Effect of air on condensation in a non-vacuum gravity heat pipe

Applied Thermal Engineering 114 (2017) 255–263

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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng

Research Paper

Effect of air on condensation in a non-vacuum gravity heat pipe J.X. Zhang a, L. Wang b,⇑ a b

School of Energy Engineering, Yulin University, Yulin 719000, China Schools of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


Condensation with air in a non-

vacuum gravity heat pipe was investigated.
A saturated moist air column is formed in the condensation tube downstream.
Degradation factors are low at the condensation tube downstream at a low heat load.
68% of the reservoir is full of air at an operating pressure of 0.24 MPa.
Vapor with air is 1.32 times pure vapor condensation length at present condition.

a r t i c l e

i n f o

Article history: Received 16 August 2016 Revised 29 November 2016 Accepted 30 November 2016 Available online 1 December 2016 Keywords: Condensation heat transfer Gravity heat tube Air Degradation factor

a b s t r a c t An experimental and theoretical investigation was performed to show the effects of air on condensation in a non-vacuum gravity heat pipe at heat loads of 0.8–5.3 kW. Parameters involving local condensation heat transfer coefficients, air mole fractions, and air storage capacity in a reservoir mounted below the condensation tube, were calculated. A degradation factor method was applied to solve vapor condensation length. Results showed that local air mole fraction increased to over 95% in the condensation tube downstream, where a saturated moist air column was formed. The reservoir effectively alleviated the adverse effects of air on the condensation section. At an operating pressure of 0.24 MPa, 68% of the reservoir was filled with air. In the condensation tube downstream with a low heat load, air seriously affected condensation heat transfer, and the average degradation factor was only 0.26. By contrast, air slightly affected condensation heat transfer in the condensation tube upstream with a high heat load, and the average and local degradation factors were 0.7 and 0.76, respectively. Vapor condensation length with air was 1.32 times as much as pure vapor condensation length at a vapor mass flux of 1.8 g/s and an operating pressure of 0.36 MPa. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Heat pipes have been applied in different applications, such as air conditioning systems, aerospace, industrial waste heat recovery, and renewable energy [1–5]. Heat pipes are highly efficient heat transfer devices in which phase change occurs repeatedly. ⇑ Corresponding author. E-mail address: [email protected] (L. Wang). http://dx.doi.org/10.1016/j.applthermaleng.2016.11.209 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

They offer high thermal conductivity and can efficiently transport large amounts of heat over long distances. A heat pipe is composed of three sections: the evaporator section at one end, where heat is absorbed and fluid is vaporized; the condensation section at the other end, where vapor is condensed and heat is rejected; and the adiabatic section in between, where the vapor and liquid phases of fluid flow in opposite directions through the tube. Heat pipes can be classified as tubular, variable conductance, thermal diodes, pulsating, loop, and micro heat pipes. Recent studies have

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Nomenclature ca cp;c D1 Do Dv a f
f G hfg hc he he hm hNu hNu L L1 L2 M m na nv p Q q R Rev r Sc

air mole concentration, mol L1 constant pressure specific heat, J kg1 K1 inner diameter of the condensation tube, m external diameter of the condensation tube, m diffusion coefficient between air and vapor, m2 s1 degradation factor average degradation factor mass flux, kg s1 latent heat, kJ kg1 convective heat transfer coefficients of the cooling water, W m2 K1 local experimental condensation heat transfer coefficients, W m2 K1 average experimental condensation heat transfer coefficients, W m2 K1 mass transfer coefficients, m s1 local condensation heat transfer coefficients of the Nüsselt theory, W m2 K1 average condensation heat transfer coefficients of the Nüsselt theory, W m2 K1 tube length, m vapor condensation length, m length of the saturated moist air column, m molecular weight, kg mol1 condensation rate, kg m2 s1 air mole fraction, mol vapor mole fraction, mol pressure, MPa heating power, W heat flux per unit tube length, W m2 gas constant, J kg1 K1 Reynolds number = qv uD1 =lv tube radius, m Schmidt number = lv =qv Dv a

