Heat transfer characteristics of thermosyphon with N2–Ar binary mixture working fluid

International Journal of Heat and Mass Transfer 63 (2013) 204–215

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Heat transfer characteristics of thermosyphon with N2–Ar binary mixture working fluid Z.Q. Long, P. Zhang ⇑ Institute of Refrigeration and Cryogenics, Shanghai Jiao Tong University, Shanghai 200240, China

a r t i c l e

i n f o

Article history: Received 24 September 2012 Received in revised form 13 March 2013 Accepted 15 March 2013 Available online 29 April 2013 Keywords: Cryogenic thermosyphon Working fluid N2–Ar binary mixture Heat transfer characteristic

a b s t r a c t The N2–Ar binary mixture is adopted as the working fluid of a cryogenic thermosyphon and the heat transfer performance of such thermosyphon is studied in the present research. The heat transfer of the binary mixture in the thermosyphon is discussed theoretically by considering the mass transfer of the components. Meanwhile, an experimental setup for investigating the heat transfer performance of the cryogenic thermosyphon is built. The condenser is cooled by the liquid nitrogen on the top and the evaporator is heated circumferentially by the resistive wire. The N2–Ar binary mixture is charged into the cryogenic thermosyphon in different compositions, including pure N2 and pure Ar. It is found that the N2–Ar binary mixture can widen the operational temperature range of the cryogenic thermosyphon and it can work in the range of 64.0–150.0 K. The dry-out limit appears in the experiments for the cases with Ar fraction below 0.503. The heat transfer rate of the dry-out limit increases with the increase of Ar molar fraction until film boiling appears on the top of the condenser. The heat transfer rate limited by the film boiling can be determined based on the empirical correlations that are used to estimate the critical heat flux of liquid nitrogen boiling on the plate. The heat transfer processes in the evaporator and the condenser are discussed, and the thermal resistances are calculated by empirical correlations. The calculated results agree well with the experimental results. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Thermosyphon is a highly efficient heat transfer device that utilizes the liquid–vapor phase change of working fluids. It is widely employed in industries and some other fields for its excellent heat transfer performance and simple structure. But the heat transfer performance of thermosyphon is mainly restricted by the thermal properties of the working fluids, which limit the operational temperature range of thermosyphon from the triple point temperature to the critical temperature. Fig. 1 shows the ideal operational temperature ranges for various working fluids [1]. The operational temperature range varies with the working fluid, for examples, water can work from 273.0 K to 647.0 K and nitrogen can only operate between 64.0 K and 126.0 K. The lower critical temperature of the fluid, the narrower the operational temperature range is, as depicted in Fig. 1. However, the thermosyphon is expected to work in a wide temperature range in some cases, especially in the cryogenic applications, where the thermosyphon works as the thermal link between the cooled device and cold source to accelerate the cooling process from room temperature to ultralow temperatures (even as low as 2–3 K in some cases [2,3]). This ⇑ Corresponding author. Tel.: +86 21 34205505; fax: +86 21 34206814. E-mail address: [email protected] (P. Zhang). 0017-9310/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2013.03.042

requires the operational temperature range of the cryogenic thermosyphon to be as wide as possible. In order to widen the operational temperature range, some researchers proposed two approaches to cope with such difficulty. One way is to use different fluids in separate thermosyphons and combine the thermosyphons structurally [4,5], but this approach has many limitations on structure, especially in the cases with ultra-low temperature, in which the systems need to be compact and the space is limited for complex structures. Another way is to fill a single thermosyphon with the mixture of the different fluids [6–8]. The latter is feasible if the mixture working fluids can make the thermosyphon operate in a wider temperature range than that of a single fluid. There were some research works on the utilization of mixture working fluids in thermosyphons having been carried out. Felder et al. [7] developed a cryogenic thermosyphon with He–Ne binary mixture working fluid, which improved the heat transfer performance, e.g., stable temperature on the cooled target. However, He acted as an incondensable gas and was resident in the condenser, which led to a large-volume condenser and the complicated configuration of such thermosyphon. The CF4–N2 binary mixture was adopted as the working fluid in a thermosyphon, which aimed at accelerating the cooling of the heat source by Lee et al. [8]. The operational temperature ranges of CF4 and N2 are 99.0–228.0 K and 64.0–126.0 K, respectively. The upper limit of

Z.Q. Long, P. Zhang / International Journal of Heat and Mass Transfer 63 (2013) 204–215

205

Nomenclature area (m2) empirical parameter (–) constant (–) specific heat capacity (kJ/(kg K)) diameter (m) acceleration of gravity (m/s2) heat transfer coefficient (W/(m2 K)) enthalpy of vaporization (kJ/kg) thermal conductivity (W/(m K)) length (m) mass (kg) pressure (MPa) Prandtl number (–) heat flux (W/m2) heating power/heat transfer rate (W) thermal resistance (K/W) Reynolds number (–) temperature (K) temperature difference (K) average temperature (K) velocity (m/s) volume (m3) molar fraction in liquid state (–) molar fraction in vapor state (–)

A B0 C, Cwl cp d g h Hfg k l m p Pr q Q R Re T DT T V Vol x y

Subscripts 1 volatile component (N2) 2 nonvolatile components (Ar) a adiabatic section ac after charging am ambient b bubble point/bubble line bc before charging c condenser con conductivity cop copper crit critical d dew point/dew line e evaporator i inner id ideal l liquid leak leak net net o operation res gas reservoir s saturated ss stainless steel t total v vapor w wall

Greek symbols b mass transfer coefficient (m/s) q density (kg/m3) r surface tension (N/m) l viscosity (Pa s)

the operational temperature range for CF4 is much higher than that of N2, and then N2 acted as the incondensable gas when the temperature of the thermosyphon was in the operational temperature range of CF4, which resulted in the failure on operation. Armijo and Carey [9] studied the thermal behavior of a thermosyphon with water–alcohol binary mixture working fluid. They found that the thermosyphon could operate normally with the binary mixture and the heat transfer limit was increased compared with pure water and pure alcohol. However, the working of a cryogenic thermosyphon is very different from that with room temperature fluids. There are some particular phenomena existing in the cryogenic thermosyphon, for examples, the appearance of incondensable gas in the case of mixture working fluid, the solidification of the working fluid and the operation near critical state.

Many works proved that the thermosyphon with binary mixture working fluid cannot work if there is no overlap for the operational temperature ranges of the components [10]; or it cannot work better if the difference between the critical temperatures of the components is too large [8]. Thus, N2–Ar binary mixture is adopted as the working fluid in a cryogenic thermosyphon in this study. The operational temperature ranges of N2 and Ar are 64.0– 126.0 K and 84.0–150.0 K, respectively, as shown in Fig. 1. In this binary mixture, N2 and Ar are the volatile and nonvolatile component, respectively. They are charged into a cryogenic thermosyphon with different compositions and the heat transfer performance of the cryogenic thermosyphon with such working fluid is investigated.

