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Purdue UniversityPurdue e-PubsInternational Refrigeration and Air ConditioningConference School of Mechanical Engineering
2018
The Effect of Refrigeration Lubricant Properties onNucleate Pool Boiling Heat Transfer PerformanceJung-Tsung HungPatech Fine Chemicals Co., Ltd., Taiwan, Republic of China, [email protected]
Yu-Kai ChenPatech Fine Chemicals Co., Ltd., Changhua County 50741, Taiwan, [email protected]
Hou-Kuang ShihPatech Fine Chemicals Co., Ltd., Taiwan, [email protected]
Shou-Ren ShengDepartment of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan, [email protected]
Chi-Chuan WangDepartment of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, [email protected]
Follow this and additional works at: https://docs.lib.purdue.edu/iracc
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.html
Hung, Jung-Tsung; Chen, Yu-Kai; Shih, Hou-Kuang; Sheng, Shou-Ren; and Wang, Chi-Chuan, "The Effect of Refrigeration LubricantProperties on Nucleate Pool Boiling Heat Transfer Performance" (2018). International Refrigeration and Air Conditioning Conference.Paper 1921.https://docs.lib.purdue.edu/iracc/1921
2318, Page 1
17th International Refrigeration and Air Conditioning Conference at Purdue, July 9-12, 2018
The Effect of Refrigeration Lubricant Properties on Nucleate Pool Boiling Heat
Transfer Performance
Jung-Tsung Hung1* [email protected],
Yu-Kai Chen1 [email protected]
Hou-Kuang Shih1 [email protected]
Shou-Ren Sheng2
Chi-Chuan Wang2 [email protected]
1Patech Fine Chemicals Co., Ltd., Changhua County 50741, Taiwan www.patechfc.com.tw
2Department of Mechanical Engineering, National Chiao Tung University, Hsinchu 300, Taiwan
ABSTRACT
Refrigeration lubricant plays a key role in lubricating and sealing during vapor compression processes.
However, it may migrate to the evaporator to influence the heat transfer characteristics, either enhancement or
degradation. The aim of this study is to fundamentally understand the effect of lubricant properties and bubble
parameters on heat transfer performance.
To clarify parameters affecting the heat transfer coefficient, several experiments were conducted on a
horizontal flat surface, and pool-boiling phenomenon was recording by high-speed camera. Comparisons of heat
transfer measurements for different refrigerant/lubricant mixtures were made, including two different
refrigerants (R-134a & R-1234ze) and eight POE lubricants with different miscibility, ISO68 to ISO170
viscosity range. This study shows that improvements over pure refrigerant heat transfer can be obtained for
refrigerant /lubricant mixtures with small lubricant mass fraction, high lubricant viscosity, and a low critical
solution temperature (CST). The presence of lubricant will decrease the departure bubble diameter and may
deteriorate heat transfer performance when the lubricant mass fraction is higher than 3%.
A mechanistic explanation was provided for the observed refrigerant/lubricant boiling phenomenon, and we
were successfully in creating a new model to quantify the effect of lubricant properties on the heat transfer
performance. This model was developed based on site-activation boiling theory, interfacial energy between metal-
liquid surface, liquid-bubble interface, and surface excess density calculation. According to the model, the
presence of lubricant layer on metal surface and surrounding the bubble will significantly alter waiting time of
boiling, bubble size, bubble departure time, activity site density of boiling incipience and superheat on heating
surface.
1. INTRODUCTION
For lubrication of the mechanical compressor in a vapor refrigeration system, polyolester refrigeration oils
(POE) are in common use. A small amount of refrigeration oil is carried out of the compressor with the
discharge vapor into the circuit of the refrigeration system. Since the oil separator cannot secure the oil in total,
the tiny amount of oil will accumulate in the evaporator and changes the thermodynamics and transport
properties of refrigerant mixtures, such as viscosity and surface tension. Consequently, lubricant oil would
impose a significant influence on the heat transfer characteristics (Hung et al, 2016).
Several studies were focused on the oil effect on heat transfer performance in POE/refrigerant systems.
