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Comparison of flooding limit and thermal performance of annular and concentric thermosyphons at different fill ratios
Accepted Manuscript Title: Comparison of flooding limit and thermal performance of annular and concentric thermosyphons at different fill ratios Author: Kyung Mo Kim, In Cheol Bang PII: DOI: Reference:
S1359-4311(16)00032-6 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.137 ATE 7555
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
2-11-2015 31-12-2015
Please cite this article as: Kyung Mo Kim, In Cheol Bang, Comparison of flooding limit and thermal performance of annular and concentric thermosyphons at different fill ratios, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.137. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Comparison of Flooding Limit and Thermal Performance of Annular and Concentric Thermosyphons at Different Fill Ratios Kyung Mo Kim, In Cheol Bang* School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan, 689-798, Republic of Korea
Highlights
Annular thermosyphon shows higher heat transfer compared to concentric thermosyphon. Annular thermosyphon requires new prediction model for flooding limit. Fill ratio of working fluid affects to the flooding limit of the annular thermosyphon.
Abstract
A passive in-core cooling system (PINCs) based on hybrid heat pipe can be adopted to enhance the passive safety of advanced nuclear power plants. A hybrid heat pipe is a heat transfer device that takes the dual roles of neutron absorption and heat removal by combining the functions of a heat pipe and a control rod. To observe the effect of neutron absorber material inside the heat pipe and fill ratio of the working fluid on the thermal performances of heat pipe including operation limit, an annular thermosyphon heat pipe (ATHP) that contains a neutron absorber inside a concentric thermosyphon heat pipe (CTHP) was experimentally studied in the condition of various fill ratios. The ATHP showed lower thermal resistances in the evaporator region with a maximum reduction of 20 % compared to those of a CTHP. In terms of the operational limits, the ATHP showed a lower entrainment limit than the CTHP due to a smaller cross-section for vapor path in the evaporator region, which resulted in high shear at the vapor-liquid interface. In addition, increasing the fill ratio enhanced the entrainment limit by 18 %.
*
Corresponding author : Tel.:+82-52-217-2915, Fax:+82-52-217-3008 E-mail: [email protected] (In Cheol Bang) 1
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Nomenclature [m2]
A
area
C
correlation coefficient
g
gravity
[m/s2]
h
latent heat
[kJ/kg]
K
Kutateladze number
L
length
m
correlation coefficient
Q
heat, power
[W]
q″
heat flux
[kW/m2]
r
radius
[m]
R
thermal resistance
[°C/W]
t
temperature difference between evaporator section and condenser section
T
temperature
[m]
[°C]
[°C]
Greek symbols ρ
density
[kg/m3]
σ
surface tension
[N/m]
Subscript avg
average
c
condenser
e
evaporator
l
liquid
lv
liquid to vapor
max
maximum
sat
saturation
v
vapor
Keywords
Hybrid control rod; Flooding limit; Annular thermosyphon; Heat pipe; Thermal resistance 2
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1. Introduction
Passive decay heat removal systems in nuclear power plants have been developed after Fukushima and Three Mile Island (TMI) accidents. However, most passive decay heat removal systems require certain signals or operation conditions for their operation, and it is possible for these to fail. Also, established emergency core cooling systems cannot operate properly due to the difficulty of depressurization in a station blackout (SBO) condition. Therefore, a new concept of passive decay heat removal system that does not require any signals or conditions to mitigate SBO accident is required. In this research, a passive in-core cooling system (PINCs) based on a hybrid control rod is suggested. A heat pipe is a device that transfers heat from the hot interface to the cold one by phase change and convection of working fluid. Heat pipes have a variety of advantages, such as high heat removal rate per unit volume, a fully passive working principle, and easy applicability [1]. Therefore, heat pipes have been used in various thermal engineering fields such as computer CPUs, spaceship nuclear reactors, and the Trans-Alaska Pipeline system. The inclusion of a neutron absorber material in the heat pipe enables it to take the roles of reactor shutdown and heat removal simultaneously. In other words, the limited heat removal capacity in an accident can be extended through the insertion of hybrid control rods into the active core. The operation of a hybrid control rod is driven by the temperature difference between the heat sink and the active core of the reactor pressure vessel (RPV), as shown in Figure 1. The existing control rods are held by a spider grid which is connected to the control rod drive mechanism (CRDM). However, hybrid heat pipes must extend from the active core to the heat sink to facilitate heat transport. Also, more passages which hybrid heat pipes can move along the axial direction at the upper head of RPV must be retained. The scheme of hybrid heat pipes is also shown in Figure 1.
Various concepts for applying heat pipes in nuclear power plants have been studied. Table 1 presents previous studies on application of heat pipes to nuclear power plants. Dunkel et al. [2] devised in-vessel and ex-vessel decay heat removal systems using heat pipes under a loss of coolant accident (LOCA) condition. The in-vessel cooling system used heat pipes to control rod channels and the ex-vessel cooling system used heat pipes installed on the ex-vessel wall. Mochizuki et al. [3] suggested a spent fuel pool cooling system using heat pipes. They confirmed the applicability of the system in terms of economics and heat removal by predicting the temperature change of the spent fuel pool at various conditions. Sviridenko [4] suggested a passive decay heat removal system using heat pipes on WWER. Various system designs have been proposed in his work. Gou et al. [5] proposed the heat pipe as a heat transfer device between 3
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the reactor vessel and the nuclear steam supply system for the purpose of simplifying the system. They showed that alkali metal heat pipes for cooling spaceship nuclear reactors had a significant heat transfer capacity. However, all previous studies were limited to the introduction of heat pipe-driven concepts and prediction of their system effects without validation. Also, most previous studies on heat pipes were limited in the measurement of effects of various parameters such as the fill ratio of the working fluid, the inclination angle, the type of working fluid on the thermal performance of concentric heat pipes in terms of thermal resistance and the heat transfer coefficient [9-14]. Mozumder et al. [9] studied about the effect of fill ratios and inclination angle on the thermal resistances of heat pipes. Several studies [10, 11] attempted to enhance the thermal performance of heat pipe using self-rewetting fluids. Other researches [12-14] investigated the heat transfer characteristics of heat pipe according to working fluids using various nanofluids. In the present study, the hybrid control rod which plays the dual roles of neutron absorber and decay heat removal device, is newly considered and studied in terms of feasibility. The maximum heat transfer capacity of a general heat pipe can be calculated with known correlations and physical models. However, the hybrid control rod contains a neutron absorber inside the heat pipe, which introduces a difference between wetted perimeter and heated perimeter because the neutron absorber material is adiabatic medium. Although the thermal performance of annular vapor-path heat pipes has been studied, most studies have not considered geometries where the wetted perimeter is different from the heated perimeter. Rosler et al. [15] experimentally observed the maximum heat removal rate for a vertical annular closed two-phase thermosyphon with low fill ratios of 3 – 30 %. R113 was used, and flow patterns according to heat loads were observed. They suggested a dry-out model for thermosyphons operating at low fill ratios, deriving the model theoretically and validating it with experimental results. Vijra et al. [16] studied the thermal performance of concentric annular heat pipe in which the wetted and heated perimeters were the same at various heat loads and inclination angles. The vertical annular heat pipe showed the lowest thermal resistance because it has the largest heat transfer area and effective gravity-assisted convection. Lin et al. [17] conducted experiments to observe the effect of fill ratio, condenser temperature, and evaporator length on geyser boiling in an annular thermosyphon. They observed that the period of geyser boiling depends on the parameters and proposed a correlation for the heat transfer coefficient of annular thermosyphons. Boo et al. [18] investigated the thermal characteristics of concentric annular heat pipes as a function of the diameter ratio between the inner and outer tubes and the fill ratio of working fluid. The effect of fill ratio on the thermal resistance increased as the diameter ratio increased. They also observed that the maximum heat 4
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removal capacity improved as the fill ratio increased. Faghri et al. [19] studied the flooding limit and heat transfer coefficients in concentric annular thermosyphons. The established correlations had provided accurate prediction in the low Reynolds number regime, but a new correlation was required for the high Reynolds number regime. Thermosyphons using water also showed significantly different experimental results compared to model predictions. Thus, they suggested a new correlation based on their experimental results and concluded the correlation must be validated with more experimental data. Other researchers [20-24] analyzed the thermal performance of annular thermosyphons and annular heat pipes according to various parameters. However, they did not address the relationship between the flooding limit and the fill ratios. The vapor path areas in these studies were the same along the evaporator, adiabatic, and condenser sections. Hence, the effect of the presence of the neutron absorber in only the evaporator section on the thermal performance was investigated experimentally. The decay heat removal capacity of the PINCs will be determined by the maximum heat removal capacity of the thermosyphon. The main operating limitation for the thermosyphon is entrainment phenomena that arise from the countercurrent flow of vapor and liquid. Thus, the enhancement of the entrainment limit is one of the main subjects in the field of heat pipe engineering. If the total volume of the thermosyphon was charged with working fluid, the maximum heat transfer rate would be the critical heat flux in pool boiling. However, the phase change would be suppressed and the heat transfer coefficient would be low. Thus, the optimum fill ratio for achieving a high heat transfer coefficient and maximizing heat removal capacity was studied.
