NBSIR 79-1911

PROCEDURES FOR TESTING, RATING,

AND ESTIMATING THE SEASONAL

PERFORMANCE OF ENGINE-DRIVEN

HEAT PUMP SYSTEMS

B. R. Maxwell

Building Thermal and Service Systems Division

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

September 1979

Sponsored by:

The Department of Energy

20 Massachusetts Ave., N.W.

Washington, D.C. 20585

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Luther H. Hodges, Jr., Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

ABSTRACT

1

A generic test and rating procedure is developed for heat engine-driven

air-to-air heat pump systems. The procedures are classified according

to whether the systems have single-speed, two-speed, or variable-speed

capability, and whether they are operating in the heating or cooling

mode. The test requirements generally consist of a series of steadystate tests to establish the impact of outdoor temperature on performance, two or more part-load (cyclic) tests to determine the effect of

"on-off" cycling, two steady-state intermediate speed tests to determine part-speed performance, and a single frost accumulation test to

estimate the effect of frost. A generalized calculation and rating

procedure is developed. The system is rated in both modes based upon

its steady-state performance at the ARI standard rating points, its

seasonal performance factor, and its seasonal operating cost. A frost

degradation coefficient is also established. The seasonal parameters

are based upon either a residential or commercial/industrial building

application which is located in either a generalized northern or southern

climate.

Key Words: Building heating and cooling; engine-driven heat pump;

heat pump; heating and cooling equipment; heating,

ventilating and air conditioning.

iii

NOMENCLATURE

BHC Average total bin hours for cooling, (hrs)

BHH Average total bin hours for heating, (hrs)

BL(T.)

3 C

D

C def

C

E

C

F

c

s C

pa

Building load at dry-bulb temperature T., (Btu/hr)

Part-load degradation coefficient

Frost degradation coefficient

Electric energy cost, ($/kWh)

Engine fuel cost, ($/kBtu)

Supplemental energy cost, ($/kBtu)

Specific heat of air-water mixture, c = .24 + .444 W , (Btu/lbm - F) pa n

COP

eye

C0P

cyc

(V

COPief (32)

COP (T.) ss 2 E

cyc

(' T

cyc

)

Cyclic coefficient of performance for one "off’V’on" cycle

Cyclic coefficient of performance at temperature T_^ Coefficient of performance under frost conditions

Steady-state coefficient of performance at temperature T.

Total input electric energy during one "off" /"on" cycle

at T , (watt-hr)

eye

E

def (32) Total input electric energy during the frost accumulation

and defrost test, (watt-hr)

i

ss

(T

j

) Steady-state electrical power input at temperature T.,

(watts) ^

et

Total electric and fuel energy required during a season,

(Btu)

w Total input electric and fuel energy in the jth temperature

bin, (Btu)

E

T

(Tj ) Cost of total input electric and fuel energy in the jth

temperature bin ($)

HDT Heating design temperature, (F)

J Bin number

LHV 3

Lower heating value of fuel (Btu/lbm or Btu/ft ) VVn

3 Fuel mass Cor volumej flow rate (lbm/hr or ft /hr)

Total number of non-zero temperature bins

n.

3 N

Number of hours in the jth temperature bin

Total heating or cooling season temperature bin hours,

(hrs)

N° Minimum compressor speed, (rpm)

iv
N

1

N

1

Maximum compressor speed, (rpm)

Intermediate compressor speed, (rpm)

PLF (X(T. )

)

Q

Heating or cooling part-load factor

Total heating or cooling done during a season, (Btu)

Q(V

Total heating or cooling done in the jth temperature

bin, (Btu)

<Wc(T

cyc

) Total heating or cooling during one "off "/"on" cycle at

T , (Btu)

eye’

^def (32> Net heating during the frost accumulation and defrost

test, (Btu)

Q-(T ) f eye

Q

f (32)

Total input fuel energy at T

c

, (Btu)

Total input fuel energy during the frost accumulation

and defrost test, (Btu) W

\W

Q

ss

(V

Input fuel energy at temperature T_^ , (Btu/hr)

Total resistance heat required during a season, (Btu)

Total resistance heat in the jth temperature bin, (Btu)

Steady-state heating or cooling capacity at temperature

T , (Btu/hr) soc Seasonal operating cost ($)

SPF Seasonal performance factor

t Time

T

al<C > Dry-bulb temperature of air entering the indoor side,

(F)

T

a2

(t > T

c

Dry-bulb temperature of air leaving the indoor side, (F)

Change-over temperature (temperature corresponding to zero heating and cooling requirements) , (F)

T

eye

Outdoor dry^bulb temperatures at which cyclic tests are conducted, (F)

T.

3 T off

Representative temperature for bin j , (F)

Outdoor temperature at which compressor is automatically

turned off (heating only)

T

H

(t) The higher of the dry-bulb temperatures of the air

entering and leaving the indoor side

T

L

(t) The lower of the dry-bulb temperatures of the air entering and leaving the indoor side

V

v

' tl w

n

Indoor air flow rate,(cfm)

3 Specific volume of air-water mixture, (ft /lbm)

Humidity ratio, (lbm water /lbm dry air)

V
X(T ) Z

Heating or cooling load factor at temperature T.

i

^ Normalized speed at intermediate speed N

Normalized part-speed capacity factor

'll 1

Efficiency of producing supplemental heat from primary

fuel (n = 0.3 if electric resistance heat is used)

s Normalized part-speed input energy factor

Subscripts

H Heating

C Cooling

ss Steady-state

eye C.yclic

j T emperature bin number

Superscripts

0

i

1

Low speed (smallest capacity)

Intermediate speed (intermediate capacity)

High speed (greatest capacity) « Designates superscripts 0 and 1

vi
TABLE OF CONTENTS

Page

ABSTRACT iii

NOMENCLATURE iv

LIST OF TABLES AND FIGURES ix

1. INTRODUCTION 1

1.1 BACKGROUND 1

1.2 OBJECTIVE AND SCOPE 1

1.3 CLASSIFICATION OF ENGINE-DRIVEN HEAT PUMP SYSTEMS. 1

1.4 PERFORMANCE CONSIDERATIONS 2

2. RECOMMENDED TESTING REQUIREMENTS 3

2.1 GENERAL 3

2.2 STEADY-STATE OPERATION 3

2.2.1 Single-Speed Operation 5 2.2.2 Two-Speed/Dual-Capacity Operation 4

2.2.3 Continuously Variable-Speed Operation .... 5

2.3 PART-LOAD (CYCLIC) OPERATION 6

2.4 FROST ACCUMULATION AND DEFROST OPERATION 7 2.5 INDOOR-SIDE AND OUTDOOR-SIDE AIR QUANTITY 8

3. RECOMMENDED TEST PROCEDURES 8

3.1 INTRODUCTION 8

3.2 STEADY-STATE TEST PROCEDURE 9

3.2.1 Applicable Test Method 9

3.2.2 Instrumentation and Required Data 9

3.2.3 Test Operating Procedure and Results 10

3.2.4 Test Tolerances 10

3.3 PART-LOAD (CYCLIC) TEST PROCEDURE 11

3.3.1 Applicable Test Method 11

3.3.2 Instrumentation and Required Data 11

3.3.3 Test Operating Procedure and Results 11

3.3.4 Test Tolerances 12

3.4 FROST ACCUMULATION AND DEFROST TEST PROCEDURE ... 12

3.4.1

Applicable Test Method 12

vii
TABLE OF CONTENTS (Continued)

Page

3.4.2 Instrumentation and Required Data 13

3.4.3 Test Operating Procedure and Results 13

3.4.4 Test Tolerances 13

4. BUILDING LOADS AND CLIMATE SPECIFICATIONS 14

4.1 INTRODUCTION 14

4.2 GENERALIZED CLIMATE 14

4.3 BUILDING LOADS 15

5. CALCULATION PROCEDURE 15

5.1 GENERAL 15

5.2 PART-LOAD (CYCLIC) PERFORMANCE 16

5 . 3 PART-SPEED PERFORMANCE 18

5.4 SEASONAL PERFORMANCE FACTOR AND SEASONAL OPERATING

COST 20

5.4.1 - Single-Speed Operation 20

5.4.2 Two-Speed/Dual-Capacity Operation 30

5.4.3 Variable-Speed Operation 25

5.5 FROST ACCUMULATION AND DEFROST CALCULATIONS 27

6. RECOMMENDED RATING REQUIREMENTS 28

7. LIMITATIONS OF THE RECOMMENDED TEST AND RATING

PROCEDURES 28

References 30

Appendix A. Propagation of Measurement Uncertainties into

the Steady-State Coefficient of Performance

COP (T.) 45

ss 2 A.l Introduction 45

A. 2 Steady-State Heating Coefficient of

Performance 46

A. 3 Sample Calculation 50

A. 4 Summary 51

viii
LIST OF TABLES AND FIGURES

Page

Table Title

1 Summary of Test Requirements 31

2 Test Operating and Test Condition Tolerances 32

3 Generalized Climates for Residential Applications . 33

4 Generalized Climates for Light Commercial/

Industrial Applications 34

5 Summary Weather Data for Representative Climates . . 35

6 Calculation Sheet for Single-Speed Heat Pumps 36

7. Calculation Sheet for Two-Speed/Dual Capacity or Variable-Speed Heat Pumps 38

8 Rating Sheet for Engine-Driven Heat Pump Systems . . 40

Figure

1 Test Requirements for Single-Speed Heat Pump

Systems 41

2 Test Requirements for Two-Speed (Dual Capacity)

Heat Pump Systems 42

3. Test Requirements for Variable-Speed Heat Pump

Systems 43

ix
1 . INTRODUCTION 1.1

BACKGROUND

The application of a heat engine to a heat pump has the inherent advantages of engine waste heat recovery to supplement the refrigeration

cycle heating mode output, and increased heat pump efficiency in both

the heating and cooling modes due to capacity modulation. There are

currently a number of innovative engine-driven heat pump development

projects in progress around the country [ref. 1-5], and there is as yet

no standardized test and evaluation procedure available for these

systems. Therefore, industry and government are unable to evaluate and

compare these new heat pumps, and to make sound decisions regarding

which are worthy of further development. A standardized test and rating

procedure, incorporating provisions specifically tailored to the nature

of each heat pump system, is required so that the results of different

research groups working on different types of engine-driven heat pump

systems may be effectively compared on the same technical basis.

1.2

OBJECTIVE AND SCOPE

The objective of this study is the development of a generic test and

rating procedure for engine-driven heat pump systems which are likely to

be employed in residential and small commercial buildings in the future.

Inherent in the development of these procedures is the formulation of

calculation procedures to estimate the seasonal performance and seasonal

cost of operation of these systems. The test procedures and the rating

and calculation procedures recommended herein apply only to prototype,

heat engine-driven, air-to-air, mechanical compression, Rankine-cycle

heat pimps operating in the heating and cooling modes. Since consideration is restricted to prototype systems, it is expected that the recommended test and rating procedures will be used by the industry as a tool

to evaluate and compare the performance of such systems, and may eventually provide a foundation for a future less burdensome test and

rating standard for factory-made systems which reach the market place.

1.3

CLASSIFICATION OF ENGINE-DRIVEN HEAT PUMP SYSTEMS

Engine-driven heat pump systems are typically classified according to

the thermodynamic power cycle of the prime mover and the thermodynamic

cycle of the refrigerator. In addition, they are often classed according to the nature of their heat source and sink (air-to-air, liquid-toliquid, etc.). For residential and small commercial applications, an air heat source and sink is the most practical and common. Since

current development efforts [1-5] involve air-to-air designs, the recommended test and rating procedures will be restricted to these heat

pumps

.

1
Of the many power cycles available for heat pump applications, the five

most common are the Brayton, Diesel, Otto, Rankine, and Stirling cycles.

The Brayton engine is normally rotary in design; the Rankine engine may

be reciprocating or rotary, and the Otto, Diesel, and Stirling engines

are all reciprocating, and they may be of a free-piston design. Since

there is no reason to exclude any of these engines from consideration in

heat pump applications, the recommended test and rating procedures will

be sufficiently general to include all of them. For purposes of generality, however, the prime mover will be conceptualized as a "black box"

which converts input fuel energy Cliquid, solid, or gaseous) into useful

work and recoverable and non-recoverable waste energy. References to a

particular engine type will not normally be made except in those instances

where uniqueness of design or operation requires it.

