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Heat transfer characteristics and operation limit of pressurized hybrid heat pipe for small modular reactors
Accepted Manuscript Research Paper Heat Transfer Characteristics and Operation Limit of Pressurized Hybrid Heat Pipe for Small Modular Reactors Kyung Mo Kim, In Cheol Bang PII: DOI: Reference:
S1359-4311(16)32341-9 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.077 ATE 9279
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
10 July 2016 6 October 2016 10 October 2016
Please cite this article as: K. Mo Kim, I. Cheol Bang, Heat Transfer Characteristics and Operation Limit of Pressurized Hybrid Heat Pipe for Small Modular Reactors, Applied Thermal Engineering (2016), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2016.10.077
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Heat Transfer Characteristics and Operation Limit of Pressurized Hybrid Heat Pipe for Small Modular Reactors Kyung Mo Kim, In Cheol Bang* Department of Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea
Abstract
In this paper, a hybrid heat pipe is proposed for use in advanced nuclear power plants as a passive heat transfer device. The hybrid heat pipe combines the functions of a heat pipe and a control rod to simultaneously remove the decay heat generated from the core and shutdown the reactor under accident conditions. Thus, the hybrid heat pipe contains a neutron absorber in the evaporator section, which corresponds to the core of the reactor pressure vessel. The presence of the neutron absorber material leads to differences in the heated diameter and hydraulic diameter of the heat pipe. The cross-sectional areas of the vapor paths through the evaporator, adiabatic, and condenser sections are also different. The hybrid heat pipe must operate in a high-temperature, high-pressure environment to remove the decay heat. In other words, the operating pressure must be higher than those of the commercially available thermosyphons. Hence, the thermal performances, including operation limit of the hybrid heat pipe, were experimentally studied in the operating pressure range of 0.2–20 bar. The operating pressure of the hybrid heat pipe was controlled by charging the non-condensable gas which is unused method to achieve the high saturation pressure in conventional thermosyphons. The effect of operating pressure on evaporation heat transfer was negligible, while condensation heat transfer was affected by the amount of non-condensable gas in the test section. The operation limit of the hybrid heat pipe increased with the operating pressure. Maximum heat removal capacity of the hybrid heat pipe was up to 6 kW which is meaningful value as a passive decay heat removal device in the nuclear power plants. Based on the experimentally measured maximum heat removal capacities, models predicting the operation limit (flooding limit) of the hybrid heat pipe were developed.
*
Corresponding author : Tel.:+82-52-217-2915, Fax:+82-52-217-3008 E-mail: [email protected] (In Cheol Bang) 1
Nomenclature
A
area
[m2]
Bo
bond number
[-]
C
correlation coefficient
[-]
D
diameter
[m]
g
gravity
[m/s2]
h
latent heat
[kJ/kg]
K
Kutateladze number
[-]
L
length
[m]
m
correlation coefficient
[-]
Q
heat, power
[W]
q″
heat flux
[kW/m2]
r
radius
[m]
R
thermal resistance
[°C/W]
T
temperature
[°C]
Greek symbols ρ
density
[kg/m3]
σ
surface tension
[N/m]
Subscript c
condenser
cs
cross-sectional
e
evaporator
h
heated
k
Kutateladze
l
liquid
lv
liquid to vapor
max
maximum
sat
saturation
v
vapor
w
Wallis
2
Keywords
Hybrid heat pipe; Operation limit; Annular thermosyphon; Heat pipe; Small modular reactor; Passive safety system
1. Introduction
Most safety systems in commercial nuclear power plants focus on feeding additional coolant to the reactor core by using pumps and by employing the pressure difference between the coolant storage tank and reactor pressure vessel. However, the Fukushima and Three Mile Island (TMI) nuclear power plant accidents showed the limitation of the existing safety systems. Therefore, passive safety systems such as passive auxiliary feedwater system (PAFS), passive containment cooling system (PCCS), and hybrid safety injection tank for high-pressure injection via the pressure balance line are being developed to cope with the extended station blackout (SBO) accident. However, passive safety systems have complex circuits, including many valves, and hence, single failure and common cause failures are possible. Therefore, a new conceptual passive decay heat removal system based on a simple operating principle is required to solve the aforementioned problems in safety systems. A passive decay heat removal device that combines the functions of the control rods currently used in nuclear reactors and the heat pipes used in thermal controlling systems such as CPU cooling systems, heat exchangers, and solar collectors was proposed [1]. Thermosyphon heat pipes transfer heat from high-temperature section to low-temperature section through the evaporation and condensation of the working fluid at interfaces, and through the convection of the working fluid by gravitational force [2]. Thus, a combination of a heat pipe and a control rod, that is, a hybrid heat pipe can transfer decay heat from the reactor core to the heat sink in the event of the shutdown of a reactor under accident conditions [3]. Many types of small modular reactors (SMRs) are under development worldwide to achieve high levels of plant safety and reliability. The main advantages of SMRs are that they are economic and safer and allow long-term operation. Most types of SMRs are integral reactors, which depend on passive safety systems; therefore, the loss of coolant accident, which is a representative postulated accident in commercial nuclear reactors, can be prevented. However, there are high uncertainties in terms of operation and capacity for passive safety systems because these systems depend on natural driving forces. To mitigate and solve the problems related to the uncertainty of the passive safety systems, diversity of the safety systems must be secured. The 3
application of hybrid heat pipes to SMRs can provide an additional heat transfer media between the heat sink and active core. Thus, providing an additional way for decay heat removal through the application of hybrid heat pipe can enhance SMR safety. Fig. 1 is the schematic diagram of NuScale SMR with a hybrid heat pipe. In the hybrid heat pipe-controlled SMR, the decay heat generated from the fuel rods will be transferred to the reactor coolant, reactor coolant to evaporator section of hybrid heat pipes, adiabatic to condenser sections of the hybrid heat pipes, and the liquid pool located outside the reactor pressure vessel. The reactor pressure vessel is insulated to minimize the heat loss through structures. It can be assumed that the total decay heat is transferred to the reactor coolant and hybrid heat pipe. The liquid temperature at the pool which acts as ultimate heat sink of the hybrid heat pipes will be increased as the decay heat removal proceeds. The stored heat of the liquid can be transferred to the environment (atmosphere inside the containment). However, the large liquid inventory of the pool is designed to secure the integrity of the reactor pressure vessel in any accidents. Therefore, the temperature increase at the heat sink will be low or negligible. The additional heat sink can be installed to prepare for the case of liquid temperature increase by connecting the liquid pool outside the reactor pressure vessel to the air cooling tower outside the containment.
Fig. 1. In-house design of hybrid heat pipe as Passive IN-core Cooling system (PINCs) in NuScale 4
For practical application of the hybrid heat pipe to SMRs, significant level of heat removal capacity must be guaranteed and modeled. Therefore, the thermal performance of the hybrid heat pipe, including its operation limits, was experimentally analyzed at high pressure. The high operating pressures were achieved through the charge of nitrogen gas to the test section as studied in previous studies [4-7], while backpressure regulator was used to maintain the constant operating pressures. The maximum heat transfer capacity of heat pipes such as concentric thermosyphons and annular thermosyphons can be predicted using known correlations and physical models. However, a neutron absorber, which is considered an adiabatic medium owing to its low thermal conductivity, introduces a difference between the wetted perimeter and heated perimeter of the hybrid heat pipe. In previous studies [8-14], the thermal performance of thermosyphons was examined through experiments and models were developed for the test section with the heated diameter equal to the hydraulic diameter. The existing models have not been validated in the highpressure range with water as the working fluid. Thus, the operating limit and heat transfer characteristics of hybrid heat pipe in high-pressure range were measured experimentally. The existing correlations for the operation limit which are based on the flooding phenomenon were modified for the modeling the operation limit of hybrid heat pipe.
2. Operation Limit (Flooding Limit) Models
The operation limits of closed two-phase thermosyphons are the sonic limit, boiling limit, flooding limit (entrainment limit), and viscous limit. The main phenomenon factor leading to the operation limit of a thermosyphon is the flooding limit. Hence, flooding phenomena were experimentally analyzed with various working fluids. Table 1 summarizes the existing correlations for the critical heat flux of a thermosyphon and presents the pros and cons of each correlation.
Table 1 A summary on correlations about critical heat flux of thermosyphon. Researchers
Notes Pros
1) Shows high prediction accuracy in relatively small diameter with modification of coefficients.
Cons
1) Effect of surface tension was not considered. 2) Prediction ability is reduced as the cross-sectional area of the flow path increases
Wallis [8]
5
Kutateladze [9]
Pros
1) Relatively high prediction ability in the flow path with large diameter
Cons
1) Diameter effect was not considered. 2) Prediction ability is reduced as the cross-sectional area of the flow path decreases.
Eqn.
QKutateladze = Ck2 hlv Aρ v1/ 2 ⎣⎡ gσ ( ρl − ρ v )⎦⎤
Cons Tien and Chung [10]
1/ 4
Ck = 3.2 tanh ( 0.5 Bo1/ 4 )
(4)
⎡ g ( ρl − ρ v ) ⎤ Bo = D ⎢ ⎥ σ ⎣ ⎦
1/ 4 ⎡ ⎛ ρv ⎞ ⎤ ⎢1 + m ⎜ ⎟ ⎥ ⎢⎣ ⎝ ρl ⎠ ⎥⎦
−2
(2)
(5)
1/ 4
⎡⎣ ρ v−1/ 4 + ρ l−1/ 4 ⎤⎦
−2
(3)
1/ 2
Pros
1) The most widely used correlation. 2) High prediction abilities for various working fluids and test conditions.