focused on loop and tubular heat pipes [1]. Loop heat pipes can be operated against gravity and exhibit maximum heat transport capability [2]. Lightweight materials are used for miniature loop heat pipes to achieve high performance [3]. Tubular horizontal heat pipes have been applied to air conditioning systems in the tropics to increase cooling and power-saving capabilities [4]. Tubular heat pipes have the highest operating temperature among different heat pipes, thereby providing viable optimization and integration for renewable energy systems [1,5]. A gravity heat pipe is a gravity-assisted tubular wickless heat pipe that plays an important role in the large-scale heating industry. Non-condensable gas (NCG) is one of the main factors that affect heat pipe performance and lifetime. NCG has two sources: (1) residual air after the heat pipe is evacuated and (2) hydrogen generated by the chemical reaction between the pipe material and the working fluid. Several researchers [6–10] have studied the effects of NCG on loop heat pipes. The majority of the NCG is located in the vapor region and the reservoir of loop heat pipes [6–8], which lead to highly elevated pressure. Therefore, NCG affects the start-up performance of loop heat pipes. Higher NCG content in the loop heat pipe results in higher temperature overshoot and liquid superheat, as well as longer startup time. Large heat load contributes to better startup performance in the presence of NCG. Huang et al. [8] proposed that gas-vapor blocks the zone between vapor and NCG in the condenser. This zone inhibits the vapor from flowing toward the condenser and prevents NCG from diffusing toward the evaporator. Prado-Montes et al. [9] found that

Sh T DT u V VR Va Vg x z

Sherwood number = hm D1 =Dv a thermodynamics temperature, K vapor superheated degree velocity, m s1 volume, m3 ratio of gas volume to overall volume in the reservoir volume of gas phase space in the reservoir, m3 volume of air in the non-vacuum gravity heat pipe, m3 mole fraction tube axis

Greek letters k thermal conductivity, W m1 K1 q density, kg m3 dl thickness of condensate, m dg thickness of gas film layer, m l dynamic viscosity, Pa s Subscript a ax av c i iþ1 in l s

v

w 0

air axial direction average cooling water the ith coordinate point at z axis the (i þ 1)th coordinate point at z axis inlet condensate saturation vapor wall initial state

3.34 g of additional NCG stops the operation of loop heat pipes at low heat load between 50 and 100 W. The part of the NCG may accumulate in the primary wick lore, which leads to a local rupture of the liquid bridge through the wick, and dry-out, which leads to the inoperability of loop heat pipes. Moreover, NCG induces the oscillatory behavior of a loop heat pipe at low heat load. The addition of 0.5–1% mass fraction of ethanol forms the Marangoni effect on the surface of the condensate film of gravity loop thermosyphon in the presence of massive NCG [10]. Other studies [11–14] focused on the effects of NCG on tubular heat pipes. The effect of NCG on the transient response of wicked tubular heat pipes has been considered [11]. NCG is mixed with the vapor at startup, separated from vapor, and pushed to the condenser’s end as the vapor pressure increases. Therefore, the presence of NCG slows the cooling rate of a wicked tubular heat pipe once it occupies much of the cooled region. NCG results in a large temperature gradient near the condenser’s end and reduces the effective thermal conductance in radically rotating tubular heat pipes [12]. Moreover, NCG affects the condensation section of a separate-type heat pipe [13]. The sophisticated physical models were carried out to model condensation heat transfer in tubular heat pipes [14]. NCG should be removed via evacuation because it degrades condensation heat transfer in the heat pipe system. However, evacuation in a gravity heat pipe system that involves many tubes increases equipment investment costs and maintenance inconvenience. The adoption of a non-vacuum gravity heat pipe can save a lot of evacuation expenses and bring a large energy saving effect in the large-scale