The refrigeration cycle most commonly employed for residential and small

commercial applications is the vapor compression Rankine cycle. Since

all current development efforts are using this cycle, the test and

rating procedures recommended in this study will be restricted to it.

The procedures will be sufficiently general, however, to be applicable

to conventional positive and variable displacement compressors, as well

as high-speed centrifugal or free-piston types.

1.4 PERFORMANCE CONSIDERATIONS

The current requirements for testing and rating of electrically-driven

unitary heat pump equipment are described in the Air Conditioning and

Refrigeration Institute CARI) Standard 240-76. Test methods used to

evaluate this equipment are described in the American Society of Heating, Refrigerating and Air Conditioning Engineers (ASHRAE) Standard 37-69.

For air-source heat pumps the current heating mode rating requirements

are based upon two steady-state tests conducted at indoor dry-bulb and

wet-bulb temperatures of 70°F (21.1°C) and 60°F (15.6°C), respectively.

One test is conducted at outdoor dry-bulb and wet-bulb temperatures of

47°F (8.3°C) and 43°F (6.1°C), and the other is conducted at 17°F

(-8.3°C) and 15°F (-9.4°C), respectively. In the cooling mode, the

rating requirements are based on one steady-state test conducted at

indoor dry-bulb and wet-bulb temperatures of 80°F C26.7°C) and 67°F

(19.4°C), respectively, and an outdoor dry-bulb temperature of 95°F

(35°C). In addition, for units which reject condensate to the outdoor

air stream, an outdoor wet-bulb temperature of 75°F C23.9°C) is required.

Knowledge of the steady-state performance of a heat pump system at the

ARI rating points is useful for single point rating and comparative

purposes, regardless of the power source. Such knowledge is insufficient, however, to assess the non- steady-state performance of the

system, and is insufficient to determine the seasonal performance of the

Systran. Experimental investigations of electric heat pumps have indicated that the "on-off” cycling that these units must undergo to satisfy

comfort requirements often has a significant effect on the performance

of the units in both modes of operation. Because of the dynamic characteristics of the heat engine, it’s expected that cycling will have an

2
even greater effect on the performance of an engine-driven system.

Experimental investigations of engine-driven heat pump systems have

shown that heating and cooling capacity and input energy are generally

nonlinear functions of outdoor dry-bulb temperature. This is particularly true in the heating mode where heat pump capacity is supplemented

with recovered engine heat. Because of differences in engine brake

thermal efficiency and heat recovery characteristics, as well as differences in heat pump efficiency, the effect of outdoor temperature must be

considered in the test and rating procedures and in the seasonal performance determinations. Additional factors which affect instantaneous and

seasonal performance are the climate in which the system operates , the

building load classification, capacity modulation, and defrost requirements. All of these factors are addressed in the recommended test,

rating, and calculation procedures which follow.

2. RECOMMENDED TESTING REQUIREMENTS

2 . 1 GENERAL

The recommended testing and rating requirements for engine-driven heat

pumps are classified basically according to whether the system has

single-speed, two-speed, or variable-speed capability, and whether it is

operating in the heating or cooling mode. The test requirements generally consist of a series of steady-state wet-coil Cor no-frost) tests

which provide data necessary to define the steady-state performance

curve, combined with two or more cyclic Cdynamic) tests to determine the

part-load performance. For variable speed systems the test requirements

also include a provision for steady-state, intermediate speed tests to

determine part-speed performance. The performance of the system under

frost accumulation and subsequent defrost operation is characterized by

a single test under high relative humidity conditions. The system is

then rated in both operating modes based upon its steady-state performance at the ART standard rating points, its seasonal performance

factor, and its seasonal operating cost. A summary of the testing

requirements is presented in table 1 and is illustrated in figures 1-3.

2.2 STEADY-STATE OPERATION

The steady-state, wet-coil Cor no-frost) testing requirements are dependent on whether the heat pump system has single-speed, two-speed, or variable-speed capability. The respective requirements are discussed

below.

2.2.1 Single-Speed Operation

A total of six steady-state, wet-coil Cor no-frost} tests shall be

conducted according to the test procedures specified in section 3.2. Of

this total, two wet-coil tests shall be conducted in the cooling mode

and the remaining four in the heating mode.

In the wet-coil cooling mode tests, the air entering the indoor portion

of the unit shall have a dry-bulb temperature of 80°F C26.7°C) and a

1 3
wet-bulb temperature of 67°F (19.4°C). The dry-bulb temperature of the

air surrounding and entering the outdoor portion of the unit shall be

95°F (35*C) in the first test, and 80°F (26.7°C) in the second. For

those units which reject condensate to the outdoor air stream, the

outdoor wet-bulb temperatures entering the outdoor unit shall be 75 °F

(23.9°C) and 64°F (17.8°C), respectively. The outdoor dry-bulb and wetbulb temperatures of the first test point coincide with the ARI standard

rating point for air-source units in the cooling mode. The 80°F (26.7°C)

dry-bulb temperature of the second point was chosen because it approximates the average operating temperature in northern climates during the

cooling season- The corresponding wet-bulb temperature was chosen so that the relative humidities of both testing points are approximately

equal.

In the heating mode tests, the air entering the indoor portion of the

unit shall have a dry-bulb temperature of 70°F (21.1°C) and a maximum

wet-bulb temperature of 60*F (15.6°C). The four wet-coil (or no-frost)

tests shall be conducted with the dry-bulb temperature of the air sur- rounding and entering the outdoor unit equal to 47°F (8.3°C), 32°F

(0°C), 17°F (-8.3*0), and -13°F C-25°C) , respectively. The corresponding wet-bulb temperatures of the entering air shall be 43°F (6.1°C)

,

30®F (-1.1*0 or less, and 15*F C-9.4

Q C), respectively, for the first

three tests, and shall be left uncontrolled for the remaining one. The

outdoor conditions of the first and third testing points coincide with

the ARI standard high and low temperature rating points for air-source

units in the heating mode. The second test point was chosen in order to

provide a reference for a subsequent frost accumulation and defrost

test, and the fourth point was chosen in order to establish low temperature system performance. The four testing points shall be used to

determine the system performance as a function of outdoor dry-bulb

temperature.

2.2.2 Two-Speed/Dual-Capacity Operation

In order to properly characterize the performance of engine-driven

systems with two-speed compressor capability, the test requirements are

separated into high-speed and low-speed requirements, and they shall be

conducted according to the test procedures specified in section 3.2. In

the cooling mode, the steady-state tests for both compressor speeds are

the same as those described in section 2.2.1 for single speed operation,

and are the minimum tests necessary to estimate the steady-state performance curve for each speed. In the heating mode, however, three highspeed compressor tests are specified over a range of low ambient temperatures, and three low-speed compressor tests are specified over a range

of higher ambient temperatures. This approach reflects the way in which

most two—speed systems are designed to operate, and also reduces the

number of tests necessary to establish the performance curve for each

compressor speed.

4
The three wet-coil (or no-frost) low-speed tests shall be conducted with

the dry-bulb temperature of the air surrounding and entering the outdoor

unit equal to 47°F (8.3 # C), 32°F (0°C) and 17°F (-8.3°C), respectively.

The corresponding wet-bulb temperatures of the entering air shall be

43°F (6 . 1°C) , 30°F (-1.1°C) and 15°F (-9.4°C). A maximum wet-bulb

temperature of 30°F (-1.1°C) was chosen for the second test in order to

reduce the accumulation of frost on the outdoor coil. Although frost

may form during this test, and during the subsequent test at 17°F (-8.3°C)

dry-bulb temperature, its effect during the time span of the tests is

not expected to be great.

The three no-frost high-speed tests shall be conducted at dry-bulb

temperatures of 17°F (-8.3°C), 2°F (-16.7°C), and -13°F (-25.0°C). The

wet-bulb temperature of the first point shall be 15°F (-9.4°C) and shall

be left uncontrolled for the remaining two.

Systems which use twin compressors, staged compression, dual firing

rates, suction/discharge valve control, etc., to achieve dual capacity

performance are subject to the same test requirements as those systems

with two-speed compressors. In these instances the term "high-speed"

shall mean operation with both compressors, or at the greatest capacity

level, and "low-speed" shall mean one compressor, or smallest capacity

operation. As indicated in table 1 and illustrated in figure 2, a total

of ten steady-state tests shall be conducted for systems with two-speed

capability.

2.2.3 Continuously Variable-Speed Operation

Experimental investigations of engine-driven heat pump systems have

shown that heating and cooling capacity, input fuel energy, and input

electric energy are generally nonlinear functions of compressor speed as well as of each other. Therefore, for those systems whose speed is

continuously variable, the test requirements and rating procedures must

include provisions to estimate the system’s performance at speeds intermediate to the maximum and minimum speed.

The steady-state test requirements for variable-speed heat pump systems

are divided into two sets. The requirements for the first set are

exactly the same as those described in section 2.2.2 for two-speed

operation. High and low compressor speed shall then mean maximum and

minimum compressor speed. As in section 2.2.2, a total of ten steadystate tests shall be conducted according to the test procedures specified

in section 3.2.

The second set of requirements consists of steady-state intermediate

speed tests conducted at a normalized speed Z according to the test

procedures specified in section 3.2. The normalized speed Z is defined

as:

5
z ( 2 . 1) N

N

0

0

where Z varies from 0 to 1, and N , N , and N

1

represent minimum speed,

maximum speed, and any intermediate speed, respectively. One wet-coil

intermediate speed test shall be conducted in the cooling mode. The

indoor conditions shall be as specified in section 2.2.1, and the outdoor dry-bulb and wet-bulb temperatures shall be 80°F (26.7°C) and 64°F

(17.8°C), respectively. The test shall be conducted at a normalized

speed of Z = 1/2.

One no-frost intermediate speed test shall be conducted in the heating

mode at the indoor conditions specified in section 2.2.1. The outdoor

dry-bulb and wet-bulb temperatures shall be 17°F C-8.3°C) and 15°F

C-9.4°C), and the test shall be conducted at Z = 1/2. The above intermediate speed test requirements are summarized in table 1 and illustrated

in figure 3. The results will be used to calculate part-speed capacity

and input energy with the calculation procedure described in section 5.3.

2.3 PART-LOAD (CYCLIC) OPERATION

Laboratory investigations (refs. 6 and 7) have shown that the heating

and cooling performance of electric heat pumps is significantly reduced

when operated under part-load, or cyclic, conditions. Performance

degradation has been shown to be directly dependent on load and to be

relatively insensitive to outdoor ambient conditions. During cyclic

wet-coil cooling tests of electric heat pumps, it has been found that

constant indoor conditions are difficult to maintain, and that dry-bulb

and wet-bulb temperature measurement errors can create large uncertainties in the cyclic sensible and latent capacities. Further cooling

tests have indicated, however, that cyclic wet-coil tests may be

replaced by simpler and more accurate dry-coil tests. Specifically, the

results showed that when steady-state and cyclic dry coil tests were

conducted, the ratio of the cyclic COP to the steady-state COP was

essentially the same as the COP ratio determined from wet-coil tests at

the same cooling load factor.

The part-load test requirements during the cooling mode shall include

one or more steady-state dry-coil tests and an equal number of cyclic

dry-coil tests. These tests shall be performed in conjunction with each

other according to the test procedures specified in sections 3.2 and

3.3, respectively. The indoor dry-bulb temperature shall be 80°F

C26.7*C) and the wet-bulb temperature shall be a value which does not

cause condensate to form on the indoor coil. It is recommended that the

temperature be equal to or less than 57°F C13.9°C). The outdoor drybulb—temperature shall be 80°F C26.7*C) and the wet-bulb temperature

shall be unspecified. For systems with single and continuously-variable

speed capability, there shall be one steady-state dry-coil test and one cyclic dry-coil test. For variable-speed systems both tests shall occur

6
at the mini mum speed since this is the speed at which cycling will

normally occur under low load conditions. For systems with two-speed

(two-capacity) capability there shall be two steady-state dry-coil tests

and two cyclic dry-coil tests, for a total of four. Since the dynamic

performance of an engine-driven system is a function of speed (capacity)

,

a steady-state and cyclic test shall occur at each of the two speeds of

operation, and they shall be performed in conjunction with each other.

