Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces

ARTICLE IN PRESS

JID: HMT

[m5G;November 29, 2019;13:0]

International Journal of Heat and Mass Transfer xxx (xxxx) xxx

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/hmt

Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces Jinbiao Xiong a,∗, Zefeng Wang b, Ping Xiong c, Tao Lu c, Yanhua Yang a a

School of Nuclear Science and Engineering, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China State Key Laboratory of Reactor System Design Technology, Nuclear Power Institute of China, Chengdu, China c College of Mechanical and Electrical Engineering, Beijing University of Chemical Technology, North Third Ring Road 15, Beijing, China b

a r t i c l e

i n f o

Article history: Received 16 July 2019 Revised 17 November 2019 Accepted 26 November 2019 Available online xxx Keywords: Quenching Fuel cladding Minimum film boiling temperature Critical vapor film thickness

a b s t r a c t In case of postulated accidents in a nuclear reactor, the fuel rods uncovered from coolant can be overheated. Immediate quenching of overheated fuel rods is desired. Quenching experiment is performed at atmospheric pressure with rodlets of the FeCrAl alloy, one of the accident tolerant fuel cladding materials, and the Zircaloy-4, the conventional cladding material. In the experiment 600 °C rodlet specimens are plunged into the subcooled water bath. A high-speed camera is employed to record quenching phenomenon. With the embedded thermocouples the rodlet temperature is measured at the frequency of 50 Hz. One-dimensional inverse heat conduction problem is solved to obtain the surface temperature and heat flux. Influence of surface condition, solid thermal properties and liquid subcooling on transient boiling heat transfer is investigated. In the film boiling regime heat transfer is mainly affected by solid thermal properties and liquid subcooling. Small solid (kρ Cp )w and large liquid subcooling results in relatively thin vapor film and more efficient film boiling heat transfer. Roughness on the polished level shows no appreciable influence on the minimum film boiling temperature, TMFB , which increases with decreasing contact angle. Surface oxidation is slow on the FeCrAl surface and hence, does not significantly affect the boiling heat transfer. However, on the Zircaloy-4 surface the oxide layer with small (ρ kCp )w increases TMFB and decreases the critical heat flux. Large (ρ Cp )w results in slow quench front propagation, long quench duration and weak subcooling effect. It is found that on each surface the vapor film collapses at the critical thickness which is irrelevant to liquid subcooling. Based on the critical thickness, a new approach for prediction of TMFB is proposed. © 2019 Elsevier Ltd. All rights reserved.

1. Introduction During a postulated accident in water-cooled nuclear reactors, e.g. the loss-of-coolant accident, the reactor core can be partially or completely uncovered from coolant and consequently becomes overheated. As one of the accident countermeasures, water is injected into reactor core by the emergency core cooling system. When the overheated fuel rods are rapidly immersed by water, film boiling start where vapor blankets insulate the fuel rods from water. As the surface temperature of fuel rod decreases close to the minimum film boiling (MFB) temperature, TMFB , intermittent liquid-solid contact occurs. As the surface temperature is further reduced, the liquid patch on the surface increases in extent and number, nucleate boiling takes place on the liquid patches, while film boiling occurs on the surface occupied by vapor. Due to effec-

∗

Corresponding author. E-mail address: [email protected] (J. Xiong).

tive heat transfer by nucleate boiling, the cooling rate in transition boiling increases remarkably. High TMFB and early quench of fuel rod is always desired to reduce the cladding temperature. In order to investigate transient boiling heat transfer from film to nucleate boiling, quenching experiments have been extensively carried out [1]. Chowdhury and Winterton [2] quenched aluminum and copper cylinders in saturated liquids and showed that small contact angle (better wettability) augments heat flux in transition boiling. Kim et al. [3] quenched the stainless sphere and rodlet in nanofluid and found that after nanoparticle deposition the surface roughness and wettability is enhanced and as consequence, the minimum film boiling temperature, TMFB , and the quench front speed are significantly increased. Li et al. [4] concluded that there is no identifiable minimum film boiling point on the super-hydrophilic porous surface. Kruse et al. [5] found the structured surface can significantly increase TMFB and enhance the film boiling heat transfer. Besides the surface properties, liquid subcooling and solid thermal properties show also influence

https://doi.org/10.1016/j.ijheatmasstransfer.2019.119131 0017-9310/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT 2

