ENERGY LABOR-s" 0 'r
NFOR
MAi
0 I CF
NTE:
Energy Laboratory
in association with
Heat Transfer Laboratory,
Department of Mechanical Engineering
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
IMPROVING HEAT PUMP PERFORMANCE
VIA COMPRESSOR CAPACITY CONTROL,ANALYSIS AND TEST,
Volume
I
by
Carl C. Hiller
and Leon R. Glicksman
Energy Laboratory Report No. MIT-EL 76-001
Heat Transfer Laboratory Report No. 24525-96, Vol. I
January 1976
2
ABSTRACT
The heat pump has long been of interest as a heating device because
of its ability to deliver more heat energy than it consumes. The present
work outlines past, present, and future developments in heat pump technology
and indicates key areas of improvement. One method of improvement, the capacity controlled heat pump, has been studied in detail.
An analysis of conventional and capacity controlled air-to-air heat
pumps has been performed, using detailed computer simulations. New system
sizing guidelines are outlined for capacity controlled units, resulting in
as much as a 30% per year energy savings over conventional heat pumps in
two of the six locations studied.
Economic studies, comparing conventional and capacity controlled heat
pumps to gas and electrical resistance heat, with and without air conditioning, indicate that capacity controlled heat pumps could soon be superior
to gas heating in some locations, depending on energy prices. All of the
economic studies have been done for a range of gas and electricity prices,
and include amortization of capital costs as well as operating costs.
Finally, preliminary development work on a new, potentially efficient
and inexpensive, continuously variable compressor capacity control device
is described. Test results on components of the early suction-valve cut-off
control mechanism indicate that it is possible to design a controllable
device to function in high speed (3600 RPM) compressors. However, more
development work is needed.
3
ACKNOWLEDGEMENTS
We would like to thank Sporlan Valve Company, Alco Valve Company,
York Air Conditioning Company, The General Electric Research Labs, and
especially Carrier Corporation for the wealth of information and helpful
insights they have given us.
We would also like to thank Thermo Engineer-
ing Inc., a heat pump contractor in Worcester, Massachusetts, for helpful
insights on installation and operation of heat pump/air conditioning systems.
This project has been funded in part by grants from industry and
foundations, through the MIT Energy Laboratory, and by the National Science
Foundation.
4
TABLE OF CONTENTS
VOLUME I
PAGE
ABSTRACT
2
ACKNOWLEDGEMENTS
3
TABL' OF CONTENTS
4
LIST OF TABLES
8
LIST OF FIGURES
9
LIST OF SYMBOLS USED IN TEXT
15
INTRODUCTION
20
CHAPTER 1.
HEAT PUMPS PAST, PRESENT, FUTURE
22
1.1
SIMPLE HEAT PUMP CYCLE
23
1.2
RELIABILITY
29
1.3
CONVENTIONAL AIR-TO-AIR HEAT PUMPS
31
1.4
NEW DEVELOPMENTS IN HEAT
UMPS
37
1.5
CAPACITY CONTROLLL) HEAT PUMPS
40
CHAPTER 2.
MODELING AND SIMULATION OF HEAT PUMP AND AIR CONDITIONING
SYSTEMS
46
SYSTEM MODELING
47
. Technique
· Comparison of Actual and Predicted Heat Pump
Performance
47
49
2.2
SYSTEM FLOW BALANCE
58
2.3
COMPRESSOR SIMULATION
62
2.1
5
PAGE
· Cylinder Processes, Valve, and Manifold Modeling
· Motor Cooling, Friction, and Suction-Discharge
Heat Transfer
· Oil Circulation Effect on Capacity
64
69
· Verification
72
of the Model
· Simulating Capacity Control
· Normal Range of Input Values and Their Effect
on Performance
i.4
CONDENSER
SIMULATION
EVAPORATOR SIMULATION
87
91
92
97
· General and Specific Models
· Verification of Models
CHAPTER
75
76
87
· General Model 'EXCH'
· Modeling A Finned Tube Condenser
· Verification of Models
2.5
72
97
98
3.
PERFORMANCE AND ECONOMICS OF CONVENTIONAL AND CAPACITY
100
CONTROLLED HEAT PUMPS
101
3.1
MODE OF ANALYSIS
3.2
EFFECT OF FAN POWER ON
3.3
PERFORMANCE OF A
3.4
EXTENDING PERFORMANCE RESULTS TO DIFFERENT
HEAT PUMP SIZES ON A PRESCRIBED HEAT LOAD
122
3.5
SEASONAL PERFORMANCE AND ECONOMIC COMPARISONS
127
ITROL OPTIONS
104
APACITY CONTROLLED HEAT PUMP
112
CHAPTER 4.
DESIGN AND TEST OF AN EARLY SUCTION-VALVE CUT-OFF MECHANISM
FOR COMPRESSOR CAPACITY CONTROL
154
4.1
COMPRESSOR CAPACITY-CONTROL VIA EARLY SUCTIONVALVE CLOSING
155
4.2
DESIGN REQUIREMENTS
161
6
PAGE
4.3
CUT-OFF MECHANISM DESIGN
164
4.4
EXPERIMENTAL CUT-OFF MECHANISM
183
4.5
EXPERIMENTAL RESULTS
186
CONCLUSIONS AND RECOMMENDATIONS
198
CHAPTER 5.
REFERENCES - AT THE END OF EACH SECTION
VOLUME II
APPENDIX A
205
THERMOPHYSICAL PROPERTIES OF REFRIGERANTS
APPENDIX B
CARRIERS
APPENDIX
229
MODEL 50 DQ SERIES SINGLE PACKAGE HEAT PUMPS
C
238
SAMPLE THERMODYNAMIC CYCLE DATA FROM SYSTEM SIMULATIONSCONVENTIONAL VS CAPACITY CONTROLLED HEAT PUMP
APPENDIX D
245
DETAILS OF SYSTEM FLOW BALANCE MODELING
APPENDIX E
263
DETAILS OF COMPRESSOR SIMULATION MODEL
APPENDIX F
317
REFRIGERANT-OIL SOLUBILITY
APPENDIX G
321
COMPRESSORDATA
APPENDIX H
PARAMETRIC STUDIES ON CARRIER 06D-537 COMPRESSOR
325
7
PAGE
APPENDIX
330
I
DETAILS
OF AIR-COOLED,
CROSS-FLOW
CONDENSER MODELING
361
APPENDIX J
COMPLEMENTS TO HEAT EXCHANGER ANALYSIS
. Overall Surface Efficiency
* Cross-Flow Effectiveness
370
APPENDIX K
FIAT TRANSFER COEFFICIENTS
. Condensation Two-Phase
· Evaporation Two-Phase
. SinglePhase
381
APPENDIX L
PRESSURE DROP RELATIONS
· Two Phase
. Single Phase in Heat Exchangers
Single Phase Line Pressure Drops
· Air
Side
397
APPENDIX M
DETAILS
OF CROSS-FLOW
EVAPORATOR MODELING
434
APPENDIX N
CAPACITY CONTROLLED 50 DQ 016 STUDIES
437
APPENDIX0
HEAT PUMP PERFORMANCE DATA FOR LOAD LINE
APPENDIX P
WEATHER DATA
"D"
STUDIES
442
8
LIST OF TABLES
PAGE
TABLE
1.5-1
COMPARISON OF COMPRESSOR CAPACITY CONTROL METHODS
45
2.1-1
SUMMARY OF REAL THERMOPHYSICAL EFFECTS AND
LIMITATIONS INCLUDED IN THE SYSTEMS MODELS
51
2.1-2
SUMMARY OF COMPUTER PROGRAMS FOR SIMULATING SYSTEM
PERFORMANCE
52
2.3-1
SUMMARY OF NORMAL RANGE OF VALUES FOR INPUT PARAMETERS OF COMPRESSOR SIMULATION
79
2.3-2
SUMMARY OF EFFECTS OF VARYING INPUT PARAMETERS
80
ON COMPRESSOR PERFORMANCE
3.5-1
MAXIMUM HEAT LOAD AND FAN DATA FOR LOAD LINE "D"
STUDIES
141
3.5-2
TOTAL SEASONAL ENERGY CONSUMPTION AND SEASONAL
PERFORMANCE FACTOR DATA
142
3.5-3
GAS AND ELECTRIC RESISTANCE FURNACE AND AIR
CONDITIONER COSTS
143
3.5-4
CONVENTIONAL HEAT PUMP COST- AND AIR FLOWS (CARRIER)
143
3.5-5
CAPACITY CONTROLLED hAT
144
PUMP COSTS
9
LIST OF FIGURES
PAGE
FIGURE
BASIC HEAT PUMP COMPONENTS
1.1-1
1.1-2 a SIMPLE REFRIGERATION CYCLE P-h DIAGRAM
27
27
b SIMPLE REFRIGERATION CYCLE T-s DIAGRAM
1.1-3
ACTUAL VS CARNOT COP'S
28
1.3-1.
TYPICAL HEAT LOAD AND HEAT PUMP CAPACITY CURVES
35
1.3-2'
VARIATION OF SATURATED VAPOR DENSITY WITH
SATURATION TEMPERATURE - REFRIGERANT 22
36
1.3-3
ACTUAL TEMPERATURE DIFFERENCES ACROSS HEAT
EXCHANGERS - CARRIER MODEL 50 DQ 016 HEAT PUMP
36
2.1-1
COMPONENTS OF A TYPICAL AIR CONDITIONING/HEAT
PUMP SYSTEM
54
2.1-2
ACTUAL HEAT PUMP THERMODYNAMIC CYCLE (EXAGGERATED)
55
2.1-3
SYSTEM MODELING TECHNIQUE
56
2.1-4
COMPARISON OF ACTUAL AND PRT)ICTED PERFORMANCE
OF CARRIER MODEL 50 DQ 016 hAT PUY0
57
a. HEATING CAPACITY
b. POWER CONSUMPTION
c. COP
2.3-1.
FOUR STEP CYLINDER PROCESS
81
2.3-2
TYPICAL VALVE, CYLINDER PRESSURE, AND MANIFOLD
PRESSURE BEHAVIOR OF RECIPROCATING COMPRESSORS WITH
PRESSURE ACTUATED VALVES
82
2.3-3
EQUIVALENT CYLINDER PRESSURE-VOLUME DIAGRAM
82
2.3-4
VARIATION OF MOTOR EFFICIENCY WITH LOAD
83
10
FIGURE
PAGE
2.3-5
VARIATION OF MOTOR SPEED WITH LOAD
83
2.3-6
COMPARISON OF ACTUAL AND PREDICTED PERFORMANCE
OF CARRIER MODEL 06D-824 COMPRESSOR
84
2.3-7
COMPARISON OF ACTUAL AND PREDICTED
OF CARRIER MODEL 06D>537
2.3-8
2.4-1
PERFORMANCE
85
COMPRESSOR
COMPARISON OF ACTUAL AND PREDICTED PERFORMANCE
OF 3 TON HERMETIC COMPRESSOR
86
FLOW ARRANGEMENTS FOR WHICH GENERAL HEAT EXCHANGER
94
MODELS 'EXCH',
AND
EVAP'
ARE VALID
2.4-2
FLOW ARRANGEMENTS FOR WHICH GENERAL HEAT EXCHANGER
MODELS 'EXCH', AND 'EVAP' ARE NOT VALID
95
2.4-3
DETERMINING SINGLE PHASE AND TWO-PHASE FRACTIONS
OF HEAT EXCHANGERS
95
2.4-4
FINNED TUBE HEAT EXCHANGER
96
2.4-5
COMPARISON OF ACTUAL AND PREDICTED CONDENSER
PERFORMANCE DURING HEAT PUMP OPERATION
96
2.5-1
COMPARISON OF ACTUAL AND PREDICTED EVAPORATOR
PERFORMANCE DURING HEAT PUMP OPERATION
99
3.3-1
HEAT OUTPUT OF CARRIER MODEL 50 DQ 016 HEAT PUMP
WITH CAPACITY CONTROL - FULL CONVENTIONAL AIR
FLOWS, 6330 CFM AND 10000 CFM
117
3.3-2
HEAT OUTPUT OF CARRIER MODEL 50 DQ 016 HEAT PUMP
WITH CAPACITY CONTROL - REDUCED AIR FLOWS 4500
117
CFM AND 7500 CFM
3.3-3
HEAT OUTPUT OF CARRIER MODEL 50 DQ 016 HEAT PUMP
WITH CAPACITY CONTROL - REDUCED AIR FLOWS 3165
CFM AND 5200 CFM
118
3.3-4
CAPACITY CONTROLLED COP PREDICTIONS, CARRIER MODEL
50 DQ 016 HEAT PUMP - FULL CONVENTIONAL AIR FLOWS,
6330 CFM AND 10000 CFM
119
3.3-5
CAPACITY CONTROLLED COP PREDICTIONS, CARRIER MODEL
50 DQ 016 HEAT PUMP - REDUCED AIR FLOWS 4500 CFM
120
AND 7500 CFM
Ir
11
PAGE
FIGURE
3.3-6
CAPACITY CONTROLLED COP PREDICTIONS, CARRIER MODEL
50 DQ 016 HEAT PUMP - REDUCED AIR FLOWS 3165 CFM
AND 5200 CFM
121
3.4-1
HEATING CAPACITY OF CONVENTIONAL AND CAPACITY CONTROLLED HEAT PUMPS COMPARED TO ASSUMED HEAT LOAD
LINE
125
3.4-2
CONF
CURVES FOR CONVENTIONAL CARRIER 50 DQ MODEL
126
SERIES HEAT PUMPS
WEATHER DATA - YEARLY AVERAGE TIME SPENT IN 50 F
TEMPERATURE BANDS
3.5-1
145
a. SAN FRANCISCO, CALIFORNIA
145
b. CHARLESTON, SOUTH CAROLINA
145
c. NEW YORK, NEW YORK
146
d. BOSTON, MASSACHUSETTS
146
e. OMAHA, NEBRASKA
147
f. MINNEAPOLIS, MINNESOTA
147
3.5-2
GAS FURNACE BURNER PRICES
148
3.5-3
EXAMPLE OF COMPRESSOR POWER REDUCTION, CARRIER MODEL
50 DQ 016 HEAT PUMP WITH CAPACITY CONTROL
148
3.5-4
COMPARISON OF TOTAL YEARLY HEATING COSTS, INCLUDING
AMORTIZATION OF CAPITAL, FOR HEAT PUMPS VS FORCED
149
AIR ELECTRICAL RESISTANCE AND GAS FURNACES WITH AIR
CONDITIONERS IN VARIOUS LOCATIONS - 10 YEAR
AMORTIZATION OF HEAT PUMPS AND AIR CONDITIONERS
a. SAN FRANCISCO
149
b. CHARLESTON
149
c.
NEW YORK
150
d.
BOSTON
150
e. OMAHA
151
f. MINNEAPOLIS
151
12
FIGURE
PAGE
3.5-5
COMPARISON OF TOTAL YEARLY HEATING COSTS, INCLUDING
AMORTIZATION OF CAPITAL, FOR HEAT PUMPS VS FORCED
AIR ELECTRICAL RESISTANCE AND GAS FURNACES WITH
AIR CONDITIONERS IN THE BOSTON AREA - 20 YEAR
A0ORTIZATtON OF HEAT PUMPS AND AIR CONDITIONERS
152
3.5-6
COMPARISON OF TOTAL YEARLY HEATING COSTS, INCLUDING
AMORTIZATION OF CAPITAL, FOR HEAT PUMPS VS FORCED
AIR ELECTRICAL RESISTANCE AND GAS FURNACES-WITHOUT
AIR CONDITIONERS
153
a. (OMAHA
b. MINNEAPOLIS
4.1-1
P-V DIAGRAMS FOR CONVENTIONAL AND CAPACITY CONT-
158
ROLLED COMPRESSORS
4.1-2
SCHEMATIC OF THE EARLY SUCTION-VALVE CUT-OFF
158
MECHANISM
4.1-3
OPERATION OF THE CUT-OFF MECHANISM THROUGH
ONE COMPLETE CYCLE
159
4.3-1
SUCTION VALVE AND CYLINDER SIDE OF HEAD PLATE-
180
3 TON COMPRESSOR
4.3-2
DISCHARGE VALVE, SUCTION/DISCHARGE MANIFOLD,
AND MANIFOLD SIDE OF HEAD PLATE - 3 TON COMPRESSOR
180
4.3-3
CUT-OFF MECHANISM DESIGN TO FIT IN A 3 TON HERMETIC
181
REFRIGERATIONCOMPRESSOR
4.3-4
SUGGESTED POWER PISTON DESIGN
182
4.4-1
EXPERIMENTAL POWER PISTON AND SPOOL VALVE
185
SLIDE VALVE AND SLIDE VALVE CHAMBER, SHOWING
185
4.4-2
PHOTO-SENSING SYSTEM AND MASK ON SLIDER
13
FIGURE
PAGE
4.5-1
SCHEMATIC OF TEST SYSTEM
192
4.5-2
CLOSE-UP VIEW OF PULSATOR CONNECTED TO TEST PARTS
193
4.5-3
SCHEMATIC VIEW OF TEST PARTS
193
4.5-w
PHOTO-SENSING SYSTEM FOR TIMER-SPOOL VALVE MOTION
194
4.5-5
SCHEMATIC MOTION/OSCILLOSCOPE TRACE FOR TIMERSPOOL VALVE
194
4.5-6
SCHEMATIC MOTION/OSCILLOSCOPE TRACE FOR SLIDE VALVE
AND POWER PISTON
195
4.5-7
TYPICAL MINIMUM TRAVEL TIME (MAXIMUM CUT-OFF)
CAPABILITY OF SPOOL VALVE
196
4.5-8
TYPICAL MAXIMUM TRAVEL TIME (MINIMUM CUT-OFF)
CAPABILITY OF SPOOL VALVE
197
A-1
VISCOSITY OF REFRIGERANT 12
208
A-2
THERMAL CONDUCTIVITY OF REFRIGERANT 12
208
A-3
VISCOSITY OF REFRIGERANT 22
209
A-4
THERMAL CONDUCTIVITY OF REK,£GERANT 22
209
A-5
SPECIFIC HEAT AT CONSTANT PRESSURE OF REFRIGERANT 12
210
A-6
SPECIFIC HEAT AT CONSTANT PRESSURE OF REFRIGERANT 22
210
B-1
INDOOR COIL - CARRIER MODEL 50 DQ 016 HEAT PUMP
235
B-2
OUTDOOR COIL - CARRIER MODEL 50 DQ 016 HEAT PUMP
236
B-3
CHARGING CHARTS - CARRIER MODEL 50 DQ 016 HEAT
237
PUMP DURING HEATING MODE
C-1
EXAGGERATED P-h DIAGRAM OF ACTUAL HEAT PUMP CYCLE
243
C-2
CYLINDER P-V DIAGRAMS
244
a, CONVENTIONALHEAT PUMP
14
FIGURE
PAGE
b. CAPACITY CONTROLLED HEAT PUMP
D-1
FLOW CHART FOR SYSTEM FLOW BALANCE MODEL
251
E-1
DEFINITION OF COMPRESSOR CAPACITY
289
E-2
FLOW CHART FOR COMPRESSOR MODEL
290
F-1
COMPARISON OF ACTUAL AND PREDICTED REFRIGERANT
12 - OIL SOLUBILITY
320
F-2
COMPARISON OF ACTUAL AND PREDICTED REFRIGERANT
22 - OIL SOLUBILITY
320
I-1
DIMENSIONS FOR FINNED TUBE HEAT EXCHANGER WITH
STAGGERED ROUND TUBES
344
I-2
FLOW CHART FOR GENERAL CONDENSER MODEL - 'EXCH'
345
1-3
FLOW CHART FOR FINNED TUBE CONDENSER MODEL
346
J-1
FINNED SURFACE
361
J-2
ELECTRICAL ANALOGY OF FINNED SURFACE
362
J-3
CROSS-FLOW EFFECTIVENESS, BOTH FLUIDS UNMIXED
367
K-1
HEAT TRANSFER CORRELATION FOR SINGLE PHASE FLOW
INSIDE CIRCULAR TUBES
376
K-2
AIR SIDE HEAT TRANSFER CORRELATION FOR CROSS-FLOW
OVER BANKS OF FINNED CIRCULAR TUBES
376
L-1
MOODY FRICTION FACTOR FOR FLOW IN CIRCULAR PIPES
391
L-2
KAYS & LONDON AIR SIDE FRICTION FACTOR CORRELATION
FOR CROSS FLOW OVER BANKS OF FINNED CIRCULAR TUBES
392
L-3
IMPROVED AIR SIDE FRICTION FACTOR CORRELATION FOR
CROSS FLOW OVER BANKS OF FINNED CIRCULAR TUBES,
392
BY HILLER
M-1
FLOW CHART FOR GENERAL EVAPORATOR MODEL 'EVAP'
410
M-2
FLOW CHART FOR FINNED TUBE EVAPORATOR MODEL
413
15
LIST OF SYMBOLS USED IN TEXT
SYMBOL
DEFINITION
A
Area
BDC
Bottom Dead Center
BP
Balance Point Temperature
CFM
Air Flow Rate (cubic feet per minute)
COP
Coefficient of Performance
Thermal Expansion Valve Coefficient
CTXV
CUTOFF
-
Parameter Specifying Amount of Capacity Reduction
(Vcu - Vmi )
D1
D
Diameter
DR
Diameter of Head of Power Piston
DSH
Diameter of Shank of Power Piston
tot
cyclic
fans
Total Yearly Enery', Consumption of A Heat Pump
With Evapoi ttor and Condenser Fans That Cycle On
And Off with the Compressor
Etot
cont.
indoor
fan
Total Yearly Energy Consumption of A Heat Pump With
A Condenser
(indoor) Fan That Runs Continuously
tot
Total Yearly Energy Consumption of A Heat Pump With
cont.
fans
Evaporator And Condenser Fans.That Run Continuously
Coefficient of Friction
F
Driving Force
16
F
-
F
Normal Force
n
h
Frictional Force
-
Enthalpy (Btu/lbm)
_
Latent Enthalpy of Vaporization (Btu/lbm)
i
-
Yearly Interest Rate (/yr)
m
-
Mass
m
-
Mass Flow.Rate
ZMC
-
Percent of Motor and Friction Heat given to Suction
h
fg
Gas in Compressor
n
-
Years of Amortization of Capital Costs
n
-
Polytropic Expansion Coefficient
Nu
-
Nusselt Number
-
Weight Percent of Compressor Oil Circulating in
Oil
System With Refrigerant
P
-
Power
P
-
Pressure
AP
-
Pressure Difference
Pr
-
Prandtl Number
Q
Heat TransferRate (Btu/hr)
Q
-
Heat
·Re
-
Reynolds Number
RPM
-
Revolutions Per Minute
SPF
-
Seasonal Performance Factor
Transfer (Btu/lbm)
Total energy produced during heating season
Total energy consumed during heating season
17
SVR
Surface to Volume Ratio In Compressor Cylinder
t
-
Time
%t
-
Percent Time On
T
-
Temperature (usually
AT
-
Temperature Difference
TDC
-
Top Dead Center
UA
-
Overall Conductance for Heat Transfer
V
-
Velocity
V
-
Volume
VD
-
Displacement Volume
VFR
-
Volume Flow Rate
VR
-
Volume Ratio
W
-
Work (Btu/lbm)
-W
Rate of Compressor Work (Btu/hr)
x
-
Travel of Sool
x
-
First derivative of Travel (Velocity -ft/sec)
x
-
Second Derivative of Travel (Acceleration - ft/sec 2)
C
Y
Vm
D
F)
(usually
I
or Power Piston (ft)
Characteristic Dimension of Duct
GREEK SYMBOLS
-
Efficient
8
-
Crank Angle
p
-
Density
F)
18
SUBSCRIPTS
SYMBOL
DEFINITION
act
Actual
avail
Available
BF
Both Indoor and Outdoor Fans
c
Control
Carnot
Carnot Cycle
cond
Condenser
cut
At beginning of Cut-Off
cyl
Inside Cylinder
D, disc
Discharge
dvc
Discharge Valve Closing
dvo
Discharge Valve Opening
ER
Electrical Resistance
evap
Evaporator
FF
Fossil Fuel
gas
Gas Furnace'
H
High Temperature Reservoir
hp, HP
-
Heat Pump
IF
-
Indoor Fan
is
Isentropic
L
Low Temperature Reservoir
load
Heat Load
19
max
Maximum
mech
-
Mechanical
min
-
Minimum
N
-
No Fan Power Included
OF
-
Outdoor Fan
req
-
Required
S
-
Suction
sat
-
Saturation Condition
svc
Suction Valve Closing
svo
-
Suction Valve Opening
xs
-
Cross-Sectional
1
-
Inlet To Compressor
2
-
Outlet From Compressor
3
-
Outlet From Condenser
4
-
Inlet To Evaporator
C
20
INTRODUCTION
A heat pump is by definition a device which moves heat from a
region of low temperature to a region of higher temperature.