2. Experiment
2.1. Test section
A hybrid control rod was prepared based on information on established control rods in the commercial pressurized water reactor, APR-1400. Stainless steel 316L test sections having 25.4 mm outer diameter and 22 mm inner diameter with length of 1000 mm were prepared. The test sections were charged with the working fluid at various fill ratios (volume ratio of working fluid to evaporator volume). A B4C pellet, which is a neutron absorber material, was then inserted in the center of the heat pipe as shown in figure 2. The B4C pellet has an outer diameter of 18.7 mm and a length of 215 mm. Its surface was treated to be smooth, suppressing the effect of the pellet on the liquid flow through the test section. 5
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2.2. Experimental Setup and Procedures
Figure 3 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 heat the test section by passing current. As shown in figure 4, 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), six Ttype TCs were installed on the wall of the condenser section, and at the inlet and outlet of the water jacket to record the temperature distribution at a given condition. Table 2 presents the experimental conditions. The experimental procedure was as follows. First, the test section was evacuated using the vacuum pump to a pressure of 20 kPa, to remove noncondensable gases. Water was then passed through the water jacket at a mass flow rate of 0.15 kg/s. The test section was then charged with the working fluid at various fill ratios (volume ratio of the working fluid to the evaporator volume). The test sections were heated gradually until a steady state was attained.
2.3. Uncertainty Analysis
The uncertainties in the parameter measurements were analyzed. Table 3 presents the measurement errors in the instruments. The uncertainties of the parameters were calculated by Kline and McClintock method [25]. From this, the measurement uncertainties in the heat flux, heat transfer coefficient, and thermal resistance were calculated as follows:
where
is the derived parameter,
n
1
i 1
xi
xi x i
2
is the measured variables,
(1)
xi
is the error of the measured
variables. The tolerances in the length and diameter of the test section were 5 mm and 1 mm. Hence, 6
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the calculated maximum uncertainty in the heat flux is 7.2%. The maximum uncertainties in the heat transfer coefficient and thermal resistance were estimated to be 5.2% and 7.6%, respectively.
3. Results and Discussion
3.1. Temperature Evolution
The temperature evolution was measured as a function of time and heat load to determine the thermal performance of the heat pipes as shown in Fig. 5 (temperature evolution of ATHP FR=100% during experiment). Steady states were attained at increments of the heat loads. The variations of temperatures at all TCs were maintained within ±1 °C at each steady state. At the initial state, a heat load of 25 W was applied to the evaporator section for 1 h to achieve a saturation temperature of 60 °C inside the heat pipe. The coolant was circulated through the water jacket when the temperatures at the evaporator and adiabatic sections reached 60 °C, and the heat load was then increased gradually. The heat loss (the ratio between the heat removal rate through the water jacket and the heat load applied in the evaporator section) was less than 10 % for each heat load. The coolant injection rate was constant for all time steps for the purpose of maintaining the same condensation condition. The wall temperatures of the condenser section were maintained at approximately 24 °C at relatively low heat fluxes; however, the wall temperatures at the bottom of the condenser section slightly increased as the heat load increased, because the amount of vapor from the evaporator section that reached the condenser section increased. At a certain heat load, the wall temperature suddenly increased because the condensed liquid could not return to the evaporator section, as a result of the countercurrent flow between vapor (opposite to gravity) and liquid (direction of gravity) reaching the flooding limit or entrainment limit. ATHPs showed flooding limits at a heat load of 1100 – 1300 W, while no flooding limit was observed in CTHPs.
3.2. Temperature Distributions in Heat Pipes
Figures 6 and 7 show the wall temperature distributions along the axial direction at steady states for the concentric and annular thermosyphons according to fill ratios. As shown in the figures, similar temperature distributions are observed until the entrainment limit is reached for each type of thermosyphon. The fill ratios of the CTHPs (50 % and 62.5 %) are less than 100 % which means under-filled condition. The liquid film thickness along the axial 7
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location would be similar at steady state with different heights of water pools. However, the difference between heights of water pools is small because the difference in fill ratios is relatively small. As a result, the similar temperature distributions of the CTHPs are observed. Operation of the concentric thermosyphon charged with 30 mL (fill ratio=37.5 %) was not achieved because a stable liquid film could not be formed along the wall of the evaporator section. However, the annular thermosyphon charged with 30 mL (FR = 100 %) showed stable operation up to the entrainment limit. Figure 8 shows the vapor and liquid distributions in the concentric and annular thermosyphons at the same fill ratio. The annular thermosyphon shows lower wall temperature distributions than the concentric thermosyphon because the water level reaches the adiabatic section due to volume expansion and relatively large fill ratios despite the amount of working fluid being the same. If the fill ratio is higher than 1.0, the thermosyphon would operate in the pool boiling regime because the adiabatic section does not contain a heat source. Thus, the annular thermosyphon which has a smaller evaporator volume is more favorable than a concentric thermosyphon at low fill ratios in terms of stable heat transfer. The heat transfer rate between the adiabatic section and the condenser section would be higher in the ATHP than in the CTHP due to the higher working fluid level at steady state. As a result, the working fluid temperatures in the adiabatic and evaporator sections of the ATHP were lower than in the CTHP at high heat flux values. Vapor and liquid velocities inside the thermosyphon were derived by numerical analysis based on governing equations [26]. The conventional vapor and liquid pressures along the axial location of the thermosyphon at moderate vapor temperature range are shown in Figure 9(a) [26, 27]. Vapor pressure drop could be caused by the inertial term and viscous friction at the interface of the liquid and vapor flows. Figure 9(b) shows the liquid and vapor velocities as a function of the axial position [26]. As shown in Figure 9, the largest interfacial velocity between the vapor and liquid flows would be observed at the top of the evaporator section. As a result, the flow resistance at the top of the evaporator section would be relatively high compared to other locations, and the temperature being highest at the top of the evaporator section for both thermosyphons.