2. Thermal behavior of binary mixture in a thermosyphon 650

650 645

645

Triple point Critical point

450

450

Cyclopropane C3H6 NH3

400

C3H6

400

R134a

350

Temperature (K)

350 R23 CO2 C2H4Xe

300 250

H2O

CH4

200 150

N2

200 R11 R22

H2 Ne

250

R21

O F2 Ar 2

100 50

300 C3H3

CF Kr 4

R13 C2H6

C3H8

R12

C4H10

150 100 50

He 0

0

Fluids

Fig. 1. The operational temperature ranges of the typical fluids.

When referring to the fluid mixtures, there are non-azeotropic mixture and azeotropic mixture. But most mixtures are non-azeotropic, including N2–Ar binary mixture. Thus, only non-azeotropic binary is discussed in this paper. The heat transfer process in a binary mixture is very different from and more complex than that of a pure fluid. It is known that the evaporation and condensation occur at saturated temperature under the constant pressure for pure fluid. However, the binary mixture evaporates and condensates at two different temperatures because of the difference on the saturation temperatures of the components at local pressure, and the corresponding temperatures of evaporation and condensation for a binary mixture are called bubble point and dew point, respectively, as shown in Fig. 2. Ts1 and Ts2 are the saturated temperatures of the pure fluids corresponding to the volatile component and nonvolatile component of a binary mixture, respectively.

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T

T

140

p =Constant

C

B

Dew point

Ts2

130

Tb'

120

Td D

Ts1

Tb

A

130

2.50 MPa

120 1.00 MPa 110

110 100

0.41 MPa

100

90

0.13 MPa

90

Bubble point

Liquid 80

80

x2(y2')

y2

0

x2'

1

Fig. 2. Typical vapor–liquid phase equilibrium diagram of a non-azeotropic binary mixture.

Heat out

It is well-known that there is a reduction in heat transfer performance of the binary mixture compared with the corresponding pure fluids, and numerous experimental and analytical investigations on the heat transfer characteristics of the binary mixtures have been carried out, including aqueous mixtures [11,12], organic–organic mixtures [13], refrigerant–refrigerant mixtures [14,15], and cryogenic liquids mixtures [16]. Almost all the research works focused on either boiling or condensation in a large open space, and nearly no attention was paid to the boiling and condensation simultaneously in a small enclosure. However, the boiling and condensation occur simultaneously in a relatively small volume when a binary mixture is applied as the working fluid of a thermosyphon, as shown in Fig. 3. The mixture vapor is generated by the boiling of the liquid mixture and then it flows to the condenser with high speed, which can be even as high as local sonic speed [17] depending on the working fluid and the heat transfer rate. The binary mixture vapor is condensed in the condenser and the condensed mixture flows down to the evaporator along the inner wall of the thermosyphon. The thermosyphon operates at a steady state continuously, and the vapor composition generated from the evaporator must be equal to that of the liquid bulk and the returning liquid in order to keep steady-state operation condition [18]. Therefore, the heat and mass transfer process in a thermosyphon with binary

Vapor bulk

Vapor flow

Condenser Liquid film

Adiabatic section

Tb

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Molar fraction of Ar

Molar fraction of nonvolatile component

Concentrated layer

Ts2 (K) Ar

Tbp

in e wl por De t va We e le lin Bu b b

140

3.50 MPa

Ts1 (K) N2

Vapor

Beyond the critical pressure of N2 (3.4 MPa)

Bubble point

Fig. 4. Phase equilibrium diagram of N2–Ar binary mixture under different pressures.

mixture can be described as follows, in which the mass transfer is considered in the boiling and condensation. The heat transfer process in the thermosyphon with binary mixture working fluid can be described in phase equilibrium diagram, as shown in Fig. 2. The molar fraction of the nonvolatile component in liquid bulk is assumed as x2 (see point A), then the corresponding molar fraction of this component in the saturated vapor is y2 (point D), smaller than x2. Inversely, the liquid state A is the saturated state of the vapor state D. But when the boiling of binary mixture occurs, there is a concentrated layer [19] near the inner wall of the evaporator, as shown in Fig. 3. The molar fraction of the nonvolatile component increases from x2 in the liquid bulk to x02 adjacent to the wall in the concentrated layer, thus the bubble point of the liquid increases from Tb to T 0b . The composition of the vapor generated in the evaporator is the same as that of the liquid bulk, i.e., y02 ¼ x2 . This process is shown as the process ABC in Fig. 2. The difference between Tb and T 0b is written as 4Tbp, defined as the temperature difference between the dew line and the bubble line at the liquid bulk composition. Regarding the condensation, the molar fraction of the nonvolatile component in the vapor bulk is y02 and it decreases and becomes smaller at the interface between the liquid film and the vapor, because the nonvolatile component is much easier to be condensed. Thus there is also a concentrated layer [20] adjacent to the condensed film. As there is a steady cycle in the cryogenic thermosyphon, the composition of the liquid film must be equal to that of the vapor bulk in the condenser and liquid bulk in the evaporator. This process is illustrated as the process CDA in Fig. 2. The equilibrium diagram of the binary mixture working fluid in the thermosyphon varies with the heating power on the evaporator, which is signified by the different operational pressure, and the binary mixture working fluid displays different thermal properties. Fig. 4 shows the phase equilibrium diagram of N2–Ar binary mixture under different pressures. When the system pressure is higher than the critical pressure of N2, N2 cannot be condensed and the amount of liquid Ar is not enough to dissolve the incondensable N2 for low Ar fraction. Therefore, the equilibrium diagram at 3.50 MPa is not an integrated one for low Ar fraction.

Tb

Evaporator

x2 Heat in Liquid bulk

Liquid bulk

3. Experimental apparatus and procedure

x2

The schematic illustration of the experimental setup is shown in Fig. 5, which is modified from the setup used in [21] by adding one more gas tank in the working fluid charging system and changing the cooling condition on the cryogenic thermosyphon. This system consists of a test section, a working fluid charging system and

Ar fraction

Concentrated layer Fig. 3. Schematic of the working fluid cycle in the thermosyphon.