Cons
1) Lack of validation for the annular vapor-path thermosyphons. ⎛ D ⎞ ⎛ ρl ⎞ = 0.64 ρ v H lv A ⎜ ⎟⎜ ⎟ ⎝ 4 L ⎠ ⎝ ρv ⎠
0.13
⎡⎣σ g ( ρl − ρ v ) ρ v2 ⎤⎦
1/ 4
(6)
Eqn.
QImura
Pros
1) Enhanced prediction accuracy for the test sections working with water compared to Tien and Chung correlation. 2) Correlation constant (R) can be modified according to working fluids.
Cons
1) Lack of validation for the annular vapor-path thermosyphons. QFaghri = Khlv Av ⎡⎣ gσ ( ρl − ρ v )⎤⎦
Eqn.
ESDU [13]
(1)
1) Combined the effects of surface tension and diameter of the test section. 2) High predictability for various working fluids. 1) Limited predictability for the thermosyphons working with water. 2) Lack of validation for the annular vapor-path thermosyphons. QTien and Chung = Ck2 hlv Av ⎣⎡ gσ ( ρ l − ρ v )⎦⎤
Eqn.
Faghri et al. [12]
−2
QWallis = Cw2 hlv Aρv1/ 2 ⎣⎡ gD ( ρl − ρv )⎦⎤
Pros
Imura et al. [11]
1/ 4 ⎡ ⎛ ρv ⎞ ⎤ ⎢1 + m ⎜ ⎟ ⎥ ⎢⎣ ⎝ ρl ⎠ ⎥⎦
Eqn.
1/ 2
Pros
⎛ρ ⎞ K =⎜ l ⎟ ⎝ ρv ⎠
1/ 4
⎡⎣ ρ v−1/ 4 + ρl−1/ 4 ⎤⎦
−2
(7)
0.14
tanh 2 Bo1/ 4 = R tanh 2 Bo1/ 4
(8)
1) The most widely used correlation with validation in wide range of operating conditions. 6
Monde et al. [14]
Cons
1) Cannot used for the annular vapor-path thermosyphon having difference between hydraulic diameter and heated diameter.
Eqn.
QESDU = f1 f 2 f 3 Acs hlv ρ v1/ 2 ⎣⎡σ g ( ρ l − ρ v )⎦⎤
Pros
1) It was developed for the annular thermosyphons.
Cons
1) Validation was conducted for the open thermosyphons.
Eqn.
QMonde
1/ 4
(9)
⎡ σ g ( ρl − ρ v ) ⎤ 0.16 = ρ v H fg A ⎢ ⎥ ρ v2 1 + 0.075 ( L Dh ) ⎣ ⎦
1/ 4
(10)
3. Experiment
3.1. Test section
A hybrid heat pipe was prepared as shown in Fig. 2. A 1-m-long stainless steel 316L test section with 25.4 mm outer diameter and 22 mm inner diameter was used as the test section. The test section was charged with 90 mL deionized water, and a B4C pellet representing a neutron absorber material (outer diameter: 17.7 mm; length: 285 mm) was installed at the center of the heat pipe [15].
Fig. 2. Composition of hybrid heat pipe.
7
3.2. Experimental Setup and Procedures
Fig. 3(a) shows the heat pipe test facility. The test facility comprises a working fluid tank, a test section, a water jacket to condense the evaporated working fluid, a pump that circulates coolant from the water storage tank to the water jacket, a vacuum pump, and two copper electrodes at the top and bottom of the evaporator section that are connected to a power supply and that heat the test section by passing current on the evaporator section. The outer walls of the evaporator, adiabatic, and condenser (water jacket) sections were wrapped by glass-fiber insulator with 50 mm thickness to minimize the heat exchange between test section and environment.
(a)
(b) Fig. 3. Schematic diagram of hybrid heat pipe test facility: (a) experimental apparatus, and (b) details of thermocouple locations in test section. 8
Twelve K-type thermocouples (TCs) were installed on the evaporator and adiabatic sections of the test section (six on the evaporator and six on the adiabatic section); four T-type TCs were installed on the wall of the condenser section as shown in Fig. 3(b) to record the temperature distribution under a given condition. Additional two T-type TCs measured the water temperatures at the inlet and outlet of the water jacket to measure the efficiency of the test section..
Table 2 Experimental conditions. Length ratio [%]
28.5 : 21.5 : 50.0
Heat load [W]
200 – 6000
Initial pressure [bar]
0.2, 3.0, 5.0, 10.0, 15.0, 20.0
Fill ratio [%]
100 % (90 ml)
Table 2 presents the experimental conditions. The experimental procedure is as follows: (1) remove the air in the test section by vacuum pump; (2) fill the test section with the working fluid; (3) pressurize the test section by nitrogen injection to set the pressure; (4) set the target pressure of the backpressure regulator; (5) load heat in the evaporator section; (6) circulate the coolant through the water jacket; (7) and record the temperature evolutions and pressure variations.
3.3. Uncertainty Analysis
The uncertainties in the parameter measurements were analyzed. Table 3 presents the measurement errors in the instruments.
Table 3 Measurement uncertainties. Parameters
Instruments
Uncertainties
Temperature
Thermocouple
± 0.1 oC
Pressure
Pressure gauge
± 0.1 kPa
9
Water flow rate
Turbine flowmeter
± 0.05 lpm
Voltage
Voltmeter
± 0.02 V
Current
Ammeter
±4A
The uncertainties of the parameters were calculated by the Kline and McClintock method [16]. The measurement uncertainties in the heat flux, heat transfer coefficient, and thermal resistance were calculated as follows:
⎛ ∂ϕ ⎞ = × Δxi ⎟ ⎜ ∑ ϕ ϕ i =1 ⎝ ∂xi ⎠
Δϕ
1
n
2
(11)
where ϕ is the derived parameter, xi represents the measured variables, and Δxi represents the error of the measured variables. The tolerances in the length and diameter of the test section were 5 mm and 1 mm, respectively. The calculated maximum uncertainty in the heat flux is 6.1%. The maximum uncertainties in the heat transfer coefficient and thermal resistance were estimated as 4.3% and 6.4%, respectively. As the heat flux increases, the voltage and current increases. The instrument uncertainties for voltage, current, length, and diameter are constant. Therefore, uncertainties for calculated heat fluxes decrease as the heat flux increases because the ratio between calculated heat flux and instrument measurement become smaller as the heat flux increases. The maximum and minimum uncertainties in the heat flux are appeared at the lowest and highest heat flux, respectively, as shown in Fig. 5. Temperature differences between average wall temperatures at each section and saturation temperatures increase as the heat flux increases. The instrument uncertainty of thermocouple is constant. Hence, the uncertainties for heat transfer coefficients and thermal resistances decrease as the heat transfer coefficient and thermal resistance increase.
10
Fig. 4. Uncertainties of calculated heat fluxes according to heat fluxes and operating pressures.
4. Results and Discussion
4.1. Wall Temperature Distributions
Wall temperatures of the test section were recorded in the axial direction according to time. Based on the wall temperature evolution data, the wall temperature distributions at steady states were expressed as shown in Fig. 5. The temperature in the adiabatic section corresponds to the saturation temperature of the operating pressure [17, 18]. Therefore, the wall temperatures in this section were maintained constant throughout the entire range of heat loads. The temperature differences between the evaporator and adiabatic sections, which can be regarded as wall superheat increased as heat load increased within 5–30°C. The nitrogen gas which was charged to the test sections for the pressurization takes an important role in the condensation heat transfer. The wall temperature in the condenser section increased as the heat load increased because of the volume expansion of the working fluid in the high heat load region, and some of the nitrogen was removed by backpressure regulator to maintain constant operating pressure. Several previous studies [19-23] on the variable conductance heat pipe which uses the noncondensable gas for the maintenance of thermal bath temperature at evaporator section reported that the restriction of the condensation heat transfer due to non-condensable gas zone at the condenser section. The nitrogen gas blocks the reach of steam moved along evaporator and adiabatic section, and impedes the condensation of the steam at the inner wall of the test section. The phenomenon can 11
be confirmed by observing the increase of condenser wall temperature. The location of steam-gas mixing zone (interface between steam and non-condensable gas) can also be observed by locations of increasing condenser wall temperature because the volume occupied by non-condensable gas will show the low wall temperature and relatively high temperature will be observed in condensation occurring volume. As the amount of nitrogen gas reduced, the amount of working fluid reaching the condenser section increased, as shown in Fig. 6. The volume fraction of the nitrogen increased with the operating pressure. For identical heat loads, the wall temperatures in the condenser section of the test section operating at a high pressure is lower than those of the section at low operating pressure. That means height of the steam-gas mixing zone for high operating pressure (distance from bottom of the evaporator section) tends to be lower than low operating pressure at identical heat loads. In the evaporator section, the boiling in liquid pool is the main heat transfer mechanism. The noncondensable gas determines the saturation pressure. Saturation temperature increases as the operating pressure increases, sequentially; evaporator wall temperature increases as the operating pressure increases. Details on variations evaporator wall temperatures according to heat loads will be discussed in Section 4.2 Evaporator heat transfer.