3.3. Thermal Resistances of Heat Pipes
The evaporator and condenser thermal resistances (Re, and Rc) for the test sections at the different operating conditions were calculated using the following equations based on the measured wall temperature distributions [28]: 8
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Re
Rc
T
e
T sat
(2)
Qe
T
sat
Tc
(3)
Qc
The internal pressures of the test sections were measured for each heat load in this study to use the precise saturation temperature in the thermal resistance calculation. The saturation temperatures were validated with the wall temperature of the adiabatic section. Figure 10 shows the dependence of the thermal resistances of the thermosyphons on the heat loads. The condenser thermal resistances were the same for all types of test section. The condenser and evaporator thermal resistances decrease as the heat load increases because the area covered by liquid film increases with the reduction of liquid film thickness. The annular thermosyphon showed a lower evaporator resistance than the concentric heat pipe because the wall temperature distributions of the ATHPs were lower than those of the CTHPs, as shown in Figures 6 and 7. The higher working fluid level for the annular thermosyphon results in natural convection between the adiabatic section and the condenser section which improves the heat transfer between those parts. Hence, the total wall temperature profile of the ATHPs will be flattened and lowered compared to that of the CTHPs. This temperature distribution induces a lower evaporator thermal resistance despite the saturation temperatures at the same heat loads being equal. The effects of the fill ratio on the thermal resistances are negligible for each test section as shown in Figure 10. At heat loads larger than 300 W, the evaporator thermal resistances decrease sharply, which indicates the onset of nucleate boiling. The limitations of thermosyphons are known to be the sonic, viscous, boiling, and entrainment limits. However, the phenomena including bubble formation and growth would not prevent the returning of liquid from the condenser section to the evaporator section in the thermosyphon. Above a certain heat load, the bubble departure frequency will increase with liquid supply to the heater surface. Thus, the onset of nucleate boiling cannot be considered a boiling limit.
3.4. Heat Transfer Coefficients of Heat Pipes
The evaporation and condensation heat transfer coefficients (he and hc) were calculated from the temperature distributions using the following equations [28]:
9
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he
hc
q e
T
e
T sat
(4)
(5)
q c
T
sat
Tc
As shown in Figure 11, the annular thermosyphon showed higher evaporation heat transfer coefficients (4200–6750 W/m2·K) compared with those of the concentric thermosyphon (3500–6500 W/m2·K), with a maximum enhancement of 20%. Also, the heat transfer coefficients increase above 400 W, which demonstrates the onset of boiling. The annular thermosyphon had condensation heat transfer coefficients similar to those of the concentric thermosyphon (100–1300 W/m2·K), because the difference of the liquid film thickness between the annular and concentric thermosyphons should be small in steady state operation at the condenser section.
3.5. Entrainment Limits of Heat Pipes
The flooding limit is the most common concern for long thermosyphon with large fill ratios, large axial heat fluxes, and small radial heat fluxes. The large vapor velocities induced by high axial heat fluxes result in high values of interfacial shear, which produce instability of the liquid film. The high shear at the vapor-liquid interface prevents the condensate from returning to the evaporator and leads to a flooding condition at the top of the evaporator section. The blocked supply of liquid causes a partial dryout of the evaporator, which gives rise to wall temperature excursions. There are two major fundamental semi-empirical correlations for predicting the flooding limit; Wallis correlation [29] and Kutateladze two-phase flow instability criterion [30]. The first is characterized by a balance between the inertial and hydrostatic forces, while the second balances the inertial, buoyant, and surface tension forces. However, the Wallis correlation does not consider the surface tension and Kutateladze criterion does not take into account the diameter effect on countercurrent flow. So, Tien and Chung [31] combined the Kutateladze and Wallis correlations in order to address the effects of the pipe diameter and the surface tension on the limiting conditions. The correlation showed good agreement with data sets for several working fluids, but not for water. Faghri et al. [19] improved the existing semi-empirical correlations to predict the flooding limit of the thermosyphon and the predicted limit mached to the existing experimental results well. Thus, Tien and Chung’s, and Faghri’s correlations were selected as models to predict the entrainment limit for an annular 10
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thermosyphon. The hydraulic diameter of the ATHP was substituted into the correlations to determine the prediction performance of these correlations for an annular thermosyphon whose wetted perimeter is different from its heated perimeter.
Q T ie n & C h u n g C k h lv A v [ g ( l v )] 2
1/ 2
Q F a g h r i K h lv A v [ g ( l v )] 1/ 2
1/ 4
1/ 4
1 m v l
1 m v l
1/ 4
1/ 4
2
(6)
2
(7)
The effect of fill ratio on the operation limit of the thermosyphon has not been considered in most correlations. Thus, the equal flooding limit is predicted at various fill ratios, as shown in Figure 12. The amount of working fluid is one of the important parameters for determining the operation limit because when the total volume of the thermosyphon is occupied by working fluid, the result would be the critical heat flux in pool boiling condition. The observed flooding limit was 30 - 50 % higher than the predicted values (844 and 851 W) because of heat transfer between the B4C pellet and the working fluid, and effect of fill ratio were not considered. The 133 % charged ATHP showed the highest entrainment limit. As the fill ratio increases the flooding limit increased, with a maximum enhancement of 18 %. The maximum heat removal capacity of the 167 % charged ATHP was lower than that of the 133 % charged ATHP and higher than that of the 100 % charged ATHP. Therefore, increasing the fill ratio can increase the entrainment limit of the annular thermosyphon and the effect of fill ratio on the entrainment limit must be considered as one of the parameters.
3.6. Prospect of Annular Thermosyphon in Nuclear Application
The maximum heat removal capacity of the ATHP simulating a hybrid control rod in APR1400 was 1300 W (87 kW/m2) for 1 m length. In a station blackout condition for APR1400, the decay heat after depletion of the steam generator inventory (loss of coolability through secondary system) is 45 MW, corresponding to about 1 % of full power [32]. To remove all the decay heat generated from the active core after loss of coolability by the steam generator, the 756 hybrid control rods must have heat removal capacities higher than 196 kW/m2. The observed maximum heat removal capacity of the hybrid control rod in this study is about 50 % lower than the required capacity for the total decay heat removal in SBO condition. A passive in-core cooling system based on hybrid control rods can 11
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remove 20 MW in the present geometry, assuming the temperature at the heat sink remains constant. The insertion of an additional 20 MW cooling capacity through hybrid control rods will delay the time to reach the core uncovery and fuel melting temperature. Twice enhanced heat removal capacity of hybrid control rods would suffice to totally remove the decay heat in a SBO accident. The strategy to enhance the heat removal rate of hybrid control rods can be summarized as follows: (1) Pressurization the interior of the hybrid control rods to use the high Merit number of working fluid (2) Increase the working fluid fill ratio or change to a different working fluid such as liquid metal or a nanofluid (3) Extension of the cross-sectional area for vapor flow by reducing the diameter of the neutron absorber material (it is possible to maintain neutron absorption capacity of the existing control rod by enrichment of the 10B isotope which is the main neutron absorbing element in the B4C pellet)
4. Conclusions The hybrid control rod was suggested as a component of passive in-core cooling system (PINCs) that can remove the decay heat generated by the active core in a commercial pressurized water reactor without external power sources. Experiments were conducted to determine the effects of the working fluid fill ratio and the cross-sectional area of the vapor path on the heat removal capacity and thermal performance of an annular thermosyphon that simulates a hybrid control rod. The following observations were made: (1) The effect of the working fluid fill ratio on the thermal resistance and heat transfer coefficients was negligible. (2) The annular thermosyphon showed a lower evaporator thermal resistance compared to a concentric thermosyphon because the increased water level enhanced the convection between the condenser and the adiabatic section. (3) The flooding limits of annular thermosyphons were lower than those of concentric thermosyphon because of the reduction of the cross-sectional area for vapor flow and the resulting increase of the shear at the vapor-liquid interface. (4) The flooding limit of an annular thermosyphon increases as the fill ratio increases, with an inflection point.
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(5) The existing correlation for predicting the flooding limit of thermosyphons could not reflect the geometry of the hybrid control rod whose wetted perimeter differs from its heated perimeter. (6) Significant heat removal capacity of hybrid control rods was observed and further studies will be conducted to enhance the heat removal rate of hybrid control rod.
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 (2013M2A8A1041442, 2013M2B2B1075734, 2013M2B2A4041473).
