NBSIR 86-3373

Impact of Refrigerant Property

Uncertainties on Prediction of

Vapor Compression Cycle

Performance

Piotr A. Domanski

David A. Didion

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Building Equipment Division

Gaithersburg, MD 20899

December 1986

Issued February 1987

Sponsored by:

Office of Buildings and Community Systems

U.S. Department of Energy through

Oak Ridge National Laboratory under

contract DE-AC05-840R21400 with

Martin Marietta Energy Systems, Inc.

NBSIR 86-3373

IMPACT OF REFRIGERANT PROPERTY

UNCERTAINTIES ON PREDICTION OF

VAPOR COMPRESSION CYCLE

PERFORMANCE

Piotr A. Domanski

David A. Didion

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Building Technology

Building Equipment Division

Gaithersburg, MD 20899

December 1986

Issued February 1987

Sponsored by:

Office of Buildings and Community Systems

U.S. Department of Energy through

Oak Ridge National Laboratory under

contract DE-AC05-840R21400 with

Martin Marietta Energy Systems, Inc.

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Executive Summary

Considerable reliance is placed on computer simul ation mode 1 s for evaluation

of potential performance enhancement concepts. As the potential of new

working fluids is evaluated, the impact of uncertain refrigerant properties

needs to be better understood to properly interpret these computer simulation

results. This paper presents a study of sensitivity of performance prediction

to refrigerant properties for a residential, split heat pump operating in the

cooling mode. The NBS steady-state heat pump model, HPSIM, was used in this

study. The individual influence of the following parametric uncertainties was

examined:

1 iquid thermal conductivity

vapor thermal conductivity

1 iquid v isco sity

vapor viscosity

liquid specific volume

vapor specific volume

1 iquid heat capacity

vapor heat capacity at constant volume and heat capacity

at constant pressure

evaporation heat transfer coefficient

condensation heat transfer coefficient

evaporation pressure drop

condensation pressure drop

The influence of a given parameter on the performance prediction was found by

executing the program, HPSIM, with the altered parameter value. Several runs

were executed for each tested parameter to cover the uncertainty range within

which the value of this parameter would be expected to be known. Comparison

of the heat pump capacity and power input with results of a run using an

unchanged value of the parameters described the sensitivity of the cycle to

each parameter. The effects on evaporator and condenser pressures and

refrigerant mass flow rate are also given in the report.

i i i
Discrepancy between heat pomp laboratory test results and computer model

predictions may stem from uncertainties in refrigerant property predictions

and inadequate hardware modeling algorithms. The impact of inaccurate

property values can be evaluated using the findings of this study*, the impact

of simplifications in mode 1 ing algorithms have to be determined individually

for each computer model.

Results of this sensitivity study are system dependent (e.g. somewhat

different results would be obtained for a system with different relative sizes

of heat exchangers), however, no change of the relative importance of the

investigated parameters should be observed.

Best knowledge of all refrigerant parameters is essential for accurate

performance predictions since the impact of individual parameter uncertainties

may superimpose. The study indicated those parameters, which at the present

state of the art, have the greatest impact on the uncertainty of performance

prediction of the heat pump operating in the cool ing mode. These parameters

are: liquid transport properties, evaporative heat transfer coefficient and

vapor density.

The effect of an individual parameter variation w ithin the tested uncertainty

limits was found to be as high as 7.5% for capacity (for liquid thermal

conductivity) and 6% for power (for vapor specific volume). Calculations,

which combined effects of individual parameter variations for a system charged

with refrigerant 22, showed that uncertainty of capacity and COP predictions

may be as high as 12.9% and 10.9%, respectively, if the involved refrigerant

parameters are known with an error equal to the maximum deviation of the

IV
considered property correlations, and if the errors superimpose. Since

properties of refrigerant 22 are among the best known, the uncertainty of

capacity and COP predictions for other refrigerants and mixtures may be

expected to be greater.

v
ABSTRACT

This paper presents a sensitivity study of a vapor compression cycle in the

form of a heat pump operating in the cooling mode. The study was performed

with the aid of a detailed heat pump canputer model’, simulation runs were made

for different parametric values and the capacity and power input were compared

with results of a run using an unchanged value of the parameters. The effects

on evaporator and condenser pressures, and refrigerant mass flow rate are

given. The independent variables (parameters) include thermodynamic and

transport properties, as well as the refrigerant flow heat transfer and

pressure drop coefficients. When considering the state-of-the-art limits of

the individual parameter uncertainties, those which had the most effect on

system performance were liquid transport properties, evaporative heat transfer

coefficient and vapor density.