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

Nomenclature Bi Cp D g h hfb hfg J k Pr q qk r R Ra Sp∗ T TMFB u Zki

Biot number, hR/kw specific heat (J/(kg · ◦ C)) diameter (mm) gravity acceleration (m/s2 ) heat transfer coefficient (W/(m2 · ◦ C)) film boiling heat transfer coefficient (W/(m2 · ◦ C)) latent heat (J/kg) objective function of optimization thermal conductivity (W/(m · ◦ C)) Prandtl number, μcp /k heat flux (W/(m2 )) heat flux at time τ k (W/(m2 )) radius (mm) Rodlet radius (mm) average surface roughness (μm) dimensionless superheat number temperature (°C) minimum film boiling temperature (°C) quench front speed (m/s) sensitivity coefficient defined by

∂ Tk+i−1 ∂ qk

Greek symbols δ film thickness (μm) ε surface emissivity Tsub liquid subcooling (°C) T w wall superheat (°C)  wave length (mm) ρ density (kg/m3 ) σ surface tension (N/m) σb Stefan-Boltzmann constant, 5.669 × 10−8 W/m2 /K4

contact angle M dynamic viscosity (Pa · s) T time (s) Subscripts b iteration step number cond conduction CHF critical heat flux cr critical f fluid fb film boiling int interface kh Kelvin-Helmholtz l liquid MFB minimum film boiling rad radiative s solid sub subcooled sat saturation v vapor w wall transient boiling heat transfer. For example, Sinha et al. [6], Lee [7], Yamada et al. [8], Yeom et al. [9] and Fudurich [10] concluded that large liquid subcooling leads to short quenching time and high TMFB . Lee et al. [11] and Kang et al. [12] found that the quenching duration increases with the thermal capacity, (ρ Cp )w , while TMFB decreases with increasing (kρ Cp )w . Quenching experiments have been carried out to understand transition boiling heat transfer on the cladding surface under the accident conditions. Sinha et al. [6] quenched Zircaloy and Inconel tubes in subcooled water and observed strong influence of oxide layer thickness on TMFB . Yeom et al. [9] investigated on transient