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[1] Reay DA, Kew PA, Heat Pipes (fifth edition), Butterworth-Heinemann, Oxford 2006. [2] Dunkel TL, Emergency heat removal system for a nuclear reactor, United States Patent 1976. [3] Mochizuki M, Nguyen T, Mashiko K, Saito Y, Singh R, Nguyen T, Wuttijumnong V, Prevention possibility of nuclear power reactor meltdown by use of heat pipes for passive cooling of spent fuel, Frontiers in Heat Pipes 2013. [4] Sviridenko I. I, Heat exchangers based on low temperature heat pipes for autonomous emergency WWER cooldown systems, Appl Therm Eng 2008; 28:327-334. [5] Gou PF, Saratoga, Fennern LE, Jose S, Sawyer CD, Gatos L, Nuclear reactor heat pipe, United States Patent 1997. [6] Hu G, Zhao S, Sun Z, Yao C, A heat pipe cooled modular reactor concept for manned lunar base application, Proceedings of 2013 21st Int Conference on Nucl Eng 2013; 2. [7] Poston D, Kapernick R, Dixon D, Reid E, Mason L, Reactor module design for a killowattclass space reactor power system, Nucl and Emerging Technol for Space 2012. [8] Hejzlar P, Todreas NE, Driscoll MJ, Passive decay heat removal in advanced LWR concepts, Nucl Eng and Design 1993;139: 59-81. [9] 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. [10] Savino R, Cecere A, Paola RC, Surface tension-driven flow in wickless heat pipes with selfrewetting fluids, Int. J. of Heat and Fluid Flow 2009;30:380-388 [11] Sato M, Abe Y, Urita Y, Paola RD, Cecere A, Savino R, Thermal performance of selfrewetting fluid heat pipe containing dilute solutions of polymer-capped silver nanoparticles synthesized by microwave-polyol process, Interdisciplinary Transport Phenomena VI 2009. [12] Kole M, Dey TK, Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids, Appl. Thermal Eng. 2013;50:763-770. [13] Septiadi WN, Putra N, Juarsa M, Putra IPA, Sahmura R, Characteristics of screen mesh wick heat pipe with nanofluid as passive cooling system, Atom Indonesia 2013;39:24-31. [14] Solomon AB, Ramachandran K, Pillai BC, Thermal performance of a heat pipe with nanoparticles coated wick, Appl. Thermal Eng. 2012;36:106-112. [15] Rosler S, Takuma M, Groll M, Maezawa S, Heat transfer limitation in a vertical annular closed two-phase thermosyphon with small fill rates, Heat Recovery System and CHP 1987;7:319-327 14
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[16] Vijra N. Singh TP, An experimental study of thermal performance of concentric annular heat pipe, American Int. J. Research in Sci, Tech, Eng, and Math 2015; 9:176-182 [17] Lin TF, Lin WT, Tsay YL, Wu JC, Experimental investigation of geyser boiling in an annular two-phase closed thermosyphon, Int. J. Heat Mass Transfer 1995;38:295-307 [18] Boo JH, Park SY, An experimental study on the thermal performance of a concentric annular heat pipe, J. Mech Sci and Tech 2005;19:1036-1043 [19] 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 [20] Nouri-Borujerdi A, Layeghi M, A review of concentric annular heat pipes, Heat Transfer Eng 2005;26:45-58 [21] Faghri A, Thomas S, Performance characteristics of a concentric annular heat pipe: Part IExperimental prediction and analysis of the capillary limit, J. Heat Transfer 1989;111:844-850 [22] Faghri A, Performance characteristics of a concentric annular heat pipe: Part II-Vapor flow analysis 1989;111:851-857 [23] Yoshida M, Imura H, Ippohshi S, Flow and heat transfer in a two-phase double-tube thermosyphon, Transaction of the Japan Society of Mechanical Engineers 1991;57:1428-1433 [24] Ismail OS, Adewoye GT, Analysis and modeling of laminar in pipes using numerical approach, J. of Software Eng. And Appl 2012;5:653-658 [25] Kline SJ and McClintock FA, Describing uncertainties in single sample experiments, Mechanical Eng 1953;75:3-8 [26] Faghri A, Heat pipe science and technology, Taylor and Francis, Washington 1995 [27] Kim KM, Bang IC, Effects of graphene oxide nanofluids on heat pipe performance and capillary limits, Int. J. Thermal Science 2016; 100:346-356 [28] Kim KM, Jeong YS, Kim IG, Bang IC, Comparison of thermal performances of water-filled, SiC nanofluid-filled and SiC nanoparticles-coated heat pipes, Int. J. Heat and Mass Transfer 2015;88:862-871 [29] Wallis G, One-dimensional two-phase flow, McGraw-Hill, New York 1969 [30] Kutateladze SS, Elements of hydrodynamics of gas-liquid systems, Fluid Mechanics-Soviet Research 1972;1:29-50 [31] Tien CL, Chung KS, Entrainment limits in heat pipes, Proc. 3 rd Int. Heat Pipe Conf 1978;3640 [32] 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
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Fig. 1. Systematic design of hybrid heat pipe as Passive IN-core Cooling system (PINCs) and hybrid heat pipe assembly.
Fig. 2. Composition of hybrid control rod.
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Fig. 3. Schematic diagram of heat pipe test facility.
Condenser (500 mm)
T 16
T 15
T 14
100 mm T 13
Evaporator (215 mm)
Adiabatic (285 mm)
T 12 T 11 T 10 T 9 T 8 T 7 T 6 T 5 T 4 T 3 T 2 T 1
50 mm
30 mm
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Fig. 4. Thermocouple locations on the test section.
Fig. 5. Wall temperature histories the test
(a)
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(b)
Fig. 6. Inner wall temperature distributions of concentric thermosyphon according to heat loads: (a) FR=50 %, (b) FR = 62.5 %.
(a)
19
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(b)
(c) Fig. 7. Inner wall temperature distributions of annular thermosyphon according to heat loads: (a) FR=100 %, (b) FR = 133 %, (c) FR = 167 %.
20
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(a)
(b)
Fig. 8. Axial variation of the liquid-vapor interface of thermosyphons: (a) concentric thermosyphon, (b) annular thermosyphon.
21
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(a)
(b)
Fig. 9. Variation of the pressure distributions and velocities of the vapor and liquid along the thermosyphon (a) Vapor and liquid pressures, (b) Vapor and liquid velocities [27].
AUTHOR: Two different versions of captions for Figures 9 were provided and the one in the main text caption have been used. Please check and confirm that it is correct.
22
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(a)
(b)
Fig. 10. Thermal resistances of each test section according to heat loads: (a) Evaporator thermal resistances, (b) Condenser thermal resistances.
23
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(a)
(b)
Fig. 11. Heat transfer coefficients of each test section according to heat loads: (a) Evaporation heat transfer coefficients, (b) Condensation heat transfer coefficients
24
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Fig. 12. Comparison of the entrainment limits according to fill ratio
25
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Table 1 A summary of the heat pipe experiment from the literatures. Researchers
Key concepts
Dunkel [2]
In-vessel heat pipe and Ex-vessel heat pipe cooling at LOCA
Mochizuki et al. [3]
Heat pipe decay heat removal system for spent fuel pool
Siviridenko [4]
Heat pipe decay heat removal system for WWER
Gou et al. [5]
Heat pipe system for heat transfer between RPV and steam supply system
Hu et al. [6]
Lithium and Potassium heat pipe for cooling system of nuclear fission reactor on Moon
Poston et al. [7]
High temperature heat pipe for small nuclear fission reactor of spaceship
Hejzlar et al. [8]
Sodium heat pipe for heat dissipation from vessel to earth
Table 2 Experimental conditions.
Length ratio [%]
215 : 285 : 500
Heat load [W]
25 – 1600
Initial pressure [kPa]
20
CTHP = 37.5, 50, 62.5 Fill ratio [%] ATHP = 100, 133, 167 %
26
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Table 3 Measurement uncertainties.