The
direction of heat flow is opposite to the direction required by the
second law of thermodynamics so that external energy must be supplied.
The net heat output of a heat pump, however, is equal to the sum of
the input energy plus the energy which was transferred, say, from
outside to inside.
Most heat pumps on the market today deliver between
one and three times as much energy as they consume.
The potential
value of this feature becomes apparent when overall efficiency of
fuel utilization is compared for heat pump, electrical resistance,
and fossil fuel heating systems:
1.
First consider a new heat pump system, with a seasonal performance
factor
SPF
Total heat deli 'red over heating season
Total energy consumed oer heating season
of 3.0, powered by electricity.
Typical values of electrical
generating and transmission efficiency are 35% and 84%
respectively.
The overall efficiency of fuel utilization
would then be
- (.35) (.84) (3.0) = .88
2.
The overall efficiency of straight electrical resistance heating
would be only
NgR = (.35) (.84) = .29
21
3.
The typical seasonal average efficiency of a fossil fuel
fired heating system is between 60 and 80%, according to
furnace manufacturers and heating contractors.
riFF
.6 to .8
The ovezall fuel utilization efficiency of a high efficiency heat
pump system, having SPF = 3.0, would hence be between 8 and 60%
greater than for the other conventional forms of heating, resulting
in reduced fossil fuel consumption.
Moreover, substantial cost
savings could be realized over electrical resistance heat, and
possibly over fossil fuel heating if fossil fuel prices continue to
rise.
Historically, unfortunately, heat pumps have suffered from
three major deficiencies; poor reliability, limited heating capacity
in colder climates, and
enerally 1 ?; seasonal performance factors.
The present work discusses p st, present, and future developments
in heat pump technology, and indicates key areas of improvement.
One
promising method of improvement, the capacity controlled heat pump,
has
been studied in detail.
22
CHAPTER
1.
HEAT PUMPS PAST, PRESENT, FUTURE
A knowledge of both basic and actual heat pump operating
cycles is a prerequisite for evaluating potential improvements.
Such background information is presented in this chapter, followed
by a discussion of past, present, and future heat pump research
efforts.
23
SECTION11
SIMPLE HEAT PUMP CYCLE
Figure 1.1-1 shows the four basic components of a heat pump;
the compressor, the condenser, the expansion device, and the evaporator.
The thermodynamic operating cycle for a heat pump is identical to the
conventional vapor-compression refrigeration cycle, shown in Figures
1.1-2a and b
.
The compressor takes superheated refrigerant vapor with
low pressure and temperature at state 1 and compresses it to a much
higher pressure and temperature at state 2.
The high pressure, high
temperature gas is then passed through the condenser (indoor coil of
a heat pump), where it gives up heat to the high temperature environment,
and changes from vapor to liquid at high pressure.
The refrigerant
exits from the condenser usually as a subcooled liquid at state 3.
Next,
the refrigerant passes through an expansion device where it drops in
pressure.
This drop in pressure is accompanied by a drop in temperature
such that the refrigerant leaves the expansion device and enters the
evaporator (outdoor coil of a heat pump) as a low pressure, low
temperature mixture of liquid and vapor at state 4.
Finally, the
refrigerant passes through the evaporator, where it picks up heat from
the low temperature environment, changing to all vapor and exiting at
state 1.
If we do a simple energy balance on the system shown in Figure
1.1-1, we find:
H
L +
24
where:
H - Heat energy rejected to the high temperature environment
QL
Heat energy taken from the low temperature environment
---Input energy required to move the quantity of heat QL from
the low temperature environment to the high temperature
environment.
The efficiency, or as it
performance
(COP), is
U
is
more commonly called, the coefficient of
then equal to the heat output divided by the work
input:
COP- - Therefore:
COP- 1+
-
4-
We thus see that the COP of a heat pump is
That
is,
always greater than one.
a heat pump always produces more heat energy than work
energy consumed, because there is
a net gain of energy
QL
which
is transferred from the low temperature to the high temperature
environment.
The heat pump is a reverse
heat engineand is thereforelimited
by the Carnot cycle COP2:
COP
Carnot
TL
Te ]
25
where:
TL
=
low temperature in cycle
T H = high temperature in cycle
The maximum possible COP for a heat pump, maintaining a fixed
temperature in the heated space, is hence a function of source
temperature, as shown in Figure 1.1-3o
However, any real heat
transfer system must have finite temperature differences across the
heat exchangers.
Also shown on Figure 11-3
are the Carnot COP for a
typical air-to-air heat pump, accounting for
AT's
across the heat
exchangers, and the actual COP for the same heat pump, accounting for
compressor efficiencies and other effects.
It is evident that the
influence of temperature difference across the heat exchangers on
COP is significant, causing a major portion of the discrepancy between
actual and ideal COP's at higher so,-ce temperatures.
increasing
Causes of the
AT's with increaELng source temperature are discussed
in section 1.3.
The remaining difference between actial and Carnot
COP's is a result of real working fluids, flow losses, and compressor
efficiency, as seen in the following example:
Assume:
Working fluid - Refrigerant 22
Compressor efficiency - 57% overall
Source temperature (outdoor air temperature) - 10°F
Sink temperature (indoor air temperature) - 70°F
26
AT across evaporator - 170 F
AT across condenser - 32°F
Superheat at.state 1 - 15°F
Subcooling at state 3 - 10°F
Then, for refrigerant 22 (see Appendix A)
T
- -7°F
T
r
sat
evap
sat
1020F
cond
h1
- 106 Btu/lbm
127 Btu/lbm
h
Wis 2i
-
i
21
Btu/lbm
Wat
act
h2at
.'7
.57
36.8 Btu/lbm
142.8 Btu/lbm
h3 - h 4 - 36.8 Btu/lbm
-
QoPh
W
2
act
h2-
act
13
h1
142.8 - 36.8
36.8
-2.88
As seen in Figure 1.1-3, the COP of the example falls very close to
the actual COP curve at the given source and sink temperature.
References
1.
ASHRAE Handbook of Fundamentals (New York: American Soc. of Heat.,
Refg., & Air-Cond. Eng., Inc., 1972) Cpt.l.
2.
Van Wylen, Gordon J., and Sonntag, Richard E., Fundamentals of
Classical Thermodynamics (New York: John Wiley & Sons, Inc. 1967)
Cpt. 6.
27
TH
essor
£:xpansion
Levice
c
OL'
TL
BASIC HEAT PUMP COMPONENTS
FIGURE 1.1-1
I
3
2Pa~~~2
2
P
T
3
r~~~~~~
~1
1
I
[I
h
State
State
State
State
1
2
3
4
-
Inlet to compressor
Outlet from compressor
Outlet from condenser
Inlet to evaporator
SIMPLE REFRIGERATION
FIGURE 11-2
CYCLE
28
T
HH - 70F'
Carnot
ni for AT's
angers
- 23.7 (F)
7
+ 16.32 (F)
COP
:-
6
5
4
3
Actual
See Example
1
-20
-10
0
10
20
30
40
TS (F)
ACTUAL vs
CARNOT COP's
FIGURE 1.1-3
50
60
70
F
29
SECTION 1.2
RELIABILITY
The heat pump first began to appear commercially in the early
195C
.
Unfortunately, most of the units which were produced through
the mid 1960's had been designed using existing air conditioning
technology, and were hence under-designed for heat pump operation.
The higher operating stresses on components while in the heating
mode, and during transition between heating and cooling, caused early
units to suffer from very poor reliability.
Another major problem
with early heat pump installations was a lack of properly trained and
equiped service personnel
Since the mid 1960's the major heat pump manufacturers have
undertaken efforts to improve reliability.
The results have been
inproved compressors, designed to withstand higher stresses, having
better bearings, improved vatting, improved motor insulation, better
motor cooling, better lubricating oils, and more.
Also, vastly improved
controls have been developed to prevent extreme conditions from
occuring during either normal operation, or during unexpected operating
modes, such as loss of refrigerant charge, fan malfunction, and the
like3 .
Efforts to better train service personnel were also undertaken.
Studies sponsored by both the Edison Electric Institute4, and the
Alabama Power and Light Company 5 have shown that, although heat pumps
now have considerably better reliability than in the past, there is still
30
room for considerable improvements, both in training of service
personnel, and in extending the usefullness of heat pumps to colder
climates.
Several ongoing research efforts to the latter end are
discussed in subsequent sections of this chapter.
References
1.
"Heat-Pump
Reliability Shows Big Gains"., Electrical World (August
1, 1973) pg. 78-80.
2.
Correspondence with various heat pump manufacturers and heating
contractors.
3.
Segerstrom, Stewart, "Heat Pumps Today", ASHRAE Journal (July,
1971) pg. 63-65.
4.
"Heat Pump Improvement", EEl Project RP59 Final Report, Publication
No. 71-901, (New York: Edison Electric Institute, May, 1971).
5.
"Utility Details its Heat-Pump Service Data", Electrical World
(March 15, 1975) pg. 148-149.
31
SECTION lo3
CONVENTIONAL AIR-TO-AIR
HEAT PUMPS
Conventional -air-to-air heat pumps
re designed to operate in
b..bthcooling and heating modes, <iA severe limitation on the suitability
of heat
umps in cold climates is the fact that conventional units are
sized for the air conditioning load, rather than the heating load.
With conventional designs, if a heat pump system were sized for the
heating load, it would be oversized for air conditioning, and the excess
capacity would result in poor humidity control during cooling because
the unit would be cycled off for a larger percentage of time.
A heat
pump sized for the air conditioning load has only limited heating
capacity, which either limits use of heat pumps to warm climates, or
requires a large amount of auxiliary heat.
Typical heat load and heat pump capacity (heat output) curves
as a function of ambient temperature are shcwn in Figure 1l3-1.
Note that above the balance point temperature (where heat supply
equals heat load), the heat pump has extreme excess capacity, and
below the balance point (BP) temperature, the heat pump has very
limited heating capacity.
The difference between the heat required
and that supplied by the heat pump is normally obtained from
auxiliary electrical resistance heaters.
A----typical
present day residential heat pump installation has
a balance point between 35 and 45°F.
According to an Edison Electric
Institute study , the above fact causes in excess of 30% of the total
32
energy consumed during a heating season to be in the form of electrical
resistance heat in locations ranging from South Carolina to Minnesota.
In commercial installations, electrical resistance heat normally
represents in excess of 18% of the total energy consumed during a
heating season, reflecting better load-matching applications.
The capacity mismatch problem is
in refrigerant mass
primarily a result of changes
flow rate due to density changes.
The variation
of saturated vapor density with saturation temperature for refrigerant
22 (freon 22) is
shown in Figure 1.3-2.
As the ambient temperature
increases, the saturation temperature and pressure inside of the evaporator correspondingly increase 2 causing vapor with greater density
The compressor, as a first approximation,
to enter the compressor.
is
a constant intake-volume pump, and hence as the density of the
entering gas increases, the mass flow rate increases.
between -30F
and 500F
For example,
saturated evaporator temperature, the mass flow
3
rate increases approximately by a factor (1.8 lbm/ft3 )/(.38 lbm/ft ) -
4.7.
Since the latent heat of vaporization
hfg
is also constant as
a first approximation, the increase in mass flow causes an increase
in the amount of heat pumped from the outdoor ambient into the
conditional space.
The increase in mass flow rate results also in
increase in the compressor work,
decrease in the work
although there is
per unit mass required.
an
usually a slight
The net result is that
a greater amount of heat, equal to the sum of both the increased
compressor work and the increased heat pumped from ambient, must be
rejected in the condenser.
33
Under conditions of high refrigerant mass flow, the dominant
resistance to heat transfer is the air-side heat transfer coefficient
rather than the refrigerant side.
Qhp
-an
be viewed
as
transfer coefficient
Qhp
UA
=
Hence, since the heat transfer
UA (Tsat
- Tair), and the overall heat
is approximately constant at high mass
flows, we see that in order to reject an increasing amount of heat
Qhp
That is,
the driving temperature difference must increase.
the saturation temperature and pressure in the condenser must increase
in order to reject an increasing amount of heat.
The resulting
behavior of the driving temperature differences across the heat
exchangers as a function of ambient temperature is shown in Figure 1.3-3
for an actual air-to-air heat pump.
1.1, an increase in the
AT's
Unfortunately, as noted in section
across the heat exchangers means an
increase in the irreversibilities in the cycle, and a drastic reduction
from theoretical maximum COP' .
It is worthwhile to note that the increased fla
rate and
resulting increased condensing pressure which occur a high ambient
temperature both produce increased stresses on the compressor and
motor.
Similarly, at low ambient temperature, high compressor
discharge gas temperatures result from the high pressure ratio across
which the refrigerant must be pumped.
The effect of either condition
is to reduce reliability of the compressor.
34
References
1.
"Heat Pump Improvement", EEI Project RP59 Final Report, Publication
No 71-901, (New York: Edison Electric Institute, May, 1971) pg. 550
2.
ASHRAE Guide & Data Book (New York: American Soc. of Heat., Refg.,
& Air-Cond. Eng., Inc., 1972) cpto 43.
36
·,
2.
VARIATION OF SATURATED VAPOR
DENSITY W;ITH SATURATION
2.
1.
TEMPERATUR - REFRIGERANT 22
1.
Ibm
1.
ft
1.
1.
1.
0
-40 -30 -20
-10
)
Saturation Temperature (F)-._
FIGURE 1.,3-2
Iv
17A
ACTUIAL TEMPERATURE DIFFERENCES
ACRC)SS HEAT FXCHANGERS CARRtIER MODEL 50 DO 016
HEAl PUMP
60
50
AT
(F)
20
Condenser
700F indoor air
852 rel.hum.
40
30
oF
708(Tam b ) + 23.7
cond
outdoor
air
-
BIP
l
10
0
-20
i
Evaporator
T ap
&
I
I
I
-10
0
10
20
.0696(Tmb)
I
I
30
40
Ambient Temperature
(F
FIGURE 1.3-3
db)
+ 16.32
m
50
(°F)
I
I
60
70
()
35
FIGURE 1.3-1
TYPICAL
HEAT LOAD & HEAT PUMP
CAPACITY
CURVES
Heat load
I
pump
ut
BP
Balance Point
T
37
SECTION 1.4
NEW DEVELOPMENTS IN HEAT PUMPS
Usual approaches to improving heat pump performance in the past
have centered upon the followingl:
1.
Improved utilization of heat exchanger surface such as
flooded evaporators and liquid free condensers.
-2.
3.
Larger heat exchanger areas for a given size unit.
Improved controls, such as defrost timers, pressure and
temperature limit controls and others.
4.
Improved compressor design, with more efficient motors
and valves, better internal flow paths, and improved
oil circulation control.
5.
Improved auxiliary heating, using better coordination
of building sensible heat
-_orage
and heating demands,
or fossil fuel supplementary heat.
Newer methods of achieving both better performance and reliability
are becoming economically feasible as energy prices rise.
Some of the
new approaches are:
1.
Solar assisted heat pumps
2.
Thermal storage heat pumps
3.
Multiple heat exchanger and/or multiple compressor heat
pumps
4.
Staged compression heat pumps
38
5.
Capacity controlled heat pumps
6.
Combinations of the above
Solar assisted heat pumps have the advantage of supplying heat
at an effective source temperature higher than ambient, thereby
increasing low temperature capacity and reducing stresses on the
compressor.
In addition, by lowering the collection temperature
of the solar collector, while increasing the collection temperature
for the heat pump, efficiency of both the heat pump and the solar
collector are increased.
Because of the intermittent nature of solar
energy, solar collection systems are usually equipped with energy
storage features.
Thermal storage, or thermal storage coupled with solar collection,
once again allows collection of heat energy at higher average temperatures,
such as diurnal, rather than nocturnal collection.
With such a system,
the problem of capacity mismatch is alleviated somewhat because excess
heat output is
stored, and used to make up insufficient capacity at
ambient temperatures below the balance point.
Solar and thermal
storage systems contain more heat exchangers than a straight air-to-air
heat pump.
Unless special care is taken, therefore, large
AT's
across the increased number of heat exchange sites can severely limit
'performance.
Cost, complexity, and reliability of extra components are
also factors to be considered in the above systems.
Multiple heat exchanger, multiple compressor, and staged compression
heat pumps also have added complexity and cost.
Such systems, however,
39
have the ability of single or multiple compressor operation for
increasing or decreasing capacity as needed, or by using staged
compression with intercooling, they can achieve more efficient low
ambie..t temperature operation.
Such systems may also provide additional
services such as domestic hot water, and may serve to regulate cooling
capacity on air conditioning operation.
-Capacity controlled heat pumps offer the ability to size the
unit for heating, rather than air conditioning, which reduces the
amount of auxiliary heat required.
Furthermore, by reducing the
capacity at ambient temperatures above the balance point, the mass
flow rate, and hence the
AT's
across the heat exchangers can be
kept low, resulting in much greater COP's than in conventional systems
at the higher ambient temperatures.
The capacity of the unit can also
be controlled during cooling to ache ve proper comfort control in the
conditioned space.
All of the preceeding new concepts hold great promise, and each
should be examined thoroughly to show which concepts or combinations
of concepts are best.
The capacity controlled heat pump concept
requires the least drastic changes in system design, and has therefore
been chosen for further study in the present work.
A more complete
description of the capacity controlled heat pump approach is given
in the following section.
Reference
1.
"Hi/Re/Li System" Brochure (Westinghouse Air Conditioning, P.O.Box
510, Staunton, Virginia 24401). Also: Consdorf, A.P., "Stage Reset
for Heat Pump Boom", Applicance Manufacturer (Nov., 1975) pg. 41-47.
40
SECTION1.5
CAPACITY CONTROLLED HEAT PUMPS
A capacity controlled heat pump is
a unit in which the pumping
ability of the compressor can be controlled to reduce or increase
The concept of compressor flow modulation
refrigerant mass flow rate.
First, by using efficient
achieves improved performance in two ways.
compressor capacity reduction to prevent the increase in mass flow
rate of refrigerant at high
ambient temperatures, the COP at higher
ambients can be significantly increased, as indicated in sections 1.1
and 1.3.
Reliability would also
on the compressor.
be increased because of reduced load
The second improvement in performance is realized
by a change in system sizing strategy.
Conventional heat pumps are sized
for the cooling load so that comfortable air conditioning is obtained.
With compressor capacity control the heat pump can be sized for a greater
heating capacity, thereby having a lower balance point and eliminating
Then, via the capacity control which
some of the auxiliary heating.
is
inherent in the concept, the capacity of the unit during cooling
can be controlled to achieve proper comfort control.
One method of system capacity control frequently
hot-gas-by-pass.
in use today is
Hot-gas-by-pass, where discharge gas from the compressor
is vented back to the suction side of the
retrofit to most systems,
but is
viewpoint because capacity is
compressor, is an easy
disasterous from an energy savings
reduced without
reducing compressor work,
41
and is
probably best avoided.
Other possible capacity control methods fall into essentially
three categories:
control.
speed control, clearance-volume control, and valve
A summary of the advantages and disadvantages of the latter
methods is given in Table 1.5-1.
Clearance volume control requires substantial amounts of
additional clearance volume to achieve the amount or flow reduction
desirable.
Fok example, to reduce the mass
flow rate by 50%, the
clearance volume must be equal to about half of the displacement
volume, adding substantially to the bulk of the compressor.
Moreover,
the large amount of residual mass causes unacceptably high discharge
temperatures with large amounts of flow reduction.
For this reason,
clearance volume control is considerably less attractive than some
other types of control.
Speed control can be done either contiauously or step-wise.
Continuously variable speed control is
one of the most efficient methods
of capacity control, and it offers good control down to about 50% of
rated speed of normal compressors.
More than 50% speed reduction is
unacceptable because of lubrication requirements of the compressors
Continuously variable speed control is
also expensive.
Usual cost
estimates range between $20 - $50/hp for motor speed control devices
on a mass
production basis2 .
Although expensive, continuously variable
speed control is not necessarily prohibitively expensive, for it might
42
be possible to replace some of the conventional starting controls
with the motor speed controls and hence reduce the cost
increment.
Step-wise speed control, as achieved for example, by using
multi-poled electric motors and switching the number of active poles,
is another viable alternative.
It might be possible to
achieve
satisfactory improvements in performance by using a finite number of
stepped changes to vary compressor capacity.
Step control is
less
costly than continuously variable speed control, but is also limited
to 50% of rated compressor speed because of lubrication requirements.
In addition, step changes in load on the compressor could put high
stresses on compressor components.
Suction valve unloading, a compressor capacity control method
often used in large air conditioning and refrigeration systems to
reduce cooling capacity when load decreases, can achieve some energy
savings
but has a number of drawbacks.
of one or more cylinders is held open so
out
In unloading, the suction valve
that gas is
pumped into and back
of the cylinder through the valve without being compressed.
Substantial losses can occur because of this repeated throttling
through the suction valve.
In addition, step-wise cylinder unloading
causes uneven stresses on the crankshaft, and provides inadequate,
if not totally unacceptable, control in smaller compressors.
method is, however, relatively inexpensive.
The
43
Two newer methods of compressor flow regulation via valve control
are late suction valve closing and early suction valve closing.
Late
suction valve closing again incurs the throttling loss by pumping gas
back out of the suction valve for part of the stroke.
Late valve
closing, however, gives more acceptable, smoother control than complete
valve unloading.
At present, however, the method is limited to a
maximum of 50% capacity reduction and to large low speed compressors3
Early suction-valve closing eliminates losses due to throttling gas
back out of the suction valves.
Instead, the suction valve, or a
secondary valve just upstream of the suction valve, is closed prematurely on the intake stroke, limiting the amount of gas taken in.
The gas inside the cylinder is expanded and then recompressed, resulting
in much lower losses.
Continuously variable capacity control over a
wide range is possible with the early valve closing approach.
The early suction-valve closing approach requires the most
development of the capacity control methods discussed above, but it also
holds promise for being one of the most efficient and inexpensive
approaches.
For this reason, the early suction-valve "cut-off"
approach was chosen for further study in the remainder of the present
work.
To properly evaluate the possible advantages and disadvantages
of compressor capacity control for heat pump improvement, development
of extensive, detailed computer simulations was undertaken, as
44
described in Chapter 2.
Much information from major heat pump
manufacturers was used in developing these simulationso
Moreover,
demonstration of the technical feasibility of the early suction-valve
cut-off approach to compressor capacity control has been initiated.
Some preliminary findings are discussed in Chapter 4.
References
1.
Discussions with General Electric Co., Schenectady, New York.
2.
Discussions with Electronic Systems Laboratory, Massachusetts
Institute of Technology, Cambridge, Mass., and General Electric
Co., Schenectady, New York.
3.
White, K.H., "Infinitely Variable Capacity Control", Proceedings
of the 1972 Purdue Compressor Technology Conference (Purdue Research
Foundation, 1972) pg. 47-51. Also: Tuymer, WJ.,
"Stepless Variable
Capacity Control", Proceedings of the 1974 Purdue Compressor
Technology Conference (Purdue Research Foundation, 1974) pg. 61-66.
45
TABLE 1.5-1
COMPARISON OF COMPRESSOR CAPACITY CONTROL METHODS
Method
Advantages
Disadvantages
Clearance
volume
control
Probably reliable
Large amounts of capacity
reduction require large
amounts of additional
clearance volume - on the
order of 1/2 of displacement
volume, resulting in high
discharge temps., and
adding substantial bulk
to compressor
S
Continuously
P
variable
Efficient, good
control, possible
elimination of some
of motor starting
circuitry
Expensive, lower speed
limit approxo, 1/2 speed
because of compressor
lubrication
Step-wise
variable
Efficient, but not as
good a control as
cont. var. spd., less
costly than cont.
var. spd.
Moderately expensive,
lower speed limit approx.
1/2 speed because of
compressor lubrication,
step changes in load
hard on compressor
Suction
Inexpensive
Poor control, losses due
to throttling, uneven
stresses on crankshaft,
step changes in load
hard on compressor
Reduced throttling
losses & better control than complete
valve unloading
Losses due to throttling,
limited to less than 50Z
capacity reduction and
to slow speed compressors
using.present methods
E
E
D
C
0
N
T
V
A valve
L
unloading
V
K
C
0
Late
Suction
valve
closing
T
R
O
im~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Early
L Suction
valve
closing
Efficient, good control, New approach - needs more
inexpensive, large
development
capacity reductions
possible
46
CHAPTER 2
MODELING AND SIMULATION OF HEAT PUMP AND AIR CONDITIONING SYSTEMS
The performance of each component of a heat pump or air
conditioning system is intricately linked to the performance of
all the other components in the system.
