Evaporation and Condensation Heat Transfer

Performance of Flammable Refrigerants in a

Brazed Plate Heat Exchanger

Sheila C. Palmer

W. Vance Payne, II

Piotr A. Domanski

U.S. DEPARTMENT OF COMMERCE

Technology Administration

Building Environment Division

Building and Fire

Research Laboratory

National Institute of Standards

and Technology

Gaithersburg, MD 20899

July 2000

0

N IST C ENTENNIA L

NIST

National Institute of

Standards and Technology

Technology Administration

U.S. Department of Commerce
Evaporation and Condensation Heat Transfer

Performance of Flammable Refrigerants in a

Brazed Plate Heat Exchanger

Sheila C. Palmer

W. Vance Payne, II

Piotr A. Domanski

U.S. DEPARTMENT OF COMMERCE

Technology Administration

Building Environment Division

Building and Fire

Research Laboratory

National Institute of Standards

and Technology

Gaithersburg, MD 20899

July 2000

"ArEs O°

U.S. DEPARTMENT OF COMMERCE

William M. Daley, Secretary

TECHNOLOGY ADMINISTRATION

Dr. Cheryl L. Shavers, Under Secretary

of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS

AND TECHNOLOGY

Raymond G. Kammer, Director
TABLE OF CONTENTS

LIST O F TA BLES .................................................................................. .. iii

LIST O F FIG U RES .......................................................................................................... iv

A BSTRA CT ........................................................................................................................

N OM EN CLA TU RE ........................................................................................................... 2

IN TRO D U CTIO N .............................................................................................................. 3

BA CK GR OU N D ............................................................................................................... 3

D A TA A CQUISITION A N D R ED U CTION ..................................................................... 7

CORRELA TION S ............................................................................................................ 12

RESU LTS ......................................................................................................................... 15

C ON CLU SION S ............................................................................................................... 16

A CK N O W LED GM EN TS ................................................................................................ 17

REFEREN CES ................................................................................................................. 18

FIGU R ES .......................................................................................................................... 21

11
LIST OF TABLES

1. Geometric specifications of the brazed plate heat exchanger ......................................... 7

2. Comparison of polarities of mixture components ........................................................... 8

3. Average relative difference (%) in calculated

heat transfer rates for refrigerants and HTF ................................................................. 10

4. Average expanded relative uncertainties (95 % confidence level) for the evaporator .. 12

5. Average expanded relative uncertainties (95 % confidence level) for the condenser ... 12

6. Evaporator correlation formats analyzed ...................................................................... 14

7. Condenser correlation formats analyzed ....................................................................... 14

8. Values for evaporator correlation constants .................................................................. 15

9. Values for condenser correlation constants .................................................................. 16

iii
LIST OF FIGURES

1. Heat and mass flux map for evaporator correlations of interest ................................. 21

2. Heat and mass flux map for condenser correlations of interest ................................... 21

3. Evaporator schem atic ................................................................................................... 22

4. C ondenser schem atic ................................................................................................... 22

5. Comparison of correlations from literature to current evaporator study ...................... 23

6. Comparison of correlations from literature to current condenser study ...................... 23

7. Comparison of evaporative Nusselt numbers for refrigerants in current study ........... 24

8. Comparison of condensation Nusselt numbers for refrigerants in current study ......... 24

9. Evaporative Nusselt number correlation for R22, R290, and R290/ 600a .................. 25

10. Evaporative Nusselt number correlation for R32/ 152a ............................................. 25

11. Condensation Nusselt number correlation for R22, R290, and R290/ 600a .............. 26

12. Condensation Nusselt number correlation for R32/ 152a ........................................ 26

iv
ABSTRACT

Average Nusselt numbers were measured for R22, R290, R290/600a, and R32/152a

undergoing evaporation and condensation in a brazed plate heat exchanger. The

refrigerants experienced wavy, stratified flow at low heat and mass fluxes, 1.3 kW/m2 to

8.3 kW/m2 and 1.6 kg/m2 s to 19 kg/m 2 s, respectively. Heat transfer correlations from

the literature for in-tube and channel flow of refrigerants with similar heat and mass

fluxes were compared to the measured Nusselt numbers. The agreement was found to be

unsatisfactory. Evaporation and condensation heat transfer correlations were developed

from the data for this study for the combined data of R22, R290, and R290/600a and the

data for R32/152a. Separate correlations were needed because the lubricant used for

R32/152a was different than the lubricant used for the other refrigerants.

