Experimental investigation on boiling heat transfer of high pressure water in a SCWR sub-channel

International Journal of Heat and Mass Transfer 105 (2017) 799–810

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Experimental investigation on boiling heat transfer of high pressure water in a SCWR sub-channel Han Wang a, Weishu Wang b,⇑, Qincheng Bi c a

School of Nuclear Science and Engineering, North China Electric Power University, Beijing 102206, PR China North China University of Water Resources and Electric Power, Zhengzhou 450011, PR China c State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, PR China b

a r t i c l e

i n f o

Article history: Received 23 June 2016 Received in revised form 28 September 2016 Accepted 28 September 2016

Keywords: Heat transfer High pressure water SCWR sub-channel DNB Heat transfer correlation

a b s t r a c t An experiment has recently been completed to obtain the wall temperature and heat transfer coefficient of water at subcritical pressures in a SCWR sub-channel. The test section was wire-electrode cut to simulate the central sub-channel of a 2
2 rod bundle. Experimental parameters covered the pressures of 11–19 MPa, mass fluxes of 700–1300 kg/m2s and heat fluxes of 200–600 kW/m2. Heat transfer characteristics in single-phase and two-phase regions were analyzed with respect to the variations of heat flux, system pressure and mass flux. For a given pressure, it was found that the wall temperature increases with increasing heat flux or decreasing mass flux in the steam-water two-phase region. Departure from Nucleate Boiling (DNB) was observed from the wall temperature profiles in the sub-channel. Experimental results showed that the soaring wall temperature at DNB becomes dramatic with the increase of pressure. Correlation assessments have also been conducted against the current set of experimental data. The comparisons indicated that the Fang correlation agrees well against the two-phase heat transfer coefficient. Heat transfer difference in the sub-channel at subcritical and supercritical pressures was compared. It was concluded that the wall temperature at sub-critical pressure may be lower or higher than that of supercritical pressure depending on q/G ratio and the occurrence of DNB. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Two-phase flow boiling heat transfer of water has been widelyapplied in industry, such as compact heat exchangers, reactor core of Boiling Water-cooled Reactor (BWR), steam generator, furnace of fossil-fired power plant etc. The critical pressure of water is 22.115 MPa, below which boiling occurs if the bulk temperature reaches the saturated temperature for a given pressure. It is recognized that two types of heat transfer deterioration, Departure from Nucleate Boiling (DNB) and Dryout, exist at subcritical pressure. DNB usually occurs at low steam-quality and high heat-flux conditions when the heat transfer transforms from nucleate boiling to film boiling, causing a rapid rise in wall temperature. Dryout occurs at high steam-quality conditions when the flow pattern transforms from an annular flow to a mist flow. The adherent liquid film is torn or evaporated due to acceleration of the core steam, which leads to heat transfer deterioration [1]. In recent years, the R&D of Supercritical Water-cooled Reactor (SCWR) becomes a hot point under the Generation-IV International ⇑ Corresponding author. E-mail address: [email protected] (W. Wang). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2016.09.088 0017-9310/Ó 2016 Elsevier Ltd. All rights reserved.

Forum [2]. SCWR is a once-through water-cooled reactor operating at a pressure of 25 MPa, which reduces the capital and operational costs by eliminating the steam generator or steam-water separator in Light Water-cooled Reactors (LWRs) [3,4]. In addition, SCWR provides a thermal efficiency of about 45% which is higher than the 33% efficiency for the current LWRs [5]. Although SCWR operates at supercritical pressure, the reactor core is in subcritical pressure region during the load up and shutdown processes or in accidents [6]. At subcritical pressures, deteriorated heat transfer of DNB causes a sudden rise in cladding temperature. The issue is more complicated in SCWR where tight rod bundle (gap of 1.44 mm) was introduced in the conceptual design. These tight rod bundles may affect the thermal boundary development and the heat transfer to the coolant. Therefore, an improved understanding of heat transfer characteristics at relevant conditions is necessary for the design of SCWR core. It is the purpose of our ongoing research to experimentally investigate the flow boiling heat transfer of water in a SCWR sub-channel. The experiments of flow boiling heat transfer in tubes have been performed by many researchers since the 1960s. Swenson et al. [7] investigated the heat transfer of water in smooth tube and internally-ribbed tube for vertical upward flow. It was found

