ; ;. ;29 78.723 777071

-07900- -7161'274- 1958175- -35787861 10337653- 3307609 -1287-409- --9-27-470 807372- -797919

-07950 -3157272- 166673' --f621-2-28--50078-10- 1957354 -1-01-74-07- - 667-468-- 817140- -607941-

-0700- 52078 148071-- 330:153- 1477241 077374 827037- -797598- -787728- -787-698-





D-16

Appendix D

The heat transfer coefficient at qualities equal to or greater than unity may be

calculated using Equation D-1. Table D-9 shows the heat transfer coefficients as

calculated by the Dittus-Boelter equation (Equation D- 1) for various internal heat

exchange accumulator diameters.

DI-Dun 0.03 0.05 0.1 0.2 0.3

DH Im 0.00752 0.01752 0.04252 0.09252 0.14252 v [m 's] 18.4805 3.4042 0.5779 0.1221 0.0514 Re 3.03E+05 1.30E+05 5.36E+04 2.46E+04 1.60E+04 Pr 0.8185 0.8185 0.8185 0.8185 0.8185 Nu 515.5990 262.0806 128.9368 69.2243 48.9943 ho fiNm-2K 11 179.257 54.67 13.448 3.610 1.703

Table D-9 Table of calculated heat transfer coefficients for various internal heat

exchange accumulator diameters using the Dittus-Boelter 4 equation

D.4 Discussion of Results

DfixA = 0.03m (Figure D-5)

The heat transfer coefficients for all lengths are all in good agreement at high

qualities. The curve formed is generally a single line and exhibits the shape that

is expected when the Jung and Radermacher method of calculation is utilised i.e.

concave curves at low qualities that join to form a single increasing line with a

positive gradient. The values of the heat transfer coefficients are relatively large

- ranging between 1688 W•rn -2 •K-l and 9881 W.m"2 .K-1 . These large values are

attributed to the high velocity of the gaseous refrigerant flowing through the

accumulator caused by a narrow accumulator diameter. Although not valid, the

Jung and Radermacher method of calculation has been extended to a quality of

0.99. This was done in order to view the behaviour of the heat transfer coefficient

according to Jung and Radermacher's equation at very high qualities in an

D-17

Appendix D

attempt to understand why this equation is not valid in this region. Figure D-5

shows that the value of the heat transfer coefficient drops slightly at a quality

0.99 when calculated using the Jung and Radermacher equation. The Dittus-

Boelter value (at a quality of 1) of 179.257 W.m -2 .K-1 is much smaller than the

value predicted by Jung and Radermacher at a quality of 0.9 (8832 W•m -2 •K-1 ).

DfixA = 0.05m (Figure D-6)

The heat transfer coefficients at the lower heat fluxes (longer coil lengths) behave

according to the characteristics as predicted by Jung and Radermacher. As the

heat flux increases (coil length decreases) the heat transfer coefficients exhibit a

totally different behaviour. The value of the heat transfer coefficient increases

rapidly to a maximum around a quality of 0.15 and then decreases, tending

toward the same value that the lower heat fluxes tended toward. This is because a

large amount of heat must be exchanged over a very short coil length at a

constant mass flow rate resulting in very high heat transfer coefficients. The

transition from liquid to vapour is therefore very quick resulting in a peak heat

transfer coefficient at a low quality. As the accumulator diameter increases, this

abnormal trend is expected to dominate as the hydraulic diameter resulting in a

larger flow area and reduced velocity. The Dittus-Boelter value is again much

smaller than any of the Jung and Radermacher values.

DHxA = 0.1m, 0.2m amd 0.3m (Figure D-7, Figure D-8 and Figure D-9)

These plots generally exhibit the same characteristics as Figure D-6. The lower

heat fluxes (longer coil lengths) follow the expected Jung and Radermacher trend

while the higher heat fluxes deviate toward a maximum near a quality of 0.15

D-18

Appendix D

and then decrease toward a common final value. As the heat exchange

accumulator diameter increases, more of the heat transfer coefficient curves tend

to exhibit the deviational behaviour i.e. increased heat transfer coefficients

(especially around a quality of 0.15).

Directly opposing this effect is the fact that the velocity of the gaseous refrigerant

slows as the accumulator diameter increases, thus decreasing the Reynolds

number which in turn decreases the value of the heat transfer coefficient. These

factors are clearly illustrated in Figure D-7, Figure D-8 and Figure D-9 where it

may be seen that the values of the heat transfer coefficients generally decrease

with an increase in accumulator diameter, BUT, the curves tend to spread out

over a greater range of heat transfer coefficients i.e. deviate from expected results

with an increase in accumulator diameter.

Relationship between Jung and Radermacher and Dittus-Boelter methods

In order to investigate whether there is a relationship between the Jung and

Radermacher and Dittus-Boelter methods of calculation, a graph of heat transfer

coefficients (calculated by the two methods) versus heat exchange accumulator

diameter was plotted. The Jung and Radermacher heat transfer coefficients where

plotted at qualities of x= 0.9 and x = 0.99 (Again, in an attempt to determine why

the Jung method is invalid). The results are illustrated in Table D-10 and the

graph shown in Figure D-10. From the results it is clearly seen that there is no

constant relationship between the two methods although some relationships are

reasonably close. The Jung and Radermacher values at a quality of x = 0.99 also

do not have any fixed relationship with any other figures.

D-19

Appendix D

D

[ml

ht. (Jung) 0.9

[Wm -2K-1 ]

ht. (Jung) 0.9

[Wm2K-1 ]

h0 (DB)

[Wm 2K ' ]

htp(0.9)/ h 0 htp(0.99)/ ho

0.03 8832.06 8713.97 179.257 49.270 48.612 0.04 3906.70 3854.46 89.415 43.692 43.108 0.05 2281.96 2251.45 54.670 41.741 41.182 0.075 964.03 951.14 23.689 40.695 40.151

0.1 552.33 544.94 13.448 41.071 40.521 0.2 159.27 157.08 3.610 44.118 43.512 0.3 79.92 78.70 1.703 46.918 46.200

Table D-10 Table illustrating relationship between Jung and Radermacher and

Dittus-Boelter (DB) methods of calculation

10000.000 10000.00

1000.00

-e- ho (DB)

-e- htp 0,119)0.99

-a- htp (Jung) 0.90

-------_______

100.00

Hea

t tr

an

sfe

r C

ol

10.00

.......- -__ t __.-_-_-_ 1.00 0 0.05 0.1 0.15 0.2

HXA Diameter [m]

0.25 0.3 0.35

Figure D-10 Graph illustrating relationship between Jung and Radermacher and

Dittus-Boelter (DB) methods of calculation

D-20

Appendix D

D.5 Conclusion

The values of the heat transfer coefficients given by the Dittus-Boelter equation

tend to be consistently lower than those given by the Jung and Radermacher

equation at high qualities. There seems to be no fixed linear relationship between

the two methods of calculation. A literature survey indicates that there is very

little evaporation theory between qualities of 0.9 and 1. This is an area that

requires more research and must be carefully investigated. For the purpose of this

study the worst case scenario will be investigated i.e. the lowest value of the heat

transfer coefficient will be used which in this case is always the heat transfer

coefficient as calculated using the Dittus-Boelter equation.

D-21

Appendix D

D.6 Nomenclature

Ac cross sectional area [m 2]

AF cross sectional gaseous flow area in the HXA [m 2 ]

AS surface area [m2 ]


Cp specific heat [J•kg - 1•K-1 ]

diameter [m]

DH hydraulic diameter [m]

Dw diameter of coil winding (taken from coil centre to centre) [m]



mass flux [kg.tn-2 .s-1 ]

g gravitational force [m.s -2 ]

enthalpy [kJ-kg -1 ]

hi heat transfer coefficient on inside of the tube [W.m -2 .K-1 ]

ho heat transfer coefficient on outside of the tube [w.m2•K-1]


Abdelsalam4

k thermal conductivity [Wm 1•K-1]

length [m]

LMTD log arithmetic mean temperature difference [K]



pressure [kPa]

D-22

Appendix D

p wetted perimeter used for calculating the hydraulic diameter [m]

Q heat flux [W]

q heat flux per unit area [W-m -2]

r radius [m]

s entropy [kJ-kg -1 K-1 ]

T temperature [K]

U overall heat transfer coefficient [w.rn-2.K-i]

V velocity [m-s-1 ]

x quality

Greek letters

P contact angle [ 0]

n pi

P density [kg-m-3 ]

a surface tension [N-m-I ]

1-t viscosity [Pa•s]


Bo boiling number, q/(G•hfg)


Pr Prandtl number, (Cp•O/k

Re Reynolds number, (G•13/0


D-23

Appendix D

Subscripts

Ave average

AC average relating to the coil

c cold fluid

cal calculated


coil referring to the coil in the heat exchange accumulator


h hot fluid

HXA heat exchange accumulator

i referring to inside surface of a pipe

IC inner surface of the coil

1 liquid

lo liquid only

OC outer surface of the coil

referring to outer surface of a pipe


sat saturation

tp two-phase

vapour

Superscripts

exponent used in Dittus-Boelter equation

D-24

Appendix D

D.7 References

Jung, D.S., Radermacher, R. Prediction of heat transfer coefficients of various


53

Holman, J.P. Heat Transfer 7 th ed. McGraw-Hill book Company (1992)





Stephan, K., Abdelsalam, M. Heat transfer correlation's for natural convection

boiling International Journal of Heat and Mass Transfer, Vol. 23 (1980) 73-87

D-25

Appendix E

Appendix E

Appendix E: Derivation of an equation that determines the

refrigerant mass flow rate for an accumulator heat

exchanger at a specified range of ambient conditions

E.1 Introduction

The aim of the paper is to develop a design process that assists in the correct

sizing of the accumulator heat exchanger before manufacture. The ideal design

process is one that facilitates a fluctuation in all the variables. The difficulty in

applying this to the accumulator heat exchanger is developing an equation that

will facilitate a range of different evaporating and condensing temperatures. This

is due to the fact that the vast majority of variables in the system are determined

by the evaporating and condensing temperatures. Developing a single equation

that is valid at a specified range of ambient conditions involves deriving an

equation that determines the length of the inner coil as a function of accumulator

diameter. This will allow the length of the coil to be determined by simply

substituting the relevant variables in to the derived equation rather than following

the entire calculation procedure as described in the previous Appendices.

The aim of this Appendix is to derive a general equation for the refrigerant mass

flow rate.

E-1

Appendix E

E.2 Derivation of a gener al equation for refrigerant mass flow

In this and similar systems the vast majority of variables in the system are

determined by the evaporating and condensing temperatures. The fact that these

temperatures vary according to the ambient temperature complicates the design

process. In order to simplify the design process, an equation that predicts the

refrigerant mass flow rate at a specified range of evaporating and condensing

temperatures will be derived. According to the A.R.I specification 540P-D4 1 ,

variables such as the refrigerant mass flow rate and efficiencies (isentropic or

volumetric) may be expressed by a single equation that is a function of

evaporating and condensing temperatures. The equation is

x = C o + C,TE + C 2 Tc + C 3 TE2 + C,I TE Tc

+ C 5T + C oT + C 7 TcT + C 8 TX ± CX Equation E-1

where x is the required variable (refrigerant mass flow rate or efficiency). The

coefficients are determined by solving a system of linear equations. Equation E-1

can be expressed by the matrices, [A]•[X] = [B]. Matrix A represents the range of

condensing and evaporating temperatures and their higher order values and

products. In this case, evaporating temperatures varying from —12°C to 12°C and

condensing temperatures ranging from 43°C to 66°C were considered at intervals

shown in Table E-1. This forms a 20 by 10 matrix (matrix A). The refrigerant

mass flow rates corresponding to the respective evaporating and condensing

temperatures, (as derived in Appendix C), formed matrix B (20 by 1) which then

allowed the system to be solved using matrix algebra (method of least squares).

E-2

Appendix E

After solving, the resulting matrix is matrix X (10 by 1) which represents

constants Co -C 9 .

M atr x [A) M atrix [8: M atrix pc TE Tc TE 2 TETC TC 2 TE ' TCTE 2 TC 2TE Tc' M

[°C] [°C] [kg /s ]

1 -11.67 43.33 136.1889 -505.661 1877.489 -1589.32 5901.065 -21910.3 81351.59 0.0032 CO 1 -5 43.33 25 -216.65 1877.489 -125 1083.25 -9387.44 81351.59 0.0104 C1 1 0 43.33 0 0 1877.489 0 0 0 81351.59 0.0158 C2 1 5 43.33 25 216.65 1877.489 125 1083.25 9387.445 81351.59 0.0212 C3 1 11.67 43.33 136.1889 505.6611 1877.489 1589.324 5901.065 21910.3 81351.59 0.0284 C4 1 -11.67 54.44 136.1889 -635.315 2963.714 -1589.32 7414.124 -34586.5 161344.6 0.0021 C5 1 -5 54.44 25 -272.2 2963.714 -125 1361 -14818.6 161344.6 0.0090 C6 1 0 54.44 0 0 2963.714 0 0 0 161344.6 0.0142 C 7 1 5 54.44 25 272.2 2963.714 125 1361 14818.57 161344.6 0.0194 C8 1 11.67 54.44 136.1889 635.3148 2963.714 1589.324 7414.124 34586.54 161344.6 0.0263 C9 1 -11.67 60 136.1889 -700.2 3600 -1589.32 8171.334 -42012 216000 0.0018 1 -5 60 25 -300 3600 -125 1500 -18000 216000 0.0084 1 0 60 0 0 3600 0 0 0 216000 0.0134 1 5 60 25 300 3600 125 1500 18000 216000 0.0183 1 11.67 60 136.1889 700.2 3600 1589.324 8171.334 42012 216000 0.0249 1 -11.67 65.56 136.1889 -765.085 4298.114 -1589.32 8928.544 -50159 281784.3 0.0016 1 -5 65.56 25 -327.8 4298.114 -125 1639 -21490.6 281784.3 0.0079 1 0 65.56 0 0 4298.114 0 0 0 281784.3 0.0126 1 5 65.56 25 327.8 4298.114 125 1639 21490.57 281784.3 0.0173 1 11.67 65.56 136.1889 765.0852 4298.114 1589.324 8928.544 50158.99 281784.3 0.0236

Table E-1 Table illustrating matrices [A] and [B]

Once solved the coefficients in matrix X are,

Co 2.23E-02 C5 3.79E-07

C1 8.75E-04 C6 -3.53E-10

C2 -1.62E-04 C7 1.56E-09

C3 -8.17E-08 C8 -1.66E-07

C4 1.19E-05 C9 -2.28E-09

Table E-2 Table shown coefficients for mass flow rate calculations

Once these variables are substituted into Equation E-1, an equation that

determines the mass flow rate at any given evaporating or condensing

temperature, within the above mentioned range, is defined.

E-3

Appendix E

E.3 Equation Accuracy

Once the constants have been determined, it is necessary to verify the

coefficients by calculating the mass flow rate using Equation E-1. The process is

repeated several times, all at different evaporating and condensing temperatures,

in order to establish the accuracy of the equation. Table E-3 shows that the

evaporating and condensing temperatures, calculated and expected refrigerant

mass flow rate and average and mean deviations. The average mean deviation is

0.24% indicating that the equation is a good representation of the mass flow rate.