(a) 0.2 bar
12
(b) 3.0 bar
(c) 5.0 bar
(d) 10.0 bar
13
(e) 15.0 bar
(f) 20.0 bar Fig. 5. Inner wall temperature distributions of hybrid heat pipe according to operating pressures
14
(a) Low heat load (b) Intermediate heat load (c) High heat load Fig. 6. Distribution of the fluid at the test section according to heat loads
4.2. Evaporation Heat Transfer
The heat transfer characteristics (evaporation heat transfer coefficient and evaporator thermal resistance) in the evaporator section were calculated using the following equations based on the measured wall temperature distributions [24]:
he =
qe′′
(T − T ) e
Re =
(12)
sat
(T − T ) e
sat
Qe
15
(13)
Fig. 7 shows the evaporation heat transfer coefficients and evaporator thermal resistances according to operating pressures and heat loads. The heat transfer in the test section operating at subatmospheric pressure was worse than operation pressures greater the atmosphere pressure owing to different boiling modes.
(a)
(b)
Fig. 7. Heat transfer characteristics at evaporator section of the test sections according to operating pressures (a) Evaporation heat transfer coefficients, (b) Evaporator thermal resistances. 16
At sub-atmospheric pressure (0.2 bar), the vapor–liquid density ratio is very large. Thus, the large-sized bubble generated in the evaporator section covers the inner wall of the test section forming liquid plugs. These plugs reach the condenser section and are destroyed at the top of the condenser section. The destroyed liquid plugs fall into the evaporator section in the form of liquid films. The heat transfer achieved by this event sequence is defined as geyser boiling [29] and shown in Fig. 9. However, the vapor–liquid density ratios in the test section operating at pressures greater than the atmospheric pressure (3–20 bar) are relatively smaller than those at sub-atmospheric pressure; hence, liquid plugs and liquid films do not easily form from the vapor as shown in Fig. 8. Hence, for evaporator section of the test sections that operating under high pressure, the heat transfer mechanism is convective pool boiling [11]. When the pressure was 3–20 bar, the effect of the vapor–liquid density ratio on heat transfer characteristics in the evaporator section was negligible. The fill ratio (that is, the ratio of the volume of the working fluid and that of evaporator section except the B4C pellet) of the working fluid was 166%. Although the bubble sizes and volumes occupied by the vapor differ with the saturation pressure, the main heat transfer medium at the wall of evaporator section is the liquid pool, which occupies most of the volume in evaporator section owing to the high fill ratio. Thus, the evaporation heat transfer coefficients are similar at high operating pressures.
17
Fig. 8. Geyser boiling in the hybrid heat pipe.
4.3. Condensation Heat Transfer
Heat removal rate through the water jacket was calculated based on the variation of water temperature (Two T-type TCs were installed on the inlet and outlet of water jacket) with flow rate data recorded by turbine flowmeter: p (Tout − Tin ) Qc = mc
(14)
The condensation heat transfer characteristics were described as mentioned by heat transfer characteristics of evaporator section:
hc =
(T
qc′′
sat
Rc =
(T
sat
− Tc ) − Tc )
Qc 18
(15)
(16)
Nitrogen is the most important factor that determines the condensation heat transfer of the pressurized heat pipes because the nitrogen in the condenser section impedes the upward flow of the working fluid and the heat transfer between the wall of the condenser section and working fluid [26]. As the heat load increases, the fraction of non-condensable gas decreases owing to the leakage of nitrogen gas to maintain the constant operating pressure. Thus, the condensation heat transfer coefficient increases as the heat load increases, as shown in Fig. 9.
(a)
(b) 19
Fig. 9. Heat transfer characteristics at condenser section of the test sections according to operating pressures (a) Condensation heat transfer coefficients, (b) Condenser thermal resistances.
The initial amounts of non-condensable gas are different according to operating pressure. The amount of non-condensable gas is remarkably low in case of the test section operating at 0.2 bar, while in the case of high-pressure operation, the test sections are charged with nitrogen. Hence, a noticeable difference was observed in the condensation heat transfer under sub-atmospheric pressure and normal pressure conditions. The charged amount of nitrogen gas increases with the operating pressure. Hence, increase of operating pressure induced a reduction in the condensation heat transfer coefficient.
4.4. Thermal Efficiencies of Heat Pipes
Thermal efficiencies of the hybrid heat pipe were checked by comparing the loaded heat on the evaporator section and removed heat through the condenser section as follows: [27, 28]
η=
p (Tout − Tin ) Qc mc = Qe Qe
(17)
If the thermal efficiency of the heat pipe is low, the rest amount of heat which was not transported to the condenser section will be used to expand the volume of working fluid resulting in the increase of system pressure in closed system. For the test sections used in this study, the system pressure was maintained constantly with backpressure regulator. As the thermal efficiency decreases, volume expansion of the working fluid will be enhanced, sequentially; the removal of nitrogen gas will be increased. Fig. 10 shows the tendency of thermal efficiency according to heat loads and operating pressures. The thermal efficiency was inversely proportional to the operating pressure as observed in the condensation heat transfer coefficient. The reduction of efficiency by the increase of operating pressure was attributed to the active two-phase heat transfer length (nitrogen gas prohibit the reach of steam to condenser section impeding the condensation, therefore; the active two-phase heat transfer length means the length of phase change occurs). Heat removal rate determines the amount of condensed liquid, liquid flow rate from condenser section to evaporator section, relative velocity between vapor and liquid in terms of operation limit. Low thermal efficiency result in the low amount of condensed liquid, low liquid flow rate in gravitational direction, eventually; low 20
operation limit. However, the effect of thermal efficiency is not considered in the existing models on critical heat flux of the thermosyphons because the efficiency affects system pressure and the system pressure effect is reflected with density ratio of vapor-liquid in the models.
Fig. 10. Thermal efficiencies of the hybrid heat pipe under various operating pressures and heat loads.
4.5. Operating Limits of Heat Pipes
The heat load, which induces a sudden increase in wall temperature, was chosen as the operating limit of the hybrid heat pipe. Fig. 11 shows the comparison of experimentally measured operation limits of hybrid heat pipes with the predicted values reflecting the reduced cross-sectional area of the vapor path. The maximum heat removal capacity of the hybrid heat pipe increased with the operation pressure (4200–5980 W). The values are 4–6 times those of hybrid heat pipes operating at 0.2 bar. The experimentally measured operating limits showed large deviations from the developed models [10-13] with regard to the critical heat flux of thermosyphon heat pipes. The correlations of Wallis and Kutateladze for the concentric flow channel were developed through water–gas countercurrent flow experiments. However, the hybrid heat pipe was designed as an annular vapor path heat pipe. Monde et al. considered the situation in which the entire open thermosyphon was occupied by the working fluid to develop their correlation. Therefore, there are limitations in applying the correlation to predict the operation limit of closed hybrid heat pipes partially filled with working fluid. 21
Tien and Chung, and Faghri et al. also proposed the correlations for the flooding limit that can be applied to annular vapor path thermosyphons. However, in hybrid heat pipes, the hydraulic diameter and heated diameter may differ because liquid flow near the B4C pellet might be less than that near the heated wall. Wallis correlation [8] (with assumption of Cw and m are unity) showed the best agreement with experimental results compared to other correlations; while the slope of the variation in operation limit was differed from the measured limits. The predictability of Wallis model will be reduced in the saturation pressure higher than 20.0 bar. The possibility of the decrease in predictability can be solved by correcting the correlation constants according to operating pressures. Correlation developed by Tien and Chung [10] predicted well in low pressures (< 5 bar). The difference between prediction and experimental results were magnified as the operating pressure increases. The prediction ability of the correlation can be enhanced with suggestion of best estimate correlation coefficients according to operating pressures. For other correlations, the main reason of the deviations of the prediction from measured values is shown in Fig. 12. There are upward (evaporator section) and downward liquid flows (adiabatic and condenser sections) in the thermosyphon. Bubbles generated in the evaporator section have upward flow due to buoyancy force. The bubble flow drags the liquid in the pool at the evaporator section. For the hybrid heat pipe, the higher shear force will be applied to the upward liquid flow at the surface of B4C pellet as compared to conventional annular thermosyphons. The bubbles are generated at the wall of inner structure in the conventional annular vapor-path thermosyphon because it is additional heat transfer medium (heat source and sink). On the other hand, the B4C pellet is adiabatic medium which does not participate in phase change. Hence, the higher shear force on B4C pellet to upward liquid flow reduces the upward liquid velocity and vapor velocity in the evaporator section, resulting in lower relative velocity between the downward liquid and upward vapor flows at the inner wall of cladding as compared to that in the cases of previously studied annular vapor-path heat pipes. The proportionality of the operation limit on operating pressure causes the deviations between predicted and experimental results. Correlations of Imura et al. [11] and ESDU [13] analyzed the similar proportionality between operation limit and pressures with the measured limits. Thus, the correlations proposed by Imura et al. [11] and ESDU [13] were selected as the models predicting the maximum heat removal capacity of the hybrid heat pipe with additional consideration of the design of the hybrid heat pipe.