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heating industry. Thus, the operating performance of a nonvacuum gravity heat pipe must be studied. NCG adversely affects condensation heat transfer. A mass fraction of air equal to 0.5% causes a reduction in the heat transfer of 50% for an analytical investigation of laminar film condensation on an isothermal vertical plate because NCG is carried by vapor to the gas–liquid interface, which increases the condensation resistance of vapor on the liquid film [15]. An increment in NCG decreases the condensation heat transfer coefficients and condensation tube wall temperature, but increases vapor condensation length [16,17]. NCG also affects the gas-liquid two-phase condensation flow pattern in horizontal and inclined tubes [18–20]. Three types of methods namely, degradation factor, heat and mass analogy, and two-phase boundary layer, are applied to analyze quantitatively the effects of NCG on condensation heat transfer. The degradation factor method determines the decreasing amount of condensation heat transfer coefficients in the presence of NCG based on the condensation heat transfer coefficients of pure vapor [21]. In the heat and mass analogy method, condensation heat transfer with NCG may be evaluated at different flowing parameters [22]. The distribution of NCG and other heat transfer parameters in the boundary layer is determined using the two-phase boundary layer method by establishing the mass, momentum, and energy conservative equations [23,24]. A few studies have considered the effect of air on condensation in a non-vacuum gravity heat pipe. Li et al. [25,26] experimentally analyzed the factors that affected the heat exchange power of a non-vacuum separate-type heat pipe. In the present work, an experimental and theoretical investigation was performed to determine the effects of air on condensation heat transfer in the condensation section of a non-vacuum gravity heat pipe.

2. Experiment 2.1. Experimental facility Fig. 1 shows a schematic diagram of the non-vacuum gravity heat pipe. The diagram consisted of evaporator, adiabatic, and condensation sections. The evaporator section has a stainless steel tube that has a 108-mm inner diameter, 5-mm thickness, and 0.3-m height. Two-thirds of its space was filled with water. Six

257

0.8-kW electric heating rods were mounted in water to generate vapor, and five 0.1-kW electric heating rods were fixed above the water to superheat vapor. The condensation section was made up of a vertical jacket heat exchanger that has an inner condensation tube and an outer jacket. The condensation tube was a copper tube with an inner diameter of 10 mm and a thickness of 2 mm. The jacket was a stainless steel tube with an outer diameter of 38 mm, a thickness of 2 mm, and a length of 0.6 m. Vapor entered downward into the condensation tube, whereas cooling water flowed upward through the annular tube between the condensation tube and the jacket. A reservoir was mounted below the condensation tube. Two-thirds of the space was filled with water, and the remaining space was used to store air in a non-vacuum gravity heat pipe. The adiabatic section connected the evaporator section to the condensation section and the reservoir with stainless tubes with an inner diameter of 10 mm. The reservoir is made up of a stainless steel cylinder with a diameter of 108 mm, a height of 180 mm, and a thickness of 5 mm. A glass tube level meter was installed on the reservoir to measure the water level and calculate the volume occupied by the saturated moist air. A one-way valve allows the condensate to flow from the reservoir to the evaporator only toward one direction. A drain valve may discharge the water in the system to the environment after the experiment. A coupling interaction of both a solenoid valve and a timing relay can control a floating ball level meter that is inserted into the water of the evaporator section to stop feeding water when the water level of the evaporator rises or begin feeding water when the water level of the evaporator drops. The water level of the evaporator is kept at 200-mm height. Two pressure gauges were mounted on the evaporator section and the reservoir to measure the operating pressure of the non-vacuum gravity heat pipe. Six T-type copper–constantan thermocouples with a diameter of 0.5 mm were welded onto the condensation tube’s outer wall to test wall temperature, whereas six thermocouples with the same size were fixed into the annular center to test the temperature of cooling water. A same-sized thermocouple was placed at the condensation tube inlet of z = 0 to test vapor temperature, as shown in Fig. 1. A floating flowmeter and a same-sized thermocouple were set at the cooling water outlet to test the mass flux and temperature of cooling water. The entire

Fig. 1. Schematic diagram of the non-vacuum gravity heat pipe.