TE

[°C]

Tc

[°C]

Calculated

m [kg/s]

Expected

m [kg/s]

A verage

Deviation

M can

Deviation

-11.67 43.33 0.0031 0.0032 0.1973 0.1973 -5 43.33 0.0103 0.0104 0.0033 0.0033 0 43.33 0.0158 0.0158 -0.0057 0.0057 5 43.33 0.0212 0.0212 -0.0068 0.0068

7.22 43.33 0.0235 0.02355 0.0043 0.0043 11.67 43.33 0.0284 0.0284 -0.0149 0.0149 -11.67 54.44 0.0021 0.0021 -1.3864 1.3864

-5 54.44 0.0090 0.0090 -0.1565 0.1565 0 54.44 0.0142 0.0142 0.0298 0.0298 5 54.44 0.0193 0.0194 0.0639 0.0639

7.22 54.44 0.0216 0.02165 0.0947 0.0947 11.67 54.44 0.0262 0.0263 0.1014 0.1014 -11.67 60 0.0018 0.0018 2.0290 2.0290

-5 60 0.0084 0.0084 0.1852 0.1852 0 60 0.0134 0.0134 0.0058 0.0058 5 60 0.0184 0.0183 -0.0800 0.0800

7.22 60 0.0206 0.02053 -0.1435 0.1435 11.67 60 0.0250 0.0249 -0.1567 0.1567 -11.67 65.56 0.0016 0.0016 -0.8890 0.8890

-5 65.56 0.0079 0.0079 -0.0507 0.0507 0 65.56 0.0126 0.0126 -0.0052 0.0052 5 65.56 0.0173 0.0173 0.0095 0.0095

7.22 65.56 0.0194 0.01942 0.0346 0.0346 11.67 65.56 0.0236 0.0236 0.0722 0.0722

A verage -0.0027 0.2386

Table E-3 Table illustrating accuracy of Equation E-1 when used to determine

mass flow rate

E-4

Appendix E

E.4 Alternative Verification Method

The actual mass flow rate may also be determined using the volumetric

efficiency. Volumetric efficiency is defined (Appendix C) as

11 =

M actual Equation E-2 M ideal

Appendix C also defines the ideal mass flow rate as

M ideal = PiQideal Equation E-3

where Q,deal is the compressor volumetric displacement specified by the

compressor manufacturers as 4.545m 3h-1 at a reciprocating speed of 2900 rpm

and a frequency of 50 Hz. The inlet density pi may be determined by adding

11.11°C to the evaporating temperature and determining the refrigerant density at

that temperature using the REFPROP 2 database. Figure shows the inlet densities

(pi) of R-22 at evaporating temperatures ranging from -12°C to 12°C (determined

using the REFPROP database).

E-5

Appendix E

26 - -

24 -

22 _

n E 20 - _ -en

_le _ _ 8:

16 - -

14-

12_ _

10 -11 -13 -9 -7 -5 -3 -1 1 3 5 7 9 11 13

Evaporating Temperature [°C]

Figure E-1 Graph illustrating density of R-22 at compressor inlet (35°C) for

evaporating temperatures ranging from -12°C to 12°C

A curve fit applied to Figure E-1 yields the following equation

y = 0.0095x2 + 0.6402x + 17.996

Equation E-4

where y represents density (p) and x represents the evaporating temperature. The

equation has a correlation coefficient of R = 0.9999. This equation may now be

used to determine the compressor inlet density of R-22 at various evaporating

temperatures ranging between -12°C and 12°C. The ideal mass flow rate may

now be determined for a range of evaporating temperatures using Equation E-3

and Equation E-4.

Equation E-1 may also be used to determine an equation for the range of

volumetric efficiencies illustrated matrix [B] in Table E-4.

E-6

Appendix E

M atr x [A ] M atrix [131M atrix [X '

11 " L'Ci TE Tc TE TETc Tc 4 -re TCTEI Tc ITE Tc"

1 -11.67 43.33 136.1889 -505.661 1877.489 -1589.32 5901.065 -21910.3 81351.59 0.2116

o- IN

m cr Ln

Lo. r,

co 0

, L

JU

LJ

OU

UU

UL

JU

1 -5 43.33 25 -216.65 1877.489 -125 1083.25 -9387.44 81351.59 0.5441 1 0 43.33 0 0 1877.489 0 0 0 81351.59 0.6931 1 5 43.33 25 216.65 1877.489 125 1083.25 9387.445 81351.59 0.7828 1 11.67 43.33 136.1889 505.6611 1877.489 1589.324 5901.065 21910.3 81351.59 0.8379 1 -11.67 54.44 136.1889 -635.315 2963.714 -1589.32 7414.124 -34586.5 161344.6 0.1411 1 -5 54.44 25 -272.2 2963.714 -125 1361 -14818.6 161344.6 0.4731 1 0 54.44 0 0 2963.714 0 0 0 161344.6 0.6238 1 5 54.44 25 272.2 2963.714 125 1361 14818.57 161344.6 0.7161 1 11.67 54.44 136.1889 635.3148 2963.714 1589.324 7414.124 34586.54 161344.6 0.7758 1 -11.67 60 136.1889 -700.2 3600 -1589.32 8171.334 -42012 216000 0.1234 1 -5 60 25 -300 3600 -125 1500 -18000 216000 0.4435 1 0 60 0 0 3600 0 0 0 216000 0.5891 1 5 60 25 300 3600 125 1500 18000 216000 0.6787 1 11.67 60 136.1889 700.2 3600 1589.324 8171.334 42012 216000 0.7370 1 -11.67 65.56 136.1889 -765.085 4298.114 -1589.32 8928.544 -50159 281784.3 0.1058 1 -5 65.56 25 -327.8 4298.114 -125 1639 -21490.6 281784.3 0.4140 1 0 65.56 0 0 4298.114 0 0 0 281784.3 0.5545 1 5 65.56 25 327.8 4298.114 125 1639 21490.57 281784.3 0.6412 1 11.67 65.56 136.1889 765.0852 4298.114 1589.324 8928.544 50158.99 281784.3 0.6982

Table E-4 Table illustrating matrices [A],[B] and [X] for volumetric efficiency

Solving the matrices using the method of least squares yields the following

values for the coefficients;

Co 1.017 C5 2.594E-5

C 1 3.170E-3 C6 2.576E-5

C2 -8.446E-3 C7 5.546E-6

C3 -1.488E-3 C8 -8.131E-6

C4 8.182E-4 C9 -6.814E-8

Table E-5 Table shown coefficients for mass flow rate calculations

Verification of the coefficients is achieved by calculating the volumetric

efficiency using Equation E-1. The process is repeated several times, all at

different evaporating and condensing temperatures, in order to establish the

accuracy of the equation. Table E-6 shows that the Average Mean deviation is

E-7

Appendix E

0.33% indicating that the equation is a good representation of the volumetric

efficiency.

TE

[°C]

Tc

[°C]

Calculated

iv

Expected /iv

A verage

Deviation

M can

Deviation

-11.67 43.33 0.2110 0.2116 0.3127 0.3127 -5 43.33 0.5433 0.5441 0.1439 0.1439 0 43.33 0.6945 0.6931 -0.2091 0.2091 5 43.33 0.7833 0.7828 -0.0706 0.0706

7.22 43.33 0.8078 0.8081 0.0328 0.0328 11.67 43.33 0.8380 0.8379 -0.0169 0.0169 -11.67 54.44 0.1452 0.1411 -2.9434 2.9434

-5 54.44 0.4724 0.4731 0.1434 0.1434 0 54.44 0.6234 0.6238 0.0558 0.0558 5 54.44 0.7150 0.7161 0.1533 0.1533

7.22 54.44 0.7418 0.7429 0.1470 0.1470 11.67 54.44 0.7783 0.7758 -0.3234 0.3234 -11.67 60 0.1225 0.1234 0.7303 0.7303

-5 60 0.4422 0.4435 0.3140 0.3140 0 60 0.5892 0.5891 -0.0221 0.0221 5 60 0.6785 0.6787 0.0223 0.0223

7.22 60 0.7047 0.7047 -0.0003 0.0003 11.67 60 0.7411 0.7370 -0.5479 0.5479 -11.67 65.56 0.1066 0.1058 -0.7155 0.7155

-5 65.56 0.4152 0.4140 -0.3025 0.3025 0 65.56 0.5559 0.5545 -0.2623 0.2623 5 65.56 0.6403 0.6412 0.1360 0.1360

7.22 65.56 0.6648 0.6665 0.2518 0.2518 11.67 65.56 0.6988 0.6982 -0.0781 0.0781

A verage -0.1270 0.3306

Table E-6 Table illustrating accuracy of Equation E-1 when used to determine

volumetric efficiency

Rearranging Equation E-2 gives

Mactual = 1v . mideal Equation E-5

The volumetric efficiency may be calculated using Equation E-1 and the

coefficients shown in Table E-5. Equation E-3 and Equation E-4 are used to

E-8

Appendix E

calculate the ideal mass flow rate. Table E-7 shows the calculated refrigerant

mass flow rates along with deviations from the actual mass flow rate.

TE

[°c]

P [kg/m3]

PQ Caic m

[kg/s]

A ctual m

[kg/s]

A verage

Deviation

M can

Deviation

-11.67 11.8187 0.0149 0.0032 0.0032 -0.2431 0.2431 -5 15.0325 0.0190 0.0103 0.0104 0.2340 0.2340 0 17.9960 0.0227 0.0157 0.0158 0.0222 0.0222 5 21.4345 0.0271 0.0212 0.0212 -0.1539 0.1539

11.67 26.7609 0.0338 0.0283 0.0284 0.1458 0.1458 -11.67 11.8187 0.0149 0.0021 0.0021 -0.2431 0.2431

-5 15.0325 0.0190 0.0090 0.0090 0.2325 0.2325 0 17.9960 0.0227 0.0142 0.0142 0.0575 0.0575 5 21.4345 0.0271 0.0194 0.0194 -0.1536 0.1536

11.67 26.7609 0.0338 0.0262 0.0263 0.1458 0.1458 -11.67 11.8187 0.0149 0.0018 0.0018 -0.1069 0.1069

-5 15.0325 0.0190 0.0084 0.0084 0.2617 0.2617 0 17.9960 0.0227 0.0134 0.0134 0.0409 0.0409 5 21.4345 0.0271 0.0184 0.0183 -0.1398 0.1398

11.67 26.7609 0.0338 0.0249 0.0249 0.1558 0.1558 -11.67 11.8187 0.0149 0.0016 0.0016 0.0741 0.0741

-5 15.0325 0.0190 0.0079 0.0079 0.2950 0.2950 0 17.9960 0.0227 0.0126 0.0126 0.0222 0.0222 5 21.4345 0.0271 0.0174 0.0173 -0.1823 0.1823

11.67 26.7609 0.0338 0.0236 0.0236 0.1669 0.1669

A verage 0.0316 0.1539

Table E-7 Table showing alternative verification method.

E.5 Discussion of Results

Equation E-1 along with the coefficients given in Table E-2 give an excellent

approximation of the mass flow rate for evaporating temperatures between -12 °C

and 12°C and condensing temperatures between 43 °C and 66°C. Both methods

of verification support this conclusion.

E-9

Appendix E

E.6 Nomenclature

C undetermined coefficient

Q volumetric displacement [m 311-1 ]

R correlation coefficient

TE evaporating temperature PC]

Tc condensing temperature [°C]


x variable

Greek letters

71 efficiency

p density [kg•rn -3 ]

Subscripts

actual refers to actual quantity

ideal refers to ideal quantity

1 refers to compressor inlet

v volumetric

E-10

Appendix E

E.7 References

1 Air conditioning and Refrigeration Institute. A.R.I. Specification 540-D4. Air

conditioning and Refrigeration Institute, 1501 Wilson Boulevard, Arlington,

Virginia 22209, U.S.A. (1990)

2 Gallager, J., McLinden, M., Morrison, G., Huber, M. NIST Thermodynamic




E-11

Appendix F

Appendix F

Appendix F: Derivation of an equation that determines the

enthalpy difference in the heat exchange accumulator for a

specified range of ambient conditions

F.1 Introduction

The ideal design process is one that facilitates a fluctuation in all the variables.

As the evaporating and condensing temperatures vary, so the enthalpy difference

across the heat exchange accumulator will vary. An equation that determines

these enthalpies at all conditions is required for a complete mathematical model

of the heat exchange process. This will assist in eventually deriving an equation

that will allow the length of the coil to be determined by simply substituting the

relevant variables in to a derived equation, rather than following the entire

calculation procedure as described in the previous Appendices.

F.2 Theoretical Backgrou nd

The temperature-entropy diagram of the entire ideal process is shown below,

Figure F-1 Temperature — entropy diagram and heat exchange accumulator.

F-1

Appendix F

The enthalpy of the refrigerant as it enters and exits the heat exchange

accumulator determines the amount of heat that is exchanged within the

accumulator. This is illustrated in the following equation

Q = m(h, —h 8 )= m(h 4 —h 5 )

Equation F-1

The equation that determines the necessary length of the coil was derived in

Appendix B and is given as

L = m(h I — h 8 ) [ 1 +o /D i ) + 1

TC • LMTD h i D i 2k h o D o Equation F-2

It is clear that the enthalpy difference is a critical variable in the calculation

procedure. A variation in evaporating or condensing temperatures will cause the

value of the enthalpy difference to change, which will then cause a change in the

required length of the coil.

F.3 Derivation of a general equation for the enthalpy difference

The enthalpies corresponding to points 1 and 8 in Figure F-1 are only a function

of the evaporating temperature. Table F-1 shows the respective enthalpies and the

enthalpy difference for evaporating temperatures ranging from -12°C to 12°C.

This data was obtained from the REFPROP 1 database.

F-2

Evaporating Temperature [°C]

Appendix F

TE

[°C]

h l

[kJ/kg]

h 8

[kJ/kg]

h 1 - h8

[kJ/kg]

alc h 1 - h

[kJ/kg]

-12 433 401.8 31.2 31.185 -10 432.7 402.6 30.1 30.054 -8 432.3 403.4 28.9 28.909 -6 431.9 404.2 27.7 27.750 -4 431.5 405 26.5 26.576 -2 431.1 405.7 25.4 25.388 0 430.7 406.5 24.2 24.185 2 430.2 407.2 23 22.968 4 429.7 407.9 21.8 21.737 6 429.1 408.7 20.4 20.491 8 428.6 409.3 19.3 19.231 10 428 410 18 17.956 12 427.3 410.7 16.6 16.667

Table F-1 Table illustrating enthalpies

Figure F-2 shows the enthalpy difference plotted as a function of the evaporating

temperature.

Figure F-2 Graph illustrating the enthalpy difference (hi - h8) for evaporating

temperatures ranging from -12°C to 12°C

F-3

Appendix F

A curve fit applied to Figure F-2 yields the following equation

y = -0.0018x2 - 0.6049x + 24.185 Equation F-3

where y represents the enthalpy difference (h i - h8) and x represents the

evaporating temperature. This equation may now be used to determine the

enthalpy difference (h i - h8) for evaporating temperatures ranging between -12°C

and 12°C. These calculated values are shown in Table F-1.

F.4 Equation Accuracy

The equation has a correlation coefficient of R 2 = 0.9999 indicating that the

equation is a good representation of the enthalpy difference (hi - h 8).

F.5 Discussion of Results

Equation F-3 gives an excellent approximation of the mass flow rate for

evaporating temperatures between -12°C and 12°C and condensing temperatures

between 43°C and 66°C.

F-4

Appendix F

F.6 Nomenclature

D diameter [m]

enthalpy [k.T.kg-i ]

k thermal conductivity [W-m -I .K-I ]

length [m]

LMTD logarithmic mean temperature [°C]

Q volumetric displacement [m3 •11-1 ]

R correlation coefficient

TE evaporating temperature [°C]

m mass flow rate [kg.s -I ]

x variable

y variable

Greek letters

rc pi

Subscripts

i refers to inner surface of pipe

o refers to outer surface of pipe

F.7 References

1 Gallager, J., McLinden, M., Morrison, G., Huber, M. NIST Thermodynamic




F-5

Appendix G

Appendix G

Appendix G: Mathematical modelling of heat transfer

within the heat exchange accumulator with the aim of

determining the required coil length

G.1 Introduction

This section of work calculates the coil length required for the amount of heat

transfer at various accumulator diameters at standard A.R.I. conditions.