Kim et al. (2013) investigated POE/R134a heat transfer in three kinds of enhance tubes. Spindler & Hahne
(2009) measured ISO55/170 POE in R-134a, and the results show HTC of 3% oil mixture is higher than the
other concentration. Mohrlok (2001) conducted POE/R507 mixture test by using smooth tube. Kedzierski
(2001) concluded that oil with higher viscosity and poor miscibility will result in higher HTC in POE/R134a
system.
For boiling mechanism survey of oil-refrigerant mixture, Kedzierski (2003) provided a semi-theoretical
model for predicting refrigerant/lubricant mixture pool boiling heat transfer. Jensen and Jackman (1984) and
Mitrovic (1998) suggested a reasonable concept for boiling of refrigerant and lubricant mixture. More volatile
component refrigerant evaporates preferentially and leaves the less volatile component (lubricant) at the heating
surface and around the bubble, forming an oil-rich layer.
In this study, we try to investigate the phenomenon and heat transfer performance in POE/R134a and
POE/R1234ze system. Furthermore, we will provide a suitable model to make a good correlation with
experimental data.
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17th International Refrigeration and Air Conditioning Conference at Purdue, July 9-12, 2018
2. EXPERIMENTAL APPARATUS AND PROCEDURES
2.1 Experimental Apparatus A schematic of the experimental apparatus is shown in Figure 1. It consists of a test vessel, a condenser, and a test
plate made of copper. A heater is installed beneath the test copper plate and adhesive material is used to minimize
the contact resistance. The heater can provide a power ranging from 9 to 63 Watts. Correspondingly, the supplied
heat flux spans from 10 to 70 W/m2. The supplied heat in passes through the test plate vaporizes the working
fluid, yet the generated vapor is condensed at the coiled condenser located at the top part of test vessel. The test
vessel is made of stainless steel with a glass window to observe the boiling phenomena. Boiling characteristics
are then recorded by visual observations from a high speed-camera (Mega speed, MS-40K. 500~1000fps).
The detailed geometry of the test section is shown in Figure 2. The copper plate contains a square area of 30 mm
30 mm and five thermocouples are installed at the grooves to measure the wall temperatures. The detailed
locations of five T-type thermocouples to are also depicted in Figure 2. The heater is attached below the test
section and it is seated on fiber glass to prevent the heat loss. An O-ring is used to the test section to prevent the
leakage of the refrigerant/lubricant mixture. A direct-current power supply is used to provide the power source of
the heater which can reach 75W. The heat loss to the backlite is estimated by two thermocouples attached below
the heater. All the data signals are collected and converted by a data acquisition system (MX100). The oil injection
facility consists of an electrical scale and a pump (MEZ, model 7AA71M06K, 1/4 hp) and a 3-way valve to inject
the oil into the system. The pump speed was controlled by an inverter. 2.2 Experimental procedures
Initially, the teat section was cleaned and checked for any possible leakage before charging the refrigerant.
Then the system was evacuated using a vacuum pump (ULVAC, GVD050A, ultimate pressure is 510-4 torr).
The vacuum pump continued working for another 30 minutes to reach a corresponding vacuum pressure lower
than 0.01 torr to ensure negligible influence of non-condensable gases. The system pressure is measured by a
pressure transducer (YOKOGAWA, FP101A-D21-L20A*B/A1, the range is 0~2MPa). The accuracy of
pressure transducer was within 0.35%, and the accuracy of T-type thermocouple was ±0.1℃.
The system pressure can be adjusted by controlling the condenser temperature. Yet the condenser
temperature is set by a low temperature thermostat whose working fluid is ethanol/water mixtures (50 wt. %).
During the tests, the saturation temperature of the system is maintained at either 0℃ or 10℃. The criteria for the
steady-state condition were variation of system pressure within ±1 kPa and mean temperature variation were
less than ±0.1℃ over five minutes. Tests were conducted subject to five different oil concentrations (0%, 1%,
3%, 5%, and 10%, in weight percentage).
The heat transfer coefficient was calculated as follows:
where Q is the heating power, Qloss is the heat loss and Qtest is the heat into the test section, Tsat is the saturation
temperature for pure refrigerant based on the measured system pressure. A0 is the surface area of copper plate.