Keywords: brazed plate heat exchanger, flammable refrigerants, evaporation,

condensation, refrigerant mixtures

1
NOMENCLATURE

English symbols

A area (m2 )

a constant determined via statistical analysis

BPHE brazed plate heat exchanger

Bo boiling number (-), q "/(G hfg)

Co convection number (-), (pVpL)0° 5 {(l-x)/x}°0 8

Cp specific heat (J/kg-K)

D hydraulic diameter (m)

Fr Froude number (-), G2 /(p 2 g D)

G mass flux (kg/m2 .s)

Ga Galileo number (-), Pf (pl - Pg)gDh3 /f 2

g gravitational acceleration (m/s2 )

HTF heat transfer fluid

h heat transfer coefficient (W/m2 .K)

i enthalpy (J/kg)

K modified boiling number used by Pierre (-), Ax hfg/ (L g)

k thermal conductivity (W/m K)

LMTD log-mean temperature difference (K)

M relative molecular mass (-)

m mass flow rate (kg/s)

Nu Nusselt number (-), h DI k

P pressure (Pa)

Pr Prandtl number (-), , cp/k

Q heat transfer rate (W)

q" heat flux (W/m2)

R thermal resistance

Re Reynolds number (-), G D/

T temperature (K)

UA overall conductance (W/K)

V volumetric flow rate (m3/s)

WWHP water-to-water heat pump

x quality (kgvor /kgto)

Greek symbols superscripts

p density (kg/m3) average

# dynamic viscosity (kg/m.s) b to h constants determined via

two-phase multiplier (-), (l+12/Xtt+l/X 2)0 5 statistical analysis

Xt Martinelli parameter (-), {(1-x)Ix} 0 9 (Pv /PL) 5 (.uL/,/#v)' alternate definition

o acentric factor (-), -log1 o (PI Pc)

subscripts

c critical out outlet V vapor

co condenser p plate w water/glycol

ev evaporator r refrigerant

f saturated liquid phase red reduced

g saturated vapor phase sat saturation

in inlet sc subcool

L liquid sh superheat

lo liquid only tp two-phase

2
INTRODUCTION

Concerns about warming of the earth's climate made low global warming potential

(GWP) a desired refrigerant attribute. Flammable refrigerants have an inherently low

GWP because molecules with hydrogen atoms have short atmospheric lives. However,

the use of flammable refrigerants raises safety concerns in the U.S. The safety concerns

would be reduced if the systems using flammable refrigerants were designed so that the

refrigerant remained outside of the conditioned space. This is accomplished by use of a

water-to-water heat pump (WWHP) in which an intermediate heat transfer fluid (HTF) is

used between the flammable refrigerant and the air being conditioned. Information must

be obtained on the performance of the intermediate heat exchanger in which the HTF and

refrigerant interact in order to determine the performance of flammable refrigerants

relative to current refrigerants and each other.

Payne et al. (1999) determined the system performance of a WWHP using flammable

refrigerants. Data from the system performance study were used to develop a heat

transfer correlation for the HTF (glycol/water) in the brazed plate heat exchanger (BPHE)

(Gasche, 1998). Data collected as part of the system performance study are used in this

study, along with the HTF heat transfer correlation, to determine average heat transfer

correlations for R22 (chlorodifluoromethane), R290 (propane), R290/600a (propane/

isobutane), and R32/152a (difluoromethane/ 1,1-difluoroethane) in BPHE evaporators

and condensers. Due to the inherent difficulty in instrumenting the interior of a BPHE,

all instrumentation for these studies was placed at the inlets and outlets of the BPHE. As

such, local heat transfer information is not available and the resulting HTF and refrigerant

correlations are for average heat transfer coefficients. While the majority of heat transfer

that occurs in the BPHE is the result of a phase change, the average heat transfer

coefficients also include a small amount of sensible heat transfer associated with

superheated vapor and subcooled liquid refrigerant.

The heat and mass fluxes for this study are low, 1.3 kW/m2 to 8.3 kW/m 2 and 1.6 kg/m2 -s

to 19 kg/m2 .s, respectively, due to the desire for small temperature differences in a BPHE

with large surface area. Large surface areas were used to ensure adequate capacity for the

system performance study (Payne et al., 1999). Low mass fluxes contribute to the

laminar liquid Reynolds numbers, 13 to 230. Low mass fluxes and Reynolds numbers in

combination with the dominance of latent heat transfer and the many changes in flow

direction caused by the corrugated plates of the BPHE suggest that the flow may be

stratified or wavy. Indeed, comparison of the mass fluxes with Baker's flow pattern map

(1954) indicates that the flow is stratified.

3
BACKGROUND

Theory

The Nusselt number for fully-developed laminar flow in a rectangular channel is

constant, its value dependent on the aspect ratio (ratio of width to height) of the channel.

The aspect ratio for the BPHE is greater than 80. If the flow in the channels of the BPHE

is fully-developed and laminar, the Nusselt number is 8.235 for a constant heat flux

boundary condition and 7.54 for a uniform wall temperature boundary condition (Kays,

1980). In a BPHE, the wall temperature changes along the length of the heat exchanger

as the fluid temperatures change on each side of the plate. If sensible and latent heat

transfer occur in the BPHE, the heat flux may not be constant either. Thus, if the Nusselt

number for flow in a BPHE could be approximated as a constant, it would have a value

between 7.54 and 8.235.