A graph of coil length versus accumulator diameter will be plotted and a general

equation for this line derived. This will allow the length of the coil to be

determined by simply substituting the relevant variables in to the derived

equation rather than following the entire calculation procedure that follows. The

derived equation will however only be valid for this system at a specified set of

circumstances, in this case at specified A.R.I. conditions. A model that will be

valid at all conditions will be developed once the results of this section of work

are correct and fully understood.

G-1

Appendix G

G.2 Theoretical Background

The Temperature-Entropy diagram of the entire ideal process is drawn below,

T

s

Figure G-1 Temperature — entropy diagram and heat exchange accumulator.

The enthalpy, entropy, temperature and pressure at each point in Figure G-1 and

the respective liquid and vapour properties of R-22 may be determined at

standard A.R.I. conditions using a database such as REFPROP 1 . Standard A.R.I.

conditions stipulate a condensing temperature of 54.44°C and an evaporating

temperature of 7.22°C.

From the T-s diagram in Figure G-1, it follows that the heat exchanged within the

heat exchange accumulator is equal to

Q = moi l —h 8 )= m(h 4 —h 5 )

Equation G-1

Assuming that the fluid specific heats do not vary with temperature and the

average heat transfer coefficients are constant throughout the heat exchanger, the

logarithmic arithmetic mean temperature difference 2 may be defined as

G-2

Appendix G

(1' )— (T — T8) LMTD = \ 1 4 vi ln[(T5 — T1)/(T4 T8 /1

Equation G-2

The average coil outer diameter and hydraulic diameter were derived in

Appendix D and are given respectively as

_ oc D AC -

TED 4

Equation G-3

Equation G-4 D HxA

DH =

OC

2

The heat transfer coefficients for single-phase fluids are calculated using the

Dittus Boelter2 equation

Nu d = hD = 0.023 Red. ' Prn

Equation G-5

pvD C D p. 4m where Re = , Pr = , v =

rcD 2 P



where D = D ic for the heat transfer coefficient based on the inner surface of the

coil and D = DH for the heat transfer coefficient based on the inner accumulator

surface.

Appendix B illustrates the derivation of the following equation used to calculate

the required coil length.

G-3

U o = - (A 0 1A,, ln(ro /ri ) 1

A, h i + 2tkL ho

1 Equation G-8

Appendix G

m(h, — h 8 ) [ 1 ± 10 0 /D i ) ± 1

TC • LMTD h,D i 2k ho D o Equation G-6


expressed in terms of the overall heat transfer coefficient 2 . The value of U is

governed in many cases by only one of the convection heat transfer coefficients.

The conduction resistance is generally small when compared with the convection

resistance's. If one value of h is markedly lower than the other value, it will tend

to dominate the equation for U. The overall heat transfer coefficient may based

on either the inside or outside area of the tube and is at the discretion of the

designer. When based on the inside area, U is defined as

U. = 1

1 + A ; A, ln(ro /r, A ; 1

h, 2rckL Ao ho

Equation G-7

and when the overall heat transfer coefficient is based on the outside area of the

tube U becomes

G-4

Appendix G

G.3 Simulation

The REFPROP database was used to determine the thermodynamic properties of

the refrigerant R-22 at the specified A.R.I. conditions. Table G-1 shows the

results of this procedure along with the coil dimensions and compressor type

obtained from a small air conditioning system. The mass flow rate, determined

using the compressor curves at A.R.I. conditions is also shown.

G-5

Appendix G

h

T

P [kJ/kg] [kJ/(kg.K)] rci [k Pa]

1

416.9

1.773

18.33

625.7 2

450

1.773

87.32

2154 3

418.7

1.682

54.44

2154 4

268

1.222

54.44

2154 5

260.2

1.198

48.8

2154 6

260.2

1.215

7.22

625.7 7

208.4

1.03

7.22

625.7 8

409.1

1.746

7.22

625.7

Constants

Refrigerant Compressor Type Evap Temp [°C]

'Cond Temp [°C] Mass Flow Rate[kg/s]

R 22 Tecumseh AJ5515E

7.22 54.44

0.021647472


Coil Inlet Temp [°C] 54.44 Coil Exit Temp [°C] 48.8 HXA Inlet Temp [°C] 7.22 HXA Exit Temp [°C] 18.33

Other Input Values

Dic [rn] 0.00811

Doc [m] 0.009525 k [W/(mK)] (Cu 50°C) 383

Vapour R22 Properties at 7.22°C

Density [kg/m 3] 26.38 Viscosity [kg/(ms)] 1.21E-05 Cp [J/(kgK)] 706.1 Thermal Cond. [Wm -1 K 1.04E-02

Liquid R22 Properties at 54.44°


Viscosity [kg/(ms)] 1.26E-04 Cp [J/(kgK)] 1426

Thermal Cond. [Wm -1 K 7.12E-02

Table G-1 Table showing thermodynamic properties of R-22 at A.R.I.

conditions and other input variables

Table G-2 shows the preliminary calculations of the variables that are not

dependent on the accumulator diameter. These calculations are the results of

equations El to E3 and E5.

G-6

Appendix G

Preliminary Calculations

v [m/s] 0.396 m(h1-h8) [W] 168.850 Re 2.70E+04 LMTD [ ° C] 38.235

Pr 2.526 DAC [m] 0.00748

Nu 106.394

h i (1447r2 K -1 ] 933.933

Table G-2 Preliminary calculations of variables not dependent on DHXA

As concluded in Appendix D, the calculation of the heat transfer coefficient on

the outer surface of the coil will assume the worst case scenario. In this case, the

worst scenario is given by the heat transfer coefficient calculated using the Dittus

Boelter equation. Table G-3 shows the calculation of the hydraulic diameter

using Equation G-4, the outer heat transfer coefficient using Equation G-5, coil

length using Equation G-6 and inner and outer overall heat transfer coefficients

using Equation G-7 and Equation G-8 respectively, for various accumulator

diameters. The accumulator diameters range from 0.03m to 0.5m at randomly

selected intervals.

G-7

Appendix G

DFixt, Calculations

D H),(A

[ml

DH Ern]

h o [wm _2 K -1 ]

L [m]

Ui

[Wm-2K-'l

Uo [wm_2K-1]

0.03 0.00752 715.207 0.392 479.759 347.804 0.04 0.01252 285.692 0.702 277.139 200.914 0.05 0.01752 156.030 1.132 174.917 126.807 0.06 0.02252 99.297 1.672 119.451 86.597 0.07 0.02752 69.213 2.318 86.617 62.794 0.08 0.03252 51.248 3.066 65.717 47.642 0.09 0.03752 39.616 3.911 51.626 37.426 0.1 0.04252 31.628 4.852 41.681 30.217

0.125 0.05502 19.889 7.606 26.651 19.321 0.15 0.06752 13.758 10.912 18.600 13.484 0.175 0.08002 10.134 14.749 13.773 9.985

0.2 0.09252 7.804 19.097 10.642 7.715 0.225 0.10502 6.212 23.942 8.491 6.156 0.25 0.11752 5.074 29.272 6.947 5.036 0.275 0.13002 4.230 35.076 5.798 4.203

0.3 0.14252 3.586 41.345 4.920 3.567 0.325 0.15502 3.082 48.069 4.232 3.068 0.35 0.16752 2.680 55.242 3.683 2.670 0.375 0.18002 2.355 62.857 3.237 2.347

0.4 0.19252 2.087 70.906 2.870 2.080 0.425 0.20502 1.863 79.385 2.563 1.858 0.45 0.21752 1.675 88.288 2.305 1.671 0.475 0.23002 1.515 97.610 2.085 1.511

0.5 0.24252 1.377 107.346 1.896 1.374

Table G-3 Calculation of variables dependent on Dm ik

G-8

Appendix G

G.4 Interpretation of Res ults

120

Le

ngth

[m

]

a

o

8 co

8

o

a,

a

a

0 0.05 0.1 0.15 0.2 0.25 0.3

Dious Iml

0.35 0.4 0.45 0.5 0.55

Figure G-2 Graph illustrating the relationship between the coil length and

accumulator diameter

The graph of length versus accumulator diameter is plotted in Figure G-2. This

graph allows the coil length to be directly determined from the graph without

following the procedures in Table G-3. To further simplify the calculation

process, the equation of the line plotted in Figure G-2 was determined using a

curve fit. The equation is calculated as

L = 383.96•DHxA2 + 26.347•DmA— 1.325

Equation G-9

The accuracy of the curve fit is indicated by the correlation coefficient (defined

as the covariance divided by the product of the sample standard deviations). In

other words, the closer the correlation coefficient to unity, the more accurate the

curve fit. In this case the correlation coefficient is 0.9999 representing a very

G-9

Appendix G

accurate curve fit. It must however be stressed that this graph and equation are

only valid for the system represented and only at standard A.R.I. conditions.

The equation represents a wide range of accumulator diameters. Once the most

practical range of accumulator operating diameters has been established, the

equation will be reformatted over a much smaller range of accumulator

diameters. In turn, this will narrow the range of the heat transfer coefficient based

on the outside of the coil, thus significantly affecting the calculation of the coil

length (as this term is always smaller than the heat transfer coefficient based on

the inside of the coil). From Equation G-6 it may be deduced that, the smaller the

outer heat transfer coefficient (larger accumulator diameter), the longer the coil

length. The heat transfer coefficient based on the outside of the coil is thus the

more dominant heat transfer coefficient.

G-10

Appendix G

G.5 Conclusion

An equation that determines the length of the coil (for this system at standard

A.R.I. conditions) as a function of the accumulator diameter was developed.

Using this procedure, similar equations at certain specified conditions may be

developed for specific systems.

When one studies Table G-3, it can be noted that the coil lengths are

exceptionally long, when it is taken into account that the last 15% (± 2m) of the

evaporator is normally used to achieve the same amount of heat transfer. The

long lengths are due to the low heat transfer coefficients. The low heat transfer

coefficients are as a result of large hydraulic diameters. The design procedure

must seriously be re-evaluated to reduce hydraulic diameters.

G-11

Appendix G

G.6 Nomenclature

A cross sectional area [m 2]

cp specific heat [J.kg - l-K-1 ]

tube diameter [m]


enthalpy [kJ-kg-I ]

hi heat transfer coefficient on inside of the tube

ho heat transfer coefficient on outside of the tube

k thermal conductivity [W.m -I .K-1 ]

tube length [m]



pressure [kPa]

Q heat flux [W]

q heat flux per unit area [Wm -2]

r radius [m]

s entropy [kJ.kg-I K-1 ]

T temperature [K]

overall heat transfer coefficient [w.m-2.K-i]

velocity [m.s-1 ]

G-12

Appendix G

Greek letters

It pi

P density [kg.m-3 ]

il viscosity [Pa•s]



Pr Prandtl number, (Cp•p.)/k

Re Reynolds number, (G•D/p)

Subscripts


d refers to diameter





o referring to outer surface of a pipe

Superscripts


G-13

Appendix G

G.7 References





Holman, J.P. Heat Transfer (7 th Ed) McGraw-Hill (1992)

G-14

Appendix H

Appendix H

Appendix H: Mathematical Sizing of Heat Exchange

Accumulator

H.1 Introduction

This section of work redesigns the heat exchange accumulator in order to reduce

the hydraulic diameter. This will have the effect of maximizing the outer heat

transfer coefficient by ensuring a high vapour velocity over the coil. The

hydraulic diameter of the pipe through which the refrigerant flows in a

conventional system will be maintained in the new heat exchange accumulator.

H.2 Evaluation of previou s design method

Appendix D determined a procedure for calculating the accumulator's hydraulic

diameter. The hydraulic diameter is directly dependent on the coil winding and

heat exchange accumulator diameter. The assumption that the coil-winding

diameter would be half that of the heat exchange accumulator diameter was made

in order to complete the analysis. This assumption causes the outer heat transfer

coefficient to be very small, as the velocity of the vapour was very low due to the

large flow area. Several modifications may be made to increase the velocity of

the vapour flow around the coil, one of which is to decrease the heat exchange

accumulator diameter and increase the ratio of the coil winding diameter to heat

exchange accumulator diameter from 50%. A coil-winding diameter of 50mm

could then have an accumulator diameter of 75mm, which would decrease the

hydraulic diameter and increase the flow rate, thus increasing the heat transfer

H-1

0 . ♦ . 0

0 . 0 .

smee

mcc

D HXA

111111111111 E. Pinsour

Appendix H

coefficient. This method would still be limited by the fact that there is a

minimum coil-winding diameter (due to practical pipe-bending limitations).

A more effective method of increasing the heat transfer coefficient would be to

fill the centre of the heat exchange accumulator and to decrease the accumulator

diameter as illustrated in Figure H-1.

Figure H-1 Figure illustrating heat exchange accumulator with solid centre

H.3 New Accumulator De sign Process

Figure H-2 Temperature — entropy diagram and heat exchange accumulator.

H-2

Appendix H

A small air conditioning system (Tecumseh AJ5515 compressor and 9.525mm

(3/8") OD copper pipe between points 8 and 1) was obtained for testing purposes.

Using this data, the refrigerant velocity between points 8 and 1 (the superheat

region) be calculated using,

m = pAV Equation H-1

V is the vapour velocity that will ideally be required in the heat exchange

accumulator. This velocity is dependent on the hydraulic diameter, which is

defined as

D = 4A

F H p Equation H-2

Referring to Figure H-3 the hydraulic diameter for the heat exchange

accumulator is

DH = 4[A

' + A

2]

Equation H-3 P

H-3

Appendix H

Figure H-3 Figure illustrating critical diameters.

Substituting the relevant variables from Figure H-3 into Equation H-3 gives

ky RD _ D 4 w AC —D I HXA, 4 [D 2 — HXA 0 + D w AC DH

TC[DID(A. + +DAC)+(DW— D Ac )±

Resulting in

2 2

D —4-D w • D Ac — D H)cA D R Equation H-4

D ED(A. + 2•D w + D /4)(Ai

NB : DAC is the average coil diameter as defined in Appendix D.

Let Dilxiko and D HXA be equal distances from D. If the distance from D w to

DED(A. is called z (Figure H-3), then the distance from D w to DI-DCAi is also equal

to z. Then,

H-4

Appendix H

Da, = D w + z

D Ham . =D w —z Equation H-5

Substituting Equation H-5 into Equation H-4 yields

D H = — D Ac Equation H-6

Rearranging gives

Z = D H ±D Ac Equation H-7

Equation H-7 is a very important equation because it allows the required heat

exchange accumulator size to be calculated. It is important to note that Equation

H-7 is only a function of the hydraulic and coil diameter and not a function of the

coil-winding diameter. This is expected because a certain hydraulic diameter

(flow area) is required, no matter what coil-winding diameter.

H.4 Design

The advantage of this design process is that the heat exchange accumulator is

designed around the coil-winding diameter. This has many advantages, for

example, different systems will have different diameter pipes in the evaporator.

Certain pipe diameters have a minimum practical bending diameters, which this

meaning that this calculation procedure may be used after a coil-winding

diameter has been selected. As an example, a 9.525mrn OD (8.11mm ID)

H-5

Appendix H

diameter pipe exists in a small air conditioning unit used for practical tests in this

research. A coil-winding diameter of 100mm is then chosen as a realistic and

inexpensive coil diameter. The accumulator will be designed to have the same

hydraulic diameter as the original system (8.11mm). Therefore, from Equation

H-7,

Z = D H +D Ac = (0.00811) + (0.009525) = 0.01559m

Equation H-5 then yields,

D = D w +z = 0.11559m

D = D w — z= 0.0844m

These answers may be verified by substituting them back into Equation H-4 and

ensuring the answer is equal to the chosen hydraulic diameter.