The cyclic test requirements during the heating mode shall include one cyclic test for single-speed and continuously-variable speed systems.

The outdoor dry-bulb and wet-bulb conditions shall be 47°F (8.3°C) and

43°F (6.1°C), respectively. Two cyclic tests shall be conducted for

two-speed Cdual-capacity) systems, one at each compressor speed. The

low-speed test shall occur at the dry-bulb and wet-bulb conditions

specified above, and the high-speed test shall occur at dry-bulb and

wet-bulb conditions of 17°F (-8.3°C) and 15°? (-9.4°C), respectively.

The indoor dry-bulb and wet-bulb temperatures shall be 70°F (21.1°C) and

60°F (15.6°C), respectively, for all cyclic heating tests.

The conditions specified for these cyclic heating tests are the same as those outlined in section 2.2.1 for two of the steady-state tests. Each

cyclic heating test shall, therefore, be performed in conjunction with

its corresponding steady-state test according to the procedures specified in section 3.2. The cyclic test requirements for heating and

cooling are summarized in table 1 and figures 1-3. The results will be

used to calculate a part-load degradation coefficient with the

calculation procedures described in section 5.2.

u

2.4 FROST ACCUMULATION AND DEFROST OPERATION

Accumulation of frost on the outdoor coil has been shown (ref. 7) to

cause a significant drop in the performance of electric heat pumps

compared to their non-frosted performance. Since frost formation occurs

most rapidly over a range of outdoor conditions in which most space

heating systems accumulate many years of yearly operation, a frost

accumulation and defrost test should be included in the test and rating

procedures for engine-driven heat pump systems.

One proposed approach to account for the deteriorating effects of frost

would be to apply a correction factor to all steady-state performance

data obtained within the frost range. The correction would be a function of outdoor dry-bulb temperature and relative humidity, and would be

based upon a series of frost accumulation tests. Because of the current

lack of experimental data regarding the performance of engine-driven

heat pump systems under frosted-coil and defrost conditions, it is very

uncertain how such a correction should vary as a function of ambient

temperature and humidity conditions. It is equally uncertain at this

time as to what minimum tests should be required of the system developer

in order to define these functions. Therefore, this approach is not

recommended for the prototype systems addressed in these procedures.

7
Instead, a single-point frost accumulation and defrost test is specified

for frost rating purposes. As actual operating data become available

under frosting conditions, the development of a more general frost

correction should be investigated.

A single-point frost accumulation and defrost test shall be performed

with the dry-bulb and wet-bulb temperatures of the air entering the

outdoor unit equal to 32°F (0°C) and 30°F (-1.1°C) , respectively. These

conditions correspond to a relative humidity of 80%. This is an average

value for most regions of the country which have a significant number of

their heating hours occurring at outdoor temperatures less than 35 °F

(1.7°C). The indoor conditions shall be 70*F (21.1°C) dry-bulb and 60°F

(15. 6° C) maximum wet-bulb temperature. For systems with two-speed

(dual-capacity) or continuous ly-variable speed capability, the test

shall occur at the lower speed (capacity) since most engine-driven

systems would normally operate at this speed when the outdoor temperature is 32* F (0°C) . The test shall be pseudo steady-state over a com- plete frost accumulation and defrost cycle, and it shall begin at

defrost termination and continue until the next defrost termination.

The time-until-defrost, the method of defrost, and the operating procedures during the defrost period shall not be specified. In this way, no single heat pump developer or type of engine-driven system will be

favored. The frost accumulation test shall be conducted according to

the test procedures specified in section 3.4, and the results are to be

reported in connection with the corresponding non-frosting steady-state

test at 32*F C0*C) specified in section 2.2.1. The calculation procedure is described in section 5.5.

2.5 INDOOR-SIDE AND OUTDOOR-SIDE AIR QUANTITY

All steady-state and cyclic heating and cooling tests shall be conducted

at the outdoor-side air quantity requirements specified in section 5. 1.4.

4

of ARI Standard 240-76 and ARI Standard 210-74, respectively. All

steady-state and cyclic heating and cooling tests shall be conducted at

the indoor-side air quantity specified in section 5. 1.4. 3 of ARI Standard 240-76 and ARI Standard 210-74, respectively. Rated heating and

cooling capacity shall refer to the capacity of the system as measured

at the highest speed at an outdoor dry-bulb temperature of 47®F (8.3°C)

and 95°F (35*C) , respectively.

3. RECOMMENDED TEST PROCEDURES

3.1 INTRODUCTION

The recommended test procedures have been divided into steady-state

procedures, part-load (cyclic! procedures, and frost accumulation and

defrost test procedures. They have been established within the general

framework of providing adequate and reliable test data on the performance of prototype heat pump systems at a reasonable investment of

funds, time, and effort by the developer. Where feasible, the steadystate test procedures have been adapted from the ASHRAE Standard 37-69,

8
and the part-load procedures have been adapted from references 6 and 7.

As additional performance data and operating experience are acquired on engine-driven systems, additions or modifications to these procedures

may be required.

3.2 STEADY-STATE TEST PROCEDURE

The following test procedures pertain to the steady-state heating and

cooling tests specified in section 2.2 and illustrated in table 1 and

figures 1-3.

3.2.1 Applicable Test Method

ASHRAE Standard 37-69 describes the following four test methods that may

be used to determine the heating and cooling capacities of unitary

electric heat pump equipment:

a) Air-Enthalpy Method - Indoor Side

b) Air-Enthalpy Method - Outdoor Side

c) Compressor Calibration Method

d) Volatile Refrigerant Flow Method,

Because of differences in engine-driven heat pump types and differences

in heat recovery equipment configuration, the test method most applicable to all equipment types is the Air-Enthalpy Method - Indoor Side.

Therefore, all steady-state heating and cooling tests on engine-driven

heat pump equipment shall employ this method as the required test method.

Prototype developers are encouraged, however, to simultaneously employ

additional measurement and analysis techniques as a check on the overall

experimental system. Performance calculations should be based, however,

only on the results of the Indoor Side Air-Enthalpy Method. Test room

requirements are the same as those specified in section 11.1 of the

ASHRAE Standard 37-69.

3.2.2 Instrumentation and Required Data

The steady-state performance tests shall have the same instrumentation

and data requirements as those specified in section 10 and table II of

ASHRAE Standard 37-69, with the following additions or modifications:

(a) Liquid or gaseous fuel quantity shall be measured with a suitable integrating type meter having an accuracy within + 2.0%

of the quantity measured.

Cb) The lower heating value (LHV) of a representative sample of

fuel shall be determined by suitable chemical or calorimetric

analysis and shall be used in all subsequent input fuel energy

calculations.

Cc) The dry-bulb temperature of the air entering and leaving the

indoor side Cor the difference between these two temperatures)

,

and the dry-bulb temperature of the air entering^

9
the outdoor refrigerant coil shall be continuously recorded

with instrumentation having a total system accuracy and precision within + 1. 0°F (0.6°C).

Cd) The electric energy usage of all components and accessories

Cfans, pumps, blowers, control circuits, etc.) shall be

measured with watt-hour meters that are accurate to within

+2.0% of the quantity measured.

3.2.3 Test Operating Procedure and Results

The engine-driven heat pump system and any associated test room reconditioning equipment shall be operated for at least one^half (1/2) hour

under equilibrium conditions before any steady-state heating or cooling

performance data are recorded. Data shall then be recorded at tenminute intervals until four consecutive sets of readings within the

tolerances specified in table 2 have been attained.

Under some conditions of heating, a small amount of frost may accumulate

on the outdoor coil, and a distinction needs to be made between frosting

and non-frosting operation during the test period. For purposes of

these procedures, the test is considered non-frosting provided that the

dry-bulb temperature of the air leaving the indoor and outdoor units

does not deviate by more than 2.0°F (1.1°C) during the test. When this

tolerance is exceeded because of frost, the defrost cycle shall be

initiated manually and the steady-state test repeated. For those

systems with controls which periodically initiate a defrost cycle based

upon time, the control system shall be modified to prevent defrost

during the steady-state heating tests.

The steady-state heating and cooling results shall include each of the

following quantities calculated using the procedures described in

section 5.1:

(a) Total heating or cooling capacity, Btu/hr (J/sec)

.

(b) Input fuel energy, Btu/hr Gl/sec).

Cc) Total electric power input to all components and accessories,

watts

.

Cd) Steady-state Coefficient of Performance.

Sections 12.1.5-12.1.7 of the ASHRAE Standard 37-69 shall apply for all

steady-state heating and cooling test results.

3.2.4 Test Tolerances

All steady-state heating and cooling tests shall be conducted within the

applicable test operating and test condition tolerances specified in

table 2. Test operating tolerance is defined as the greatest permissible difference between maximum and minimum instrument observations

during the test. Test condition tolerance is defined as the maximum

permissible variation of the average of the test observations from the

desired test condition. Variations greater than those prescribed in

table 2 shall invalidate the test.

10
3.3 PART-LOAD (CYCLIC) TEST PROCEDURE

The following test procedures pertain to the cyclic dry-coil and nonfrosting tests specified in section 2.3 and illustrated in table 1 and

figures 1-3.

3.3.1 Applicable Test Method

All part -load (cyclic) tests shall employ only the Air-Enthalpy Method - Indoor Side, and each test shall be performed in conjunction with its

corresponding steady-state test as described in section 2.3.

3.3.2 Instrumentation and Required Data

The instrumentation and data requirements for the cyclic test shall be

the same as those specified in section 3.2.2 for steady-state tests. An

additional requirement is that the instrumentation used to measure the

air temperature entering and leaving the indoor side, or the difference

between these two temperatures, shall have a response time of 2.5 seconds

or less. Response time is defined as the time required for the instrumentation to attain 63% of the final steady-state temperature difference

when subjected to a step change of 15°F (-9.4°C) or more.

3.3.3 Test Operating Procedure and Results

Each cyclic test shall immediately follow the corresponding steady-state

test described in section 2.3 and illustrated in table 1. At the conclusion of the steady-state test the engine-driven heat pump system

shall be manually cycled "off" and "on" until steadily repeating ambient

conditions are achieved in both the indoor and outdoor test chambers,

but for not less than two complete "off,, / M on

M cycles. Without disrupting the cycling process, the system shall then be operated for an additional "off” /"on" cycle during which the required test data shall be

taken. During this test cycle the indoor and outdoor conditions shall

remain within the tolerances specified in table 2.

A complete "off" /"on" cycle shall be defined as an "off" period of 24

minutes and an "on” period of six minutes. This results in a cycling

rate of two cycles per hour which is approximately the rate at which

thermostats are set in order to maintain building temperature variations

within 3°F (1.7°C) when operating under a 20% heating or cooling load.

For those engine-driven systems which permit the compressor to be

quickly disengaged from the prime-mover, cycling "off” and "on" shall

refer to the refrigerant compressor operation. For those systems whose

refrigerant compressor is permanently coupled to the prime-mover,

cycling "off" and "on" shall refer to the initiation of that action

which results in the most rapid stopping and starting of the refrigerant

compressor, respectively. Depending on the type of engine, this may

require decreasing or stopping the fuel flow to the engine, stopping or

11
diverting the working fluid from the engine’s expander, equalizing

pressures across the expander, etc. The indoor fan shall cycle "off"

and "on" with the compressor, but its cycling times may be delayed or modified by controls which are normally installed with the system.

Operation and control of the engine and associated components during the

"off” and "on" periods shall be determined by the manufacturer. Any

fuel consumed by the engine and any electric power used by pumps, fans,

blowers, controls, etc., during the "off" period shall be measured,

however, and included with "on" period energy in subsequent performance

calculations. Also, provisions should be made to measure and include

any "coast-down" heating or cooling which may occur after action has

been initiated to stop the refrigerant compressor. If, during the

cyclic heating tests, the engine continues to operate during the "off"

period, the recovered engine waste energy shall be measured and included

with "on" period energy.