It is therefore useful
to predict the effects of changes in system design or operating
conditions with the aid of a computer simulation model.
This
chapter is devoted to developing a series of general and specific
models which can be used to predict performance of heat pump or
air conditioning systems.
Verification of the models using
actual performance data is given in each section.
Moreover,
many useful subprograms, applicable to more than just air conditioners
or heat pumps are presented.
47
SECTION 2.1
SYSTEM MODELING
Technique
The four major components of an air conditioning or heat pump
systen,
or any other refrigeration system, are the compressor, condenser,
evaporator, and expansion device.
There are a number of other
components that must also be considered, however, when accurately
modeling a system.
Components of a typical air conditioning/heat
pump system are shown in Figure 2.1-1.
In the present models, there
is assumed to be no heat transfer with the ambient except by the
heat exchangers (coils) and the compressor.
The compressor is
assumed to loose a small amount of heat to the ambient, as explained
in section 2.3.
The net effect of piping and components other
than the major four is to produce pressure drops in the system which
must be considered when
etermining
system flow balance.
An
exaggerated P-h diagram, showing the type of actual thermodynamic
cycle studied is given in Figure 2.1-2.
Many real physical limitations and effects have been included
in the system models.
For example, ideal gas assumptions are not
used, rather, actual thermodynamic properties generated from basic
quations are employed.
Appendix A discusses the basic equations
and presents computer subprograms for producing the thermodynamic
properties of refrigerants 12, 22, and 502.1
Other factors accounted
48
for include: checks for liquid line flashing, adequate oil return in
suction and discharge risers, and excessive compressor discharge
temperature; effect of motor cooling on compressor performance, effect
of oil circulation on system capacity, and more.
A complete summary
of real thermophysical effects and limitations accounted for
present systems
in
the
models is given in Table 2.1-1.
The systems models developed here can be divided into four
separate segments:
1.
System flow balance
2.
Compressor
3.
Condenser
4.
Evaporator
The first step in simulating system performance is to establish
the evaporating and condensing pressures at which the system
is operating.
In steady state operation, the system seeks an
operating condition which achieves both a mass flow or pressure
balance between the compressor and the expansion device, and an
energy balance on the amount of heat collected by the evaporator,
input by the compressor, and rejected by the condenser.
earlier, each portion of the model is
.As
outlined in Figure 2.1-3, it is
As stated
dependent on the other segments.
possible, by assuming certain
thermodynamic states in the cycle, to separate the flow or pressure
balance considerations
from the energy balance requirements.
Once the
49
flow balance condition has been found, using the compressor and
system flow balance models, the energy balance calculations, using
the condenser and evaporator models, indicate resulting values of the
assumd
thermodynamic states.
be madeand the calculations
values
agree.
New estimates of the states can then
repeated until
With practice,
assumed and predicted
the above procedurenormallyrequires
only one or two iterations.
An unusual
procedure
is
employed
flow and energy balance conditions.
for determining the preceeding
During heat pump operation, the
indoor coil acts as the condenser and can be assumed to have a constant
inlet air temperature.
The outdoor air temperature flowing over the
evaporator, however, is
variable over a wide range, causing performance
of the unit to be primarily a function of outdoor air conditions.
Rather than specifying outdoor air temperature and determining the
resulting flow and energy bal ace
conditions, the method used here is
to specify the evaporating pressure, determine the flow balance
condition, and then later determine the outdoor air temperature
required to give an energy balance for the given flow condition.
iteration on outdoor air temperature is
much simpler than an iteration
on total system conditions, and saves considerable time.
is
The
The procedure
outlined more completely in the flow chart in Figure 2.1-3.
Comparison of Actual and Predicted Heat Pump Performance
The present systems models have been used to simulate the performance of the Carrier model 50 DQ 016 unitary heat pump
system.
50
Physical data for this unit is summarizedin AppendixB. Figures
2.1-4a, b, and c compare actual and predicted performance during
the
heating mode.
within 8
Accuracy of the heating capacity prediction is
at 0°F and improves rapidly to near 0% error at temperatures
throughout most of the heat pump operating range.
Accuracy of the
total power consumption prediction is within 11% at 0°F and improves
to within 4
range.
at 200 F, where.it remains for the rest of the operating
Accuracy for the prediction of overall COP, including indoor
and outdoor fan power, is within 6% at 0°F and improves rapidly to
within 4% at higher operating temperatures.
Performance predictions
for the Carrier 50 DQ 016'heat pump with capacity control modifications
are presented in Chapter 3.
Examples of the details of
the system
simulation, illustrating temperatures, pressures, mass flow, power
consumption,
P-V diagrams, and more, are given in Appendix C for
both the conventional and capacity controlled 50 DQ 016 systems.
The remaining sections of this chapter are devoted to developing
and verifying the individual segments of the systems models.
A
summary of computer programs developed for use in the simulations
is
given in Table 2.1-2.
Reference
1.
Kartsounes, G.T., and Erth, R.A., "Calculation of the Thermodynamic
Properties of Refrigerants 12, 22, and 502 Using A Digital Computer",
Proceedings of the 1972 Purdue Compressor Technology Conference
(Purdue Research Foundation, 1972) pg. 285-290.
51
TABLE 2.1-1
SUMMARY OF REAL THERMOPHYSICAL EFFECTS AND LIMITATIONS
INCLUDED IN THE SYSTEMS MODELS
1.
Real gas properties, generated from basic equations are used.
No ideal gas assumptions are made. Computer subprograms are
presented for reproducing properties of refrigerants 12, 22,
and 502.
2.
Equivalent length method is used to determine pressure drop
through liquid and vapor lines, and other components.
3.
Fressure drops may be calculated for flow in tubes with any surface
rou3hness, not just for smooth tubes. A computer subprogram for
reproducing the entire Moody friction factor plot is included.
4.
Two-phase and single phase pressure drops are calculated for flow
through heat exchangers.
5.
All pressure drop and heat transfer relations are developed for
flow in laminar, transition, and turbulent flow regimes.
6.
A check for adequate oil entrainment in suction and discharge risers
is included.
7.
A check for liquid line flashing (flashing of liquid into vapor
due to excessive pressure drop) i included.
8.
Moisture removal ability of evaporator is included, using a
computer subprogram which reproduces psychrometric chart data.
9.
A check for excessive compressc
discharge temperature is (T
>280 0 F)
is included.
10.
Effect of refrigerant-oil solubility and oil circulation on capacity
is included.
11.
Effect of motor cooling on compressor performance is included.
12.
An approximate method of accounting for suction-discharge manifold
heat transfer inside compressor is included.
13.
Variation of motor efficiency with load on compressor is
14.
Variation of motor speed with load on compressor
15.
Mechanical friction due to rings,
is
included.
included.
pistons, and bearings in compressor
is approximated.
16.
Valve dynamics, suction and discharge plenum pressure pulsations, and
cylinder/plenum interactions are approximated.
17.
Compressor capacity control can be studied, using a number of different
types of control, including variable clearance volume, early suction
valve closing,
late suction valve closing and others.
52
TABLE 2.1-2
SUMMARY OF COMPUTER PROGRAMS FOR SIMULATING
SYSTEM PERFORMANCE
Mainline Programs
System flow balance - balances pressure drop or flow rates
of the compressor with the expansion
device, accounting for pressure drop
through all components.
Condenser
-
determines amount of heat rejected
by the system, given flow rates, and
inlet conditions
Evaporator
-
determines amount of heat absorbed by the
unit, given flow rates, inlet conditions,
and desired exit superheat
Subprograms
COMP
- determines compressor performance for
use in mainline programs, given inlet
temperature and pressure, and discharge
pressure
EFFM
-
determines compressor motor efficiency
as a function of load
OIL
-
determines refrigerant-oil solubility for
refrigerants 12 and 22, in order to predict
effect of oil circulation on capacity
TRIAL
-
determines remaining superheated vapor
properties, given pressure and any other
property, i.e. temperature, enthalpy,
entropy, or specific volume
-
produce thermodynamicproperties of
SPFHT
VAPOR
SATPRP
SPVOL
TSAT
refrigerants 12, 22, and 502
TABLES
.
EXCH
-
general cross-flow condenser model used
in condenser mainline program
EVAP
-
general cross-flow evaporator model used
in evaporator mainline program
53
XMOIST
-
reproduces psychrometric chart data for
use in general model EVAP
EXF
-
determines cross-flow effectiveness for
both fluids mixed and single passes
using the effectiveness-NTU method of
heat exchanger analysis
SEFF
-
determines overall surface efficiency of
extended surfaces, accounting for contact
resistance between extended and base surfaces
EHTC
-
determines evaporation two-phase heat
transfer coefficient
CHTC
-
determines condensation two-phase heat
transfer coefficient
SPHTC
-
determines single phase heat transfer
coefficients
PDROP
-
determines pressure drop through heat
exchangers, accounting for liquid, twophase, and vapor regions
DPLINE
-
determines pressure drop in single phase
regions other than heat exchangers and
expansion device, using equivalent
length method
FRICT
-
determines Moody friction factor for use
in single phase pressure drop evaluation,
including rough tubes as well as smooth.
HEAT
-
determines amount of suction/discharge
manifold heat transfer
54
- Tisrrbtnr
Cnool
in
Fil ter/
drier
[Aiquid
line
expansion
- Heating
valve
- - Cooling
COMPONENTS OF A TYPICAL
AIR
CONDITIONING/HEAT
FIGURE 2.1-1
PUMP SYSTEM
55
Condenser
-
-
-
4
P
r
e
S
u
r
Li
11
di
e
(P)
'IVJ L'
States:
1 - Inlet to compressor
L
cooling
2 - Exit from compressor
3 - Exit from condenser
Y - Suction-discharge
heat transfer
4 - Inlet to evaporator
__
Enthalpy
(h)
ACTUAL HEAT PUMP THERMODYNAMIC CYCLE
FIGURE 2,1-2
s
(EXAGGERATED)
56
Start
Specify
Tat
eap
evapI
_
&desired superheat
_
Guess temp. of liquid
leaving condenser
~~~~~~~~.!
I
i
_
Iterate on T
sat until
cond
.system flow balance
condition
_
is found
-
r
_.
_
Determine
heat transfer in condenser &
exit liquid temp.
Iterate on air temp. entering evap.
until desired exit superheat
and heat transfer is achieved
SYSTEM MODELING TECHNIOTJE
FIGURE 2.1-3
I
Check
Initial assumption
&
L
57
FIGURE21-4
COMPARISON OF ACTUAL AND PREDICTED PERFORMANCE OF
CARRIER MODEL 50 DQ 016 HEAT PUMP
---0A_
.
Actual
Predicted
e
-
IOutdoi r air - 85X rel.hum.,
kIndoom r air - 70 F
240
Heating
200
Capacitr
j
finn, \
160
of
Btu/hr/
120
eating Capacitv
Includes Indoor Fan
(a)
Motor Heat
80
40
-
C
n
"1(3
I
!
10
0
20
30
I
m
50
40
db)
Outdoor Air Temperature (F
60
a
7n
-
24
1
20
w
kw
16
-
12
Total Power Consum ption,
Including Indoor & Outdoor
Fan Power
(b)
-_..--
8
4
0
m
-1()
40
30
20
10
Outdoor Air Temperature (F
O
50
db) ---
60
3
COPBp
70
-I
2
COP - Including
Indoor & Outdoor
Fan Power
(c)
1
0
I
-10
0
I
I
10
I
20
·
*
30
·
·
40
*
·
50
Outdoor Air Temperature (F db)--"
· ~~~~
br)
1u
58
SECTION2.2
SYSTEM FLOW BALANCE
Determining
tem requires
flow balance conditions in any refrigeration sys-
a knowledge of components and piping arrangements for
each particular system, such as that shown in Figure 2.1-1.
Using
this knowledge, the present model iterates to match the available
pressure drop across the expansion device with that necessary to
pass the flow rate produced by the compressor under the assumed conditions.
The procedure is outlined in the flow chart of Appendix D.
The equivalent length method is used to determine pressure
drop through all components except the heat exchangers and the expansion device.
That is, components such as mufflers and filter/
driers are modeled as an equivalent length of straight pipe.
As a
first approximation, it is assumed that pressure drop through the
heat exchangers is entirely two-phase flow.
The latter assumption
can be corrected later to account for single-phase regions in the
coils, but such a correction is not usually necessary.
The primary function of the expansion device is to maintain
a minimum pressure ratio between suction and discharge sides of the
system.
Secondary functions often found for the device are to main-
tain constant exit superheat from the evaporator or subcooling from
the condensor.
Such control is achieved by varying the orifice open-
ing of the expansion device, thereby varying system pressure ratio
59
and compressor flow rate slightly.
The control which expansion
devices exert over evaporator pressure, however, is secondary.
The primary factor affecting evaporator pressure is the pumping
rate of the compressor relative to the vapor generation (heat transfer) rate in the evaporator.
The latter fact becomes important
when studying capacity controlled compressors.
Modeling of the expansion device depends on the type used
in a particular system.
Three frequent types of expansion devices
are capillary tubes, fixed orifices, and thermal expansion valves.
Capillary tubes and fixed orifices rely on fixed restrictions to
govern flow, and they often provide less than desirable control over
heat exchanger conditions.
Thermal expansion valves are variable
orifice devices in which the amount of orifice opening is
varied
according to some desired control function, such as maintaining
constant superheat of vapor leaving
e evaporator, or constant sub-
cooling leaving the condenser, as mentioned above. In suchapplications,
a remote sensing bulb is used to determine the temperature
to be controlled.
The reader should consult literature on particular
typesof expansion
devices
ation is
if more informationconcerning
their
oper-
desired.
An important part of manyexpansion devices is a refrigerant
distributor,
used to proportionflow evenly to sub circuits
heat exchangers.
in the
On expansion devices with distributors, part of
60
the total pressure drop occurs across the distributor nozzle and
tubes, which rely on a relatively large pressure drop to achieve
thorough mixing and even distribution of the two-phase flow.
Per-
formance data for various nozzles and tubes can be obtained from the
manufacturers
The present flow balance model is
constructed to simulate
the Carrier model 50 DQ 016 unitary heat pump system, which has
components as shown in Figure 2.1-1.
The unit is equipped with
thermal expansion valves for maintaining constant superheat, and
with distributor nozzles and tubes.
Data on the components of this
unit is given in Appendix B.
Examiniation of published performance data and correspondence
with expansion valve manufacturers
revealed that flow through an
expansion valve orifice can be approximated by a simple incompressible nozzle expression:
I- CTXV
rpP
!
Where:
mai
-
p
- density of liquid entering valve
bP
-
CTV .
mass flow rate through valve
pressure drop through
valve
a parameter accounting for flowcoefficient
and
variable orifice opening
The orifice opening, and, hence, the CTX
V
, of the expansion valves
61
in the 50 DQ 016 unit vary with saturation conditions in the evaporator, in order to maintain constant exit superheat.
to determine the variation of C
as atually
V
It was.possible
for the heating expansion valve
installed in the unit, by the use of charging chart data.
Charging charts, which are normally used for field servicing of
systems,
indicate normal suction and discharge pressures at the com-
pressor for a given
unit,
inlet air conditions.
as a function of evaporator and condenser
Knowledge of the suction and discharge pres-
sures permitted accurate guesses for refrigerant density entering
the valve, and, in conjunction with compressor performance data,
made possible the determination of mass flow rate through the valve.
The variation of CTXV with saturation temperature in the evaporator
could hence be determined.
Details, flow chart,
flow balance model are given
and program listing for the system
n Appendix D.
Reference
1.
Correspondence with Sporlan Valve Co., St. Louis, Mo., and Alco
Controls Division, Emerson Electric Co., St. Louis, Mo.
62
SECTION 2.3
COMPRESSOR SIMULATION
A great deal of-attention has been devoted to the topic of
compressor simulation in recent years
1,' 2,
3
3
Most previous models,
however, have either been too simple to be of quantitative design
use, or have been so complex as to be unwieldy and expensive to use.
Moreover, such complex models have generally relied upon experimentally determined parameters in order to produce acceptable results.
Also, for the most part, previous models have not been designed to
study overall performance of refrigeration compressors, where motor
cooling and other important effects must be considered, but, rather,
they concentrate on cylinder and valve processes only.
The compressor model presented in the present study has been
developed to simulate overall performance of hermetic or semi-hermetic refrigeration compressors, as well as non-hermetic, non-refrigeration compressors, with a high degree of accuracy, while requiring
a minimum of inputs.
Through the use of approximate representations
of valve dynamics, manifold pressure pulsations, and manifold heat
transfer, the present model can easily be used to study the effects
of design changes, such as capacity control modifications, internal
heat transfer, motor changes, and others, on overall performance.
The present model is not, however, suited to study factors related
specifically to valve dynamics.
If dynamic valve motion is the topic
of interest, more complex models must be used4 ' 5 ' 6
63
In addition to approximate representations of valve dynamics,
manifold pressure pulsations, and manifold heat transfer, the present compressor model also includes the effects of motor cooling,
frictional losses due to bearings, pistons, and rings, motor efficiencr and speed variation with load, the effect of oil circulation
on performance, and checks for excessive discharge temperature and
motor overload.
Finally, the present model is also equipped to
study a variety of compressor capacity control schemes, including
clearance volume control, late suction valve closing, and early
suction valve closing, as described in section 1.5.
In order to
allow the reader to use the present compressor model to simulate a
variety of compressors, recommended ranges are given for a number
of input parameters, depending on the characteristics of the compressor to be studied.
The present model uses real g,_ properties, generated from
basic equations, rather than ideal gas relations.
Appendix A con-
tains a discussion of computer programs for producing thermodynamic
properties of refrigerants
2, 22, and 502.
A difficulty with the
real gas approach is that, since thermodynamic property relations
are usually given as functions of temperature and pressure, finding
properties at a given state is usually an iterative process.
For
example, to find the remaining state properties of superheated vapor,
given pressure and entropy, it is necessary to iterate on temperature
64
until the correct entropy is found.
Discussion of the compressor model can be divided into three
major sections:
1.
Cylinder processes, valve, and manifold modeling
2.
Motor cooling, friction, and suction-discharge heat
transfer
3.
Oil circulation effect on capacity
Let us consider each section separately:
Cylinder Processes, Valve, and Manifold Modeling
All positive displacement compressors can be modeled by a
four step cylinder process, as shown in Figure 23-1:
1.
Intake and mixing with residual mass
2.
Compression
3.
Discharge
4.
Re-expansion of residual mass
The present model treats the compression and re-expansion processes
as non-isentropic, through the use of an isentropic efficiency term.
It is important to note that, since the above isentropic efficiency
is
concerned only with specific portions of the total compressor
processes, values usually greater than 90Z are to be expected.
comparison, the overall compressor isentropic efficiency is
By
typically
60i or less. Specific losses, such as motor cooling, and others to be
mentioned later, contribute the major portions of the overall low
efficiency.
65
Correctly modeled, the intake and discharge processes should
include the effects of.valve dynamics and manifold pressure pulsations.
The present model accounts for the above effects, but in an
approximate and, therefore, easily managable way:
Let us consider typical pressure and valve behavior for a reciprocating compressor, as shown in Figure 2.3-2.
A number of important
observations can be made:
1.
The actual discharge manifold pressure is
not constant,
but rather it "pulses" as a rate related to the number
of cylinders, RPM, and dimensions of the discharge manifold.
2.
The actual suction manifold pressure also varies, but
usually with much lower amplitude than the discharge
manifold pressure.
3.
The pressure in the discharge manifold increases above
the average value during the discharge portion of the
compressor stroke.
4.
There is a rise time associated with the opening of suction and discharge valves, which is related to the pressure
difference acting across the valve, and the valve inertia
(pressure actuated valves).
This
rise time causes the
cylinder pressure to increase well above discharge manifold pressure at the beginning of the discharge portion
66
of the stroke.
Similarly, cylinder pressure falls some-
what below suction manifold pressure on the intake portion of the stroke.
Many discharge valves are spring
biased so that they will close rapidly, which causes an
even greater cylinder pressure overshoot on discharge.
5.
As the flow through the valves lessens and the pressure
difference across the valves correspondingly drops, the
valves start to close.
The closing action of the valves
restricts the flow and causes the pressure difference to
increase again, which reopens the valve.
Such action
causes peaks in the cylinder pressure on discharge or
intake, and increases the average effective pressure difference across the valves.
6.
The net result of manifold pressure pulsations and valve
dynamics is to raise the cylinder pressure an average
amount above the average discharge manifold pressure on
discharge, and to lower the cylinder pressure an average
amount below the average suction manifold pressure on intake.
7.
Many suction and discharge valves exhibit a closing delay
shown in Figure 2.3-2 as
s
for the discharge valve.
Such closing delay is
for the suction valve, and
D
caused
by bouncing of the valve on its seat, by cylinder/manifold
67
pressure interactions, sticking of the valve on its
stop due to oil "stiction", inertia of the valve, or a
combination of the above.
The delay in closing of the
suction valve allows gas to be pumped back out of the
valve after bottom dead center (BDC), and hence reduces
the effective displacement volume.
The delay -in closing
of the discharge valve allows discharge manifold gas
to leak back into the cylinder after top dead center (TDC),
and hence increases the effective clearance volume.
The most correct way of modeling the intake and discharge processes
would be to include dynamic simulation of valve motion and manifold/
cylinder pressure interactions.
latter approach.
There are two drawbacks with the
First, most such dynamic simulations require some
form of experimentally determined information, such as flow coefficients.
Second, the computational time becomes prohibitive, and the method
unwieldy, when dynamic simulations are nested within the many
iteration loops necessary in an overall performance simulation.
The technique used in the present model for representing valve
dynamics and manifold/cylinder pressure interactions consists of two
parts.
First, the variations of cylinder and manifold pressure on
discharge and intake are modeled as a constant pressure overshoot or
undershoot, as shown in Figure 2.3-3.
The cylinder pressure on
discharge is assumed constant and is greater than the average discharge
68
manifold pressure by an amount
APD .
That is,
Pcyl
Similarly, the average cylinder pressure on intake is
constant and is less
an amount
AP S.
-
PD + APD
assumed
than the average suction manifold pressure by
That is
Pcyl
S
°
PS - APS
The second part of
the approximate valve dynamics model is that the closing delay of
the discharge valve is
modeled as an increase in the effective
clearance volume, and the closing
delay of the suction valve is
modeled as a decrease in the effective displacement volume.
effective values of
APD ,
APS , ED
and
ED
Actual
will vary not only
with compressor speed, size, valve design, and manifold design, but
also with pressure ratio, refrigerant, and flow rate, although the present model uses constant values for a given compressor.
A large
number of experimental compressor measurements, for a variety of
compressors
1, 2, 7 , have been studied to establish a range of values
that can be expected for
APD , AP S ,
are summarized in Table 2.3-1.
ED
and
8 S , and the results
When data on a particular compressor
of interest, or on one similar to the one of interest, is not
available, values near the upper limits given in Table 2.3-1 should
be used to obtain the most conservative results.
Detailed derivations,
flow charts, and program listings for all portions of the present
model are given in Appendix D.
i
69
Motor Cooling, Friction, and Suction-Discharge Heat Transfer
The net effect of motor cooling, internal friction, and
suction/discharge manifold heat transfer is to transfer heat to the
section gas, producing a decrease in refrigerant density entering
the cylinder, and reducing mass flow rate.
Determining the amount
of heat given to the suction gas is an iterative process.
A first
guess for the temperature of the suction gas entering the cylinder
is made and, using the cylinder process protion of the model, the
resulting refrigerant mass flow rate and motor power are calculated.
Next,
frictional losses in the compressor and resulting friction
waste heat are calculated.
The mechanical efficiency of reciprocating
compressors, accounting for frictior in
bearings, pistons, and rings,
can be expected to range between 90 - 98% for medium and large compressors, and could be somewhat less in small, fractional horsepower,
compressors
.
All of the simulations to daL
have used a 96% mechanical efficiency.
with the present model
Once power requirements of
the compressor are determined, including frictional
motor speed and motor efficiency
are determined.
losses, actual
Curves showing the
assumed variation of motor efficiency and motor speed
given in Figures 2.3-4 and 23-5.
with load are
The latter curves are fairly
representative of squirrel-cage induction motors in the 3 to 10 horse-
9
power range .
Smaller motors would have lower efficiency curves, and
larger motors would have slightly higher efficiency.
Most of the heat
70
generated by motor inefficiency and friction in hermetic and semihermetic compressors is given to the suction gas.
however, usually less than 20Z10, is
A small portion,
lost to the ambient by convection
and radiation from the compressor shell.
Next, an estimate of heat transfer between the suction and
The calculation is done in an
discharge manifolds is made.
approximate manner because there are a variety of manifold designs.