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Fig. 5. Schematic illustration of the experimental setup [21].

a vacuum dewar. The test section includes a liquid nitrogen reservoir and a cryogenic thermosyphon. The cryogenic thermosyphon is bolted to the bottom of the liquid nitrogen reservoir. The liquid nitrogen at atmospheric pressure is adopted as heat sink, and it contacts directly with the top surface of the condenser of the cryogenic thermosyphon to provide excellent cooling. Two heaters made of resistive heating wire are wound around the evaporator and the condenser, respectively, as shown in Fig. 5. Heater 1 acts as the heat source of the cryogenic thermosyphon and it is estimated that more than 300.0 W heating power can be provided by a DC source. Heater 2 is applied to control the condenser temperature higher than the triple point of Ar, i.e. 84.0 K, to avoid the operation failure of the cryogenic thermosyphon caused by the solidification of Ar (explained in more detail later on) at low heating powers in the case of pure Ar working fluid. The detailed configuration of the cryogenic thermosyphon is shown on the right side of Fig. 5. It consists of the condenser, the adiabatic section and the evaporator, which are 150.0, 50.0, and 70.0 mm in length, respectively, and the inner diameters are all 10.0 mm. The condenser and evaporator are made of copper and the walls are thickened to ensure the isothermality for each part. The adiabatic section is a segment of stainless steel pipe with an outer diameter of 14.0 mm and a thickness of 2.0 mm. The thermal conductivity of stainless steel at liquid nitrogen temperature (77.3 K) is about 8.0 W/(m K), much lower than that of copper, which ranges in 450–600 W/(m K) in the experiments. Thus the adiabatic section effectively reduces the heat transfer through the thermal conduction from the evaporator to the condenser. Furthermore, multi-layer insulation material is used to cover the cryogenic thermosyphon to reduce the heat leak through radiation. The cryogenic thermosyphon is connected to the working fluid charging system by a stainless steel pipe with an outer diameter of 3.0 mm and a thickness of 0.5 mm, and the pipe length in the dewar is about 1.0 m, which can provide a long heat transfer path and therefore reduce the heat leak through heat conduction. Six platinum thermometers with an uncertainty of ±0.1 K are mounted along the cryogenic thermosyphon to measure the temperature distribution; the ones on the evaporator and the condenser are inserted into the holes drilled in the walls to measure the temperature of the inner wall as accurately as possible. The cryogenic

grease is used to ensure good thermal contact between the thermometers and the walls. The pressures in the gas reservoir and cryogenic thermosyphon are monitored by the pressure sensors (NS Sensor, Model: NS-F) marked as P1 and P2 in Fig. 5 with an uncertainty of ±1.0 kPa. The working fluid is charged after the system is evacuated by a molecular vacuum pump (Pfeiffer Vacuum, Model: TSH 071), P1 and P2 are monitored to control the charging amount. When the binary mixture of N2 and Ar is applied, N2 is charged firstly and then Ar is charged. The heat transfer performance of the cryogenic thermosyphon with N2–Ar binary mixture in different compositions (including pure N2 and pure Ar) is tested in the experiments. The volume filling ratios of working fluid are 1.0 for all mixture compositions, which are defined as the ratio of the volume of liquid working fluid to the volume of the evaporator at the charging state. The heating power on the evaporator is increased step-wisely until the heat transfer limit of the cryogenic thermosyphon during the test, and the temperature distribution and pressure are recorded for each heating power after reaching a steady state. The operation conditions in the experiments are listed in Table 1, where the molar fraction of Ar in the binary mixture working fluid, x2, net heat transfer rate, Qnet, operational pressure, p, average evaporator temperature, T e , and average condenser temperature, T c are presented.

Table 1 Operation conditions of the experiments. No.

x2 (–)

Qnet (W)

p (MPa)

T e (K)

T c (K)

1 2 3 4 5 6 7 8 9 10 11

0 0.121 0.208 0.314 0.417 0.503 0.606 0.697 0.798 0.892 1

1.0–115.7 1.0–121.9 1.0–131.3 1.0–140.0 1.2–150.5 1.0–155.7 1.0–155.2 1.0–156.5 1.0–156.0 1.0–156.0 1.0–156.1

0.141–2.400 0.153–2.323 0.146–2.407 0.136–2.413 0.130–2.475 0.135–2.575 0.142–2.191 0.147–2.201 0.134–2.048 0.129–1.991 0.088–2.054

80.5–121.3 82.9–129.6 83.5–140.1 82.8–140.9 83.1–147.6 85.1–145.7 87.6–146.2 87.8–141.5 87.9–144.4 89.6–143.8 85.1–142.7

79.7–97.3 80.7–98.4 80.4–100.1 79.7–100.2 79.4–101.8 79.9–103.7 80.4–103.4 80.7–103.3 80.0–103.7 79.5–102.5 84.6–102.5

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4. Data reduction and uncertainty analysis 4.1. Data reduction The charging amount of the working fluid is determined by the mass difference of gaseous working fluid in the gas reservoir before and after charging.

mc ¼ Volres ½qðT am ; pbc Þ  qðT am ; pac Þ

ð1Þ

where Volres is the volume of the gas reservoir, Tam is the ambient temperature, pbc and pac are the pressures in the gas reservoir before and after charging, respectively. The net heat transfer rate in the cryogenic thermosyphon is determined by the heat balance.

Q net ¼ Q  Q leak  Q con

ð2Þ

where Q is the heating power applied on the evaporator; Qleak is the heat leak obtained from the heat loss analysis based on the temperature of the evaporator in each experiment, including the heat conduction through the wires of thermometers and heater, and radiation heat transfer, and it is negligibly small (smaller than 0.05 W) according to the heat leak analysis; Qcon is the heat conducted from the evaporator to the condenser via the wall of the adiabatic section. It can be estimated from

Q con ¼ ðT 2  T 4 ÞAa kss ðT a Þ=la

ð3Þ

T2 and T4 are the corresponding temperatures shown in Fig. 5. kss(Ta) is the thermal conductivity of stainless steel, which changes with the temperature of the adiabatic section Ta (i.e., T3). Therefore, the maximal value of Qcon is estimated to be 0.52 W according to the experimental data. An important parameter to evaluate the heat transfer performance of the cryogenic thermosyphon is the thermal resistance R.

DT R¼ Q net

Q net Hfg qv A

5. Results and discussion 5.1. Operational temperature range Fig. 6(a) shows the typical temperature distribution of the cryogenic thermosyphon under different heat transfer rates. The temTable 2 Summary of the uncertainty analysis. Parameter

Uncertainty

Parameter measured Diameter, d (mm) Length, l (mm) Temperature, T (K) Pressure, p (MPa)

±0.02 ±1.0 ±0.1 ±0.001

Parameter derived Q, Qnet (%) Mass, m (%) Thermal resistance, R (%) Velocity, V (%) Reynolds number, Rev, Rel (%)

±0.5, 2.0 ±2.0 ±5.0 ±4.9 ±8.5, ±8.1

a

ð5Þ

180

Unsteady state

150

Beyond heat transfer limit

140 T=126.0 K

130 120 110 100 90 T=85 K

80 0

25

Rel ¼

4Q net pdi ll Hfg

50

75

100

125

150

175

200

225

250

275

Position (mm)

b

75 Working fluid: N2-Ar bianry mixture, Ar molar fraction 0.503

74

Adiabatic section

Evaporator

72

Temperature (K)

ð6Þ

where Hfg is the enthalpy difference between the enthalpies of the liquid and vapor of binary mixture at the operational pressure, di and A are the inner diameter and the cross sectional area of the inner space of the cryogenic thermosyphon, respectively. For the falling liquid film on the inner wall of the condenser, the Reynolds number can be calculated by [21,22]