The cyclic test results shall include the following quantities calculated

for the complete test cycle using the procedures described in section 5.2

(a) Total heating or cooling capacity over the test cycle,

Btu (J)

.

(b) Total input fuel energy over the test cycle, Btu (J)

.

(c) Total electric power input to all components and accessories

over the test cycle, kWh.

(d) Cyclic Coefficient of Performance.

The steady-state and cyclic test results shall be used to calculate a part-load degradation coefficient C^ according to the calculation procedures outlined in section 5.2.

3.3.4 Test Tolerances

The cyclic heating and cooling tests shall be conducted within the test

operating and test condition tolerances specified in table 2. In order

to meet the required air temperature tolerances, it is recommended that

electric resistance heaters be installed in the indoor and outdoor

chambers to offset the fluctuating heating and cooling* loads imposed by

the cycling equipment.

3.4 FROST ACCUMULATION AND DEFROST TEST PROCEDURE

The following test procedures pertain to the single-point frost accumulation and defrost test specified in section 2.4. The results of the test

will be combined with the results of a steady-state non-frosting test,

performed under the same ambient conditions, to form a single-point

frost degradation coefficient C , „ according to the procedures outlined

in section 5.5.

6

3.4.1 Applicable Test Method

The frost accumulation and defrost test shall be conducted using the

Air-Enthalpy Method — Indoor Side.

12
3.4.2 Instrumentation and Required Data

The instrumentation and data requirements shall be the same as those

specified in section 3.2.2 for steady-state tests. They shall also

include the 2.5-second response requirement for temperature instrumentation specified in section 3.3.2 for cyclic tests.

3.4.3 Test Operating Procedure and Results

The engine-driven heat pump system shall be operated for at least onehalf (1/2) hour under equilibrium ambient conditions prior to the actual

test. Then, in order to assure that the outdoor refrigerant coil is

frost-free at the start of the test, the system shall be operated

through a manually induced but normally terminated defrost period. The

test shall then commence at defrost termination and shall continue

through the frost accumulation and subsequent defrost periods. It shall

terminate at defrost termination. Defrost initiation and termination

shall be governed by the normal controls associated with the system.

Data shall be taken at ten-minute intervals during the frost accumulation heating period, and the times at defrost initiation and termination

shall be recorded. Since defrost method, control, and mode of operation

will generally be dependent upon specific equipment configuration and

engine type, they shall be determined by the manufacturer and shall not

be part of these test procedures. However, the total fuel consumed by

the engine, the total electric power used by associated components

(excluding resistance heaters which may be installed) , and the total

heating and cooling done during the defrost period shall be measured and

included in the overall performance calculations.

The test results shall include the following quantities calculated for

the frost accumulation and defrost cycle (defrost termination to defrost

termination) using the procedures described in section 5.5

(a) Net heating capacity, Btu (J)

(b) Total input fuel energy, Btu CJ)

(c) Total electric power input, kWh

(d) Frosting-defrost Coefficient of Performance

These results shall be combined with the results of the steady-state

non-frosting test to determine a frost degradation coefficient

^ using the procedures outlined in section 5.5.

3.4.4 Test Tolerances

The test operating and test condition tolerances which must be maintained

during the frost accumulation and defrost test are specified in table 2.

The indoor and outdoor conditions shall be based only on the values

occurring during the heating period.

13
4. BUILDING LOADS AND CLIMATE SPECIFICATIONS

4.1 INTRODUCTION

The seasonal performance and seasonal cost of operation of any heat pump

system depends not only upon the instantaneous performance of the system

under specific indoor and outdoor conditions, but also upon the type of

building in which it's installed and its thermal load, and the climate

in which the building is situated^ Because of the wide range of heating

and cooling climates in the United States, and the even wider range of

building types and thermal requirements, it becomes impossible to adequately characterize the performance of a heat pump system for all

regions of the country with one or two seasonal indicators. Because of

waste heat recovery, however, engine-driven heat pump systems are most

applicable to northern climates where the energy requirements are predominantly heating and the engine's recovered waste heat can be effectively utilized. There will be applications, however, in which the

system is located in a southern climate. In these instances, the cooling requirements may be approximately equal to, or even greater than,

the heating requirements. In order to provide the prototype developer

some latitude and flexibility in establishing the seasonal performance

of his product, the following evaluation approach is recommended for

seasonal calculations:

(a) assume a generalized northern climate and a generalized

southern climate in which an engine-driven heat pump system is

most likely to be located.

(b) for each climate, assume representative heating and cooling

design temperatures at which the system heating and cooling

capacities equal the building energy requirements

.

Cc) assume heating and cooling loads typical of a residential

building, and of a light commercial/ Indus trial building.

Cd] for both seasons, use the temperature bin method to determine

the seasonal performance factor and the seasonal operating

cost based upon the appropriate building type and the choice

of one of the two generalized climates.

While this seasonal rating approach suffers the inevitable disadvantages

associated with climate and building generalization, it does provide a suitable technique for assessing the relative seasonal performance of

different heat pump systems which are designed for the same market and

the same general climate.

4.2 GENERALIZED CLIMATE

Tables 3 and 4 list temperature bin information and the fractional hours

in each bin during the heating and cooling season for the generalized

northern and southern climates. The tables are based upon residential

and commercial/industrial applications, respectively. The fractional

hours in each bin for northern climate were determined by averaging

weather data from six U.S. cities, and the fractional hours for the

14-
southern climate were obtained by averaging data from eight cities.

Table 5 lists average heating degree days DD, heating design temperature

HDT, and total bin hours in heating BHH, and cooling BHC, for each

climate. The cooling design temperature is 95°F (35°C) for both climates.

4.3 BUILDING LOADS

Heating and cooling requirements are determined for residential applications and for light commercial/ industrial applications by assuming a linear relationship between building load and outdoor temperature. The

heating and cooling load lines extend from zero load at a specified

change-over temperature T , to values which equal the steady-state

heating and cooling capacities at assumed outdoor design temperatures of

HDT and 95°F (35°C), respectively. The building load-temperature relationship is given by:

BL (T .

)

3

Q (HDT) [5j - 2]

b O _ —

C

T . 3 < T

c

Q (95) [5j - 3]

BL(V

" ' 95-- T

i '

(4.1)

where j = 1, 2, 3,...,n. Q (HDT) and Q (95) are the measured steadystate heating and cooling clpacities of tEe system at the assumed design

temperatures, and n represents the total number of non-zero temperature

bins. T. is the representative temperature of the jth bin and is given

by: J

T. = T + 2 - 5j , 3 c T. = T —3 + 5 j , 3 c The change-over temperature T , for residential applications is assumed

to be 65°F (18.3°C). For ligSt commercial/ industrial applications, T

was determined to be 55°F (12.8*CJ. This results from assuming a

u constant building internal load Q. equal to one-third of the building

shell cooling load at 95°F C35°C)^ or equivalently: Q. = BL('95)/4. The

residential heating and cooling load lines are illustrated in figures 1-3.

5. CALCULATION PROCEDURE

T. < T

3 c T. > T

3 c

C4.2)

5 . 1 GENERAL

The steady-state heating and cooling capacity Q (T ) at each test point

shall be calculated using the appropriate equations^ specified in

section 3.7 of the ASHRAE Standard 37—69. For heat pump systems which

may not have indoor-air circulating fans furnished as part of the system,

their measured heating and cooling capacities shall be adjusted by

15
adding or subtracting, respectively, 1250 Btu/hr per 1000 SCFM (0.78 watts

per dm /s) of indoor air flow to or from the measured values. Similarly,

366 watts of electrical energy per 1000 SCFM shall be added to the total

measured steady-state electrical power input E (T . )

.

ss 3 The input fuel energy rate Q^(T.) under steady-state conditions at bin

temperature T . shall be determined from:

• • Q

f

(T ) = m

f

(T )

• (LHV) (5.1)

where m (T.) is the fuel mass (or volume) flow rate at temperature T.

and is determined from the fuel quantity measured over the specified"*

test period. LHV is the lower heating value of the fuel expressed on a mass (or volume) basis.

The steady-state coefficient of performance COP (T.) of an enginedriven heat pump system based upon source energy

S

sh^tll be determined

from:

COP (T.) ss 3

Q (T.) ss 3 (5.2)

Q-(T.) + 3.413

f 3

: (T . )1

0.3 J

Where E (T.) is the steady-state electrical power input at temperature

ss 3 T., 3.413 converts watts to Btu/hr, and the factor 0.3 is an approximation for the efficiency of electric power generation and transmission.

The steady-state capacity, input electric power, and input fuel energy

at bin temperatures other than the test points shall be determined

through linear interpolation of data from the test points immediately

adjacent (above and below) to the bin temperature in question. In those

instances where the bin temperature is either greater than or less than

the test points, the data shall be linearly extrapolated from the

two closest points. For residential heating applications, table 3

indicates that steady—state tests are conducted at bin temperatures T.

where j = 4, 7, 10, 13, 16. For commercial/indus trial applications, ^ table 4 indicates heating tests are conducted at bin temperatures T.

where j = 2, 5, 8, 11, 14. j

5.2 PART-LOAD (CYCLIC) PERFORMANCE

In order to determine the seasonal performance of engine-driven heat

pump equipment, several part-load parameters must first be defined or developed. A heating or cooling load factor X(T.) is defined by:

3

16
X(T ) ={ (5.3)

0

|BL (T.)

Q (T.) ss 3

T. < T

3 off

BL (T . ) < Q (T.)

3 ss 3

BL(T.) > Q (T.)

3 ss' 2

where T is the outdoor temperature at which the compressor is automatically turned off during the heating season (if applicable)

.

The results of the cyclic and steady-state heating and cooling tests

shall be used in the following equations to calculate (a) Total heating

or cooling during one "off” /"on" cycle Q (T ) , (b) cyclic coefficient of performance for the test cycle 65F ) , (c) cyclic degradation coefficient C^, and (d) a part- load ^ctor^LF [X(T . ) ] at bin

temperature T.. T denotes the dry-bulb temperature at^which cycling

tests are coniuctecP’

r<(80 o F and 47°F) .

Q (T

eye eye

60 V c r

) = . P.a

v' [1 + W ] n

(5.4)

(time indoor- fan goes off)

-f

where T = |[TH

(t) T

L

(t)] dt

(time indoor fan goes on)

and V, c , v', W , TTT (t), and T_ (t) are defined in the nomenclature,

pa n n H L

COP (T ) eye eye

Q (T ) eye eye

Q-(T ) + 3.413

f eye

E (T ) eye eye O

(5.5)

where Qf (T ) is the total input fuel energy during the complete 30

minute tesB^cycle. It is based upon the mass (or volume) of fuel

consumed and the fuel's LHV. E (T ) is the total input electric

energy measured during the test

C^ycleTC

For those heat pump systems

which may not have indoor-air circulating fans, the calculated heating

or cooling, and the measured input electric energy during one cycle

shall be adjusted for the effect of a fan. The correction procedure

shall be the same as that described in section 5.1 for steady-state

17
tests, except that the correction shall equal the total energy

transferred during the time of fan operation instead of a fixed energy

rate.

Heating and cooling tests of electric heat pumps have indicated (refs. 6

and 7) that the cyclic-to-steady-state COP ratio [COP (T ) / (COP (T )

]

at any temperature T. decreases approximately linearly7 as the load factor

X(T . ) decreases. Assuming a similar variation for engine-driven heat

pum^»s, a part-load degradation coefficient C^ shall be calculated as follows:

C

D

1

T—

1

1

"cop

eye

(t

eyen

COP (T )

L ss eye

1

t

—

1

1

fQ (T ) " eye eye

0.5Q (T )

i- ss eye J

(5.6)

where 0.5 Q (T ) is the total heating or cooling which would occur during the 8^5 AAur test cycle if steady-state conditions existed. C^

is determined from the results of the steady-state and cyclic heating

and cooling tests specified in section 2.3, and it is equal to one minus the zero-load factor intercept of the cyclic-to-steady-state COP

ratio [1 - COP (T.)/C0P (T.) at X(T.) = 0], Laboratory tests of

electric heat pAmps'' [ref . S 8] lave show! that C^ is constant over a wide

range of load factors [X(T.)], and is relatively independent of outdoor

temperature. Denoting COP'' (T.)/C0P (T.) as a heating or cooling partload factor PLF[X(T.)], theA

C

C "'and t8l linear relationship between PLF

(X(T.)) and X(T.) miy be used to express PLF(X(T.),) as follows:

PLFCXCT.)) =

c5p

y, C

(T

3.T = 1 - Cptl-XCTj)] (5.7)

This expression shall be used to determine the heating or cooling cyclic

coefficient of performance COP ^(T.) at any temperature T_.