boiling heat transfer on Zircaloy surface and demonstrated strong effect of surface oxidation and roughness on quenching behavior. Kang et al. [13] quenched a super-hydrophilic zirconium surface in saturated water and observed significant higher TMFB on the super-hydrophilic surface than that on a plain surface. Ebrahim et al. [14] explored the effects of liquid subcooling, material properties and surface conditions on film pool boiling using zirconium, stainless steel and Inconel-600 rodlets and concluded that smaller (kρ Cp )w , better wettability and porous surface lead to higher TMFB . Oxidation-resistant accident tolerant fuel (ATF) claddings, e.g. FeCrAl alloy, are developed to eliminate hydrogen generation due to steam oxidation of cladding at high temperature [15–18]. The ATF claddings have different surface characteristics and thermal properties, compared with zirconium-based cladding. Hence, investigation on the transient boiling heat transfer performance is an indispensable part in research and development activities of the ATF cladding. Quenching experiments have been carried out for the candidate ATF claddings or coatings. Kang et al. [12] performed quenching experiments for FeCrAl alloy and chemical vapor deposited (CVD) silicon carbide (SiC) and Zircaloy-4. In their experiment weak influence of oxidation on quenching was observed for the ATF claddings. Lee et al. [7] investigated the transient boiling heat transfer with different metallic rods, some of which are coated with chromium (Cr) to mimic the ATF coating. Their experiments showed that the Cr-coating delays quenching time and that the surface oxidation strongly affects film boiling heat transfer and TMFB . Seshadri et al. [19] coated Chromium, FeCrAl and Molybdenum on Zircaloy-4 rodlets. Different from Kang et al. [12] micro- and nano-pores were observed on FeCrAl-coated surfaces. The porosity increases the capillary wicking rate and consequently leads to higher TMFB and more efficient film boiling heat transfer. Wang et al. [20,21] conducted Leidenfrost experiments on the ATF cladding material surface, including SiC and FeCrAl. They found that the Leidenfrost temperature decreases with the solid thermal effusivity (kρ Cp )w . More recently, Lee et al. [22] quenched Cr-alloy-coated cladding and Zircaloy-4 in water pool. They observed remarkable influence of oxidation on TMFB on Zircaloy-4 specimen, while the oxidation effect is weak on Cr-alloy-coated cladding. In order to provide further insights into transient boiling heat transfer on the ATF cladding, the FeCrAl alloy and Zircaloy-4 rodlet specimens are quenched in distilled water bath at different subcoolings. The one-dimensional inverse heat conduction problem is solved for the quench process to obtain the surface temperature and heat flux. Effects of surface conditions, including surface roughness, wettability and oxidation, solid thermal properties and liquid subcooling on the transient boiling heat transfer are investigated.

2. Experiment apparatus and test specimen The quenching experiment apparatus consists of a pneumatic guide rail, a water bath, a ceramic heating furnace, and a data acquisition system, as shown in Fig. 1. The rodlet specimen is screwed on a stainless tube which is connect with the pneumatic guide rail. The guide rail driven by compressed air can plunge the specimen rapidly into the distilled water bath. Before quenching, the rodlet specimen is heated up to the desired temperature (600 °C) in the heating furnace. Beneath the furnace locates the water bath which is a quartz tank with the two Joule heaters which are employed to adjust liquid subcooling. A K-type thermocouple is installed in the water bath to monitor water temperature. A high-speed camera, the Phantom VEO 710L, is employed to visualize the transient pool boiling behavior. The photograph frequency is set as 800 fps with the resolution of 480 × 720 px2 .

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

3

Fig. 1. Quenching experimental apparatus and specimen. Table 1 Thermal and surface properties of the FeCrAl and Zircaloy-4 specimen.

FeCrAl#11 FeCrAl#2 Zircaloy-4 1

ρ (kg/m3 )

k(W/(m · K))

cp (J/(kg · K))

Ra (μm)

Contact angle Fresh surface

After quench

7100

11(50 °C)– 20(600 °C) 13.3(50 °C)–19.1(600 °C)

460(20 °C)– 750(600 °C) 286(20 °C)–345(600 °C)

1.6 0.2 0.2

109.4° (±5.3˚) 93.4° (±1.5)˚ 103.8° (±1.6)˚

112.9° (±4.7°) 101.8° (±3.6)˚ 100.0° (±3.0)˚

6500

Thermal properties is given according to Kanthal APM.