Key Words: Air conditioner, heat pump, sensitivity study,

thermodynamic properties, transport properties,

vapor compression cycle

vi
TABLE OF CONTENTS

Page

EXECUTIVE SUMMARY iii

AB STRACT v i

LIST OF FIGURES viii

1. INTRODUCTION 1

2. HEAT PUMP SIMULATION MODEL USED 3

3. RESULTS 6

3.1 Sensitivity to Liquid Viscosity Change 7

3.2 Sensitivity to Vapor Viscosity Change 9

3.3 Sensitivity to Liquid Thermal Conductivity Change 9

3.4 Sensitivity to Vapor Thermal Conductivity Change 11

3.5 Sensitivity to Liquid Specific Volume Change 12

3.6 Sensitivity to Vapor Specific Volume Change 14

3.7 Sensitivity to Liquid Heat Capacity Change 16

3.8 Sensitivity to Change of Vapor Heat Capacity

at Constant Pressure and Vapor Heat Capacity

of Constant Volume 17

3.9 Sensitivity to Change of Evaporative Heat

Transfer Coefficient 19

3.10 Sensitivity to Change of Condensation Heat

Transfer Coefficient 21

3.11 Sensitivity to Change of Evaporation Pressure Drop 23

3.12 Sensitivity to Change of Condensation Pressure Drop 23

3.13 Sensivitity to Change of More than One Parameter 23

3.14 Combined Effect of Refrigerant Properties Uncertainties

on Prediction of System Performance 25

4. CONCLUSIONS 29

5. REFERENCES 31

APPENDIX A. EVALUATION OF THE THERMODYNAMIC PROPERTIES OF VAPOR ... 33

APPENDIX B. EVALUATION OF THE INSIDE TUBE HEAT TRANSFER COEFFICIENT

AND PRESSURE DROP OF REFRIGERANT 39

v i i
LIST OF FIGURES

Figure 1. Schematic of a heat pump simulated by the heat pump

model, HPSIM 4

Figure 2. Logic of the heat pump model used in the sensitivity

study 5

Figure 3. Sensitivity of performance of a heat pump to a change

in liquid viscosity 8

Figure 4. Sensitivity of performance of a heat pump to a change

in liquid thermal conductivity 10

Figure 5. Sensitivity of performance of a heat pump to a change

in liquid specific volume 13

Figure 6. Sensitivity of performance of a heat pump to a change

in vapor specific volume 15

Figure 7. Sensitivity of performance of a heat pump on a change

in the heat capacity of liquid 18

Figure 8. Sensitivity of performance of a heat pump on a change

in the evaporative heat transfer coefficient 20

Figure 9. Sensitivity of performance of a heat pump on a change

in the condensation heat transfer coefficient 22

Figure 10. Sensitivity of performance of a heat pump on a change

in the evaporative pressure drop 24

viii
1. INTRODUCTION

Over the past decade, there has been considerable attention devoted to the

performance of refrigeration systems in both simulation model studies and

laboratory measurement studies. The accuracy of these studies tacitly depends

on knowledge of the various refrigerant thermodynamic and transport properties

as well as other flow parameters. The uncertainty with which the property

values are known is primarily a function of the state-of-the-art accuracy of

the particular property measurement technique. In the case of refrigerant

mixtures, there exists very little measured data, and it is therefore

necessary to employ mixing rules along with component data. This can increase

the uncertainty from 10 to 50%. For example, vapor density can be evaluated

quite well and usually is known within 2 percent uncertainty [1]*, on the other

hand, the specific volume of a liquid mixture may have an uncertainty of as

much as 15 percent if density is evaluated by a mixing rule in the

neighborhood of critical temperature of the lower boiling component [2]. In

the case of evaporative heat transfer coefficients, the actual mixture value

has been shown to be as much as 40% lower than that predicted by the ideal

mixture weighting factor method [3].

The different refrigerant property and flow parameters affect the system

performance with varying degrees of sensitivity. It is therefore necessary

to establish the system sensitivity to each property value if the most

effective information is to be obtained. Of course, accurate knowledge of

refrigerant properties does not change the way the real system operates.

However, the qualitative knowledge of the impact made by properties on

performance on a one by one basis is desirable because it can establish the

limits of uncertainty associated with simulation of refrigerant systems.
This, in turn, will indicate the areas most in need of further research on

prediction and measurement methodologies for refrigerants and refrigerant

mixtures.

Tie sensitivity analysis reported here was performed by simulating the

performance of a 2.5 ton split, residential, air-to-air heat pump charged with

Refrigerant 22. The heat pump was simulated in the cooling mode at DOE test A

conditions [4]. Simulation of the system without altering any parameter was

performed first. Then, simulation runs were performed with a specific

parameter changed by an assigned multiplication factor. The change of system

performance reflected system sensitivity to the altered parameter.

All simulation runs were performed with imposed refrigerant superheat of 10°F

at the compressor can inlet, and imposed refrigerant subcooling of 10°F at the

expansion device inlet. These restrictions are related to the common

laboratory practice of selecting optimum refrigerant charge and expansion

device size for a given system. These restrictions also ensure that when

simulating the system with altered parameters, the observed change in performance indeed results from the altered parameter with optimized cycle by the

same criteria, and not from a change in operating conditions.

The range over which a selected parameter was altered depended basically upon

the uncertainty band with which this parameter is generally known and upon

a need for presenting results of this study in some uniform fashion. The

uncertainty with which a given parameter is known depends on the methodology

by which the parameter is determined. If parameter determination is based on

laboratory measurement, the difference between values of this parameter

2
reported by two reputable sources may be considered as the uncertainty of this

parameter. If this parameter is determined by a theoretical correlation based

on fundamental knowledge of the molecule, the difference between a predicted

value and a laboratory measurement is considered the uncertainty.

An uncertainty band usually increases significantly if refrigerant mixtures

instead of single refrigerants are considered. This is a result of the need

for some type of mixing rule to determine the desired property based on

properties known for single refrigerants. Proper assessment of possible

uncertainties is complicated in some cases by the lack of reliable data and by

the large discrepancies between existing data sources for the majority of

compounds.

2. HEAT PUMP SIMULATION MODEL USED

A computer model of a heat pump, HPSIM [5], used in this study, is a 'first

principles' model, which was developed with emphasis on modeling phenomena

taking place in the system on a local basis. The structure of HPSIM is

modular with simulation of each major component handled by an independent

subroutine. The model consists of 41 subprograms for heat pump component

simulation, and heat transfer, fluid mechanics, and fluid property

calculation. The program totals approximately 5000 Fortran statements.

3
For use in this sensitivity study the model, HPSIM, was modified in two

areas

- convergence tolerances were tightened throughout the program to

obtain final convergence of the thermodynamic cycle within an

enthalpy value 0.15 Btu per pound of circulating refrigerant,

the logic of the program was changed to allow, in addition to

existing features, the imposition of a preset value of subcooling at

the expansion device inlet for any given cycle.