Tw is the mean average wall temperature of the copper plate, which can be calculated from the measurements of
inside temperatures as
Where Tc is the arithmetic mean of five inside wall temperature, δℎ is the distance between the thermocouples
and the outer surface of the copper plate. The uncertainty of the heat flux is 3% to 11.2%, and the heat transfer
coefficient is 3.1% to 11.4%.
Fig.1 Schematic diagram of experimental setup
Fig.2 Details of the test section
(1) h =Q − Qloss
A0(Tw − Tsat )=
Qtest
A0(Tw − Tsat )
(2) Tw = Tc −Qtest × δℎ
kA0
2318, Page 3
17th International Refrigeration and Air Conditioning Conference at Purdue, July 9-12, 2018
3. EXPERIMENTAL RESULTS AND DISCUSSION 3.1 Refrigeration oil basic data
We have developed various types of POE lubricants (viscosity range from 68 to 170cst) for pool boiling
experiments. Some related thermo-physical properties and critical separation temperature (CST) for R134a and
R1234ze are listed in Table 1. POEA types are fully miscible with R-1234ze, but partial miscible with R-134a;
the low temperature affinities of POEB are better than POEA and perform lower CST in R134a and R1234ze.
With partial miscibility with R1234ze, POEC and POED are chose for comparison with POEA/B in R1234ze.
3.2 Oil concentration, heat flux and saturated temperature effect on heat transfer
Pool boiling heat transfer test results are shown in figure 3~8 (saturated temperature 0°C/10°C, heat flux
ranges from 10W to 70W, in R134a and R1234ze). Higher heat flux and higher saturated temperature will result
in higher HTC in pure refrigerant, but the phenomenon is such different in oil-refrigerant mixture. We use h/h0
as indicator to check the oil effect on heat transfer. The raising tendencies of h/h0 for 3% oil concentration with
increasing heat flux are significant, but for higher (5% and 10%) or lower (1%) concentrations the effects are
indistinctive. The results show that 3% oil seems the concentration with better HTC in all test conditions. The
tests under lower saturated temperature perform higher boost effect on HTC for oil-refrigerant mixture.
3.3 Oil viscosity and oil /refrigerant type effect on heat transfer
Take different type oils for comparison, the boost effects on HTC of high miscible POEB are higher than
partial miscible POEA’s. The influence of oil is significant in R134a system than that in R1234ze system. If we
further compare the oil viscosity effect on heat transfer, the h/h0 enhance phenomenon is significant for ISO170
POE than ISO68 POE
Fig.3 HTC of POEA 68 in R134a, 0°C Fig.4 HTC of POEA 170 in R134a, 0°C
Fig.5 HTC of POEB 68 in R134a, 0°C Fig.6 HTC of POEB 170 in R134a, 0°C
Table1 POE basic Data
Properties
at 0°C
Density
kg/m3
Heat
Condutivity
W/(m*K)
Surface
Tension
kg/s2
Kinematic
viscosity
cm2/s
cp
J/kg×K
CST in
R134a
20wt% °C
CST in
R1234ze
20wt% °C
POEA 68 969 0.095 32.6 1213 2301 -18 <-60
POEA 120 972 0.0606 32.4 2972 2277 -10 <-60
POEA 170 974 0.0414 32.2 4683 2265 -6 <-60
POEB 68 1034 0.0148 38.7 750 2502 <-60 <-60
POEB 120 1011 0.0126 35.8 1927 2418 -44 <-60
POEB 170 1000 0.0114 34.6 3278 2338 -28 <-60
POEC 170 982 0.0392 34.1 3715 2274 not miscible -55
POED 150 981 0.0843 36.5 2527 2197 not miscible -25
2318, Page 4
17th International Refrigeration and Air Conditioning Conference at Purdue, July 9-12, 2018
3.4 Oil concentration, viscosity and oil / refrigerant type effect on bubble diameter
Bubble diameter data are shown in Table 2. It’s obvious that higher oil concentration or higher saturated
temperature result in small bubble diameter. Bubbles are a little larger in R1234ze than that in R134a. But we
cannot find the significant relationship between viscosity and bubble diameter, and indistinctive influence on
bubble diameter for different oil type.