An LED panel is installed in the opposite side of the water bath to illuminate the specimen. The Fe25Cr5Al (24.3w%Cr; 5.0w%Al) and Zircaloy-4 specimens are 20mm-in-diameter, 115 mm long rodlets with hemispherical bottom head. The screw thread is fabricated in the top end of rodlets to connect with the stainless tube on the guide rail. Four K-type thermocouples, 0.8 mm in diameter, are installed in the 1 mm-in-diameter holes which are drilled from the top of rodlets. The centerline of the holes is 1.5 mm from the rodlet surface. The location of thermocouples is illustrated in Fig. 1. With Z = =0 defined on the bottom plane of cylindrical section of rodlet, the four thermocouples locate at the height of z = =25mm, 50 mm and 75 mm. On the plane of z = =50 mm two thermocouples are installed to investigate azimuthal temperature difference during the quenching process. All the temperature readings are recorded with the data acquisition system at the frequency of 50 Hz. Two FeCrAl and one Zircaloy-4 specimens are quenched in the experiment. The thermal properties and surface parameters are summarized in Table 1. The Zircaloy-4 specimen and one of the FeCrAl (FeCrAl#2) specimens is mirror polished. Both of them have the average roughness Ra = =0.2 μm. The average surface roughness of the other FeCrAl specimen (FeCrAl#1) is 1.6 μm. For all the specimens the surface roughness is measured along 9 lines in the axial or radial direction with Mitutoyo SJ-210. After polishing and before each quench test, all of the specimen surfaces are cleaned in a water bath with the ultrasonic wave to remove the dust. The surface morphology is scanned with TESACN VEGA3 scanning electron microscope (SEM) system. The SEM images of

specimens are shown in Fig. 2. Comparing with the FeCrAl#1 surface, the scratches become shallow on the FeCrAl#2 and Zircaloy-4 samples which are polished with finer sand paper. The contact angle is measured at 5 positions on each specimen surface at room temperature with KRUSS droplet shape analyzer DSA30. The contact angle given in Table 1 is the average value of the five measurements, while the uncertainty of contact angle indicates the maximum variation of the five measurements. The contact angle of the fresh specimens is between 90˚ and 110˚, and the finely polished FeCrAl#2 has smaller contact angle than FeCrAl#1. 3. Data reduction The surface temperature and heat flux of quenched rodlets are derived via solving one-dimensional (1D) inverse heat conduction problem (IHCP) in the cylindrical coordinate, i.e.

  ∂T 1 ∂ ∂T ρw c p,w = kw r ∂τ r ∂r ∂r

(1)

where kw , ρ w and cp, w are the thermal conductivity, density, and heat capacity of solid. The axisymmetric boundary condition is defined in the center of rodlet, i.e.

∂ T (r, τ ) = 0, when r = 0 ∂r

(2)

On the cylindrical outer wall,

kw

∂ T (r, τ ) = q(τ ), when r = R ∂r

(3)

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

JID: HMT 4

ARTICLE IN PRESS

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

q(τ ) is the surface heat flux to be derived. The initial uniform distribution of temperature in the rodlet is assumed, i.e.

T (r, 0 ) = T0

(4)

It should be noted that considerable heat conduction in the axial direction occurs near the quench front. However, since the thermocouples are located close to the surface, the one-dimensional assumption is sufficient to predict the surface temperature and heat flux even near the quench front. The sequential function specification method (SFSM) [23] is employed to solve the IHCP. While deriving the heat flux at time index k, q(τ k ), the heat flux in the history, i.e. before τ k , is already known. The estimated temperature Tk+i−1 is affected by surface heat flux from τ k to τk+i−1 . Assuming that the surface heat flux is constant from τ k to τk+m−1 , Tk+i−1 is only determined by q(τ k ), also symbolized as qk . The surface heat flux qk is derived based on the optimization problem with the objective function as below

J ( qk ) =

m 

(Yk+i−1 − Tk+i−1 )2

(5)

i=1

Yk+i−1 and Tk+i−1 are the measured and estimated temperature, respectively. The optimization process is to minimize the difference between the estimated and measured temperatures in the future m-1 time steps. Based on the linear least square method, the surface heat flux at τ k is iteratively calculated by

m

q(τk )b+1 = q(τk )b +

i=1



Yk+i−1 − (Tk+i−1 )b m  i  2 i=1 Zk

 i  Zk

b

(6)

b

where the subscript b indicates the iteration step. Zki is the sensitivity coefficient defined by

Zki =

∂ Tk+i−1 ∂ qk

(7)

Differentiating Eqs. (1) through (4) with respect to the surface heat flux qk , we obtain the control equation of sensitivity coefficient