In some designs suction-discharge heat transfer is
negligible, while
in others it is deliberately large to aid in protection against liquid
slugging of the compressor (often used in small hermetic compressors).
Moreover, available data on heat transfer coefficients inside of
compressor passages is rare and is
11,' 12
not well correlated l
12. The
present model for suction/discharge manifold heat transfer is for
heat flow from hot to cold gas streams separated by a thin metal wall.
The wall is
modeled as a flat plate with negligible resistance to heat
flow, and some simple assumptions are made concerning relative flow
areas on suction and discharge sides of the manifold.
The purpose of
the model is not to simulate the flow paisages inside the compressor
exactly, since even when details of the flow passages are known, exact
simulation of the heat transfer would still be difficult at best.
Rather, the purpose of the heat transfer model is to allow the
investigator to simulate a desired temperature rise in the suction
gas at a given condition, and to study the variation of that temperature
rise with flow conditions.
Table 2.3-1 gives some approximate values
71
for rise in suction gas temperature due to suction/discharge manifold
heat transfer, learned from literature on the subject
13
.
When specific
information on compressors of the type of interest, or on similar types,
is not available, the following guidelines are recommended for low
saturated suction temperature conditions:
1.
Large - non-hermetic and semi-hermetic compressors moderate temperature rise, on the order of 20OF at low
suction pressures and high discharge pressures.
2.
Small - non-hermetic compressors - higher temperature
rise due to larger surface-to-volume ratios in the flow
passages - on the order of 30OF at low suction pressures
and high discharge pressures.
3.
Small - hermetic compressors - higher temperature rise
due to larger surface-to-volume ratios in the flow
passages, and possibly much highe; temperature rise if
internal heat transfer is promotedto protect against
liquid slugging - on the order of 0 to 500F, at low
suction pressures and high discharge pressures.
Finally, after having estimated all internal heat transfer effects
on the suction gas, including friction, motor cooling, and suction/
discharge heat transfer, a new estimate of the state of the suction
gas entering the cylinder can be made and the entire process repeated
until the actual state of gas entering the cylinder is
and procedures are outlined in Appendix E.
found.
Details
72
Oil Circulation Effect on Capacity
Cooperl4 has pointed out that circulation of lubricating oil
with the
refrigerant
as much as 20%.
can reduce available compressor capacity by
The reduction of capacity is
caused by some of the
refrigerant remaining in solution with the oil as it leaves the
evaporator.
Solubility of oil-refrigerant mixtures has been discussed
by Bambachn 5 and Spauschus
.
The present compressor model is equipped
to determine oil-refrigerant solubilities as a function of temperature
and pressure, for refrigerants 12 and 22, as discussed in Appendix F.
Details for determining effect on capacity are given in Appendix E.
Oil circulation rates for particular compressors have been obtained
from the manufacturers, and are typically between 0 and 15% of the
total oil-refrigerant mixture flow rate by weight.
Verification of the Model
Three different compressors have been studied-for the purpose
of verifying the present compressor model:
1.
Carrier 06D-824
This is a relatively large, semi-hermetic
refrigeration compressor of nominal 9 ton capacity.
2.
Carrier 06D-537
This is a large, semi-hermetic refrigeration
compressor of nominal 14 ton capacity.
The 537 is a larger
version of the 824 compressor above, having the same bore,
but a longer stroke.
73
3.
A relatively small, nominal 3 ton, fully hermetic
refrigeration compressor.
(Manufacturer wishes to remain
unidentified)
All ?~cessary data for the above compressors has been supplied by the
manufacturers.
Comparisons of actual and predicted performance for
the above compressors are given in Figures 23-6,
respectively.
Input data fr
23-7,
and 2.3-8
the simulations is given in Appendix G.
It can be seen that the simulations of the 06D-824 compressor
are highly accurate.
The worst error for predicting power consumption
is about 8%, occuring at the extreme limit of low suction temperature,
and improves rapidly to within 5% over most of the operating range.
Similarly, the worst error for predicting capacity is about 15% at the
extreme limit of low suction temperature, and improves rapidly to
within 6
over most of the operating range.
The accuracy of the 06D-537 simulations (the compressor in the
Carrier model 50 DQ 016 unitary heat pump discussed in section 2.1)
is not quite as good as the 06D-824 simulation.
predicting power consumption is
The worst error for
about 21%, occuring at the extreme
limit of high suction temperature and low condensing temperature, and
improves rapidly to within 7
with either increasing condensing
temperature or decreasing suction temperature.
The worst error for
predicting capacity is about 11% at the extreme limit of low suction
temperature, and improves rapidly to within 5% over most of the
remaining operating range.
74
It is worthwhile to study why there is a difference in accuracy
between the 06D-824 and 537 simulations.
Both models are of similar
design, differing primarily in the length of the stroke.
plate, valve, and manifold design is
The head
very similar, if not identical,
in both compressors, because they are of the same model series.
As
noted, the region of greatest inaccuracy for the 537 simulation is
at low condensing temperatures and high suction temperatures, indicating
a high refrigerant flow rate.
A possible explanation is
that the
manifold and valve design are adequate for the 824 compressor under
the above conditions, while they are not large enough for the 537
compressor, with its higher mass flow, causing some form of flow
restriction due to the higher flow rate of the 537 compressor which
the present model does not account for.
Moreover, as shown in the
parametric studies to be discussed shortly, compressor power requirements are highly sensitive to increased head pressure in the low head
pressure - high suction pressure region.
The accuracy of the 3-ton compressor simulations is also within
acceptable limits.
is
The worst error for predicting power consumption
about 16%, occuring at the extreme limit of high suction temperature
and low condensing temperature, and increases to within 8% at higher
condensing temperatures,
Accuracy for predicting capacity is
11 over the'entire operating range.
within
75
There are several important differences in modeling the smaller
3-ton compressor compared to the larger semi-hermetic units.
One
important difference is that the smaller unit runs at 3500 RPM
compared to 1750 RPM for the larger units.
speeds, te
When running at higher
amount of closing delay for suction and discharge valves
becomes more pronounced.
The larger surface-to-volume ratio of
smaller compressors also makes cylinder heat transfer more significant
than in larger compressors and causes smaller compressors to have
lower isentropic compression and expansion efficiency than larger
units.
Larger surface-to-volume ratio also increases suction/discharge
manifold heat transfer.
refrigerant is
The percentage of oil circulating with the
often greater in smaller compressors for a similar
reason.
Simulating Capacity Control
Capacity control via cle arance volume control is easily simulated
by changing the clearance volume as input to the model.
Capacity con-
trol via late suction valve closing is easily simulated by specifying
the closing delay parameter
OS
for the suction valve.
A slight
modification would be desirable, however, to account for throttling
of the gas as it is forced back through the suction valve.
In order to simulate capacity control via motor speed control,
the efficiency of the speed control device and its effect on motor
waste heat must be considered.
Furthermore, possible effects on
76
valve dynamics should be explored.
The speed control method has
not been included in the present model.
The present model has been specially equipped to model the
early suction valve closing (or "cut-off") method of capacity control.
One additional parameter, as described in Appendix E, is required to
indicate the amount of capacity reduction desired.
of the gas in the cylinder after cut-off is
The expansion
modeled in a way similar
to the re-expansion portion of the stroke.
A flow chart for the entire compressor model, including early
suction-valve cut-off control, is given in Appenix E, along with
derivations and a program listing for the entire compressor simulation.
Normal Range of Input Values and Their Effect on Performance
Table 2.3-1 indicates approximate normal ranges for the important
input variables.
There will always be particular compressors that
exceed the normal limits however, because of practical manufacturing
limitations or unique design approaches.
Results of parametric studies, showing
effects of changing
the parameters given in Table 2.3-1 on capacity, power, and overall
efficiency, over the entire operating range of the 06D-537 compressor,
are given in Appendix H.
2.3-2.
A summnary of the results is
given in Table
It is important to note that compressors which are designed
to have low values of
8S
and
0D
normally have high values of
I
77
APD
and
APD , and conversely, compressors with low values of
normally have higher values of
0S
and
ED.
APD
The effect of varying
oil circulation from 0 to 10% by weight has little or no effect on
flow and power of the compressor.
Rather, the effect is
to reduce
cooling capacity in the evaporator by reducing the amount of
refrigerant available for evaporation, since some of the refrigerant
remains disolved in the oil as it leaves the evaporator.
is
The effect
strongly a function of evaporator superheat, percent oil circulation,
and refrigerant.
The higher the superheat leaving the evaporator,
or the lower the oil circulation rate, the less the capacity reduction
will be.
References
1.
Proceedings of the 1972 Purdue Compressor Technology Conference
(Purdue Research Foundation, 1972).
2.
Proceedings of the 1974 Purdue Compressc
(Purdue Research Foundati )n, 1974).
3.
Gatecliff, G. W., "A Digital Simulation Of A Reciprocating Hermetic
Compressor Including Comparisons With Experiment", Ph.D. Thesis,
University of Michigan, 1969.
4.
MacLaren, J.F.T., "Review of Simple Mathematical Models of Valves
in Reciprocating Compressors", Proceedings of the 1972 Purdue
Compressor Technology Conference (Purdue Research Foundation, 1972)
Technology Conference
pg. 180-187.
5.
MacLaren, J.F.T., Kerr, S.V., and Tramschek, A.B.,
"A Model Of A
Single Stage Reciprocating Gas Compressor Accounting For Flow
Pulsations", Proceedings of the 1974 Purdue Compressor Technology
Conference (Purdue Research Foundation, 1974) pg. 144-150.
78
6.
Bredesen, AoMo, "Computer Simulation Of Valve Dynamics As An Aid
To Design", Proceedings of the 1974 Purdue Compressor Technology
Conference (Purdue Research Foundation, 1974) pg. 171-177.
7.
Davis, H., "Effects Of Reciprocating Compressor Valve Design On
Performance And Reliability", Io Mech. E. Conference "Industrial
Reciprocating And Rotary Compressor Design And Operational Problems",
Paper No. 2, London, 1972o
8.
Derived from internal combustion engine motoring tests - Taylor, C.
F., The Internal Combustion Engine in Theory and Practice, Volume
I (New York: John Wiley & Sons, Inc., 1960) Cpt. 9o
9.
Handbook of Air Conditioning System Design (New York: McGraw - Hill
Inc., 1965) pg. 8-21.
10. Discussions with Carrier Air Conditioning Co., Syracuse, New York.
11. Jensen, O., "Investigation Of The Thermodynamics Of A Reciprocating
Compressor", Proceedings of the 1972 Purdue Compressor Technology
Conference (Purdue Research Foundation, 1972) pg. 16.
12. Hughes, J.M., Qvale, E. B., and Pearson, J.T., "Experimental
Investigation Of Some Thermodynamic Aspects Of Refrigerating
Compressors", Proceedings of the 1972 Purdue Compressor Technology
Conference (Purdue Research Foundation, 1972) pgo 518.
13. Jensen, O., op. cit, pg. 9-17.
14. Cooper, K. W., and Mount, A.G., "Oil Circulation - Its Effect On
Compressor Capacity, Theory And Experiment", Proceedings of the
1972 Purdue Compressor Technology Conference (Purdue Research
Foundation, 1972) pg. 52-59.
15. Bambach, G., "Das Verhalten Von Mineralol - F12 - Gemischen in
Kaltmaschinen", C. F. Muller, Karlsruhe, 1955.
16. Spauschus, "Vapor Pressures, Volumes, & Miscibility Limits of
R22 Oil Solutions", ASHRAE Journal (Dec., 1964) pg. 65, also:
ASHRAE Transactions, Vol. 70, 1964.
79
TABLE 2.3-1
SUMMARY OF NORMAL RANGE OF VALUES FOR INPUT
PARAMETERS OF COMPRESSOR SIMULATION
1800 RPM OR BELOW
VARIABLE
LARGE
0 - 10
eD
o
- ?n
AEq
--
1 -
APS
nis
nmech
MEDIUM
SMALL
SMALL
0 - 10°
o
- ?0n
0 - 10°
n - no
5 - 20°
-v
10 - 30 psi
APD
3600 RPM
-v
-v
10 - 30 psi
5 psi
1 -
10 - 30 psi
5 psi
1 -
UNKNOWN
°
no
-
-
VERY SMALL
10 - 50 psi
5 psi
1-
5 psi
.94 - .98
.90 - .94
.85 - .90
.88 - .95
.94 - .98
.94 - .98
.92 - .96
°90 - .96
an - 1 n
0--
.-
An _
n
n _l n
I n
RAMORE SUBJECT TO DESIGN VARIATIONS
%oil
0 - 5%
0 - 10%
0- 10%
0 - 10%
0
Suct-Disc ATA < 20°F
ATS < 30°F
AT < 50°F
ATS < 50 F
S Heat Trans. TMc
.pr
-
*'J
0-
L.J
-
** --
J
Where:
SVR
=
Surface to Volume Ratio of Cylinder
LARGE = SVR < 2.8 i
in
MEDIUM = 2.8 < SVR
< 3.2-
SMALL = 3.2 < SVR < 4
1
L
in
VERY SMALL = 4 < SVR
eD
-
Discharge Valve Closing Delay (Degrees after TDC)
ES
=
Suction Valve Closing Delay (Degrees after BDC)
APD
=
Equivalent Cylinder Pressure Overshoot on Discharge
AP S
-
Equivalent Cylinder Pressure Undershoot on Intake
is=
i
Compression and Expansion Isentropic Efficiency
mech =
Compressor Mechanical Efficiency Due to Friction
%MC
Percent of Motor and Friction Heat Given to Suction Gas
%Oil
Weight Percent of Oil Circulating in System
AT S
=
Additional Suction Gas Superheat Due to Suction-Discharge Heat
Transfer at Low Suction Pressure-High Discharge Pressure (High
Pressure Ratio) Condition
80
TABLE 23-2
SUMMARY OF EFFECTS OF VARYING INPUT PARAMETERS ON
CARRIER MODEL 06D-537 COMPRESSOR PERFORMANCE
CHNECAG
CHANGE IN
CHANGE IN OVERALL
IN FLOW POWER
EFFICIENCY
CHANGE
VARY
PARAMETER FROM - TO
-4)
(-3
- 10° ATDC
-4%
-3X
O
Inversely related to
0 - 200 ABDC
-4%
-4%
0%
Inversely related to
80
s
APD
"mech
REMARKS
APs
10 - 30 psi
+3%
-3Z
More significant effect
at low pressure ratiossee Appendix H
-10%
-3%
-4%
More significant effect
at low suction pressuressee Appendix H
94 - 98%
+1%
-7%
+6%
94 - 98%
+2%
-4%
+4%
1-
AP S
nis
(0%)
-
5 psi
-3%
OTHER EFFECTS
%MC
80 - 100%
%Oil
Suct.-Disc.
Heat Trans.
0 - 10%
- Negligible
- Negligible effect on flow, power, or overall
efficiency, but large effect on evaporator
capacity (10% capacity reduction)
- 300°F additional superheat at low suction
pressure and high discharge pressure reduces
flow by 7% with negligible effect on power,
and hence reduces overall compressor
efficiency by 4%. At lower pressure ratios,
the additional superheat is much less, and
the effect of suction-discharge heat transfer
is negligible.
81
Suction and Discharge Manifolds
tl
I-D
----o1
_mA
A.
TDC
BDC
BDC
Intake &
Mixing
With
Compression
Discharge
Residual
FOUR STEP CYLINDER PROCESS
FIGURE 2,3-1
Re-expansion
82
_
.
.
Avg.
Disc.
Man.
PD
Press.
;charge
.ve
:ion
p
P
Avg.
Suct.
Man.
Press.
PS
00
TDC
180 °
360°
BDC
TDC
Crank Angle ----TYPICAL VALVE, CYLINDER PRESSURE, AND MANIFOLD PRESSURE
BEHAVIOR OF RECIPROCATING
COMPRESSORS
WITH PRESSURE
ACTUATED VALVES
FIGURE 2.3-2
.
.
.
.
Equivalent
Ap Cylinder
D Pressure
Overshoot
P
AP
PS
.
Equivalent
Cylinder
S Pressure
Undershoot
.
Vmin
V
max
Cylinder Volume
EQUIVALENT CYLINDER PRESSURE - VOLUME DIAGRAM
FIGURE 2.3-3
83
---
100
l
90
80
nmotor
Piece-wise linear
curve fit
70
60
.
,
n
.8 < PP < 1.0
.6 < PP < .8
.4 < PP < .6
S
50
30
n
=
=
=
.4 r =
.2 rl =
.1 n =
.2 < PP <
.1< PP <
0 < PP <
40
n
(-.25)PP + 1.07
(-.10)PP + .95
.89
(.375)PP + .74
(1.30)PP + .55
(6.85)PP
20
10
0
0
10
20
30
40
50
60
70
80
90
100
PP (% Motor Power)VARIATION OF MOTOR EFFICIENCY WITH LOAD
FIGURE 2.3-4
100
99
PSS'
98
/ of.
sync.
97
spee
96
95
94
0
10
20
30
40
50
60
PP'(% Motor Power)
70
80
-
VARIATION OF MOTOR SPEED WITH LOAD
FIGURE 2.3-5
90
100
84
FIGURE23-6
COMPARISON OF ACTUAL AND PRFnICTED PERFORMANCE OF
CARRIER MODEL 06D-824 COMPRESSOR
20
--Go--
Actual
Predicted
Cooling
Capacity
/1000'
10
of
\Btu/hr
!
Saturated Suction Temperature (F)
-
lb
16
12
Power
Input
10
(kw)
8
6
4
2
0
-10
0
10
20
30
40
Saturated Suction Temperature (F) -
50
60
85
FIGURE 2.3-7
COMPARISON OF ACTUAL AND PREDICTED PERFORMANCE OF
CARRIER MODEL 06D-537 COMPRESSOR
Actual
-)-
Pvod 4 ,A
I
Cooling
Capacity
/1000'\
of
\Btu/hr/
60
Saturated Suction Temperature (F)
_
I
Power
Input
(kw)
80
- ----0~
-
Saturated Suction Temperature (OF)-m.
86
FIGURE 2.3-8
COMPARISON OF ACTUAL AND PREDICTED PERFORMANCE OF
3 TON ERMETIC COMPRESSOR
Actual
-(E--
Predicted
aPA
DU
am
1.° 0 "_
v r
Cooling
Capacity
00hooos\
{
-I
20°F Superheat
50
_
40
,
30
m
20
I
P..
ofd
\Btu/hf
10
.,
0
I
-1( )
0
10
20
30
I
A
40
Saturated Suction Temperature (°F)
I
50
60
>
LI
j I
4
I
Power
Input
sate'
3
C
crr--=~O- - 0
(kw)
2
1
!
Jlr\
-UV
0
10
20
30
40
Saturated Suction Temperature (F)
&
50
_
--
.
i
60
87
SECTION 2.4
CONDENSER SIMULATION
Described here is a general model which determines heat
transfer performance of most cross-flow type condensers found in
heat pump or air conditioning devices.
The model determines
automatically, for any set of operating conditions, the fractions
of the heat exchanger devoted to desuperheating, condensing, and
subcooling of the condensing medium.
Also described is use of the general model, referred to as
'EXCH', to model a finned tube type condenser, with staggered round
tubes.
Details, flow charts and program listings for both general
model 'EXCH', and the finned tube condenser model are given in
Appendix
I.
Comparison of actual and predicted performance using the above
models is included for a particular condensing unit, installed in the
Carrier model 50 DQ 016 heatpump
unit.
Accuracy appears to be
within 5% over the entire heat pump operating range.
General Model - 'EXCH'
A normal condenser has three distinct heat transfer regions:
desuperheating (single phase vapor), condensing (two-phase), and
subcooling (single phase liquid).
condenser performance is
The most important factor governing
the location of the two-phase region in the
air flow, relative to the single phase regions.
If the flow of
88
refrigerant through the condenser is
as shown in Figure 2.4-1,A,
then
desuperheating, condensing, and subcooling regions all experience
the same entering air temperature and performance is
easily determined.
If refrigerant flow through the condenser is as shown in Figure 2.4-1,
C, performance of the condenser is almost the same as for case A.
In both cases C and A, the desuperheating region would be relatively
short, because the wall temperature rapidly falls below saturation
temperature in most instances.
Since the amount of single phase
heat transfer in case C is small compared to the two-phase heat
transfer, the fact that the single phase regions are located ahead
of the two-phase region, relative to the air flow, has little effect
on two-phase heat transfer.
However, if the two-phase region is
located ahead of either of the single phase regions, relative to the
air flow, as shown in Figure 2.4-2, the amount of heat transfer in
the single phase region
can be severly affected.
The present model may be used to predict performance of
condensers of the type shown in Figure 2.4-1 A, B, and C.
In each
case, the single phase regions are either ahead of the two-phase
region, or are completely separate from it, relative to the air flow.
It is possible to construct a single accurate model for the above
cases because of the small effect of the single phase regions on the
two-phase region heat transfer, and because heat transfer in the twophase region is unaffected by the type of flow arrangement, be it
89
cross-flow, counter-flow, or any other.
The insensitivity of the
two-phase heat transfer to flow configuration occurs because the
evaporating medium remains at approximately constant temperature,
regardless of the air temperature flowing over any portion of the
two-phase region.
The present model is only partially useful for
simulating condensers as shown in Figure 2.4-2, where the two-phase
region is ahead of either of the single phase regions, relative to
the air flow.
A sub-section analysis is usually required for the
latter cases, and hence a general model is more difficult to
construct.
Such cases are rarely encountered in normal air conditioning
applications because of their poorer performance compared to the
former flow configurations.
The present model represents all three cases shown in Figure
2.4-1 as single pass cases.
Thus, the multiple pass case, with
the last pass on the leading e.dge, as shown in C, is approximated
as the single pass case shown in A.
must of course be equivalent.
Heat transfer and flow areas
The latter approximation is valid
as long as the fractions of coil surface devoted to the single phase
regions are not much greater than about twice the fractions of the
surface devoted to the passes on the leading edge of the coil.
There
is no such limit of usefulness if the actual flow configuration to be
modeled is of the single-pass type.
For the single pass or single
pass approximation cases, it is a simple process to determine the
90
fraction of the total heat exchanger surface devoted to two-phase,
desuperheating, and subcooling regions of the coil, as indicated
in Figure 2.4-3.
Details are given in Appendix I.
The general model
'EXCH' uses the effectiveness-NTU method
of heat exchanger analysis.
Expressions or graphs of effectiveness
vs NTU are available in the literature 1 for various flow arragements.
The maximum difference between cross-flow, both fluids unmixed
effectiveness, and cross-flow, one fluid mixed effectiveness is
20Z.
It is
about
often acceptable, therefore, to model both cases using
the cross-flow, both fluids unmixed expression of effectiveness.
Normally, the latter case does not have a closed form expression,
however, an accurate, closed form approximation has been developed by
the author and is
presented in Appendix J.
The usefulness of this general condenser model depends on the
ability to properly determine the necessary heat transfer coefficients,
thermodynamic properties, and geometry factors.
Single phase vapor
and liquid heat transfer coefficients may be determined using
developed flow correlation
such as by McAdams:
Nu - .023 Re 8 Pr'4
Where:
Nu - Nusselt number
Re - Reynolds number
Pr - Prandtl number
a fully
I
91
The actual average heat transfer coefficient may be slightly higher
than that found using the above relation because of entrance effects.
It is preferable to use coefficients developed from actual heat
exchanger tests if available.
Kays
& London, Compact Heat Exchangers 3
is a useful reference for such information.
Suggested two-phase
condensation heat transfer relations are those developed by Traviss,
.
at MIT
The Traviss relations have been developed for forced
convection condensation inside tubes, in laminar, transition, and
turbulent flow regimes.
Air side heat transfer correlations vary with heat exchanger
design and must be determined for each design studied.
many useful correlations are available in Kays & London.
Once again,
Similarly
the geometry factors are a function of condenser design, and the
themodynamic properties depend on the medium being condensed.
The
reader will find useful insights for determining these inputs in the
following discussion, describing use of the general model 'EXCH
to
simulate a finned-tube type condenser.
Modeling of a Finned Tube Condenser
In order to use the general condenser model 'EXCH' to predict
the performance of a particular condenser, another model, which deter-mines the heat transfer coefficients and pressure drops under the
desired flow conditions, must be constructed.
A model of an air-cooled,
cross-flow, finned tube condenser with staggered round tubes, as shown
92
in Figure 2.4-4, has been developed as part of the present work,
which accepts information on heat exchanger geometry and flow conditions
and produces the necessary heat transfer coefficients and the like.
Physical dimensions necessary for the analysis include:
fin thickness,
fin pitch, horizontal and vertical tube spacings, tube inside and
outside diameter, and others.
Additional inputs include temperatures,
flow rates, and number of parallel flow sections in the coil.