In a BPHE, each contact of the corrugated plates re-initiates flow similar to that in an

entrance region. The relatively short distance between the contact points also contributes

to mixing of the bulk flow. Thus, the flow in a BPHE is not likely to be approximated by

the laminar fully-developed Nusselt number. A first attempt to characterize heat transfer

in a BPHE might include the use of entry length heat transfer correlations. This would

capture the behavior due to continually re-initiated flow but would disregard the mixing

that occurs between each re-initiation. In the entry region, the local Nusselt number is

often expressed as a function of the Reynolds and Prandtl numbers, the distance from the

entrance, and the tube diameter (Incropera and DeWitt, 1990). The passages of the BPHE

are such that the entire distance the fluid travels before encountering a change in direction

is of the same magnitude as the hydraulic diameter of the BPHE. Thus, the it may be

possible to express the Nusselt number as a function of the Reynolds and Prandtl

numbers alone. This is one of several possible relationships considered in the present

study.

Literature on Evaporation

A number of studies have been done on the heat transfer and pressure drop characteristics

of BPHEs for liquids, e.g., Bogaert and Bolcs (1995) and Tinaut et al. (1992). Thonon et

al. (1997) examined the transition from nucleate to convective boiling in compact heat

exchangers and concluded that it depends on the product of the boiling number and

Martinelli parameter but did not develop a heat transfer correlation.

Kattan et al. (1998) classified flow regimes for heat transfer in horizontal tube flow and

developed corresponding local heat transfer correlations. The flow regime of interest for

the present study, stratified flow, was one of several for which Kattan et al. did not

develop a correlation.

Kedzierski and Kim (1998) examined boiling heat transfer for a variety of pure

refrigerants and refrigerant mixtures using a tube with a twisted-tape insert. They

developed a correlation for the evaporation heat transfer Nusselt number by

hypothesizing that it depended on the Prandtl, Reynolds, and Boiling numbers, the

4
reduced pressure, the acentric factor (w), and the twist ratio. Since the present study did

not use twisted-tape inserts, the twist ratio was not relevant.

Smith et al. (1993) studied refrigerant evaporation in horizontal tubes at low heat and

mass fluxes. For this flow regime, wavy/stratified flow, Smith considered several

published correlations including those of Kandlikar (1990), Jung et al. (1989), Pierre

(1956), and Shah (1982) and then developed new correlations for R12 and R134a,

R22/123, and R22/141b. Because few BPHE correlations are available, Smith's R12 and

R134a correlation was used by Bansal and Purkayastha (1998) in an NTU-e model for

alternative refrigerants (R22 and R290) in BPHE. The correlation relates the refrigerant

Nusselt number (Nu) to the Nusselt number for the liquid phase of the refrigerant (Nuj)

and the boiling number (Bo):

Nu = NuL[4.3 + 0.4(Bo .104

)' 3

] (1)

Because Smith's correlation used heat and mass flux ranges similar to those observed in

the present study and has been applied to determine BPHE evaporator capacity, it was

chosen for further discussion here. Additional correlations by Smith incorporate the

Martinelli parameter (X) and the Froude number (Fr). These correlations, for R22/123

and R22/114, respectively, are:

Nu = NuL[aXbFrc + dBoe] (2)

Nu = aNuLXbFrCBod (3)

Two of the published correlations examined by Smith et al. (1993) were deemed

unacceptable for use in developing the BPHE correlation for this study, those of

Kandlikar (1990) and Jung et al. (1989). Kandlikar's correlation employs an empirical

fluid-dependent parameter, Ff, values of which are not available for all of the fluids

considered in the present study. Jung et al. (1989) developed a local evaporative heat

transfer correlation for refrigerants in horizontal flow boiling regime which was

dependent on bubble contact angle, information that is not available in the present study.

In addition, the form of Jung's correlation cannot be linearized, a restriction placed on

correlations considered in the present study to assure that all statistical analyses could be

carried out with equal accuracy. The heat and mass flux regions for the remaining

correlations considered by Smith et al. (1993) are illustrated in Figure 1.

Pierre (1956) developed a model for evaporation of R12 and R22 inside plain horizontal

tubes. The overall form of the average Nusselt number (Nu) is given as:

Nu = aReo Kb (4)

where:

Re GD (5)

5f

5
Shah (1982) developed local heat transfer correlations for vertical and horizontal flow in

tubes and annuli and expressed the Nusselt number as a function of the liquid Nusselt

number, the Froude number, and the convection number (Co):

Nu = aNuLFrbCoc (6)

Literature on Condensation

Figure 2 is a map representing some of the condensation correlations found in the

literature. The map also contains information on the heat and mass fluxes of interest in

the present study. A discussion of the details of the correlations from the literature is

provided below.

Panchal (1984) studied the condensation of ammonia and R22 in plate-fin heat

exchangers to determine the overall heat transfer coefficient. A correlation was not

developed. Guo and Anand (1999) developed a correlation for the condensation of

R410A in rectangular channels, meant to simulate the flow channels in plate-fin heat

exchangers. The mass flux range considered was 30 kg/m2.s to 200 kg/m2 -s. From the

information provided in the paper, the heat flux range was determined to be

approximately 5.6 kW/m2 to 38 kW/m2 .

Soliman et al. (1968) developed a correlation for condensing heat transfer with turbulent

flow based on the liquid shear stress at the tube wall. Fluids considered had Prandtl

numbers ranging from one to ten. Calculation of the wall shear stress required

knowledge of local quality and thermophysical properties. The heat and mass flux ranges

for which the correlation holds were not specified. This correlation was not pursued

further here due to the lack of information on the heat and mass fluxes.