     ∂ ∂T 1 ∂ ∂ ∂T ρ cp = kr ∂ t ∂ qk r ∂r ∂ r ∂ qk

(8)

The initial condition can be written as

∂ T (r ) = 0, when t = 0 ∂ qk

(9)

The boundary conditions can be written as

  ∂ ∂ T  k =0 ∂ r ∂ qk r=0   k ∂∂r ∂∂qT  = 1, when t = tk  ∂ Tk r=R ∂  k = 0, when t = tk ∂ r ∂ qk

(10) (11)

r=R

When the error between the measured temperature and estimated temperature reaches the stopping criterion, i.e. (qk ) ≤ ε = 10−6 , the iteration is stopped for the time step τ k , and moves on to the next step τk+1 . The algorithm of IHCP is shown in Fig. 3. Based on the derived surface heat flux and temperature, the boiling curve which relates the surface heat flux and the surface superheat can be obtained. Based on the boiling curve, the minimum heat flux (MHF) point in the film boiling regime is defined as the minimum film boiling (MFB) point. Fig. 2. SEM images of test specimen surfaces.

4. Result and discussion 4.1. Development of quenching in height Fig. 4 illustrates the photographed quenching behaviors corresponding to different regimes of boiling heat transfer. With the

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

5

and the Grashof number is defined by

Grv (λ0 ) = gρv (ρl − ρv )λ30 /μ2v

(14)

The capillary wavelength is defined by

λ0 =

Fig. 3. Algorithm of inverse heat conduction problem.

Fig. 4. High-speed photography of quenching behaviors of FeCrAl#1 at subcooling of 10 °C, (a) film boiling; (b) initial film collapse; (c) transition boiling; (d) singlephase natural convection.

initial surface temperature higher than TMFB , transient boiling heat transfer starts from film boiling where the rodlet specimen is cooled via radiative and convective heat transfer [9,12]. Intermittent liquid-solid contact can also occur in the film boiling regime when the surface roughness is large. Vapor is vented through the vapor film at relatively high speed. Velocity gradient at the liquid-vapor interface leads to Kelvin–Helmholtz waves. According to Nishio and Ohtake [24], in the case of quenching vertical surface in saturated fluid, the Kelvin–Helmholtz wavelength can be calculated with

 λkh = 16.2

P rv3 S p∗3 Grv (λ0 )

1/11 λ0

(12)

where the dimensionless superheat number

S p∗ =

C p,v (Tw − Tsat ) h f g + 0.5C p,v (Tw − Tsat )

(13)



σ /g(ρl − ρv )

(15)