22
Fig. 11. Comparison of operation limits predicted by models and experimental data
(a)
(b)
Fig. 12. Upward liquid velocities according to types of thermosyphons: (a) Hybrid heat pipe, (b) Annular vapor-path thermosyphon
QModified Imura
⎛ A ⎞⎛ ρ ⎞ = ρ v H lv Ah ⎜ cs ,e ⎟⎜ l ⎟ ⎝ Ah ⎠⎝ ρ v ⎠
0.13 4
σ g ( ρl − ρ v ) ρ v2
QModified ESDU = f1 f 2 f 3 f 4 Acs hlv ρ v1/ 2 ⎣⎡σ g ( ρ l − ρ v )⎦⎤
23
1/ 4
(18) (19)
f 4 = ( Ah Acs ,e )
0.1
(18)
The difference between the heated and hydraulic diameters, which is caused by the presence of the adiabatic medium—B4C pellet—in the evaporator section, induced the deviation of experimental results from existing correlations. The cross-sectional areas of the vapor paths in the evaporator, adiabatic, and condenser sections are also different because the B4C pellet is installed only in the evaporator section. Thus, Imura correlation was modified to consider the difference in vapor path area and heating area by revising the constant 0.64 to 1.0. In the ESDU correlation, the crosssectional area of the vapor path was used, but the effect of the heated area was not considered. Hence, an additional factor, f4 related to the difference between the cross-sectional area of the vapor path and heated area is used. The suggested models showed good agreement with the experimental results within ±15% deviations, as shown in Fig. 13.
Fig. 13. Comparison of operation limits predicted by the revised models and experimental data
4.6. Prospect of Hybrid Heat Pipe on SMR
The full power of the NuScale SMR is 150 MWth to generate 50 MWe. The NuScale reactor uses the same fuel as that used in standard light water reactors with height reduction of 2 m. There are 37 fuel assemblies installed (a fuel assembly is 17 × 17, enriched up to 4.95%). If four guide tubes 24
and control rods are used in a single fuel assembly, the total number of control rods is 148 ea. After 2 h from the initiation of an accident, the total decay heat generated from the core will be 1.5 MW corresponding to 1% of the full power (from typical decay heat curve). Thus, the required heat removal capacity of a single hybrid heat pipe to remove the total decay heat will be 10 kW. The measured maximum heat removal capacity of the hybrid heat pipe is approximately 6 kW at an operating pressure of 20 bar. The hybrid heat pipe can remove 60% of the total decay heat if all of the control rods are replaced with hybrid heat pipes. To use the liquid pool outside the reactor pressure vessel as a heat sink, the hybrid heat pipe that will be applied to the SMR should be longer than 20 m. Hence, the effect of length of the hybrid pipe on the operation limit and heat transfer characteristics must be studied further for accurate modeling. To further improve the decay heat removal rate by hybrid heat pipes, the following work will be conducted. (1) Measurement of the operation limit of hybrid heat pipes operating above pressures of 20 bar (2) Surface modification, such as deposition of porous media, to enhance the maximum heat removal capacity of hybrid heat pipes (3) Observation of the effect of clearance on the heat transfer characteristics and operation limit (Reduction of B4C pellet size through enrichment of 10B isotope, which is the main neutron absorbing element in the B4C pellet, or through use of other neutron absorbing isotopes)
5. Conclusions
Hybrid heat pipe was proposed as a passive decay heat removal device for SMRs to improve the safety system of reactors. These pipes have unique geometry owing to the presence of neutron absorber material inside them, and they must have a high maximum heat removal capacity to remove the significant decay heat from the core. Thus, the heat transfer characteristics and operation limits of hybrid heat pipes were experimentally measured at high pressures, which were not considered in previous researches. The following results were obtained: (1) The effect of the vapor–liquid density ratio on the evaporation heat transfer was negligible at pressures above the atmospheric pressure. (2) The differences in the evaporation heat transfer between test sections operating at subatmospheric pressure and normal pressures result from the different boiling mechanisms (geyser boiling and convective pool boiling). (3) With an increase in the operation pressure, the condensation heat transfer decreases because the amount of non-condensable gas injected into the test section for pressurization 25
increases, impeding the heat transfer between the wall and working fluid in the condenser section. (4) The operation limit increases with operating pressure with the maximum heat removal capacity of 5980 W (at 20 bar). (5) The existing correlations for predicting the operation limit of thermosyphons showed deviations from experimental results owing to presence of the neutron absorber material and high-operating-pressure environment. (6) New correlations to predict the critical heat flux of hybrid heat pipes were developed by modifying the correlations of Imura et al. and ESDU based on the experimental data.
Acknowledgement
This work was supported by the Nuclear Energy Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning. (NRF22A20153413555, 2013M2B2B1075734, 2014M2A8A4021514)
26
REFERENCES
[1] Jeong YS, Kim KM, Kim IG, Bang IC, Hybrid heat pipe based passive in-core cooling system for advanced nuclear power plant, Appl. Thermal Eng 2015;90:609-618 [2] Reay DA, Kew PA, Heat Pipes (fifth edition), Butterworth-Heinemann, Oxford 2006. [3] Kim KM, Bang IC, Comparison of flooding limit and thermal performance of annular and concentric thermosyphons at different fill ratios, Appl. Thermal Eng 2016;99:179-188. [4] Joung W, Gam KS, Kim YG, Yang I, Hydraulic operating temperature control of a loop heat pipe, Int. J. Heat Mass Transfer 2015;86:796-808. [5] Chen L, Deng BL, Zhang XR, Experimental investigation of CO2 thermosyphon flow and heat transfer in the supercritical region, Int. J. Heat Mass Transfer 2013;64:202-211. [6] Huang J, Wang L, Shen J, Liu C, Effect of non-condensable gas on the start-up of a gravity loop thermosyphon with gas-liquid separator, Exp. Ther. Fluid. Sci 2016;72:161-170. [7] Mantelli MBH, Angelo WB, Borges T, Performance of naphthalene thermosyphons with noncondensable gases-Theoretical study and comparison with data, Int. J. Heat Mass Transfer 2010;53:3414-3428. [8] Wallis G, One-dimensional two-phase flow, McGraw-Hill, New York 1969. [9] Kutateladze SS, Elements of hydrodynamics of gas-liquid systems, Fluid Mechanics-Soviet Research 1972;1:29-50 [10] Tien CL, Chung KS, Entrainment limits in heat pipes, Proc. 3rd Int. Heat Pipe Conf 1978:3640 [11] Imura H, Sasaguchi K, Kozai H, Critical heat flux in a closed two-phase thermosyphon, Int. J. Heat Mass Transfer 1983;26:1181-1188 [12] Faghri A, Chen MM, Morgan M, Heat transfer characteristics in two-phase closed conventional and concentric annular thermosyphons, J. Heat Transfer 1989;111:611-618. [13] Engineering Science Data Unit, heat pipes-Performance of two-phase closed thermosyphons, Data item No. 81038, ESDU, London, 1981. [14] Monde M, Mitsutake Y, Enhancement of CHF in open thermosyphon with heated bottom chamber, Int. J. Heat Mass Transfer 2000;43;3341-3346 [15] Kim KM, Kim IG, Jeong YS, Bang IC, Heat removal capacity of heat pipe design for in-core passive decay heat removal system, Proceedings of NURETH-16, August 30-September 4, 2015 – Chicago (USA).
27
[16] Kline SJ and McClintock FA, Describing uncertainties in single sample experiments, Mechanical Eng 1953;75:3-8. [17] Kole M, Dey TK, Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids, Appl. Therm. Eng. 2013;50:763-770. [18] Solomon AB, Ramachandran K, Pillai BC, Thermal performance of a heat pipe with nanoparticles coated wick, Appl. Therm. Eng 2012;36 106-112. [19] Sauciuc I, Akbarzadeh A, Johnson P, Temperature control using variable conductance closed two-phase heat pipe, Int. Comm. Heat Mass Transfer 1996; 26: 427-433. [20] Peterson PF, Tien CL, Gas-concentration measurements and analysis for gas-loaded thermosyphons, J. Heat Transfer 1988;110:743-747. [21] Watanabe K, Kimura A, Kawabata K, Yanagida T, Yamauchi M, Development of a variableconductance heat-pipe for a sodium-sulfur (NAS) battery, Furukawa Review 2001;20:71-76. [22] Ungureanu I, Barbu V, Variable conductance heat pipe model for temperature control of processes, 5th Int. Conf. Computational Mechanics and Virtual Engineering, October 24-25, 2013 – Brasov (Romania). [23] Ishizuka M, Sasaki T, Miyazaki Y, The development of titanium-ammonia variable conductance heat pipe, The 6th Int. Symp. Transport Phenomena in Thermal Engineering, May 913, 1993 – Seoul (Korea) [24] Mozumder AK, Akon AF, Chowdhury MSH, Banik SC, Performance of heat pipe for different working fluids and fill ratios, J. Mecha. Eng 2010;41:96-102. [25] Faghri A, Heat pipe science and technology, Taylor and Francis, Washington 1995. [26] Hijikata K, Chen SJ, Tien CL, Non-condensable gas effect on condensation in a two-phase closed thermosyphon, Int. J. Heat Mass Transfer 1984;27:1319-1325 [27] Amiri A, Sadri R, Shanbedi M, Ahmadi G, Chew BT, Kazi SN, Dahari M, Performance dependence of thermosyphon on the functionalization approaches: An experimental study on thermos-physical properties of graphene nanoplatelet-based water nanofluids, Ener. Conv. Manag 2015;92:322-330 [28] Shanbedi M, Heris SZ, Baniadam M, Amiri A, Maghrebi M, Investigation of heat-transfer characterization of EDA-MWCNT/DI-water nanofluid in a two-phase closed thermosyphon, Ind. Eng. Chem. Res 2012;51:1423-1428
28
Table Captions Table 1 A summary on correlations about critical heat flux of thermosyphon. Table 2. Experimental conditions. Table 3. Instrument uncertainties.