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Nomenclature cp d G h H Hfg K L Nu P Pr q Q Re t x

specific heat [J/kgK] hydraulic diameter [mm] mass flux [kg/m2s] heat transfer coefficient [kW/m2K] enthalpy [kJ/kg] latent heat of vaporization [kJ/kg] temperature [K] length of the test section [m] Nusselt number [–] pressure [MPa] Prandtl number [–] heat flux [kW/m2] mass flow rate [kg/s] Reynolds number [–] temperature [°C] equilibrium steam quality [–]

that heat transfer deterioration occurred at a small steam quality of 0.03 in the smooth tube, while no remarkable wall temperature increase was observed in the internally-ribbed tube until the steam-quality reaches 0.9. The internally-ribbed tube postpones the occurrence of DNB to high steam quality compared to the smooth tube. Marek et al. [8] conducted an early experimental investigation on heat transfer and pressure drop in 3
3 and 4
4 rod bundles. Circumferential temperature distribution along the heater was obtained. In analogy with the pressure drop, a new correlation was deprived to predict the Nusselt number in rod bundles. Li and Hahne [9] experimentally research the boiling heat transfer on finned tub bundle with the working media of R11. They found that boiling heat transfer is strongly enhanced by the twophase flow induced by the tubes, especially in the intermediate region between natural convection and fully developed boiling. Qu and Mudawar [10] investigated the flow boiling heat transfer of water in two-phase micro-channels. Experimental results showed that the boiling heat transfer coefficient is a strong function of mass flux, but only a weak function of heat flux. Eleven heat transfer correlations were assessed against the test data. Comparisons signified that none of the correlations gives satisfying predictions on two-phase heat transfer coefficient. Kumamaru et al. [11] and Koizumi et al. [12] from Japan Atomic Energy Research Institute performed a set of post-dryout heat transfer experiments with steam-water two-phase flow in a 5
5 rod bundle. Several heat transfer correlations were compared with the experimental data, which showed that the performance of classical empirical correlations in predicting heat transfer coefficient relates to the flow conditions. A new correlation was proposed by improving the Groeneveld correlation [13]. Anghel and Anglart [14] also experimentally studied the post-dryout heat transfer of high-pressure water in vertical tube and annuli. It was found that the flow obstacles affect the onset of dryout and post-dryout significantly. Predicted heat transfer coefficients by eight correlations are highly deviated from the test data due to the introduction of the flow obstacles. Over the past twenty years, researchers of Chen et al. [15], Pan et al. [16], Wang et al. [17] and Shen et al. [18] from the State Key Laboratory of Multiphase Flow in Power Engineering at Xi’an Jiaotong University performed a series of steam-water two-phase heat-transfer experiments at subcritical pressures and accumulated a huge number of experimental data. Remarkable achievements have been obtained in heat transfer characteristics, heat transfer mechanisms analyses and correlation assessments.

Greek letters k thermal conductivity [W/mK] l dynamic viscosity [Pas] q density [kg/m3] j electrical resistance [X  m] r surface tension [N/m] subscripts b bulk g vapor phase in inlet l liquid phase w wall wi inner wall wo outer wall sat saturated tp two phase

From the literatures mentioned above, it is seen that a lot of works have been done on boiling heat transfer of water at subcritical pressures. However, the majority of past experiments were performed with smooth tube or large-scale rod bundle, few publications could be seen on boiling heat transfer in sub-channel using water as the test fluid. In nuclear reactor core, heat is generated from the fuel rods and transferred to the outside coolant, which is different from the in-tube flow. Therefore, it is necessary to perform specific experiments in the flow geometry relevant to tight fuel bundle. A Fuel Qualification Test (FQT) is being planned to irradiate a fuel bundle at supercritical pressure conditions inside the LVR-15 research reactor in Rez, Czech Republic [19]. The proposed fuel bundle consists of four fuel rods of 8 mm in outer diameter and a length of 600 mm. It is inserted into a square assembly box with rounded corners (see Fig. 1). Recent heat-transfer experimental data in the 2
2 rod bundle at supercritical pressure have been reported by Wang et al. [20,21] and Gu et al. [22,23]. However, research on the flow boiling heat transfer in relevant flow channel has not been seen in publication. The main purpose of this paper is to present the heat transfer characteristics of water in a SCWR-FQT sub-channel and improve the understanding on flow boiling in tight rod bundle.

Fig. 1. Cross-sectional geometry of the fuel channel in the Fuel Qualification Test [19].