The estimated Kelvin–Helmholtz wavelength is between 21.3 mm and 18.3 mm for our experiment when the surface temperature varies from 300 ◦ C to 600 °C. The estimated wavelength is in fair agreement with our observation in the case Tsub = 5◦ C. On FeCrAl#2 and Zircaloy-4 specimen the observed Kelvin– Helmholtz wavelength is 18.8 mm and 16.4 mm respectively, whenTsub = 5◦ C. The wavelength is measured with the pixel analysis (0.155mm/pixel) taking the rodlet diameter as the reference length. As the rodlet cools down, collapse of vapor film starts. The initial collapse of vapor film is observed on the bottom head. Later on, film collapse propagates upward, as shown in the photograph (b) and (c) in Fig. 4. In the high-speed photograph the quench front is identified as the location where the vapor film collapses and the intensive boiling starts. Across the quench front the boiling transits from film boiling to transition boiling. In the regime of transition and nucleate boiling below the quench front, large bubbles can be observed near the rodlet surface. Some bubbles can detach from the solid surface and condensate in the subcooled water bath. Due to efficient boiling heat transfer via bubble nucleation, the rodlet cools down rapidly. Finally, heat transfer mode becomes singlephase natural convection when the superheat of rodlet surface is not high enough to allow activation of bubble nucleation site. The quenching and boiling curves obtained with different thermocouple readings under the liquid subcooling of 10°C are given in Figs. 5 and 6 for Zircaloy-4 and FeCrAl#2 specimen. Generally, the TMFB is relatively low at the higher elevation. Similar trend has been reported by Fudurich [10] and Mori et al. [25]. During film boiling the upward natural convection flow occurs in the liquid near the specimen surface. The liquid is heated up continuously while flowing upward. As will be shown in the later section, TMFB is very sensitive to liquid subcooling. The difference in TMFB may be attributed to the thermal stratification in the water bath, especially near the rodlet surface. In the case of FeCrAl#2 specimen such difference is more pronounced which can be attributed to the larger ρ Cp , which leads to more severe thermal stratification. Comparing the quenching and boiling curves obtained with the T2 and T3 thermocouples, it can be found that the quenching is at the same pace, however, the critical heat flux (CHF) can be very different. However, there is no obvious trend of CHF variation in the axial direction. The CHF is related to maximum heat transfer rate by wall boiling, i.e. bubble nucleation on the solid surface. The bubble nucleation site density is very sensitive to the surface temperature, cavity size, contact angle etc. We may attribute the difference in the CHF to the local surface condition. The results presented hereafter are that obtained with the T3 thermocouple readings, if not claimed. 4.2. Reproducibility In order to investigate reproducibility of the experiment result, five repetitive quenching tests are first performed for each fresh specimen under the liquid subcooling of 10°C. As shown in Fig. 7, for the FeCrAl#1 specimen the quench and boiling curves in all the runs overlap, except the first run. The difference in the first run may be attributed to the effect of remaining dust on the surface after polishing, even though the surface is already cleaned in the ultrasonic water bath. Due to the superior oxidation resistance of FeCrAl alloy [26], no significant growth of oxide layer is expected

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

JID: HMT 6

ARTICLE IN PRESS

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

Fig. 5. Quenching curves at different thermocouples with the liquid subcooling of 10 °C. Fig. 6. Derived boiling curves at different thermocouple positions at liquid subcooling of 10 °C.

after the quenching test. As Fig. 9-a shows, the oxide layer of FeCrAl after all the quench tests is still negligibly thin. The repetitive runs with the Zircaloy-4 specimen shows more appreciable difference, especially in the first four runs, as shown in Fig. 8. Oxidation resistance of Zircaloy-4 is relatively weak, the polished surface is continuously oxidized in the successive quenching tests. As shown in Fig. 9b, the oxide layer after all the quenching tests is about 2μm thick. As already reported by Sinha et al. [6] and Yeom et al. [9], TMFB increases with increasing oxide layer thickness which is consistent with our observation in Fig. 8. The effect of surface oxidation of Zircaloy-4 will be discussed in detail in the later section. In the 4th and 5th quenching of Zircaloy-4 the difference becomes less significant. Hence, we may conclude that the oxide layer becomes stable and the quench results is reproducible after the 4th quench test. 4.3. Effect of surface conditions The effects of surface oxidation can be discussed based on the five repetitive runs. Minor difference between the repetitive runs with FeCrAl alloy indicates weak effect of surface oxidation on transient boiling heat transfer during quenching, which has also been reported by Kang et al. [12]. Both of the FeCrAl surfaces become more hydrophobic (with larger contact angle) after oxidation. Comparing with the uncertainty, the effect of quenching on contact angle is negligible on FeCrAl#1 and Zircaloy-4 specimen. In the