29
Figure Captions Fig. 1 In-house design of hybrid heat pipe as Passive IN-core Cooling system (PINCs) in NuScale. Fig. 2. Composition of hybrid heat pipe. Fig. 3. Schematic diagram of hybrid heat pipe test facility: (a) experimental apparatus, and (b) details of thermocouple locations in test section. Fig. 4. Uncertainties of calculated heat fluxes according to heat fluxes and operating pressures. Fig. 5. Inner wall temperature distributions of hybrid heat pipe according to operating pressures. Fig. 6. Distribution of the fluid at the test section according to heat loads. Fig. 7. Heat transfer characteristics at evaporator section of the test sections according to operating pressures (a) Evaporation heat transfer coefficients, (b) Evaporator thermal resistances. Fig. 8. Geyser boiling in the hybrid heat pipe. Fig. 9. Heat transfer characteristics at condenser section of the test sections according to operating pressures (a) Condensation heat transfer coefficients, (b) Condenser thermal resistances. Fig. 10. Thermal efficiencies of the hybrid heat pipe under various operating pressures and heat loads. Fig. 11. Comparison of operation limits predicted by models and experimental data. Fig. 12. Upward liquid velocities according to types of thermosyphons: (a) Hybrid heat pipe, (b) Annular vapor-path thermosyphon. Fig. 13. Comparison of operation limits predicted by the revised models and experimental data
30
Highlights
1. Thermal performances and operation limits of hybrid heat pipe were experimentally studied. 2. Models for predicting the operation limit of the hybrid heat pipe was developed. 3. Non-condensable gas affected heat transfer characteristics of the hybrid heat pipe.
31
S1359-4311(16)32341-9 http://dx.doi.org/10.1016/j.applthermaleng.2016.10.077 ATE 9279
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
10 July 2016 6 October 2016 10 October 2016
Please cite this article as: K. Mo Kim, I. Cheol Bang, Heat Transfer Characteristics and Operation Limit of Pressurized Hybrid Heat Pipe for Small Modular Reactors, Applied Thermal Engineering (2016), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2016.10.077
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Heat Transfer Characteristics and Operation Limit of Pressurized Hybrid Heat Pipe for Small Modular Reactors Kyung Mo Kim, In Cheol Bang* Department of Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan 44919, Republic of Korea
Abstract
In this paper, a hybrid heat pipe is proposed for use in advanced nuclear power plants as a passive heat transfer device. The hybrid heat pipe combines the functions of a heat pipe and a control rod to simultaneously remove the decay heat generated from the core and shutdown the reactor under accident conditions. Thus, the hybrid heat pipe contains a neutron absorber in the evaporator section, which corresponds to the core of the reactor pressure vessel. The presence of the neutron absorber material leads to differences in the heated diameter and hydraulic diameter of the heat pipe. The cross-sectional areas of the vapor paths through the evaporator, adiabatic, and condenser sections are also different. The hybrid heat pipe must operate in a high-temperature, high-pressure environment to remove the decay heat. In other words, the operating pressure must be higher than those of the commercially available thermosyphons. Hence, the thermal performances, including operation limit of the hybrid heat pipe, were experimentally studied in the operating pressure range of 0.2–20 bar. The operating pressure of the hybrid heat pipe was controlled by charging the non-condensable gas which is unused method to achieve the high saturation pressure in conventional thermosyphons. The effect of operating pressure on evaporation heat transfer was negligible, while condensation heat transfer was affected by the amount of non-condensable gas in the test section. The operation limit of the hybrid heat pipe increased with the operating pressure. Maximum heat removal capacity of the hybrid heat pipe was up to 6 kW which is meaningful value as a passive decay heat removal device in the nuclear power plants. Based on the experimentally measured maximum heat removal capacities, models predicting the operation limit (flooding limit) of the hybrid heat pipe were developed.
*
Corresponding author : Tel.:+82-52-217-2915, Fax:+82-52-217-3008 E-mail: [email protected] (In Cheol Bang) 1
Nomenclature
A
area
[m2]
Bo
bond number
[-]
C
correlation coefficient
[-]
D
diameter
[m]
g
gravity
[m/s2]
h
latent heat
[kJ/kg]
K
Kutateladze number
[-]
L
length
[m]
m
correlation coefficient
[-]
Q
heat, power
[W]
q″
heat flux
[kW/m2]
r
radius
[m]
R
thermal resistance
[°C/W]
T
temperature
[°C]
Greek symbols ρ
density
[kg/m3]
σ
surface tension
[N/m]
Subscript c
condenser
cs
cross-sectional
e
evaporator
h
heated
k
Kutateladze
l
liquid
lv
liquid to vapor
max
maximum
sat
saturation
v
vapor
w
Wallis
2
Keywords
Hybrid heat pipe; Operation limit; Annular thermosyphon; Heat pipe; Small modular reactor; Passive safety system
1. Introduction
Most safety systems in commercial nuclear power plants focus on feeding additional coolant to the reactor core by using pumps and by employing the pressure difference between the coolant storage tank and reactor pressure vessel. However, the Fukushima and Three Mile Island (TMI) nuclear power plant accidents showed the limitation of the existing safety systems. Therefore, passive safety systems such as passive auxiliary feedwater system (PAFS), passive containment cooling system (PCCS), and hybrid safety injection tank for high-pressure injection via the pressure balance line are being developed to cope with the extended station blackout (SBO) accident. However, passive safety systems have complex circuits, including many valves, and hence, single failure and common cause failures are possible. Therefore, a new conceptual passive decay heat removal system based on a simple operating principle is required to solve the aforementioned problems in safety systems. A passive decay heat removal device that combines the functions of the control rods currently used in nuclear reactors and the heat pipes used in thermal controlling systems such as CPU cooling systems, heat exchangers, and solar collectors was proposed [1]. Thermosyphon heat pipes transfer heat from high-temperature section to low-temperature section through the evaporation and condensation of the working fluid at interfaces, and through the convection of the working fluid by gravitational force [2]. Thus, a combination of a heat pipe and a control rod, that is, a hybrid heat pipe can transfer decay heat from the reactor core to the heat sink in the event of the shutdown of a reactor under accident conditions [3]. Many types of small modular reactors (SMRs) are under development worldwide to achieve high levels of plant safety and reliability. The main advantages of SMRs are that they are economic and safer and allow long-term operation. Most types of SMRs are integral reactors, which depend on passive safety systems; therefore, the loss of coolant accident, which is a representative postulated accident in commercial nuclear reactors, can be prevented. However, there are high uncertainties in terms of operation and capacity for passive safety systems because these systems depend on natural driving forces. To mitigate and solve the problems related to the uncertainty of the passive safety systems, diversity of the safety systems must be secured. The 3
application of hybrid heat pipes to SMRs can provide an additional heat transfer media between the heat sink and active core. Thus, providing an additional way for decay heat removal through the application of hybrid heat pipe can enhance SMR safety. Fig. 1 is the schematic diagram of NuScale SMR with a hybrid heat pipe. In the hybrid heat pipe-controlled SMR, the decay heat generated from the fuel rods will be transferred to the reactor coolant, reactor coolant to evaporator section of hybrid heat pipes, adiabatic to condenser sections of the hybrid heat pipes, and the liquid pool located outside the reactor pressure vessel. The reactor pressure vessel is insulated to minimize the heat loss through structures. It can be assumed that the total decay heat is transferred to the reactor coolant and hybrid heat pipe. The liquid temperature at the pool which acts as ultimate heat sink of the hybrid heat pipes will be increased as the decay heat removal proceeds. The stored heat of the liquid can be transferred to the environment (atmosphere inside the containment). However, the large liquid inventory of the pool is designed to secure the integrity of the reactor pressure vessel in any accidents. Therefore, the temperature increase at the heat sink will be low or negligible. The additional heat sink can be installed to prepare for the case of liquid temperature increase by connecting the liquid pool outside the reactor pressure vessel to the air cooling tower outside the containment.
Fig. 1. In-house design of hybrid heat pipe as Passive IN-core Cooling system (PINCs) in NuScale 4
For practical application of the hybrid heat pipe to SMRs, significant level of heat removal capacity must be guaranteed and modeled. Therefore, the thermal performance of the hybrid heat pipe, including its operation limits, was experimentally analyzed at high pressure. The high operating pressures were achieved through the charge of nitrogen gas to the test section as studied in previous studies [4-7], while backpressure regulator was used to maintain the constant operating pressures. The maximum heat transfer capacity of heat pipes such as concentric thermosyphons and annular thermosyphons can be predicted using known correlations and physical models. However, a neutron absorber, which is considered an adiabatic medium owing to its low thermal conductivity, introduces a difference between the wetted perimeter and heated perimeter of the hybrid heat pipe. In previous studies [8-14], the thermal performance of thermosyphons was examined through experiments and models were developed for the test section with the heated diameter equal to the hydraulic diameter. The existing models have not been validated in the highpressure range with water as the working fluid. Thus, the operating limit and heat transfer characteristics of hybrid heat pipe in high-pressure range were measured experimentally. The existing correlations for the operation limit which are based on the flooding phenomenon were modified for the modeling the operation limit of hybrid heat pipe.
2. Operation Limit (Flooding Limit) Models
The operation limits of closed two-phase thermosyphons are the sonic limit, boiling limit, flooding limit (entrainment limit), and viscous limit. The main phenomenon factor leading to the operation limit of a thermosyphon is the flooding limit. Hence, flooding phenomena were experimentally analyzed with various working fluids. Table 1 summarizes the existing correlations for the critical heat flux of a thermosyphon and presents the pros and cons of each correlation.
Table 1 A summary on correlations about critical heat flux of thermosyphon. Researchers
Notes Pros
1) Shows high prediction accuracy in relatively small diameter with modification of coefficients.