1.0W 2.0W 5.0W 10.1W 15.1W 20.4W 30.1W 40.3W 50.0W 59.9W 69.8W 79.4W 90.9W 100.2W 111.3W 120.7W 130.8W 141.2W 150.8W 155.7W 159.5W

Condenser

160

73

Q di Rev ¼ net lv Hfg A

Adiabatic section

Evaporator

170

ð4Þ

where DT is the temperature difference, DT e ¼ T e  T o in the evaporator and DT c ¼ T c  T o in the condenser. T e and T c are the average temperatures of the measured temperatures on the evaporator and the condenser, respectively, To is the operational temperature of the cryogenic thermosyphon determined by the phase diagram of N2– Ar binary mixture according to the operational pressure. The operational pressure is measured at the steady state for each heating power to determine the thermal properties of the working fluid, and then the velocity and the Reynolds number of the vapor flow can be calculated by the following equations.

V¼

parameters including the mass of the working fluid, heat transfer rate, thermal resistance, velocity, Reynolds number can be calculated. The uncertainty introduced by the estimation of the thermal properties is also taken into consideration in the calculation of the uncertainties of the derived parameters, and the main experimental uncertainties are summarized in Table 2.

Temperature (K)

208

Qnet

Condenser

0W 0.5 W 1.0 W 1.5 W 2.0 W 3.0 W 5.0 W 10.2 W 15.0 W 20.0 W

71 70 69 68 67 66 65

ð7Þ

4.2. Uncertainty analysis Based on the measurement uncertainties of the diameter, length, temperature and pressure, the uncertainties of the derived

64 63

0

25

50

75

100

125

150

175

200

225

250

275

Position (mm) Fig. 6. Temperature distributions of the cryogenic thermosyphon in the experiments (Ar molar fraction: 0.503), a: typical temperature distribution when the heat sink is liquid nitrogen, b: the heat sink is G–M cryocooler.

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5.2. Heat transfer limit and calculation 5.2.1. Description of the heat transfer limit As reported, the heat transfer limit of a thermosyphon will be influenced by many factors, including the filling ratio of the working fluid [25–28], the configuration of the thermosyphon [26,28], the operation inclination angle [27,29], and some other operation conditions [30,31]. It is found that the heat transfer limit of the cryogenic thermosyphon also varies with the composition of the binary mixture working fluid in this study. Fig. 7 shows the heat transfer limit of the cryogenic thermosyphon with different compositions in N2–Ar binary mixture working fluid and the schematics of the dry-out limit in the cryogenic thermosyphon and film boiling in the heat sink. As shown in Fig. 7(a), the heat transfer limit for the cryogenic thermosyphon increases almost linearly from 115.7 W in the case of pure N2 working fluid to about 156.0 W when the molar fraction of Ar in the mixture reaches 0.503. Then the heat transfer limit remains nearly constant beyond Ar molar fraction of 0.503. Thus it can be inferred that the presence of nonvolatile component (Ar) in the working fluid can promote the heat transfer limit of the cryogenic thermosyphon. The dry-out limit appears in the cases of Ar molar fractions below 0.503 and then the heat transfer limit is limited by the film boiling in the heat sink, as illustrated in Fig. 7(b) and (c). The corresponding temperature and pressure variations around the heat transfer limits are shown in Fig. 8.

a

170 160

156.0 W

150

Heat transfer limit (W)

peratures rise with the increase of the heat transfer rate. It can be noticed that the evaporator temperatures cannot reach a steady state at the heat transfer rate of 159.5 W, but rise continuously. This phenomenon signifies the maximal heat transfer rate that can be transferred from the evaporator to the condenser is 155.7 W. When the heating power applied on the evaporator exceeds this value, the superfluous heat cannot be removed from the evaporator by the operation of the cryogenic thermosyphon, which results in the continuous rise of the evaporator temperature, as shown by the unsteady temperatures in Fig. 6(a). In other words, 155.7 W is the heat transfer limit. It is found in the experiments that the temperature of the evaporator rises close to the critical temperature of Ar at the heat transfer limit, i.e., 150.0 K in the case of binary mixture working fluid, no matter what the fraction of Ar is. But if the working fluid is pure N2, the temperature of the evaporator at the heat transfer limit is slightly lower than 126.0 K (the critical temperature of N2), and cannot reach as high as 150.0 K. This phenomenon is also noticed in the experiments conducted by Zhang et al. [23]. Thus, the binary mixture can widen the operational temperature range of the cryogenic thermosyphon with the upper limit to 150.0 K. In order to determine the lower limit, the cryogenic thermosyphon with N2– Ar binary mixture is further operated on a G–M cryocooler as the heat sink. As shown in Fig. 6(b), the temperature of the condenser is controlled at about 64.0 K. The cryogenic thermosyphon can reach a steady state at 64.0 K without heating load, at which there is almost no temperature difference between the condenser and the evaporator. This phenomenon can verify the successful operation of the cryogenic thermosyphon at 64.0 K; otherwise, the temperature of the evaporator will rise continuously to much higher than that of the condenser because of the heat leak, which appears when the temperature of the condenser is controlled at 63.0 K or below. The results of the subsequent heating experiments shown in Fig. 6(b) also indicated that the successful operation of the cryogenic thermosyphon at the condensation temperature of 64.0 K. Similar operation of the cryogenic thermosyphon with pure N2 was conducted by Nakano et al. [24]. Thus, the N2–Ar binary mixture working fluid widens the operational temperature range of the cryogenic thermosyphon to 64.0–150.0 K.

140

Film boiling limit

130 Dry-out limit 120 Experimental data Eq. (9) Calculated results [21] Eq. (10) Eq. (11)

110 100 90 0.0

0.2

0.4

0.6

0.8

1.0

Ar molar fraction (-)

b

c

Fig. 7. The heat transfer limit of the cryogenic thermosyphon in the experiments.