H.5 Heat Transfer Coefficients

The heat transfer coefficient on the inside of the coil is calculated using the

Dittus Boelter Equation' (the refrigerant is a liquid in the coil). The heat transfer

coefficient of the vapour passing over the coil is dependent on the quality of the

refrigerant. For qualities equal to or greater than unity, the Dittus Boelter

equation will be employed, other wise the method of Jung and Radermacher 2 will

be used. Table H-1 shows the basic refrigerant properties at A.R.I. conditions.

H-6

Appendix H

h (kJ/kg]

s kJ/(kg.K)J

T (°C]

P ' ficPa]

1 416.9 1.773 18.33 625.7 2 450 1.773 87.32 2154 3 418.7 1.682 54.44 2154 4 268 1.222 54.44 2154 5 260.2 1.198 48.8 2154 6 260.2 1.215 7.22 625.7 7 208.4 1.03 7.22 625.7 8 409.1 1.746 7.22 625.7

Constants

Refrigerant Compressor Type Evap Temp [°C] Cond Temp [°C] Mass Flow Rate[kg/s]

R 22 Tecumseh AJ5515E 7.22 54.44 0.021647


Coil Inlet Temp [°C] 54.44 Coil Exit Temp [°C] 48.8 HXA Inlet Temp [°C] 7.22

HXA Exit Temp [°C] 18.33

Other Input Values

D io [m] 0.00811

Doc [m] 0.009525 k [W/(mK)] (Cu 50°C 382

Vapour R22 Properties at 7.22°

Density [kg/m3] 26.38 Viscosity [kg/(ms)] 1.21E-05 Cp [J/(kgK)] 706.1


Liquid R22 Properties at 54.44°


Viscosity [kg/(ms)] 1.26E-04 Cp [J/(kgK)] 1426


Table H-1 Tables illustrating basic refrigerant properties at A.R.I. conditions

Once these basic conditions are known, the method of Jung and Radermacher

may be used to calculate the outer heat transfer coefficient for qualities ranging

between 0.1<x<0.9. In order to calculate heat transfer coefficients using this

method, the length of the pipe must be known. It is however, the aim of this work

to determine the required length. Therefore the heat transfer coefficients for a

variety of lengths ranging from 0.1m to 100m will be studied. Table H-2

H-7

Appendix H

illustrates the Jung and Radermacher calculation procedure for a coil length of

0. 1m.


[°C] [kPa] [kg/m3] (kJ/kg] [kJ/kg .K] [micropoise] [W/(m.K))

7.22 625.7 1255 52.8 1.173 2053 9.89E-02 Liquid

7.22 625.7 26.38 253.5 0.7061 120.9 1.04E-02 Vapour

Constants

I

Preliminary Calculations II = 35

Surface Tension (mJ.m"2 .1 11.79 I i,, (ml 0.00811 As (re .1 2.5478E-03 mu, 1Pa.si 2.0530E-04

Heat Transfer (WI 168.850 D,,, (IN 0.1 Ac (m 2) 5.1657E-05 mu, (Pa.sJ 1.2090E-05

Refrig. Mass flow pcg.s"' ] 0.0216 D Ac (ml 0.00748 q (w/m 2 I 6.6272E+04 Bo 7.8797E-04

Coil Inner Diameter l'inl 0.00811 x (ml 0.01559 G Pcgas.m`)1 4.1906E+02 Pr, 2.4354E+00

Coil Outer Diameter (ml 0.009525 D,,,,,, (ml 0.11559 h,5 (J/kg) 2.0070E+05 bd piki 7.1474E-04

Coil Length (MI 0.1 D,,,,,, (nil 0.08441 s IN/m) 1.1790E-02 h,„ pallm 2 .K1 7.2735E+03

Gravity IM.s -21 9.81 Tsat pc! 2.8037E+02

Local Heat Transfer Coefficients (W/m 2 .1(1

x X„ N1 1N5 N F h,, h 5, Integration

0.1 1.39037 1.8833E+00 1.036 1.03600 2.389 872.905 9620.34

0.15 0.91687 1.1332E+00 0.917 1.133E+00 3.118 833.888 10842.09 511.561

0.2 0.67014 7.7307E-01 0.817 7.731E-01 3.873 794.410 8699.76 488.546

0.25 0.51727 5.6368E-01 0.729 5.637E-01 4.674 754.435 7626.10 408.146

0.3 0.41256 4.2775E-01 0.645 4.278E-01 5.537 713.923 7064.46 367.264

0.35 0.33595 3.3293E-01 0.565 3.329E-01 6.482 672.827 6783.05 346.188

0.4 0.27720 2.6333E-01 0.486 2.633E-01 7.532 631.094 6668.80 336.296

0.45 0.23054 2.1030E-01 0.406 2.103E-01 8.716 588.658 6660.22 333.225

0.5 0.19245 1.6872E-01 0.323 1.687E-01 10.072 545.442 6721.04 334.531

0.55 0.16065 1.3535E-01 0.236 1.354E-01 11.656 501.352 6828.41 338.736

0.6 0.13361 1.0810E-01 0.143 1.081E-01 13.546 456.269 6967.06 344.887

0.65 0.11024 8.5499E-02 0.040 8.550E-02 15.862 410.041 7126.09 352.329

0.7 0.08977 6.6545E-02 -0.076 6.655E-02 18.796 362.468 7297.08 360.579

0.75 0.07160 5.0498E-02 -0.212 5.050E-02 22.681 313.274 7472.76 369.246

0.8 0.05527 3.6821E-02 -0.378 3.682E-02 28.153 262.058 7645.59 377.959

0.85 0.04039 2.5119E-02 -0.596 2.512E-02 36.617 208.183 7805.67 386.282

0.9 0.02664 1.5115E-02 -0.918 1.511E-02 51.990 150.513 7935.08 393.519

0.95 0.01360 6.6540E-03 -1.522 6.654E-03 91.787 86.447 7983.11 397.955

0.99 0.00308 1.0863E-03 -3.339 1.086E-03 323.648 23.855 7728.42 314.231 Average 7652.60 7584.999

Table H-2 Table illustrating Jung and Radermacher calculation procedure for a

coil length of 0.1m

The heat exchange accumulator diameters are also calculated according to

Equation H-5. The outer (x=1) and inner (x=0) heat transfer coefficients may be

calculated using the Dittus-Boelter equation,

H-8

Appendix H

Dittus Boelter Heat Transfer Coefficient Outer Inner

DH[m] 0.00811 0.00811

v [m/s] 15.8855 0.3961 Re 2.81E+05 2.70E+04 Pr 0.8185 2.5259

Nu 485.3189 106.3941

h (14/m -2 K -1 I 624.152 933.933

Table H-3 Heat transfer coefficients as calculated by the Dittus-Boelter

Equation

Figure H-4 shows the outer heat transfer coefficients as calculated by the two

different methods and plotted on one set of axes.

10000 . _

- _ _ _ -

, --- 7220.518 -

_--- .,..44.4

.........

--- ...---

...440' Coil L

--G.

—de

—14

2 ion _,...

o

—0.

—4-

824.152

--..

100 I I I I +-- ' i i

- —S

0.00 0.10 0.20 0.30 0.40 0.50 0.80 0.70 0.80 0.90 I

1.00 1.10

Quality

Figure H-4 Outer heat transfer coefficients at A.R.I. conditions

Once again, as concluded in Appendix D, the worst case scenario will be

assumed, and calculations will be based on the lowest outer heat transfer

coefficient viz. the Dittus Boelter coefficient. Appendix B derived the following

equation that calculates the required coil length,

H-9

Appendix H

L m(h, —h s )[ 1 + 100 /D 1 ) ± I TC • LMTD h i D ; 2k h o D o

Equation H-8

Substituting all known variables from the above mentioned example into this

equation yields a coil length of 0.422m.

H.6 Heat Exchange Accu mulator Size

The heat exchange accumulator now has all the required dimensions for A.R.I.

conditions, they are

D,, 0.1m

Inner Coil Diameter 0.00811m

DHxAo 0.1156m

DIDCAi 0.0844m

Coil Length 0.422m

The required height of the accumulator is now a simple calculation.

H-10

Appendix H

H.7 Conclusion

A calculation procedure that determines the correct sizing of the heat exchange

accumulator was developed. The advantage of the procedure is the fact that the

accumulator is sized according to the minimum practical coil bending diameters,

which allows this procedure to be applied to any pipe diameter.

H.8 Nomenclature

A cross sectional area [m 2 ]

AF cross sectional gaseous flow area [m 2]

Cp specific heat [J.kg- 1.K-1 ]

D tube diameter [m]


Dw coil winding diameter [m]

enthalpy [k.l.kg-1 ]

h, heat transfer coefficient on inside of the tube [Wm -2 .K-1 ]

h0 heat transfer coefficient on outside of the tube [Wm -2 .K-1 ]

k thermal conductivity [Wm -1 .K-1 ]

tube length [m]


m mass flow rate [kg.s-1 ]

pressure [kPa]

p wetted perimeter

Q heat flux [W]

q heat flux per unit area [Win -2]

H-11

Appendix H

r radius [m]

s entropy [kJ.kg-1K-1 ]

T temperature [K]

overall heat transfer coefficient [W.m -2.K-1 ]

velocity [m.s-1 ]

x refrigerant quality

z variable

Greek letters

TC Pi

P density [kg.m-3 ]

IA viscosity [Pa•s]



Pr Prandtl number, (Cp•i.t)/k

Re Reynolds number, (G•D4t)

Subscripts







H-12

Appendix H

Superscripts


H.9 References


2 Jung, D.S., Radermacher, R. Prediction of heat transfer coefficients of various


53

H-13

Appendix I

Appendix I: Sizing of a heat exchange accumulator for a

small air conditioning system

I.1 Introduction

This appendix designs a heat exchange accumulator for a small air conditioning

unit. The mathematical model that was developed in the preceding appendices

will be used to predict accumulator size. The accumulator will then be built

according to the dimensions derived in this work.

1.2 Practical system

The small air conditioning system that will be used for practical test has the

following characteristics

Compressor Tecumseh AJ5515E

Model Mech Air WP157E

Cooling Capacity 3780W

Heating Capacity 2850W

PC Cooling 1645W

Air Flow Rate 0.169m3/s

Refrigerant Charge 0.83kg R-22

Electrical Specifications 220V, 50Hz, 8.5A

Number of evaporator coil passes 36

Number of condenser coil passes 75

Table I-I Air conditioner specifications

I-1

Appendix I

Figure I-1 Diagram of air conditioner used for practical tests

Section Length [mm] OD [mm] Wall thickness [mm]

ID [mm]

Ll 1150 7.94 0.71 6.52

L2 350 9.525 0.81 7.905

L3 50 9.525 0.81 7.905

IA 140 7.94 0.71 6.52

L5 75 19 0.81 17.38

L6 550 7.94 0.71 6.52

L7 420 9.525 0.81 7.905

L8 50 9.525 0.81 7.905

L9 1150 12.7 0.81 11.28

Exp Coil 1000 2.82 0.61 1.6

Table 1-2 Critical lengths and diameters relating to Figure I-1

1-2

Appendix I

1.3 Heat exchange accumulator design

The pipe diameters of sections L4 and L9 are important for the heat exchange

accumulator design. The coil diameter will be the same as L4 while the

accumulator will have a hydraulic diameter equal to L9' s inner diameter.

Appendix D derived the following formula for the average coil diameter (DAC)

oc D AC = 4 Equation I-1

Appendix H derived the following equations in conjunction with Figure 1-2

Z = DH +DAC Equation 1-2

Duo = D, + Z

Equation 1-3

DllxA1 = Dw - z

Equation 1-4

Figure 1-2 Figure illustrating critical diameters.

1-3

Appendix I

Choosing D, = 0.1m and substituting the relevant numbers from Table 1-2 into

the equations above yields the following dimensions

D, 0.1m

DAC 0.006236 m

z 0.001752 m

DmA0 0.1175 m

DHXAI 0.08248 m

Table 1-3 Table illustrating accumulator dimensions

Investigation reveals that the majority of air conditioners in South Africa operate

at an evaporating temperature of 7°C and a condensing temperature of 50°C.

Table 1-4 shows the basic refrigerant properties at the above mentioned

conditions.

1-4

Appendix I

h (kJ/kg]

s J/(kg.K)

T pc]

P (k Pal

1 416.8 1.774 18.11 621.5 2 446.1 1.774 79.95 1948 3 418.5 1.688 50 1948 4 262 1.204 50 1948 5 254.2 1.18 44.26 1948 6 254.2 1.193 7 621.5 7 208.2 1.029 7 621.5 8 409 1.746 7 621.5

Constants

Refrigerant Compressor Type Evap Temp [°C] Cond Temp [°C] Mass Flow Rate[kg/s

R 22 Tecumseh AJ5515E 7 50 0.02218


Coil Inlet Temp [°C] 50 Coil Exit Temp [°C] 44.26 HXA Inlet Temp [°C] 7 HXA Exit Temp [°C] 17.11

Other Input Values

Dio [rn] 0.00652

Doc [rn] 0.00794

k [W/(mK)] (Cu 50°C) 382

Vapour R22 Properties at 7°C

Density [kg/m 3] 26.2 Viscosity [kg/(ms)] 1.21E-05 Cp [J/(kgK)] 705.3 Thermal Cond. [Wm -1 1.04E-02

Liquid R22 Properties at 50°C



Cp [J/(kgK)] 1348

Thermal Cond. [Wm -1 7.36E-02

Table 1-4 Refrigerant R-22 properties at an evaporating temperature of 7°C and

a condensing temperature of 50°C

The refrigerant data in Table 1-4 may now be used to calculate the respective heat

transfer coefficients using the Dittus Boelter' equation. As concluded in

Appendix D, the worst case scenario will be assumed, and calculations will be

based on the lowest outer heat transfer coefficient viz. the coefficient determined

using the Dittus Boelter equation.

I-5

Appendix I

hD Nu

D k = — = 0.023 Re D8 Pt'

where Re = pVD Pr = Pu V = 4m 1-1, ,

C k , prcD 2



Equation 1-5

Dittus Boelter H T C Outer Inner

DH [ml 0.01128 0.00652 v [m/s] 8.4702 0.6150 Re 2.07E405 3.30E+04 Pr 0.8177 2.4001 Nu 380.1076 123.3018 h (Wm "2K''] 351.128 1392.44

Table 1-5 Dittus Boelter heat transfer coefficients

Appendix B derived the following equation that calculates the required coil

length,

L m(h, — h 8 )[ 1 ± 143 0 /D ; ) + 1

n • LMTD h i l) ; 2k h o D o Equation 1-6


equation yields a coil length of 0.762m

1-6

Appendix I

1.4 Conclusion

The correct size of the heat exchange accumulator for an evaporating temperature

of 7°C and condensing temperature of 50°C was developed to fit into a small air

conditioner. The required heat exchange may now be achieved. An investigation

into the change of required coil length with a change in ambient conditions must

now be investigated.

1.5 Nomenclature

Cp specific heat [J.kg - 1.1(-1 ]

D tube diameter [m]


Dw coil winding diameter [m]

enthalpy [kJ.kg-I ]

hi heat transfer coefficient on inside of the tube [w.m-2.K-i]

ho heat transfer coefficient on outside of the tube [W.m -2 .K-I ]

k thermal conductivity

tube length [m]


m mass flow rate [kg•s -I ]

pressure [kPa]

s entropy [k.J•kg -1 K-1 ]

T temperature [K]

V velocity [m-s-1 ]

z variable

1-7

Appendix I

Greek letters

It pi

p density [kg-m-3 ]

11 viscosity [Pa•s]



Pr Prandtl number, (Cp.IA)/k

Re Reynolds number, (G•D/p.)