Parameters
Instruments
Uncertainties
Temperature
Thermocouple
± 0.1 oC
Pressure
Pressure gauge
± 0.1 kPa
Water flow rate
Turbine flowmeter
± 0.05 lpm
Voltage
Voltmeter
± 0.02 V
Current
Amperometry
± 4A
27
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S1359-4311(16)00032-6 http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.137 ATE 7555
To appear in:
Applied Thermal Engineering
Received date: Accepted date:
2-11-2015 31-12-2015
Please cite this article as: Kyung Mo Kim, In Cheol Bang, Comparison of flooding limit and thermal performance of annular and concentric thermosyphons at different fill ratios, Applied Thermal Engineering (2016), http://dx.doi.org/doi: 10.1016/j.applthermaleng.2015.12.137. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Comparison of Flooding Limit and Thermal Performance of Annular and Concentric Thermosyphons at Different Fill Ratios Kyung Mo Kim, In Cheol Bang* School of Mechanical and Nuclear Engineering, Ulsan National Institute of Science and Technology (UNIST), 50 UNIST-gil, Ulju-gun, Ulsan, 689-798, Republic of Korea
Highlights
Annular thermosyphon shows higher heat transfer compared to concentric thermosyphon. Annular thermosyphon requires new prediction model for flooding limit. Fill ratio of working fluid affects to the flooding limit of the annular thermosyphon.
Abstract
A passive in-core cooling system (PINCs) based on hybrid heat pipe can be adopted to enhance the passive safety of advanced nuclear power plants. A hybrid heat pipe is a heat transfer device that takes the dual roles of neutron absorption and heat removal by combining the functions of a heat pipe and a control rod. To observe the effect of neutron absorber material inside the heat pipe and fill ratio of the working fluid on the thermal performances of heat pipe including operation limit, an annular thermosyphon heat pipe (ATHP) that contains a neutron absorber inside a concentric thermosyphon heat pipe (CTHP) was experimentally studied in the condition of various fill ratios. The ATHP showed lower thermal resistances in the evaporator region with a maximum reduction of 20 % compared to those of a CTHP. In terms of the operational limits, the ATHP showed a lower entrainment limit than the CTHP due to a smaller cross-section for vapor path in the evaporator region, which resulted in high shear at the vapor-liquid interface. In addition, increasing the fill ratio enhanced the entrainment limit by 18 %.
*
Corresponding author : Tel.:+82-52-217-2915, Fax:+82-52-217-3008 E-mail: [email protected] (In Cheol Bang) 1
Page 1 of 27
Nomenclature [m2]
A
area
C
correlation coefficient
g
gravity
[m/s2]
h
latent heat
[kJ/kg]
K
Kutateladze number
L
length
m
correlation coefficient
Q
heat, power
[W]
q″
heat flux
[kW/m2]
r
radius
[m]
R
thermal resistance
[°C/W]
t
temperature difference between evaporator section and condenser section
T
temperature
[m]
[°C]
[°C]
Greek symbols ρ
density
[kg/m3]
σ
surface tension
[N/m]
Subscript avg
average
c
condenser
e
evaporator
l
liquid
lv
liquid to vapor
max
maximum
sat
saturation
v
vapor
Keywords
Hybrid control rod; Flooding limit; Annular thermosyphon; Heat pipe; Thermal resistance 2
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1. Introduction
Passive decay heat removal systems in nuclear power plants have been developed after Fukushima and Three Mile Island (TMI) accidents. However, most passive decay heat removal systems require certain signals or operation conditions for their operation, and it is possible for these to fail. Also, established emergency core cooling systems cannot operate properly due to the difficulty of depressurization in a station blackout (SBO) condition. Therefore, a new concept of passive decay heat removal system that does not require any signals or conditions to mitigate SBO accident is required. In this research, a passive in-core cooling system (PINCs) based on a hybrid control rod is suggested. A heat pipe is a device that transfers heat from the hot interface to the cold one by phase change and convection of working fluid. Heat pipes have a variety of advantages, such as high heat removal rate per unit volume, a fully passive working principle, and easy applicability [1]. Therefore, heat pipes have been used in various thermal engineering fields such as computer CPUs, spaceship nuclear reactors, and the Trans-Alaska Pipeline system. The inclusion of a neutron absorber material in the heat pipe enables it to take the roles of reactor shutdown and heat removal simultaneously. In other words, the limited heat removal capacity in an accident can be extended through the insertion of hybrid control rods into the active core. The operation of a hybrid control rod is driven by the temperature difference between the heat sink and the active core of the reactor pressure vessel (RPV), as shown in Figure 1. The existing control rods are held by a spider grid which is connected to the control rod drive mechanism (CRDM). However, hybrid heat pipes must extend from the active core to the heat sink to facilitate heat transport. Also, more passages which hybrid heat pipes can move along the axial direction at the upper head of RPV must be retained. The scheme of hybrid heat pipes is also shown in Figure 1.
Various concepts for applying heat pipes in nuclear power plants have been studied. Table 1 presents previous studies on application of heat pipes to nuclear power plants. Dunkel et al. [2] devised in-vessel and ex-vessel decay heat removal systems using heat pipes under a loss of coolant accident (LOCA) condition. The in-vessel cooling system used heat pipes to control rod channels and the ex-vessel cooling system used heat pipes installed on the ex-vessel wall. Mochizuki et al. [3] suggested a spent fuel pool cooling system using heat pipes. They confirmed the applicability of the system in terms of economics and heat removal by predicting the temperature change of the spent fuel pool at various conditions. Sviridenko [4] suggested a passive decay heat removal system using heat pipes on WWER. Various system designs have been proposed in his work. Gou et al. [5] proposed the heat pipe as a heat transfer device between 3
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the reactor vessel and the nuclear steam supply system for the purpose of simplifying the system. They showed that alkali metal heat pipes for cooling spaceship nuclear reactors had a significant heat transfer capacity. However, all previous studies were limited to the introduction of heat pipe-driven concepts and prediction of their system effects without validation. Also, most previous studies on heat pipes were limited in the measurement of effects of various parameters such as the fill ratio of the working fluid, the inclination angle, the type of working fluid on the thermal performance of concentric heat pipes in terms of thermal resistance and the heat transfer coefficient [9-14]. Mozumder et al. [9] studied about the effect of fill ratios and inclination angle on the thermal resistances of heat pipes. Several studies [10, 11] attempted to enhance the thermal performance of heat pipe using self-rewetting fluids. Other researches [12-14] investigated the heat transfer characteristics of heat pipe according to working fluids using various nanofluids. In the present study, the hybrid control rod which plays the dual roles of neutron absorber and decay heat removal device, is newly considered and studied in terms of feasibility. The maximum heat transfer capacity of a general heat pipe can be calculated with known correlations and physical models. However, the hybrid control rod contains a neutron absorber inside the heat pipe, which introduces a difference between wetted perimeter and heated perimeter because the neutron absorber material is adiabatic medium. Although the thermal performance of annular vapor-path heat pipes has been studied, most studies have not considered geometries where the wetted perimeter is different from the heated perimeter. Rosler et al. [15] experimentally observed the maximum heat removal rate for a vertical annular closed two-phase thermosyphon with low fill ratios of 3 – 30 %. R113 was used, and flow patterns according to heat loads were observed. They suggested a dry-out model for thermosyphons operating at low fill ratios, deriving the model theoretically and validating it with experimental results. Vijra et al. [16] studied the thermal performance of concentric annular heat pipe in which the wetted and heated perimeters were the same at various heat loads and inclination angles. The vertical annular heat pipe showed the lowest thermal resistance because it has the largest heat transfer area and effective gravity-assisted convection. Lin et al. [17] conducted experiments to observe the effect of fill ratio, condenser temperature, and evaporator length on geyser boiling in an annular thermosyphon. They observed that the period of geyser boiling depends on the parameters and proposed a correlation for the heat transfer coefficient of annular thermosyphons. Boo et al. [18] investigated the thermal characteristics of concentric annular heat pipes as a function of the diameter ratio between the inner and outer tubes and the fill ratio of working fluid. The effect of fill ratio on the thermal resistance increased as the diameter ratio increased. They also observed that the maximum heat 4
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removal capacity improved as the fill ratio increased. Faghri et al. [19] studied the flooding limit and heat transfer coefficients in concentric annular thermosyphons. The established correlations had provided accurate prediction in the low Reynolds number regime, but a new correlation was required for the high Reynolds number regime. Thermosyphons using water also showed significantly different experimental results compared to model predictions. Thus, they suggested a new correlation based on their experimental results and concluded the correlation must be validated with more experimental data. Other researchers [20-24] analyzed the thermal performance of annular thermosyphons and annular heat pipes according to various parameters. However, they did not address the relationship between the flooding limit and the fill ratios. The vapor path areas in these studies were the same along the evaporator, adiabatic, and condenser sections. Hence, the effect of the presence of the neutron absorber in only the evaporator section on the thermal performance was investigated experimentally. The decay heat removal capacity of the PINCs will be determined by the maximum heat removal capacity of the thermosyphon. The main operating limitation for the thermosyphon is entrainment phenomena that arise from the countercurrent flow of vapor and liquid. Thus, the enhancement of the entrainment limit is one of the main subjects in the field of heat pipe engineering. If the total volume of the thermosyphon was charged with working fluid, the maximum heat transfer rate would be the critical heat flux in pool boiling. However, the phase change would be suppressed and the heat transfer coefficient would be low. Thus, the optimum fill ratio for achieving a high heat transfer coefficient and maximizing heat removal capacity was studied.