4. MECHANISM SPECULATION & MODEL DEVELOPMENT
Boiling incipience on metal surface is a heterogeneous nucleation phenomenon. Therefore, interfacial
properties of solid/liquid/vapor are deemed to be of the most importance. The effects of these properties on boiling
inception of oil-refrigerant mixture were studies in this work. We tried to provide the suitable mechanism of
nucleate boiling heat transfer and give the new modified model for the oil effect on boiling inception superheat
and bubble size.
Fig.7 HTC of POEB 68 in R134a, 10°C Fig.8 HTC of POEB 170 in R134a, 10°C
Fig.9 HTC of POEA 170 in R1234ze, 0°C Fig.10 HTC of POEC 170 in R1234ze, 0°C
Table2 Bubble diameter
Fig.11 Picture of boiling, 1% POEA 170 in 134a, 0°C
R134a
0°C 0% 1% 3% 5% 10%
POEA 170 0.59 0.38 0.29 0.23 0.19
POEA 120 0.59 0.41 0.30 0.26 0.14
POEA 68 0.59 0.39 0.30 0.21 0.19
POEB 170 0.59 0.34 0.28 0.22 0.18
POEB 120 0.59 0.44 0.34 0.26 0.18
POEB 68 0.59 0.42 0.31 0.23 0.16
10°C 0% 1% 3% 5% 10%
POEA 170 0.42 0.33 0.23 0.16 0.15
POEA 120 0.42 0.32 0.20 0.17 0.13
POEA 68 0.42 0.31 0.22 0.17 0.14
POEB 170 0.42 0.31 0.22 0.18 0.13
POEB 120 0.42 0.37 0.24 0.17 0.12
POEB 68 0.42 0.36 0.22 0.18 0.13
Bubble diameter mm R1234ze
0°C 0% 1% 3% 5% 10%
POEA 170 0.62 0.47 0.35 0.26 0.16
POED 150 0.62 0.48 0.30 0.22 0.17
10°C 0% 1% 3% 5% 10%
POEA 170 0.47 0.38 0.26 0.20 0.10
POED 150 0.47 0.38 0.21 0.17 0.12
Bubble diameter mm
2318, Page 5
17th International Refrigeration and Air Conditioning Conference at Purdue, July 9-12, 2018
4.1 A Site-Activation Model for Pool Boiling Heat Transfer without Oil Hsu’s (1961, 1962) site-activation model can be used to show the mechanism of bubble incipience. By
combine the studies from Zuber (1961), Rohsenow (1998) and Han (1965a, 1965b), we illustrate the basic concept
of heterogeneous boiling in Fig.12
At stage (d), a piece of superheated transient thermal layer is torn
off from heating surface by the departing bubble, and at the same
time, the cold fluid from the main body of the fluid flows on to the
heating surface; At stage (a), after a waiting time, th, this cold liquid
layer is heated to a condition such that the tiny bubble in that cavity
is able to grow laterally with a very high rate, such that a very large
piece of thermal layer is picked up in a very short time interval
(stage (b)). At stage (c), the bubble is going to depart from the
heating surface which will bring the situation immediately to stage
(d) again. This cyclic process furnishes a way to transfer the heat
from the heating surface to the main body of the fluid.
4.1.1 Waiting Period (th)
The bubble nucleus will not grow unless the surrounding liquid is warmer than the bubble temperature so
that there is a net heat flux into the bubble to provide the heat of vaporization. When the bubble starts to grow,
the waiting period ends. Equation (3) ~ (11) describe the criterion of boiling incipience based on Clausius-
Claperon equation for superheat.
Equation (12) ~ (17) describe how to give the solution for temperature profile at constant heat flux case. For
a give differential equation and boundary equations, Neumann solution can be used for calculation.
The waiting time is calculated by considering criterion of boiling incipience and temperature profile near
surface. Fig.13 illustrates the process of calculation and physical meanings of these equations.
4.1.2 Bubble Growing and Departure Period (td)
According the studies of Cole (1960, 1967), Ivey (1967), Griffith (1959) and Han (1965b), bubble departure
diameter can be calculated by equation (18) and (19). Then thermal layer thickness, bubble departure diameter
and departure time can be obtained by using equation (20) ~ (22).