Cons
1) Effect of surface tension was not considered. 2) Prediction ability is reduced as the cross-sectional area of the flow path increases
Wallis [8]
5
Kutateladze [9]
Pros
1) Relatively high prediction ability in the flow path with large diameter
Cons
1) Diameter effect was not considered. 2) Prediction ability is reduced as the cross-sectional area of the flow path decreases.
Eqn.
QKutateladze = Ck2 hlv Aρ v1/ 2 ⎣⎡ gσ ( ρl − ρ v )⎦⎤
Cons Tien and Chung [10]
1/ 4
Ck = 3.2 tanh ( 0.5 Bo1/ 4 )
(4)
⎡ g ( ρl − ρ v ) ⎤ Bo = D ⎢ ⎥ σ ⎣ ⎦
1/ 4 ⎡ ⎛ ρv ⎞ ⎤ ⎢1 + m ⎜ ⎟ ⎥ ⎢⎣ ⎝ ρl ⎠ ⎥⎦
−2
(2)
(5)
1/ 4
⎡⎣ ρ v−1/ 4 + ρ l−1/ 4 ⎤⎦
−2
(3)
1/ 2
Pros
1) The most widely used correlation. 2) High prediction abilities for various working fluids and test conditions.
Cons
1) Lack of validation for the annular vapor-path thermosyphons. ⎛ D ⎞ ⎛ ρl ⎞ = 0.64 ρ v H lv A ⎜ ⎟⎜ ⎟ ⎝ 4 L ⎠ ⎝ ρv ⎠
0.13
⎡⎣σ g ( ρl − ρ v ) ρ v2 ⎤⎦
1/ 4
(6)
Eqn.
QImura
Pros
1) Enhanced prediction accuracy for the test sections working with water compared to Tien and Chung correlation. 2) Correlation constant (R) can be modified according to working fluids.
Cons
1) Lack of validation for the annular vapor-path thermosyphons. QFaghri = Khlv Av ⎡⎣ gσ ( ρl − ρ v )⎤⎦
Eqn.
ESDU [13]
(1)
1) Combined the effects of surface tension and diameter of the test section. 2) High predictability for various working fluids. 1) Limited predictability for the thermosyphons working with water. 2) Lack of validation for the annular vapor-path thermosyphons. QTien and Chung = Ck2 hlv Av ⎣⎡ gσ ( ρ l − ρ v )⎦⎤
Eqn.
Faghri et al. [12]
−2
QWallis = Cw2 hlv Aρv1/ 2 ⎣⎡ gD ( ρl − ρv )⎦⎤
Pros
Imura et al. [11]
1/ 4 ⎡ ⎛ ρv ⎞ ⎤ ⎢1 + m ⎜ ⎟ ⎥ ⎢⎣ ⎝ ρl ⎠ ⎥⎦
Eqn.
1/ 2
Pros
⎛ρ ⎞ K =⎜ l ⎟ ⎝ ρv ⎠
1/ 4
⎡⎣ ρ v−1/ 4 + ρl−1/ 4 ⎤⎦
−2
(7)
0.14
tanh 2 Bo1/ 4 = R tanh 2 Bo1/ 4
(8)
1) The most widely used correlation with validation in wide range of operating conditions. 6
Monde et al. [14]
Cons
1) Cannot used for the annular vapor-path thermosyphon having difference between hydraulic diameter and heated diameter.
Eqn.
QESDU = f1 f 2 f 3 Acs hlv ρ v1/ 2 ⎣⎡σ g ( ρ l − ρ v )⎦⎤
Pros
1) It was developed for the annular thermosyphons.
Cons
1) Validation was conducted for the open thermosyphons.
Eqn.
QMonde
1/ 4
(9)
⎡ σ g ( ρl − ρ v ) ⎤ 0.16 = ρ v H fg A ⎢ ⎥ ρ v2 1 + 0.075 ( L Dh ) ⎣ ⎦
1/ 4
(10)
3. Experiment
3.1. Test section
A hybrid heat pipe was prepared as shown in Fig. 2. A 1-m-long stainless steel 316L test section with 25.4 mm outer diameter and 22 mm inner diameter was used as the test section. The test section was charged with 90 mL deionized water, and a B4C pellet representing a neutron absorber material (outer diameter: 17.7 mm; length: 285 mm) was installed at the center of the heat pipe [15].
Fig. 2. Composition of hybrid heat pipe.
7
3.2. Experimental Setup and Procedures
Fig. 3(a) shows the heat pipe test facility. The test facility comprises a working fluid tank, a test section, a water jacket to condense the evaporated working fluid, a pump that circulates coolant from the water storage tank to the water jacket, a vacuum pump, and two copper electrodes at the top and bottom of the evaporator section that are connected to a power supply and that heat the test section by passing current on the evaporator section. The outer walls of the evaporator, adiabatic, and condenser (water jacket) sections were wrapped by glass-fiber insulator with 50 mm thickness to minimize the heat exchange between test section and environment.
(a)
(b) Fig. 3. Schematic diagram of hybrid heat pipe test facility: (a) experimental apparatus, and (b) details of thermocouple locations in test section. 8
Twelve K-type thermocouples (TCs) were installed on the evaporator and adiabatic sections of the test section (six on the evaporator and six on the adiabatic section); four T-type TCs were installed on the wall of the condenser section as shown in Fig. 3(b) to record the temperature distribution under a given condition. Additional two T-type TCs measured the water temperatures at the inlet and outlet of the water jacket to measure the efficiency of the test section..
Table 2 Experimental conditions. Length ratio [%]
28.5 : 21.5 : 50.0
Heat load [W]
200 – 6000
Initial pressure [bar]
0.2, 3.0, 5.0, 10.0, 15.0, 20.0
Fill ratio [%]
100 % (90 ml)
Table 2 presents the experimental conditions. The experimental procedure is as follows: (1) remove the air in the test section by vacuum pump; (2) fill the test section with the working fluid; (3) pressurize the test section by nitrogen injection to set the pressure; (4) set the target pressure of the backpressure regulator; (5) load heat in the evaporator section; (6) circulate the coolant through the water jacket; (7) and record the temperature evolutions and pressure variations.
3.3. Uncertainty Analysis
The uncertainties in the parameter measurements were analyzed. Table 3 presents the measurement errors in the instruments.
Table 3 Measurement uncertainties. Parameters
Instruments
Uncertainties
Temperature
Thermocouple
± 0.1 oC
Pressure
Pressure gauge
± 0.1 kPa
9
Water flow rate
Turbine flowmeter
± 0.05 lpm
Voltage
Voltmeter
± 0.02 V
Current
Ammeter
±4A
The uncertainties of the parameters were calculated by the Kline and McClintock method [16]. The measurement uncertainties in the heat flux, heat transfer coefficient, and thermal resistance were calculated as follows:
⎛ ∂ϕ ⎞ = × Δxi ⎟ ⎜ ∑ ϕ ϕ i =1 ⎝ ∂xi ⎠
Δϕ
1
n
2
(11)
where ϕ is the derived parameter, xi represents the measured variables, and Δxi represents the error of the measured variables. The tolerances in the length and diameter of the test section were 5 mm and 1 mm, respectively. The calculated maximum uncertainty in the heat flux is 6.1%. The maximum uncertainties in the heat transfer coefficient and thermal resistance were estimated as 4.3% and 6.4%, respectively. As the heat flux increases, the voltage and current increases. The instrument uncertainties for voltage, current, length, and diameter are constant. Therefore, uncertainties for calculated heat fluxes decrease as the heat flux increases because the ratio between calculated heat flux and instrument measurement become smaller as the heat flux increases. The maximum and minimum uncertainties in the heat flux are appeared at the lowest and highest heat flux, respectively, as shown in Fig. 5. Temperature differences between average wall temperatures at each section and saturation temperatures increase as the heat flux increases. The instrument uncertainty of thermocouple is constant. Hence, the uncertainties for heat transfer coefficients and thermal resistances decrease as the heat transfer coefficient and thermal resistance increase.
10
Fig. 4. Uncertainties of calculated heat fluxes according to heat fluxes and operating pressures.
4. Results and Discussion
4.1. Wall Temperature Distributions
Wall temperatures of the test section were recorded in the axial direction according to time. Based on the wall temperature evolution data, the wall temperature distributions at steady states were expressed as shown in Fig. 5. The temperature in the adiabatic section corresponds to the saturation temperature of the operating pressure [17, 18]. Therefore, the wall temperatures in this section were maintained constant throughout the entire range of heat loads. The temperature differences between the evaporator and adiabatic sections, which can be regarded as wall superheat increased as heat load increased within 5–30°C. The nitrogen gas which was charged to the test sections for the pressurization takes an important role in the condensation heat transfer. The wall temperature in the condenser section increased as the heat load increased because of the volume expansion of the working fluid in the high heat load region, and some of the nitrogen was removed by backpressure regulator to maintain constant operating pressure. Several previous studies [19-23] on the variable conductance heat pipe which uses the noncondensable gas for the maintenance of thermal bath temperature at evaporator section reported that the restriction of the condensation heat transfer due to non-condensable gas zone at the condenser section. The nitrogen gas blocks the reach of steam moved along evaporator and adiabatic section, and impedes the condensation of the steam at the inner wall of the test section. The phenomenon can 11
be confirmed by observing the increase of condenser wall temperature. The location of steam-gas mixing zone (interface between steam and non-condensable gas) can also be observed by locations of increasing condenser wall temperature because the volume occupied by non-condensable gas will show the low wall temperature and relatively high temperature will be observed in condensation occurring volume. As the amount of nitrogen gas reduced, the amount of working fluid reaching the condenser section increased, as shown in Fig. 6. The volume fraction of the nitrogen increased with the operating pressure. For identical heat loads, the wall temperatures in the condenser section of the test section operating at a high pressure is lower than those of the section at low operating pressure. That means height of the steam-gas mixing zone for high operating pressure (distance from bottom of the evaporator section) tends to be lower than low operating pressure at identical heat loads. In the evaporator section, the boiling in liquid pool is the main heat transfer mechanism. The noncondensable gas determines the saturation pressure. Saturation temperature increases as the operating pressure increases, sequentially; evaporator wall temperature increases as the operating pressure increases. Details on variations evaporator wall temperatures according to heat loads will be discussed in Section 4.2 Evaporator heat transfer.