Each
parallel flow sub-circuit is a complete heat exchanger in itself,
and it is therefore necessary to model only one sub-circuit in order to
determine total heat transfer behavior.
is
More detailed information
given in Appendix I.
Expressions for the heat transfer coefficients and for pressure
drop through the unit are presented in Appendices K and L respectively.
The air side heat transfer coefficient and pressure drop expressions
were modified from Kays & London, as were those for the single phase
vapor and liquid regions on the condensing side.
The condensation
two-phase heat transfer correlations used are from Traviss
forced convection condensation inside of tubes.
,
for
All pressure drop
and heat transfer coefficient relations have been developed for
laminar, transition, and turbulent flow regimes.
used is refrigerant 22.
is
The condensing medium
Information on refrigerants 12, 22 and 502
given in Appendix A.
Verification of Models
The Carrier model 50 DQ 016 heat pump has heat exchangers of the
93
finned, staggered tube type previously described.
Necessary dimensions,
condenser performance, and compressor performance data were obtained
from Carrier, as were charging chart data, (see Appendix B).
The
charging charts give evaporating and condensing pressures as a function
of evaporator and condenser inlet air conditions.
It was therefore
possible to determine the refrigerant flow rate and condenser inlet
conditions as a function of evaporator inlet air temperature and
relat-ivehumidity.
Using this information, the performance predictions
of the model were compared to published performance data during the
heat pump operating mode.
tion
Results are shown in Figure 2.4-5 as a func-
of evaporator inlet air temperature.
Accuracy is
within 5X over
the entire heat pump operating range.
References
1.
Kays, W. M. and London, A. L., Compact Heat Exchangers (Palo Alto,
California: The National Press, 955) pg. 27, 33.
2.
Rohsenow, W. MH. and Choi, H. Y., Heat, Mass, and Momentum Transfer
Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1961) pg. 192.
3.
Kays & London, 2p. cit
4.
Traviss, D. P., Baron, A. G., and Rohsenow, W. M., "Forced
Convection Condensation Inside Tubes", Report No. 72591-74;
Heat Transfer Laboratory, Massachusetts Institute of Technology,
Cambridge, Mass. (ASHRAE Contract No. RP 63).
94
Air
Air
low
Refg.
flow
unmixed
F
Refg.
flow
mixed
Case
Case A
Single pass - Refrigerant flow
unmixed
B
Single pass - Refrigerant flow
mixed
Air
Flow
Refg.
flow
FLOW ARRANGEMENTS FOR WHICH
GENERAL HEAT EXCHANGER MODELS
'EXCH' AND 'EVAP' ARE VALID
mixed
FIGURE 2.4-1
Case
C
Multi-pass - with initial and final
passes on leading edge
of coil,
mixed
95
`
Air
Air
Flow
Flow
Refg.
flow
mixed
Case
Case A
Multi-pass - with final pass on
trailing edge of coil,
refrigerant flow mixed
Multi-nass - with final pass on
trailing edge of
coil, refrigerant
flow unmixed
FLOW ARRANGEMENTSFOR WHICH GENERAL HEAT EXCHANGER
MODELS 'EXCH' AND 'EVAP' ARE NOT VALID
FIGURE 2.4-2
Air
Flow
1-1111*
DETERMINING SINGLE PHASE AND TWO-PHASE
FRACTIONS OF HEAT EXCHANGERS
FIGURE 2.4-3
""'"
`Y
Desuperheating
Region
96
Air
/ v -I
Flow
SubCircuit
FIGURE 2.4-4
FINNED TUBE HEAT EXCHANC
1
240
200
~AI~~IAI
-
UlLkP4.L
_UL
-
Btu/hr
A-f-.-II
IL.LU
CI.L J
-3
I·
LLU;.&L
1 C~U
/
Condenser Performance During Heat
Pump OEperation (indoor coil)
Unit: (Carrier Model 50 DQ 016
Indoor Air: 70*F
Outdooir Air: 85% rel. hum.
1000's
of
UJ .
--4
--
Actual
Predicted
160
120
80
0
I
10
20
·
30
Outdoor Air Temperature
FIGURE 2.4-5
r
40
(F
r
50
db)---
--
60
97
SECTION 2.5
EVAPORATOR SIMULATION
General and Specific Models
Many evaporators and condensers used in air conditioning or
heat pump applications are of the cross-flow type.
The present
evaporator model is similar to the condenser model of section 2.4
except for the ability to determine moisture removal from the air
flowing over the coil.
As in the condenser model, the evaporator
model' consists of a general model 'EVAP', and a specific model for
a given type of coil.
The general model 'EVAP' uses two different methods of heat
exchanger analysis.
For the case when no moisture removal occurs,
the effectiveness-NTU method is
applicable, as in the condenser.
In
the event of moisture removal (which is determined automatically
by the model), a modified version of the effective surface temperature
approach discussed by McElgin and WiieyI is used.
It is
assumed that
all moisture removal, if it occurs, takes place only in the two-phase
region.
As in the condenser model, it is a simple process to determine
the fraction of total heat exchanger surface devoted to two-phase and
single phase heat transfer.
Details of the general model 'EVAP', and
of the finned tube evaporator model of the Carrier 50 DQ 016 heat
pump simulations are given in Appendix M.
The evaporation two-phase
heat transfer correlation used comes from Tong, Boiling Heat Transfer
And Two-Phase Flow .
Expressions for all heat transfer coefficients
98
and pressure drops are given in Appendices K and L respectively.
Verification of Models
Both the evaporator and condenser coils of the Carrier model
50 DQ 016 unitary heat pump are of the type shown in Figure 2.4-4
Comparison of predicted and published performance of the evaporator
(outdoor coil) of the 50 DQ 016 unit during the heating mode is
given in Figure 2.5-1.
Accuracy is within 5% over the entire heat
pump operating range.
References
1.
McElgin, J. and Wiley, D. C., "Calculation of Coil Surface Areas
for Air Cooling and Dehumidification", Heating, Piping, & Air
Conditioning (March, 1940) pg. 195-201.
2.
Tong, L. S., Boiling Heat Transfer And Two-Phase Flow (New York:
John Wiley & Sons, Inc., 1965) Cpt.5.
99
.00
-1
Comparison of Actual and Predicted
Evaporator Performance During Heat
Pump Operation (outdoor coil)
Unit: Carrier Model 50 DQ 016
TA
--- £1..L
A.7nJ
I V
.
J.LLUUL
160
1000' s
Outdoorr Air: 85% rel. hum.
of
Btu/hr
--
120
8
Actual
- - Predicted
!
80
40
I
0
10
20
II
·
30
'
40
50
Outdoor AiL Temperature (°F db)--
FIGURE25-1
I
-
60
100
CHAPTER 3.
PERFORMANCE AND ECONOMICS
OF
CONVENTIONAL AND CAPACITY
CONTROLLED HEAT PUMPS
The early suction-valve cut-off method of compressor capacity
control has been used to study the performance of capacity controlled
heat pumps.
Heat output and COP curves are presented for a particular
unit, the Carrier model 50 DQ 016 unitary heat pump with capacity
control.
Various control options, influenced by the significant
effect of fan power, are discussed.
The performance results are then
generalized to other heat pump sizes, and economic comparisons are
made for various heat pumpsizes on a given building heat load curve.
Both
conventional and capacity controlled heat pumps
are compared to
conventional gas and electrical resistance heat, with and without
air conditioning.
The comparisons are done for various gas and
electricity prices, and forsix different locations in the country.
101
SECTION 3.1
MODE OF ANALYSIS
The computer models of Chapter 2 are readily used to simulate
capacity controlled heat pump performance.
The method of compressor
capacity or flow control examined is the early suction-valve cut-off
method, as described in sections 1.5 and 2.3.
Flow control is achieved
by closing the suction valve, or a secondary valve just upstream of
the suction valve, prematurely on the intake stroke, limiting the
amount of gas taken in.
Gas in the cylinder at the time of early
suction-valve closing is then expanded and recompressed, resulting
in low losses.
The amount of capacity reduction is controlled by
varying the time after top dead center at which the suction valve is
closed.
Development tests of a mechanism to achieve such control
are presented in Chapter 4.
The performance of capacity controlled heat pumps was determined
exactly as outlined in Chapter 2 for conventional units, except
that the capacity reduction parameter 'CUTOFF' was specified as
an additional independent variable, and the thermal expansion valve
setting
CTXV' was also specified as an independent variable.
It was found that, for any given heat pump, there is an optimum
combination of capacity reduction and thermal expansion valve settings
for maximizing COP,
The optimum combination of settings varies not
only as a function of ambient temperature, but also as a function
102
Furthermore, there are three different
of air flow rates and fan powers.
ways of evaluating COP, as described in section 3.2,each of which
is optimized differently.
No simple scheme for determining the
optimum combinations of settings could be found, making the
optimization process time consuming and expensive.
For the latter
reasons, a simplified approach was used to determine performance,
which produces results that are always less than the optimum possible.
The method used to determine the performance results presented in
section 3.3 was as follows:
First, a thermal expansion valve setting,
CTXV, was specified, which corresponded to some ambient temperature
condition on the non-capacity controlled unit.
Each such setting
has been referred to as a "balance point" setting, because capacity
reduction occurs only at ambient temperatures higher than the balance
point temperature.
Next, the condensing pressure existing in the non-
capacity controlled unit at the given expansion valve or ambient
temperature setting was determined.
held
fixed
by using
was then
This condensing pressure
increasing amounts of compressor capacity reduction
as ambient temperature increased.
Each reduced capacity or "balance
point" performance curve in section 3.3, then, corresponds
t
a part-
icular CTXV setting and a particular condensing temperature.
Prior to determining the simplified performance curves as
described above, an investigation of factors limiting the allowable
amountof capacity reduction was undertaken.
Allowable amounts of
r
103
air flow reduction were also studied.
For given air flow rates and
a given thermal expansion valve setting, it was found that the
maximum permissible amount of capacity reduction is limited by the
ability of the condenser to achieve full condensation.
The latter
occurs because the reduced refrigerant flow allows the condensing
pressure and temperature to drop, reducing the temperature difference
available for heat transfer between the air and the refrigerant.
This
problem can be eliminated by reducing the thermal expansion valve
Allowable amounts
opeining under such extremes of capacity reduction,
of air flow reduction are different for conventional and capacity
Reducing air flows on non-capacity controlled
controlled units.
units causes larger
AT's
across the heat exchangers at high ambient
temperatures, and reduces COP.
Large amounts of air flow reduction
are allowable on capacity controlled systems, however, because the
refrigerant flow rate can be controlled to
significant overall increases in COP.
:eep AT's
low, allowing
Reduction of air flow to as
much as one half of the conventional air flow rates for a given unit
is
usually acceptable for a given heat pump with capacity control.
Greater reductions are not advisable because of excessive reduction
of air side heat transfer coefficient.
flow reduction is
More discussion of air
given in the following section.
104
SECTION 3.2
EFFECT OF FAN POWER ON CONTROL OPTIONS
The purpose of applying compressor capacity control to a heat
pump/air conditioning system is to allow sizing of the unit for a
lower than normal balance point temperature on heating, while still
maintaining adequate air conditioning performance, and to increase
COP above the balance point temperature by preventing the increase of
AT's
across the heat exchangers.
There are, however, three different
ways of evaluating COP, each of which is
optimized by a different
control strategy:
1.
&HP
-
COP
(no fan power included)
C
2. COPOF -' +
3.COPoF
3.
-(gc +
6
Oar+ PIF
COPc
BF - (~c +
(outdoor fan power included)
O
P IF ++ P OF
(both indoor and outdoor fan power
included)
Where:
QHP
Heat output of condenser (btu/hr)
1W
-
input power to compressor motor (btu/hr)
PIF
'
indoor fan power (which is the same as the heat gain
C
from the indoor fan motor, assuming the motor is
inside the heated space) (btu/hr)
P
OF
'
outdoor fan power (btu/hr)
I
105
In cases where both indoor and outdoor fans cycle on and off when the
compressor cycles on or off,
COPBF
is
the meaningful COP
to maximize.
In applications where the indoor fan runs continuously, such as for
COPoF
ventilation requirements,
is the correct COP
to maximize.
In special applications, where both evaporator and condenser fans
must run continuously, as in some heat reclaiming systems,
is
the correct COP to maximize.
COPNF
The fact that each of the above
applications requries that a different COP be maximized can be shown
mathematically as follows:
Consider a heating season quantized into discrete time durations
at different temperature levels,
ti
Ti.
We wish to minimize
Qload
total energy consumed in satisfying the heat load,
over the
entire heating season, for a given heat pump, having given fan
power requirements.
Case 1
For the case of both fans cycling off when the heat pump cycles
off, the total energy consumed over the entire heating season is:
Etot
-
~ [power]
ti
+
[power]
tj
cyclic
below
above
fans
balance
point
balance
point
Where:
Z [power] ti
i
[
+POF +PI
+PER
ti
below
below
balance
balance
point
point
106
and is the same for all of the above cases
[ (w
ZI[ower] tj
+
+ PIF)(
PO
above
balance
above
balance
point
point
PER Powerto run auxiliary electrical
(Z t)
t)l tj
percent
time oh
Then, using the definition of
load+
(Zt )
resistance heaters
COPBF , and noting that in this case
p)
I
We find:
(load
Etot
cycli
fans
-E [
i
+
COP
below
) tj
Eq. 3.2-1
BFj
j
balance
point
Case 2
For the case of continuous indoor fan, the total energy consumed
over the heating season is:
Eto t
cont.
+
below
balance
indoor
point
{[(c + PoF) ( t) + PIFltj}
above
balance
point
fan
'Then, using
the definition of
COP
a
OF
load - IF
(z t)
,
and noting that in this case
107
We find:
=r[ ]I
Et o t
] tj
- -
COPF
J~~F
below
cont.
indoor
- PIF )
(Qload
above
balance
balance
point
fan
tj
+ PIF
J
above
balance
point
point
Eq. 3.2-2
Case
3
-For the case of both evaporator and condenser fans running continuously, the total energy consumed over the heating season is:
E
tot
cont.
fans
I
-z[
+
{[(Ij)(z tJ) + PIF + PF] t
below
balance
above
balance
point
point
Then, using the definition cof COPNF , and noting that in this case
(Xt ) -
Qloadt
-
IF
i
:1
J
We find:
(4 load
Eto t
cont.
fans'
-=E
]
below
balance
point
t
+?
j
PF)
I
l
Nc :2
-]tj
+ (PIF+POF)
above
tj
above
balance
point
balance
point
Eq. 3.2-3
In each of the above cases, it is apparent that reducing fan power
while keeping air flow fixed will reduce total energy consumption.
108
Once minimum fan powers are established for a particular unit in a
given installation, total energy consumption is minimized by
maximizing the respective COP's
at each temperature level.
Reducing fan power while keeping air flow fixed will reduce
total
energy consumption in all of the above cases.
The effect of
fan power on performance of capacity controlled heat pumps, however,
is
much more pronounced than on conventional heat pumps.
Fan power
in conventional installations is between 10 and 30% of the total
power consumption at high ambient temperatures, and increases to
between 20 and 40% at low ambient temperatures, excluding auxiliary
heat.
By comparison, a capacity controlled heat pump, retaining
conventionally sized fans and ducts, would have fan powers as much
as 50 to 60X of the total power consumption at high ambient
temperatures, if large amounts of capacity reduction were used.
There are essentially three ways of reducing fan power
requirements
1.
Use more efficient fans
2.
Decrease flow resistance by increasing duct size
3.
Reduce air flow
Many fans used for indoor air circulation are of the centrifugal type,
to reduce noise.
Efficiency could be improved by using different.
blading designs, such as airfoil blades, as opposed to curved or
inclined blades.
Alternatively, simply using larger fans running
I
109
As
at slower speeds can achieve significant fan power reductions
energy prices increase, it is steadily becoming economically feasible
For
to install larger ducting, in order to reduce indoor fan powero
exarmple, pressure drop through the ducting system is proportional
to the square of the air velocity, assuming constant air density.
That is,
AP a V
.
The flow rate of the air, however, is equal to
the product of the air velocity and the cross-sectional area of the
duct,
CFM = VA
xs
Thus, for a given air flow rate, the pressure
.
loss through the ducting system varies as the square of the duct
cross-sectional area,
A 2
A11
AP
AP22
To reduce pressure drop by a factor of one half, while keeping air
flow rate constant, we need only increase duct flow area by a factor
A2
1/2
of
- (2)
= 1.41. Furthermore, if -e assume round, or
rectangular ducting, and maintain similar aspect ratios,
and perimeter
a Y , where
Y
is
A
Ks
a y2
the diameter or length of one
Therefore, to reduce pressure drop by 50%, we
side of the duct.
need only (1.41)1/2
=
1.19 , a 19% increase in duct material.
The
amount of fan power reduction varies with the type of fan and the
operating conditions, but would typically be between 10 and 50% for
a 50% decrease in.pressure drop.
duct sizing is
The true economic value of larger
dependent on the absolute magnitudes of increased
110
material and installation costs, compared to absolute magnitudes of
energy cost savings over the expected lifetime of the installation.
Reducing fan power by reducing air flow requires careful
examination.
causes larger
Reducing air flow on non-capacity controlled units
AT's
across the heat exchangers, and causes a
reduction in heat output.
At ambient temperatures above the
balance point, large amounti of air flow reduction on a non-capacity
controlled unit are unacceptable because the compression work is
forced to increase substantially, causing a reduction in overall
COPBF
even though fan power is reduced.
Fairly large air flow
reductions can be made at temperatures below the balance point of
a conventional unit and still result in an increase in COPBF ,
because the increases in
AT's
across the heat exchangers are
substantially lower at lower ambient temperatures.
However, any
reduction of air flow at temperatures below the balance point would
almost certainly result in greater total energy consumption, because
the loss
in capacity would be greater than the reduction of fan
power, and more auxiliary heat would be required. negating the
inerease in COPBF.
Reducing air flows on capacity controlled heat pumps
acceptable and highly recommended.
a given
point
both
It must be remembered that, for
building, a capacity controlled
temperature, and is
is
heat
pump has a lower balance
hence larger than a conventional non-capacity
I
ll
controlled unit for the same application.
If the capacity controlled
heat pump used the higher air flows associated with a normal unit of
comparable size, ducting much larger than that for the smaller noncapacity controlled heat pump would be required.
Contrary to the non-
capacity controlled case, large air flow reductions are acceptable
in capacity controlled units because the
AT's across the heat
exchangers are not allowed to rise, being controlled by the amount
of refrigerant flow reduction.
In the present study, it was found
that air flow reductions of up to one half of the normal air flows for
a given heat pump could be tolerated.
Employing smaller fans allows
us to use essentially the same size ducting as would be used with the
smaller conventional heat pump in a given installation.
A penalty
is paid in reduced low ambient temperature capacity, but since the
balance point temperature is lower, the effect of reduced performance
is minimal.
Performance curves of heat puml; having various air flow
rates and fan powers are presented in the following section.
4
.
112
SECTION 3,3
PERFORMANCE OF A CAPACITY
CONTROLLED HEAT PUMP
Capacity and performance predictions for the Carrier model
50 DQ 016 unitary heat pump with capacity control features are shown
in Figures 3.3-1 through 3.3-6. In all cases, the thermal expansion
valve setting is indicated by the balance point temperature to which
it corresponds on the non-capacity controlled unit.
Both the thermal
expansion valve setting and the condensing temperature are held
constant at the balance point value for each reduced capacity curve.
That is, each capacity controlled or "balance point" curve corresponds
to a particular condensing temperature and a particular thermal
expansion valve setting.
For convenience, the above performance pre-
dictions are also given in tabular form in Appendix N .
Reduced air
flow cases have been determined by assuming new sets of thermal
expansion valve (CTXV)
settings for the non-capacity controlled units.
In such cases, new non-capacity controlled CTXV
settings were found
which would still produce constant superheat, and which would in
addition produce approximately the same subcooling as in the full air
flow case.
Comparing Figures 3.3-1,2 and 3, we see that for the non-capacity
controlled or conventional unit, reduced air flow rates have a greater
effect on reducing heating capacity at high ambient temperatures than
they do at low ambient temperatures.
Such behavior is
a result of the
113
higher refrigerant flow rates and
T's
across the heat exchangers
that occur at higher ambient temperatures, as discussed in section 1.3.
Comparing Figures 3.3-1 and 3.3-2, we see that the capacity controlled
10°Bi
case has almost the same heat output for either the full
conventional air flows of Figure 3.3-1, or the reduced air flows of
Little difference in heat output is observed because
Figure 3.3-2.
the increase in
AT's
across the heat exchangers at low ambient
temperatures, with reduced air flows, is much smaller than at higher
ambients, and the use of capacity control keeps the
AT's low.
Figures 3.3-4 through 3.3-6 show the effect of fan power on the
various COP's of both conventional and capacity controlled units.
Outdoor fan powers have been determined from published performance
data, corresponding to smaller fans and motors.
powers could also be achieved by ke
Lower outdoor fan
ing the larger fans and running
them at lower speeds to reduce air flow, but detailed performance
data was not available on the outdoor fans.
data was available on the indoor fans.
Detailec performance
Indoor fan powers are
determined from performance data on the conventional 50 DQ 016 fans,
running at different speeds, while maintaining air pressure drops
of approximately .5 in wg (inches of water gauge), .7 in wg, and .6
in wg. for 6330 CPM, 4500 CFH , and 3165 CFM air flows respectively.
Fan motor efficiency is
included in the indicated fan powers.
The
pressure drops used for the various air flow rates reflect using
114
smaller duct sizes for the reduced air flow cases, as discussed in
section 3.5.
Comparing the non-capacity controlled or conventional COPBF
curves of Figures 3.3-4, 3.3-5, and 3.3-6, we see that the loss of
heating capacity at higher ambient temperatures and increased compression work more than offset the reduction in fan power from reduced
air flows, and hence
COPBF
for the full air flow case.
is lower for reduced air flow cases than
At low ambient temperatures, however,
compression work is not increased substantially for reduced air flow
cases, and capacity does not fall as markedly, such that
COPBF
is
larger for reduced air flow cases than for the full air flow case.
Unfortunately, the loss of capacity at low ambient temperatures is
greater than the reduction of fan power from reduced air flows, and
since the difference must be made up with electrical resistance heat
at temperatures below the balance point, the increase in COPBF
is
negated by increased electrical resistance heat requirements.
Viewing the capacity controlled cases of Figures 3.3-4, 3.3-5
and 3.3-6, it is apparent, as discussed in section 32,
that fan
power has a much more pronounced effect on capacity controlled units
than on conventional units.
Consider Figure 3.3-4:
The COPN
curves
for the capacity controlled cases with full air flow show marked
improvements over the non-capacity controlled case.
However, the
power requirements of the compressor have been reduced to such an
115
extent that the fan powers required for full conventional air flow
become a very large portion of the total power consumption
seen in the
COPoF
and
COPBF
As
curves, the reduction of heating
capacity drops much faster than the total power requirement because
of the high percentage of fan power, which results in low
COP's
when fan power is included.
Comparing
COPBF
curves of Figures 3.3-4 through 3.3-6, we see
that low balance point capacity controlled heat pumps become justified
only at low fan powers.
As discussed in section 3.2, however, a low
air flow, low fan power capacity controlled heat pump is probably
the most desirable configuration because it allows use of smaller
duct sizes than high air flow cases.
of increasing
It appears, from the viewpoint
COPBF , that reducing the
than the 200 balance point
CTXV
setting to values less
(BP) value is at best only marginally useful.
Remembering, however, that there is an additional gain to be had from
reducing auxiliary heating with a lower balance point, we reserve final
judgement until total energy consumption and cost figures are computed
in later sections.
As indicated earlier, air flow rates and fan powers cannot
be specified arbitrarily, but rather are related to duct sizing, fan
sizing, heat load, and heating capacity of a particular unit.
Different
climate conditions in different parts of the country affect the size
of ducting, air flows, and unit capacity.
The overall performance of
116
various sizes of conventional and capacity controlled heat pumps on
a particular building heat load curve, accounting for the complex
interactions mentioned above, are examined in remaining sections of
this chapter.
117
FIGURE 3,3-1
240
Heat Output of Carrier Model 50 DO 016
Heat Pump With Capacity Control Full Conventional Air Flows
Indoor Air:
6330 CFM, 70°F
Outdoor Air: 10000 CFM, rel.hum. 857Z
200
Conv.
53BP
160
1000's
of
Btu/hr
120
80.
-10°BP
40
0
-10
0
10
20
30
40
Outdoor Air Temperature (F
200
160
50
60
70
db)-
Tfrillnr 7 7 )
rlgU ~C O, -,'
Heat Output of Carrier Liodel5n
016
Heat Pump With Capacity Control Reduced Air Flows
Indoor Air: 4500 CFM, 70°F
Outdoor Air: 7500 CFM, rel.hum. 85%
Conv.