Heat pump components considered in HPSIM are shown in Figure 1. A

thermodynamic cycle simulated by the model is presented along with the logic

of the model in Figure 2.

Figure 1. Schematic of a heat pump simulated by the

heat pump model, HPSIM.

4
Symbols

H8 - refrigerant enthalpy at the expansion device inlet

H9 - refrigerant enthalpy at the evaporator inlet

P3 - refrigerant pressure at the compressor can inlet

P4 - refrigerant pressure at the compressor can outlet

TSUP3 - refrigerant vapor superheat

at the compressor can inlet

TSUB8 - refrigerant subcooling at the expansion device inlet

Figure 2. Logic of the heat pump model used in the sensitivity study.

5
The most important correlations for this sensitivity study are those

associated with evaluating the refrigerant thermodynamic state, heat transfer

and pressure drop. The correlations used were:

thermodynamic properties of vapor

single-phase heat transfer coefficient

evaporation heat transfer coefficient

condensation heat transfer coefficient

single-phase pressure drop

evaporation pressure drop

condensation pressure drop

- Downing [6] - Colburn [7] - Pierre [8] - Traviss et al. [9] - Fanning [10] - Pierre [11] - Lockhart - Martinelli [12]

Equations for calculation of thermodynamic properties of vapor are presented

for reference in Appendix A Other above listed correlations are shown in

Appe ndix B.

Other properties which impact on performance was studied here included:

density, heat capacity, thermal conductivity and absolute viscosity of liquid,

and thermal conductivity and absolute viscosity of vapor. The first four of

these were correlated as function of temperature only, last two as

function of temperature and pressure. These correlations are described in

Appendix A of the report on the heat pump model, EPSIM [5].

3 . RESULTS

Results presented here refer strictly to the refrigerant side of the given

thermodynamic cycle*, ie., capacity change refers to capacity delivered by the

modeled coil not including the heat added by the indoor fan. By the same

principle, power input change refers to compressor power only and does not

include power of fans or controls.

6
Results are presented in the form of figures for those parameters which,

when al tered within the applied range changed system capacity or energy

input by more than 0.5 percent. The figures shew changes of capacity (%),

energy input (%), refrigerant mass flow rate (%), condenser inlet pressure

(psi) and evaporator outlet pressure (psi) as a function of change in a

value of a specific property.

3.1 Sensitivity to Liquid Viscosity Change

Liquid viscosity data can be obtained in a number of ways. Liquid viscosity

obtained by direct laboratory measurement or by a very limited extrapolation

from measured data are most reliable with a generally stated uncertainty of

less than 5% [1]. The best theoretical correlations provide data of an uncertainty of 15% [13]. Methods for predicting viscosity of liquid mixtures are

remarkably poor (uncertainties up to 23% [13]) even when the viscosities of the

pure components are accurately known.

Simulation results are shown in Figure 3. Simulation of liquid viscosity at a

higher value has a detrimental effect on refrigerant pressure drop and the

inside tube heat transfer coefficient, for both two-phase and single-phase

flow. As a result suction pressure at the compressor decreases, discharge

pressure increases, and mass flow rate of refrigerant is decreased, which is

followed by a decrease of system capacity by 4% at 50% increase of vicosity.

Compressor power also decreases but more slowly than capacity, making the

system less efficient. A lower value of 1 iquid viscosity is associated with

similar but opposite trends.

7
CHANGE

IN

PRESSURE

(pal)

CHANGE

IN

PERFORMANCE

<%)

Figure 3. Sensitivity of performance of a heat pump to a change in liquid

visco sity.

8
3 .2 Sensitivity to Vapor Viscosity Change

Viscosity of a pure gas is usually a well know property with uncertainty less

than 2% [13]. On the other hand, viscosity of a gas mixture (if determined

through the use of pure component data and mixing rules rather than measurements on the mixture, of which there are few) may have an uncertainty of up to

17% [13]. Fortunately, however, simulation runs showed a very weak sensitivity

(maximum .2%) of capacity and energy input to vapor viscosity which was varied

up to + 5 0%.

3 .3 Sensitivity to Liquid Thermal Conductivity Change

Thermal conductivity of liquid, if assessed from experimental data, is known

with up to 10% uncertainty [13]. Theoretical prediction methods for this

property value can have an uncertainty of up to 30%. Prediction methods for

mixtures also have 30% uncertainties if 'correct' viscosities of components

are known.

Simulation results are presented in Figure 4. Change of liquid refrigerant

thermal conductivity does not affect refrigerant pressure drop in the system.

The observed change in level of evaporator and condenser pressures is a result

of change of the inside tube heat transfer coefficient, both single-phase and

two-phase, which increases with increase of liquid thermal conductivity. The

consequence of the improved heat transfer is that the internal saturation

temperature (and thus pressure) equilibrium levels the simulation converges to

are closer to the external source and sink values. This increase of

evaporator pressure and decrease of condenser pressure allows the compressor

to pump more refrigerant consequently causing increased system capacity.

9
5

4 -

/

Figure 4. Sensitivity of performance of a heat pump to a change in liquid

thermal conductivity.

10
Compressor power follows the mass flow rate pattern but not as strongly as

capacity, which results in more efficient operation of the system.

It is interesting to note that sensitivity of performance is not the same over

the range +50% at which liquid conductivity was altered. Greater impact

(degradation) is exhibited for decreased conductivity than the improvement of

performance for increased conductivity (-7.6% versus 2.8%). This behavior can

be explained by the fact that the liquid thermal conductivity profoundly

affects the inside tube heat transfer resistance. Increase of 1 iquid

conductivity decreases the inside tube resistance with decreasing impact on

overall heat transfer resistance, making the air-side resistance an even more

dominant factor, while decreasing the liquid conductivity increases the inside

tube resistance which becomes more significant and influential part of the

overall heat transfer resistance of the heat exchanger.