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device was covered with an adiabatic material to reduce the effects of heat loss on measurement accuracy. To reduce heat loss, the whole experimental device is coated with a 30-mm thick soft foam plastic thermal insulation layer. The heat loss accounts for 0.7–3% of overall heat; thus, its influence on the experimental data can be neglected. Prior to the start-up of the non-vacuum gravity heat pipe, 65% of the space was full of water, whereas 35% was full of air at a pressure of 0.1 MPa and a temperature of 293 K. Approximately 1.1 m water level difference was retained between the evaporator section and the reservoir. The entire system ran steadily without noise during the experiment. The maximal pressure and temperature were 3.6 MPa and 403 K, respectively. The pressure drop from the evaporator section to the reservoir was 5 kPa. 2.2. Data processing Fig. 2 shows the schematic diagram of condensation with the air in the condensation tube. Vapor was carried with the air as it flowed downward into the condensation tube. It condensed on the wall and formed a condensate, whereas the air accumulated on the condensate surface. Cooling water flowed upward through the annular tube and absorbed the latent heat released by vapor condensation. The local condensation heat transfer coefficients and the air mole fraction were calculated according to the wall temperatures of the condensation tube and the central temperatures of the cooling water. The condensation heat flux per unit condensation tube length can be calculated with the cooling water convective heat transfer when the condensation heat transfer is stable.

q¼

Gc cp;c ðT c;iþ1  T c;i Þ p D o Dz

ð1Þ

The vapor condensation rate on the condensate surface can be obtained using the following formula.

q m¼ hfg

xa ¼

qa Dv a dxa xa

dr

ð3Þ

pa qa Ra T ax ¼ p p

ð4aÞ

where p is the operating pressure. The pressure drop in the condensation tube is less than 5 kPa, which is 5% of the operating pressure. Therefore, the effect of pressure drop may be neglected. It is assumed that the gas volume V 0 is no variation in the nonvacuum gravity heat pipe at any pressure. Given vapor working pressure pv and temperature T, when the condensation heat transfer is in a stable state at the condensation section of non-vacuum gravity heat pipe, the ideal gas state equation can be expressed as

pv ¼ qv Rv T

ð4bÞ

pv nv R ¼ V0 T

ð4cÞ

Combining Eq. (4b) into Eq. (4c), which can be rearranged as

qv Rv ¼

nv R V0

ð4dÞ

At the initial state, only air is in the gas phase space of nonvacuum gravity heat pipe, and no vapor is generated. The ideal gas state equation can be expressed as

p0 R ¼ T 0 na V 0

ð4eÞ

Because air is stagnant in non-vacuum gravity heat pipe during the whole condensation, air mole fraction na is no variation, which is also the value at given vapor working pressure pv and temperature T. Substituting Eq. (4e) into Eq. (4d), the following formula is obtained.

qv Rv ¼ nv

ð2Þ

Fick’s law by Lewis and Whitman [27] states that the vapor condensation rate also depends on the local air mole fraction, xa , and can be expressed as.

m¼

From the ideal gas state equation, the local and average air mole fractions can be described with

p0 T 0 na

ð4fÞ

Let the average mole fraction of air is

xa;av ¼

na na þ nv

ð4gÞ

Substituting Eq. (4g) into Eq. (4f), average mole fraction of air is simplified to


xa;av ¼

qv Rv T 0 p0

1 þ1

ð4hÞ

The following formula can be obtained by substituting Eq. (4a) into Eq. (3).



m

qa Dv a

dr ¼

dT : T

ð5Þ

The vapor condensation rate can be determined by integrating the following formula from r ¼ ½0; dg  to T ¼ ½T ax ; T w .

m¼


 2qa Dv a T ax ln Do Tw

ð6Þ

Thickness of gas film layer in Eq. (6), dg , can be calculated with.

dg ¼

Dv a hm

ð6aÞ

According to heat and mass analogy, mass transfer coefficients, hm , can be expressed as the following formula.

hm ¼ Fig. 2. Schematic diagram of condensation with air in the condensation tube.