Traviss et al. (1973) developed a heat transfer correlation for in-tube condensation of R12

and R22 which was dependent on the liquid phase Reynolds and Prandtl (Pr) numbers

and the Martinelli parameter. The heat flux range considered was approximately

8 kW/m 2 to 85 kW/m2 ; The mass flux range was 784 kg/m2.s to 7450 kg/m2 -s. For the

liquid Reynolds numbers of interest in the present study, the correlation is:

Nu f(X,)PrL Reo9

F2 (7)

F2 = 5PrL+ 5 1n{ + PrL(0.0936ReL 5-1)

In order to use this correlation for the data in the present study, f(X) was assumed to be a

linear function of the Martinelli parameter and the values for the coefficients and

exponents in the expression for F2 were assumed to be the same as those given by Traviss

(1973).

6
Shah (1979) developed a simplified correlation for film condensation of water, R1 1, R12,

R22, R113, methanol, ethanol, benzene, toluene, and trichloroethylene applicable for

mass fluxes from approximately 11 kg/m2 .s to 211 kg/m2 s and heat fluxes from

0.16 kW/m2 to 1900 kW/m2 . The correlation allowed determination of the average twophase heat transfer coefficient from the liquid heat transfer coefficient and the reduced

pressure (Ped):

Nu = Nu (0.55 ,. + (8)

/red )

In the correlation developed by Kaushik and Azer (1988) for steam, R113, and R11 in

smooth and internally finned tubes, the two-phase Nusselt number was a function of the

liquid phase Reynolds and Prandtl numbers, the reduced pressure, and a geometric

parameter (the ratio of the hydraulic diameter to the heat exchanger length). In the

present study, the same heat exchanger was used to obtain all data. As such, the

geometric parameter has no influence on the heat transfer correlation.

For condensation of a variety of refrigerants in tubes with twisted-tape inserts, Kedzierski

and Kim (1998) used all of the parameters used by Kaushik and Azer and added the

acentric factor and the Jacob number. The Jacob number is the ratio of sensible to latent

heats where the sensible heat transfer is determined from the difference between the

saturation and wall temperatures. In the present study, wall temperatures were not

measured. Thus, the Jacob number could not be evaluated.

The correlation developed by Chitti and Anand (1996) for smooth tube condensation of

R22 and R32/125 includes terms that depend on the properties of the HTF. This

approach was deemed unacceptable in the present study as it was desired to have a

correlation that relied only on measured quantities and calculated properties of the

refrigerant.

DATA ACQUISITION AND REDUCTION

Brazed plate heat exchanger

BPHEs are used for the evaporator and condenser of the WWHP. In each of these heat

exchangers, heat is transferred between the refrigerant and the HTF. The BPHE is

described below in Table 1 (SWEP, n.d.).

7
Table 1. Geometric specifications of the brazed plate heat exchanger.

Type B25-30

Number of plates 30

Number of thermal plates 28

Number of glycol/water channels 15

Plate gap 0.002 m

Heat transfer area per plate 0.0546 m2

Channel cross-sectional flow area 0.000226 m2

Experimental setup

Gasche (1998) and Payne et al. (1999) provide the details on the experimental setup and

methods used to acquire the data analyzed in this report. Flow paths and measured data

are illustrated in the schematic of Figures 3 and 4. General test conditions included

3.9 °C superheating at evaporator outlet and 3.9 °C subcooling at the condenser outlet.

The mixtures considered are zeotropic and experience a temperature glide of

approximately 6 °C during the phase change process.

Data were taken for operation of the WWHP in both heating and cooling modes. The

fixed test conditions for the cooling mode are the indoor dry-bulb temperature of 26.7 °C,

the temperature of the HTF entering the condenser of 25 °C, and the HTF temperature

difference of 5.6 °C across both the evaporator and condenser. In the heating mode, the

fixed test conditions are the indoor dry-bulb temperature of 21.1 °C and the temperature

of the HTF at the evaporator inlet of 0 °C.

Refrigerants analyzed

The refrigerants tested in the WWHP investigation and originally considered in this study

include R22, R290, and mixtures of R290/600a (70/30 by mass), R32/152a (50/50 by

mass), and R32/290 (50/50 by mass). The R32/290 was not used in developing the

correlations described in this report due to an average difference of more than 23 %

between the refrigerant and glycol energy balances. The discrepancy was likely due to

the very different polarities of R32 and R290. Polarities for refrigerants used in mixtures

in this study are provided in Table 2. The dipole moments (polarities) of R290 and

R600a are similar in magnitude as are the dipole moments for R32 and R152a. The

dipole moments of R32 and R290 are, however, quite different. The property model for

mixtures used in REFPROP 6.01, the source for all property data for this study, was

developed from experimental data for binary mixtures with components of similar

8
polarities and, most likely, cannot accurately simulate properties of mixtures of

refrigerants with significantly different polarities (McLinden, 1999).

Table 2. Comparison of polarities of mixture components.