Fig.13 Boiling incipience
𝑟𝑐∗ =
𝛿
2𝐶1 1 − 𝜉𝑠𝑎𝑡 ± 1 − 𝜉𝑠𝑎𝑡
2 −4𝐴𝐶3
𝛿𝜃𝜔 (4) 𝑞0 =
𝐾
𝛿 𝜃𝑠𝑎𝑡 +
2𝐴𝐶3
𝛿+ 2𝜃𝑠𝑎𝑡 +
2𝐴𝐶3
𝛿
2𝐴𝐶3
𝛿 (3)
𝐴 =2σ𝑇𝑠𝑎𝑡
𝜆𝜌0
(5) ξ =𝜃
𝑞𝛿𝐾
(6) 𝜃 = T − 𝑇∞ (7) 𝜃𝑏 = 𝜃𝑠𝑎𝑡 +
2𝜎𝑇𝑠𝑎𝑡
𝜆𝜌𝑟 𝛿 − 𝑥𝑏
𝐶3 (8)
r𝑛 = 1
sin 𝜑 rc = 𝐶2rc (9) b = 1 + cos 𝜑 rn = 𝐶3r𝑛 , 𝐶3 =
𝐶1
𝐶2 (10) b =
1 + cos 𝜑
sin 𝜑 rc = 𝐶1rc (11)
𝜕2𝜃
𝜕𝑥2 =1
𝛼
𝜕𝜃
𝜕𝑡, 𝑡 > 0, 𝑥 > 0, 𝜃 = 𝑇 𝑥, 𝑡 − 𝑇𝑖 Constant heat flux (12) ϕ =
T 𝑥, t − 𝑇𝑖
𝑇0 − 𝑇𝑖 (13) η =
𝑥
2 αt (14)
Neumann Solution 𝑘 𝑇 𝑥, 𝑡 − 𝑇𝑖
2𝑞0 𝛼𝑡=
1
𝜋exp −𝜂2 − 𝜂 𝑒𝑟𝑓𝑐(𝜂) (15)
𝑘 𝑇 0, 𝑡 − 𝑇𝑖
2𝑞0 𝛼𝑡=
1
𝜋 (16) δ = 2
𝛼𝑡
𝜋 (17)
Fig.12 Bubble generating cycles
𝑓 =1
𝑡𝑑 + 𝑡ℎ
2318, Page 6
17th International Refrigeration and Air Conditioning Conference at Purdue, July 9-12, 2018
4.2 Modified Site-Activation Model for Oil-Refrigerant Mixture for Pool Boiling
When refrigeration lubricant migrates into the evaporator, it plays a key role on influence of the heat
transfer characteristics, either enhancement or degradation. The aim of this section is to fundamentally
understand the effect of lubricant properties and bubble parameters on heat transfer performance.
4.2.1 Influence of bulk refrigerant properties
Simple mixing rule can be used as calculating mixture properties. In equation (23) ~ (25), bulk properties
(the properties of mixture which is away from surface) can be easily obtained, such as surface tension, heat
capacity and heat conductivity.
4.2.2 Influence of bubble incipience temperature: Boiling-point elevation
Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher
when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This
happens whenever a non-volatile solute. Equation (26) ~ (29) describe how to evaluate the degree of boiling point
elevation. For refrigerant-lubricant system, polymer-like model can be used to obtain activity coefficient, such as
Flory-Huggins equation (Equation (30) and (31), Flory (1953)). This elevation phenomenon will lead to higher
superheat and reduce heat transfer coefficient.
4.2.3 Surface Excess Density Consideration
In oil-refrigerant mixture, oil is much bigger than refrigerant (such as polymer-solvent system), oil-refrigerant
interaction becomes geometrically asymmetric and the mixing is non-random (Hung, 2014), so thermodynamic
properties of mixture are far from ideal. Therefore, when we try to realize the phenomenon happened on the solid-
liquid surface, the most importance is to get four key factors: adsorption Gibbs free energy of oil on surface (ws1),
adsorption Gibbs free energy of refrigerant on surface (ws2) (ws1 – ws2 = χs), energy gap between oil and refrigerant
(χ) and repeat unit of oil comparing to refrigerant (r). In this study, χs can be calculated by ‘Frontier molecular
orbital theory’ and polymer conformation, χ is high positive correlation with energy gap we developed previously.