.

5 .

3

PART-SPEED PERFORMANCE

The capacity, input electric energy, and input fuel energy of enginedriven heat pump systems are generally nonlinear functions of compressor

speed as well as one another. The performance of variable-speed heat

pumps at compressor speeds intermediate to the maximum and minimum speed

shall be determined through the use of a normalized part-speed input

energy factor \p . When the total input fuel and electric energy at

18
temperature T. is denoted by E^ _£T.), where superscript i designates

intermediate 'Jpeed (Z=i) , then E^ ^T . ) may be determined from

E^ (T ) = E° (T ) + ^[E* (T ) - E° (T^ ) ] (5.8)

The superscripts 0 and 1 denote values at minimum speed (Z=0) and

maximum speed (Z=l) , respectively, ip shall be determined from:

1 / 2

"

ip 1 = £

^ = ilf

1/2

a

1/2

i i— 1/2

a ; 0<a <a

(5.9)

1 - Jfe 1 / 2

"

1 - a

1/2

J

, i 1/2. 1/2. i—

,

(a -a ) ; a <a <1

where a is a normalized part-speed capacity factor defined at temperature T . by:

3 BL (T.) - Q° (T.) a

1 = 2 -S-S-JQ„ (T.) - (T (T ) ss j ss j

(5.10)

1/2 1/2 The values of ip and a required in equation (5.9) are determined

for both operating modes from equations (5.8 and 5.10), respectively.

Their evaluation is based upon intermediate speed tests at Z=l/2 specified in section 2.2.3 and conducted at outdoor-dry-bulb temperatures of

80°F (26. 7°C) and 17°F (-8.3°C).

Equations (5.8 - 5.10) indicate that ip 1

and a

1

vary from zero to one and

that the relationship between them is approximated by two straightline segments with the discontinuity at Z=l/2. Experimental data indicate that the relationship for heating is different than for cooling,

but that each is essentially independent of outdoor temperature.

The purpose of equations (5.8 - 5.10) is to provide means for estimating

the total input fuel and electric energy E (T ) at any speed and temperature. Accordingly, these equations shall be used in the following

calculation procedure:

(a)

(b)

1/2 1/2 Determine 'p and a from equations (5.8 ant). 5.10)

heating and cooling using measured values of Q (T . ) and

4

(T.), (Z=0 , 1).

SS ^

Determine a

1

at intermediate speed Z=i from equation (5.10)

(c) Determine ip 1 from equation (5.9) based upon the results of (a)

and (b)

.

19
5.4

(d) Determine E^(Tj) from equation (5.8).

SEASONAL PERFORMANCE FACTOR AND SEASONAL OPERATING COST

5.4.1 Single-Speed Operation

The total heating or cooling done in the jth temperature bin is

Q(T.) = n. BL(T.) (5.11)

3 3 3 where n. is the number of heating or cooling hours in the jth bin, and

BL(T.) Ind T. are given by equations (4.1 and 4.2), respectively. The

total heating or cooling done during a season is equal to the summation

of the energy in each non-zero temperature bin and may be expressed as

n Q(T ) n

Q

= N .1. —r~— = N .1. 3=1 N j=l BL(T.)

3 (5.12)

n

n is the number of non-zero temperature bins, N = Z n. is the total

3=1 3 heating or cooling season hours in all the bins. (n./N) are the fractional bin hours and are listed in tables 3 and 4 fol residential and

commercial/industrial applications, respectively.

When the steady-state heating or cooling capacity at temperature T. is

greater than the building load [Q (T.) > BL(T.)], the total input"1 fuel

and electric energy in the jth temperature bin'' is:

n. BL (T .

)

f Ct i = _3 —2

T U

j

; COP (T.)

eye y

(5.13)

Equations (5.3, 5.7, and 5.2) may be used to express equation (5.13)

in terms of the load factor X(T.), part-load factor PLF[X(T.)], and the

3 . 3 input fuel and electric energy Q.. (T . ) and E (T . ) . Accordingly

t i ss i

n. X(T .

)

E fT 3 = 3 3

3 PLF (X(T . ) ) vv e

ss

(v (5.14)

When BL _(T. ) > Q (T.), equations (5.3 and 5.7) indicate that X(T.) = PLF(X(T . )}-, = 1. Equation (5.14) is, therefore, also applicable inder

these conditions (assuming that T. > T ). It does not, however,

include the supplemental energy required when BL (T . ) > Q (T . )

.

The

total input fuel and electric energy (excluding reiistancl h4at) for the

entire heating or cooling season becomes (for T. > T __):

3 off'

20
SPF

a

E = N E E (T ) 3= 1 - J ' N

n N E

j=l

- - n

.

2

L

X(T ) 1

mm m mm w 1^413 * 0.3 ss

v j; (5.15)

During heating when BL(T.) > Q (T.), the supplemental energy required

in the jth bin is: J ss 3 W= n

j

t BL <V ' Q

ss

(T

: )]/ri s (5.16)

D is the efficiency of producing the supplemental energy from primary

fuel. If electrical resistance is used, it is assumed that r| =0.3.

The supplemental energy required for the entire heating season becomes:

QR

N

j=n' N

n QR(T .

)

n /n

N

jSn , L-l tBL CT.)-Q

ss

<T.)] /lls (5.17)

where n* is the lowest temperature bin at which BL(T.) > Q (T.). The

seasonal performance factor SPF is defined as: ^ ss j

SPF =

et

+ qr

(5.18)

Substituting equations (5.12, 5.15, 5.17), into equation (5.18) yields:

n

E

Jfci

n_U

N

BL (T )

n /n.\ X(T . ) T. ai ?

j =1\N / PLF (X(T_. )

) j^f

(T

j

^ +

0.3

Ess

( V

n n 7i BL (T . ) - Q (T.)

3 ss 3 (5.19)

/n

The second summation in the denominator is zero for .cooling calculations.

An estimate of the seasonal operating cost SOC, is given by:

SOC = N .E.. 3=1

X(T ) PLF (X (T )

)

Qf (T.)(CF

) + <C

E

) Ess

(T3

n

+

:Snn

.

C

"

r- —L

S

l N

• L. oJ SS 3 (5.20)

21
C , C , and C denotes the cost of engine fuel ($/Btu), the cost of

electric energy ($/Wh), and the cost of supplemental energy ($/Btu). If

the supplemental energy is electric resistance heat, then C

g =C

E

and

n =1. As before, the second summation is zero during cooling. The

average total bin hours for heating and cooling, and for either climate

and for both building applications are given in table 5. The steadystate capacity Q (T.), input electric energy E (T.), and input fuel

energy (T.) afSbii temperatures other than til ttst points shall be

determine! ftom linear interpolation of the test data as described in

section 5.1.

The residential or commercial/ industrial SPF and SOC shall be determined

from equations (5.19) and (5.20) for both the heating and cooling

seasons, and for either climate. Table 6 is a calculation sheet which

may be used for systematically calculating these seasonal parameters.

5.4.2 Two-Speed/Dual-Capacity Operation

The seasonal performance factor SPF and the seasonal operating cost SOC

of those engine-driven systems with two-speed compressor capability, or with some other means of achieving dual-capacity operation, are determined from:

SPF =

n ~n

, N

BL(T.)

1 vv +

.?

,

N

(5.21)

SOC = n

J=n’

Vlii

N

(5.22)

where n., N, n

T , and C are defined in section 5.4.1, and [n./N] are listed In tables 3 andS

4. E^(T.) represents the total fuel Pnd electric

energy input to the jth temperature bin, E^, (T.) represents the total

cost of that energy, and Q (T.) denotes any supplemental energy required.

Evaluation of these quantitieP is discussed subsequently. The building

load BL(T.) is given by:

BL(T ) = (HDT)(5j-2)/(T +5) , J s s c

BL (T ) = q] (95)(5j-3)/(95-T ) , J s s c

T . <T

3 c (5.23)

T . >T

3 c

22
where the superscript 1 denotes high-speed (greatest capacity) operation, and superscript 0 will subsequently denote low-speed (smallest

capacity) operation.

*2

The steady-state heating and cooling capacities Q (T.), electrical

power input E ^ and input fuel energy rate Q ^ (T . f

S reqAired in subsequent calculations at bin temperatures other thaA the test points shall

be calculated (as described in section 5.1) through interpolation of the

two test points adjacent to the bin temperature in question. As shown

in figure 2, low speed (2=0) tests are conducted over the 47°F to 17°F

temperature range, and high speed (Z=l) tests are conducted over the

17°F t o -13°F range. Tables 3 and 4 give the bin temperatures which

correspond to the test points for residential and commercial/industrial

applications, respectively. If the bin temperature in question lies

outside the range of test points, the result shall be linearly extrapolated from the two closest test points.

E

t (T.)/N, E

t

’(T.)/N, and Qr(T.)/N required in equations (5.21 and 5.22) are Aetermined According to tAe operating regimes I — IV discussed below:

Regime I :

' o BL(T.) < Q (T.) and the system cycles between off and low-speed (smallest

capacity) operation in order to meet the building load. It is assumed

that T. > T

J off

V!ii_

N

n

.

N

X°(T )

J PLF°[X° (T_. ) ]

Q°

f

(T ) + 3.413

'*0

E

U

(T.) ss r

0.3 C5.24)

et

? (T.)

N

n ’ X° (T^

)

l?J PLF°[(X°(T

j

)])

Q?(Tj )(V + CC

E

) e“

s (T.) (5.25)

o BL(T

i }

where X (T . ) =

J -o Q (T.) ss 2

(5.26)

(5.27)

PLF°[X°(T )] = C° [ 1-X° (T^ )

]

(’5.28)

23
Regime II :

* i

BL(T.) > Q (T.) and the system operates continuously at high-speed

(greatest clpaiity) with supplemental heat required during the

heating mode to meet the building load.

VLi

N

E ' (T . ) T r

N

n.—

N

/ E

1

(T.)

Q

f

(I.) + 3.413

[?) [$<v &g +

[

cE ] *i»<v

(5.29)

(5.30)

Q_(T.

N M3 BL (T . ) - Q

1

(T.)

1 s. s .1.

(5.31)

If T. < T Q^(T.) = E

1

(T.) = Q

1

(T . ) =0, and SPF = n

3 off f 2 ss 2 ss 3

<

Regime III ;

* o — — * 1

Q (T.) < BL(T.) < Q (T.) and the system cycles between off and highspied"' (greatest capacity^ operation in order to meet the building load.

It is assumed that T . > T

3 off*

1,

hi

x ( v

E^(TJ

PLF (X (T ))

X

X (TJ lil „ r^i x (T

i N l- N J PLF

1

(X

1 (T.))

v 3

r* i 1

E (T.)

ss 3 0.3 J Q^(T ) + 3.413

Q^(I.)(C

?

) + (C E) E^CTj)

(5.32)

(5.33)

Qr

(T .)

(5.34)

BL(T ) where X (T.) = — J

3 Q

1

(T .

)

ss 3

(5.35)

PLF

1 (X^T )) f= 1 C

1

[1 - X

1

^)] (5.36)

24
Regime IV : *0 — — *1

Q (T.) < BL(T.) < Q (T.) and the system cycles between high-speed

(freaiest capacity) operation and low-speed (smallest capacity) operation. It is assumed that T. > T

3 off

VV

N

n

.

LN j

X° (1j

)

Q°(T.) + 3.413(^3^

'E° (T .