H. Wang et al. / International Journal of Heat and Mass Transfer 105 (2017) 799–810

2. Experimental facility and procedures 2.1. Experimental loop The experiments were performed in a high-pressure steamwater test loop schematically shown in Fig. 2. Distilled and deionized feed water from the water tank was driven through a filter by a high pressure plunger-type pumps up to 40 MPa. Part of the water returned to the water tank through a bypass loop, the other was driven to the test section. Before flowing into the test section, the feed water delivered through a mass flow meter and flowed into a preheater to be heated to the test state. The hot water flowing from the test section was cooled with a condenser. Finally, it flowed back to the water tank and re-circulated. The pressure and the mass flux in the test section were controlled by adjusting the main valve and bypass valve, respectively. 2.2. Test section geometry The geometry of the sub-channel test section and thermocouple arrangements are displayed in Fig. 3. This geometry is introduced to simulate the central sub-channel of the 2
2 rod bundle in the SCWR-FQT [19]. The test section was made of stainless-steel (321) with a full length of 680 mm and a wall thickness of 2.5 mm. The shaded region in Fig. 3 is the metal wall and the inner area inside the metal wall is the flow channel. The hydraulic equivalent diameter of the present flow channel is 5.32 mm. Along the flow direction, the wall temperatures on four cross-sections were collected. At each of the cross-section, eight thermocouples were welded on the outer-surface to measure the outer wall temperatures. The test section was covered by thick aluminosilicate fiber felt to minimize the heat loss, which is lower than 5% from the heat balance experiment. The test section was processed from a solid stainless steel (321) rod with high-speed wire electrode cutting to obtain the exact shape of the inner flow channel. The surface roughness of the inner-surface was measured by a high-precision roughometer, which gives an average surface roughness of 2.8 lm. The photograph of the test section in illustrated in Fig. 4. The wall temperatures were measured using U0.2 mm standard NiCr–NiSi

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thermocouples while the fluid temperatures were measured by U3 mm K-type sheathed thermocouples. The fluid pressure at the inlet of the test section was measured by a Rosemount 3051 capacitance-type pressure transmitter and the pressure drop of the test section was measured with a Rosemount 3051 capacitance-type differential pressure transducer. All data were collected and recorded by an IMP 3595 data acquisition system. 2.3. Test matrix and procedure The experiment was performed at steady-state experimental conditions within a range of pressures from 11 to 19 MPa, mass flux from 700 to 1300 kg/m2s and heat fluxes from 200 to 600 kW/m2. The test matrix is listed in Table 1. A constant power profile was applied to the test section. During the experiment, the pressure, mass flow rate and power were set to the desired values for each run. The inlet fluid temperature was increased gradually in steps through raising the power to the pre-heater. Measurements of the pressure at the inlet of the test section, mass flow rate, power to the test section, inlet/outlet fluid temperature, outer wall temperature and pressure drop over the test section were recorded at each step. The test was done when any wall temperature exceeded 650 °C or when the maximum heating power was achieved. 3. Experimental data reduction and uncertainty analysis 3.1. Data reduction The heat flux on the inner surface of the test section is calculated as

q¼

Power Aheated

ð1Þ

where Power is the applied power in kW, Aheated is the heated area along the flow direction and is expressed as


Aheated ¼ 4


pdo 4

 þd
L

Fig. 2. Schematic diagram of the high-pressure steam-water test loop.

ð2Þ

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Fig. 3. Structure of the sub-channel test section.

where do is the outer diameter of the artificial heated tube and d is the width of the connecting wall on the fluid side (see Fig. 3). The mass flux is defined as

x¼

Q G¼ Aflow

pD1 ðL1  Lsc Þq1 þ

where Q is the mass flow rate in kg/s, Aflow is the flow area in m and is expressed as 2

Aflow ¼ Pitch 

pd2o 4

ð4Þ

where Pitch is the center distance between two adjacent artificial tubes. The bulk enthalpy is evaluated from the heat balance

Power z Q L

ð5Þ

where Hin is the inlet fluid enthalpy and z is the axial distance at the location from the start of the heated length. In single-phase region, Hin is evaluated with the inlet pressure and inlet bulk temperature using the NIST database [24], while in two-phase region, Hin is obtained from the saturated water enthalpy, the saturated steam enthalpy and the steam quality.

P

pDn Ln qn þ pdzq Aflow GHfg

ð3Þ 2

Hb ¼ Hin þ

The steam quality at the axial location z of the test section is calculated from thermal balance equation

ð6Þ

where Dn, Ln and qn are the inside diameter, heated length and heat flux of the nth pre-heater. Lsc is the sub-cooled length within L1, which could be calculated by

Lsc ¼

Aflow Gcp DT sub pD1 q1

ð7Þ

where DTsub is the temperature difference of the saturated fluid temperature and the inlet fluid temperature of the first preheater. In the experiments, the heat absorbing efficiency was calibrated and the system heat balance was ensured to the maximum, thus, the steam quality in this paper is considered an equilibrium steam quality. The heat transfer coefficient is defined as

h¼

q t wi  t b

ð8Þ

where tb is the bulk temperature. Experimental measurements of the outside wall temperature have been converted into inside wall temperature using the

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Fig. 5. Inner wall temperature calculation at thermocouple locations 1–4 (unit in mm).