Repeat unit can be obtained by using polymer steric effect studies (Taft (1952), Taylor (1948), Flory (1953)).
Scheutjens & Fleer (1979), Roe (1974) provided a series of equations for describing the excess polymer
concentration profile on solid surface. When χs and χ are both large, adsorption layer will form on surface. That
means the surface prefers the polymer to the solvent and polymer adsorption happened. In most practical cases,
the free energy gained when a monomer is brought from the bulk solution to the wall is relatively large (i.e., it is
comparable to the thermal energy kT); this is called strong adsorption. If χs and χ are both small, the surface
prefers the solvent to the polymer, the chains avoid the vicinity of the surface; a polymer solution then shows a
depletion layer near the surface. Equation (32) ~ (40) and Figure 14, 15 are shown for illustrating this theory.
𝐷𝑏 = 𝐶2 𝜎𝑔0
𝑔 𝜌𝑙 − 𝜌𝑣
12 𝐽𝑎∗
54 (18) Ja∗ ≡
𝜌𝜄𝑐𝜄𝑇𝑠𝑎𝑡
𝜌𝜈ℎ𝑓𝑔 (19)
𝑑𝑅
𝑑𝑡=
𝜑𝑐𝜑𝑠
𝜑𝑣
𝑞0
𝐿𝜌𝜈+
𝜑𝑏
𝜑𝜐
𝜅
𝛿𝑛𝑐
△ 𝑇𝑤 −△ 𝑇𝑠𝑎𝑡
𝐿𝜌𝑣=
𝜑𝑐𝜑𝑠
𝜑𝑣
𝑞0
𝐿𝜌𝑣+
𝜑𝑏
𝐿𝜌𝑣 𝑞0 −
𝜅 △ 𝑇𝑠𝑎𝑡
𝛿𝑛𝑐 =
𝑞0
𝐿𝜌𝑣 𝜑𝑐𝜑𝑠
𝜑𝑣+
𝜑𝑏
𝜑𝑣 −
𝜑𝑏𝜅 △ 𝑇𝑠𝑎𝑡
𝜑𝑣𝐿𝜌𝑣𝛿𝑛𝑐 (20)
δ𝑛𝑐 = 𝜋𝛼𝑡 (21) R − R𝑐 =𝑞0
𝐿𝜌𝑣 𝜑𝑐𝜑𝑠
𝜑𝑣+
𝜑𝑏
𝜑𝑣 𝑡𝑑 −
𝜑𝑏κ △ 𝑇𝑠𝑎𝑡
𝜑𝑣𝐿𝜌𝑣𝑇𝛿𝑛𝑐
4𝑡𝑑𝜋𝛼
(22)
σ𝑚𝑖𝑥 = 𝜎𝑖 × 𝑤𝑖 (23) Cp𝑚𝑖𝑥 = 𝐶𝑝𝑖 × 𝑤𝑖 (24) κ𝑚𝑖𝑥 = 𝜅𝑖 × 𝑤𝑖 (25)
𝜇1∗ 𝑔 = 𝜇1
∗ 𝑙 + 𝑅𝑇𝑙𝑛𝑎1 = 𝜇1∗ 𝑙 + 𝑅𝑇𝑙𝑛𝛾1 1 − 𝑥2 (26)
𝑙𝑛𝛾1 1 − 𝑥2 = 𝜇1
∗ 𝑔 − 𝜇1∗ 𝑙
𝑅𝑇=
∆𝐺𝑣𝑎𝑝
𝑅𝑇=
∆𝐻𝑣𝑎𝑝
𝑅𝑇−
∆𝑆𝑣𝑎𝑝
𝑅 (27)
when 𝑥2 = 0,𝛾1 = 1, 𝑡ℎ𝑒𝑛 ∆𝐻𝑣𝑎𝑝
𝑅𝑇𝑏=
∆𝑆𝑣𝑎𝑝
𝑅 (28)
𝑙𝑛𝛾1 + 𝑙𝑛 1 − 𝑥2 =∆𝐻𝑣𝑎𝑝
𝑅𝑇−
∆𝐻𝑣𝑎𝑝
𝑅𝑇𝑏=
∆𝐻𝑣𝑎𝑝
𝑅 𝑇𝑏 − 𝑇
𝑇𝑇𝑏 ≈
∆𝐻𝑣𝑎𝑝
𝑅𝑇𝑏2 ∆𝑇 (29)
𝑙𝑛𝛾1 = 𝑙𝑛 1 − 1 −1
𝑛 𝜑2 + 1 −
1
𝑛 𝜑2 + 𝜒12𝜑2
2 (30) 𝜑2 =𝑛𝑥2
𝑥1 + 𝑛𝑥2 (31)
ϕ𝑖 =𝜙∗
𝑟
1
𝑝𝑖 𝑝 𝑖, 𝑠 𝑝 𝑖, 𝑟 − 𝑠 + 1
𝑟
𝑠=1
(32) ϕ∗ =𝑛𝑟
𝐿𝑝(𝑟) (33) p r = wp r − 1 = w𝑟−1𝑝(1) (34) 𝑤 =
𝑾
𝑃∗ 𝜔𝑖𝑗 = 𝜆𝑗−𝑖𝑝𝑖 (35)
𝜆0 = 𝑙 =1
2, 𝜆−1 = 𝜆−1 = 𝑚 =
1
4 (36) ln𝑃∗ = 𝜒(𝜙∗ − 𝜙∗
0) + ln𝜙∗ (37) ln 𝑃∗ = 𝜒𝑠𝛿1,𝑖 + 𝜒 𝜙𝑖 − 𝜙∗0 + ln 𝜙𝑖
0 (38)
Γ1 = 𝜑1𝑖 − 𝜑1
∗ Γ2 = −Γ1
𝑀
𝑖=1
(39) 𝑑𝜎
𝑑 ln 𝐶= −𝑅𝑇𝛤 Gibbs adsorption equation (40)
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4.2.4 Influence of contact angle on surface and departure bubble size