Dipole moment at normal boiling point (debye)

Mixture:components (1/:2) ' :: Component ' 1 Component2 _ 

R290/600a 0.000 ' 0.132

R32/152a ' ' 1.978 · 2.262

R32/290 1.978 0.000

Data analysis

The following assumptions were made in analyzing the data:

1. steady-state operation,

2. heat loss to the surroundings is negligible,

3. fluid flow is equally distributed throughout all channels of the heat exchanger,

4. no conduction occurs via channel walls or the fluid itself in the direction of

fluid flow, and

5. thermal properties of the working fluids are constant throughout the heat

exchangers and can be evaluated at an average temperature.

For the evaporator, the temperature used to evaluate thermophysical properties of the

refrigerant is determined by averaging the saturation pressure calculated from the

measured inlet temperature and outlet pressure. The average temperature of the

refrigerant is then taken as the saturation temperature at this average pressure. For the

condenser, the refrigerant temperature used for evaluating thermal properties is the

average of the saturation temperatures evaluated at the measured inlet and outlet

condenser pressures.

The overall energy balance for both the evaporator and condenser is:

Qw =(UA) LMTD= ALMTD (9)

hwA +hA P +p +hrA

where the heat transfer rate, Qw, is determined from the HTF. The log-mean temperature

difference is LMTD, Rp is the resistance of the plate, A is the total heat transfer area, and

hw and h, are the heat transfer coefficients for the HTF and refrigerant, respectively.

The HTF heat transfer rate (Qw) for the evaporator (ev) and condenser (co) is calculated

as:

Qw,e = mw,evCp,w (Tw,ev,in- Twevout )

wco = mwcop.w (Twco,out - Twcoin ) (0)

9
where mw is the HTF mass flow rate and Cp is the HTF specific heat.

The heat transfer rate for the refrigerant (Q) is:

Qr,ev = mr (r,ev,out -r,ev,in )

Qrco =mr (r,coin - r,co,out) (11)

where mr is the refrigerant flow rate and i represents enthalpy. The inlet refrigerant

enthalpy, i. , was assumed to be equal to the refrigerant enthalpy entering the expansion

valve. Table 3 summarizes the variation in heat transfer rates as calculated using

refrigerant and glycol properties for each refrigerant in both the evaporator and

condenser. The relative difference in heat transfer rates is determined from the

expression:

% difference ( Q -Qr)100 (12)

where the upper signs are for the evaporator and the lower signs are for the condenser.

Table 3: Average relative difference (%) in calculated heat transfer rates for refrigerants

and HTF.

Evaporator Condenser

Refrigerant Heating mode Cooling mode Heating mode Cooling mode

R22 2.1 -1.5 -1.1 -3.1

R290 2.0 -0.4 -2.0 -0.8

R290/600a -6.7 -3.5 2.4 1.3

R32/152a 18 5.8 -16 -5.9

The average magnitude of the difference in heat transfer rates between the HTF and

refrigerant is less than 18 % in all cases. The uncertainties seen with the mixtures in

Table 3 are most likely due to the refrigerant properties as calculated by REFPROP. This

is evidenced by the less than 5 % disagreement in the energy balance seen with the pure

fluids. The correlations were developed using the water-side heat flux which was

measured with less uncertainty that the refrigerant-side.

The log-mean temperature difference, LMTD, used in Eqn. 9 is for the entire heat

exchanger and is determined from a weighted average of the LMTDs for each segment of

the heat exchanger; superheat, two-phase, and subcooled (Kedzierski, 1997):

10
LMTDev = QHT

QHTF,ev,sh + HTF,ev,tp

LMA/TDHT,ev,sh LMTDHi-,ev,tp

(13)

LMTDco = ^QHF

QHTF,co,sh + QHTF,co,tp QHTF,co,sh

LMTDHTF,co,sh LMTDF,co,tp LMTD ,co,sh

An alternate method far determining LMTD is to neglect the refrigerant subcooling and

superheating and use the refrigerant saturation temperature instead of the actual

refrigerant inlet and outlet temperatures in the expression for LMTD. This approach may

be reasonable for cases; with small percentages of the overall heat transfer occurring in the

subcooled and superheated regions. The expressions for LMTD in this case are:

LlTDev/ '= (TW out --Trn v- (TW,in - r,satout )ev L{TD,( =

ln T

w '

ot - Tr in

Twin rsat ev (13)

LA/rTDco'T' (Twin_ - r,sat,out co - (Twout - Trsat.in )co LrTD co T -T

ln wi - r,sat,out

Tw, out - r,sa,,in o,

where T,, is the measured refrigerant inlet temperature and Tsat is the saturation

temperature of the refrigerant evaluated at the refrigerant pressure.

Comparison of the two definitions for LMTD shows that the relationship between heat

transfer and weighted average LMTD (Eqn. 12) is more nearly linear for all but one

refrigerant in one heat exchanger (R290/600a in the evaporator). Thus, the weighted

average LMTD is used to determine the heat transfer coefficient in this study.