The thermal conductivity and electric resistance of the metal tube vary linearly with temperature and are calculated as

Fig. 4. Photograph of the sub-channel test section.

conduction heat-transfer equations, which were obtained by the method of Zhou [25]. The non-uniform cross-section of the test section was equivalent as a circular tube in using the heat transfer equations. Specially, the thermocouple locations 1–4 and corresponding inside wall temperatures were considered as a circular tube with an O.D. 14.44 mm and I.D. 9.44 mm, as shown in Fig. 5. Similar method was employed to the measuring points 5–8 which was assumed to be a circular tube with an O.D. 10.32 mm and a wall thickness of 2.5 mm. For an electrically-heated long circular tube, the axial and circumferential heat conduction could be neglected. Therefore, the one-dimensional steady heat conduction equation is simplified as


 1 d dt kr þU¼0 r dr dr

ð9Þ

where U is the Joule heat generated by the AC current and is calculated by

U¼

I2 R AL

ð10Þ

where I is the electric current, R is the electric resistance calculated by R ¼ j  L=A, and A is the cross-sectional area of the metallic tube.

k ¼ k0 ð1 þ btÞ

ð11Þ

j ¼ j0 ð1 þ atÞ

ð12Þ

where k0 and j0 are the thermal conductivity and electric resistance at 0 °C, a and b are the coefficients against temperature variation. Simultaneous equations (9)–(12) yields

  1 b dt dt 1 þ at M ¼0   2 r 1 þ bt dy dy 1 þ bt  y o dy 2

d t

ð13Þ

where ro is the outer diameter of the tube, y = ro  r and 2

M ¼ AI 2jk0
103 . 0

Expanding Eq. (13) using Maclaurin Series to its sixth power finally obtains the inner wall temperature expression

twi ¼ two 

 M 1 þ at wo 2 y y2 y3 y4 y 1þ þ þ þ 2 1 þ bt wo 3R 4R2 5R3 6R4

My2 B1 My3 B2 My4 B3 þ þ 2 2 12 ð1 þ bt wo Þ 30R ð1 þ bt wo Þ 360R2 ð1 þ bt wo Þ2 # M2 y4 B4 þ ð14Þ 90 ð1 þ bt wo Þ4 þ

where

B1 ¼ 3b þ 2abt wo  a

ð15Þ

B2 ¼ 5b þ 4abt wo  a

ð16Þ

Table 1 Test matrix of the flow boiling heat-transfer experiment. Pressure (MPa)

Mass flux (kg/m2s)

Inlet subcooled degree (°C)

11

700 1000 1300

112.8 111.3 102.5

15

700 1000 1300

133.7 140.9 120.6

19

700 1000

154.8 150.1

Heat flux (kW/m2) 400 200 200

400 400 400 400

600 600 600 600 600 600 600

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B3 ¼ 52b þ 46abtwo  6a

ð17Þ

B4 ¼ 9b2  2ab þ 16ab2 two  2a2 btwo þ 7a2 b2 t 2wo

ð18Þ

For the present experiment, the electrical resistance and thermal conductivity are the function of temperature and expressed as follows (for stainless steel 321 material)

j ¼ 7:74
107
ð1:0 þ 7:45
104 tÞ

ð19Þ

k ¼ 14:41
ð1:0 þ 1:033
103 tÞ

ð20Þ

3.2. Uncertainties analysis The uncertainties of measured parameters depend on the precision of the measuring instruments and the testing range in the experiment. The measuring error of pressure is determined by the precision of the Rosemount 3051 pressure transmitter and IMP 3595 DAQ board, which are 0.05% and 0.02%, respectively. The measuring error of mass flow rate depends on the 0.075%-precision SIEMENS mass flowmeter and the DAQ board. The uncertainty in bulk fluid temperature is 0.4 °C determined by the U3 mm K-type sheathed thermocouple, while is 1.5% in wall temperature measured by the U0.2 mm NiCr–NiSi thermocouples. The uncertainty of wall heat flux is 5.3% which was calculated by the precision of the current transformer, voltage transformer, thermal efficiency, heated area and the DAQ board. The uncertainty in heat transfer coefficient is determined by the uncertainties of heat flux and wall-to-bulk temperature difference. In boiling heat transfer region, the temperature difference between the heated wall and the bulk fluid is quite small, which results in a maximum uncertainty of about 11.1% in heat transfer coefficient. Table 2 tabulates the uncertainties in measured and calculated parameters.

Fig. 6. Heat efficiency at various heat flux and mass flux conditions.

4. Experimental results and discussion 4.1. Thermal efficiency of the test section In each of the heat transfer experiments, the thermal efficiency was carefully checked to ensure the credibility of the experimental data. Fig. 6 illustrates the heat efficiency of the test section with the variation of heat flux and mass flux in singlephase heat transfer region. It is seen that the heat efficiency increases slightly with mass flux and heat flux. A maximum efficiency of about 0.96 was observed at the high mass flux of 1300 kg/m2s. Fig. 6 signifies that the heat efficiency falls within the range from 0.93 to 0.96, which is acceptable in performing the heat-transfer experiment. Another way to ensure the heat transfer reliability is to compare the test data with the classical Dittus–Boelter correlation [26]. This correlation has been proved by many authors to have good performance in predicting single-phase heat transfer coefficient. Fig. 7 shows the variation of experimental and predicted heat transfer