3 .4 Sensitivity to Vapor Thermal Conductivity Change

Vapor thermal conductivity is usually known with an uncertainty smaller than

10% though the error can be as high as 28% [13]. Thermal conductivity of

mixtures evaluated by a mixing correl ation may carry an uncertainty of similar

magnitude even if accurate values for components thermal conductivities are

know.

Simulation runs performed w ith vapor thermal conductivity altered from -50% to

+50% showed very weak sensitivity of performance of the system to this property. Capacity varied from -0.5% to 0.4% respectively, while compressor power

varied less than 0.1%.

11
3 .5 Sensitivity to Liquid Specific Volume Change

Specific volume of liquid is usually known with uncertainty smaller than 1%.

For liquid mixtures, the straight mixing rule (Amagat's law) is usually

satisfactory and does not add more than 9b in uncertainty at lov reduced

temperatures. A method based on the principle of corresponding states

provides specific volume for some liquid mixtures with uncertainty up to 10%

[1]. None of these methods should be used at reduced temperature exceeding

0.9 for the more volatile component where prediction uncertainty may be as

high as 100% [2]*, an equation of state capable of handling both the liquid and

vapor should be used instead [14],

In the heat pump simulation program used in this study, liquid specific volume

at saturation is calculated by an independent spline which is a function of

temperature only. The value obtained from such a spline was al tered w ithin

+10% in this study. It has to be mentioned that liquid specific volume has

impact on the value of the latent heat and the width of the two-phase region

(see equation (A4)) affecting the amount of heat per one pound of refrigerant

that can be pumped by the cycle. Simulation results are presented in Figure

5. An increase in liquid specific volume decreases latent heat, increases

single-phase and two-phase pressure drop, and increases the condensation heat

transfer coefficient. The evaporation heat transfer coefficient evaluated by

Pierre's correlation [8], used in this study, is insensitive to liquid

specific volume, though other type correlations based on Lockhar t- Mar tinel 1 i

parameter would show a decrease of the heat transfer coefficient with

increased liquid specific volume. Ihe first two factors are dominant, with

the latent heat being most influential*, system capacity decreases inspite of

12
CHANGE

IN

CHANGE

IN

PRESSURE

(psl)

PERFORMANCE

(%)

Figure 5. Sensitivity of performance of a heat pump to a change in liquid

specific volume.

13
increased refrigerant mass flaw rate. Resnlts for decreased liquid specific

volume are symmetrical but with opposite signs than those found for increased

specific volume. However, the overall performance sensitivity to this

property is minimal.

3 .6 Sensitivity to Vapor Specific Volume Change

Vapor specific volume was altered in this study within the range +10% which

covers uncertainties with which this property is generally known. This 10%

range may be exceeded in the case of mixture vapor volumes where an

unanticipated nonideality in the mixture may alter the vapor pressure

substantially; otherwise the state-of-the-art is better than 2%.

Change of specific volume of vapor affects the latent heat value similarly as

specific volume of liquid but in opposite direction (see equation (A4)), i.e.,

the increase of vapor specific volume increases the width of the two-phase

region. Vapor heat capacity, enthalpy and entropy are also affected

(equations (A3), (A5) and (A6) , respectively). Other effects associated with

increase of vapor specific volume are: refrigerant mass flcwr rate decrease,

pressure drop of singl e- phase vapor flow and two-phase flow increase, and

condensation heat transfer coefficient increase. The changes of condensation

heat transfer coefficient and pressure drop have minor and opposite affects

(Figure 6). Increase of the latent heat appears to be the dominating factor,

overcoming the impact of reduction of refrigerant mass flow rate (8.2%)

resulting in slightly increased capacity (0.4%). System performance improves

substantially at higher specific volume since the slight capacity increase is

acccmapnied by decreased energy consumption.

14
CHANGE

IN

PRESSURE

(pal)

CHANGE

IN

PERFORMANCE

(%)

Figure 6. Sensitivity of performance of a heat pump to a change in vapor

specific volume.

15
3 .7 Sensitivity to Liquid Heat Capacity Change

Prediction me thods for liquid heat capacity are usually accurate within 15%

below the normal boiling point, but at higher reduced temperatures the

uncertainty may be greater [1], Specific heat of liquid mixtures has an

additional 5% uncertainty due to the mixing rules for component heat

capacities [13].

Liquid heat capacity as a thermodynamic property, is related to other properties tlirough the slopes of saturated liquid and saturated vapor lines outlining the two-phase region. In assessing sensitivity of system performance

on liquid specific heat it is important to realize that the outcome will

depend on the origin of the uncertainty.

Liquid heat capacity may be determined by direct measurement or by vapor phase

measurement and theoretical relations outlining the two-phase region.

Simulation results for these two cases will differ since in the first case

only uncertainty of a value of the liquid heat capacity will affect the

accuracy of performance prediction, while in the latter case additionally to

the liquid heat capacity, uncertainties of vapor phase measurements and

theoretical relations are possibly involved.

In simulation runs, reported here, a value of liquid specific heat was altered

exclusively. (This creates some theoretical inconsistencies since dh/dT for

saturated liquid was not changed.) As a result, the scope of sensitivity

analysis is limited to the effect of altered liquid heat capacity through

change of the inside tube heat transfer coefficients in the heat exchangers.

Consideration of uncertainty of liquid heat capacity that would originate frcm

16
inaccurate outline of the two-phase region would require modifying of the

thermodynamic properties algorithm which was not practical for this study.

The results, shown in Figure 7, can be explained as follows:

a decrease in liquid heat capacity decreases both single-phase and two-phase

condensation heat transfer coefficient (pressure drop is not affected) forcing

condenser pressure to increase. This increase is reinforced by increased

evaporator pressure, 'pulled up' by the condenser, and increased mass flow

rate caused by increased density of the suction vapor. Capacity decreases,

in spite of greater refrigerant mass flow rate, because refrigerant enthalpy

change in the evaporator decreased.