(a) 0.2 bar
12
(b) 3.0 bar
(c) 5.0 bar
(d) 10.0 bar
13
(e) 15.0 bar
(f) 20.0 bar Fig. 5. Inner wall temperature distributions of hybrid heat pipe according to operating pressures
14
(a) Low heat load (b) Intermediate heat load (c) High heat load Fig. 6. Distribution of the fluid at the test section according to heat loads
4.2. Evaporation Heat Transfer
The heat transfer characteristics (evaporation heat transfer coefficient and evaporator thermal resistance) in the evaporator section were calculated using the following equations based on the measured wall temperature distributions [24]:
he =
qe′′
(T − T ) e
Re =
(12)
sat
(T − T ) e
sat
Qe
15
(13)
Fig. 7 shows the evaporation heat transfer coefficients and evaporator thermal resistances according to operating pressures and heat loads. The heat transfer in the test section operating at subatmospheric pressure was worse than operation pressures greater the atmosphere pressure owing to different boiling modes.
(a)
(b)
Fig. 7. Heat transfer characteristics at evaporator section of the test sections according to operating pressures (a) Evaporation heat transfer coefficients, (b) Evaporator thermal resistances. 16
At sub-atmospheric pressure (0.2 bar), the vapor–liquid density ratio is very large. Thus, the large-sized bubble generated in the evaporator section covers the inner wall of the test section forming liquid plugs. These plugs reach the condenser section and are destroyed at the top of the condenser section. The destroyed liquid plugs fall into the evaporator section in the form of liquid films. The heat transfer achieved by this event sequence is defined as geyser boiling [29] and shown in Fig. 9. However, the vapor–liquid density ratios in the test section operating at pressures greater than the atmospheric pressure (3–20 bar) are relatively smaller than those at sub-atmospheric pressure; hence, liquid plugs and liquid films do not easily form from the vapor as shown in Fig. 8. Hence, for evaporator section of the test sections that operating under high pressure, the heat transfer mechanism is convective pool boiling [11]. When the pressure was 3–20 bar, the effect of the vapor–liquid density ratio on heat transfer characteristics in the evaporator section was negligible. The fill ratio (that is, the ratio of the volume of the working fluid and that of evaporator section except the B4C pellet) of the working fluid was 166%. Although the bubble sizes and volumes occupied by the vapor differ with the saturation pressure, the main heat transfer medium at the wall of evaporator section is the liquid pool, which occupies most of the volume in evaporator section owing to the high fill ratio. Thus, the evaporation heat transfer coefficients are similar at high operating pressures.
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Fig. 8. Geyser boiling in the hybrid heat pipe.
4.3. Condensation Heat Transfer
Heat removal rate through the water jacket was calculated based on the variation of water temperature (Two T-type TCs were installed on the inlet and outlet of water jacket) with flow rate data recorded by turbine flowmeter: p (Tout − Tin ) Qc = mc
(14)
The condensation heat transfer characteristics were described as mentioned by heat transfer characteristics of evaporator section:
hc =
(T
qc′′
sat
Rc =
(T
sat
− Tc ) − Tc )
Qc 18
(15)
(16)
Nitrogen is the most important factor that determines the condensation heat transfer of the pressurized heat pipes because the nitrogen in the condenser section impedes the upward flow of the working fluid and the heat transfer between the wall of the condenser section and working fluid [26]. As the heat load increases, the fraction of non-condensable gas decreases owing to the leakage of nitrogen gas to maintain the constant operating pressure. Thus, the condensation heat transfer coefficient increases as the heat load increases, as shown in Fig. 9.
(a)
(b) 19
Fig. 9. Heat transfer characteristics at condenser section of the test sections according to operating pressures (a) Condensation heat transfer coefficients, (b) Condenser thermal resistances.
The initial amounts of non-condensable gas are different according to operating pressure. The amount of non-condensable gas is remarkably low in case of the test section operating at 0.2 bar, while in the case of high-pressure operation, the test sections are charged with nitrogen. Hence, a noticeable difference was observed in the condensation heat transfer under sub-atmospheric pressure and normal pressure conditions. The charged amount of nitrogen gas increases with the operating pressure. Hence, increase of operating pressure induced a reduction in the condensation heat transfer coefficient.
4.4. Thermal Efficiencies of Heat Pipes
Thermal efficiencies of the hybrid heat pipe were checked by comparing the loaded heat on the evaporator section and removed heat through the condenser section as follows: [27, 28]
η=
p (Tout − Tin ) Qc mc = Qe Qe
(17)
If the thermal efficiency of the heat pipe is low, the rest amount of heat which was not transported to the condenser section will be used to expand the volume of working fluid resulting in the increase of system pressure in closed system. For the test sections used in this study, the system pressure was maintained constantly with backpressure regulator. As the thermal efficiency decreases, volume expansion of the working fluid will be enhanced, sequentially; the removal of nitrogen gas will be increased. Fig. 10 shows the tendency of thermal efficiency according to heat loads and operating pressures. The thermal efficiency was inversely proportional to the operating pressure as observed in the condensation heat transfer coefficient. The reduction of efficiency by the increase of operating pressure was attributed to the active two-phase heat transfer length (nitrogen gas prohibit the reach of steam to condenser section impeding the condensation, therefore; the active two-phase heat transfer length means the length of phase change occurs). Heat removal rate determines the amount of condensed liquid, liquid flow rate from condenser section to evaporator section, relative velocity between vapor and liquid in terms of operation limit. Low thermal efficiency result in the low amount of condensed liquid, low liquid flow rate in gravitational direction, eventually; low 20
operation limit. However, the effect of thermal efficiency is not considered in the existing models on critical heat flux of the thermosyphons because the efficiency affects system pressure and the system pressure effect is reflected with density ratio of vapor-liquid in the models.
Fig. 10. Thermal efficiencies of the hybrid heat pipe under various operating pressures and heat loads.
4.5. Operating Limits of Heat Pipes
The heat load, which induces a sudden increase in wall temperature, was chosen as the operating limit of the hybrid heat pipe. Fig. 11 shows the comparison of experimentally measured operation limits of hybrid heat pipes with the predicted values reflecting the reduced cross-sectional area of the vapor path. The maximum heat removal capacity of the hybrid heat pipe increased with the operation pressure (4200–5980 W). The values are 4–6 times those of hybrid heat pipes operating at 0.2 bar. The experimentally measured operating limits showed large deviations from the developed models [10-13] with regard to the critical heat flux of thermosyphon heat pipes. The correlations of Wallis and Kutateladze for the concentric flow channel were developed through water–gas countercurrent flow experiments. However, the hybrid heat pipe was designed as an annular vapor path heat pipe. Monde et al. considered the situation in which the entire open thermosyphon was occupied by the working fluid to develop their correlation. Therefore, there are limitations in applying the correlation to predict the operation limit of closed hybrid heat pipes partially filled with working fluid. 21
Tien and Chung, and Faghri et al. also proposed the correlations for the flooding limit that can be applied to annular vapor path thermosyphons. However, in hybrid heat pipes, the hydraulic diameter and heated diameter may differ because liquid flow near the B4C pellet might be less than that near the heated wall. Wallis correlation [8] (with assumption of Cw and m are unity) showed the best agreement with experimental results compared to other correlations; while the slope of the variation in operation limit was differed from the measured limits. The predictability of Wallis model will be reduced in the saturation pressure higher than 20.0 bar. The possibility of the decrease in predictability can be solved by correcting the correlation constants according to operating pressures. Correlation developed by Tien and Chung [10] predicted well in low pressures (< 5 bar). The difference between prediction and experimental results were magnified as the operating pressure increases. The prediction ability of the correlation can be enhanced with suggestion of best estimate correlation coefficients according to operating pressures. For other correlations, the main reason of the deviations of the prediction from measured values is shown in Fig. 12. There are upward (evaporator section) and downward liquid flows (adiabatic and condenser sections) in the thermosyphon. Bubbles generated in the evaporator section have upward flow due to buoyancy force. The bubble flow drags the liquid in the pool at the evaporator section. For the hybrid heat pipe, the higher shear force will be applied to the upward liquid flow at the surface of B4C pellet as compared to conventional annular thermosyphons. The bubbles are generated at the wall of inner structure in the conventional annular vapor-path thermosyphon because it is additional heat transfer medium (heat source and sink). On the other hand, the B4C pellet is adiabatic medium which does not participate in phase change. Hence, the higher shear force on B4C pellet to upward liquid flow reduces the upward liquid velocity and vapor velocity in the evaporator section, resulting in lower relative velocity between the downward liquid and upward vapor flows at the inner wall of cladding as compared to that in the cases of previously studied annular vapor-path heat pipes. The proportionality of the operation limit on operating pressure causes the deviations between predicted and experimental results. Correlations of Imura et al. [11] and ESDU [13] analyzed the similar proportionality between operation limit and pressures with the measured limits. Thus, the correlations proposed by Imura et al. [11] and ESDU [13] were selected as the models predicting the maximum heat removal capacity of the hybrid heat pipe with additional consideration of the design of the hybrid heat pipe.