Table 2 Uncertainties in measured and calculated parameters. Parameter

Uncertainty

Pressure [MPa] Pressure drop [kPa] Electrically-heated power [kW] Mass flow rate [kg/s] Fluid temperature [°C]) Wall-to-bulk temperature difference [°C] Heat flux [kW/m2] Heat transfer coefficient [kW/m2K] Steam quality [–]

0.2% 0.7% 3.3% 1.02% 0.4 9.8% 5.3% 11.1% 7.2%

Fig. 7. Single-phase heat transfer coefficient with bulk temperature.

coefficient with bulk temperature. It is seen that the test data shows good agreement with the Dittus–Boelter correlation [26] within ±5% error range in single-phase subcooled-water region. These results help to validate the experimental system, procedure and data reduction in this paper. 4.2. Heat transfer difference of the heated walls In the experiments, the outside wall temperatures at the measuring points 1, 2, 3 and 4 are almost the same. Hence, the average wall temperature of the four measuring points is labeled as the connecting-wall temperature. Similarly, the average wall temperature of the measuring points 5, 6, 7 and 8 is labeled as the circular-wall temperature. Fig. 8 expresses the variations of inner wall temperature and heat transfer coefficient with bulk enthalpy at the connecting-wall and the circular-wall. It is seen that the wall temperature of the circular wall is lower than that of the connecting wall within the entire bulk enthalpy region. As a consequence, the corresponding heat transfer coefficient of the circular wall is relatively higher. The reason for this phenomenon may be attributed the non-uniform cross-sectional flow area. It is noted that the flow area adjacent to the connecting wall is smaller than the circular wall, which results in a lower flow quantity near the connecting wall. Since the bulk fluid velocity attached to the wall is supposed to be zero due to the non-slipping boundary

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Fig. 8. Heat transfer difference along the circumference of the test section.

condition, the mean flow velocity near the connecting wall becomes smaller. Therefore, the heat transfer between the connecting wall and the bulk fluid becomes worse and leads to a higher wall temperature compared to the circular wall. It should be emphasized that although the heat transfer of the connecting wall is worse, there is no actual connecting wall in a real SCWR sub-channel. That is to say, the connecting walls, which suppress the cross-flow and turbulence mixing between neighboring channels, are artificial compared with the real central sub-channel in the 2
2 rod bundle. Consequently, heat transfer analysis to the connecting wall does not provide any engineering application value. The existence of the connecting wall is to form the test section to simulate the central sub-channel of the 2
2 rod bundle in SCWR-FQT. Hence, in what follows, the wall temperature at the circular wall is used to clarify the general heat transfer characteristics in the central sub-channel at subcritical pressures. 4.3. Heat transfer along the flow direction Fig. 9. Wall temperature profiles along the flow direction.

The variations of wall temperature along the flow direction are shown in Fig. 9 with the four measuring cross-sections of mp-1, mp-2, mp-3 and mp-4. It is seen that the wall temperatures of the four cross-sections are nearly overlapped before the bulk enthalpy of 1800 kJ/kg. With the increase of steam quality, deteriorated heat transfer occurred causing a significant increase in wall temperature. The steam quality corresponding to the soaring wall temperature becomes lower along the flow direction, signifying that heat transfer deterioration occurs first at the outlet part of the flow channel (mp-4). The highest peak in the wall temperature is observed at mp-4 which is used for monitoring during the experiment, followed by mp-3 and mp-2. After the deteriorated heat transfer, the wall temperature declines with the increase of steam quality and re-increases in high steam-quality region. In addition, it seems that the wall temperature at mp-1 is lower than those

of the other three cross-sections and no remarkable deteriorated heat transfer was observed in the two-phase region. Since the thermocouple of mp-1 was arranged only 150 mm from the inlet of the test section, the flow may not be fully-developed due to the entrance effect. Therefore, the wall temperatures at the third cross-section are used in the following analysis to avoid the entrance effect. 4.4. Effects of system parameters on heat transfer 4.4.1. Effect of heat flux Fig. 10 illustrates the variations of wall temperature and heat transfer coefficient plotted against bulk enthalpy and heat flux at

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Fig. 10. Effects of heat flux on heat transfer characteristics: (a) wall temperature; (b) heat transfer coefficient.