Opposite performance trends are associated with an increase of liquid heat

capacity with sane difference in pressure change. This difference can be

explained by the fact that condenser pressure decrease is limited by

refrigerant saturation temperature which has to be above the outdoor

temperature.

3 .8 Sensitivity to Change of Vapor Heat Capacity at Constant Pressure and Vapor

Heat Capacity at Constant Volume

Sensitivity on vapor heat capacity at constant pressure and vapor heat

capacity at constant volume was tested by altering both these properties at

the same time by ±10%. This range covers the likely uncertainties associated

with these properties.

17
CHANGE

IN

CHANGE

IN

PRESSURE

(pal)

PERFORMANCE

(%)

Figure 7 .

1

- \Condenser inlet

LIQUID HEAT

CAPACITY CHANGE <%) " 10 20 30 40 50

-50-40 -30 -20 -10 6

Evaporator outlet

Sensitivity of performance of a heat pnmp on a change in the heat

capacity of liquid.

18
Simulation runs showed insignificant impact on system performance resulting

from the vapor heat capacities changes. Heat pump capacity and power values

remained within 0.1% of the original level for 10% variation in heat

capacitie s.

3.9 Sensitivity to Change of Evaporative Heat Transfer Coefficient

The evaporative heat transfer coefficient is one of the most difficult

parameters to predict and thus has the widest variation in uncertainty. It is

not uncommon that different correlations are in disagreement by as much as

50%. Aside from evaluating the impact of the uncertainty of the evaporative

heat transfer coefficient for pure components in smooth tubes, analysis of

tubes with enhanced internal surfaces and refrigerants comprised of nonazeotropic mixtures should be also considered. For this later case, validated

mixing rules are virtually unknown; however it is known that simple weighting

of pure component data can result in a 40% over prediction from measured data

tm|

The effect of changed evaporative heat transfer coefficient is not equally

strong for its degradation and enhancement (Figure 8). The impact is stronger

with degraded coefficient because in this case the inside tube heat transfer

resistance contributes more significantly to efficiency of the heat exchange.

An increase of evaporative heat transfer coefficient allows for smaller

temperature difference between the ambient air and refrigerant in the

evaporator causing evaporator pressure to increase. Subsequently, the suction

vapor density increases enabling the compressor to pump more refrigerant.

Since heat transfer resistance on the condenser side is not changed, the

19
5

Figure 8 •

4 -

3 -

-7 L

Sensitivity of performance of a heat pump on a change in the

evaporative heat transfer coefficient.

20
increased refrigerant mass flow rate requires higher condenser temperature

(pressure) in order to condense the refrigerant at this higher mass flow rate.

Capacity of the system increases along with refrigerant mass flow rate (both

curves coincide).

3.10 Sensitivity to Change of Condensation Heat Transfer Coefficient

Uncertainties in determination of the condensation heat transfer coefficient

are similar to those of the evaporation heat transfer coefficient. The

condensation heat transfer coefficient may also be enhanced by roughed inner

surface or be degraded if a mixture is used. Therefore, just as with the

evaporative coefficient, the selection of the appropriate value is application

as well as property dependent.

Simulation results are shown in Figure 9. A change of the condensation heat

transfer coefficient makes greater impact when the coefficient is degraded

than when it is improved. Decrease in the condensation heat transfer

coefficient causes a rise in condenser pressure in order to condense flowing

refrigerant. Increased condenser pressure is associ ated w ith only a weak

evaporator pressure increase, thus the refrigerant mass flcnr rates remain

almost unchanged. Stronger changes (decreases) in capacity with decreased

heat transfer coefficient is a result of a decreased enthalpy change in the

evaporator resulting from higher condenser pressure and higher liquid enthalpy

at the expansion device inlet with enthalpy at the evaporator outlet almost

unchanged. Compressor power change corresponds to changes in the condenser

pressure which changed compressor compression ratio.

21
Figure 9.

UiO

z

<

2

COO

U.CEUJ

0.

*

1 Power

CONDENSATION

HEAT TRANSFER

COEFFICIENT

CHANGE (%)

0

-1

-2

-50-40 -30

7E 10 20

Mess flow rste

_

«' Cspscity

Sensitivity of performance of a heat pump on a change in the

condensation heat transfer coefficient.

22
3.11

Sensitivity to Change of Evaporation Pressure Drop

The evaporative pressure drop was altered in the range from -50% to +100%, to

cover possible uncertainty for pressure drop evaluation as well as cases of

increased pressure drop in tubes with roughed inner surface for enhanced heat

transfer coefficient. Simulation results are quite linear (Figure 10).

Increased pressure drop decreases the compressor suction pressure and suction

vapor density. Refrigerant mass flow rate decreases and pressure in the

condenser also decreases since a smaller temperature difference between the

ambient air and the condenser is required to condense refrigerant flowing at

the lower rate. Refrigerant mass flow rate decrease results in capacity

decrease (both curves coincide).

3 .12 Sensitivity to Change of Condensation Pressure Drop

Condensation pressure drop was altered within the same range as evaporative

pressure drop: -50%, +100%. Simulation results showed small sensitivity to

altered two-phase pressure drop in the condenser. Capacity and power were

changed within -0.1 and +0.1% range.

3.13 Sensitivity to Change of More than One Parameter

Performance sensitivity to more than one parameter's variation can be

evaluated by reading the figures for the individual parameters involved and

multiplying the individual performance changes. For example, if a roughened

inside tube surface enhanced the inside tube heat transfer coefficient by 40%

at the expense of increased pressure drop of 40%, the resultant change of

system capacity, if such tubes were employed in the evaporator, would be

23
Figure 10. Sensitivity of performance of a heat pump on a change in the

evaporative pressure drop.