Subscripts







Superscripts


1.6 References


1-8

Appendix 3

Appendix J

Appendix J: Investigation of the influence of varying

ambient temperatures on coil length

J.1 Introduction

Appendix I designed a heat exchange accumulator for a small air conditioner at

an evaporating temperature of 7°C and condensing temperature of 50°C. This

appendix investigates what effect a change in evaporating and condensing

temperatures will have on the coil length.

J.2 Investigation

Investigation reveals that the majority of air conditioners in South Africa operate

at an evaporating temperature of 7°C and a condensing temperature of 50°C.

Should these temperatures vary from these design values, the required length of

the accumulator coil will change. A 10°C increase and decrease in ambient

temperatures will be investigated. The two extreme cases will have evaporating

temperatures of —3°C and 17°C with respective condensing temperatures of 40°C

and 50°C.

Table J-1 shows the basic refrigerant properties at an evaporating temperature of

—3°C and a condensing temperature of 60°C.

J-1

Appendix 3

h [kJ/kg]

s kJ/(kg. K))

T pc]

P [k Pa]

1 412.8 1.788 8.11 450.8 2 445.7 1.788 73.22 1538 3 417.4 1.702 40 1538 4 248.8 1.163 40 1538 5 241.4 1.14 34.29 1538 6 241.4 1.153 -3 450.8 7 196.5 0.9874 -3 450.8 8 405.4 1.76 -3 450.8

Constants


R 22 Tecumseh AJ5515E -3 40 0.0195



Other Input Values

D ic [m] 0.00652

Doc [m] 0.00794 k [W/(mK)] (Cu 50°C) 382

Vapour R22 Properties at -3°C





Cp [J/(kgK)] 886.7


Table J-1 Refrigerant R-22 properties at an evaporating temperature of -3°C

and a condensing temperature of 60°C

The refrigerant data in Table J-1 may now be used to calculate the respective heat

transfer coefficients using the Dittus Boelter l equation. As concluded in

Appendix D, the worst case scenario will be assumed, and calculations will be

based on the lowest outer heat transfer coefficient viz. the coefficient determined

using the Dittus Boelter equation.

J-2

Appendix 3

Nu = hD —= 0.023Re°1;8 Pr"

Equation J-1

pVD C 4m where Re = , Pr = , V =

k prcD 2




D H [m] 0.01128 0.00652

v [m/s] 10.1684 0.5205 Re 1.90E+05 2.67E+04 Pr 0.7890 1.5931

Nu 350.1799 92.0762

h (Wm -2 K - / .1 305.445 1119.32

Table J-2 Dittus Boelter heat transfer coefficients

Appendix B derived the following equation that calculates the required coil

length,

L m(h 1 – h) [ 1 ± ln(D o /D I ) + 1 IT • LMTD h i D i 2k h o D o

Equation J-2


equation yields a coil length of 0.745m

Table J-3 shows the basic refrigerant properties at an evaporating temperature of

17°C and a condensing temperature of 40°C.

J-3

Appendix 3

h (kJ/kg]

s kJ/(kg. K))

T foci

P (k Pa]

1 420.5 1.76 28.11 836.7 2 448.8 1.76 89.89 2434 3 418.7 1.673 60 2434 4 275.8 1.245 60 2434 5 267.5 1.219 54.23 2434 6 263.2 1.219 17 836.7 7 220.1 1.07 17 836.7 8 412.2 1.732 17 836.7

Constants


R 22 Tecumseh AJ5515E 7 50 0.022177



Other Input Values

D ic [m] 0.00652

Doc [rn] 0.00794 k [W/(mK)] (Cu 50°C) 382

Vapour R22 Properties at 17°C





Cp [J/(kgK)] 1490


Table J-3 Refrigerant R-22 properties at an evaporating temperature of -3°C

and a condensing temperature of 60°C

The refrigerant data in Table J-3 may now be used to calculate the respective heat

transfer coefficients using the Dittus Boelter l equation which assumes the worst

case scenario (Appendix D).

J-4

Appendix 3

Nu D = 111)- = 0.023 Re D8 Pr °

Equation J-3

pVD C where Re = , Pr = P , V = 4m

k prcD2




DH [m] 0.01128 0.00652 v [m/s] 6.3135 0.6461 Re 1.98E+05 3.63E+04 Pr 0.8546 2.6079 Nu 373.3402 136.3192 h [Wm -2 K -1 .1 365.066 1425.08

Table J-4 Dittus Boelter heat transfer coefficients

Substituting all known variables from the above mentioned example into

Equation J-2 yields a coil length of 0.784m

J.3 Conclusion

A 10°C increase in each of the evaporating and condensing temperatures causes a

2.89% increase in the required coil length while a 10 °C decrease in each of the

evaporating and condensing temperatures causes a 2.23% decrease in the

required coil length. These variations are exceedingly small when one considers

that the calculated heat transfer coefficients may be up to 20% inaccurate. The

coil length derived in Appendix I will thus be used to build the heat exchange

accumulator.

J-5

Appendix

J.4 Nomenclature

Cp specific heat [J.kg- 1.K-1 ]

D tube diameter [m]


D, coil winding diameter [m]

enthalpy [kJ.kg-1 ]

h, heat transfer coefficient on inside of the tube [Wm 2•K -1]

ho heat transfer coefficient on outside of the tube [W.m -2 .K-1 ]

k thermal conductivity [W.m -1 .K-1 ]

tube length [m]



pressure [kPa]

s entropy [kJ•kg-1 K-1 ]

T temperature [K]

velocity [m•s -1 ]

x variable

Greek letters

TC Pi

p density [kg.m-3 ]

11 viscosity [Pa•s]

J-6

Appendix J



Pr Prandtl number, (Cp•1,)/k

Re Reynolds number, (G•D/p)

Subscripts







Superscripts


J.5 References


J-7


T

Condenser

T

Compressor

Capillary Tube

T

Accumulator

T -T- ©

T

T

Watt Meter

Evaporator

T Environmental Chamber

Appendix K

Appendix K

Appendix K: Experimental Testing and Data Manipulation Procedure

K.1 Introduction

This appendix discusses the experimental system, method and equipment used to

obtain the experimental data as well as the procedures used.

K.2 Experimental Set-up

A schematic diagram of the system including measurement points is shown.

T Thermocouple OO Sight Glass 0 Pressure Gauge

Figure K- 1 Schematic diagram of experimental set-up with measuring points.

K-1

Appendix K

K.3 Experimental Procedure

The air conditioner (York Miac, WP157E) was slightly modified to allow the

accumulator to fit on the outside of the casing encompassing the system. The

modifications consisted of cutting two small holes in the casing, one near the

evaporator exit tube and the other near the compressor exit tube. The respective

outlet tubes where then redirected through the holes in the casing. Two 90°

elbows where fitted on the end of the tubes which redirected the tubes back into

the system where they rejoined the existing circuit. This modification allowed the

accumulator to be installed by simply removing the elbows, thus leaving an inlet

and outlet tube at the respective evaporator and condenser outlets, to which the

accumulator could then be connected. The system was otherwise used in the

condition that it was received from the manufacturer.

K.3.1 Charging the System

In the case of baseline tests the accumulator was removed and a vacuum of 50

mm Mercury' drawn. The system was then charged with nitrogen to a pressure

of 600 kPa and allowed to stand overnight. This ensured that all traces of

moisture and other foreign liquids or gases were vaporized and removed. It

also served as a pressure test that would indicate leaks in the system. After

standing overnight the nitrogen was evacuated until a vacuum of 50mm

Mercury was maintained. The system was then charged with 0.83 kg of

refrigerant-22 using a Dial-a-Charge Charging Cylinder (portable-charging

cylinder from Robinair Manufacturing Corp.) The same method was used

when the accumulator was incorporated into the system. The charge of

refrigerant-22 was then increased to 0.91 kg. The amount of additional charge

K-2

Appendix K

was calculated by charging the system until there was 100% liquid showing in

the sight glass after the condenser. This meant that all the superheating would

be done in the accumulator. This method was verified by calculating the

amount of refrigerant per unit length in the baseline system and then using the

same value in the accumulator system.

K.3.2 Experimental Data Equipment

K.3.2.a Temperature Readings

All temperature readings where taken with K-type (chromel-alumel)

thermocouples that measured the surface wall temperature of the copper

tubes comprising the system. The thermocouples where electrically insulated

from the copper tubes by placing a single layer of PTFE-100 tape around the

tube. The ends where spot welding together and then secured to the tube

using plastic cable ties and the entire joint insulated from the environment

using a waterproof insulating tape. The entire length of the thermocouple

was coated with Teflon to ensure that there were no external influences from

water etc. The thermocouples where calibrated and observed to have

accuracy's of ± 0.2°C. According to manufacturers specifications the

response time for a K-type thermocouple is 5 seconds for 17°C step change

in temperature.

K-3

Appendix K

K.3.2.b Pressure Readings

Refrigerant pressures were measured on either side of the compressor. Two

pressure gauges obtained from Control Instruments where used. They where

ASHCROFT gauges, one having a range of 0-1000 kPa used on the

evaporator side of the compressor, and the other having a range of 0-2500

kPa used on the condenser side of the compressor. The low pressure gauge

was calibrated using a MAXITEST GAUGE and had a maximum error of 2

kPa at a pressure of 800 kPa. The average error for this gauge was 2 kPa

which translated to a 0.2% average error of the full-scale reading. The high

pressure gauge was also calibrated using a MAXITEST GAUGE and had a

maximum error of 5 kPa at a pressure of 1500 kPa. The average error for

this gauge was 5 kPa which translated to a 0.2% average error of the full-

scale reading. Atmospheric pressure was measured using a mercury

barometer.

K.3.2.c Input Power

The power consumed by the system was measured using a current

transformer and a Conway Electrical Enterprises Wattmeter having an 1%

error, 48 mS2 resistance and 63 i_tH inductance when a 5 A alternating

current was flowing. The current transformer was used to ensure that the

current always remained below 5 A. The compressor was disconnected and

the fan run at each speed to determine the power consumed by the fan. This

value was then subtracted from the total input power to give the power

consumed by the compressor.

K-4

Appendix K

K.3.3 Experimental Results and Data Manipulation

The system was switched on and the ambient temperatures and humidity

ratio's set at the desired values. The ambient temperatures and humidity where

controlled by environmental chambers placed before the respective evaporator

and condenser inlets. The system was allowed to run for a minimum period of

an hour to allow the system to stabilize and thus reach steady state conditions.

Three sets of the desired readings where then taken at twenty minute intervals.

This gave three sets of three readings, each set representing a good average at

each interval and the averages of the intervals representing a good average at

the operating conditions.

The set of three readings taken at each of twenty minute intervals where

averaged and these averages used in the following calculations.

K.3.3.a Thermodynamic properties

Refrigerant enthalpies at the various points were determined using

determined using the respective pressure (p c or pE) and temperature relating

to that point (K1, K2 or Ex i ) and the REFPROP 2 database. The enthalpy of

the air was determined using the atmospheric pressure and wet (TEWBI or

Tcwsi) and dry (TEA1 or Tcm) bulb temperatures before the evaporator or

condenser.

K-5

Appendix K

K.3.3.b Refrigerant Side Calculations

Compression Ratio (pc/PE)

The compression ratio was calculated by dividing the condensing pressure

by the evaporating pressure

Compressor Isentropic Efficiency (i i)

The compressor isentropic efficiency was calculated using the following

equation derived in Appendix C (Table C5).

= b[3]x3 + b[2]x2 + b[1]x + b[0] Equation K-1

where Th represents the isentropic efficiency of the compressor, b[0,1,2,3]

are coefficients defined in Table C5 in Appendix C and x represents the

compression ratio.

Power Transferred to the Refrigerant (PAct)

The actual power transferred to the refrigerant is equal to the actual

compressor power consumption multiplied by the isentropic compressor

efficiency.

PAct = 11 i' 13

Equation K-2

Refrigerant Mass Flow Rate (m)

The refrigerant mass flow rate was calculated using the following equation

K-6

Appendix K

PAct MCalc = (h2 — h 1 ) Equation K-3

where mcalc is the calculated refrigerant mass flow rate, h2 is the enthalpy of

the refrigerant at the compressor outlet and h1 is the enthalpy of the

refrigerant at the compressor inlet. This calculated value was then compared

to the value obtained using the compressor curves (mc on,p)(shown in

Appendix C). The mean deviation ( \MMean Dev) between the two mass flow

was then calculated. The refrigerant mass flow rate obtained from the

compressor curves (mconp) will be used for further calculation as this is

value specified by the compressor manufacturer and likely to be more

accurate in the practical application of the compressor as these value are

determined from test situations and do not have compounded errors from

calculation procedures.

Evaporator Capacity (QE)

The cooling capacity of the evaporator is calculated using

QE = MComp•(h1 — h5) Equation K-4

where mcomp is the refrigerant mass flow rate determined from the

compressor curve, h 1 the enthalpy at the compressor inlet and h5 is the

enthalpy of the refrigerant at the capillary.

Condenser Capacity (Qc)

The heat exchanged through the condenser is calculated using

K-7

Appendix K

Qc = mcomp•(h2 — h5) Equation K-5

where mc omp is the refrigerant mass flow rate determined from the

compressor curve, h2 the enthalpy at the compressor outlet and h 5 is the

enthalpy of the refrigerant at the capillary tube.

Energy Balance

The energy balance is completed using

Qc = QE + PAct Equation K-6

The accuracy of the energy balance (E BalMean Dev) is determined by

calculating the mean deviation between the two terms on either side of

Equation K-6.

Coefficient of Performance (COP)

The COP of the systems is calculated using

COP = QE/F'

Equation K-7

K.3.3.c Air Side Calculations

Air Mass Flow Rates

The mass flow rate of the air flowing across the evaporator (mE A) and

condenser (mcA) are calculated using

m = p•v•A Equation K-8

K-8

Appendix K

where p is the density of the air, v the velocity of the air and A the area of

the respective condenser or evaporator.

Evaporator Capacity (QE)

The cooling capacity of the evaporator may also be calculated using

QE = MEA'(hEA1 hEA2)

Equation K-9

where mEA is the air mass flow rate over the evaporator, hEA1 the enthalpy of

the air before the evaporator and hEA2 is the enthalpy of the air after the

evaporator. The accuracy of this value is determined by calculating its mean

deviation (QE Mean Dev) from the QE value calculated using Equation K-4.

Condenser Capacity (Qc)

The heat exchanged through the condenser may also be calculated using

Qc = MCA•(hCA2 hCA I)

Equation K-10

where mcA is the air mass flow rate over the condenser, hcAl the enthalpy of

the air before the condenser and hcA2 is the enthalpy of the air after the

condenser. The accuracy of this value is determined by calculating its mean

deviation (Qc Mean Dev) from the Qc value calculated using Equation K-5.

K-9

Appendix K

K.4 Application Example

A set of test results is shown in Table K-1. All the calculations as explained

above have been performed in the example.