the pressure of 15 MPa and mass flux of 1000 kg/m2s. As shown in Fig. 10(a), the wall temperature increases with heat flux in singlephase heat-transfer region where the bulk enthalpy is lower than 1400 kJ/kg. Beyond this bulk enthalpy, the bulk temperature increases gradually but the wall temperature stays nearly unchanged at the high heat flux of 600 kW/m2. Obviously, subcooled boiling occurs before the thermal-equilibrium steam quality reaches 0. In the saturated boiling heat-transfer region, the difference in wall temperature at various heat fluxes is negligible prior to the onset of heat transfer deterioration. However, significant wall temperature difference could be observed after the occurrence of heat transfer deterioration. A local wall-temperature hump of about 475 °C appears at the high heat flux of 600 kW/m2, and this hump lowers to 365 °C as the heat flux decreased to 400 kW/m2. A further reduce in heat flux does not lead to the soaring wall temperature anymore. Flow boiling heat transfer comes to an end once the steam quality is higher than 1.0, where the flow channel is cooled by single-phase superheated steam. The effect of heat flux on heat transfer coefficient is displayed in Fig. 10(b). In single-phased subcooled-water region (lower than 1400 kJ/kg) and superheated-steam region (higher than 2600 kJ/kg), the heat transfer coefficients at the three heat fluxes are almost the same. In two-phase region prior to the sudden rise of wall temperature, heat transfer coefficient increases with increasing heat flux. This may be attributed to the enhanced effect of heat flux on bubbly generation from the heated wall, since nucleate boiling is the main heat-transfer mode in low steamquality region. 4.4.2. Effect of pressure The variations of wall temperature and heat transfer coefficient with bulk enthalpy and system pressure are shown in Fig. 11. It is seen in Fig. 11(a) that the wall temperatures overlap with each other in low-enthalpy single-phase region in which the bulk temperatures are insensitive to pressure change. With the increase of bulk enthalpy, the bulk flow enters into twophase region at 11 MPa first, followed by 15 MPa and 19 MPa. In this region, the wall temperature keeps nearly constant, but the temperature level is promoted with increasing pressure as the saturated bulk temperature is increased with pressure. Deteriorated heat transfer occurs at the pressures of 15 MPa and 19 MPa with a slight rise in wall temperature near the bulk enthalpy of 2000 kJ/kg. In high steam-quality region, the wall

temperatures increase with bulk enthalpy accordingly. The higher the pressure is, the higher the wall temperature will be. From the distributions of heat transfer coefficient plotted in Fig. 11(b), it is concluded that the effect of pressure on heat transfer coefficient is weak in the subcooled-water region and superheated-steam region. However, in the steam-water two-phase region prior to the slight heat transfer deterioration, heat transfer coefficient rises remarkably with the increase of pressure. The reasons for this phenomenon are as follows. Firstly, the latent heat of water decreases with increasing pressure, signifying that the superheat degree for bubble generation is decreased. As a consequent, the bubbles are easier to be formed as the pressure increases to a higher level. Secondly, the liquid surface tension decreases with pressure, which also facilities the bubble formation. Therefore, boiling heat transfer is enhanced with the increase of pressure. 4.4.3. Effect of mass flux Fig. 12 expresses the profiles of wall temperature and heat transfer coefficient plotted against bulk enthalpy and mass flux at the pressure of 15 MPa and heat flux of 400 kW/m2. At a high mass flux of 1300 kg/m2s, the wall temperature increases gradually with bulk enthalpy in single-phase subcooled region. As the bulk flow approaches the saturated temperature, the wall temperature remains steady in the two-phase region until the steam quality reaches about 0.85, and finally increases with bulk enthalpy in the superheated region. When the mass flux is decreased to 1000 kg/m2s, the wall temperature profile varies similarly except that a mild heat transfer deterioration appears at a steam quality of about 0.28. A further decrease in mass flux leads to a higher peak of the wall temperature. In a word, the maximum soaring wall temperature decreases with increasing mass flux, and no deteriorated heat transfer was observed as the mass flux increased to a certain level. As shown in Fig. 12(b), the heat transfer coefficients increase with increasing mass flux in single-water region and single-steam region. The increase of mass flux not only promotes the forced convection turbulence intensity, but also boosts the bubbly-carrying ability of the bulk flow, both of which enhance heat transfer. However, the heat transfer coefficients are nearly the same in the two-phase region prior to the soaring wall temperature, in which the effect of forced convection on heat transfer becomes weak and flow boiling is the dominant heat transfer mode.

H. Wang et al. / International Journal of Heat and Mass Transfer 105 (2017) 799–810

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Fig. 11. Effects of pressure on heat transfer characteristics: (a) wall temperature; (b) heat transfer coefficient.

Fig. 12. Effects of mass flux on heat transfer characteristics: (a) wall temperature; (b) heat transfer coefficient.

4.5. Deteriorated heat transfer at subcritical pressures

Fig. 13. Deteriorated heat transfer at various test parameters.