22
Fig. 11. Comparison of operation limits predicted by models and experimental data
(a)
(b)
Fig. 12. Upward liquid velocities according to types of thermosyphons: (a) Hybrid heat pipe, (b) Annular vapor-path thermosyphon
QModified Imura
⎛ A ⎞⎛ ρ ⎞ = ρ v H lv Ah ⎜ cs ,e ⎟⎜ l ⎟ ⎝ Ah ⎠⎝ ρ v ⎠
0.13 4
σ g ( ρl − ρ v ) ρ v2
QModified ESDU = f1 f 2 f 3 f 4 Acs hlv ρ v1/ 2 ⎣⎡σ g ( ρ l − ρ v )⎦⎤
23
1/ 4
(18) (19)
f 4 = ( Ah Acs ,e )
0.1
(18)
The difference between the heated and hydraulic diameters, which is caused by the presence of the adiabatic medium—B4C pellet—in the evaporator section, induced the deviation of experimental results from existing correlations. The cross-sectional areas of the vapor paths in the evaporator, adiabatic, and condenser sections are also different because the B4C pellet is installed only in the evaporator section. Thus, Imura correlation was modified to consider the difference in vapor path area and heating area by revising the constant 0.64 to 1.0. In the ESDU correlation, the crosssectional area of the vapor path was used, but the effect of the heated area was not considered. Hence, an additional factor, f4 related to the difference between the cross-sectional area of the vapor path and heated area is used. The suggested models showed good agreement with the experimental results within ±15% deviations, as shown in Fig. 13.
Fig. 13. Comparison of operation limits predicted by the revised models and experimental data
4.6. Prospect of Hybrid Heat Pipe on SMR
The full power of the NuScale SMR is 150 MWth to generate 50 MWe. The NuScale reactor uses the same fuel as that used in standard light water reactors with height reduction of 2 m. There are 37 fuel assemblies installed (a fuel assembly is 17 × 17, enriched up to 4.95%). If four guide tubes 24
and control rods are used in a single fuel assembly, the total number of control rods is 148 ea. After 2 h from the initiation of an accident, the total decay heat generated from the core will be 1.5 MW corresponding to 1% of the full power (from typical decay heat curve). Thus, the required heat removal capacity of a single hybrid heat pipe to remove the total decay heat will be 10 kW. The measured maximum heat removal capacity of the hybrid heat pipe is approximately 6 kW at an operating pressure of 20 bar. The hybrid heat pipe can remove 60% of the total decay heat if all of the control rods are replaced with hybrid heat pipes. To use the liquid pool outside the reactor pressure vessel as a heat sink, the hybrid heat pipe that will be applied to the SMR should be longer than 20 m. Hence, the effect of length of the hybrid pipe on the operation limit and heat transfer characteristics must be studied further for accurate modeling. To further improve the decay heat removal rate by hybrid heat pipes, the following work will be conducted. (1) Measurement of the operation limit of hybrid heat pipes operating above pressures of 20 bar (2) Surface modification, such as deposition of porous media, to enhance the maximum heat removal capacity of hybrid heat pipes (3) Observation of the effect of clearance on the heat transfer characteristics and operation limit (Reduction of B4C pellet size through enrichment of 10B isotope, which is the main neutron absorbing element in the B4C pellet, or through use of other neutron absorbing isotopes)
5. Conclusions
Hybrid heat pipe was proposed as a passive decay heat removal device for SMRs to improve the safety system of reactors. These pipes have unique geometry owing to the presence of neutron absorber material inside them, and they must have a high maximum heat removal capacity to remove the significant decay heat from the core. Thus, the heat transfer characteristics and operation limits of hybrid heat pipes were experimentally measured at high pressures, which were not considered in previous researches. The following results were obtained: (1) The effect of the vapor–liquid density ratio on the evaporation heat transfer was negligible at pressures above the atmospheric pressure. (2) The differences in the evaporation heat transfer between test sections operating at subatmospheric pressure and normal pressures result from the different boiling mechanisms (geyser boiling and convective pool boiling). (3) With an increase in the operation pressure, the condensation heat transfer decreases because the amount of non-condensable gas injected into the test section for pressurization 25
increases, impeding the heat transfer between the wall and working fluid in the condenser section. (4) The operation limit increases with operating pressure with the maximum heat removal capacity of 5980 W (at 20 bar). (5) The existing correlations for predicting the operation limit of thermosyphons showed deviations from experimental results owing to presence of the neutron absorber material and high-operating-pressure environment. (6) New correlations to predict the critical heat flux of hybrid heat pipes were developed by modifying the correlations of Imura et al. and ESDU based on the experimental data.
Acknowledgement
This work was supported by the Nuclear Energy Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning. (NRF22A20153413555, 2013M2B2B1075734, 2014M2A8A4021514)
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REFERENCES
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[16] Kline SJ and McClintock FA, Describing uncertainties in single sample experiments, Mechanical Eng 1953;75:3-8. [17] Kole M, Dey TK, Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids, Appl. Therm. Eng. 2013;50:763-770. [18] Solomon AB, Ramachandran K, Pillai BC, Thermal performance of a heat pipe with nanoparticles coated wick, Appl. Therm. Eng 2012;36 106-112. [19] Sauciuc I, Akbarzadeh A, Johnson P, Temperature control using variable conductance closed two-phase heat pipe, Int. Comm. Heat Mass Transfer 1996; 26: 427-433. [20] Peterson PF, Tien CL, Gas-concentration measurements and analysis for gas-loaded thermosyphons, J. Heat Transfer 1988;110:743-747. [21] Watanabe K, Kimura A, Kawabata K, Yanagida T, Yamauchi M, Development of a variableconductance heat-pipe for a sodium-sulfur (NAS) battery, Furukawa Review 2001;20:71-76. [22] Ungureanu I, Barbu V, Variable conductance heat pipe model for temperature control of processes, 5th Int. Conf. Computational Mechanics and Virtual Engineering, October 24-25, 2013 – Brasov (Romania). [23] Ishizuka M, Sasaki T, Miyazaki Y, The development of titanium-ammonia variable conductance heat pipe, The 6th Int. Symp. Transport Phenomena in Thermal Engineering, May 913, 1993 – Seoul (Korea) [24] Mozumder AK, Akon AF, Chowdhury MSH, Banik SC, Performance of heat pipe for different working fluids and fill ratios, J. Mecha. Eng 2010;41:96-102. [25] Faghri A, Heat pipe science and technology, Taylor and Francis, Washington 1995. [26] Hijikata K, Chen SJ, Tien CL, Non-condensable gas effect on condensation in a two-phase closed thermosyphon, Int. J. Heat Mass Transfer 1984;27:1319-1325 [27] Amiri A, Sadri R, Shanbedi M, Ahmadi G, Chew BT, Kazi SN, Dahari M, Performance dependence of thermosyphon on the functionalization approaches: An experimental study on thermos-physical properties of graphene nanoplatelet-based water nanofluids, Ener. Conv. Manag 2015;92:322-330 [28] Shanbedi M, Heris SZ, Baniadam M, Amiri A, Maghrebi M, Investigation of heat-transfer characterization of EDA-MWCNT/DI-water nanofluid in a two-phase closed thermosyphon, Ind. Eng. Chem. Res 2012;51:1423-1428
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Table Captions Table 1 A summary on correlations about critical heat flux of thermosyphon. Table 2. Experimental conditions. Table 3. Instrument uncertainties.
29
Figure Captions Fig. 1 In-house design of hybrid heat pipe as Passive IN-core Cooling system (PINCs) in NuScale. Fig. 2. Composition of hybrid heat pipe. Fig. 3. Schematic diagram of hybrid heat pipe test facility: (a) experimental apparatus, and (b) details of thermocouple locations in test section. Fig. 4. Uncertainties of calculated heat fluxes according to heat fluxes and operating pressures. Fig. 5. Inner wall temperature distributions of hybrid heat pipe according to operating pressures. Fig. 6. Distribution of the fluid at the test section according to heat loads. Fig. 7. Heat transfer characteristics at evaporator section of the test sections according to operating pressures (a) Evaporation heat transfer coefficients, (b) Evaporator thermal resistances. Fig. 8. Geyser boiling in the hybrid heat pipe. Fig. 9. Heat transfer characteristics at condenser section of the test sections according to operating pressures (a) Condensation heat transfer coefficients, (b) Condenser thermal resistances. Fig. 10. Thermal efficiencies of the hybrid heat pipe under various operating pressures and heat loads. Fig. 11. Comparison of operation limits predicted by models and experimental data. Fig. 12. Upward liquid velocities according to types of thermosyphons: (a) Hybrid heat pipe, (b) Annular vapor-path thermosyphon. Fig. 13. Comparison of operation limits predicted by the revised models and experimental data
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Highlights
1. Thermal performances and operation limits of hybrid heat pipe were experimentally studied. 2. Models for predicting the operation limit of the hybrid heat pipe was developed. 3. Non-condensable gas affected heat transfer characteristics of the hybrid heat pipe.
31