2. Experiment
2.1. Test section
A hybrid control rod was prepared based on information on established control rods in the commercial pressurized water reactor, APR-1400. Stainless steel 316L test sections having 25.4 mm outer diameter and 22 mm inner diameter with length of 1000 mm were prepared. The test sections were charged with the working fluid at various fill ratios (volume ratio of working fluid to evaporator volume). A B4C pellet, which is a neutron absorber material, was then inserted in the center of the heat pipe as shown in figure 2. The B4C pellet has an outer diameter of 18.7 mm and a length of 215 mm. Its surface was treated to be smooth, suppressing the effect of the pellet on the liquid flow through the test section. 5
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2.2. Experimental Setup and Procedures
Figure 3 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 heat the test section by passing current. As shown in figure 4, 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), six Ttype TCs were installed on the wall of the condenser section, and at the inlet and outlet of the water jacket to record the temperature distribution at a given condition. Table 2 presents the experimental conditions. The experimental procedure was as follows. First, the test section was evacuated using the vacuum pump to a pressure of 20 kPa, to remove noncondensable gases. Water was then passed through the water jacket at a mass flow rate of 0.15 kg/s. The test section was then charged with the working fluid at various fill ratios (volume ratio of the working fluid to the evaporator volume). The test sections were heated gradually until a steady state was attained.
2.3. Uncertainty Analysis
The uncertainties in the parameter measurements were analyzed. Table 3 presents the measurement errors in the instruments. The uncertainties of the parameters were calculated by Kline and McClintock method [25]. From this, the measurement uncertainties in the heat flux, heat transfer coefficient, and thermal resistance were calculated as follows:
where
is the derived parameter,
n
1
i 1
xi
xi x i
2
is the measured variables,
(1)
xi
is the error of the measured
variables. The tolerances in the length and diameter of the test section were 5 mm and 1 mm. Hence, 6
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the calculated maximum uncertainty in the heat flux is 7.2%. The maximum uncertainties in the heat transfer coefficient and thermal resistance were estimated to be 5.2% and 7.6%, respectively.
3. Results and Discussion
3.1. Temperature Evolution
The temperature evolution was measured as a function of time and heat load to determine the thermal performance of the heat pipes as shown in Fig. 5 (temperature evolution of ATHP FR=100% during experiment). Steady states were attained at increments of the heat loads. The variations of temperatures at all TCs were maintained within ±1 °C at each steady state. At the initial state, a heat load of 25 W was applied to the evaporator section for 1 h to achieve a saturation temperature of 60 °C inside the heat pipe. The coolant was circulated through the water jacket when the temperatures at the evaporator and adiabatic sections reached 60 °C, and the heat load was then increased gradually. The heat loss (the ratio between the heat removal rate through the water jacket and the heat load applied in the evaporator section) was less than 10 % for each heat load. The coolant injection rate was constant for all time steps for the purpose of maintaining the same condensation condition. The wall temperatures of the condenser section were maintained at approximately 24 °C at relatively low heat fluxes; however, the wall temperatures at the bottom of the condenser section slightly increased as the heat load increased, because the amount of vapor from the evaporator section that reached the condenser section increased. At a certain heat load, the wall temperature suddenly increased because the condensed liquid could not return to the evaporator section, as a result of the countercurrent flow between vapor (opposite to gravity) and liquid (direction of gravity) reaching the flooding limit or entrainment limit. ATHPs showed flooding limits at a heat load of 1100 – 1300 W, while no flooding limit was observed in CTHPs.
3.2. Temperature Distributions in Heat Pipes
Figures 6 and 7 show the wall temperature distributions along the axial direction at steady states for the concentric and annular thermosyphons according to fill ratios. As shown in the figures, similar temperature distributions are observed until the entrainment limit is reached for each type of thermosyphon. The fill ratios of the CTHPs (50 % and 62.5 %) are less than 100 % which means under-filled condition. The liquid film thickness along the axial 7
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location would be similar at steady state with different heights of water pools. However, the difference between heights of water pools is small because the difference in fill ratios is relatively small. As a result, the similar temperature distributions of the CTHPs are observed. Operation of the concentric thermosyphon charged with 30 mL (fill ratio=37.5 %) was not achieved because a stable liquid film could not be formed along the wall of the evaporator section. However, the annular thermosyphon charged with 30 mL (FR = 100 %) showed stable operation up to the entrainment limit. Figure 8 shows the vapor and liquid distributions in the concentric and annular thermosyphons at the same fill ratio. The annular thermosyphon shows lower wall temperature distributions than the concentric thermosyphon because the water level reaches the adiabatic section due to volume expansion and relatively large fill ratios despite the amount of working fluid being the same. If the fill ratio is higher than 1.0, the thermosyphon would operate in the pool boiling regime because the adiabatic section does not contain a heat source. Thus, the annular thermosyphon which has a smaller evaporator volume is more favorable than a concentric thermosyphon at low fill ratios in terms of stable heat transfer. The heat transfer rate between the adiabatic section and the condenser section would be higher in the ATHP than in the CTHP due to the higher working fluid level at steady state. As a result, the working fluid temperatures in the adiabatic and evaporator sections of the ATHP were lower than in the CTHP at high heat flux values. Vapor and liquid velocities inside the thermosyphon were derived by numerical analysis based on governing equations [26]. The conventional vapor and liquid pressures along the axial location of the thermosyphon at moderate vapor temperature range are shown in Figure 9(a) [26, 27]. Vapor pressure drop could be caused by the inertial term and viscous friction at the interface of the liquid and vapor flows. Figure 9(b) shows the liquid and vapor velocities as a function of the axial position [26]. As shown in Figure 9, the largest interfacial velocity between the vapor and liquid flows would be observed at the top of the evaporator section. As a result, the flow resistance at the top of the evaporator section would be relatively high compared to other locations, and the temperature being highest at the top of the evaporator section for both thermosyphons.