Fig. 13 illustrates the typical wall temperature variations at deteriorated heat transfer condition in the sub-channel. At the pressure of 15 MPa, mass flux of 1000 kg/m2s and heat flux of 600 kW/m2 (black box line), DNB occurred at a steam quality of about 0.28 with a sharp increase in wall temperature from 348 °C to 474 °C. Beyond the wall temperature peak, the wall temperature declines with bulk enthalpy until the steam quality reaches 0.78. As the annular flow regime transfers into mist flow in high steam-quality region, the wall temperature increases again with bulk enthalpy. However, this increase in wall temperature is much milder compared with the case of DNB. At the same mass flux and heat flux conditions, DNB becomes severe as the pressure promotes to 19 MPa (red circle line). The wall temperature suddenly soars from 368 °C to 527 °C in a narrow steam-quality range and declines soon afterwards. Moreover, the steam quality corresponding to the onset of DNB is reduced to 0.09 as the pressure increases to 19 MPa. Comparison of the two profiles indicates that the decrease in pressure not only lowers the maximum wall temperature of DNB, but also postpones the onset of DNB to high

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Table 3 Selected correlations for saturated flow boiling heat transfer. References

Parameters ranges

Gungor and Winterton [29]

Based on a database of 3693 data points, including R12, R22, R113 and water. D = 2.95–32 mm; P = 0.08–202.6 bar

Kandlikar [30]

For water, refrigerants and nitrogen. D = 4.6–32 mm; P = 0.6–64.2 bar; G = 13–8179 kg/m2s; q = 0.3–2280 kW/m2

Correlations   0:41  x 0:75 ql htp ¼ hl 1 þ 3000Bo0:86 þ 1:12ð1x Þ q g

where hl is the single-phase heat transfer coefficient, Bo is the boiling number defined as Bo ¼ q=ðGHfg Þ htp ¼ hl  max½E; S For water, E ¼ 0:6683Co0:2 þ 1058Bo0:7 and S ¼ 1:136Co0:9 þ 667:2Bo0:7  0:8 qg 0:5 where Co is the convection number and defined as Co ¼ 1x q x l

Chen [31]

For water and organic fluids. P = 0.56–35.28 bar; q = 6.2–2400 kW/m2; x = 0.01–0.71, ul = 0.061–4.481 m/s

h ¼ hNB þ hFC

 0:79 0:45  k C q0:49 0:24 0:75 where hNB ¼ 0:00122 r0:5l l0:29plH0:24l q0:24 DT sat DP sat S and hFC ¼ 0:023

h

i0:8

Gð1xÞd

ll

l

fg

g

kl Pr 0:4 F. For detailed variables, please refer to l d

Refs. [27,31] Fang [32]

For R134a, based on 2286 published test data

.   1:023l Nu ¼ 0:00061ðS þ FÞRel Pr l0:4 Fa0:11 ln l b w

where S = 30000Bo1.13 for Bo < 0.0026, S = 36 for Bo P 0.0026, and  x 0:95  q 0:4 l F ¼ 1x q g

Fa is the Fang number and defined as Fa ¼

ðql qg Þr G2 d

Fig. 14. Comparisons of calculated two-phase heat transfer coefficient against the experimental data: (a) Gungor–Winterton correlation [29]; (b) Kandlikar correlation [30]; (c) Chen correlation [31]; (d) Fang correlation [32].

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H. Wang et al. / International Journal of Heat and Mass Transfer 105 (2017) 799–810 Table 4 Prediction accuracy in two-phase heat transfer coefficient. References

Average error (%)

Standard deviation (%)

Gungor and Winterton [29] Kandlikar [30] Chen [31] Fang [32]

67.6 66.4 35.1 13.9

95.3 96.2 97.6 40.1

% of data predicted within ±10%

±25%

±50%

21.5 17.7 13.4 18.7

39.2 39.2 39.7 46.2

59.7 59.1 73.4 80.1

P Av erage error ¼ 206 i¼1 error i =206
100: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P206 2 Standard dev iation ¼ i¼1 ðerror i  Av erage errorÞ =205
100:

error ¼

htp;cal htp;exp ; htp;exp

Fig. 15. Wall temperature variations at different pressure regions: (a) q/G = 0.2; (b) q/G = 0.6.

steam-quality direction. At the pressure of 19 MPa and heat flux of 600 kW/m2, a lower mass flux of 700 kg/m2s (blue triangle line) leads to a significant wall temperature rise of about 212 °C. No data was recorded after the last wall temperature of 581 °C since the test section burned out immediately. 4.6. Assessment of heat transfer correlations The prediction of steam-water two-phase heat transfer coefficient is much more complicated owing to the phase transition, mass transfer, momentum transfer and energy transfer. The heat transfer correlations for flow boiling have been recently reviewed by Asadi et al. [27] and Fang et al. [28]. From these reviews, it is seen that the correlations developed so far vary greatly and none of the correlation is applicable to all flow geometries at wide range of parameters. Several widely-used correlations are selected to compare with the sub-channel experimental data, as listed in Table 3. The calculated two-phase heat transfer coefficients by the above-listed four correlations have been compared with a total of 206 experimental data, as shown in Fig. 14. Table 4 tabulates the average error, standard deviation and data captured within various error ranges of the four correlations. It is seen in Fig. 14(a) that the correlation of Gungor and Winterton [29] significantly overpredicts the boiling heat transfer coefficient in low heat-transfer region (lower than 20). Above this value, the predicted heat transfer coefficients are slightly higher than the experimental data. Overall, 39.2% of the experimental data are successfully captured within the ±25% error band and 59.7% of the heat transfer coefficients are predicted within the ±50% error band. The calculated heat transfer coefficient by Kandlikar correlation [30] is displayed