Base 1H

Date: 21/12/98

Patmos 83.7

Experimental Values Ave. S Dev Experimental Values Ave. S Dev

pc 1675 1680 1680 1678 2.887 P E 412 412 415 413 1.73

Tc 41.3 41.4 42 41.57 0.379 TE 0 1.9 2 1.3 1.13

TCAI 25 25 25.2 25.07 0.115 TEA, 24.9 25 25.1 25 0.10

TcA2 40.8 40.7 40.8 40.77 0.058 TEA2 9.1 9.6 9.5 9.4 0.26

P 1160 1160 1160 1160 0 Ex, 35.7 35.7 35.6 35.67 0.06

K, 23.9 23.9 21.2 23 1.559 K2 88.7 87 87.3 87.67 0.91

TCWB1 17.6 17.7 17.4 17.57 0.153 TEWB1 17.7 17.8 18.1 17.9 0.21

1 CWB2 20.3 20.7 20 20.33 0.351 TEWB2 9.2 9.4 9.7 9.4 0.25

Refrigerant Side

Pc [kPa] 1762.03 h5 [kJ/kg] 243.1

PE [kPa] 496.70 PAct [W] 491.95

Pc/PE 3.55 MCalc [kg/s] 0.01495

b[3] -9.77E-04 mcomp [kg/s] 0.01548

b[2] -3.07E-02 m Mean Dev 3.54

b[1] 1.73E-01 QE [W] 2774

b[0] 2.41E-01 Qc [W] 3284

1, 0.42 QE+ PAct 3266

h1 [kJ/kg] 422.3 E Bal Mean Dev 0.53

h2 [kJ/kg] 455.2 COP 2.39

Air Side

vCA [m/s] 3.018 vEA [m/s] 3.415

PCA [1(9/m3] 0.973 PEA [k9/m3] 0.972

ACA [m2] 0.123 AEA EA 0.036

mcA [kg/s] 0.36 mEA [kg/s] 0.120

CpcA [kJ/kg K] 1.007 CpEA [kJ/kg K] 1.005

hcAl [kJ/kg]

hcA2 [kJ/kg]

56.39

66.03

hEA, [kJ/kg]

h EA2 [kJ/kg]

57.47

31.89

Qc [W] 3467 QE [W] 3057

QC Mean Dev 5.6 QE Mean Dev 10.2

Table K-1 Table showing experimental results and their manipulation

according to the method discussed in this Appendix

K-10

Appendix K

K.5 Conclusion

Using the above-mentioned experimental equipment, procedures and data

manipulation, all the required variables may be calculated and the systems

performance efficiently evaluated. From the application example the systems

refrigerant energy balance is 0.53% out and the airside values are all within

10.2% of the refrigerant side. The differences between the airside and refrigerant

side balances are 5.6% on the condenser side and 10.2% on the evaporator side.

K.6 Nomenclature

A area [m2]

b constant

Cp specific heat [J.kg - 1.1C 1 ]

COP coefficient of performance

E Bal energy balance

Ex 1 expansion device inlet

h enthalpy [kJ-kg-1 ]

K compressor

m mass flow rate [kg-s -1 ]

P pressure [kPa]

P power [W]

Q heat transferred [W]

T temperature [K]

v velocity [m.s -1 ]

x compression ratio

K-11

Appendix K

Greek letters

p density [kg.rn -3 ]

11i isentropic efficiency

Subscripts

Act Actual

atmos atmospheric

C condenser

Calc calculated

CA condenser air

Comp compressor curves

CWB condenser wet bulb

E evaporator

EA evaporator air

EWB evaporator wet bulb

Mean Dev mean deviation

K.7 References

Althouse, A.D., Turnquist, C.H., Bracciano, A.F. Modern Refrigeration and Air

Conditioning Goodheart-Willcox Company, Inc. South Holland, Illinois (1982)





K-12

Appendix L

Appendix L: Initial Experimental Testing and Verification of Results

L.1 Introduction

This appendix discusses the initial experimental results obtained using the

baseline and accumulator system. The performances of the accumulator and

baseline systems are compared and then conclusions regarding the operation of

the system with the accumulator in place drawn.

L.2 Experimental Metho d

L.2.1 Test 1 — Baseline test at low fan speed

The baseline system was switched on at the low fan speed setting. This speed

translated to air mass flow rates of 0.096 kg/s over the evaporator and 0.23

kg/s over the condenser. The condenser and evaporator ambient temperatures

were set at 25°C and the humidity ratio at the evaporator inlet set between 50

and 60%. The system was allowed to run for a minimum period of an hour to

allow the system to stabilize and thus reach steady state conditions.

Table L-1 shows the readings that where taken and symbol used to record the

data.

L-1

Appendix L

Symbol Units Description

Patmos [kPa] Atmospheric Pressure

PE [kPa] Pressure before Compressor

Pc [kPa] Pressure after Compressor

K1 [°C] Refrigerant temperature before Compressor

K2 [°C] Refrigerant temperature after Compressor

Ex1 [°C] Refrigerant temperature before Expansion coil

TEA 1 [°C] Dry bulb air temperature before evaporator

TEA2 [°C] Dry bulb air temperature after evaporator

TCA 1 [°C] Dry bulb air temperature before condenser

TCA2 [°C] Dry bulb air temperature after condenser

TEWB 1 [°C] Wet bulb air temperature before evaporator

TEWB2 11 °C] Wet bulb air temperature after evaporator

TCWB 1 [°C] Wet bulb air temperature before condenser

TCWB2 [°C] Wet bulb air temperature after condenser

P [W] Input Power

Table L-1 Table showing measured properties and symbols under which the

quantity was recorded

Sets of three readings were taken at twenty-minute intervals. Each set of three

readings were averaged to give an experimental average at each twenty-minute

interval. One test comprised three different sets of three readings (taken over a

40-minute period). Three different tests, all at the same ambient conditions,

were completed on three different days. This gave three test results which,

when averaged, gave a good representation of the measured values at the

specified ambient conditions.

L-2

Appendix L

L.2.2 Test 2 — Baseline test at high fan speed

The baseline system was switched on at the high fan speed setting. This speed

translated to air mass flow rates of 0.12 kg/s over the evaporator and 0.36 kg/s

over the condenser. The condenser and evaporator ambient temperatures were

set at 25°C and the humidity ratio at the evaporator inlet set between 50 and

60%. The system was allowed to run for a minimum period of an hour to allow

the system to stabilize in an attempt to reach steady state conditions. The same

set of results as those indicated in Table L-1 were recorded.

L.2.3 Test 3 — Accumulator test at low fan speed

The accumulator was added and the system charged (according to the charging

procedure described in Appendix K). At this stage no other modifications

where made to the system. The system was turned on at the low fan speed

setting and the condenser and evaporator ambient temperatures set at 25°C.

The humidity ratio at the evaporator inlet set between 50 and 60%. The system

was allowed to run for a minimum period of an hour to allow the system to

stabilize in an attempt to reach steady state conditions.

The above-mentioned readings (Table L-1) along with the following

temperatures (Table L-2) where recorded.

L-3

Appendix L

Symbol Units Description

Al [°C] Refrigerant temperature at accumulator inlet

A2 [°C] Refrigerant temperature at accumulator outlet

A3 [°C] Refrigerant temperature at coil inlet

A4 [°C] Refrigerant temperature at coil outlet

Table L-2 Extra measurements and corresponding symbols taken with

accumulator added to baseline system

L.2.4 Test 4 — Accumulator test at high fan speed

This test was completed in the exact same manner as test 3 excepting for the

fact that the system was turned onto the high fan speed setting.

L.3 Experimental Result s

L.3.1 Test 1 — Baseline test at low fan speed

The results in Table L-3 show the averages values of three different tests

completed under the same set of ambient conditions. It also shows the

analyzed data according to the calculation procedure shown in Appendix K.

L-4

Appendix L

RH 54% patmos 83.7 kPa

Test 1 Test 2 Test 3 Ave. S. Dev Test 1 Test 2 Test 3 Ave. S. Dev

pc 1990 1970 1967 1976 ' 12.6 pE 458 450 460 456 5.36

Tc 47.4 46.7 46.6 46.9 0.45 TE 3.07 2.37 2.87 2.77 0.36

TCA1 25 25.1 25 25 0.06 TEA1 25.3 25 24.9 25.1 0.20

TCA2 48.6 47.9 47.9 48.1 0.43 TEA2 8.83 9.1 10.7 9.56 1.03

P 1160 1160 1173 1164 7.70 Ex1 42.4 41.7 41.7 42 0.38

K1 20.3 17.4 21.6 19.8 2.13 K2 91.8 88.8 91 90.5 1.55

TCWB1 17.7 15.7 18.8 17.4 1.58 TEWB1 17.8 18 18.8 18.2 0.52 TCWB2 22.1 20 22.6 21.5 1.39 TEWB2

8.37 8.9 8.67 8.64 0.27

Refrigerant Side pc [kPa] 2059.22 h5 [kJ/kg] 251.1 pE [kPa] 539.78 PAct 525.49

Pc/PE 3.81 mCalc [kg/s] 0.01514 b[3] 3.40E-03 mcomp [kg/s] 0.01708 b[2] -6.71E-02 m Mean Dev 11.34 b[1] 3.02E-01 QE [W] 2875 b[0] 8.67E-02 Qc [W] 3467 1, 0.45 QE+PAct 3400 h1 [kJ/kg] 419.4 E Bal Mean Dev 1.94 h2 [kJ/kg] 454.1 COP I 2.47

Air Side vcA [m/s] I 1.92 vEA [m/s] I 2.75

pCA kg/m3] 0.971 PEA kg/m3] 0.970

AcA [m2] MCA [kg/s]

0.12

0.23 [m2] AEA [M

mEA [kg/s]

0.036

0.096

C [kJ/kgK] pCA 1.007 CPEA [kJ/kgK] 1.005

hCA1 [kJ/kg] 55.8 hEA1 [kJ/kg] 58.66

hCA2 [kJ/kg] 70.8 hEA2 [kJ/kg] 30.02

Qc [W] 3448 QE [W] 2746


Table L-3 Experimental averages and calculations for Test 1 - Baseline test

at low fan speed

L-5

Appendix L

L.3.2 Test 2 - Baseline test at high fan speed




RH 55%

Patmos 83.7 kPa


pc 1678 1660 1657 1665 11.7 PE 413 413 415 414 1.07

Tc 41.6 40.5 40.5 40.8 0.64 TE 1.3 0.2 1.13 0.88 0.59 TCA1 25.1 25 25.1 25 0.04 TEA1 25 25.1 25 25 0.03 TcA2 40.8 40.5 40.3 40.5 0.25 TEA2 9.4 8.9 10 9.44 0.57

P 1160 1140 1153 1151 10.2 Ex, 35.7 35.2 35 35.3 0.34 K 1 23 24.1 23.8 23.6 0.58 K2 87.7 82.5 82.9 84.4 2.87

TCWB1 17.6 17.5 18.2 17.8 0.39 TEWB1 17.9 17.5 18.2 17.87 0.37

I cwB2 20.3 18.8 20.7 20 0.99 TEWB2 9.43 8.7 9.73 9.29 0.53

Refrigerant Side pc [kPa] 1748.67 h5 [kJ/kg] 242.6

PE [kPa] 497.44 PAct Mil 488.97

Pc/PE 3.52 mcaic [kg/s] 0.01641 b[3] -1.18E-03 mcomp [kg/s] 0.01544 b[2] -2.90E-02 m Mean Dev 6.26 b[1] 1.67E-01 QE [W] 2781 b[0] 2.49E-01 Qc [W] 3241 Il i 0.42 QE+PAct 3270 h1 [kJ/kg] 422.7 E Bal Mean Dev 0.89 h2 [kJ/kg] 452.5 COP I 2.42

Air Side vcA [m/s] I 3.02 vEA [m/s] I 3.42

PCA kgirril 0.971 PEA kg/m3] 0.971 ACA [m2] 0.12 AEA [m2] 0.036 mcA [kg/s] 0.36 mEA [kg/s] 0.119

CpcA [kJ/kgK] 1.007 CpEA [kJ/kgK] 1.005

hcAl [kJ/kg] 57.2 hcA2 [kJ/kg] 65.4

hEA , [kJ/kg] 57.57 h EA2 [kJ/kg] 31.66

Qc [W] 2939 QE [W] 3092


Table L-4 Experimental averages and calculations for Test 2 - Baseline test at

high fan speed

L-6

Appendix L

L.3.3 Test 3 - Accumulator test at low fan speed




RH 54%

Patmos 83.8 kPa

est 1 Test 2 Test Ave. S Dev est 1 Test 2 Test Ave. S De 11 Pc imunsuimakiginia PE mausaikumm

C IMILLIIMENIALILI ItIrMifilitnitlini EA,

ELVILikilitilliti '' IIMINEMZIUNI 0 CA1

cA2 BralligiliffillIAMI EA2 111211U1111MINkil ' I p

.

MUM lika BM Era Xi wimairmazza . •

A3 48.5 45.7 45.7 46.6 Al 2.2 3.0 2.8 0.5

A4 39.4 37.8 37.2 38.1 A2 3.8 8.6 5.9 2.5

CWB1 • • .. • • EWB1 • • S . I •'

I CWB2 8.5 11.4 22.2 20.7 1.9 rEWB2 ti•b 8.3 S./ 8.5 0.2

Refrigerant Side

Pc [kPa] 2044.91 h5 [1(J/kg] 246 pE [kPa] 542.63 PAct Mil 528.07

Pc/PE 3.77 mcaic [kgis] 0.01443 b[3] 3.20E-03 mcomp [kg/s] 0.01730 b[2] -6.54E-02 m Mean Dev 19.94 b[1] 2.96E-01 QE [W] 2909 b[0] 9.38E-02 Qc [W] 3542 11, 0.45 QE+ PAct 3437 hl [kJ/kg] 414.1 E Bal Mean Dev 3.06 h2 [kJ/kg] 450.7 COP I 2.49

Air Side

VCA [m/s] I 1.92 vEA [mis] ' 2.75

PCA kg/m1 0.973 pEA kg/m1 0.971 ACA [m2] 0.12 AEA [MI 0.036

mcA [kg/s] 0.23 mEA [kg/s] 0.096

CpcA [kJ/kg ] 1.007 CpEA [kJ/kg (16°C 1.005

licki [kJ/kg] 51.9 hEm [kJ/kg 58.61

hcA2 [kJ/kg] 65.5 h EA2 [kJ/kg] 29.69

QC [W] 3114 QE [W] I 2774

QC Mean Dev I 13.7 QE Mean Dev 4.9

Table L-5 Experimental averages and calculations for Test 3 - Accumulator

test at low fan speed

L-7

Appendix L

L.3.4 Test 4 - Accumulator test at high fan speed




RH 55%

Patmos 83.8 kPa

est 1 Test 2 Test Ave. S Dev est 1 Test 2 Test Ave. S De 0 pc magrimiga ma um PE UM MUMS um

c itailitallikrillitainj E IIIIIIIIMMINIII • CA1 irakiniaffallail EA1 itlanfilitlintai I CA2 111011i1 ' 1 NIVI1 1al EA2 1• •• MU • , 1112111112111ELIBINUM xl triElkik11111111k1 ' . o

A3 36.8 37.1 36.3 36.8 0.4 Al 20.5 16.3 19.5 18.8 2.2

A4 33.8 33.1 33.4 33.4 0.4 A2 24.2 21.1 23.1 22.8 1.5

CWB1 " • • • • •• , EWB1 •• • •• • e • I Dwg2 20.4 20.5 20. 1 20.b U.1 I EwB2 10.b 9.b 9.6 1U.0 U.