The temperatures of the evaporator rise continuously after the heat transfer rate exceeds 121.9 W, as shown in Fig. 8(a), indicating the heat transfer limit of the cryogenic thermosyphon is 121.9 W at this Ar molar fraction (0.121). The temperatures of the adiabatic section and the condenser remain unchanged, thus it can be inferred that the heat transferred from the evaporator to the condenser does not change with the increase of the heating power, but remains constant. This phenomenon indicates that all the working fluid in the cryogenic thermosyphon cycles in the form of vapor or liquid film. The liquid film dries thinner down to the lower part of the evaporator and then eventually dries out, and no extra working fluid can be used to transfer more heat, as shown in Fig. 7(b). Therefore, the cryogenic thermosyphon comes to its dry-out limit. The presence of Ar in the working fluid can enhance the heat transfer of the cryogenic thermosyphon, and the heat transfer limit increases with the increase of Ar molar fraction. But this rising trend is limited by the film boiling of liquid nitrogen in the heat sink, as illustrated in Fig. 7(a) and (c). The film boiling here differs from the conventional boiling limit in the thermosyphon [17]. Fig. 8(b) shows the temperature and pressure variations near the film boiling: the temperatures of the evaporator rise sharply when the heat transfer rate exceeds 156.0 W after a short quasi-steady period, thus the heat transfer limit can be concluded to be 156.0 W. The heat transferred by the cryogenic thermosyphon is eventually taken away by the vaporization of the liquid nitrogen on the top surface of the condenser, which is a circular area with 35.0 mm in diameter (the corresponding heat flux of 156.0 W is 16.2 W/cm2). Thus the heat flux on the top surface of the condenser

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a

180

Working fluid: N2-Ar binary mixture

T2

with Ar molar fraction of 0.121

160

T3

150

T4

2.6 2.4

Beyond heat transfer limit

2.2

T5

140

T6

130

2.0

127.3 W 115.5 W

p

121.9W 1.8

120

1.6

110 100

1.4

90

1.2

80

0

 3  3 Q crit Ae g q2l lt di le =lt  qv =ql ¼ Hfg 3ll le 4ð0:8lc þ 2la þ 0:75le Þ 1  qv =ql

2.8

10

20

30

40

50

60

Pressure (MPa)

Temperature (K)

170

T1

1.0

Time (min)

b

T1

240 220

T4

50.1 W

Beyond heat transfer limit 159.8 W

T5

180

3.5

0:25 qcrit ¼ K q0:5 v Hfg ½rgðql  qv Þ

3.0

p

2.5

156.0 W

150.7 W

139.7 W 140

2.0

120 1.5

100 80

0

20

40

60

80

100

0:25 q0:5 v Hfg ½rgðql  qv Þ

and Kutateladze correlation [34]

T6

160

p 24

4.0

Pressure (MPa)

Temperature (K)

with Ar molar fraction of 0.798

T3

200

By using the same principle as the Improved Cohen and Bayley model [32], Long and Zhang [21] calculated the heat transfer rate of dry-out limit with Nusselt condensation theory and heat and mass balance, which agreed well with the experimental data. This method is also used to calculate the dry-out limit in this study. When the film boiling occurs in the heat sink, the heat transfer limit of the cryogenic thermosyphon is determined by the critical heat flux of film boiling of liquid nitrogen at the atmospheric pressure, as shown in Fig. 7(c). The critical heat flux can be estimated by many empirical correlations, and the most frequently used ones are the Zuber correlation [33]

qcrit ¼

Working fluid: N2-Ar binary mixture

T2

1.0

Time (min) Fig. 8. Typical temperature and pressure variations for dry-out limit in the cryogenic thermosyphon and the film boiling of liquid nitrogen: (a) dry-out limit in the cryogenic thermosyphon; (b) film boiling of liquid nitrogen.

ð9Þ

ð10Þ

ð11Þ

The value of constant K in Eq. (11) is recommended to be 0.135 for cryogenic fluids by Bewilogua et al. [35]. The comparison of the calculated results with the experimental results of the heat transfer rates of dry-out limit and film boiling is shown in Fig. 7(a). The Improved Cohen and Bayley model [32] and Zuber correlation [33] display better agreement. Furthermore, it can be noticed that the heat transfer rate of dry-out limit for the cryogenic thermosyphon with N2–Ar binary mixture increases with Ar molar fraction both in the experimental and calculated results when Ar molar fraction in the working fluid is smaller than 0.503. Then the heat transfer limit keeps nearly constant at about 156.0 W because of the film boiling of the liquid nitrogen at Ar molar fractions larger than 0.503. 5.3. Thermal resistance

can easily reach the critical heat flux of liquid nitrogen due to the increase in the heat transfer rate. Then the formation of the vapor film on the top surface of the condenser deteriorates the heat transfer between the condenser and the liquid nitrogen. Thus, a large amount of heat accumulates on the condenser, leading to the sharp rise of the temperatures of the condenser and the adiabatic section, see Fig. 8(b). Consequently, the inner pressure also rises sharply with the increase of the temperatures. After the film boiling occurs, the heating power is reduced to 50.1 W to avoid overheating on the evaporator. 5.2.2. Calculation of the heat transfer limit The heat transfer rate of dry-out limit in a thermosyphon can be calculated by several methods. Improved Cohen and Bayley model [32] is a widely-used correlation, formulated as Eq. (8).



Q crit Ae qv Hfg ¼



rgðql  qv Þ q2v

g q2l ðdc =de Þ

0:25 "

Volt =ðpdc Þ

#3

3ll le ½rg q2v ðql  qv Þ0:25 0:8lc þ la þ ðde =dc Þ2=3 ðla þ 0:75le Þ  0 3 Vol Vole =Volt  qv =ql  ð8Þ 1  qv =ql

in which the thermal properties of the working fluid and the structure of the thermosyphon are considered based on the heat and mass balance principle of the working fluid. In the presented study, the inner diameters of each part of the cryogenic thermosyphon are the same and the filling ratio Vol0 is 1.0, then Eq. (8) can be reduced to

5.3.1. Experimental data and discussion The thermal resistance for a thermosyphon mainly includes two parts: the thermal resistance in the evaporator and the condenser, respectively. The other types of thermal resistance are negligibly small [17], such as the conduction thermal resistance through the walls and the one caused by the pressure drop of the vapor flow. Fig. 9 shows the thermal resistances in the evaporator and the condenser. The heat transfer rates shown by the labels only stand for the heat transfer rate level, but not the exact value. 5.3.1.1. Thermal resistance in the evaporator. The thermal resistance in the evaporator is mainly the boiling thermal resistance of the liquid working fluid. As stated previously, there is a reduction in the heat transfer of binary mixture because of the existence of the concentrated layer (see Fig. 3) that makes the bubble point rise from Tb to T 0b . This phenomenon is obvious in the thermal resistance of the boiling in the evaporator, as shown in Fig. 9(a). When the heating power is lower than 120.0 W, the maximal boiling thermal resistance appears at Ar molar fraction of 0.606 in N2–Ar binary mixture working fluid. Comparing Fig. 9(a) to the phase equilibrium diagram of the binary mixture in Fig. 4, it can be found that the temperature difference between the bubble point in the liquid bulk Tb and that in the binary mixture adjacent to the wall T 0b (i.e., the bubble points at the two sides of the concentrated layer) is the largest around the Ar molar fraction of 0.6. The larger 4Tbp leads to larger thermal resistance, and such phenomenon was also noticed in [36]. When the heating power exceeds 120.0 W (higher than the heat transfer limit of the cryogenic thermosyphon with pure N2 working fluid), the evaporator temperature is higher than the critical temperature of N2 (see Fig. 6). In this case, the boiling in the evaporator