The HTF heat transfer coefficient, hw, is determined from the liquid Nusselt number

(NUL) correlation development of Gasche (1998):

NuL = 0.16Re 8 9 Pr0 3 (14)

L L (14)

hw = NuLkL /D

where the exponent on the Prandtl number depends on whether the fluid is being heated

(0.4) or cooled (0.3). Eqn. 14 differs in two ways from that developed by Gasche. First,

several data points were inadvertently omitted from the statistical analysis used to

determine the values for the constants in Gasche's work. These points are included in the

determination of the constants for this work. Secondly, Eqn. 14 does not include the ratio

11
of bulk fluid viscosity to viscosity at the plate surface temperature which Gasche

included. The constants in the correlation were determined with and without the

viscosity ratio term and were found to be identical in both cases. Thus, the viscosity ratio

term has no influence on the heat transfer coefficient and is not included in the correlation

for simplicity.

The energy balance of Eqn. 9 was solved for the refrigerant heat transfer coefficient, h,,

and the refrigerant Nusselt number was determined from the expression:

Nu = (15)

kL

Uncertainty analysis

Before any correlations were considered, data points with expanded relative uncertainty

(95 % confidence level) of the two-phase Nusselt number greater than 50 % were

removed. For the evaporator, this resulted in the removal of just five points, all of them

for R290. For the condenser, five points were removed, three for R22 and two for R290.

Data points for which LMTD was undefined due to a negative temperature difference in

the natural log term were also eliminated. The negative temperature difference resulted

because the uncertainty in the temperature measurement was greater than the actual

temperature difference between the fluids. This affected only R290 in the condenser,

requiring the removal of four additional data points. After the removal of data due to the

Nusselt number uncertainty criteria, LMTD criteria, and statistical analyses, the average

expanded relative uncertainties were determined for the primary calculated parameters

and are provided in Tables 4 and 5.

Table 4. Average expanded relative uncertainties (95 % confidence level) for the

evaporator.

UNCERTAINTY (%)

R22 R290 R290/600a R32/152a

Parameter heat cool heat cool heat cool heat I cool

hr 25 12 21 15 19 15 9.9 9.0

LMTD 11 6.1 9.2 7.5 9.0 8.4 7.0 4.7

m, 0.08 0.08 0.08 0.08 0.07 0.07 0.09 0.08

NuL' 17 17 17 17 17 17 17 17

Nu, 25 12 21 15 19 15 9.9 9.0

Qr 0.2 0.2 0.3 0.3 0.3 0.3 0.2 0.2

Qw 11 6.0 11 6.1 11 6.1 12 6.1

ReL 1.2 1.1 1.1 1 1.1 1.1 1.1.2 1.1

- estimated from Gasche (1998)

12
Table 5. Average expanded relative uncertainties (95 % confidence level) for the

condenser.

l_______ UNCERTAINTY (%)

R22 R290 R290/600a R32/152a

Parameter heat cool heat cool heat cool heat cool

h, 30 13 18 14 5.8 7.8 10 9.6

LMTD 9.4 4.8 7.4 5.3 5.9 3.9 6.4 3.4

mr 0.09 0.08 0.08 0.08 0.07 0.07 0.09 0.08

NuL 17 17 17 17 17 17 17 17

Nu, 30 13 18 14 5.8 7.9 11 9.7

Qr 0.20 0.20 0.25 0.25 0.24 0.24 0.19 0.19

Qw 8.0 6.1 7.9 6.2 7.3 6.2 9.3 6.1

ReL 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2

- estimated from Gasche (1998)

CORRELATIONS

The heat and mass flux ranges for the evaporator and condenser correlations in the

literature that were considered as comparisons for this study are shown as shaded regions

in Figures 1 and 2. These illustrations, similar to that used by Smith et al. (1993), also

contain regions covering the heat and mass flux ranges for the data of this study. As seen

from the figures, the heat and mass fluxes for this study are generally lower than those for

the studies in the literature. Only the Shah evaporator correlation has any overlap with

the data considered here. Thus, it is not expected that any of the correlations will fit the

present data well, as seen for R22 in Figures 5 and 6 which show the two-phase Nusselt

number predicted by various correlations versus the two-phase Nusselt number

determined from the data for this study. Very few of the two-phase Nusselt numbers

from the correlations are within 25 % of the calculated Nusselt numbers.

In addition to examining the accuracy of using correlations from the literature for the data

of this study, the behavior trends for the refrigerants in this study were compared with

one another. Two distinct data trends are noticeable in Figure 7, a plot of the two-phase

Nusselt number versus the liquid refrigerant Reynolds number for the evaporator. The

liquid refrigerant Reynolds number is determined using the mass flux (G) for the liquid

portion of the flow (1- x):

G(1-x)D ReL- G- (16)

/AL

If a distinct curve could be seen in Figure 7 for each refrigerant, the correlation of the

Nusselt number using solely Reynolds and Prandtl numbers would be suggested. Use of

the Prandtl number might collapse all curves into one. This is not the case for the data in

13
Figure 7. The R32/152a data has distinctly lower Nusselt numbers at given Reynolds

numbers than the data for the other refrigerants. This is likely attributable to the fact that

R32/152a used a different lubricant than the other refrigerants. Mineral oil was used with

all refrigerants except R32/152a which used a polyol ester oil (POE). The use of a

different lubricant was necessary due to immiscibility and poor oil return in R32/152a.