ShDv a D1

ð6bÞ

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On the basis of convective mass transfer correlation [28], Sherwood number, Sh, can be determined by.

Sh ¼ 0:023 Re0:83 Sc0:44 v

ð6cÞ

The condensation tube central temperature can be obtained by substituting Eq. (2) into Eq. (6) as follows.

T ax ¼ T w eao q ; where a0 ¼

dg 2qa hfg Dv a

ð7Þ 4

and Dv a ¼ 0:254  10

m =s. Given that the 2

condensation tube is made up of copper, the conductivity coefficient is approximately 120 W m1 K1 and the thermal resistance is approximately 4.6e5 K W1, which is negligible. Thus, the experimental condensation heat transfer coefficients can be determined according to Newton’s cooling law.

q T ax  T w

he ¼

ð8Þ

Vapor mass flux at the inlet can be determined through the heating power. The heating power is expressed as heat load and ranges from 0.8 kW to 5.3 kW.

Q hfg

Gv ¼

ð9Þ

The temperature reference point of vapor superheated degree is the saturated temperature at given pressure. Vapor superheated degree is the temperature difference between the inlet vapor temperature and saturated vapor temperature at a given pressure.

DT ¼ T in  T s jp

ð10Þ

Air volume in the reservoir V a significantly affects operating pressure. VR is defined as the ratio of V a to the reservoir volume V.

VR ¼

Va  100% V

ð11Þ

Without considering air solution and absorption, the system remains constant temperature T 0 , and constant pressure p0 at the initial time. Air mole concentration is equal everywhere and can be calculated as follows.

ca ¼

na p ¼ 0 ; V g RT 0

Fig. 3. Condensation tube wall temperature at various vapor mass fluxes.

The condensation tube wall temperature rises as vapor mass flux increases. At a cooling water mass flux of 2 L/min, the condensation tube wall temperature drops along the tube length at vapor mass flux of 1.8 g/s. For example, the condensation tube wall temperature decreases by 83 °C from 108 °C at z = 0 m to 25 °C at z = 0.48 m at a vapor mass flux of 0.7 g/s. This scenario indicates that a large amount of vapor condenses at z < 0.48 m. The condensation section at z > 0.48 m is occupied by the saturated moist air because the condensation tube wall temperature is almost atmosphere temperature. Driven by vapor that continuously enters into the condensation tube, air is detained at the condensation tube downstream, which forms a saturated moist air column. For the condensation of vapor flowing through the condensation tube in Ref. [21], the condensation tube wall temperature decreases by 25 °C along the 2 m-long tube at a vapor mass flux of 0.7 g/s, which is considerably less than the condensation tube temperature drop in the present experiment.

ð12Þ

where p0 = 0.1 MPa and T 0 = 293 K. Air mole concentration in the non-vacuum gravity heat pipe is 0.042 mol/L.

2.3.2. Local condensation heat transfer coefficients Fig. 4 shows the local condensation heat transfer coefficients along the tube length. The local condensation heat transfer coeffi-

2.3. Results and discussion The experiment on the non-vacuum gravity heat pipe was executed at a vapor mass flux of 0.7–2 g/s, a cooling water mass flux of 50–200 g/s, and a superheated degree of 0–30 K. Vapor mass flux was the main factor that affected the condensation heat transfer. As indicated by the experimental data of the tested temperature and pressure, the air mole fraction and condensation heat transfer coefficients were calculated using Eqs. (1)–(8). Their uncertainties were analyzed via a standard error propagation method. The uncertainty on air mole fraction was less than 12%, and the one of condensation heat transfer coefficients were less than 5.3%. They are mainly caused by a system error because flowmeter and pressure gauge need a visual inspection to obtain the experimental data. Measurement range of flowmeter is in 0–18 L/min, the uncertainty is 2.5–4%. Measurement range of pressure gauge is 0– 0.6 MPa, the uncertainty is 2.5%. 2.3.1. Condensation tube wall temperature Fig. 3 shows the condensation tube wall temperature at various vapor mass fluxes. DT ¼ 0 represents a zero superheated degree.