3.3. Thermal Resistances of Heat Pipes
The evaporator and condenser thermal resistances (Re, and Rc) for the test sections at the different operating conditions were calculated using the following equations based on the measured wall temperature distributions [28]: 8
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Re
Rc
T
e
T sat
(2)
Qe
T
sat
Tc
(3)
Qc
The internal pressures of the test sections were measured for each heat load in this study to use the precise saturation temperature in the thermal resistance calculation. The saturation temperatures were validated with the wall temperature of the adiabatic section. Figure 10 shows the dependence of the thermal resistances of the thermosyphons on the heat loads. The condenser thermal resistances were the same for all types of test section. The condenser and evaporator thermal resistances decrease as the heat load increases because the area covered by liquid film increases with the reduction of liquid film thickness. The annular thermosyphon showed a lower evaporator resistance than the concentric heat pipe because the wall temperature distributions of the ATHPs were lower than those of the CTHPs, as shown in Figures 6 and 7. The higher working fluid level for the annular thermosyphon results in natural convection between the adiabatic section and the condenser section which improves the heat transfer between those parts. Hence, the total wall temperature profile of the ATHPs will be flattened and lowered compared to that of the CTHPs. This temperature distribution induces a lower evaporator thermal resistance despite the saturation temperatures at the same heat loads being equal. The effects of the fill ratio on the thermal resistances are negligible for each test section as shown in Figure 10. At heat loads larger than 300 W, the evaporator thermal resistances decrease sharply, which indicates the onset of nucleate boiling. The limitations of thermosyphons are known to be the sonic, viscous, boiling, and entrainment limits. However, the phenomena including bubble formation and growth would not prevent the returning of liquid from the condenser section to the evaporator section in the thermosyphon. Above a certain heat load, the bubble departure frequency will increase with liquid supply to the heater surface. Thus, the onset of nucleate boiling cannot be considered a boiling limit.
3.4. Heat Transfer Coefficients of Heat Pipes
The evaporation and condensation heat transfer coefficients (he and hc) were calculated from the temperature distributions using the following equations [28]:
9
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he
hc
q e
T
e
T sat
(4)
(5)
q c
T
sat
Tc
As shown in Figure 11, the annular thermosyphon showed higher evaporation heat transfer coefficients (4200–6750 W/m2·K) compared with those of the concentric thermosyphon (3500–6500 W/m2·K), with a maximum enhancement of 20%. Also, the heat transfer coefficients increase above 400 W, which demonstrates the onset of boiling. The annular thermosyphon had condensation heat transfer coefficients similar to those of the concentric thermosyphon (100–1300 W/m2·K), because the difference of the liquid film thickness between the annular and concentric thermosyphons should be small in steady state operation at the condenser section.
3.5. Entrainment Limits of Heat Pipes
The flooding limit is the most common concern for long thermosyphon with large fill ratios, large axial heat fluxes, and small radial heat fluxes. The large vapor velocities induced by high axial heat fluxes result in high values of interfacial shear, which produce instability of the liquid film. The high shear at the vapor-liquid interface prevents the condensate from returning to the evaporator and leads to a flooding condition at the top of the evaporator section. The blocked supply of liquid causes a partial dryout of the evaporator, which gives rise to wall temperature excursions. There are two major fundamental semi-empirical correlations for predicting the flooding limit; Wallis correlation [29] and Kutateladze two-phase flow instability criterion [30]. The first is characterized by a balance between the inertial and hydrostatic forces, while the second balances the inertial, buoyant, and surface tension forces. However, the Wallis correlation does not consider the surface tension and Kutateladze criterion does not take into account the diameter effect on countercurrent flow. So, Tien and Chung [31] combined the Kutateladze and Wallis correlations in order to address the effects of the pipe diameter and the surface tension on the limiting conditions. The correlation showed good agreement with data sets for several working fluids, but not for water. Faghri et al. [19] improved the existing semi-empirical correlations to predict the flooding limit of the thermosyphon and the predicted limit mached to the existing experimental results well. Thus, Tien and Chung’s, and Faghri’s correlations were selected as models to predict the entrainment limit for an annular 10
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thermosyphon. The hydraulic diameter of the ATHP was substituted into the correlations to determine the prediction performance of these correlations for an annular thermosyphon whose wetted perimeter is different from its heated perimeter.
Q T ie n & C h u n g C k h lv A v [ g ( l v )] 2
1/ 2
Q F a g h r i K h lv A v [ g ( l v )] 1/ 2
1/ 4
1/ 4
1 m v l
1 m v l
1/ 4
1/ 4
2
(6)
2
(7)
The effect of fill ratio on the operation limit of the thermosyphon has not been considered in most correlations. Thus, the equal flooding limit is predicted at various fill ratios, as shown in Figure 12. The amount of working fluid is one of the important parameters for determining the operation limit because when the total volume of the thermosyphon is occupied by working fluid, the result would be the critical heat flux in pool boiling condition. The observed flooding limit was 30 - 50 % higher than the predicted values (844 and 851 W) because of heat transfer between the B4C pellet and the working fluid, and effect of fill ratio were not considered. The 133 % charged ATHP showed the highest entrainment limit. As the fill ratio increases the flooding limit increased, with a maximum enhancement of 18 %. The maximum heat removal capacity of the 167 % charged ATHP was lower than that of the 133 % charged ATHP and higher than that of the 100 % charged ATHP. Therefore, increasing the fill ratio can increase the entrainment limit of the annular thermosyphon and the effect of fill ratio on the entrainment limit must be considered as one of the parameters.
3.6. Prospect of Annular Thermosyphon in Nuclear Application
The maximum heat removal capacity of the ATHP simulating a hybrid control rod in APR1400 was 1300 W (87 kW/m2) for 1 m length. In a station blackout condition for APR1400, the decay heat after depletion of the steam generator inventory (loss of coolability through secondary system) is 45 MW, corresponding to about 1 % of full power [32]. To remove all the decay heat generated from the active core after loss of coolability by the steam generator, the 756 hybrid control rods must have heat removal capacities higher than 196 kW/m2. The observed maximum heat removal capacity of the hybrid control rod in this study is about 50 % lower than the required capacity for the total decay heat removal in SBO condition. A passive in-core cooling system based on hybrid control rods can 11
Page 11 of 27
remove 20 MW in the present geometry, assuming the temperature at the heat sink remains constant. The insertion of an additional 20 MW cooling capacity through hybrid control rods will delay the time to reach the core uncovery and fuel melting temperature. Twice enhanced heat removal capacity of hybrid control rods would suffice to totally remove the decay heat in a SBO accident. The strategy to enhance the heat removal rate of hybrid control rods can be summarized as follows: (1) Pressurization the interior of the hybrid control rods to use the high Merit number of working fluid (2) Increase the working fluid fill ratio or change to a different working fluid such as liquid metal or a nanofluid (3) Extension of the cross-sectional area for vapor flow by reducing the diameter of the neutron absorber material (it is possible to maintain neutron absorption capacity of the existing control rod by enrichment of the 10B isotope which is the main neutron absorbing element in the B4C pellet)
4. Conclusions The hybrid control rod was suggested as a component of passive in-core cooling system (PINCs) that can remove the decay heat generated by the active core in a commercial pressurized water reactor without external power sources. Experiments were conducted to determine the effects of the working fluid fill ratio and the cross-sectional area of the vapor path on the heat removal capacity and thermal performance of an annular thermosyphon that simulates a hybrid control rod. The following observations were made: (1) The effect of the working fluid fill ratio on the thermal resistance and heat transfer coefficients was negligible. (2) The annular thermosyphon showed a lower evaporator thermal resistance compared to a concentric thermosyphon because the increased water level enhanced the convection between the condenser and the adiabatic section. (3) The flooding limits of annular thermosyphons were lower than those of concentric thermosyphon because of the reduction of the cross-sectional area for vapor flow and the resulting increase of the shear at the vapor-liquid interface. (4) The flooding limit of an annular thermosyphon increases as the fill ratio increases, with an inflection point.
12
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(5) The existing correlation for predicting the flooding limit of thermosyphons could not reflect the geometry of the hybrid control rod whose wetted perimeter differs from its heated perimeter. (6) Significant heat removal capacity of hybrid control rods was observed and further studies will be conducted to enhance the heat removal rate of hybrid control rod.
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 (2013M2A8A1041442, 2013M2B2B1075734, 2013M2B2A4041473).