)

+ X (T ) (Tj ) + 3.413

'e 1

(T.)^ ss 1

V 0.3 ,

(5.37)

e

t

'(t ) Nn.-1

N x°(t ) Q°(T.) (C?

) + (CE) E°

s (T.)

+ X (T ) Q^(T.) (CE

) + (CE) E^(T.)

(5.38)

VV

-v--°

0 where X (T.) =

<£Q (T.) , _ss J_

.BL (T .

)

!_

qL(V ss 3

* 0

Q„(T.)

ss j

(5.39)

(5.40)

X

X

(T.) = 1 - X°(T.) . 3 J (5.41)

The residential and commercial/industrial SPF and SOC of two-speed /dual”

capacity heat pump systems shall be determined from equations 5.21 and

5.22 for both seasons and for either climate using equations 5.23 - 5.41 as required. Table 7 is a calculation sheet which may be used for

systematically calculating these seasonal parameters.

5.4.3 Variable-Speed Operation

The evaluation of the seasonal performance factor SPF and the seasonal

cost of operation SOC of variable speed heat pumps is very similar to

the procedure described in section 5.4.2 for two-speed heat pumps. The

SPF and SOC are given by equations 5.22 and 5.22 , respectively. The

building load BL(T.) is given^by equation 5.23 , and the steady-state

heating and coolinj capacity Q (T.), electrical power input E (T.),

and input fuel energy Q (T.) art determined from linear interpolation of

25
adjacent test points. Superscripts 0 and 1 shall designate minimum and

maximum speed, respectively. The total input fuel and electric energy

EL(T.)/N, its total cost E

t

'(T.)/N, and the supplemental heat required

T j J are determined according to operating regimes I-III. Regimes I [BL(T.) < Qg S

(T.)] and II [blO^) > Q^C^)] are exactly the same as in

section 5.4.2. E_(T.)/N, E'(T.)/N, and Q (T ) /N are given by equaT j 13 K 3 tions 5.24-5.26 for regime I and by equations 5.29 - 5.31 for

regime II.

Regime III :

,0 - ;i

Q (T.) < BL (T . ) < Q (T.), T. > T ff , and the system is operating

ss 3 J as J 3 continuously at a speed such that Q (Tj) = BL(T.). Therefore, Q (T . )

/

N=0 and X(T . )=PLF[X(T . ) ]=1. Superscript i denotes normalized " J intermediate-speed (Z-i) . The total input fuel and electric energy are obtained from equation 5.8 .

E

T

(T ) E^(T ) E°(T ) M » . J ~ J.i . N N N

+ ip'

r E^(Tj E°(T.)

N N

C5.42)

et

'(t ) —— J N

E°(l)

where J—

N

e

t

(V

N

E^(T )’ E°(T )

. — —1 Mi —j N

'n

.

N

N N

rn.l r. n / E° (T . ) \ ”[nJ W+ 3.413 (-BJ-)

Q^CT.) + 3.413pf_l

(K„ (T.)

0

f

N

(5.43)

(5.44)

0 w1

N

(E^(T )’

. i. J N

‘

n

.

N

n." .J. N

• 10

?

(T.)(C

f

) + (CE) Ess

CT.)

Q

f

(V<V + (cE

) i^CT )

C5.45)

26
ip 1

is the normalized part-speed input energy factor and is given by

equation. 5.9. as a function of the normalized part-speed capacity

factor a

1

, a

1

, in turn, is deterji^ed at intermediate speed Z=i from

equation 5.10 . The values of ip and a required in eauation 5.9

are determined for both heating and cooling from equations 5.8 and

5.10 . Table 7 is a calculation sheet which may be used to systematically calculate the heating and cooling SPF and SOC of variablespeed systems for both seasons, and for either climate or building

application.

5.5 FROST ACCUMULATION AND DEFROST CALCULATIONS

The frost degradation coefficient is defined by:

'def

C0Pdaf (32:>

COP (32) ss (5.46)

where COP (32) is the steady-state coefficient of performance at the

32°F (0°cf

S

test point. It is determined from equation 5.2 using the

calculation procedures described in section 5.1. OOP f (32) is the

coefficient of performance under frosting-defrost conditions, and is

determined from:

COP

def (32)

W32)

V32) Ww325

(5.47)

Q^(32) is the total input fuel energy during the complete frost accumulation and defrost test. It is based upon the mass (or volume) of fuel

consumed and the fuel's LHV. E^

e^(32) is the total input electric

energy measured during the test. (^^(32) is the net heating done

during the test period, and is determined from:

W32)

60 v c r pa

v (1 + W ) n

.

»

n

(5.48)

(time indoor fan goes off)

where T = j

[T^t) - T al (t)] dt

(time indoor fan goes on)

and V, c , v ', W , T 0 (t), and T . (t) are given in the nomenclature, pa n n a/ al

The flowrate V shall be an average value calculated at several intervals

throughout the heating portion of the test. For those systems without

indoor-air circulating fans, the calculated heating done and the measured

input electric energy shall be adjusted for the effect of a fan. The

27
correction procedure shell be the seine es thet described in section 5 • 1

for steedy-stete tests, except thet the correction shell equel the totel

energy trensferred during the time of fen operetion insteed of e fixed

energy rete.

6. RECOMMENDED RATING REQUIREMENTS

The objective of the procedures recommended in this study hes been to

provide feir end eccurete methods for testing prototype engine-driven

heet pump systems heving different design cherecteristics , end for

estimeting their seesonel performence end seesonel opereting cost.

Inherent in this objective is e requirement thet the results of the

tests end celculetions be reported in such e wey thet the performence of

different prototype systems mey be effectively compered. Teble 8 is e reting sheet which requires thet the system under test be reted reletive

to its:

(e) Steedy-stete cepecity Q (T.), et the ARI reting points of

95°F (35°C) , 47°F (8.3°0f, Ind 17°E C-8.3°C), respectively.

(b) Steedy-stete coefficient of performence COP (T.), et the ARI

reting points. ^ (c) Seesonel performence fector SPF, for both heeting end cooling.

(d) Seesonel opereting cost SOC, for both heeting end cooling.

(e) Frost degredetion fector, C^^.

The seesonel peremeters SPF end SOC shell be besed upon the residentiel

building epplicetion for those systems which heve cooling cepecities et

the ARI reting point of 60,000 Btu/hr (17.6 kW) or less. The light

commerciel/industriel building epplicetion shell epply for those systems

with cooling cepecities greeter then 60,000 Btu/hr (17.6 kW)

7. LIMITATIONS OF THE RECOMMENDED TEST AND RATING PROCEDURES

There ere e number of limitetions essocieted with the recommended test

end reting procedures. Some ere inherent in eny test end reting progrem

which ettempts to cherecterize the performence of e system besed upon e finite end smell number of test points. These limitetions ere elmost

unevoideble end will not be discussed. The remeining limitetions ere more fundementel end indicete e need for further investigetion. These

ere discussed below:

(e) As discussed in section 2.2 end illustreted in figures 1-3

end teble 1, there ere e lerge number of steedy-stete tests

required. It is felt thet these tests ere required to ede—

quetely predict the performence of the system over e broed

renge of outdoor temperetures . As more opereting dete becomes

eveileble on engine-driven systems, however, it mey be possible to eliminete some of the steedy-stete tests.

28
(b) Cyclic testing of different engine-driven heat pump systems is

required under a variety of ambient conditions and cycling

rates. These tests should confirm and improve the accuracy

and generality of the procedure discussed in section 5.2 for

determining cyclic performance degradation. It is conceivable

that sufficient testing may lead to a default C

D

which may be

predicted based upon a system’s design and operating mode. If

such a prediction was possible, it might eliminate the need

for costly and time- consuming cyclic testing.

(c) It was noted in section 2.4 that the ideal way to account for

the deteriorating effects of frost on the outdoor coil would

be to apply a correction factor to all steady-state performance data obtained within the frost range, but that insufficient data currently exists to establish that correction

factor. Laboratory and field testing over a range of outdoor

temperatures and relative humidities is therefore required in

order to develop a general frost correction which may be

effectively applied to a broad range of engine-driven heat

pump systems.

(d) The recommended test and rating procedures have assumed that

the engine's waste heat is diverted to the outdoor side during

the cooling mode, and is therefore not utilized. While this

approach is generally justified for engine-driven systems

designed for northern climates where the cooling load is low

relative to the heating load, it will be unfair to those

systems which are located in southern climates and are .. designed to utilize the waste heat for such purposes as domestic or commercial hot water heating. Under these circumstances the test and rating procedures should be modified to

credit the heat pump system with engine waste heat utilization. This will require changes in the instrumentation

requirements, test requirements, and calculation procedures.

In addition, seasonal performance factor and seasonal operating cost determinations will require the specification of a generalized domestic or commercial hot water heating load.

Also required is the specification of an alternate means of

supplying energy to heat the hot water when the heat pump

system is on the "off" part of its operating cycle.

(e) The recommended test and rating procedures have been limited

to prototype, air-to-air, mechanical compression heat pump

systems. These procedures could readily be modified for

application to possible future commercially produced systems.

Considerable work would be required, however, to adapt these

procedures to absorption systems, or to mechanical compression

systems which do not use ambient air as the heat source or heat sink medium.

29
References

1. Gordian Associates, Inc., "Heat Pump Technology," Report Prepared

for the U.S. Department of Energy, Dec. 1977, pp. 72-93.

2. Auxer, W. L. , "Development of a Stirling Engine Powered Heat

Activated Heat Pump,',' Proceedings of the 12th Intersociety Energy

Conversion Engineering Conference, Washington, D.C., Sept. 1977,

pp. 397-401.

3. Friedman, D. , "Light Commercial Brayton/Rankine Space Conditioning

System," Proceedings of the 12th Intersociety Energy Conversion

Engineering Conference, Washington, D.C., Sept. 1977, pp. 172-178.

4. Swenson, P. F. , and Rose, R. K. , "Development of the High Seasonal

Performance Factor Gas Heat Pump," Proceedings of the 12th Intersociety Energy Conversion Engineering Conference, Washington, D.C.,

Sept. 1977, pp. 390-396.

5. Sarkes, L. A., Nicholls, J. A., and Menzer, M. S. "Gas-Fired Heat

Pumps: An Emerging Technology," ASHRAE Journal, Mar. 1977, pp.

36-41.

6. Kelly, G. E., and Parken, W. H. Jr., "Method of Testing, Rating and

Estimating the Seasonal Performance of Central Air-Conditioners and

Heat Pumps Operating in the Cooling Mode," National Bureau of

Standards, Washington, D.C., NBSIR 77-1271, April 1978.

7. Parken, W. H. , Kelly, G. E. , and Didion, D. A., "Method of Testing,

Rating and Estimating the Heating Seasonal Performance of Heat

Pumps," National Bureau of Standards, Washington, D. C. (in

publication)

.

8. Kline, S. J., and McClintock, F. A., "Describing Uncertainties in

Single-Sample Experiments," Mechanical Engineering, January 1953.