Fig. 4. Local condensation heat transfer coefficients along the tube length.

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cients increase as the vapor mass flux at the condensation tube inlet increases because vapor condensation belongs to the laminar film condensation heat transfer at a low vapor mass flux, and the local condensation heat transfer coefficients are small. The Reynolds number of vapor in the present experiment ranges from 3700 to 20,000. Higher velocity vapor flowing at the inlet induces turbulent filmwise condensation. Therefore, a turbulent film condensation heat transfer occurs at a high vapor mass flux, which improves the local condensation heat transfer coefficients. In Ref. [21], pure vapor condensation length is 1 m at a vapor mass flux of 0.9 g/s. In the inverted U-type condensation tube of Ref. [18], vapor flows upward into the condensation tube, and the air is compressed into the condensation tube downstream. Vapor condensation length is 1.5 m at an air mass fraction of 0.017. However, in the present experiment, vapor condensation length is approximately 0.38 m at a vapor mass flux of 0.7 g/s. Vapor condensation length exhibits no evident variation with the increment in vapor mass flux and still condenses in the 0.5-m tube length because the reservoir mounted below the condensation tube deposits stagnant air, which alleviates the adverse effect of air on condensation heat transfer. Moreover, operating pressure rises at a high vapor mass flux, which increases the amount of vapor to complete condensation within a limited space. 2.3.3. Air mole fraction Fig. 5 shows the local air mole fraction along the tube length. The local air mole fraction increases along the condensation tube length. In the condensation tube downstream at z > 0.48 m, the local air mole fraction is larger than 95%, which indicates that vapor ends condensation, and a saturated moist air column is formed in the area. However, the local air mole fraction at the condensation tube outlet only increases 2–3 times when vapor with air flows through and condenses in a vertical tube [17]. 2.3.4. Distribution of VR Fig. 6 shows the distribution of VR at different operating pressures. It has water vapor because the saturated moist air is deposited in the gas phase space of the reservoir. Air in the non-vacuum gravity heat pipe is not discharged during the start-up time, which causes an increment in operating pressure. VR is reduced as operating pressure rises when condensation is in a steady state. The higher the vapor mass flux is, the higher the operating pressure is, and the smaller the VR is. This phenomenon is caused by the

Fig. 6. Distribution of VR at different operating pressures.

condensation of a large amount of vapor. An increased amount of condensate flows into the reservoir and improves its water level, which reduces the space occupied by the saturated moist air. A high operating pressure decreases stagnant air volume, which improves the water level of the reservoir. By contrast, lower vapor mass flux results in lower operating pressure and larger VR. Therefore, the reservoir has an effective regulating function in the nonvacuum gravity heat pipe operation. It can contain an increased amount of air to alleviate the adverse effect of air on condensation heat transfer at a low vapor mass flux or heat load and store an increased amount of condensate to assure a sufficient condensation region at a high vapor mass flux or heat load. 3. Effects of air on vapor condensation length 3.1. Degradation factor method Previous studies [16,21] have developed the degradation factor correlations of condensation heat transfer, in which vapor with NCG flows through the condensation tube. In consideration of the unique feature of condensation with air in a non-vacuum gravity heat pipe, the degradation factors of the condensation section must be calculated to show a decreasing amount of the vapor condensation caused by the presence of air. Lee and Kim [21] proposed that the degradation factor, f , was defined as the ratio of the condensation heat transfer coefficients tested through the experiment to the condensation heat transfer coefficients calculated using the Nusselt analytic method.

f ¼ he =hNu ;

ð13Þ

In the present research, he is the local experimental condensation heat transfer coefficients and hNu is the local condensation heat transfer coefficients of the Nüsselt theory. Therefore, f is also called as the local degradation factor. Where hNu is calculated based on Nüsselt’s theory [28].