24
1.020 * 0.993 = 1 .013 where:

1.020 corresponds to 2% capacity increase due to the increased inside

tube heat transfer coefficient (read from Figure 8),

0.993 corresponds to 0.7% capacity decrease due to increased evaporative pressure drop (read from Figure 10) .

This superimposing of effects can be done since system sensitivity was

evaluated based on comparable thermodynamic cycles optimized by the same

criteria by imposing 10°F vapor superheat at the compressor can inlet and 10°F

liquid subcooling at the expansion device inlet. This procedure was also

verified by results of simulation runs in which more than one parameter was

varied.

3.14 Combined Effect of Refrigerant Properties Uncertainties on Prediction of

System Performance

Accuracy of performance prediction may suffer for two reasons: inadequate

hardware modeling algorithms, and inaccurate fluid property prediction. The

performance prediction uncertainty band due to inadequacy of hardware modeling

algorithms is, by definition, specific for each particular computer model.

This uncertainty band can be found by comparing simulation and laboratory test

results for different model heat pumps. Differences of disagreement between

predicted and tested performance for different heat pump models would indicate

the uncertainty band due to the inadequacy of simulation model algorithms.

This study was performed to provide a methodology for evaluation of

sensitivity of performance prediction on uncertainties of refrigerant

properties. This methodology depends on combining effects of individual

parameters on system performance. Though results were generated simulating a

25
heat pump charged with refrigerant 22, the methodology is applicable to any

refrigerant since it was formulated on a relative basis. Sensitivity of

performance prediction is difficult to determine rigorously because the errors

with which fluid properties values are used in the simulation process are

unknown. In addition, errors in fluid property values may have a cancelling

effect in affecting the performance prediction, or a superimposing effect

causing the simulation results to be far off.

He uncertainty band due to inaccurate refrigerant property values will be

different for different refrigerants since not all refrigerants have been

equally investigated and their properties equally well known. In order to

provide an indication of the uncertainty in performance prediction which may

result from uncertainty in fluid properties, a case for refrigerant 22 is

presented below.

Previous sections and figures allow identification of the parameters which

have the most significant impact on performance predictions and should be

considered. These parameters are: liquid thermal conductivity, liquid

viscosity, vapor specific volume, evaporation and condensation heat transfer

coefficients, and evaporation pressure drop. It is assumed here that all

property uncertainties taken into account have a superimposing effect on

system capacity. Two scenarios are considered: one when the error in

performance prediction is equal to the mean deviation for a given property

correlation, and the second when the maximum deviation is taken into account.

For R-22 there are a few correlations that were checked against a broad data

bank and mean and maximum deviations were evaluated. These correlations for

the following parameters are:

26
Mean Deviation (%) Mai Deviation (%) Source

liquid thermal conductivity 2.1 8.5 [15]

liquid viscosity 2.5 5.9 [15]

evaporation heat transfer coefficient 25 .0 58.0 [16]

For the condensation heat transfer coefficient mean and maximum dev iations

were assumed to be the same as for the evaporation heat transfer coefficient.

Deviations for vapor specific volume were assumed to have values of 0.5% (max)

and 0 .25% (min) .

Reading system performance change for each property from the figures and

combining the individual effects yielded an uncertainty of 3.7% for capacity,

and 3.1% for COP prediction in the minimum deviation case, and respective

uncertainties of 12.9% and 10.9% for the maximum deviation case. The most

influential single parameter appeared to be the evaporative heat transfer

coefficient which contributed approximately 60% to the calculated

uncertainties for capacity and COP predictions.

As far as other refrigerants and their mixtures are concerned, it is expected

that performance prediction uncertainty will be greater. An important

conclusion that can be drawn for all refrigerants from the R22 example is that

an error in the value of the evaporation heat transfer coefficient has a

significant weight and evaluation of this parameter alone may provide a rough

indication of the performance prediction uncertainty for single component

refrigerants. For refrigerant mixtures a significant impact on performance

prediction may come from errors in values of liquid transport properties and

liquid specific volume. Influence of these properties may differ

27
significantly from one mixture to another depending on the experimental data

base and correlations used.

28
4. CONCLUSIONS

Results of this study provide information on the effect uncertainties of

individual parameters have on system performance prediction. This

information should be helpful in evaluation of uncertainties in performance

prediction for innovative refrigerants and their mixtures for which complete

property information is usually not available. The results indicate liquid

transport properties, evaporative heat transfer coefficient and vapor density

as those properties whose uncertainties have the most significant impact.

The effect of an individual parameter variation within the tested uncertainty

limits was found to be as high as 7.5% for capacity (for liquid thermal

conductivity) and 6% for power (for vapor specific volume). In reality the

uncertainty of system performance prediction may be much higher since the

value of each parameter is known with some uncertainty and they all influence

the predicted level of performance. An example analysis for refrigerant 22

showed uncertainty of capacity and COP predictions can be as high as 12.9% and

10.9% if involved refrigerant parameters are known with an error equal to the

maximum deviations of the considered property correlations. Since properties

of refrigerant 22 are among the best known, the uncertainty of capacity and

COP predictions for other refrigerants may be expected to be greater.

Discrepancy between heat pump laboratory test results and computer model

predictions stem from uncertaintie s in refrigerant property prediction and

inadequate hardware modeling algorithms. Inaccurate refrigerant properties

values should have a similar impact on performance predictions obtained by any

computer model. This impact can be evaluated using findings contained in this

report. The impact of inadequate modeling algorithms is specific for each

29
computer model and has to be evaluated using the particular model

individually.

Results of this sensitivity study are system dependent (e.g. somewhat

different results would be obtained for a system with different relative

sizes of heat exchangers), however, no change of the relative importance of

the investigated parameters should be observed.