By using a POE with R32/152a, oil/ refrigerant miscibility was obtained. The distinctly

different behavior of R32/152a from the other refrigerants shown in Figure 7 is

accommodated by developing a correlation for it separate from the correlation developed

for the combined data of R22, R290, and R290/600a. The difference between R32/152a

and the other refrigerants is not as distinct in the condenser as it is in the evaporator (see

Figure 8). However, the difference is statistically significant and, thus, indicated the need

for separate condenser correlations.

In all, 13 evaporator and 6 condenser correlation forms were selected from those in the

literature for examination in this study. The forms of the correlations are provided in

Tables 6 and 7. Some correlations, e.g, those of Shah and Traviss, were developed by

combining dimensionless parameters from the literature correlations in formats that could

be linearized. The Guo correlation does not contain the Jacob number because the wall

temperature is not known for the data in this study. In some cases, the exponents on NUL,

ReL, and PrL were not determined by statistical analysis but were pre-set to values

typically found in the literature. All correlations considered, except Pierre's, contain

either ReL and PrL or NuL because NuL is itself a function of ReL and PrL as shown in Eqn.

14.

14
Table 6. Evaporator correlation formats analyzed.

No. Form Source

1 Nu = a ReLb PrL: Bod we Kedzierski (1998)

2 Nur = a Reob Kc Pierre (1956)

3 Nu, = a NuLb Frc Cod Shah (1982)

4 Nu= a NuLbFrc Cod (b 1) Shah (1982)

5 Nur = a NULb Bo' Frd Coe variation of Shah

6 Nu, = a NuL Bo" Frd Coe variation of Shah

7 Nu = a NuLb Bo' Frd Xe Smith (1993)

8 Nu, = a NuL Bo" Frd Xne Smith (1993)

9 Nu, = a NuLb Bo: Frd W)e Cof XtgM h combination of 1-8

10 Nu, = a NUL BoC Frd Ce Cof X g Mh combination of 1-8

11 Nu = a ReLb Pr': Bo d c e Frf Cog Xth combination of 1-8

12 Nu, = a ReLO-8 PrL0' 4 Bod o e Frf Cog Xth combination of 1-8

13 Nu, = a ReLb PrL' 4 Bod we Frf Co Xth combination of 1-8

Table 7. Condenser correlation formats analyzed.

No. Form [ Source

1 Nu = a L

b ReL PrLd Gae Guo (1999)

2 Nu, = a ReLb PrL' Xad Traviss (1973)

3 Nu, = a NuLbPred Shah (1979)

4 Nu = a ReLb PrL' Pred d _e Kedzierski (1998)

5 Nur = a NuLb L( Gad X e Pred f g combination of 1-4

6 Nur = a ReLb PrL': L

d Gae XP, Ped g Ch combination of 1-4

The correlation forms considered in this study were chosen for the dimensionless

parameters they employed and for their ease of linearization. The linearization

characteristic was necessary in order that statistical analysis tools for linear functions

could be employed to their fullest capacity. For example, correlation 1 in Table 6 and its

linearized counterpart are:

Nur = aReL PrL Bo oe

ln(Nur) = lna + b lnReL + c n PrL+ d lnBo + eln w

The possible dimensionless parameters that influence the two-phase Nusselt number for

the BPHE are selected from those used in correlations for similar flow regimes in the

literature. Where needed, the correlation for the HTF heat transfer coefficient, Eqn. 14, is

used for the refrigerant liquid-phase Nusselt number, NuL.

As mentioned previously, two correlations were developed for each heat exchanger, one

for the combined data of R22, R290, and R290/600a and one for R32/152a. The

15
constants in each correlation were determined using statistical analysis software. After

the constants were found for all correlations, the best correlation was chosen as the one

for which the standard deviation of the residuals was a minimum. In the process of

developing each correlation, only those terms in the correlation deemed to be statistically

significant were retained. After ensuring that all terms in the correlation were significant,

data points were removed from the data set if they were determined to be highly

influential or outliers. Originally, 131 data sets were considered for R22, R290, and

R290/600a. After elimination of data due to high Nusselt number uncertainty, undefined

LMTD, and poor statistics, 106 data points were used for the evaporator correlation and

107 data points were used for the condenser correlation. Because the original data set for

R32/152a was small (20 points) and none of the points had high Nusselt number

uncertainty or undefined LMTD, all data points were retained in examining all

correlations for the evaporator and condenser.

RESULTS

Evaporator

The evaporator correlation for R22, R290, and R290/600a results from correlation

number 1 in Table 6:

Nur = aRe~ PrL Bodoe (18)

The values for the constants in the final correlations are provided in Table 8. Figure 9 is

a graph of Nu4 calculated from the data versus Nu, determined from the correlation for

R22, R290, and R290/600a. Lines for the mean and ±25 % tolerance are shown on the

figure, revealing that Eqn. 18 correlates 65 % of the data within approximately ±25 %.

The evaporator correlation for R32/152a results from correlation number 9 in Table 6:

Nur = aNubBoCFrdoeCofX8Mh (19)

The values for the constants in Eqn. 19 are provided in Table 8. Figure 10 shows the

relationship between calculated and correlated Nu4 for R32/152a. Eqn. 19 correlates

100 % of the data within ±25 %.