Z.Q. Long, P. Zhang / International Journal of Heat and Mass Transfer 63 (2013) 204–215

a

0.45

10.0 W 20.0 W 30.0 W 40.0 W 50.0 W 60.0 W 70.0 W 80.0 W 90.0 W 100.0W 110.0 W 120.0 W 130.0 W 140.0 W 150.0 W

0.40 0.35

Re (K/W)

0.30 0.25 0.20 0.15 0.10 0.05 0.00

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ar molar fraction

b

10.0 W 20.0 W 30.0 W 40.0 W 50.0 W 60.0 W 70.0 W 80.0 W 90.0 W 100.0 W 110.0 W 120.0 W 130.0 W 140.0 W 150.0 W

0.40

Ar is solidified in the condenser 0.35

Rc (K/W)

0.30 0.25 0.20 0.15 0.10

Temperature control on the condenser 0.05 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ar molar fraction Fig. 9. The thermal resistance in the evaporator and condenser of the cryogenic thermosyphon: (a) thermal resistance in the evaporator, Re; (b) thermal resistance in the condenser, Rc.

is intensive enough to enhance the mass transfer and minimize the resistance introduced by the concentrated layer. Therefore, the boiling thermal resistance becomes almost irrelevant to the composition of the binary mixture and keeps almost constant in a small range: 0.11–0.15 K/W, as shown in Fig. 9(a). 5.3.1.2. Thermal resistance in the condenser at heat transfer rate lower than 60.0 W. In terms of the condenser, the relation between the thermal resistance and the composition can be divided into two periods as the increase of the heating power: Ar solidification period and co-condensation period. At heating powers lower than 60.0 W, the thermal resistance rises with the increase of Ar molar fraction. The temperature of the entire or part of the condenser is lower than the triple point of Ar, i.e., 84.0 K (see Fig. 6), and then Ar is solidified once it reaches the condenser wall and sticks to it. Consequently, the heat transfer between the vapor and condenser is deteriorated by the solid Ar layer. The thickness of the solid Ar increases with the increase of the Ar fraction in the binary mixture, which results in the rise of the condensation thermal resistance at the same heat transfer rate, see Fig. 9(b). When Ar molar fraction is smaller than 0.3, the amount of solid Ar is so small that it can only weaken the heat transfer slightly, and the thermal resistance is still dominated by the condensation thermal resistance of pure N2, which increases with the increase of the heat transfer rate, as shown in Fig. 9(b). Such characteristic of condensation thermal resistance of pure fluids is mainly determined by the thermal properties of the working fluid [23]. However, it can be noticed that the thermal resistance decreases with the increase of heat transfer rate in 10.0–50.0 W when Ar molar fraction is larger than 0.3. This is because the conduction thermal resistance through the solid Ar layer on the condenser in-

211

ner wall becomes the main thermal resistance in the condenser. It can be assumed that the temperature on the interface between the solid Ar layer and the liquid film is constantly 84.0 K (the triple point of Ar), the increase of the condenser temperature owing to the increase of heat transfer rate makes the solid Ar layer thinner for the same working fluid composition. Consequently, the thermal resistance in the condenser decreases. The thermal conductivity of the solid Ar layer is much smaller than the condenser wall (made of copper), thus the reduction on thickness of the solid Ar layer improves the heat transfer in condenser remarkably, see the transition of the thermal resistance from 10.0 W to 50.0 W for the same composition. However, the thermal resistance in the condenser decreases suddenly in the cases of the heat transfer rate in 10.0–50.0 W when the working fluid is pure Ar, as shown in Fig. 9(b). This is because Heater 2 (see Fig. 5) is switched on to control the condenser temperature to be higher than the triple point of Ar until the heat transfer rate reaches 60.0 W to avoid the operation failure of the cryogenic thermosyphon. The heating on the condenser minimizes the temperature difference between the evaporator and condenser and consequently makes the thermal resistance smaller. 5.3.1.3. Thermal resistance in the condenser at heat transfer rate higher than 60.0 W. The temperature of the condenser is high enough to avoid the solidification of Ar when the heat transfer rate is higher than 60.0 W, then the thermal resistance in the condenser is dominated by the condensation thermal resistance of N2–Ar binary mixture vapor. The heat transfer performance is also reported to be weakened in the case of binary mixture vapor condensation [37–39], in which the condensation occurs in the cases of vertical plate, horizontal tube, heat exchangers, vertical channels, and so on. The initial state of the mixture vapor in these cases is either stationary or forced flow. However, there is no obvious heat transfer deterioration in Fig. 9(b) when the heat transfer rate is higher than 60.0 W. The condensation thermal resistance changes almost linearly with the change of the mixture composition. According to the experiments and modeling conducted by Thonon and Bontemps [13], the heat transfer characteristics of a binary mixture vapor condensation were close to that of pure fluids at high Reynolds number (Rev > 1500). Furthermore, Kotake [20] figured out that the higher vapor velocity resulted in shorter length of developing regions of the concentration, which indicated that the high vapor velocity worked efficiently in mixing the two components of the binary mixture, thus resulting in thinner concentrated layer. According to Eqs. (5) and (6), the vapor velocity is found to range from 0.011 m/s to 0.218 m/s, and the Reynolds number of the vapor flow Rev increases from around 100 at 1.0 W to around 18,000 at 156.0 W. The velocity here is much higher than the case discussed by Kotake [20], and the Reynolds number exceeds 1500 when the heat transfer rate is as small as 15.0 W. The high vapor velocity and Reynolds number weaken the effect of concentrated layer on the heat transfer performance in the N2–Ar binary mixture, which is different from the conventional binary vapor condensation. Thus the condensation thermal resistance can be evaluated by considering the binary mixture vapor as a single vapor. Although the concentrated layer does not significantly deteriorate the heat transfer of condensation, it determines the composition of the vapor adjacent to the condenser wall and the condensed liquid, which plays an important role in the steady operation of the cryogenic thermosyphon and the thermal resistance calculation. 5.3.1.4. Total thermal resistance. The total thermal resistance in the experiments can be calculated from Eq. (4), where DT is the difference between the average temperatures of the condenser and evaporator. Fig. 10 shows the total thermal resistance of the entire