Refrigerant Side pc [kPa] 1781.06 h5 [kJ/kg] 240.3

PE [kPa] 520.39 PAct [W] 507.44

Pc/PE 3.42 maaic [kg/s] 0.01709

b[3] -6.85E-04 mcomp [kg/s] 0.01682

b[2] -3.32E-02 m Mean Dev 1.59 b[1] 1.81E-01 QE [W] 3081

b[0] 2.31E-01 Qc [W] 3581

rl i 0.44 CIE+ PAct 3589

h1 [kJ/kg] 423.5 E Bal Mean Dev 0.22 h2 [kJ/kg] 453.2 COP I 2.65

Air Side vcA [m/s] ! 3.02 vEA [mist] 3.42

PCA kg/M31 0.972 PEA kgim, I 0.971 ACA [m2] 0.12 AEA IrT11 0.036

MCA [kg/s] 0.36 mEA [kg/s] 0.119

Cpcp, hCA1

[kJ/kg [kJ/kg]

] 1.007 56.5

CpEA [kJ/kg hEA1 [kJ/kg]

] 1.005 58.98

hcA2 [kJ/kg] 66.9 h EA2 [kJ/kg] 33.39

Qc [W] I 3764 QE [W] I 3056

QC Mean Dev 5.1 CIE Mean Dev 0.8

Table L-6 Experimental averages and calculations for Test 4 - Accumulator

test at high fan speed

L-8

Appendix L

L.4 Verification of Baseli n e Test Results

The baseline tests were verified using a steady-state mathematical model for the

high-pressure side of a unitary air conditioning unit s . This verification comprised

a three-way comparison in which the experimental results were compared to

results obtained from this mathematical model and an to those of a simulation

program (HPSIM 2) that predicts the performance of air-conditioners and heat

pumps that operate on the vapour-compression cycle. Table L-7 and Table L-8

show the comparison of the results. Exp represents the experimental data, Model,

the data derived from the above-mentioned model and HPSIM 2, the data from

this simulation program. % dev 1 and % dev2 respectively represent the deviation

of the model from the experimental results and the deviation of the simulation

program from the experimental results.

txp Model I-11-'51M To devl % devZ

m [kg/s] 0.0192 0.0199 0.0220 -3.85 -14.51 p [kW] 1.527 1.390 1.400 8.94 8.19

QE [kW] 3.916 4.366 3.805 -11.63 2.74

Qc [kW] 5.325 5.752 5.205 -8.02 2.15

COPcooiing 2.563 3.140 2.771 -22.56 -8.30

COPHeating 3.489 4.137 3.771 -18.65 -8.12

Table L-7 Table showing the comparison of the low fan speed experimental

results to that of the steady-state model of the high-pressure side of a unitary air

conditioning unit' and to the results obtained using HPSIM 2 .

L-9

Appendix L

txp model HPSIM 70 aevi % aevz

m [kg/s] 0.0175 0.0194 0.0203 -11.36 -16.59 p [kW] 1.41 1.36 1.22 3.30 13.25

QE [kW] 3.73 4.18 3.60 -12.51 2.91

Qc [kW] 5.04 5.54 4.82 -9.96 4.26

COPcoohng 2.64 3.07 2.95 -16.31 -11.83

COP H eating 3.58 4.07 3.95 -13.71 -10.34

Table L-8 Table showing the comparison of the high fan speed experimental

results to that of the steady-state model of the high-pressure side of a unitary air

conditioning unit s and to the results obtained using HPSIM 2 .

It can be concluded that all deviations are within an acceptable range thus

indicating that the results may be used with confidence. The deviations that do

occur may be attributed to accuracy's of the measuring data and losses that occur

in the real system.

The accumulator system could not be simulated on this model or simulation

program.

L.5 Discussion of Results

Table L-9 shows the experimental averages of various system properties, their

difference and their percentage difference at the low fan speed setting (air mass

flow rates of 0.096 kg/s over the evaporator and 0.23 kg/s over the condenser),

while Table L-10 shows the experimental averages of various system properties,

their difference and their percentage difference at the high fan speed setting (air

mass flow rates of 0.12 kg/s over the evaporator and 0.36 kg/s over the

condenser)

L-10

Appendix L

Low Fan Speed Comparison Property Unit Baseline Accumulator Error

Condensing pressure kPa 1975.56 1961.11 -0.73% Evaporating pressure kPa 456.11 458.83 0.60%

Pressure Ratio - 3.81 3.77 -1.22% Compressor Insentropic Efficiency - 0.45 0.45 0.11% Calculated R22 Mass Flow Rate kg/s 0.0151 0.0144 -4.73%

Comp Curves R22 Mass Flow Rate kg/s 0.0171 0.0173 1.31% Compressor Power Consumption W 1164.44 1168.89 0.38%

QE W 2874.61 2908.92 1.19%

Qc W 3467.29 3542.27 2.16%

QE+Pact W 3400.10 3436.99 1.08% Coefficient of Performance - 2.47 2.49 0.81% Condenser Air Inlet Temp. °C 25.03 25.09 0.06°C

Condenser Air Outlet Temp. °C 48.13 47.33 -0.80°C Evaporator Air Inlet Temp. °C 25.07 25.06 -0.01°C

Evaporator Air Outlet Temp. °C 9.56 9.47 -0.09°C Compressor Inlet Temperature °C 19.78 12.20 -7.58°C

Compressor Outlet Temperature °C 90.50 86.49 -4.01°C Capillary Tube Inlet Temperature °C 41.96 38.01 -3.94°C

Table L-9 Comparison of baseline and accumulator systems at the low fan speed setting.

High Fan Speed Comparison Property Unit Baseline Accumulator Error

Condensing pressure kPa 1748.67 1781.06 1.85% Evaporating pressure kPa 497.44 520.39 4.61%

Pressure Ratio - 3.52 3.42 -2.64% Compressor Insentropic Efficiency - 0.42 0.44 2.69%

Calculated Mass Flow Rate kg/s 0.0164 0.0171 4.13% Comp Curves Mass Flow Rate kg/s 0.0154 0.0168 8.91%

Compressor Power Consumption W 1151.11 1163.33 1.06%

QE W 2781.05 3081.06 10.79%

Qc W 3241.21 3580.56 10.47%

QE+PTheo W 3270.02 3588.50 9.74% Coefficient of Performance - 2.42 2.65 9.62% Condenser Air Inlet Temp. °C 25.04 24.88 -0.17°C

Condenser Air Outlet Temp. °C 40.50 40.97 0.47°C Evaporator Air Inlet Temp. °C 25.03 24.98 -0.06°C

Evaporator Air Outlet Temp. °C 9.44 10.30 0.86°C Compressor Inlet Temperature °C 23.63 25.23 1.60°C

Compressor Outlet Temperature °C 84.37 85.70 1.33°C Capillary Tube Inlet Temperature °C 35.29 33.50 -1.79°C

Table L-10 Comparison of baseline and accumulator systems at the high fan speed setting.

L-11

Appendix L

A comparison of baseline and accumulator experimental data is discussed under

the following headings:

Condensing Pressure

At both fan speeds the condensing pressure has very little deviation (below 2%,

14kPa), this is expected as the accumulator only influences the high pressure side

after the refrigerant has passed through the condenser. The accumulator is thus

far away from the compressor having little effect on the condensing pressure and

thus temperature.

Evaporating Pressure

At low fan speeds there is little deviation but at the higher fan speed, there is

almost a 5% (22.9kPa) increase in the evaporating pressure. This is favorable as

the work that is required by the system decreases as the two pressure lines move

toward one another.

Pressure Ratio

The pressure ratio decreases with the addition of the accumulator at both speeds.

This is favourable and is attributed to the increase in the evaporating pressure

while the condensing pressure stays relatively constant.

Compressor Isentropic Efficiency

There is almost a 3% increase in the isentropic efficiency for the higher fan

speed, although the lower fan speed has a very small increase it is basically

negligible. The increase at the higher fan speed is attributed to the increase in

L-12

Appendix L

evaporating pressure (with constant condensing pressure) and thus decreases the

pressure ratio.

Refrigerant Mass Flow Rate

According to the mass flow rates obtained from the compressor curves, there is a

general increase in refrigerant mass flow rate when the accumulator is added,

especially at the higher fan speed (8.91%, 0.0014 kg/s). This is expected because

the compressor suction line has saturated, or nearly saturated, refrigerant vapour

when the accumulator is added. A higher mass flow rate increases the refrigerant

side heat transfer coefficient resulting in higher evaporating pressures (and thus

temperatures). This shows that there is a positive influence once the accumulator

is added.

Compressor Power Consumption

Both cases show a slight increase in power consumption. This is expected with a

higher evaporating pressure and refrigerant mass flow rate. This increase is

however, very small (12W at the high fan speed) and when one considers the

8.91% increase in refrigerant mass flow rate, it is a small sacrifice for a large

gain.

Cooling Capacity (QE)

The accumulator increases the cooling capacity in both scenarios. At the low fan

speed the increase is very small (1.19%, 34.3W) but at the high fan speed setting,

the increase is more than 10% (300 W) and is a direct result of the fact that the

refrigerant is sub-cooled through the accumulator before entering the evaporator.

L-13

Appendix L

Heat Exchanged over the condenser (Qc)

There is a general increase with the accumulator added to the system. Very small

gains are obtained at the low fan speed setting but over 10% (339 W) at the

higher fan speed setting. These gains are consistent with the energy balance, as

there is a very small increase in compressor power consumption and roughly

10% increase in heat exchanged through the evaporator.


The COP is increased in both scenarios with the high fan speed setting

dominating with a 9.62% (0.23) increase. This increase is directly related to the

increase in heat exchanged through the evaporator.

Condenser Air Inlet and Outlet Temperatures

There is very little variation in these temperatures. The inlet conditions are not

expected to vary that much as these temperatures are experimentally controlled.

The small variations show good and effective experimental control. The outlet

temperatures have small variations (less than 0.47°C) due to the small variation

in the condensing temperature (less than 1.85%, 32 kPa). This is good

experimental agreement from two factors that directly influence one another.

Evaporator Air Inlet and Outlet Temperatures

The air inlet temperatures are expected to have small variations as they are

experimentally controlled. There is a 0.86°C increase in the outlet temperature.

Although ideally a decrease in this temperature is desired, the other benefits and

gains obtained far outweigh this small loss.

L-14

Appendix L

Compressor Inlet and Outlet Temperatures

At low fan speed settings the compressor inlet temperature drops by 7.5°C with

the addition of the accumulator. This is due to the fact that the baseline and

accumulator evaporating pressures at low fan speed are very close (2.72 kPa

difference) and a pressure drop occurs across the accumulator causing the

compressor inlet temperature to be lower with the addition of the accumulator.

The 1.6°C gain in inlet temperature at the high fan speed setting is expected as

the evaporating pressure (and thus temperature) increase substantially (22 kPa)

with the addition of the accumulator and thus even with the pressure drop across

the accumulator, the inlet temperature is higher. The outlet temperatures are

relatively consistent which is expected as the condensing pressures (and thus

temperatures) have small deviations.

Capillary Tube Inlet Temperature

Both fan speed setting show a decrease of up to 9.4% (3.9°C) in temperature.

This is expected as it shows that the accumulator is sub-cooling the refrigerant

after the condenser. This advantageous and the gains are seen in the evaporator

performance.

L-15

Appendix L

L.6 Conclusion

The advantages of the accumulator at the low fan speed setting are very small

and would not warrant the cost of the accumulator and extra piping. However at

the high fan speed setting, the benefits speak for themselves; evaporating

pressure is increased by 4.6%, the refrigerant mass flow is increased by 8.9%, the

cooling capacity increased by over 10% and the condenser capacity increased by

over 10%. All of these benefits are gained at the cost of a 1% increase in

compressor power consumption. The increased evaporating pressure which

results in a lower pressure ratio over the compressor would assist in prolonging

the compressor life. The accumulator is definitely a beneficial component in the

system.

All the tests completed in this section where completed with the only

modification to the system being the addition of the accumulator. The next step

in the testing process is to eliminate the last 10-15% of the evaporator to create

the liquid overfeeding operation (flooded evaporator). This operation is discussed

in the next Appendix.

L-16

Appendix L

L.7 Nomenclature

A area [m2]

b constant

Cp specific heat [J.kg - 1.1(-1 ]




enthalpy [k.T.kg-i ]

K compressor


pressure [kPa]

power [W]


T temperature [K]

v velocity [m•s -1 ]

x compression ratio

Greek letters

P density [kg.m-3 ]

11i isentropic efficiency

Subscripts

Act Actual

atmos atmospheric

L-17

Appendix L

C condenser

CC calculated at condenser

Cale calculated

CA condenser air



E evaporator

EE calculated at evaporator

EA evaporator air



L.8 References

Petit P., Meyer J.P. A steady state model for the high-pressure side of a unitary

air conditioning unit To be published (1999).

ENERFLOW Technologies HPSIM Version 1.0 University of Potchestroom,

South Africa (1994).

L-18

Appendix M

Appendix M: Liquid Overfeeding Experimental Testing

and Analysis of Results

M.1 Introduction

This appendix discusses the experimental results obtained using the baseline and

accumulator system. The evaporator was modified to ensure liquid overfeeding

(flooded evaporator) in the system. The performances of the accumulator with

and without liquid overfeeding (LOF) are compared to the baseline system.

M.2 Liquid Overfeeding

For many years liquid recirculating refrigeration systems have been designed

with 100% wet evaporators, but in small air conditioning systems, a flooded

evaporator has meant a more complicated system design. Traditional overfeed

systems are those in which excess liquid is forced, either mechanically or by gas

pressure, through organised-flow evaporators, separated from the vapour, and

returned to the evaporators l . In the case of this system, the excess liquid is forced

over the coil within the accumulator by gas pressure where it is evaporated. The

evaporator is shortened so that it becomes flooded (100% utilised) and in the case

that excess liquid should pass through the evaporator, the liquid overfeeding

operation protects the compressor from liquid slugging. The "dry-coil" region of

the evaporator was therefore removed from the test air conditioner to ensure a

liquid overfeeding operation. In the case of the test system, 15% of the

evaporator was removed. Full use of the evaporator is important in small and

M-1

Appendix M

mobile air conditioning units where the space available for the evaporator is very

limited.

M.3 Experimental Metho d

When compared to the accumulator system without liquid overfeeding, the

cooling capacity and refrigerant mass flow rate are expected to drop slightly as

the size of the evaporator will be decreased to achieve liquid overfeeding. For

this reason, no tests were completed on the low fan speed setting due to the very

small influence of the accumulator without liquid overfeeding. All tests in this

section were completed at the high fan speed setting (air mass flow rates of 0.12

kg/s over the evaporator and 0.36 kg/s over the condenser) as the accumulator

only has a significant effect on the system at this speed.

M.3.1 Test 1 - Baseline test at high fan speed

This test is the same as Test 1 in Appendix L. The baseline system was

switched on at the high fan speed setting. The condenser and evaporator

environmental chambers were set at 25°C and the humidity ratio at the

evaporator inlet set between 50 and 60%. The system was allowed to run for a

minimum period of an hour to allow the system to stabilize in an attempt to

reach steady state conditions.

Table M-1 shows the readings that where taken and symbol used to record the

data.

M-2

Appendix M

Symbol Unit Description

Patmos [kPa] Atmospheric Pressure

PE [kPa] Pressure before Compressor

Pc [kPa] Pressure after Compressor

K1 [°C] Refrigerant temperature before Compressor

K2 [°C] Refrigerant temperature after Compressor

Ex1 [°C] Refrigerant temperature before Expansion coil

TEA1 [°C] Dry bulb air temperature before evaporator

TEA2 [°C] Dry bulb air temperature after evaporator

TCA 1 [°C] Dry bulb air temperature before condenser

TcA2 [°C] Dry bulb air temperature after condenser

TEWBI [°C] Wet bulb air temperature before evaporator

TEWB2 [°C] Wet bulb air temperature after evaporator

TCWB1 [°C] Wet bulb air temperature before condenser

Tcwa2 [°C] Wet bulb air temperature after condenser

P [W] Input Power

Table M-1 Table showing measured properties and symbols under which the

quantity was recorded

Sets of three readings were taken at twenty-minute intervals. Each set of three

readings was averaged to give an experimental average at each twenty-minute

interval. One test comprised three different sets of three readings (taken over a

40-minute period). Three different tests, all at the same ambient conditions,

were completed on three different days. This gave three test results which,

when averaged, gave a good representation of the measured values at the

specified ambient conditions.

M-3

Appendix M

M.3.2 Test 2 — Accumulator test at high fan speed

This test is the same as Test 3 completed in Appendix L. The above-mentioned

readings (Table M-1) along with the following temperatures (Table M-2)

where recorded.