Table 8. Values for evaporator correlation constants.

constant R22, R290, and R290/600a R32/152a

(Eqn. 18) (Eqn. 19)

a 2.7 1

b 0.55 0.42

c 0.50 0

d 0 0.088

e 0 1.5

f - 1.5

g - 0

h 1.5

16
Condenser

The condenser correlations for R22, R290, and R290/600a and R32/152a both result from

correlation number 5 in Table 7:

Nur = aNuLGa XtPdco (20)

The values for the constants in the condenser correlations are provided in Table 9.

Table 9. Values for condenser correlation constants.

constant R22, R290, and R290/600a l R32/152a

a 1 1

b 0.387 0.298

c 0.0824 0

d 0.346 0.346

e 0 0

f 1.5 1.5

g 1.5 1.5

Figure 11 is a graph of the NuT calculated from the data versus the Nur determined from

the correlation for R22, R290, and R290/600a. Lines for the mean and ±25 % tolerance

are shown on the figure and Eqn. 20 correlates 90 O% of the data within ±25 %. Figure 12

provides this same information for R32/152a where Eqn. 20 correlates 80 % of the data

within ±25 %.

CONCLUSIONS

Average evaporation and condensation heat transfer correlations were developed for low

heat and mass fluxes for R22, R290, and R290/600a as well as for R32/152a in BPHEs.

The need for separate correlations may be attributable to the use of difference lubricants

for the refrigerants; mineral oil was used with R22, R290, and R290/600a, and POE was

used with R32/152a.

The accuracy of the data used in this study, as shown in Tables 4 and 5, and the resulting

correlations reflect the fact that data were acquired as part of a study of overall WWHP

performance. The measurements made in this study are typical of those taken during

actual system operations and, thus, allow the correlations developed to be used in actual

system design. It is important to note that the Reynolds numbers of this study were lower

than shown for any of the referenced data taken by other investigators. This study has

filled a low Reynolds number gap and also shown the importance of accurate refrigerant

properties for refrigerant mixtures having very different dipole moments.

17
ACKNOWLEDGMENTS

This work was jointly funded by NIST, the United States Naval Academy Research

Council and the US Department of Energy (project no. DE-AI01-97EE23775), under

manager Esher Kweller. The authors express their appreciation to Dr. Mark Kedzierski

of NIST for his help in the statistical analysis of the data and to Lt. Cmdr. Dan Ray of the

US Naval Academy for his thorough review of this work.

18
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19
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1,pp. 113-122.

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20
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21
1000

Pierre

100

·S . h ah (1982)

o- 10

'1 -

Smith R20.41B Smith R22/123

0.1

0.1 1 10 100 1000

Mass flux, G (kg/m 2 s)

Figure 1. Heat and mass flux map for evaporator correlations of interest

10000

1000

100

10

0- ml. -------- (1979) _--Shah 

0.1

1 10 100 1000 10000

Mass flux, G (kg/m 2s)

Figure 2. Heat and mass flux map for condenser correlations of interest.

22
800

60 4·/~ ~~0I _ _9 oi I

0O ;AlRe,

Figure 7. Comparison of evaporative Nusselt numbers for refrigerants in current study.

8 E a

zK e ri a c3

20 A A ; O R22-

200 ________________R 1 - _ __ X X __ __________ 22

8 X~ 2 A.AA~~~0 |I-~ *1 R290

A^TK i AA R290/600a |

R32/152a

0 0060 80 1 00 1 2 010 0 180

Re,

Figure 7. Comparison of evaporndensative Nusselt numbers for refrigerant in current study.

23

i g .^ , + =o a ] a '

3" 60 I A 

X0 A A ,.22 0----

|ax R32/152a

0 50 100 150 200 250

Re,

Figure 8. Comparison of condensation Nusselt numbers for refrigerant in current study.

23
80

. , A R22

>;3 ' / i w , . ~ R290/600a 40

A /,-LA' Mean

0/ ' -.

0 20 40 60 80

Correlation Nur

Figure 9. Evaporative Nusselt number correlation for R22, R290, and R290/600a.

25 A

Ic~~ I-~ ^J^~I~~~~ ^X R32/152a ~ 5 ._As _ Mean

5 1- _ ' i ___- - -+25%

/X-[\ - --25%

0 5 10 15 20 25

Correlation Nu,

Figure 10. Evaporative Nusselt number correlation for R32/152a.

24
120

80

Z

60 R2

E R

[] R290

3 40 X 40 1 I /~ I /____llMean~X~Ba~WC~fLI ' JI/ ~h A A R290/600a

2xx~ / J _ _~~~~~ _+25%

20

0 20 40 60 80 100 120

Correlation Nu,

Figure 11. Condensation Nusselt number correlation for R22, R290, and R290/600a.

70

40 __l

50 -_ -/t X_____________ _______________ ____ _an_ Mean 

i ' · .-'i - 1 7 .

I 30. ___ ___ ____- _ _--25%

10 _ _/

0 10 20 30 40 50 60 70

Correlation Nu,

Figure 12. Condensation Nusselt number correlation for R32/152a.

25
i