Z.Q. Long, P. Zhang / International Journal of Heat and Mass Transfer 63 (2013) 204–215

cryogenic thermosyphon calculated from experimental data. The trend shown in Fig. 10 also displays the characteristics of the thermal resistance in thermosyphon with pure working fluid: it decreases sharply with the increase of the heat transfer rate at low heat transfer rates and then becomes constant at high heat transfer rates, which is discussed in detail by Zhang et al. [23] and Nakano et al. [24]. The black square dot line and the red circle dot line are the experimental results for the case of pure N2 and pure Ar, respectively, which are much lower than the other cases at low heat transfer rates. The increment in thermal resistance of the cryogenic thermosyphon with N2–Ar binary mixture not only results from the resistance introduced by the concentrated layer, but also the solidification of Ar in the condenser. 5.3.2. Thermal resistance calculation The thermal resistance can be represented by 1/(hA), where h is heat transfer coefficient and A is heat transfer area. The calculation of the heat transfer coefficient for the phase change of binary mixture was widely studied, and many methods and empirical correlations were proposed under different conditions. The evaporation and condensation occur simultaneously in a small cylindrical volume in this study, and some particular phenomena occur during the operation, such as violent boiling, high vapor speed, and near critical operation. Thus the calculation methods for the heat transfer coefficients of boiling and condensation should be adopted according to the characteristics of the heat transfer process in the cryogenic thermosyphon. 5.3.2.1. Boiling thermal resistance at heat transfer rate lower than 120.0 W. As shown in Fig. 9(a), the thermal resistance below 120.0 W shows similar characteristics of the pool boiling for the conventional binary mixtures at room temperature. In this case, many correlations were proposed to calculate the heat transfer coefficient based on the theoretical analysis and experimental data. Schlunder [36] proposed a correlation for the nucleate boiling of binary mixture by considering the mass transfer in the concentrated layer, written as

he 1 ¼ hid 1 þ ðhid =qÞðT s2  T s1 Þðy1  x1 Þð1  expðB0 q=ðql bl Hfg ÞÞÞ ð12Þ hid ¼

1 x1 =h1 þ x2 =h2

ð13Þ

Total thermal resistance R (K/W)

where q is the heat flux on the heating surface; Ts1 and Ts2 are the saturation temperatures of the volatile component and the nonvol-

10 8

Ar molar fraction 0 1 0.121 0.208 0.314 0.417 0.503 Natural convection and Ar solidification 0.606 0.697 0.798 Beyond heat transfer limit 0.892

3.5 3.0 2.5 2.0 1.5

atile component of the binary mixture at the operational pressure, respectively; x1 and y1 are the molar fraction of the volatile component in the liquid and vapor bulk of the binary mixture, respectively; bl is the mass transfer coefficient of the liquid bulk. The thermal properties of the binary mixture in this equation are the ones of the liquid bulk, and the composition of the liquid bulk is determined by the concentrated layer discussed in Section 2. The factor B0 is fitted empirically for different mixtures. bl = 2  104m/s and B0 = 1 are recommended by Schlunder [36] for the most binary mixtures. It has been proved that this correlation agreed well with the experimental data of the boiling of the SF6–CF2Cl2 mixture [36]. Another frequently used correlation is Thome correlation [18]:

he 1 ¼ hid 1 þ DT l =DT bp

ð14Þ

where hid is calculated by Eq. (13), DTbp is the temperature difference between the bubble points at the two sides of the concentrated layer, as shown in Fig. 3, DTl is the ideal superheat on the heating surface, and it is calculated from

D T l ¼ x1 D T 1 þ x 2 D T 2

ð15Þ

where x1 and x2 are the molar fractions of the volatile component and the nonvolatile component in liquid bulk of binary mixture, respectively; DT1 and DT2 are the wall superheat for the boiling of the pure fluids corresponding to the volatile component and the nonvolatile component, respectively. This method for calculating the variation of nucleate boiling heat transfer coefficient uses only phase equilibrium data and the superheat on the wall. The calculated result of Eq. (14) was compared with the experimental data for the pool boiling of six binary mixtures by Thome [18], showing good accuracy. While for high heat flux, Eq. (14) underestimates the experimental data and Inoue and Monde [14] proposed Eq. (16) modified from Eq. (14) for the calculation of nucleate boiling heat transfer coefficient in the cases of high heat fluxes.

he 1 ¼ hid 1 þ CðDT l =DT bp Þ

ð16Þ

where C ¼ 0:45  105 q þ 0:25; 104 6 q 6 105 W=m2 . It was shown that the deviation between the calculated heat transfer coefficients and the experimental results of the R12–R113 binary mixture was within an accuracy of ±10% in [14]. Fig. 11 shows the calculated results by Eq. (12), Eq. (14) and Eq. (16) for three heat transfer rates of 20.0 W, 40.0 W, and 70.0 W. As can be seen from the figure, the Thome correlation [18] displays the best agreement for all cases with the accuracy of ±12%. While

0.30 0.25 0.20

Re (K/W)

212

0.15 0.10 Experiment

1.0 0.5 0

20

40

60

80

100

120

140

160

Net heat transfer rate Qnet (W) Fig. 10. The total thermal resistance of the entire cryogenic thermosyphon with N2–Ar binary mixture working fluid.

0.00

Calculation

20 W 40 W 70 W

0.05

0.0

0.2

0.4

0.6

Eq. (14) Eq. (12) Eq. (16) 0.8

1.0

Ar molar fraction Fig. 11. Comparison of the calculated thermal resistances with the experimental results.

213

Z.Q. Long, P. Zhang / International Journal of Heat and Mass Transfer 63 (2013) 204–215

the other two correlations underestimate the boiling thermal resistance with the maximal deviation of 32% from the experimental results. 5.3.2.2. Boiling thermal resistance at heat transfer rate higher than 120.0 W. For the boiling thermal resistance of N2–Ar binary mixture in the evaporator, there is no heat transfer deterioration in mixture working fluid when the heat transfer rate is over 120.0 W, as shown in Fig. 9(a). This may owe to the high heat flux and the temperature rise on the evaporator. The temperature on the evaporator is much higher than the critical temperature of N2, i.e., 126.0 K (see Fig. 6). Thus the boiling is so violent that the heat transfer performance behaves similarly to that of pure fluid, and the correlations developed for the boiling of binary mixture by considering the heat transfer deterioration are no longer applicable. Then we can calculate the boiling thermal resistance by using the empirical correlation of nucleate boiling for pure fluid [40],

cpl ðT w;e  T o Þ ¼ C wl Hfg



q ll Hfg

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:33

r

gðql  qv Þ

Prsl

ð17Þ

where all the thermal properties are for the binary mixture and they are calculated by Aspen Properties 11.1 with PRBM property method. The value of the index S = 1.7 is recommended by Rohsenow [40]. Cwl = 0.004 is the empirical constant determined from experimental data for the boiling in the thermosyphon [28]. The temperature difference

T w;e  T o ¼

Q net Ae he

ð18Þ

where Ae is the heat transfer area in the evaporator. Substituting Eq. (18) into Eq. (17) yields

he ¼

 0:67 " rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi#0:33 1 cp;l Q net gðql  qv Þ ll C wl Prsl Ae Hfg r

ð19Þ

Fig. 12 compares the calculated results of Eqs. (14) and (19) with the experimental results for all the cases within a deviation of ±20%. Thus, we can conclude that the heat transfer deterioration appears in the boiling of N2–Ar binary mixture when the wall temperature is below the critical temperature of N2 and the heat transfer coefficient can be calculated by the correlations developed for the pool boiling of binary mixtures; when the heat transfer rate is high enough to make the wall temperature exceed the critical temperature of N2, the binary mixture can be treated as a single fluid for all the mixture compositions.