I 30
MODE

OF

OPERATION zowH

<333s33

<J

CM

>>a 3

<3

H 3 c H H

CO CO3l-i 3 Q CJ

Pd >*

Pd CJ

04

CO

>• o Q Ed 2 < H H Pd <2 H H

CO CO

<c SH3 W

s-l O pq O 2

T3 \mi PQ 3 Q O

a,E 3

a) s— H

waosozM3oo

CJ

CM

CMm

r-'. m

CTl •K

Pm oO

CO

II

PQQ

5-i OO3G

•K

•ic H

m 3 « 9 • CM CO m

vO

CO

i-H • CM CO rH CM CM • • • CO m CM *

-KCN rH CO

CO• CO• CM• CM CO m CO• CO s in

CO\ eg iH

»-H eg r-H r-H o • CM

CM• rH• r—1 • CO m CM *

-K CO CO CM rH rH cO • • • CM CO m

-cr cO

CM. • m • CM rH CN tH »-H eg r-H rH o CM • rH • CO mCM

•KK CO CO CM

Csl

H CO • • • CM CO m 3• sr• cO

rH

m • CM rH

r-H rH r"H rH r-H vO CM • • • CO m

CM

cn o uo

C

G

G c G

sO cn rH 1 1 O

O

O o O

•H 3 3 3 3 O eg eg CO mi mi mi mi 3

00 <r CO rH rH CJ CJ

a

a CJ * * 1 01 0) <u <u 0) CO CO CO CO 3

Pm9o CO Pd cO H CO pS CO H 3'

Pm Pm II Pd Z CO

a 3 0 0 H Pd Pd Pd PS O PQ S PS CJ 3

kQ 2 Pm Pd 3 o 3 O PS. Q PS 3 3

II it pa

H Pd P-4. 3 Z

Pd o Pd 3 3 O 3

PQQ PQ o Pd O'

O z 3 3 O Q Q CQ Ed PS o 3 g 2 2 PS Ed HI PS

pS

M pj5

H 3 H o CJ o Z O CJ- <2 <2 3 H' o 2 o • z Z 3 Z O 3

T3 i—i Q ><! rJ H. Hi 3 O 3 3

P-4 2 <2

H

H 3 3 a

M

M

H CO- 3 3 < a o

Pd

O Pd Pd <2 3 z 3

PC

H

H

H 3 3 <2 3 • &M 0LOv *

ARI

Standard

Rating

Points

**

Includes a

steady-state

dry

coil

test;

indoor

DB=80°F;

indoor

WB
TEST

OPERATING

AND

TEST

CONDITION

TOLERANCES

CO 00

4J c

rH -H 3 y

CO 0) 0) u

1-1 c

<D

AU 1-1 •H O A O 3 TJC y iH 3

rH M-l

CO

O > y

0) 3 £ rH

4-1 CO>

T3

<0 6

<U 3 y s X -rH CD X

CO

y e £

•h

y

4-1

A4-1 oC CD

4-1

4-1 CO

«oy

<-( oo

co c

x: -h

CO 4-1 CO co y y x: y3 l-i 4-1 O

co

h

i-c y

Q. • E r-

y *H

4-1 oy

xi

rH 1-1 3 O

X3

O I *3

4-1

C

y th 3 y • y x: 0 4-10 o o •OCX c o • •h in y rH y 4J —

A co u co b C o

CO

y o

4-J TJ X>

CO c

<v o CO

CO 4-J

y •H

4-1 CO oo cy

y

y

C o y

4-1 tH 3

rH c 4-1 oo o o 3 c o rH y

•H

y 4J

y

r-Hy

a

O rH 3 £ o •H ”3 y y o O 4-1 y y

rH 1 a. -a

•H s-% rH O y y 3 y •3 A X) l 4-1 1 >, y 4-1 y o c y o pti •H 3

He He

He

32
TABLE 3

GENERALIZED CL ELATES FOR RESIDENTIAL APPLICATIONS

Temperature

3in Number

j

Representative

Bin Temperature

Tj (F)

Bin Temperature

Range

(F)

Fraction of Total

Bin Hours,

Northern

Cl imate

Temperature

n ./N

Southern

Cl imate

1 62 60-64 .115 . 155

2 57 55-59 .106 .139

3 52 50-54 .096 . 136 *#4 47 45-49 .092 .133

5 42 40-44 .097 . 129 a 6 37 35-39 .109 .115

E * 7 32 30-34 .118 .091 A 3 27 25-29 .086 .052

T 9 22 20-24 .058 .026

I 5f*10 17 15-19 .039 .013

II 11 12 10-14 .028 .005 G 12 7 5-9 .020 .002 *13 ? 0-4 .015 .001

14 -3 (-5) - (-1) .010 —

15 -8 (-10) - (-6) .006 TM

*16 -13 (-15) - (-11) .003 —

C 1 67 65-69 .293 .213

0

•? 72 70-74 .271 .238

0 3 77 75-79 .200 .201 L 4 82 80-84 .131 . 153

T

5 87 85-89 .071 .110

6 92 90-94 .028 .059 G 7 97 95-99 .005 .023

3 102 100-104 0 .003

* Steady-state testing point

ff Standard ARI rating point

33
:able 4

GENERALIZED CL ELATES FOR COMMERCIAL/ INDUSTRIAL APPLICATIONS

Temperature

Sin Number

j

Representative

Sin Temperature

Tj (F)

Bin Temperature

Range

(F)

Fraction of Total

Bin Hours,

Northern

Climate

Temperature

nj/N

Southern

Climate

1 52 50-54 .124 . 193

;f*2 47 45-49 .120 .189

3 42 40-44 .126 . 184 H 4 37 35-39 .141 .164

£ *5 32 30-34 .151 . 129 A 6 27 25-29 .110 .074

T 7 22 20-24 .074 .036

i if *8 17 15-19 .049 .023 N 9 12 10-14 .036 .007

G 10 7 5-9 .026 .003

*11 2 0-4 .019 .001

12 -3 (-5) - (-1) .013 —

13 -8 (-10) - (-6) .008 —

*14 -13 (-15) - (11) .003 —

1 57 55-59 .170 .125

C 2 62 60-64 . 186 . 139

0 3 67 * 65-69 . 189 . 156

0 4 72 70-74 . 175 .175

L 5 77 75-79 .129 .148

I 6 82 80-34 .084 .113 N 7 87 85-39 .046 .081

G 3 92 90-94 .018 .044

9 97 95-99 .004 .017

10 102 100-104 — .002

* Steady-state Casting point

ir Standard ARI rating point
TABLE 5

SUMMARY WEATHER DATA FOR REPRESENTATIVE CLIMATES ,

Heating Design

Temperature (F)

(HDT)

Avg. Total Bin Hours

Generalized

Climate

Degree

Days

(DD)

Building

Application Heating

(BHH)

Cooling

(BHC)

Northern 7000 =5

Residential 6240 2497

Comm. / Ind. 4877 3860

Southern 3500 15

Residential 4800 3980

Comm. / Ind

.

3388 5391

35
TABLE 6. CALCULATION SHEET FOR SINGLE-SPEED HEAT PUMPS

MODE OF OPERATION : | | Heating Q Cooling

BUTI.DING APPLICATION :

[ | Residential Qj Comnercial/Industrial

CLIMATE : Q Northern Q Southern

Bin Hours Heating: BHH = (HRS)

2

(SPF) Heating

(J) ( ) 2 +

2

(K) (L)

( ) + ( )

(SPF) Cooling = II wS ( ) 2

( ) (K)

(SOC) bating BHH +

(N)_ - ( ) [( ) + ( )] = ?.

(S0C) Cooling

= BHC

[(§>

+ s'

(N)

II r^i + )]- ?

36

m
TABLE 6. (continued)

FUEL COST: °F

“ ($/kBtu)

°E = —

($kWh)

G

S = ($/kBtu)

J K L M N

\

1

[(Heating or

Cooling) /N] 6

Q(t.)/n

(kBtu/N)

[(Fuel +

Electric

Energy) /N]

7

(kBtu/N)

[(Supplemental

Energy) /N] 8

(kBtu/N)

[(Fuel +

Electric

Energy

Cost) /N]

($/N)

[(Supplemental

Energy

Cost) /N] 10

($/N)

i

i

11 ^

2 = 2 = 2= 2 - V—

(J) (K) (L) (M)

, (N)

Ref. 1:

Ref. 2:

Ref. 3:

Ref. 4:

Ref. 5:

Ref. 6:

Ref. 7:

Ref. 8:

Ref. 9:

Ref. 10:

Table 3 or 4

Interpolation of Test Data

Use eqn. (4.1)

Use eqn. (5.3)

Use eqn. (5.7)

0(Tj)/N = (col. C) (col. G)

(Fuel + Electric Energy) /N = (col.C) (col.H)

(col, I)

col.F 4-

(Supplemental Energy) /N = (col.C)(col.G - col.D )/^g

r(col.C) (col.H)"1 r (Fuel 4- elect, energy cost)/N =

(col. I)

(col.

(Supplemental energy cost)/N = (Cs)(col.L)

.413 (col. E)

0.3

, )(CF) + (CE

) (col .E

37
TABLE 7. CALCULATION SHEET FOR TTO-SPEED/DUAL CAPACITY OR VARIABLE -SPEED HEAT PUMPS

SYSTEM TYPE : | j Two-Speed Fj Variable Speed

MODE OF OPERATION : Ii Heating Fj Cooling

BUILDING APPLICATION :

| i Residential Q Carmercial/ Industrial CLIMATE : I

j Northern F] Southern

Bin Hours - Heating: BHH = (HRS)

Bin Hours - Cooling: BHC = (HRS)

Supplemental Heat Generating Efficiency: = (%)

(SPF) Heating z + r

(Q) (R)

( ) + ( ).

^FF^ Cooling

= 2

(P)2

(Q)

_ (

(

)

)

=

(SOC) Heating

= BHH

[cl) +

(T)] = ( )[( ) + ( )]=

(S0CWing " BHC

[<!) +

(T)] = ( )[( ) + ( )]= $_

38
TABLE 7. (Continued)

FUEL COST: Cp = ^

=

_(S/kBtu)

($/kVh)

(S/kBtu)

FOR VARIABLE-SPEED OPERATION

1/2

(Heating)

1/2 = (Heating) ,

(Cooling)

(Cooling)

M N 0

P Q R S T

Load

Factor6 ^(T.)

Part Inad

Factor

PLF°

Part Load

Factor8

PL's1

[(Heating or

i9 Cooling) /il] y Q(Tj)/N

(kBtu/N)

[(Fuel +

Elect. in Energy) /N]

iU

Ej.(Tj)/N

(kBtu/N)

[(Supplemental

Energy) /N] 11 Qr(t

j )/n

(kBtu/N)

[(Fuel +

Elect. Energy

Cost) /N]

12 %(Tj)/N

($/N)

[Supplemental

Energy Cost/N]

($/N)

/

2

- i t = 2

=

i 2 = 2 =

(P) i(Q) (R) 1 (S) (T)

Ref. 1:

Ref. 3:

Ref. 4:

Ref. 9:

Ref. 11:

Ref. 13:

Table 3 or 4 Ref. 2 : Interpolation of Test Data

Use Eqn. (5.23)

Regime I: BL(Tj) < qggdj)

Regime II: BL(Tj) > QgS

(Tj)

Regime III or-IV: o“

s

(Tj )

'< BLfTj) '<

Q(Tj)/N = (Col. C) (Col. J)

Qr(Tj ) /N = (Col. C) [Col . J - Col. E]/n

s Supplemental Energy Cost/H = (C^) (Col. R)

Value of Equation Co be used for:

Ref

No. Term

Two-Speed

Regime

Variable-Speed

Regime

I II 1 III IV I II III

5 X

0 ^) 5.27 0 ; 0 5.40 5.27 0 —

6 X

1 (Tj

)

0 1 5.35 5.41 0 1 —

7 PLF° 5.28 o ! 0 0 5.23 0 —

8 PLF1 0 i 5.36 0 0 1 —

10 Epd^/N 5.24 5.29 5.32 5.37 5.24 5.29 5.42

12 E£(T.)/N 5.25 5.30 5.33 5.38 5.25 5.30 5.43

39
TABLE 8

RATING SHEET FOR ENGINE-DRIVEN HEAT PUMP SYSTEMS

ENGINE TYPE: BRAYTON DIESEL RANKINE STIRLING OTHER

SYSTEM TYPE : SINGLE- SPEED TWO- SPEED VARIABLE-SPEED

BUILDING APPLICATIONS : RESIDENTIAL COMMERCIAL /INDUSTRIAL

BUILDING APPLICATIONS:

CLIMATE: NORTHERN SOUTHERN

FUEL COST: ELECTRIC $/kWh ENGINE $ /kBtu

SUPPLEMENTAL

-

PERFORMANCE PARAMETER SYMBOL UNITS HEATING COOLING

ARI Q (95) ss kBtu/hr

STANDARD RATING Q (47) ss kBtu/hr

CAPACITY <L (i7 > ss kBtu/hr

ARI STANDARD COP (95) ss -

COEFFICIENT OF COP (47) ss -

PERFORMANCE COP (17) ss

-

SEASONAL PERFORMANCE

FACTOR SPF

SEASONAL COST OF

OPERATION soc $

FROST DEGRADATION

COEFFICIENT C def

-

40
Building

load

or

system

capacity

Figure 1. Test requirements for single-speed heat pump systems.