1000's
of
30°3P
120
Btu/hr
200RP
80
10BP
40
o
-10
I
0
I
*I
10
20
30
Outdoor Air Temperature (F
I
...
40
50
db)
60
70
118
't.n f%
4U
.
Heat Output of Carrier Model 50 DQ 016
Heat Pump With Capacity Control 200 . Reduced Air Flows
Conv.
Indoor
t
1000's
of
Btu/hr
160
w
Outdoc
120
80
23=BP
14°BP
-
40
o-1
-10
-
0
.
10
20
I
30
I
1
40
50
Outdoor Air Temperature (F
FIGURE 3,3-3
db)
·
-
60
70
119
FIGURE 3,3-4
CAPACITY CONTROLLED COP PREDICTIONS
CARRIER MODEL 50 DO 016 FAT PUMP - FULL CONVENTIONAL AIR FLOWS
6330 CFM,
Indoor air:
Outdoor air: 10000 CFM,
700 F,
rel.hum. 85%,
tu/hr
tu/hr
indoor fan nower 9425
outdoor fan power 5300
_ 10BP
37 BP
53°RP
4
Conv.
3
COPNF
2
No fan power included
1
0
-10
_
I
0
10
I
I
20
30
I
I
40
Outdoor Air Temperature (F
50
I
60
70
db)
37°P
1NnO
53oRP
L
4*·I
2
3
~Conv.
I
COPoF
2
Outdoor fan power included
1
0
I
-10
0
a
I
10
20
30
I
I
i
40
50
60
Outdoor Air Temperature (F
db) ---
L_
1
'
70
.
,/ -nP
-
Conv.
. I10°BP
=.. ,
3
COPBF
Both indoor and outdoor
fan power included
1
0
I
-10
0
I
10
I
20
t
30
.
.
40
Outdoor Air Temperature (F
50
db)
,
60
70
120
FIGURE 3.3-5
CAACIT' CONTROLLFTn CP PRE)ICTITONS
O 6 EAT PUMP - REDUCED AIR FLO.!S
CARRIER MODEL 50 Dnn
Indoor air:
Outdoor air:
4500 CFM,
7500 CFM,
indoor fan power 6910 Rtu/hr
outdoor fan power 2650 tu/hr
70°F,
rel.hum. 857,
-
-
1n1RP
ORP
20=
Conv.
COPNF
43
2
'
fan power included
No
1
0
-10
I
I
0
10
LI
I
--
A
-
I
,
I
60
50
40
30
20
Outdoor Air Temperature (°F db)
70
-.
'.
4
20°RP
I inOp
Conv.
I
3
COPo
IPO
2
Outdoor fan power included
1
0
,a
a
I
.0
10
0
20
30
IBF
60
50
40
Outdoor Air Temperature (F
COPB
aa
a
I
70
db)
4
30 & 20°RP
3
Conv.
lO°RP
2
2
Both indoor and outdoor
fan power included
1
0
-10
a
0
_,
aI
*
10
20
,
30
Outdoor Air Temperature
I
I
50
60
I
40
(F
db)
-
g
70
121
FIGURE 33-6
CAPACITY CONTROLLED COP PREDICTIONS
CARRIER MODEL 50 DO 016 HFAT PUMP - REDUCED AIR FLOT.IS
Indoor air:
Outdoor air:
3165 CFM,
5200 CFM,
70°F,
rel.hum. 85%,
indoor fan Dower 3535
outdoor fan power 1818
56
14°P
23PConv.
/-
A
tu/hr
tu/hr
I
TP
Conv.
COPNF
2
No fan power included
1 _
0 I
-1 0
I
0
I
I
10
20
30
40
Outdoor Air Temperature (F
50
db)
60
!
70
-
14°BP
23°RP
I.
4
3
Conv.
COPOF
2
Outdoor fan power included
1
0
-3 0
I
IL
0
Ia
10
I
20
I
30
J
40
Outdoor Air Temperature (F
I
1
50
60
a
70
db)--4
4
140BP
23°BP
3
Convy.
COPBF
2
Both indoor and outdoor
fan power included
1
0
-10
I
0
I
&
!
10
20
30
40
Outdoor Air Temnperature (F
50
db)
I
6n
70
122
SECTION 3.4
EXTENDING PERFORMANCE RESULTS TO DIFFERENT HEAT PUMP
SIZES ON A PRESCRIBED HEAT LOAD
Performance predictions for the Carrier model 50 DQ 016 heat
pump with capacity control have been presented in section 33°
To
properly determine the economic merits of capacity control, however,
we must compare performance of different size units on the same
The Carrier 50 DQ model series unitary heat
building heat load.
pumps provide a convenient range of sizes for comparison
1
It is possible to define a heat load line on which the Carrier
50 DQ model series heat pumps have balance points of convenient
interest.
Figure 3.4-1 shows the prescribed load line, referred to as
load line "D", in comparison with heating capacity curves of various
50 -DQ series heat pumps.
The heating capacities shown for both
the conventional and capacity controlled heat pumps on Figure 34-1
are only approximate, since actual heat output varies with the amount
Actual values, corrected for various amounts
of air flow reduction.
of air flow reduction, are given in tables in Appendix
.
The
Carrier 50 DQ model series did not have a heat pump with a capacity
curve corresponding to a 21 ° blance point on load line D, so all
values indicated for that case have been interpolated.
Approximate
COPNF
curves for the conventional 50 DQ series
heat pumps are given in Figure 3.4-2.
We shall make a number of
123
conservative assumptions regarding relative positions of the
COPNF
curves with and without capacity control and air flow changes:
1.
We assume that the
COPNF
values of the conventional 006
can be made to equal the conventional 016 values by improved
system design at no cost,.
2.
We assume that
COPNF curves for the 008 and fictional
heat pumps are equal to those of the 016 at the same
fractions of conventional air flow and similar balance
point CTXV settings.
For example, the
COPNF
curve for the
008 with 29° balance point CTXV setting and air flows 1/2
of conventional 008 air flows, is assumed the same as the
curve for the 016 with a 29° balance point CTXV
COPNF
setting and air flows 1/2 of conventional 016 air flows.
3.
We assume that
COPNF
values for the conventional 004 can
be improved by a factor of 50% of the difference between
conventional 016 and 004 values, by improved system design
at no cost.
We are working with
COPNF
values at this point because the
magnitude of fan powers will vary depending on the duct sizes in a
particular region of the country.
COPBF
values can be calculated
·at different locations using the expression:
COPNF +
COPBF
BF
+
I
PIF
c
P
c
124
Where fan powers are eauated
for particular, fan/motor
combinations
in a given duct size with a given air flow rate, and compressor power
is calculated from assumed heating capacity and
COPNF values.
The
above assumptions give conservative predictions for the attractiveness
of capacity controlled heat pumps. As shownin section 3.5, even
though the COPNFvalues of the 008 and fictional heat pumpsare
deliberately underestimated, they often appear more attractive
than
the 016 or 006 units in climates where the 006 would be the conventional
unit installed.
In warmer climates,
where the 004 would be the conven-
tional unit, the larger capacity controlled units have difficulty in
recovering their increased capital investment, even though the 004 is
less efficient.
Assumedvalues of COPNFand heat output for the
various units and air flow rates are given in tables in Appendix 0
Reference
1.
"Single
Package Heat Pumps - 50 DQ", Form 50 DQ-4P, (Carrier
Corporation), 1971).
125
FIGURE 3.4-1
HEATING
CAPACITY
OF CONVENTIONAL
AND CAPACITY CONTROLLD
COMPARED TO ASSUMED HEAT LOAD LINE
wFAT PMPS
Carrier 50 DQ
model series
heat pumrs
70°F Indoor air
85% rel.hum. outdoor air
----
Conventional
-
Capacity controled
t.
1000's
of
Btu
hr
Outdoor Air Temperature (F
db)
_-
126
008
016
4.0
9
I
3.0
COPNF
2.0
1.0
0
-10
0
10
20
30
40
50
Outdoor Air Temperature (F)
-
60
70
COPNF CURVES FOR CONVENTIONAL CARRIER 50 DQ MODEL SERIES HEAT PUMPS
FIGURE 3.4-2
.
.
127
SECTION 3.5
SEASONAL PERFORMANCE AND ECONOMIC COMPARISONS
Conventional and capacity controlled heat pumps are compared
here to conventional gas and electrical resistance heat, with and
without air conditioning, on load line "D" presented in the previous
section.
The comparisons are done for various gas and electricity
prices, and for six different locations in the country:
1.
San Francisco, California
2.
Charleston, South Carolina
3. New York, New York
4.
Boston, Massachusetts
5.
Omaha, Nebraska
6.
Minneapolis, Minnesota
Weather data for each of these locations wav obtained from the U.S.
Department of Commerce, Weather Bureaul.
f show the time duration at 5F
Figures 35-la
through
temperature levels throughout the
heating season of each location, averaged over a 10 year period.
information is also given in tabular form in Appendix
P
.
This
All
performance comparisons are made assuming that the heating season can
be quantized into the 50F temperature bands discussed above, and that
all locations have constant 85% relative humidity.
Conventional gas furnances are sized to meet the maximum heat
128
load at the coldest expected temperature for a given location.
Furthermore, in a forced hot air furnace, the type we shall be
concerned with here, the air flow rate is determined by the desired
maximum temperature rise of the air through the furnace.
A typical
high efficiency gas furnace is designed to have about an 800F air
temperature rise at maximum output, and would have a seasonal average
efficiency of about 75% at best2 .
Gas burner prices vary depending
on the manufacturer, but reasonable estimates for typical high
efficiency models can be made.
Figure 35-2
shows typical purchase
price as a function of heating capacity for high efficiency gas
furnaces3 .
The cost of fans for the forced hot air furnaces can be
estimated from wholesale price data, as discussed later.
Cost and
efficiency of oil fired furnaces is comparable to gas furnaces, and
the cost of oil is often comparable to that of gas on a dollar per
BTU basis, hence, yearly operating costs of gas and oil furnaces are
similar.
The question of fan power as related to duct sizing was discussed
in section 3.2.
As electricity prices rise, it is becoming economically
feasible to install larger ducting, regardless of the type of heating
system, be it gas, oil or heat pump.
For this reason, we shall assume
that the conventional gas furnaces of the present study are equipped
with ducts which reduce the usual air pressure drop of around .5 in wg
down to a more economical level of .26 in wg.
As discussed in
129
section 3.2, such larger ducts would require only an 18% increase in
duct material.
heat pumps,
All comparisons in the present study assume that the
regardless of size, use the same ducts as the gas furnace
at each location.
We shall assume that the air flow rates of non-capacity controlled
units remain unchanged.
However, for capacity controlled units with
balance point temperatures lower than the conventional heat pump at
a given location, we assume the following:
1.
Outdoor air flow rates are 1/2 of the full air flow rates
of a non-capacity controlled unit of comparable size.
2.
Indoor air flow rates are either 1/2 of the full air flow
rates of a non-capacity controlled unit of comparable size,
or are equal to the conventional gas furnace air flow rate
at a given location, whicbhver is greater.
Air pressure drop for air flcr rates other than that of the conventional
gas furnace can be computed from the following expression:
APHp
gas
CFM
2
gas
Fan power requirements for both the gas furnace fans and the heat
pump fans have been determined from published performance data on the
fans of the Carrier 50 DQ series heat pumps.
All indoor fans (condenser
fans) are of the centrifugal. type, with scroll, and all outdoor fans
are propeller-direct drive type.
Fans from smaller units, or the
130
conventional fans running at slower spee4 have been use4 for the
reduced ar
pump
flow of the capacity controlled heat pumps.
installations
All heat
are assumed to have 100% backup electrical resis-
tance heaters, and all use
electric resistance auxiliary heat.
table
maximum heat
3.5-1 summarizes
the
load, air flow rates,,air
pressure drops, and fan powers for both gas furnace and heat pumps
of various balanced points, for all six locations.
give the condenser heat output,
all
QHP
COPNF
,
Tables in Appendix0
and COPBF
values for
heat pumps, corrected for different percentages of full air flow
rates, at each location in the country.
It should be noted that all
heat pumps are assumed turned off and 100% electrical resistance heat
used at temperatures below -10 F, because of excessive compressor
discharge gas temperature.
.Total energy consumption over the heating season.at each
location
was calculated with the heating season quantized into-50F
temperature bands, and the heat pump performance assumed at the mean
temperature of the band.
Total seasonal energy consumption-of gas,
electrical resistance, and heat pump heating is summarized in Table
3.5-2
for each location, including seasonal performance factors
delivered
SPFSPFTotal
Ttl heat
e energy
gy
umd
for the various heat pumps.
Total seasonal energy consumption of heat
pumps was calculated using equation 3.2-1.
Total seasonal energy
consumption of gas furnaces includes a portion of electrical energy
131
due to furnace fans, and was calculated in a manner similar to that
for the heat pumps, using a seasonal average efficiency of 75% as
compared to 65% for most existing gas or oil furnaces .
Straight
electrical resistance heating is assumed to be forced hot air type also,
with the same fans as the gas furnace.
Finally comes the question of total yearly cost for the various
heating systems.
First, we shall assume that maintenance costs for
all systems can be neglected.
This is a good approximation providing
there are no major failures, such as compressor failure, since the
cost of normal maintenance is much smaller than the total yearly cost
of energy
.
Second, we assume that installation costs are equal for
all types of systems.
Actually, heat pump installation costs are
currently higher than for gas furnaces, but wider use of heat pumps
should reduce the cost differential, as greater numbers of properly
trained service personnel, ad
available.
improved installation practices become
Installation costs for forced hot air electrical resistance
heat would be somewhat less than for gas or heat pump heating, but as
will be seen shortly, the error in assuming equal installation cost is
far
outweighed by the high operating cost of pure electrical
resistance heat.
We have assumed that all of the various heat pump
sizes, and the pure electrical resistance heat have the same indoor
ducting size as the gas furnace does at each different location.
The
installation cost of the ducting, therefore, need not be included in
132
Total yetaly
the analysis.
major
costs;
cost
cpartisots
hence
includ
oiilyti
yearly energy cost, and amortization of capital.
Total
yearly energy costs for the various heating systems are easily computed
for various prices of electricity and natural gas using the data of
Table 3.5-2.
The yearly cost
Capital
of capital can be computed from the expression:
Initial capital cost
1 + i (n + 1)]
n
cost per
year
2
Where:
i
- interest rate, percent per year
n
- number of years over which the cost is amortized (expected
life)
Current interest rates on home mortgages are around 9
per year.
We
shall assume, therefore, an effective interest rate of 10% per year
for the heating systems of interest in the present study.
A reasonable
life expectancy of a gas furnace or of electrical resistance heaters
is about 20 years.
We shall use, therefore, a 20 year amortization
period for such heating systems.
The.current life expectancy of an
air conditioning or heat pump system is on the order of 10 years.
With improved heat pumps, having greater reliability, now becoming
available, and with improved training of installation and servicing
personnel, life expectancy could be increased to around 20 years.
We
133
shall use a 10 year amortization period for both heat pumps and air
conditioners in most of our comparisons.
A 20 year amortization
period case has been included for the Boston area for comparison,
altho-gh most manufacturers agree that a 20 year lifetime is unrealistic
with prtsent equipment.
The heat pumps we have been concerned with in
our study up to this point are designed to provide both heating and
air conditioning.
pumps
It is fitting, therefore, to compare the heat
to gas and electrical resistance heating systems with air
conditioners added.
Most of the economic comparisons given here are
between heat pumps and gas or electrical resistance heat plus air
conditioning.
Comparisons of the above heat pumps to gas and
electrical resistance heating without air conditioning have been
included for the Minneapolis and Omaha areas although in reality,
if the air conditioning feature were not needed, a more efficient
heat pump having lower cost could be created, as will undoubtedly be
the case in the future.
Initial capital costs for gas furnaces, electrical resistance
beaters, and the various heat pump sizes, along with necessary air
conditioner costs are computed in Tables 3.5-3 through 3.5-5.
The
following factors are considered in the cost of capacity controlled
heat pumps:
1.
A capacity controlled heat pump uses most of the components
of the original heat pump design on which it is based.
134
However, a saller
compressor motor is
as shown in Figure 35-3,
required, because,
with compressor flow modulation,
lower compressor power requirements exist.
Credit is
given for smaller compressor motors at the rate of
$18/hp savings to the consumer .
2.
Smaller fans and/or fan motors are required compared to
the original heat pumps, because of reduced air flow rates.
Cost
credits are given for the difference in fan and fan
motor costs,
as determined from 1975 wholesale price data7
on comparable equipment.
3.
The cost
of the early suction-valve cut-off control
mechanism, described in detail in Chapter 4, is
assumed to
be $5/cylinder plus $30 additional controls.
4.
An average cost of the auxiliary electrical resistance
heaters for use in the heat pumps is
assumed to be $3/1000
Btu/hr, as derived from average price data from different
size heaters
The cost
of the pure electrical resistance heating system consists of
the same fans as used in the gas furnace plus
assumed to be $3/(1000 Btu/hr).
cost of the heaters,
The effect of inflation on initial
capital costs can be neglected in the present study for
reasons:
the following
The current rate of inflation is an average of about 10
year.
The rate of increase in furnace prices, however, is somewhat
less.
Furthermore, even if the price of the gas furnaces or the
per
135
electrical resistance heat doubled, when amortized over a 20 year period,
the increase in yearly cost is
minor.
By comparison, the rate of
increase in heat pump prices is very small,
decrease.
and prices could actually
Due to the costly failures of heat pumps in the 1950's,
manufacturers are reluctant to produce heat pumps at a high rate until
a better equipped, larger, and more well trained installation and
repair network is established.
Higher production rates, and increased
competition could actually lower prices, once the spectre of costly
and inadequate maintenance is
laid to rest.
Total yearly cost plots, comparing gas furnaces and pure electrical
resistance heat with air conditioning to various capacity controlled
heat pumps, and to the conventional heat pump for a given location,
are shown as a function of gas and electricity prices for all six
locations of the country in Figures 3.5-4a through f.
a
They include
0l per year interest rate, 20 year amortization of furnace and
electrical resistance heaters, and 10 year amortization of heat pump
and air conditioner costs.
Figure
3.5-5 shows the effect of a 20
year amortization rate for the heat pumps and air conditioners, in the
Boston area.
Figures 35-6a
and b show cost comparisons for the Omaha
and Minneapolis areas without air conditioning.
The first observation is that pure electrical resistance heating
is extremely expensive compared to all of the other forms of heating
considered, under all conditions studied.
For example, in the New York
area, at the current electricity price of about 5¢/kw-hr, electrical
136
resistance heat costs almost twice as much as the closest heat pump,
some $1500/year more for the assumed load!
It is
very difficult to
keep accurate information on gas and electricity prices in this era
of rapidly increasing prices, but in all locations, electricity is
probably less than 5¢/kw-hr currently, and gas, when available, is
proabably around $3/million btu.
A reasonable estimate for relatively
near term ( 5 years or less) delivered price of natural gas is
$5/million
Btu because of inflation, shortages, and impending federal deregulation
of the inter-state price of natural gas.
The future prices of gas
and electricity are difficult, if not impossible
to accurately predict.
Most estimates by experts, however, fall within the limits of $10/
million Btu for gas,
year time span.
and 10¢/kw-hr for electricity in the next 10-15
Within the above limits, we can conclude the following:
San Francisco
Studying the San Francisco plots in Figure 3.5-4a, we see that
for such a mild
climate, the larger capacity controlled heat pumps,
having lower balance point temperatures, will never be economically
competetive with the conventional (460
that area.
However, we also
balance point) heat pump for
see that the conventional 460 BP heat
pump is very close to being ecoinmaicallycompetitive
with gas heat
Charleston
In the Charleston area, as
seen in Figure 3.-4b
large (210 BP)
heat pumps are once again not economically feasible because of the
137
mild climate.
Intermediate size heat pumps (32 and 370 BP) become
economically competitive with the conventional (460 BP) unit at
electricity prices greater than about 85¢/kw-hr.
To be better
than gas heat, however, the delivered price of gas would have to be
greater than about $9/million Btu.
The conventional (460 BP) heat
pump is much closer to being economically competitive with gas.
New York
Figure 3.5-4c shows that in the New York area, the 320 BP capacity
controlled heat pump becomes more economic than the conventional 370 BP
heat pump at electricity prices greater than around 5.8¢/kw-hr.
The
21°BP capacity controlled heat pump becomes better than the 32 BP unit
at prices greater than about 8.6¢/kw-hr.
All of the heat pumps are in
the realm of being possibly competitive with gas heating, but at
current prices, gas is the most economical heating method.
Boston
Figure 3.5-4d shows that in the Boston area, the 320 BP capacity
controlled heat pump becomes better than the conventional 37 BP unit
at electricity prices greater than about 4.6¢/kw-hr.
Since current
electricity prices in Boston are near this level already, the 320 BP
capacity controlled heat pump is already economically feasible in
comparison to the conventional unit,
The 210 BP capacity controlled
heat pump becomes better than the 320 BP unit at electricity prices
greater than about 6.2¢/kw-hr, and hence will soon be the more
138
heat ,pump.ohe :I40 BP heat pump cannot operate'quite
desirable
as
-efli'tciently as the 2i°BP unit in the Boston area because of limited
low temperature -peration and :because .of the higher air f-lowand-f an
power :requirements
under the assumed conditions
21BP heat.pumps are
The
T 37, 32,, and
1 -wll within the -realm-ofbeing economically
competitive-wih gas heating, but at current prices, gas is still
,the bast ,aiternattve, ifit
Omaha and
is available.
ifnneapolis
As ..seen nn Fgures 3,'594e and f, forcolder
climates, the larger
capacity controlled heat pumps, having loer :balance ,points, are
already the most economic-heat pumps.-even at today's electricity
prioes..
In addition, all are in the realm of possible competition
with gas heating, but once again, at current gas and electricity
pToes.,
gatss t.he -most -eonomiica aIternative
when available.
ComparingFigure 3.5-5 with Figure '3.5-4d for the Boston area,
we see that., with a .20 year amortization period, the capacity controlled
,heat pumpsbecomebetter than the conventional heat pumpeven at
today's electricity
competitive
year.life
prices., and therefore,
with gas heating.
the heat pumpsbecomemore
As -mentioned earlier, however, a 20
expectancy s probably unmreldaitdcfor current components.
Comparing Figures 3.5-6a and b to Figures '3,5-4e and f for Omahaand
Minneapolis,
,conditioners)
we see
to
gas
that comparing heat pumps (which are also air
heating without air conditioning makes the
139
the heat pumps appreciably less competitive with gas heating, but
still not out of the realm of viability, should gas prices rise.
As mentioned earlier, if the air conditioning feature is not
desired, different types of heat pumps, more efficient and less costly,
could be designed.
Such heat pumps, for example, water sink, and/or
storage systems, are currently under development by the industry9 .
It can be concluded that capaicty controlled heat pumps hold the
potential for being economically competitive with gas or oil heating
in colder climates if gas or oil prices rise faster than electricity
prices.
Furthermore, the colder the climate, the more desirable a
low balance point capacity controlled heat pump becomes, compared
to conventional heat pumps.
A comparison of heat pumps to gas or
oil heating is not the entire picture, however, in the question of
space heating.
In many parts of the country today, new building
starts simply cannot get natural gas or oil
or heating.
In such
cases, the choice of heating often becomes that between electrical
resistance or heat pump systems, and the capacity controlled heat
pump would appear to be the best choice.
References
1.
U.S. Dept. of Commerce Weather Bureau, Climatography of the U.S.Series No. 82, Decennial Census of U.S. Climate, Summary of Hourly
Observations.
2.
Discussions with heating. contractors, and the National Bureau
of Standards.
140
3.
Discussions with various heating contractors, for Carrier®
burners, and others.
4.
Bonne, U., Johnson, A.E., Glatzel, J., and Torborg, R., "Analysis
of New England Oil Burner Data. Effect of Reducing Excess Firing
Rate on Seasonal Efficiency", Final Report, Contract NB8-514736,
(for Center for Building Technology, National Bureau of Standards,
August, 1975).
5.
"Utility Details its Heat-Pump Service Data", Electrical World
(March 15, 1975) pg. 148-149.
6.
From discussions with heat pump manufacturers.
7.
Grainger's Wholesale Net Price Motorbook No. 341 Spring 1975,
(Boston: W. W. Grainger, Inc., 1975)
8.
Derived from Carrier ® Dealer Price Lists, 1975,
9.
Many examples in the literature, for example: Comly, J.B., Jaster,
H., Quaile, J.P., "Heat Pumps-Limitations and Potential", Report
No. 75 CRD 185, General Electric Company Corporate Research and
Development, Schenectady, New York.