30
REFERENCES

1. National Engineering Laboratory, East Kilbride, Scotland. Private

communication with D. A. Didion, 1983.

2. Morrison, G. , The Importance of Including the Liquid Phase in Equations

of State for Nonazeotropic Refrigerant Mixtures, ASHRAE Transactions . Vol . 91, Pt. 1 , 19 85.

3. Radermacher, R. , Ross, H. , and Didion, D. , Experimental Determination of

Forced Convection Evaporative Heat Transfer Coefficients for Nonazeotropic refrigerant mixture, ASME Winter Annual Meeting, Paper No. 83-

WA/MT-54, 1983.

4. Federal Register, Part III, Test Procedures for Central Air Conditioners,

Including Heat Pumps, Vol. 44, No. 249, p. 76708, December 27 , 1979.

5. Domanski, P. and Didion, D. , Computer Modeling of the Vapor

Compression Cycle with Constant Flow Area Expansion Device,

National Bureau of Standards, Building Science Series 155,

Washington, D.C. , 1983.

6. Downing, R. C. , Refrigerant Equations, ASHRAE Transactions . Vol. 80, Part 2, 1974

7. Colburn, A. P. , A Method of Correlating Forced Convection Heat Transfer

Data and a Comparison with Fluid Friction, ATrhE Transactions . Vol. 29,

p. 174, 1930.

8. Pierre, B. , Stromningsmot stand vid Kikande Koldmedier, Kylteknisk

Tidskrift, No. 6, December 1957.

9. Traviss, D.P. , Baron, A. B. , and Rohsenow, W.M. , Forced-Convection

Condensation Inside Tubes, Technical Report No. 72591-74, Massachusetts

Institute of Technology, Cambridge, Massachusetts, 1971.

10. American Society of Heating, Refrigerating, and Air Conditioning

Engineers, Inc. , ASHRAE Handbook , Fundamentals Volume . Atlanta, Ga.

,

1985.

11. Pierre, B. , Flow resistance with Boiling Refrigerants, ASHRAE Journal . September, 1964.

12. Lockhart, R.W. and Martinelli, R. C. , Chemical Engineering Progress, Vol.

45, p. 39, 1949.

13. Reid, C. R. , Prausnitz, J.M. , and Sherwood, T.K. , The Properties of

Gases and Liquids, McGraw-Hill, Inc., 1977.

14. Morrison, G. and McLinden M. , Application of a Hard Sphere Equation of

State to Refrigerants and Refrigerants Mixtures, National Bureau of

Standards, Technical Note, Washington, D. C. , 1986, to be published.

31
15. Japanese Association of Refrigeration, Thermophysical Properties of

Refrigeration - R-22 , Osaha, Japan, 1975.

16. Gungor, K. E. and Winterton, R. M. S. , A General Correlation for Flow

Boiling in Tubes and Annul i, Int. J. Heat and Mass Transfer, Vol. 29,

No. 3, pp. 351-358, 1986.

32
APIENDIX A. EVALUATION OF THE THERMODYNAMIC PROPERTIES OF VAPOR

Equations used for evaluation of the thermodynamic properties were presented

by Downing [6], These equations are given below with appropriate constants

for Refrigerant 22.

Saturated Vapor Pressure

P = pressure (psia)

T = vapor temperature (R)

A = 29.3 57 5 45

B = -3 845 .1932

C = -7 .8610312

D = 2.190 93 90E-3

E = 0.44574670

F = 6 86 .1

(Al)

where

33
Equation of State

p = RT , A2 + K2T + C2 exo(-KT/ TC) , A3 + B3 T + OeiD(-CT7TC) , . V — h a i

' ^

V b (V - b) (V - b)

t A4 + B4T i AS + BST + CS exu(-KT/ TC) , A6 + B6T

(V-b) 4 (V-b) 5 exp (ALPHA' V)

P = pressure (psia)

H* —

x — temperature (R)

TC = 664.50, critical temperature (R)

V = specific volume (ft**3/lb)

A2 = -4.3 53 547

A3 = -0.017464

A4 = 2 .3 10142E-3

AS = -3 .724044E-5

A

= 1.3 633 87E+8

ALPHA = 548.2

B2 = 2.407252E-3

£3 = 7 .627 89E-5

B4 = -3.6 05723E-6

B5 = 5 .355 465E-8

B6 = -1.672612E+5

b = 0.002

C2 = -44.06686

C3 = 1.4 83 7 6 3

C5 = -1.845051E-4

C6 = -1 .672612E+5

K = 4.2

R = 0 .124098

34
Heat Capacity of Vapor at Constant Volume

Cy a + bT + cT JK*T exp(-KT/TC)

TC

2 (A3)

+ S3 + S

2( V - b)

2 4( V - b)4

where

Cy = heat capacity of vapor at constant volume (Btu/lb*F)

a = 0.02812836

b = 2.255408E-4

c = -6 .5096 07 E8

f = 257.341

J = 0.185053

Other symbols as defined for the equation of state.

35
Latent Heat of Vaporization

( A4

where

i.£g = latent heat of vaporization (Btn/lb)

J = 0.185053

V = specific volume of satnrated vapor (ft**3/lb)

= specific volume of satnrated liquid (ft**3/lb)

Other symbols are as described for the vapor pressure equation.