Base on Gibbs adsorption equation (Rosen (1978)), interfacial force between liquid and surface ϒls can be
reduced by adding oil and prefer adsorbing on surface. By using energy gap model we developed previously, we
can find interfacial force between oil and refrigerant vapor (ϒlv ) is smaller than surface tension of pure refrigerant.
By using Fig.16 and equation (41), contact angle become smaller if ϒls and ϒlv are small. That will lead to small
holding force between bubble and surface (this value equals to ϒlv*sinβ ). As a result, departure of bubble will
become easier, and lead to small bubble size. Although less heat transfer occurs with a smaller bubble, the site
density can be increased as a direct consequence of small bubble size. An enhancement of the boiling is achieved
if the increase in site density more than compensates for the decrease in bubble size. This view point can be proved
by Hsu (1962) theory. A site will be active if the bubble is released from the surface before it grows beyond the
thermal boundary layer. A bubble that grows beyond δ while attached to the surface condenses and causes the site
to be inactive. For a given cavity distribution, more of the larger cavities will be active for the oil-refrigerant
mixture than for pure refrigerant (Kedzierski, 1999).
4.2.5 Influence of oil concentration and oil viscosity Kedzierski (2003), Jensen (1984) and Mitrovic (1998) provided the relationship between bubble size and
oil concentration (Equation (45)). Based on this equation, an increasing oil concentration will lead to small size
bubble (The most important the meaning of xb in equation (45) is weight fraction of oil concentrated on surface
layer, not in bulk mixture). Viscosity of oil will be taken into consideration when we check the influence of heat
transfer performance. The higher oil viscosity will decrease diffusivity coefficient DAB (Equation (43) and (44)),
as a result, the bubble size should be smaller.