141
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143
TABLE 3.5-3
GAS AND ELECTRICAL RESISTANCE FURNACE AND AIR CONDITIONER COSTS
LOCATION
SAN kRANCISCO
CHARLESTON
NEW YORK
BOSTON
OMAHA
MINNEAPOLIS
GAS
$
350
400
500
520
600
650
ELEC.
(FANS INCL.)
AoC.
RES.
'$
$
227
311
424
452
481
1020
1020
1950
1950
1950
1950
565
TABLE 3.5-4
CONVENTIONAL HEAT PUMP COSTS AND AIR FLOWS(CARRIER)
COST
$
UNIT
50
50
50
50
50
DQ
DQ
DQ
DQ
DQ
CONVENTIONAL AIR FLOWS
INDOOR
OUTDOOR
(CFM)
004
006
008
1200
2418
FICT
3304
5600
016
6616
1200
2100
3220
4500
6330
(CFM)
1750
3700
5200
7500
10,000
CARRIER
50 DA 004
CARRIER
50 DA 006
144
TABLE
.5,5
CAPACITY CONTROLLED HEAT PUMP COSTS
-Outdoor -Compressor
-Indoor
Cost - Cost Conv.+(Ncyl) ( 500+$30
Controls Fan & Motor Fan & Motor Motor
Credit
Credit
Credit
LOCATION
SAN FRANCISCO
&
CHARLESTON
SIZE
COST BREAKDOWN
TOTAL COST
460BP
390 BP
320 BP
21 BP
1200
2418 + 4(5) + 30- 23 - 15 - 13
3304 + 4(5) + 30 - 15 - 17 - 27
5600 + 6(5) + 30 - 80 - 50 - 49
1200
2417
3295
5481
370 BP
320°BP
210 BP
140 BP
2418
3304 + 4(5) + 30- 15 - 17 - 27
5600 + 6(5) + 30 - 80 - 50 - 49
6616 + 6(5) + 30- 45 - 75 - 78
2418
3295
5481
6478
145
FIGURE 3.5-1
WEATHER DATA
YEARLY AVERAGE TIME SPENT IN 5F
TEMPERATURF BANDS
2400,
2200 1600
(a) SAN FRANCISCO
1400
1200
hours 100'
year
800
600
400
200
0
1
0 -20
·
-10
·
0
I
10
1-
20
30
.-
i
40
i1
Ambient TemperaL-re (F
.
A^
14UU
--
50
60
7,
l-
70
.
A-
90
-
100
db)
_
r
1200
1000
E
80
K
(b)
_
CHARLESTON
.
hours
year
800
-
600
-
r
_-
400
200
0
-30
-20
_. waft
-10 0
-
10
.
20
30
40
_
50
Ambient Temperature (F
_
60
db) --
m
70
i
-
80
h
90 100
146
.
I
^^
1000
K
800
hours
year 600
400
200
O
-30 -20 -10
0
10
30
20
50
40
Ambient Temperature
60
80
70
90
100
(°F db)
^^
lU00 r
.
I
1000
(d) BOSTON
=
hours
year
600
400
200
0
m
A
-30 -20 -10
-~
0
-j-F
10
I
20
I
l_
30
!
40
II
50
I
-I
60
Ambient Temperature (F db) -----
·
l-
70
!
I
_
.
80
_
_
__
-___
90
100
147
.
And
lzUk)
r'
1030
hours
year
(e) OMAHA
800
600
400
K
I
l
200
0
I
-
-30
.
-
-
-20 -10
-
-
0
-
-
10
-
-
20
=
-
J
l
L
=
!
ml
30
40
50 60
Ambient Temperature (F db)
-
70
.
I
l-
i
-
-I--,
-
80
90
100
80
90
100
AA,
1
1
(f) MINNEAPOLIS
hours
year
-30
-20 -10
0
10
20
30
40
50
Ambient Temperature (F
60
db)-
70
148
FIGURE 3.5-2
rAC F1TTQGA'F
IDTTDFlIDPDDP'C
1
$
0
40
80
120
160
200
240
Furnace eat Output (1000's of Btu/hr)--
FIGURE 3.5-3
EXAMPLE OF COMPRESSOR POJE R REDUCTION
CARRIER MODEL 50 D 016 HEAT PUMP WITH CAPACITY
CONTROL
20
LV.
16
12
'BP
8
'BP
1
KW
'RP
4
0
0
10
20
30
40
50
Outdoor Air Temperature (F) -
60
70
149
FIGURE 3,5-4
COMPARISON OF TOTAL YEARLY FEATING COSTS,
INCLUDING AMORTIZATION OF CAPITAL,FOR
HEAT PPS
vs FORCED AIR ELECTRICAT RESISTANCE A)
-GAS FURNACES WITH AIR
Amortization'
CONDITIONERS
10X/yr int.
IN VARIOUS
LOCATIONS
Gas furnace - 20 yr, Air cond. Elec. res.
~fAA
AWUL
2000
Total
Cost
of
1500
ras
Price
1000
6
106Rtu
Heating
or
500
10ft 3
O
u
z
4
6
8
Electricity Price (/kw-hr) (a)
In
SAN FRANCISCO
eat
2500
Elec. res
pumps
2000
21 BP
Total
Cost
of
1500
37"BP
32 BP
Heating
as
Price
1000
Gas furnace
10 Btu
500
2
4
4
t'
Electricity Price (/kw-hr)v
(b)
CHARLESTON
vr
- 20 yr, Heat pumps - 10 vr
10 3 ft3
u
.JL
o
150
tps
4000
-I Otftps
Elec. res.
37 ORP
:0- 32°'
21aFP
TO 13000
Total
-
jfm
Cost
Gas
6 Price
of
Heating 2 0 0 0
4
/
Gas furnace
2
1000
k
1n6 tu
or
103ft3
I
0
I ,
0
,
2
I,
I
4
,
A
6
a
in
8
Electricity Price (/kw-hr)(c)
NEW YORK
Peat
ennn
N I[
11 I
-I pumps
m
Elec.
es.
ri
37 BP
14'BP
321
IP
Total 4000
Cost
of
Heating
I
30 00
m
Gas
I
-
(Gr 2000
I
w
.
is furnace
'%r^
106Atu
6
,0 13ft3
v
I
0
-4
or
;_
CI
Price
3
12
--
Iill!J
6
I
.
2
I
I
4
Electricity
Price
(d)
i
6
(f/kw-hr)
BOSTON
8
10
=
151
6nn In
A
Peat
Total
Dumps
Cost
of
37
Heatir.R
R
32 p
21 °RBP
14 OBp
20
Gas
Price
10C
10tu
or
-"
(e)
0 ft 3
t/kw-hr)
10
OpAHA-
RBnn
I
neat
PUmIs
Total
Cost
37 °Bp
of
3
Reating 4
2
20Bp
1 ORp
14
204
op
Cas
Price
06tu
or
0fp
-'-cN
/kw-hr)
MNAP%0LIq
10
152
FIGURE 3.5-5
COMPARISON OF TOTAL YEARLY VFATING COSTS,
INCLUDING AMORTIZATION OF CAPITAL, FOR
HEAT PUMPS vs FORCED AIR ELECTRICAL RESISTANCE AND
GAS FURNACES WITHI AIR CONDITIONERS
IN THE BOSTON AREA
furnace - 20 yr,
Amortization:
10/yr int. Gas
Elec. res. - 20 vr,
eAf
Juvw
Air cond. - 20 vr
Reat pumps - 20 yr
[-
-1
Elec. res..
I
Total
eat
pumps
37.yrP
32·RP
21°RP
4000
Cost
of
3000
Heating
//~J
,I
I
Gas
6
Price
2000
4
1000
"
I
Gas furnace
2
2
a:
0
2
I
4
a
6
Electricity Price (kw-hr) BOSTON
I
8
0
1(cI
106Btu
or
-fhi
10 ft
v
153
FIGURE 3.5-6
COMPARISON OF TOTAL YEARLY
EATING COSTS,
INCLUDING AMORTIZATION OF CAPITAL,
FOR
HEAT PUMPS vs
FORCED AIR ELECTRICAL RESISTANCE AND
GAS FURNACES WITHOUT AIR
COJTDITIONERS
Gas furnace - 20 yr,
Elec. res.
Air cond.
- 20 yr,
- none
eat pumps- 10 yr
Heat
.. ,.n
VVuU
5000
Cost
4000
37Bp
:7
Elec. res.- _
t
pumVs
-
320RP
-
21°BP
140RP
Total
of
Heating
-_
(IM
I3000
,Z
2000
i
1000
a, 8
Price
_
J
w
>i6
-
-
Gas furnace
0
!
2
0-9Z_-r
- 'a -'
4
6
Electricity Price (/kw-hr)---(a)
4i
8
$6
4
106Btu
or
2
-1
-
*6
0
t
103ft3
10
OMAHA
geat
Q^na
ouu
-r^
pumup
37 BP
32*BP
t
210°P
600
14 0BP
Total
Cost
Ga S
,-I
Pri,ce
..A
of
400
Heatin 0 0
f ) 200
6
Lt6
2
$
(
Electricity Price (kw-hr)
(b)
MINNEAPOLIS
=
103ft3
154
CHAPTER 4
DESIGN AND TEST OF AN EARLY SUCTION-VALVE CUT-OFF MECHANISM
FOR COMPRESSOR CAPACITY CONTROL
A detailed description of the early suction-valve cut-off
method of compressor capacity control, and a mechanism for achieving
such control, are presented in this chapter.
The mojor components
of the device have been constructed and were tested under simulated
compressor conditions
155
SECTION 4.1
COMPRESSOR CAPACITY CONTROL VIA EARLY SUCTION-VALVE CLOSING
Closing the suction valve of a compressor prematurely on the
inta-
stroke is an efficient means of capacity control.
Such an
approach is efficient because, instead of throttling the gas into
and back out of the cylinder, as with some conventional capacity
reducing devices such as valve unloaders or late suction valve
closing devices,
cylinder.
a reduced amount of gas is taken into the
The gas in the cylinder after the suction valve (or a
secondary valve just upstream of the normal suction valve) is closed
is then expanded until the piston reaches bottom dead center (BDC), and
then recompressed.
The expansion and recompression process is shown
compared to a normal compressor in the P-V diagram of Figure 4.1-1.
The amount of capacity or flow redurcion is controlled by controlling
the time after top dead center (TDC) at which the suction valve is
closed.
If power to run the early suction-valve closing (cut-off)
device is available, then complete capacity variation from 0 to 100%
is possible.
The present work is concerned with a cut-off mechanism which has
few moving parts, and which may be installed on most existing compressor
designs, including hermetically sealed compressors, with very little
modification.
A simple schematic of the device is illustrated in
Figure 41-2.
The mechanism has essentially three moving parts:
156
1.
Timer-spool valve
2.
Power piston
3.
Slide valve.
The slide valve is a secondary valve which is installed as close as
possible upstream of the normal suction valve.
It is
the slide
valve which is closed during the intake stroke to limit the amount
of gas taken into the cylinder.
Motion of the slide valve is
essentially "bang-bang" motion, to avoid throttling losses through
the valve during closing, and is caused by motion of the power piston.
Power to move the power piston is supplied directly from the pressure
differential between suction and discharge sides of the compressor.
Timing control of the power piston/slider combination is provided
by the timer-spool valve.
The timer-spool valve operates like a
normal spool valve in that its function is
power piston.
However, timing control of the power piston is governed
by the travel time of the spool.
valve is
to reverse the flow to the
The travel time of the time-spool
a function of its mass and the pressure differential acting
across the two ends of the spool.
Tests have shown that frictional
forces may be neglected, being significantly less than the inertia
forces required to move the spool.
valve is
A unique feature of the timer-spool
the fact that it is powered and timed directly by cylinder
pressure, and the device needs no connection to the crankshaft.
The
travel time of the timer-spool valve, and hence the closing point of
157
the slider valve, may be controlled merely by setting an appropriate
control pressure,
condition.
Pc , which is constant for any particular operating
The control pressure
P
can be supplied through a simple
pressure regulator from discharge pressure, and can be actively
controlled in a manner similar to thermal expansion valves to maintain
a desired operating condition, such as constant condensing pressure.
Operation of the above cut-off mechanism
through one complete cycle
is described in Figure 4.1-3.
Reference
1.
Proceedings of the 1972 and 1974 Purdue Compressor Technology
Conference (Purdue Research Foundation, 1972 and 1974).
158
P
P
P
p
P
8
-V
min
V'
dvc
P-V
V
'svo
V
V-
Vvc
dvo
V
NVU
_
max
&
V
Vdvc
DIAGRAMS FOR CONVFNTIONAL AND CAPACITY
CONTROlLED
COMPRSSntS
FIGURE 4.1-1
Suction pressure
Control
P
c
pressul
Timer-spool
Discharge pressure
SCHEMATIC OF THE EARLY SUCTION-VALVE
FIGURE 4.1-2
CUT-OFF
MECHANISM
159
FIGURE 4.1-3
OPERATION OF THE CUT-OFF MECHANISM THROUGH ONE COMPLETE CYCLE
S
t
f
(a)
At tnn dad
pressure
center
rvinder
is anproximatelv
at
discharge pressure, the slide
valve is open, and the timerspool valve is to the left as
shown, because
Pvl
s
cyl > Pcc
P
(b)
After TDCcylinder pressure falls
rapidly to suction pressure, at
which time the normal suction
valve opens and admits gas into
the cylinder. At some point
during the rapid drop in pressure
the control pressure P becomes
greater than the cylinger pressure Pyl and the timer-spool
valve
begins to move.
P
a
t-%
%;_\
After a travel
time determined
by the mass of the timer-spool
valve and the applied pressure
differential (P - Pc),
P
the
timer-spool valve - reverses
the pressure differential across
the power piston, causing the
slide valve to snap closed.
160
P
(d)
S
__
gas in tne cyllnder arter
the slide valve is closed is
then expanded until the piston
reaches BDC, while the slide
valve remains closed. The small
volume between the slide valve
and the normal suction valve is
also reduced in pressure.
Ine
P
(e)
P
P
C
P
P
c
_
The gas in the cylnaer is compressed. The normal suction valve
is closed because of the pressure differential across it.
when the cylinder pressure rises
above P , the timer-spool valve
moves bck to its original
position, causing the slide
valve to reopen.
(f)
The gas in the cylinder is
discharged and the cycle is
repeated.
161
SECTION 4.2
DESIGN REQUIREMENTS
A number of design limitations for the device presented in
section 4.1 are apparent:
1.
The design presented is powered by the pressure difference across the compressor.
There must, therefore, exist
a limiting pressure differential below which the device
cannot function without excessive power consumption, and,
hence, there is a limit to the amount of capacity reduction possible.
2. The percentage of mass flow and power required by the device will grow as greater amounts of capacity reduction
are used because total compressor power is reduced.
3. The diameter and travel of the timer-spool valve should
be kept as small as possible, to reduce the power requirement,
and the effect on clearance volume of the compres-
sor.
The diameter and travel must, however, be large
enough to provide adequate passage areas for flow to and
from the power piston.
Moreover, the mass of the timer-
spool valve must be balanced against the desired minimum
effective operating pressure differential and resulting
driving force.
(Trade-off between spool diameter, spool
material, and maximum cut-off condition.)
162
4.
The diameter ;and travel 'of the power piston should be
kept as small as possible to reduce power consumption
-and amount .of hot discharge gas vented to the suction
gas.
The travel of the power piston, however, must be
large enough to provide adequate 'flow area for the slide
valve.
Moreover, the mass of the power piston and slide
valve must be balanced against the minimum available
driving pressure differential and resulting driving force,
to provide adequate response time while overcoming slider
valve friction.
(Trade-off between piston diameter, pis-
ton mass and/or material, and maximum cut-off condition.)
5.
The volume of flow passages between power piston and
timer-spool valve, and between timer-spool valve and
cylinder, should be as small as possible, to reduce power
consumption and increase response time.
The above limitations require that we determine the following
information before we proceed with design of the cut-off mechanism
for any particular compressor:
1.
Compressor speed
2.
Minimum and maximum travel time of timer-spool valve
3.
Travel time of power piston and slide valve at maximum
cut-off condition (maximum
4.
travel time)
Required flow area for slide valve, and, hence, required
travel of power piston
163
Required flow areas for power piston and timer-spool
5.
valve
Suction and discharge pressures at maximum and minimum
6.
cut-off
Compressor speed is dictated by the particular compressor
being studied.
Required flow area for the slide valve can be as-
sumed equal to the flow area provided for the normal suction valve
Required travel of the slide valve and
as a first approximation.
power piston can then be estimated by space constraints, strength
of materials constraints, and fabrication procedure constraints.
Required flow areas for the power piston and spool valve passages
must be determined by trial and error, since initially we do not
know the size of either power piston or spool valve.
Maximum
travel time for the power piston and slide valve are fixed for a
given compressor, the limiting factor being throttling of the suction gas.
Minimum and maximum travel times for the timer-spool
valve, and suction and discharge pressures at minimum and maximum
cut-off
are
determined
ticular application.
from
the intended control function in a par-
In the present work, the capacity controlled
heat pumpstudies of Chapter 3 have provided the latter information.
· Quantitive discussion of the above parameters is given in the following section on cut-off
mechanism design.
164
SECTION 4.3
CUT-OFF MECHANISM DESIGN
The challenging task in designing the cut-off mechanism is to
create a device that will function both controllably and reliably
for long periods of time with low power consumption.
Because the
design task becomes more difficult as the speed of the compressor
is increased, and the size is
decreased, present design efforts
center on a device to function in a small 3 ton, 2 cylinder, high
speed (3600 RPM) hermetic refrigeration compressor.
This compressor,
when installed in a heat pump, would yield approximately a nominal
2.8 ton heating capacity.
Figure 4.3-1 shows the suction valve and the cylinder side of
the head plate of the compressor in question, while Figure 4.3-2
shows the discharge valve, the suction/discharge manifold, and the
manifold side of the head plate.
Figure 4.3-3 shows how the cut-off
mechanism is designed to fit into the compressor.
A separate cut-off
mechanism is
required for each cylinder, but only one control pressure
regulator is
required, and it may be located either inside or outside
of the hermetic shell.
Note that the actual mechanism is very
small, and therefore is
easily added to the compressor.
The only
changes required are a new head plate, and a slightly modified
suction/discharge manifold.
The normal valves in the above compressor,
which remain intact, are of the ring-plate type.
The slide valve
has therefore been designed as a semi-ring valve, and would have a
165
rotary sliding motion.
The rotary sliding motion requires something
other than a rigid connection between the power piston and the slide
valve, but motions are relatively small, so the problem should be a
minor one.
The required travel of the outer edge of the slide valve
is found to be .187 inches when enough port area is provided to
equal the original port area shown in Figure 43-2.
If the slide
valve is recessed into the'head plate slightly, then the suction/
discharge manifold can remain unchanged except possibly for a slight
recess to clear the power piston chamber which protrudes from the
head plate.
We need to estimate the minimum and maximum travel time of the
timer-spool valve, and the suction and discharge pressures at
maximum and minimum cut-off before we can size the various components.
Using values obtained from the capacity controlled heat pump studies
of Chapter 3, we find for t
14 F balance point
case (the most
severe case of low operating pressure differential
nd minimum
travel times):
Maximum cut-off occurs at evaporator entering air temperature
650F
(Vcut mi n ) -
Cutoff
T
16°F
sat
cond
T
s
evap
1 -
480 F
VD
P
sat
cond
Psat
evap
s
260 psia
96 psia
166
Minimum cut-off occurs at evaporator entering air temperature
. 140 F
Cutoff T
T
sat
cond
sat
-
0
1160 F
Pat
sat
cond
260 psia
-30°
P
36 psia
evap
sat
evap
The maximum cut-off condition corresponds to a 62% capacity reduction
compared to the conventional compressor operating with the same
suction and discharge pressures.
The actual value of the"cutoff"
parameter to achieve 62% capacity reduction would vary with different
compressors and with different pressure levels.
We shall assume, how-
ever, that the present 3 ton high speed compressor, and the Carrier
14 ton 06D-537 compressor of the heat pump simulations in Chapters 2
and 3, behave in the same manner.
The latter assumption is probably
far from true, but at least it provides us with data for a first
design study.
From the definition of
the capacity control parameter "cutoff"
we can find the time ater TDC at which the slide valve must be closed
to give the desired maxinm
cut-off.
Our assumed maximum capacity
reduction condition is 62% reduction with cutoff - .64.
In reality
the cut-off mechanism will consume part of the mass flow produced by
the compressor,
so that less than cutoff -
capacity reduction.
If
.64 is required for 62%
we assume that the cut-off mechanism requires
167
about 15% of the reduced mass flow output of the compressor, then,
as a first approximation, only cutoff = .60 is required.
(The
"cutoff" parameter is not synonomous with percent capacity or
masp flow reduction.) The time after TDC at which the slide valve
must be closed to give the desired maximum flow reduction is found
using the approximate expression for cylinder volume as a function
of crank angle (see Appendix
V =
E
)
+ (1- Cos )
V.D
2
(V
CUTOFF -- 1-
-= 1
-V
Vcutmin
vD
V
cut + VR
=D
where:
V ut
= Volume of cylinder when suction valve is closed
Vmin
-
Minimum cylinder volume
VD
=
Displacement volume per cylinder
VR
=V
8
= O at TDC
min/
V
D
* Therefore:
.60
cutoff
-1
= Cos
[1 + 2(.6 - 1)]
(clearance volume)
168
- 77.90 ATDC
- 1.36 radians
then, at 3600 RPM,
t 60
-
.0036 sec ATDC
cutoff
At 3600 RPM, total tinme per revolution is .0167 sec, and for one
half revolution -
.0083 sec.
The maximum allowable travel time of the power piston and slider
valve, in order to avoid excessive throttling of the suction gas
through the valve as it closes, has been calculated to be about
.0016 sec. in the above 3600 RPM compressor.
The time after TDC
at which the timer-spool valve must reach full travel is
.002 sec ATDC for the maximum cutoff condition.
thus about
Assuming
conservatively that the motion of the timer-spool valve does not
start until cylinder pressure drops to suction pressure, we can
determine the fastest necessary travel time of the spool.
Using
ideal gas laws we can estimate the time required for the cylinder
pressure to fall from discharge pressure
PD
to suction pressure
PS:
PVn
coast
n
1.2 - Polytropic Expansion
Exponent
Then
PD V D n min PS
S V 8VO n
svo
suction valve opening
169
1
(062)
60 psa
\96 psia
VD
=
esvO
t
svo
.14
Cos =
(062)
32.9
1 - 2 (.14°
=
.062)]
57 RAD
= .0015 sec ATDC
The minimum required travel time of the timer-spool valve is hence
.0005 sec., occuring at the maximum cut-off condition.
The maximum required travel time of the timer-spool valve occurs
at minimum cutoff, near the balance point ambient temperature.
The
closing point of the slider valve would be just after BDC, with the
timer-spool valve reaching full travel approximately at BDC, .0083
At the minimum cut-off condition the suction pressure is
sec ATDC.
dbout 36 psia, giving an opeiing point for the suction valve about
.0028 sec ATDC.
The maximum travel time of the timer-spool valve
would hence be about .0083 -
.0028 = .0055 sec.
In summary, the design conditions are as follows:
3600 RPM
1.
Compressor speed
2.
Minimum required travel time of timer-spool valve .0005 sec.
3.
Maximum required travel time of timer-spool valve .0055 sec.
4.
Maximum allowable travel time of power piston and slide
valve
.0016 sec
170
.187 in.
5.
Required travel of power pistoh
6.
Required flow passage areas - determined later
7.
Suction & Discharge pressures at maximum cut-off 96 psia
and slide valve
and 260 psia
8.
Suction & discharge pressures at minimum cut-off 36 psia
and 260 psia
Design of timer-spool valve
Tests have shown that nylon is
valve because it is
a good material for the spool
light in weight and has moderately good
resiliency, which gives it good life characteristics when repeatedly
hitting the end walls of the spool valve chamber.
The durability
of nylon under conditions of high temperature (3000F) and chemical
attack from refrigerant or contaminants is
unknown.
There exist
a number of similar materials, however, which have been developed
for the space program, and which should have adequate durability in
the compressor environment.
tests
For the latter reason, calculations and
performed using nylon are felt to be indicative of achievable
performance levels.
Assuming the spool starts with zero velocity and acceleration,
the equation of motion for the spool is:
m
- F - Ff
where Ff= Frictional Force
F - Driving Force
171
Integrating twice, assuming
F and Ff are independent of x , we get:
(F - Ff) tc
t + C
m
-
(F-Ff) 2 + C1 t + C2
m
2
1
2
and using zero velocity and travel at t
-
0 , the equation of motion
for the timer-spool valve reduces to:
t2
2
(F -F)
m
2mx
22
(F -Ff)
Neglecting friction, which has been experimentally verified as a
valid assumption, we have:
2mx
F-
t
2
For a spool similar to that shown in Figure 4.1-2, having a
diameter of .125 in, the mass is estimated to be .00025 lbm.