Al [°C] Refrigerant temperature at accumulator inlet

A2 [°C] Refrigerant temperature at accumulator outlet

A3 [°C] Refrigerant temperature at coil inlet

A4 [°C] Refrigerant temperature at coil outlet

Table M-2 Extra measurements and corresponding symbols taken with

accumulator added to baseline system

M.3.3 Test 3 — Liquid overfeeding test at high fan speed

This test was completed in the exact same manner as test 2 excepting for the

fact that 15% of the evaporator was eliminated, thus ensuring a liquid

overfeeding operation.

M-4

Appendix M

MA Experimental Result s

M.4.1 Test 1 - Baseline test at high fan speed

The results in Table M-3 show the averages values of three different tests



RH 55%

Patmos 83.67 kPa


pc 1678 1660 1657 1665 11.67 pE 413 413.3 415 413.8 1.072 Tc 41.57 40.47 40.47 40.83 0.635 TE 1.3 0.2 1.133 0.878 0.593

Tcm 25.07 25 25.07 25.04 0.038 TEA .' 25 25.07 25.03 25.03 0.033 TcA2 40.77 40.47 40.27 40.5 0.252 TEA2 9.4 8.9 10.03 9.444 0.568

P 1160 1140 1153 1151 10.18 Ex, 35.67 35.2 35 35.29 0.342 K, 23 24.13 23.77 23.63 0.578 K2 87.67 82.5 82.93 84.37 2.866

TcwB , 17.57 17.5 18.2 17.76 0.386 TEwBi 17.87 17.5 18.23 17.87 0.367 i cwB2 20.33 18.83 20.7 19.96 0.989 TEWB2 9.433 8.7 9.733 9.29 0.532

Refrigerant Side

Pc [kPa] 1748.67 h5 [kJ/kg] 242.6

PE [kPa] 497.44 PACt [W] 488.97

Pc/PE 3.52 mcaic [kg/s] 0.01641 b[3] -1.18E-03 mcomp [kg/s] 0.01544 b[2] -2.90E-02 m Mean Dev 6.26 b[1] 1.67E-01 QE PM 2781 b[0] 2.49E-01 0c [W] 3241 1, 0.42 QE+PAct 3270 h1 [kJ/kg] 422.7 E Bal Mean Dev 0.89 h2 [kJ/kg] 452.5 COP 2.42

Air Side vCA [m/s] 3.018 vEA [m/s] 3.415

PCA [kg/m3] 0.971 PEA [kg/m3] 0.971 ACA [m2] 0.123 AEA [m2] 0.036

mcA [kg/s] 0.359 mEA [kg/s] 0.119


hcA, [kJ/kg]

hcA2 [kJ/kg]

57.21

65.4

hEA„ [kJ/kg]

hEA2 [kJ/kg]

57.57

31.66

Qc [W] 2939 QE Pi 3092


Table M-3 Experimental averages and calculations for Test 1 - Baseline test

at high fan speed

M-5

Appendix M

M.4.2 Test 2 - Accumulator test at high fan speed




RH 55%

Patmos 83.83 kPa

Test 1 Test 2 Test 3 Ave. S Dev

•

Test 1 Test 2 Test 3 Ave. S Dev

Pc 11 ifimpiti PE .• . . . e

Tc 42.6 0.6 TE 1.6 1.6 1.6 0.1

CA1 LigmagitiLthanziam EA1 =glum =MUM • CA2 larjaisMaariatiagra EA2 2EMBEIll mai I

I " 114211111111111011112111LIkil xi IINIMEMIRMIllikil 1 . 1

A3 36.8 37.1 36.3 36.8 0.4 20.5 16.3 19.5 18.8 2.2

A4 33.8 33.1 33.4 33.4 0.4 24.2 21.1 23.1 22.8 1.5

CWB1 • • • .• . • EWB1 • • • . 1.

1 co/B2 20.4 20.5 20. / 20.5 U.1 TEWB2 10.5 9.6 9.6 10.0 0.5

Refrigerant Side pc [kPa] 1781.06 115 [kJ/kg ] 240.3 pE [kPa] 520.39 PAct [W] 507.44

Pc/PE 3.42 mcaic [kg/s] 0.01709 b[3] -6.85E-04 mcomp [kg/s] 0.01682 b[2] -3.32E-02 m Mean Dev 1.59 b[1] 1.81E-01 QE [W] 3081 b[0] 2.31E-01 Qc [W] 3581 11, 0.44 QE+PAct 3589 h1 [kJ/kg] 423.5 E Bal Mean Dev 0.22 h2 [kJ/kg] 453.2 COP 2.65

Air Side vcA [m/s] 3.018 vEA [m/s] 3.415

PCA [kg/nil 0.972 pEA [kg/m3] 0.971 ACA [m2] 0.123 A [M21 EA 0.036 mcA [kg/s] 0.359 mEA [kg/s] 0.119

CpcA [kJ/kgK] 1.007 CpEA [kJ/kg 1.005

hcAl [kJ/kg] 56.45 h EA1 [kJ/kg] 58.98

hcA2 [kJ/kg] 66.92 hEA2 [kJ/kg] 33.39

Qc [W] 3764 QE [W] 3056


Table M-4 Experimental averages and calculations for Test 2 - Accumulator

without liquid overfeeding and at high fan speed

M-6

Appendix M

M.4.3 Test 3 - Liquid overfeeding test at high fan speed




RH 53%

Patmos 83.83 kPa

Test 1 Test 2 Test 3 Ave. S Dev Test 1 Test 2 Test 3 Ave. S Dev

pc 1680 1663 1673 1672 8.389 pE 425 422.7 425 424.2 1.347 Tc 40.67 40.1 40.2 40.32 0.302 TE 3.267 2.367 2.333 2.656 0.53

TcAI 25.1 24.93 25.1 25.04 0.096 TEA1 25.07 24.93 25.03 25.01 0.069 TCA2 39.57 39.33 39.4 39.43 0.12 TEAZ 10.17 9.467 10.33 9.989 0.46

P 1140 1140 1140 1140 0 Ex, 32.63 32 32.3 32.31 0.317 K1 23.6 22.73 24.9 23.74 1.091 K2 77.97 77.57 79.8 78.44 1.191

A3 35.7 34.93 34.97 35.2 0.433 Al 15.47 15.53 17.17 16.06 0.963 A4 32.33 31.77 32.17 32.09 0.291 A2 19.9 20.07 21.27 20.41 0.746

Tcwgi 17.23 16.9 17.5 17.21 0.301 TEwEli 17.17 17 17.4 17.19 0.201

I cwB2 20.03 19.67 20.27 19.99 0.302 I EWB2 9.367 8.767 9.6 9.24 0.43

Refrigerant Side

Pc [kPa] 1756.06 h5 [kJ/kg] 238.8

PE [kPa] 508.06 PAct [W] 490.64

Pc/PE 3.46 mcolo (kg/s] 0.01986 b[3] -1.07E-03 mcomp [kg/s] 0.01611 b[2] -2.99E-02 m Mean Dev 23.27 b[1] 1.70E-01 QE [W] 2962 b[0] 2.45E-01 Qc [W] 3360 1, 0.43 QE+PAct 3452 hl [kJ/kg] 422.6 E Bal Mean Dev 2.76 h2 [kJ/kg] 447.3 COP 2.60

Air Side vCA [m/s] 3.018 vEA [m/s] 3.415

PCA [kg/m1 0.970 pEA [kg/m3] 0.970

ACA [m2] 0.123 AEA [rn2] 0.036

mcA ' [kg/s] 0.359 mEA [kg/s] 0.119


hcAl [kJ/kg] 55.12 h EA1 [kJ/kg] 55.08 hcA2 [kJ/kg] 65.09 hEA2 [kJ/kg] 31.55

Qc [W] 3575 QE [W] 2806


Table M-5 Experimental averages and calculations for Test 3 - Accumulator

with liquid overfeeding operation and at high fan speed

M-7

Appendix M

M.5 Discussion of Results

Table M-6 shows the experimental averages of various system properties, their

difference and their percentage difference at the high fan speed setting.

Accumulator / Liquid Overfeeding Comparison Acc-Baseline LOF - Baseline

Property Unit Difference Difference

Condensing pressure kPa 1.85% 0.42% Evaporating pressure kPa 4.61% 2.13% Pressure Ratio - -2.64% -1.67% Compressor Insentropic Efficiency - 2.69% 1.32% Calculated Mass Flow Rate kg/s 4.13% 21.06% Comp Curves Mass Flow Rate kg/s 8.91% 4.35% Compressor Power Consumption W 1.06% -0.97% QE W 10.79% 6.50% Qc W 10.47% 3.66% QE+PAct W 9.74% 5.58% Coefficient of Performance - 9.62% 7.53% Condenser Air Inlet Temp. °C -0.17°C 0°C Condenser Air Outlet Temp. °C 0.47°C -1.07°C Evaporator Air Inlet Temp. °C -0.06°C -0.02°C Evaporator Air Outlet Temp. °C 0.86°C 0.54°C Compressor Inlet Temperature °C 1.6°C 0.11°C Compressor Outlet Temperature °C 1.33°C -5.92°C Capillary Tube Inlet Temperature °C -1.79°C -2.98°C

Table M-6 Comparison of the accumulator system with/without LOF in

relation to the baseline system at the high fan speed setting.

A comparison of baseline and accumulator experimental data is discussed under

the following headings:

Condensing Pressure

The LOF operation has a very small influence on the condensing pressure. There

is a small increase (0.4%, 7.4 kPa) which is much smaller then the 1.85% (32.39

kPa) increase without LOF. This is favorable, as a decrease in condensing

pressure is actually ideal.

M-8

Appendix M

Evaporating Pressure

The LOF system provides a smaller increase in evaporating pressure (2.1%, 10.6

kPa) than that of the accumulator system without LOF (5%, 22.9kPa). An

increase in evaporating pressure is desirable as it decreases the work that is

required by the system. The smaller increase is attributed to the smaller size of

the evaporator.

Pressure Ratio

The addition of the accumulator reduces the pressure ratio. The reduction in

pressure ratio with LOF is slightly less than that without. A decrease in pressure

ratio is desirable as it means less work and longer life for the compressor.

Compressor Isentropic Efficiency

Once again the accumulator without LOF has a better isentropic efficiency than

that with LOF. This is due to the lower evaporating pressure due to the smaller

evaporator. There is a small increase in both scenarios when compared to the

baseline system.

Refrigerant Mass Flow Rate

According to the mass flow rates obtained from the compressor curves, there is a

general increase in refrigerant mass flow rate when the accumulator is added. A

4% (0.0007 kg/s) increase is obtained with LOF compared to the 8.91% (0.0014

kg/s) with the accumulator without LOF. The evaporator is effectively shorter,

but supplies saturated (or nearly saturated vapour) to the accumulator. The

shorter length ensures a smaller increase in mass flow rate.

M-9

Appendix M

Compressor Power Consumption

The LOF operation decreases the power consumed by the compressor when

compared to the baseline operation. The accumulator without LOF gives rise to a

slight increase in power consumption. Although the decrease is quite small 1%

(11W) it is favourable when compared to an increase in power consumption.

Cooling Capacity (QE)

The accumulator increases the cooling capacity in both scenarios. The increase is

more than 10% (300 W) without LOF and 6.5% (180W) with LOF. The smaller

cooling capacity with LOF is directly related to the fact that the evaporator is

15% smaller. Essentially by decreasing the evaporator size by 15% (with the

accumulator in place), the cooling capacity only drops by 4.5% and effectively

increases by 6.5% when compared to the baseline operation. This is the

advantage of the LOF operation.

Heat Exchanged over the evaporator (Qc)

Generally, the accumulator increases the heat exchanged over the condenser. The

increase amounts to over 10% (339 W) without LOF and 3.7% with LOF. These

gains are consistent with the energy balance (QE + PAct).

M-10

Appendix M


The COP increases from 2.4 for baseline operation to 2.65 with the addition of

the accumulator without LOF. LOF operation increases the system COP to 2.6

(7.5%). The advantage of the LOF system over the system without LOF is that

reducing the evaporator size by 15% only causes 1.9% decrease in the COP. This

means that manufacturers can fit evaporators that are 15% smaller in to these

units which assists in decreasing the physical size of the unit whilst increasing

the system's COP. The 15% cost saving could also cover the cost of the

accumulator. The 7.5% increase in COP is the same as that obtained by Mei and

Chen2 .

Condenser Air Inlet and Outlet Temperatures

There is very little variation in these temperatures. The inlet conditions are not

expected to vary that much as these temperatures are experimentally controlled.

The small variations show good and effective experimental control. The outlet

temperatures have small variations (±1°C) due to the small variation in the

condensing temperature (less than 1.85%, 32 kPa). This is good experimental

agreement from two factors that directly influence one another.

Evaporator Air Inlet and Outlet Temperatures

The air inlet temperatures are expected to have very small variations as they are

experimentally controlled. The maximum variation in the outlet temperature was

an increase of 0.86°C at the evaporator outlet. Due to the fact that the evaporator

is flooded, one would expect the evaporator air outlet temperature to decrease

due to the increased heat transfer coefficient. The increase is attributed to the fact

M-11

Appendix M

that the evaporating pressures (and thus temperature) increase with the addition

of the accumulator when compared to the baseline case, thus increasing the air

outlet temperature. Although a decrease in this temperature is expected, the other

benefits and gains obtained far outweigh this very small loss.

Compressor Inlet and Outlet Temperatures

The compressor inlet temperature increases as a result of increase in the

evaporating pressure (and thus temperature) with the addition of the accumulator.

LOF reduces the compressor outlet temperatures by almost 6°C, which assists in

increasing the compressor life and isentropic efficiency as well as lowering the

condensing temperature. This decrease has a positive impact on the compressor,

particularly for units operating at high ambient temperatures. Higher discharge

temperatures also tend to carbonise oil, which could be detrimental to a

reciprocating compressor.

Capillary Tube Inlet Temperature

The capillary tube inlet temperature decreases by 3°C with the LOF operation

and by 1.8°C without LOF. This is expected as it shows that the accumulator is

sub-cooling the refrigerant after the condenser. This is advantageous and the

gains are seen in the evaporator performance.

M-12

Appendix M

M.6 Conclusion

The LOF cycle accomplishes several purposes;

The evaporator is 100% utilized,

The compressor efficiency is improved because saturated, or near saturated,

vapor is supplied to the compressor suction, thus increasing the flow rate,

It provides additional liquid sub-cooling, and

The compressor discharge temperature is lowered thus having a positive

effect on the compressor.

The greatest advantage of using the LOF system along with the accumulator is

the fact that the size of the evaporator may be decreased by 15% whilst

increasing the cooling capacity and COP. These gains are achieved with a slight

decrease in compressor power consumption.

M-13

Appendix M

M.7 Nomenclature

A

area [m2]

b constant

Cp specific heat [J.kg-i -K-1 ]




h enthalpy [k.T.kg-1 ]

K compressor


P pressure [kPa]

P power [W]


T temperature [K]

v velocity [m.s-1 ]

x compression ratio

Greek letters

p density [kg.m-3 ]

Ili isentropic efficiency

Subscripts

Act Actual

atmos atmospheric

C condenser

Calc calculated

M-14

Appendix M

CA condenser air



E evaporator

EA evaporator air



M.8 References

1 ASHRAE Handbook: Refrigeration American Society of Heating, Refrigeration

and Air-conditioning Engineers, Atlanta (1998) Chapter 1, 1.1

2 Mei, V.C., Chen, F.C., Chen, T.D., Jennings, L.W. Experimental Study of a

Liquid Overfeeding Air Conditioner ASHRAE Transactions v 102 n 1 (1996) 63-

67

M-15

Documents

Design methodology and experimental verification used to