"

hNu

Fig. 5. Local air mole fraction along the tube length.

ghfg k3l q2l ¼ 4ll ðT s  T w Þz

#1=4 ;

ð14Þ

where T w is needed to solve hNu at any z location. In consideration of pure vapor flowing into the condensation tube, condensation heat transfer in the condensation tube is equal to convective heat trans-

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fer taken away from cooling water in the annular tube. Thus, the following equation can be obtained.

hc ðT w  T c Þ ¼ hNu ðT s  T w Þ

ð15Þ

Eq. (14) is substituted into Eq. (15) and rearranged into

" # 3 1=4 1 ghfg q2l kl ðT s  T w Þ þ ðT s  T c Þ ¼ ðT s  T w Þ3=4 : hc 4l l z Let a ¼ h1c

hgh

2 3 fg ql kl 4ll z

i1=4

ð16Þ

, h ¼ ðT s  T w Þ1=4 , and b ¼ T s  T c . Eq. (16)

may transform into

h4  ah3 þ b ¼ 0:

ð17Þ

hNu along the condensation tube length can be obtained by substituting h in Eq. (17) into Eq. (14). Thus, the average degradation factor can be calculated as

RL
f ¼ R 0 he  dz ¼ he : L h  dz hNu 0 Nu

ð18Þ

The experimental observation shows that vapor condenses while the saturated moist air is deposited at the condensation tube upstream. Thus, the condensation tube L is divided into two sections. The tube section used as the vapor condensation has L1 length, and the tube section used to store the saturated moist air column has L2 length. L; L1 and L2 are expressed as

L ¼ L1 þ L2 :

ð19Þ

The Lv tube length is used to condense the same amount of pure vapor. Given the same heat load, the following equation can be established.

he  L1  ðT w  T ax Þ ¼ hNu  Lv  ðT w  T s Þ:

ð20Þ

Therefore, L1 can be expressed with an average degradation factor.

Lv
T w  T ax ¼f  L1 Tw  Ts

ð21Þ

On the basis of the ideal gas state equation, L2 can be determined using

L2 p0 ¼ : L p

ð22Þ

Fig. 7. Distribution of the local degradation factor along the condensation tube length.

coefficients. Air exhibits large degradation during condensation heat transfer because vapor flows through the condensate surface into the saturated moist air column, which is formed by stagnant air via diffusion. This decreases the condensation heat transfer coefficients. Because the local degradation factor is higher and varies intensively at z < 0.14 m, the average degradation factor at z < 0.14 m is calculated. Fig. 8 shows the variation of the average degradation factor with the average air mole fraction. At a high vapor mass flux, the condensation section is filled with vapor, and the operating pressure evidently rises. The average air mole fraction is also reduced, which improves the average degradation factor. This finding indicates that air exhibits large degradation during vapor condensation at a small heat load. For example, the average air mole fraction is 40% at a vapor mass flux of 1.8 g/s, and the average degradation factor reaches 0.74. However, the condensation section is filled with minimal vapor at a low vapor mass flux, and the operating pressure is reduced. The average air mole fraction increases, and the average degradation factor decreases. These observations indicate that air exhibits large degradation during

The ratio of vapor condensation length with air to pure vapor condensation length can be determined by substituting Eqs. (21) and (22) into Eq. (19).