in Fig. 14(b), in which it is observed that the performance is quite similar to that of Gungor and Winterton correlation [29]. Chen correlation [31] overpredicts the heat transfer coefficient by 35.1%, which is much improved compared to the above two correlations. As illustrated in Fig. 14(c), about 39.7% and 73.4% of the experimental data are captured within an accuracy of ±25% and ±50%, respectively. Fig. 14(d) gives the performance of Fang correlation [32] in predicting flow boiling heat transfer coefficient. The average error is 13.9% and the standard deviation is 40.1%, both of which are the best among the selected four correlations. About 46.2% and 80.1% of the experimental data are successfully predicted within the ±25% and ±50% error bands. Although this correlation was put forward based on the data of R134a, the performance is also satisfying for water in sub-channel. 4.7. Heat transfer at different pressure regions Heat transfer experiment of water has been performed at supercritical pressure by Wang et al. [33] using the present test section. At supercritical pressures, the bulk fluid experiences no phase transition, but the thermophysical properties of water vary drastically at the vicinity of the pseudo-critical temperature. It would be interesting to compare the heat transfer characteristics in super/ sub-critical pressure regions. The variations of wall temperature plotted against bulk enthalpy at the pressure of 15 MPa and 25 MPa are illustrated in Fig. 15. At a low q/G ratio of 0.2 in Fig. 15(a), it is seen that the wall temperatures under the two pressures collapse well prior to the bulk enthalpy of 1500 kJ/kg. As the bulk enthalpy surpasses 1600 kJ/kg, the wall temperature at supercritical pressure increases gently with bulk enthalpy, whereas flow

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boiling occurs at sub-critical pressure and the wall temperature keeps nearly unchanged. In high enthalpy region, the wall temperatures at the two pressures both rise with bulk enthalpy, but the profiles become steeper compared with those in low enthalpy region. As the q/G ratio increases to 0.6 shown in Fig. 15(b), the wall temperature at 25 MPa increases with bulk enthalpy faster, but the profile is similar to that at q/G ratio of 0.2. However, a remarkable heat transfer deterioration appears at 15 MPa characterized by the sharp rise in wall temperature. As mentioned previously, DNB occurs in the steam-water two-phase region at a low steam quality of about 0.28. From the two plots, it is concluded that the largest heat transfer difference lies in the middle-enthalpy region, where phase transition occurs at subcritical pressure but the bulk flow remains single-phase at supercritical pressure. 5. Conclusions Flow boiling heat transfer of water in a central sub-channel has been investigated experimentally over a wide range of parameters. According to the experimental data, the following conclusions could be drawn. (1) Along the flow direction, the wall temperature profiles at the four measuring cross-sections overlapped for single-phase sub-cooled water and superheated steam. However, the wall temperatures vary differently in the two-phase region with an earlier wall temperature rise occurred near the outlet. (2) System parameters play important roles on two-phase heat transfer. With the increase of heat flux, deteriorated heat transfer may occur at certain steam quality. The increase of pressure not only promotes the saturated bulk temperature, but also improves the two-phase heat transfer coefficient prior to the wall temperature rise. Deteriorated heat transfer in the two-phase region was eliminated as the mass flux increased to a certain level. (3) DNB type of heat transfer deterioration was observed in the flow channel. DNB occurs at relatively low steam quality with a high heat flux. The DNB type deterioration becomes severe with increasing pressure or decreasing mass flux. (4) For the steam-water two-phase heat transfer coefficient, four correlations were assessed against the current set of experimental data. It was found that the correlation of Fang et al. [32] is acceptable, but still needs further improvements for sub-channel. (5) Wall temperature difference at subcritical and supercritical pressures was compared for the present flow channel. The wall temperature in two-phase region is lower than that at supercritical pressure for small q/G ratio. However, the case is inverse at large q/G ratio since deteriorated heat transfer may occur at subcritical pressure. Acknowledgements This research was financially supported by National Natural Science Foundation of China (Nos. 11605057 and 51406026), Program for Innovative Research Team (in Science and Technology) in University of Henan Province (No. 16IRTSTHN017), Plan for Scientific Innovation Talent of Henan Province (154100510011). References [1] J.X. Shi, B.Z. Sun, G.L. Zhang, Prediction of dryout and post-dryout wall temperature at different operating parameters for once-through steam generators, Int. J. Heat Mass Transfer 103 (2016) 66–76. [2] US DOE, Nuclear Energy Research Advisory Committee and Generation IV International Forum, A Technology Roadmap for Generation IV Nuclear Energy System, 2002.

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