13
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[1] Reay DA, Kew PA, Heat Pipes (fifth edition), Butterworth-Heinemann, Oxford 2006. [2] Dunkel TL, Emergency heat removal system for a nuclear reactor, United States Patent 1976. [3] Mochizuki M, Nguyen T, Mashiko K, Saito Y, Singh R, Nguyen T, Wuttijumnong V, Prevention possibility of nuclear power reactor meltdown by use of heat pipes for passive cooling of spent fuel, Frontiers in Heat Pipes 2013. [4] Sviridenko I. I, Heat exchangers based on low temperature heat pipes for autonomous emergency WWER cooldown systems, Appl Therm Eng 2008; 28:327-334. [5] Gou PF, Saratoga, Fennern LE, Jose S, Sawyer CD, Gatos L, Nuclear reactor heat pipe, United States Patent 1997. [6] Hu G, Zhao S, Sun Z, Yao C, A heat pipe cooled modular reactor concept for manned lunar base application, Proceedings of 2013 21st Int Conference on Nucl Eng 2013; 2. [7] Poston D, Kapernick R, Dixon D, Reid E, Mason L, Reactor module design for a killowattclass space reactor power system, Nucl and Emerging Technol for Space 2012. [8] Hejzlar P, Todreas NE, Driscoll MJ, Passive decay heat removal in advanced LWR concepts, Nucl Eng and Design 1993;139: 59-81. [9] 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. [10] Savino R, Cecere A, Paola RC, Surface tension-driven flow in wickless heat pipes with selfrewetting fluids, Int. J. of Heat and Fluid Flow 2009;30:380-388 [11] Sato M, Abe Y, Urita Y, Paola RD, Cecere A, Savino R, Thermal performance of selfrewetting fluid heat pipe containing dilute solutions of polymer-capped silver nanoparticles synthesized by microwave-polyol process, Interdisciplinary Transport Phenomena VI 2009. [12] Kole M, Dey TK, Thermal performance of screen mesh wick heat pipes using water-based copper nanofluids, Appl. Thermal Eng. 2013;50:763-770. [13] Septiadi WN, Putra N, Juarsa M, Putra IPA, Sahmura R, Characteristics of screen mesh wick heat pipe with nanofluid as passive cooling system, Atom Indonesia 2013;39:24-31. [14] Solomon AB, Ramachandran K, Pillai BC, Thermal performance of a heat pipe with nanoparticles coated wick, Appl. Thermal Eng. 2012;36:106-112. [15] Rosler S, Takuma M, Groll M, Maezawa S, Heat transfer limitation in a vertical annular closed two-phase thermosyphon with small fill rates, Heat Recovery System and CHP 1987;7:319-327 14
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[16] Vijra N. Singh TP, An experimental study of thermal performance of concentric annular heat pipe, American Int. J. Research in Sci, Tech, Eng, and Math 2015; 9:176-182 [17] Lin TF, Lin WT, Tsay YL, Wu JC, Experimental investigation of geyser boiling in an annular two-phase closed thermosyphon, Int. J. Heat Mass Transfer 1995;38:295-307 [18] Boo JH, Park SY, An experimental study on the thermal performance of a concentric annular heat pipe, J. Mech Sci and Tech 2005;19:1036-1043 [19] 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 [20] Nouri-Borujerdi A, Layeghi M, A review of concentric annular heat pipes, Heat Transfer Eng 2005;26:45-58 [21] Faghri A, Thomas S, Performance characteristics of a concentric annular heat pipe: Part IExperimental prediction and analysis of the capillary limit, J. Heat Transfer 1989;111:844-850 [22] Faghri A, Performance characteristics of a concentric annular heat pipe: Part II-Vapor flow analysis 1989;111:851-857 [23] Yoshida M, Imura H, Ippohshi S, Flow and heat transfer in a two-phase double-tube thermosyphon, Transaction of the Japan Society of Mechanical Engineers 1991;57:1428-1433 [24] Ismail OS, Adewoye GT, Analysis and modeling of laminar in pipes using numerical approach, J. of Software Eng. And Appl 2012;5:653-658 [25] Kline SJ and McClintock FA, Describing uncertainties in single sample experiments, Mechanical Eng 1953;75:3-8 [26] Faghri A, Heat pipe science and technology, Taylor and Francis, Washington 1995 [27] Kim KM, Bang IC, Effects of graphene oxide nanofluids on heat pipe performance and capillary limits, Int. J. Thermal Science 2016; 100:346-356 [28] Kim KM, Jeong YS, Kim IG, Bang IC, Comparison of thermal performances of water-filled, SiC nanofluid-filled and SiC nanoparticles-coated heat pipes, Int. J. Heat and Mass Transfer 2015;88:862-871 [29] Wallis G, One-dimensional two-phase flow, McGraw-Hill, New York 1969 [30] Kutateladze SS, Elements of hydrodynamics of gas-liquid systems, Fluid Mechanics-Soviet Research 1972;1:29-50 [31] Tien CL, Chung KS, Entrainment limits in heat pipes, Proc. 3 rd Int. Heat Pipe Conf 1978;3640 [32] 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
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Fig. 1. Systematic design of hybrid heat pipe as Passive IN-core Cooling system (PINCs) and hybrid heat pipe assembly.
Fig. 2. Composition of hybrid control rod.
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Fig. 3. Schematic diagram of heat pipe test facility.
Condenser (500 mm)
T 16
T 15
T 14
100 mm T 13
Evaporator (215 mm)
Adiabatic (285 mm)
T 12 T 11 T 10 T 9 T 8 T 7 T 6 T 5 T 4 T 3 T 2 T 1
50 mm
30 mm
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Fig. 4. Thermocouple locations on the test section.
Fig. 5. Wall temperature histories the test
(a)
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(b)
Fig. 6. Inner wall temperature distributions of concentric thermosyphon according to heat loads: (a) FR=50 %, (b) FR = 62.5 %.
(a)
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(b)
(c) Fig. 7. Inner wall temperature distributions of annular thermosyphon according to heat loads: (a) FR=100 %, (b) FR = 133 %, (c) FR = 167 %.
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(a)
(b)
Fig. 8. Axial variation of the liquid-vapor interface of thermosyphons: (a) concentric thermosyphon, (b) annular thermosyphon.
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(a)
(b)
Fig. 9. Variation of the pressure distributions and velocities of the vapor and liquid along the thermosyphon (a) Vapor and liquid pressures, (b) Vapor and liquid velocities [27].
AUTHOR: Two different versions of captions for Figures 9 were provided and the one in the main text caption have been used. Please check and confirm that it is correct.
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(a)
(b)
Fig. 10. Thermal resistances of each test section according to heat loads: (a) Evaporator thermal resistances, (b) Condenser thermal resistances.
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(a)
(b)
Fig. 11. Heat transfer coefficients of each test section according to heat loads: (a) Evaporation heat transfer coefficients, (b) Condensation heat transfer coefficients
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Fig. 12. Comparison of the entrainment limits according to fill ratio
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Table 1 A summary of the heat pipe experiment from the literatures. Researchers
Key concepts
Dunkel [2]
In-vessel heat pipe and Ex-vessel heat pipe cooling at LOCA
Mochizuki et al. [3]
Heat pipe decay heat removal system for spent fuel pool
Siviridenko [4]
Heat pipe decay heat removal system for WWER
Gou et al. [5]
Heat pipe system for heat transfer between RPV and steam supply system
Hu et al. [6]
Lithium and Potassium heat pipe for cooling system of nuclear fission reactor on Moon
Poston et al. [7]
High temperature heat pipe for small nuclear fission reactor of spaceship
Hejzlar et al. [8]
Sodium heat pipe for heat dissipation from vessel to earth
Table 2 Experimental conditions.
Length ratio [%]
215 : 285 : 500
Heat load [W]
25 – 1600
Initial pressure [kPa]
20
CTHP = 37.5, 50, 62.5 Fill ratio [%] ATHP = 100, 133, 167 %
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Table 3 Measurement uncertainties.
Parameters
Instruments
Uncertainties
Temperature
Thermocouple
± 0.1 oC
Pressure
Pressure gauge
± 0.1 kPa
Water flow rate
Turbine flowmeter
± 0.05 lpm
Voltage
Voltmeter
± 0.02 V
Current
Amperometry
± 4A
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