The travel of the spool would be .090 in.
Using the minimum travel
time of .0005 sec, the required driving force would hence be
F -
.47 lbf.
(P + P)
Assuming that control pressure
P
-
cmavail
avail
P
<
178 psia
c-
2
2
we find
,efind
172
then
2
Fmax
. r-(p
4
avail
cmax
_p)s
avail
avail
F
1.01 lbf
max
avail
We see that with the specified spool size there is more than enough
driving froce available to operate the timer-spool valve.
The
control pressure for the maximum cut-off operating condition would
be set equal to
P -P
c
+
.47 lbf
471bf
s
2
4
-
96 psia + 38.3 psi
Pc- 134.3 psia
and, at minimum cut-off
F
-
P
- 36 psia + 3.08 psi
req
.038 lbf
- 39 psia
The above control pressures should be easily obtainable with a
relatively simple pressure regulator operating from discharge
pressure.
Design of the power piston
Friction and mass of the slide valve must be known before the
173
power piston can be designed.
The slide valve shown in Figure
4.3-3 should probably be made of high strenth polished steel, as
are normal suction and discharge valves.
Using a thickness of .008
in., as in many normal suction valves, the mass of the slider would
be about .005 lbm.
Frictional force on the slide valve is expected
to be proportional to the normal force, as in conventional sliding
friction.
Ff
= fF
n
where:
f
-
F
- normal force
n
Ff
coefficient of friction
resulting frictional force
-
The normal force F
arises from the pressure difference between
suction pressure and pressure of tl. expanded gas inside the cylinder
after cut-off.
The minimum pressure in the cylinder, occuring at
BDC, can be estimated using ideal gas laws and is found to be about
35 psia.
The resulting pressure difference across the slide valve
is hence 96-35
61 psi.
The coefficient of friction for rough-
polished high strength spring steel on rough-polished low carbon
steel was found from measurements to be approximately .18.
We shall
use the latter value in the design of the test parts, but in reality
steel on steel would not be' a good combination for extended running.
A more probable combination would be something like a high strength
174
steel slide valve running on a sintered carbide, molybdenum impregnated
seat pressed into the head plate.
The latter combination of steel
slide valve and dry-lubricant seat would have a much lower coefficient
of friction, possibly .1 or less.
is
The flow area of the slide valve
approximately .6 in2, yielding for the lower value of coefficient
of friction,
Ff = 3.66 lbf.
Knowing the mass and friction of the
slide valve, we can proceed to size the power piston.
A power piston design which should be easy to produce and assemble
in the mechanism is shown in Figure 43-4
Material would probably
be a high strength steel, with an adequate radius between head and
shank to reduce stress concentrations.
In addition, it is important
to provide some sort of spring or cushioning material on the ends of
the piston or cylinder to prevent damage to both when hitting the
end walls continually.
Providing such resilient surfaces is not
viewed as a major problem.
The equation motion for the power piston-
slide valve assembly is similar to that of the spool valve:
2mx
2 m
(F - Ff)
t
Using a steel power piston having a head diameter (D H )
a shank diameter of
to be .0028 lbm.
(DsH)
of .25 in and
.050 in, mass of the piston is estimated
Using the maximum travel time of .0016 sec, with
a travel of .187 in, and a slide valve mass of .005 lbm, the
required driving force becomes:
175
*.PFr=
req
3.66 lbf + 2.87 lbf
= 6.48 lbf
Available driving force at the maximum cut-off condition would be:
'T
4
F
avail
F
,
avail
D2
H
D
2
S[D
H 1 (P-
P
)
7.7 lbf
which is sufficient.
Flow passage sizing
The maximum volume flow rate into the power piston chamber is
approximately
'
VFR
max
imax
power
piston
xs
power
piston piston
- .0066 ft3/sec
The speed of sound at discharge temperature and pressure in R-22
is
about 580 ft/sec, yielding a minimum allowable flow area of about
.0066ft 3/sec
Aflow
'
580 ft/sec
-
=
00164
n2
power
piston
Assuming the flow passages leading to the power piston are rectangular,
.045 in X .125 in,
sufficient,
the available flow area is
.0056 in2, which is
176
The maximum volume flow rate into the timer-spool valve chamber
is:
max
timerrpool spool
spool
valve
timerspool
valve
valve
= .00255 ft3/sec
then:
Aflow
flow
timerspool
valve
-4
6.2 x 10
in
2
Assuming a round flow passage, the minimum allowable diameter of
the passage would be:
Dlow
- .028 in
timerspool
valve
power consumption
During each complete revolution or cycle of the compressor, the
power piston chamber is
filled with gas at discharge pressure and then
completely emptied twice.
By comparison, the spool valve chamber is
filled and emptied only once.
The connecting passages between the
spool valve and the power piston, and between the cylinder and the
spool valve, are each raised to discharge pressure and lowered to
177
The total mass vented
suction pressure once during the cycle.
from discharge to suction pressure during once complete cycle is
hence:
mto
= m
power
piston
t
+ m
+ mspool
passages
valve
If we assume the length of each flow passage leading to the power
piston is
.6 in, and the length of the flow passage leading from
the cylinder to the spool valve is 1 in, then, at the maximum cutoff condition:
PD
=
P
- 96 psia
S
TD
260 psia
T
a
216°F
= 75°F
3.57 lbm/ft 3
PD
Ps
=
1.61 lbm/ft 3
and
m
M l
3.71 x 103
-
power
piston
.21 x 13
-__
lbm
lbm
cimer
spool
valve
pAsmsag
passages
mtot
a
-
.82 x 10
lbm
4.74 x 10-5 lbm
Total mass flow consumption is
5nconsumed
Ued = (4.74 x 10
1
-
5
10.2 (hr)
cyl
hence
5.
lbm'
cycle
) (
;cycles, ) (60m
min
3600
hr
3600 m in
178
The mass flow rate of the 2 cylinder compressor under study is
approximately 130 lbm/hr under the above suction and discharge
pressures and 62% capacity reduction.
therefore requires
mass
(2) (10.2)
130
-
The cut-off mechanism
15.7%
flow, as originally assumed.
of the total resultant
Since 16% of the total
compressor flow goes to operating the cutoff mechanism in the small
compressor being studied, the
COPNF
be reduced by approximately 15Z from
value at maximum cut-off would
that predicted without
considering the power required to run the mechanism.
COPBF
Overall
would be reduced somewhat less because of the large effect
of fan power on total system power consumption, a reduction of
COPBF
by 10% seems probable.
A reduction of
COPBF
is unacceptable for the capacity controlled heat pump.
by 10%
It should
be remembered, however, that the design condition was a 140F balance
point, which means that the unit would put out a maximum of about
1.4 tons at 140F ambient temperature, which signifies an extremely
small
heat load.
In reality, we would use a much larger heat pump
and compressor to achieve a 14°F balance point in a normal heat
load application.
A design balance point of 21°F or higher would
be a more realistic application for the small 3 ton compressor of the
present study.
Relaxing the maximum capacity reduction operating
point to the 21 F balance point curve would provide a higher pressure
differential for operating the cut-off mechanism, and would require
179
less cut-off and result in higher mass flow from the compressor.
The
size of the mechanism would thereby be reduced, and the percentage
of flow required to run the cut-off mechanism would be significantly
reduced.
The forces required to actuate the cut-off mechanism are strongly
dependent on compressor speed.
In addition, as displacement per
cylinder is increased (i.e. surface to volume ratio is decreased)
the percentage of mass flow required to operate the cut-off mechanism
decreases.
Therefore, large slow speed compressors require
considerably less power to run the cut-off mechanism than do small,
high speed compressors.
180
SUCTION VALVE AND CYLINDER SIDE OF HEAD PLATE - 3 TON COMPRESSOR
FIGURE 4,3-1
DISCHARGE VALVE, SUCTION/DISCHARGE MANIFOLD,
AND MANIFOLD SIDE OF HEAD PLATE - 3 TON COMPRESSOR
FIGURE 4,3-2
182
n
_
_
·
·
paas
A
_
i
iI
.-
,
f
/
-11,
1
J
!l
I
I I
i,
SUGGESTED POWER PISTON DESIGN
FIGURE 4.3-4
_
181
Suction
Discharge
__ __ J
__
_ t
FIGURE 4.3-3
)FF
TI.CHANISM
DESIGN TO
IN A 3
TON .FRMETIC
:GERATION CPRESSOR
ide valve
own open)
,rge manifold
Bead plate
Cylinder jacket
Section
A-A
183
SECTION44
EXPERIMENTAL CUT-OFF MECHANISM
Sizes of the timer-spool valve and power piston as experimentally
tested were larger than described in the previous section.
Larger
components were used because of the difficulty with making small
components on the machining equipment available.
Figure 4.4-1
shows the actual spool (nylon) and power piston (steel) as tested.
Diameter of the spool was 3/16 in.
Mass of the spool as measured
on an electronic balance was found to be .19 grams = .00042 lbmo
Travel of the spool was .090 in, and, using the minimum travel time
of .0005 sec, the required driving force was
maximum cut-off the control pressure
P
c
P
c
F = .78 lbf.
At
would be set to:
= 96 psia + 28 psi
= 124 psia
and, at minimum cut-off:
Pc
= 36 psia + .23 psi
= 36.23 psi
Maintaining the latter small pressure differential would be a
difficult task, so the experimental device was expected to have
slightly inadequate minimum cut-off (maximum spool travel time)
behavior.
The test power piston shown in Figure 44-1
consisted of a
steel piston silver soldered to a piece of .032 in O.D. stainless
steel tubing.
The piston was silver soldered only on the short end
184
of the tubing to avoid weakening
the other end of the tbing.
Unfortumately, as discussed later, the end which was
silver soldered
failed early in the testing because of loss
of strength and stress
concentrations from the soldering process,
Diameter of the piston
was .388 in., with an assembled mass of 1.4 grams - .0031 lbm.
Mass of the test slide valve shown in Figure 4.4-2 was adjusted to
.005 Ibm as assembled with the mask for the photo-sensing
equal
system.
The coefficient of friction between the spring steel slide
valve and the low carbon steel slide valve seat was measured to be
Frictional force on the slide valve at the simulated maximum
.18.
cut-off condition would -be 6.4 ibf.
Total required driving force
using a travel of .187 in and a travel time of .0016 sec would then
be 9.1
bf.
Available driving force would be:
Pa ail
(PD - P)
[D
2
DS 2 ]
- 14,6 lbf
Hence we see that more than enough driving force would be available.
185
I
I
EXPERIMENTAL
POWER ?ISTON
(LEFT)
AND SPOOL VALVE (RIGHT)
FIGURE 4.4-1
SLIDE VALVE & SLIDE VALVE CHAMBER, SHOWING
PHOTO-SENSING
SYSTEM & MASK ON SLIDER
FIGURE 4.4-2
186
SECTION 4.5
EXPERIMENTAL RESULTS
PURPOSE
The purpose of the test apparatus was to simulate pressure
vs. time behavior inside a compressor cylinder.
The entire cut-
off mechanism was then tested operating relative to the simulated
cylinder pressure trace.
Compressed air was used as the working
fluid.
APPARATUS
A schematic of the test system is shown in Figure 4.5-1.
The major component of the system is the pressure pulsator, a
rotary valve device which can produce a square wave pressure pulse
of variable high pressure/low pressure pulse duration.
Coupled
to a 3600 RPM motor through a stepped pulley drive, the pulsator
can be used to simulate cylinder pressure vs. time traces for
various compressor speeds and various pressure
positive displacement compressors.
ratios across
Compressed air is supplied to
all components of the test system from a large 200 psig laboratory
compressor.
Air from the compressor is delivered to a large pres-
sure storage vessel at the test site, and from there is distributed
through various pressure regulators and accumulators which damp
out pressure pulsations from components such as the pulsator.
187
Figure 4.5-2 shows a close-up view of the pulsator, connected
to the timer-spool valve, power piston, slide valve chamber,-and
supporting components.
A Kistler 601A dynamic pressure transducer
is located flush with the deliverty port from the pressure pulsator
and measures pressure output from the pulsator directly as it is
A cross-sectional
applied to the end of the timer-spool valve.
schematic of the test apparatus is shown in Figure 4.5-3.
The
spool valve runs directly against the end surfaces of both the pressure pulsator and the control pressure chamber.
Motion of the
timer-spool valve is detected using fiber optic bundles which pass
through the width of the spool valve chamber and stop very close
to the spool itself, as shown in Figure 4.5-4.
A photo-sensing
system is connected to the free ends of the fiber optics bundles.
Total travel time and percent of travel is measured by the action
of the center land of the spool blocking off the light beam.
Motion of the spool and resulting signal output are shown schematically in Figure 4.5-5.
The power piston shank was silver soldered to the slide valve
as shown in Figure 4.4-2.
The slide valve chamber, also shown in
Figure 4.4-2, was provided with slots vented to atmosphere, over
which the slide valve moved.
The slots were always covered by
the slide valve, having been provided not to allow air flow, but
rather to properly model the frictional force on the slider.
188
The entire slide valve chamberwas sealed and pressurized to
create the normal force on the slide valve.
The slide valve was
found to have an excellent seal against loss of air pressure through
the slots.
Motion of the slide valve-power piston assembly was
monitored onceagainusingfiber optics and a photo-sensing
also
shown in Figure 4.4-2.
A mask was mounted on the
slide
system,
valve
and carefully located such that motion of the assembly could be
accurately measured.
output
Motion of the assembly and resulting signal
are shown schematically in Figure
4.5-6.
Slide valve chamber pressure, control pressure, and power
piston
supply
pressure were all measured with calibratedbourdon
tube pressure gauges, pressure in each case being static rather
than dynamic.
The response time for the photo-sensing
was on the order of 10-6sec.
system used
The Kistler pressure transducer was
calibrated dynamically by first statically calibrating a Tyco 0-200
psi static-dynamic pressure transducer, and then
calibrating the
Kistler against the Tyco.
RESULTS
Experimental results for the motion of the timer-spool valve
are given in Figures 4.5-7 and 4.5-8.
The minimum travel time of
the timer-spool valve can be seen to be approximately .0005 sec.,
which agrees well with our design calculations.
Note that the
timer-spool valve has a tendency to bounce upon hitting the steel
189
end walls.
Bouncing of the spool did not affect motion of the
power piston, but could possibly reduce life of the spool.
Long
term durability of the spool could be assured by using resilient
end walls instead of steel.
Required durability of the spool for
a 20 year lifetime, assuming that the cut-off mechanism would be
in use one half of each year, would be:
Required
Durability
=
(3600
cyes
min
cles) (60 min)
24
day
days)
yr
C( 20 yrs) = 1.89 x 1010 cycles
It should be noted that the nylon spool valve shown in Figure 4.4-1
has successfully passed a 1 million cycle durability test with no
change in operating behavior, while running against bare steel end
walls.
The maximum travel time after top dead center achievable
with the above nylon spool is slightly faster than desired because,
as expected, the low control pressure necessary to produce the
desired travel time could not be practically achieved.
Motion of
the timer-spool valve becomes erratic at control pressures less
than about 1 psi above simulated suction pressure.
Performance of the entire cut-off mechanism, including power
piston and slider, was also examined.
but brief.
Performance was satisfactory
The power piston shown in Figure 4.4-1 consisted of a
steel piston silver soldered to a piece of .032 in. O. D. stainless
steel tubing.
Various methods of attaching the piston to the
190
tubing were tried, including anaerobic sealing, heat shrinking,
and silver soldering, but only soldering was successful.
Solder-
ing was done only on the short side of the tubing (the portion of
tubing which carries no axial load).
Unfortunately, the heat re-
quired for silver soldering weakened the tubing and gave rise to
stress concentrations.
When installed for testing, the short end
of the stainless steel tubing broke off at the solder joint within
seconds after the power piston was first put into motion.
The
power piston continued to function, however, without support at
the rear of
the piston.
Tests were run for approximately 15
minutes before the other part of the tubing broke off at the front
surface of the piston.
Failure in the latter case was probably
a result of fatigue caused by oscillation of the piston without a
rearwardsupport.
No pictures were made recording response of the slide valve
before the power piston failed completely.
The following observa-
tions were made, however, while studying performance before failure
occured.
1.
No power piston or slide valve bounce occured, even
with no pressure in the slide valve chamber.
2.
Travel time of the power piston and slide valve was less
that .001 sec. at power piston supply pressures greater
than 80 psig and with slide valve chamber pressure less
191
than 30 psig.
3.
(No higher slider pressures were tried.)
At short travel times (maximum cut-off condition) for
the timer-spool valve, the power piston-slide valve assembly had more than adequate response time.
4. At long travel times (minimumcut-off condition) of the
timer-spool valve, the power piston-slide valve assembly
had faster than expected response.
The performance of the power piston-slider assembly was as good as
or better than expected, except for the last point mentioned above.
The earlier than expected closing time of the slide valve was
probably a result of an inaccurately machined spool, which opened
the port leading to the power piston sooner than desired.
192
Pressure
Regulators.
Ci~v~ 9v,~1
rpwa
4
J
I
Accum
III
Precision
f
otor
Voltage
Sunolv For
Photo Collector
k
0
-- e
Oscillb'-Cd~ot
%,%JLL
U
-. J 1
Pressure
Chamber
SCHEMATIC OF TEST SYSTM
FIGURE ,4.5-1
193
CLOSE-UP VIEW OF PULSATOR CONNECTED TO TEST PARTS
FIGURE 4,5-2
AdIoI
I_
-r
_
r
_
_
MnA
PFnr
to -Sens.
ten
lide Valve
Pres
nts
to
nosphere
(P)
P
PC
c
'/
Power Piston Pressure
SCHEMATIC VIEW OF TEST PARTS
FIGURE 4.5-3
194
Photc
:ter
lens
(Phot
Lb)
Fiber Optics Bundles
Viewing Center Land of Spool
PHOTO-SENSING SYSTEM FOR TIMER-SPOOL VALVE MOTION
FIGURE 4.5-4
Oscilloscope Trace
Aatual
Because of
inaccurately
machined spool
Spool Motion
'H'
Beginning of motion
End of motion
SCHEMATIC MOTION/OSCILLOSCOPE TRACE FOR TIMER-SPOOl VAILVI:
FIGURE 4.5-5
195
Oscilloscope Trace
Ideal
Slider Motion
.
Actual
Because of
inaccurately
located mask
~LLI,
11
LI
Beginning of motion
End
of motion
SCHEMATIC MOTION/OSCILLOSCOPE TRACE FOR SLIDE VALVE & POWER PISTON
FIGURE 4.5-6
196
Spool
Valve
Motion
Qcm min)
70 psi
Simulated
Cylinder
Pressure
(PMax-P
mn )
75 psi
(5 msec/div)
I
TDC
I
BDC
I
TDC
0
.0083
see
8ec
.0167
sec
Travel Time Less
Than- ,.9005 sec
d
TYPICAL
.
TDC
BDC
0
TDC
.0083
.0167
seC
sec
Bsc
MINIMUM TRAVEL TIME
(MAXIMUM CUT-OFF)
FIGURE 4,5-7
CAPABILITY
OF SPOOL VALVE
197
A
Spool
Valve
Motion
(P
-
-
c Pmin)
1 psi
Simulated
Cylinder
Pressure
(P
-P
axpsin
70 psi
(5 usec/div)
I
TDC
I
B1)C
I
TDC
0
.0083
.0167
sac
see
sec
Travel
Bounces on
Tuma
TDC
BDC
0
TDC
.0083
.0167
8ec
sec
TYPICAL
sec
MAXIMUM TRAVEL TIME
(MINIMUM CUT-OFF)
FIGURE 4.,5-8
CAPABILITY
OF SPOOL VALVE
)
198
CHAPTER
5
CONCLUSIONS AND RECOMMENDATIONS
199
CHAPTER
5
CONCLUSIONS AND RECOMMENDATIONS
Two major drawbacks with conventional air-to-air heat pumps
are limited low temperature heating capacity and much less than
opti
m
COP
at higher ambient temperatures.
Both of these problems
are related to widely changing refrigerant density, and hence mass
flow rate, with changing suction pressure.
Low ambient temperature heating ability can be improved by
using a larger than normal heat pumpfor a given heat load.
A large
heat pump can provide a 15 to 25%per year energy savings over
conventionally sized heat pumps in colder climates because of reduced
auxiliary electrical resistance heat. However,since most air-to-air
heat pumpsare also used as air conditioners, poor comfort control
during cooling can result from using larger than normal heat pumps.
Larger ducting to accomodate the lar
r air flows adds further to the
total cost of the larger unit.
The use of capacity controlled compressors can eliminate the
problem of poor comfort control during air conditioning operation,
and can significantly
increase the COPBF(with both fan powers
included) of large heat pumps, resulting in
an additional
5 to 15%
per year energy savings over that obtained by reducing auxiliary
electrical resistance heat if the larger ducting normally used with
a larger heat pumpis employed. Alternatively,
since capacity con-
trolled heat pumps use lower air flows than conventional units of
comparable size, smaller than normal ducting may be used.
The latter still
200
results in the gains from reduced auxiliary heat, but produces lesser
gains from increasing
COPBF.
The seasonal performance and economic comparisons of the present
study have been done using duct sizes for the large capacity controlled
heat pumps which are too small for conventional large heat pumps
with their higher air flows.
Using a 10%/yr interest rate, 10 year
amortization of heat pumps and air conditioners, and 20 year amortization of gas and electrical resistance furnaces, the present studies
show that in colder climates, such as Boston or Minneapolis, capacity
controlled heat pumps having balance points as low as 21°F or 140F
are more economical than conventionally sized heat pumps even at
today's electricity prices.
Larger capacity controlled heat pumps are
not economically competitive with conventionally sized heat pumps in
warmer climates, but heat pumps are more economical than electrical
resistance heating in all locations studied.
None of the heat pumps
studied are economically competitive with gas or oil heating in
colder climates at present energy prices.
The latter situation could
easily change depending on relative prices of gas, oil, and electricity.
If more durable heat pumps, which could be amortized over 20 years
instead of 10 years were available, heat pumps would be close to
competing with fossil fuel heating systems plus air conditioners even
at today's energy prices.
Air-to-air heat pumps are somewhat less
attractive compared to fossil fuel heating systems if the air conditioning
201
feature is not desired.
It should be noted that the assumptions used in the present
work for the control function of the capacity controlled heat pump
produce performance predictions that are always less than the optimum
possible.
Optimization of air flow rates, expansion valve settings,
and amounts of capacity reduction would yield substantially increased
performance.
Fan power has a marked effect on performance of capacity
controlled heat pumps.
in
COPBF
reduced.
1.
In order to realize the potential increases
with capacity control, fan power must be substantially
Three methods of reducing fan power are:
Use more efficient fan designs (different blade shapes,
shrouding, and the like)
2.
Reduce air flow resistance (such as larger duct sizes)
3.
Reduce air flow (fan power is readily reduced by using
large fans running at reduced speed and air flow)
A more careful study of fan power reduction and optimization of
reduced air flow rates is highly recommended for both conventional
and capacity controlled heat pumps.
The significant effect of fan power on conventional and capacity
controlled air-to-air heat pumps highlights the importance of investigating other types of heat pumps.
One promising type of heat pump
would use a water cooled condenser, circulating the water throughout
202
the building, with fans in each room to increase heat transfer, while
having low flow losses0
Solar augmented and heat storage heat pumps
are other types which are recommended for further study.
In all of
the above heat pumps, however, attention must be given to reducing
AT's
across the heat exchange sites.
Another area of research which is needed is concerned with
improving low ambient temperature heating capacity of heat pumps.
The capacity controlled heat pump concept could make it possible
to use new working fluids, having greater vapor density at evaporator
temperatures corresponding to low ambient air temperature, and having
a smaller density change with change in pressure.
The increased
heating capacity caused by increased mass flow at low ambient temperatures would reduce the amount of auxiliary heat required by a given
heat pump.
Results of initial design and development work on an early suctionvalve cut-off mechanism indicate that it is possible to design a
controllable
device to function in high speed (3600 RPM) compressors,
with little modification to existing compressor designs.
The design
presented would have a power requirement of about 15% of the total
reduced compressor power in the small compressor studied,which is
felt to be unacceptable.
However, the nominal 3 ton compressor
studied would yield a heating capacity of only about 1.4
tons with a
large amount of capacity reduction, and would in reality not be used
203
for a capacity controlled heat pump.
A capacity controlled heat pump
would have a large compressor, and power requirements of the cut-off
mechanism in larger or lower speed compressors would be significantly
less.