5.3.2.3. Condensation thermal resistance. The binary mixture vaporizes in the evaporator and flows to the condenser, and then it is condensed in the condenser. A layer of solid Ar sticks to the inner wall of the condenser when the temperature of the condenser is below the triple point of Ar at the heat transfer rate lower than 60.0 W. The thermal resistance of the condensation is difficult to be evaluated theoretically or by the empirical correlations, as it is difficult to determine the thickness and the distribution of the solid Ar layer only by the temperature distribution and operational pressure. Therefore, the condensation thermal resistance can only be analyzed qualitatively at the heat transfer rate lower than 60.0 W, as discussed in Section 5.3.1.2. As stated before, the thermal resistance in the condenser for the heat transfer rates over 60.0 W is dominated by the condensation thermal resistance and it can be evaluated by considering the binary mixture vapor as a single vapor. Thus the conventional empirical correlations for the calculation of the condensation in binary mixture are not proper in this case and the Nusselt film condensation theory [40] is an appropriate one to treat the N2–Ar mixture as one fluid. According to Eq. (7), it is found that the maximal value of Rel in the experiments is about 1700 in the case of the largest heat transfer rate, i.e., 156.0 W, smaller than the critical Reynolds number for the turbulent film condensation, 1800 [22]. Therefore, the film condensation in the condenser can be regarded as laminar. Then the heat transfer coefficient is

" #1=4 1 4 k3 g q ðq  qv ÞHfg hc ¼ pffiffiffi   l l l ll lc ðT o  T w;c Þ 2 3

where To and Tw,c are the operational temperature and the wall temperature of the condenser, respectively. In view of the heat transfer process in the condenser, the temperature difference To  Tw,c can be written as

T o  T w;c ¼

ð21Þ

" pffiffiffi#4=3 " #1=3 k3l g ql ðql  qv ÞHfg Ac 2 2 hc ¼  ll Q net lc 3

ð22Þ

Fig. 13 shows the comparison of the calculated results by Eq. (22) with the experimental results of the condensation thermal resistance, in which the condensation thermal resistance is still underestimated when the heat transfer rate is 60.0 W. This is because the temperature at the top surface of condenser is still below the triple

0.20

0.3

+20% 0.2

-20% 0.1

0.1

0.2

0.3

0.4

0.5

Re experimental results (K/W) Fig. 12. Comparison of the calculated results by Eqs. (14) and (19) with the experimental results.

60.0 W 70.0 W 80.0 W 90.0 W 100.0 W 110.0 W 120.0 W 130.0 W 140.0 W 150.0 W

0.18

Rc calculation (K/W)

10.0 W 20.0 W 30.0 W 40.0 W 50.0 W 60.0 W 70.0 W 80.0 W 90.0 W 100.0 W 110.0 W 120.0 W 130.0 W 140.0 W 150.0 W

0.4

Re calculation (K/W)

Q net Ac  h c

where Ac is the area of the condenser inner wall. Substituting Eq. (21) into Eq. (20) yields

0.5

0.0 0.0

ð20Þ

+20%

0.16

0.14

0.12

-20% 0.10 0.10

0.12

0.14

0.16

0.18

0.20

Rc experimental results (K/W) Fig. 13. Comparison of the calculated results by Eq. (22) with the experimental results of the condensation thermal resistance.

214

Z.Q. Long, P. Zhang / International Journal of Heat and Mass Transfer 63 (2013) 204–215 0.34

Rt calculation (K/W)

0.32 0.30

+15% 60.0 W 70.0 W 80.0 W 90.0 W 100.0 W 110.0 W 120.0 W 130.0 W 140.0 W 150.0 W

0.28 0.26 0.24

-15% 0.22 0.20 0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

Rt experimental results (K/W) Fig. 14. The comparison of the calculated total thermal resistance to the experimental ones.

point of Ar at 60.0 W (see Fig. 6), thus the heat transfer in the condenser is weakened by the solidification of Ar. 5.3.2.4. Total thermal resistance. As stated previously, the main components of the total thermal resistance are the boiling thermal resistance and the condensation thermal resistance. The comparison of the calculated results of the two thermal resistances with the experimental total thermal resistance of the cryogenic thermosyphon is shown in Fig. 14, with a deviation within ±15%. Hence, the appropriate methods for calculating the thermal resistances (heat transfer coefficients) of the cryogenic thermosyphon with mixture working fluid are presented by analyzing the heat transfer characteristics in the evaporator and condenser. They are Thome correlation [18] and nucleate boiling correlation [40] for the boiling in the evaporator and the Nusselt film condensation theory [40] for the condensation in the condenser, respectively. 6. Conclusions The heat transfer characteristics of a cryogenic thermosyphon filled with N2–Ar binary mixture as the working fluid in different compositions are studied. The heat transfer performance, i.e., the heat transfer limit and thermal resistance, is studied experimentally and calculated by the empirical correlations. The conclusions are summarized as follows: (1) The N2–Ar binary mixture working fluid can widen the operational temperature range of the cryogenic thermosyphon from 64.0 K to 150.0 K, wider than that of the thermosyphon with pure N2 and pure Ar working fluid. (2) The dry-out limit occurs in the cases of small Ar molar fractions (smaller than 0.503), and the heat transfer limit of the cryogenic thermosyphon increases with the increase of Ar molar fraction. Thus the presence of Ar in the working fluid can promote the heat transfer limit of the cryogenic thermosyphon. The further increase of the heat transfer limit is limited by the film boiling of liquid nitrogen in the heat sink when Ar molar fraction is 0.503 or higher, and the heat transfer limit keeps nearly constant at about 156.0 W. The corresponding heat flux is equal to the critical heat flux of liquid nitrogen boiling at atmospheric pressure, which is estimated to be about 16.2 W/cm2. (3) The boiling of N2–Ar binary mixture in the evaporator shows the typical characteristics of pool boiling of binary mixture with the heat transfer reduction compared with that of the pure fluids because of the existence of the concentrated layer

for the heat transfer rate lower than 120.0 W. At the heat transfer rates higher than 120.0 W, the thermal resistance in the evaporator shows no relevance to the composition due to the intensive boiling. However, in terms of the condensation, the vapor velocity is as high as 0.218 m/s when the heat transfer rate is high enough to avoid the solidification of Ar, which results in the intensive mixing of the two components and then intensifies the mass transfer process in the vapor concentrated layer. Consequently, the condensation of the binary mixture vapor in the cryogenic thermosyphon behaves as a single working fluid. Both the boiling and condensation thermal resistance can be calculated by appropriate empirical correlations and the deviations of the calculated results for the total thermal resistance compared with the experimental ones are within ±20%.

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