Adsorption layer Depletion layer
Fig.14 Polymer adsorption on metal surface
Fig.16 Contact angle & boiling incipience
cos 𝛽 = 𝛾𝑣𝑠 − 𝛾𝑙𝑠
𝛾𝑙𝑣 (41) 𝐷𝑏 ,𝑚𝑖𝑥 = 𝐶2
𝛾𝐴𝐵𝑔0
𝑔 𝜌𝑙 − 𝜌𝑣
12 𝐽𝑎∗
54 (42)
D𝐴𝐵 =𝑘𝐵𝑇
6𝜋𝜂𝑟 Stokes–Einstein equation
(43) r𝑏 ∝ 𝐷𝐴𝐵 (44)
r𝑏 ∝𝑙𝑒(1 − 𝑥𝑏)
𝑥𝑏 𝑙𝑒 𝑚𝑒𝑎𝑛𝑠 𝑜𝑖𝑙 𝑙𝑎𝑦𝑒𝑟 𝑡ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 (45)
Fig.15 Coverage of polymer adsorption
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4.3 Calculation Results for the New Modified Model
4.3.1 Surface coverage on metal surface Following are the calculation results for surface coverage calculation (Table 3, 4 and Fig.17, 18).
R134a has higher χs and λ (χs=0.4, λ=0.5) value than R1234ze (χs=0.3, λ=0.4), therefore, it forms a strong
adsorption layer on the metal surface and has high coverage near surface monolayer (R134a=25.8%,
R1234ze=10%). When we increase the oil concentration (3% to 10%), it is reasonable to get higher coverage.
4.3.2 Heat transfer coefficient, bubble size and bubble frequency Fig.19 shows the comparison of experiment data and model calculation results for heat transfer coefficient,
and Fig.20 is for the comparison of bubble size. The results show that the tendency is the same, and the accuracy of this correlation is acceptable.
Fig.21 illustrates the bubble frequency on nucleate boiling. The higher oil concentration in mixture will
decrease the bubble size but increase site density. As a result, the bubble frequency is increasing.
Fig.17 Refrigerant effect on adsorption
Fig.19 HTC comparison for data & calculation
Fig.18 Concentration effect on adsorption
Fig.20 Diameter comparison for data & calculation
Table 3 POEA 170 in R134a
3% Calculation
Heat flux (W) 10 30 50 70
monolayer vol% 25.80% 25.80% 25.80% 25.80%
tc (s) 0.0150 0.0028 0.0014 0.0009
td (s) 0.0544 0.0179 0.0107 0.0076
t (s) 0.0694 0.0207 0.0121 0.0085
bubble d (mm) 0.285 0.285 0.285 0.285
f (1/s) 14.4 48.2 82.8 118
ΔT1 (°C) 3.64 4.74 5.5 6.11
ΔT2 (°C) 1.15 2.62 3.76 4.69
ΔT (°C) 4.79 7.36 9.26 10.8
h (W/m^2K) 2090 4080 5400 6470
h/h0 0.8782 0.9927 1.0325 1.0537
χs=0.4 χ=0.5
Table 4 POEA 170 in R1234ze
3% Calculation
Heat flux (W) 10 30 50 70
monolayer vol% 10.00% 10.00% 10.00% 10.00%
tc (s) 0.0095 0.0021 0.0011 0.0007
td (s) 0.1750 0.0580 0.0350 0.0250
t (s) 0.1845 0.0601 0.0361 0.0257
bubble d (mm) 1.24 1.24 1.24 1.24
f (1/s) 5.42 16.6 27.7 38.9
ΔT1 (°C) 2.85 3.98 4.75 5.36
ΔT2 (°C) 2.5 5.47 7.65 9.54
ΔT (°C) 5.35 9.45 12.4 14.9
h (W/m^2K) 1870 3170 4020 4700
h/h0 0.9212 0.9109 0.9054 0.9021
χs=0.3, χ=0.4
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5. CONCLUSIONS
Several pool boiling experiments are conducted in POE-refrigerant mixture system for measuring transfer
coefficient, bubble size and bubble frequency. Through this study, we discovered some factors of mixture will
influence the performance in nucleate pool boiling. Small amount addition of oil into refrigerant will enhance heat
transfer and reduce bubble diameter, but when oil concentration is up to 10%, the HTC will decrease dramatically.
The oil effect on performance in R134a system is more significant than that in R1234ze system.
Based on Hsu’s site-activation model, the boiling incipience mechanisms of pure refrigerant have been
illustrated. We successfully combine several polymer solution theories and create a new modified site-activation
model for oil-refrigeration mixture. On the basis of our calculation, several key factors will play an important role
in pool boiling heat transfer, such as adsorption energy on metal surface, interaction force between refrigerant and
oil, and oil concentration.
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