36
Enthalpy of the Vapor

i = aT + + cTl - I + jpv + J

2 3 T

A2 A3

V

" b

2( V - b)

2

( A5

)

+ M +

A5 + —M—/exp (ALPSA * V)

3 ( V - b)

3 4( V - b)

4 ALffiA

+ Jexp(-KT/TC) (•a)

a ^ a

V

‘ b

2( V - b)

C5

4 ( V - b)

+ 62.4009

where

i = enthalpy of vapor (Btn/lb)

symbols A2, A3, A4, A5, A6, C2, C3, K, P, T, TC, V,

ALPHA are as described for the equation of state

symbols J, a, b,c, f are as described for the heat capacity equation

37
Entropy of the Vapor

S = a(lnlO)log T + bT + cT

2

2 — + JR ( ln20) log ( V - b)

2T

J (A6)

B2 +B3 +B4 +

BS

V ~ b

2( V - b)

2 3( v - b) * 4(V-b) 4

+ — /exp( ALPHA * V)

ALPHA

+ J Keip(-KT/TC)

TC

C2 + Q

V " b 2(V - b)*

C5

4( V - b)

4 0.0453335

where S = entropy of the vapor (Btu/(lb*F))

symbols B2 , B3 , B4 , BS , B6 , C2, C3, C4 , CS , K, T, TC, V,

ALPHA are as described for the equation of state,

symbols J, a, b, c, f are as described for the heat capacity

equa tion.

38
APPENDIX B. EVALUATION OF THE INSIDE TUBE HEAT TRANSFER COEFFICIENT AND

PRESSURE DROP OF REFRIGERANT

The following are inside tube heat transfer and pressure drop correlations

used in the model, HPSIM. List of symbols is given at the end of this

appe ndix.

Single-Phase Heat Transfer Coefficient [7]

h = 0.023 - * Re0 * 8 * Pr0 ' 333 (Bl)

D

Evaporative Heat Transfer Coefficient [ 8]

v 0.5

h = 0.0009 ft • Re (J * Ax * i fg /L)

Condensation Heat Transfer Coefficient [9]

(B2)

h = _^L

°* 9

' ReL

• Pr * Fl^/F2 (B3)

D

where: J3 = 1.00 for FI £ 1

P = 1.15 for FI > 1

FI = 0.15 (Xtt~1 + 2.85 X

tt

0 * 524

)

F2 = 0.7 07 * PrL* Re^°

5 for ReL

< 50

F2 = 5 * PrL

+ 5

* ln(l + PrL

(0. 09636 * ReL

°* 585-l)) for 50 < Rej^ < 1125

39
F2 = 5 * PrL

+ 5

* In ( 1 + PrL

) + 2 .5 * ln(0. 00313 * ReL

° * 812

)

for < 1125 (63)

Single-Phase Pressure Drop [10]

AP = 2 ’ f

‘ G

2

* L/(D • p)

where f = 0.046 * Re-0,2

Two- Phase Pressure Drop With Evaporation [11]

AP = ( f * L/D + Ax/xm )G

2

* Vffi where: f = 0.0185 * Re(L/(J * i fg * Ax)) 0 * 25

Two- Phase Pressure Drop with Condensation [12]

AP = APl

* <t>

where: APL

= 2 f ( ( 1 - x)G)

2

* L/ (D * p L

)

fL

= 0.046 * ReL

*0,2

<J)= 10 0 (A0 + A1 • B + A2 • B

2 + A3 • B3 + A4 • B

4

)

<t> = correlated based on [12]

A0 = 1.4

A1 = 0.87 917

A2 = 0.14062

( B4

( B5

( B6

40
A3 = 0.0010417

A4 = -0.0007 8125

B = Log10Xtt

List of Symbols

0^ = specific heat at constant pressure

D = inner tube diameter

f = Fanning friction factor

G = — , refrigerant mass flux

jtD

h = forced convection heat transfer coefficient

i£g = latent heat of evapora tion/ condensa tion

J = mechanical equivalent of ' heat

k = thermal conductivity

L = tube length

m = refrigerant mass flow rate

P = pressure

Pr = Prandtl number

k

GD

Re = Reynolds number

Ix = local quality, x^ refers to mean quality

V = specific volume

Vm

= + x

ffi (Vy ~ VjO , two-phase mean specific volume

<5> = Lockhart-Mar tinelli correction factor for two-phase pressure drop

0.9 V 0.5 [i 0.1

X..+ = (- -) (—) (—) , two-phase flow Lockhart- Martinel 1 i zz * v

v

parameter for turbulent both liquid and vapor

41
P - density

H = absolute viscosity

Subscripts refer to:

L = liquid

V = vapor

e = mean value
U.S. OEPT. OF COMM. 1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Pub! ication Date BIBLIOGRAPHIC DATA

SHEET (See instructions) 86-3373 FEBRUARY 1987

4. TITLE AND SUBTITLE

Impact of Refrigerant Property Uncertainties on Prediction of Vapor

Compression Cycle Performance

5. AUTHOR(S)

Piotr A. Domanski and David A. Didion

6. PERFORMING ORGANIZATION (If joint or other than N BS. see instructions) 7. Contract/ Grant No.

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9.

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

Oak Ridge National Laboratory

Department of Energy

Oak Ridge, Tennessee 37830

10.

SUPPLEMENTARY NOTES

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

11.

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

bi bliography or literature survey, mention it here)

This paper presents a sensitivity study of a vapor compression cycle in the

form of a heat pump operating in the cooling mode. The study was performed

with the aid of a detailed heat pump computer model; simulation runs were made

for different parametric values and the capacity and power input were compared

with results of a run using an unchanged value of the parameters. The effects

on evaporator and condenser pressures, and refrigerant mass flow rate are

given. The independent variables (parameters) include thermodynamic and transport properties, as well as the refrigerant flow heat transfer and pressure

drop coefficients. When considering the state-of-the-art limits of the

individual parameter uncertainties, those which had the most effect on system

performance were liquid transport properties, evaporative heat transfer

coefficient and vapor density.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) air conditioner, heat pump, sensitivity study, thermodynamic properties,

transport properties, vapor compression cycle

13.

AVAILABILITY

2^ u nlimited P°r Official Distribution. Do Not Release to NTIS

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

20402. ^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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