41
Building

load

or

system

capacity

Figure 2. Test requirements for two-speed (dual capacity)

heat pump systems.

42
Building

load

or

aystom

capacity

T

Figure 3. Tesc requirements for variable-speed heat pump systems.

43
.
APPENDIX A

PROPAGATION OF MEASUREMENT UNCERTAINTIES INTO THE

STEADY-STATE COEFFICIENTS OF PERFORMANCE COP^CT^)

A. 1 Introduction

Questions often arise regarding the reliability of laboratory measurements

and the calculated performance of equipment which is based on these measurements. In multi-sample measurements, sufficient readings of the variable

are normally taken so that reliability can be established by statistical

means. Unfortunately, the time required and the operating and personnel

costs of many engineering experiments are often too great to permit multisample measurements. The experimenter is then restricted to single-sample

measurements and the questions of reliability and measurement uncertainty

often become significant. This appendix will discuss valid and acceptable

methods of estimating and describing the uncertainties in single-sample

measurements, as well as discuss a recommended method for calculating the

propagation of these uncertainties into the results. These methods will

then be applied to estimating the uncertainty associated with the steadystate coefficient of performance COPgg(Tj) given by eqn. (5.2).

In order to eliminate confusion regarding terminology, several fundamental concepts should be reviewed. As defined in ASHRAE Standard 41.5-75,

the difference between the true value of a measured quantity and the

observed value of the quantity is termed the "error" of the measurement.

The "accuracy" of a measurement is indicated by the size of the error,

and is often termed the systematic error. This type of error persists

in all repetitions of the measurement and can be corrected through calibration. The "precision" of a measurement is indicated by how sharply the

measurement is defined. It is an error which causes the readings to take

random values on either side of some mean value, and is often termed the

random error. The "uncertainty" of the measurement is the estimated value

of the error. Although the uncertainty of a measurement may reflect both

accuracy and precision errors (systematic or random) we will only consider

precision errors, since it is presumed that accuracy errors could be

eliminated through careful calibration. A "variable" will mean a basic

quantity observed in the laboratory (pressure, temperature, volume, etc.),

and its recorded values or readings will be called data . The term result

will refer to the value obtained by making corrections to or calculations

with the data. "Propagation of uncertainty" shall mean the way in which

uncertainties in the variables affect the uncertainty in the results.

The conventional means for stating the uncertainty of a variable is a statement of the best estimate of the true value together with a statement

about the magnitude of the error in the estimate (uncertainty). The best

estimate of the true value is normally the mean of the readings, and the

uncertainty is estimated based upon specified odds (confidence level). The

recommended format for describing the best value of a variable is.

45
V= M + W, (P percent) (Al)

where V is the variable, M is the best value, W is the uncertainty, and

P is the confidence level expressed as a percentage. The implication of

eqn. (Al) is that the best value of V is M with a P percent probability

that the true value lies within + W of the value M.. Determination of

the uncertainty W with a given level of confidence (given odds) is often

based upon the experience and judgment of the experimenter, and is a value selected such that he would be willing to wager (with P percent

confidence) that the error is less than W. Eqn. (Al) provides a method

by which the experimenter can describe the uncertainties associated with

his basic measurements. It then becomes necessary to determine how these

uncertainties propagate into the results.

If we let the result R be a function of n independent variables v^,

. . . , v , and each of the independently measured variables has an

uncertainty A v ^ , ^

2

, . . ., AVn , then the uncertainty in the result

AR is shown in Ref. 8 to be:

The effect of large uncertainties in the variables is emphasized by this

equation, and it shows that a specified reduction in a large uncertainty

has a greater effect than a comparable reduction in a small uncertainty.

It has been found from experience that a nondimens ional form of eqn. (A2)

is often more useful because it expresses the uncertainties on a percentage

basis, and is generally easier to use. Dividing every term of eqn. (A2)

by R gives:

AR = R

Av

nR

2n 1/2

(A3)

Eqns. (A2) and (A3) are important in instrumentation selection since they

show the experimenter where large uncertainties occur, and he may then

improve the instrumentation or experimental techniques in these areas.

A. 2 Steady-State Heating Coefficient of Performance

The steady-state coefficient of performance COP^gCT-) of an enginedriven system is given by eqns. (5.1) and (5.2), ana is repeated here

for convenience:

46
COP SS (Tj) = Q„<T.)

SS J m

f (I

j

)LHV + 3.413 E SS (T .)

» 3

The COPgg(Tj ) is a function of several variables, each of which is

subject to an uncertainty:

cop

SS (Tj) - fCQggCTj), AjCTj), LHV, E ss

(Tj )

)

acoPssdj) SCOPggCTj)

3y forming the required derivatives

3(Wv ’ 3Af(Tj)

(A4)

(A5 )

3 COPSS (Tj) 3C0P ss (Tj) —* , and

3 LHV

it can be shown that:

3ESS<Tj)

, substituting into eqn. (A3) and simplifying,

ACOP (T.)

SS 2 COPssdj)

r^wy' 4*

_ Qss^ Tj^ -

LHV * A* (T. ) f 3

3if (Tj )LHV + 3.413 E ss ( Tj )/

3

.

(A6)

f A (T )

• ALHV 1

2

• 3.413 A E (T )/ . 3 1

2'

f 3 4- SS j

A

f (Tj )LHV + 3.413 Egs (Tj)/.3 _Af (Tj)LHV + 3.413 E ss (Tj)/.3

-

1/2

The term ^Qgg^j )/Qss^j ^ -‘- s determined for the heating mode with the

procedure described below.

Using the appropriate equations given in ASHRAE Standard 37-69, the

steady-state heating capacity Qsg(Tj) is:

QssCIj) - 60- 1096 CAj.24 + .444 Wj [Ta2 - T

al ]

P P

_,i/

2

v n ^

R

a

Tn[1+Wn]J

(A7)

47
where C is the discharge coefficient of the air flow measuring nozzle,

A

n

is the nozzle area in ft , P n and T

n are the static pressure and

temperature at the nozzle throat in in. Hg absolute and °R, respectively,

P

y

is the velocity pressure at the nozzle throat in in. ^0, and R

a is

the universal gas constant in units of (in. Hg -f t^) / (lbm-°R) . The

remaining terms are defined in the nomenclature. Eqn. (A7) may be

simplified by letting:

k = 60 • 1096 C

6 =Ta2

- T

al

.24 + . 444W

a ~

9 -

(i + V

p p v n R T

a n

1/2

1/2

(A8)

Qgs(Tj) then becomes:

Qss

(T.

j ) = KA

n

a80 (A9)

Letting the uncertainties associated with the parameters An

, a, 8, and 9

be denoted by AA

n , Act, A8 , and AQ, respectively, and assuming K is a constant, eqn. (A3) can be used to show that the nondimensionalized uncertainty in Qgg ( Tj

) is:

*q

cc (t.)

SS 2 =z

Q S g( T j)

AA

“ n

2

+

Act 2

+ Tiil

2 +

A9

2

"

. V a L

s 9

-t 1/2

(A10)

The nondimensionalized uncertainties in a, 8, and 9 may be determined

through the use of eqns. (A8) and (A3), and are:

Acta

.111 W + .162

n

. 222 W„ + .342 W„ + .12

n n

AW. (All) n

48
_A£ ,

3

A6

9

4

(t

, - T I

L a2 al_,

[

Ta2

- T

al]

1 2

APv L

PVJ

+ 1

AP

L nj

“at

n

T

2

L n _

1 1/2

(A12)

(A13)

Eqns. (All to A13) may now be substituted into eqn (A10) to yield

A ^SS^ T

j )/Qss

(T

j ), and this in turn may be substituted into eqn. (A6)

to give the final nondimens ional expression for the uncertainty in

the steady-state coefficient of performance. Accordingly?

4 C0P

SS

( V . COPssCTj)

r aa i

2 n +

An

_. 222

.111 W + .162

n

n

2 2

AWn

rci2

?

11

*1

Hrt 1 2

+

1 - A

! 1

2

+

1 r aP ' n

i 2

+ i

-AT i

n

[

T

a2

- T

al] J 4

L m 4

L

Pn J

4 T„

m. ^ —

LHV * aA.CT.)

f J

*

f (Tj)LHV + 3. 413Eg

S (Tj )/ .

(A14)

A (T )

• aLHV--

f j

_ Af (Tj)LHV + 3.413 Ess (Tj)/.3-

3.413 aE (T .)/.

b b J

jA

f (T

j

)LHV + 3.413

1/2

Eqn. (A14) shows that the uncertainty in COP

ss (Tj) is a function of nine

measured parameters, each with its own measurement uncertainty. Therefore,

I 49
COPggCTj) = f (A„, wn , Ta2 - Tal , pv> Pn> T

n> if (Tj), LHV, EggCTj)). (A15)

A. 3 Samp»le Calculation

As an illustration of the previous concepts, consider the following

example taken from the experimental results of a Stirling engine-driven

heat pump system operating at an outdoor temperature of 50°F. The

measured values of the variables required in eqn. (A4) are:

Qss ( 5°) = 67,800 Btuh

Af(50) = 2.44 Ibm/hr

LHV = 19,930 Btu/lbm

EssCTj) = 820 W

Substitution into eqn. (A4) yields C0Pgg(50) = 1.17 as the calculated

result. The uncertainty in this result is given by eqn. (A14). The

uncertainties of the individual measurements were estimated with a 95% confidence level (19 to 1 odds) to be:

AA

n = 0.01 (.1%)

^ - AW

n = 3.5 x 10 Ibm moisture per Ibm dry air

A[T - T ] a2 al

[Ta2

“ T

al^

APv

AP

n

n

AT.

'n (T.) AA f

A LHV

= 0.01 (1%)

= 0.005 (0.5%)

= 0.01 ( 1 %)

= 0.005 (0.5%)

= .0244 lbm/hr (1%)

= 100 Btu/lbm (0.5%)

AE

ss ( tj) = 8 W (1%)

50
NBS-114A IREV. 9-78)

-r

:

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR

4. TITLE AND SUBTITLE

79-1911 _____

PROCEDURES FOR TESTING, RATING, AND ESTIMATING THE SEASONAL

PERFORMANCE OF ENGINE-DRIVEN HEAT PUMP SYSTEMS

3. R«cjn»(

5. Publication Date September 1979

7. AUTHOR(S)

Dr. Barry R. Maxwell

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fSfre.r. city, state, ZIP)

The Department of Energy

20 Massachusetts Ave. , NW

Washington, D.C. 20545

13. Type of Report & Period Covered

- i 15. SUPPLEMENTARY NOTES

Dr. Maxwell conducted this study during a year in residence at NBS under the Mgga is attached.

16. ABSTRACT (A 200~word or leas factual summary of moat significant information. If document includes a significant bibliography or

literature survey, mention it here.) A generic test and rating procedure is developed for heat engine-driven air-to-air

heat pump systems. The procedures are classified according to whether the systems

have single-speed, two-speed, or variable-speed capability, and whether they are operating in the heating or cooling mode. The test requirements generally consist

of a series of steady-state tests to establish the impact of outdoor temperature on performance, two or more part-load (cyclic) tests to determine the effect of "on-off"

cycling, two steady-state intermediate speed tests to determine part-speed performance,

and a single frost accumulation test to estimate the effect of frost. A generalized

calculation and rating procedure is developed. The system is rated in both modes

based upon its steady-state performance at the ARI standard rating points, its

seasonal performance factor, and its seasonal operating cost. A frost degradation

coefficient is also established. The seasonal parameters are based upon either a residential or commercial/industrial building application which is located in either

a generalized northern or southern climate.

17. KEY WORDS ( six to twelve entries ; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Building heating and cooling; engine-driven heat pump; heat pump; heating and cooling

equipment; heating, ventilating and air conditioning.

18. AVAILABILITY (Xj Unlimited

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| | Order From Sup. of Doc., U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

Order From National Technical Information Service (NTIS), Springfield,

VA. 22161

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