L p Tw  Ts ¼  Lv ðp  p0 Þ 
f T w  T ax

ð23Þ

3.2. Distribution of the degradation factor Fig. 7 shows the distribution of the local degradation factor along the condensation tube length. The highest value of the local degradation factor is reached at z = 0.14 m; it decreases sharply between 0.14 m and 0.16 m and more slowly along the condensation tube length after 0.16 m. This phenomenon indicates that the condensation heat transfer coefficients with air are nearly equal to the pure vapor condensation heat transfer coefficients. Air slightly affects condensation heat transfer because vapor that pours into the condensation tube from the inlet carries air into the condensation tube downstream via convective flowing. However, the local degradation factor is reduced at z > 0.14 m. This observation indicates that the condensation heat transfer coefficients with air are significantly less than the pure vapor condensation heat transfer

Fig. 8. Variation of the average degradation factor with the air mole fraction.

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vapor condensation at low heat load. For example, the average air mole fraction is 0.74 at a vapor mass flux of 1.8 g/s, and the average degradation factor is 0.26 at a vapor mass flux of 0.7 g/s. Previous studies [7,12] confirmed that the degradation of condensation due to NCGs can be aggravated at low heat loads. In the loop heat pipe, the reservoir is next to the wicked evaporator. The presence of NCG in the reservoir increases the temperature difference between the wick and the loop operating temperature. The increase of the operating temperature attributed to that NCGs breaks the original energy/pressure balance of the components in the loop heat pipe, which leads to the further change of heat and mass transfer and the redistribution of the working fluid in the loop. 3.3. Effect of air on vapor condensation length Fig. 9 shows the variation of L=Lv with increasing vapor mass flux. As vapor mass flux increases, L=Lv decreases, which indicates that vapor condensation length with air is nearly equal to pure vapor condensation length. At low heat load, vapor condensation length with air is larger than pure vapor condensation length because of the serious degradation of air during condensation heat transfer. For example, the average air mole fraction is 0.74 at a vapor mass flux of 0.7 g/s, and L=Lv is equal to 4.5. However, at high heat load, the degradation of air during condensation heat transfer weakens, and the vapor condensation length with air is nearly equal to pure vapor condensation length. In the present experiment, the average air mole fraction is 0.4 at a vapor mass flux of 1.8 g/s, and L=Lv is 1.32. This scenario occurs because the reservoir is mounted below the condensation tube, which effectively alleviates the adverse effect of air on condensation heat transfer. 4. Conclusion In this work, an experimental and theoretical investigation on the condensation section of a non-vacuum gravity heat pipe was conducted to determine the effects of air on condensation heat transfer. Heat transfer parameters, including the local condensation heat transfer coefficients, air mole fraction, operating pressure, and air storage capacity in the reservoir, were calculated according to the tested operating pressure and the condensation tube wall temperatures and the cooling water central temperatures. The effect of air on the condensation section of the non-vacuum gravity heat pipe was also analyzed. The following conclusions were obtained from the results.

Fig. 9. Variation of L=Lv with increasing vapor mass flux.

(1) A saturated moist air column is formed in the condensation tube downstream of the non-vacuum gravity heat pipe, where the local air mole fraction rises significantly and reaches above 95%. Therefore, the condensation tube wall temperature and the local condensation heat transfer coefficients decrease significantly. The decreasing amount is considerably less than the corresponding values tested under the condition in which vapor with air flows through the condensation tube. (2) The reservoir below the condensation tube regulates the condensation heat transfer of the non-vacuum gravity heat pipe. It can alleviate the adverse effect of air on condensation heat transfer and store excess condensate. (3) At the condensation tube downstream with a low heat load, the adverse effect of air during condensation heat transfer is serious, and the average degradation factor is 0.26. However, slight degradation of condensation heat transfer due to air occurs at the condensation tube upstream with a high heat load, and the average degradation factor is 0.7. Moreover, the local degradation factor reaches 0.76. At a vapor mass flux of 1.8 g/s and an operating pressure of 0.36 MPa, the vapor condensation length with air is 1.32 times as much as pure vapor condensation length. (4) In our future research, we will investigate the dynamic changes of the saturated moist air column in a mediumscale experimental device to provide technical support for the optimization of non-vacuum gravity heat pipe.

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