contrast, the contact angle on the finely polished FeCrAl#2 specimen surface increases slightly after quenching, which is contradictory to Ali et al. [27] who reported decrease of the contact angle after oxidation on the Fe12Cr5Al (12w%Cr; 4.4w%Al) and Fe13Cr4Al (13w%Cr; 3.9w%Al) surfaces. It should be noted that the FeCrAl alloy utilized here has higher content of chromium and aluminum which leads to stronger oxidation resistance and condenser oxide layer. As will be discussed later, better wettability helps increase TMFB , which leads to different quenching behavior on the two FeCrAl specimens. For selection of ATF cladding materials, the contents of FeCrAl alloy, especially chromium and aluminum content, should be determined to compromise between oxidation resistance and quenching performance. Appreciable effects of surface oxidation are found on Zircaloy4 specimen. According to Yeom et al. [9], the effect of surface oxidation on transient boiling heat transfer can be attributed to modification of near-surface thermal properties by the oxide layer. The oxide layer (~2W m−1 K−1 ) has lower thermal conductivity than Zircaloy-4 (~18W m−1 K−1 ). Difference in thermal conductivity leads to small (kρ Cp )w of oxidized surface. Upon liquid-solid contact, the interface temperature, Tint , can be given by



Tw − Tint = Tint − T f

(kρCp ) f (kρCp )w

(16)

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

JID: HMT

ARTICLE IN PRESS

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

7

Fig. 7. Quench and boiling curves of five repetitive quench experiments of fresh FeCrAl#1 specimen in water bath with subcooling of 10 °C.

Fig. 8. Quench and boiling curves of five repetitive quench experiments of fresh Zircaloy-4 specimen in water bath with subcooling of 10 °C.

Small (kρ Cp )w leads to low liquid-solid interface temperature, Tint , which eases liquid spreading on the solid surface and consequently, increases TMFB . Besides increasing TMFB , the oxide layer is found to reduce the CHF, which is contrary to the observation in a heating-up experiment. A thick oxide layer which usually corresponds to small contact angle can promote bubble nucleation on the solid surface. When the oxidized surface is heated, more nucleation site can be activated and the CHF increases. However, when the CHF occurs in the quenching process, the oxide layer acts as an insulation barrier which limits heat flux coming out from the hightemperature base metal, even though the fully developed nucleate boiling can provide efficient heat transfer from solid to fluid. The quench and boiling curves obtained with the two FeCrAl specimens are compared in Fig. 10. Lower TMFB is observed on the FeCrAl#1 specimen which has larger surface roughness. However, Sinha et al. [6] and Yeom et al. [9] found that large surface roughness led to high TMFB , which is opposite to our observation. We should note here that in Sinha et al.’s experiment Ra varies from 1.27 μm to 6.60 μm, while Yeom et al. [9] compared the experiment results with the surfaces of Ra =0.2 μm and 11.4 μm. In our experiment the surface roughness is on the polished level, i.e. Ra = 0.2 μm and 1.6 μm. Bernardin and Mudawar [28] argued that TMFB

is not significantly affected by the roughness on the polished level, which is in consistent with our experiment. Besides insignificant effect on TMFB , the surface roughness at polished level shows no effect on film boiling heat transfer either. In the contrast, wettability (contact angle) is the key factor leading to the discrepancy in TMFB on the FeCrAl specimens. Better wettability (smaller contact angle) promotes liquid spreading once liquid-solid contact occurs, which increases the area covered by liquid. Hence, better wettability leads to early initiation of nucleate boiling in the film boiling regime and increases TMFB . Similar effect of contact angle has also been reported by Kang et al. [13] and Kim et al. [3,29]. 4.4. Effects of solid thermal properties When the high-temperature rodlet plunges into the water bath, energy is transferred to liquid during the initial liquid-solid contact. A thermal layer forms near the liquid-vapor interface. In the thermal layer the temperature is higher than elsewhere in the water bath. The thermal layer decreases the convective heat transfer between liquid-vapor layer and the subcooled water bath. Large (kρ Cp )w of FeCrAl alloy results in more intensive heat transfer during the initial liquid-solid contact and consequently, the thermal

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT 8

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

Fig. 9. The SEM image of specimen cross section after quenching.

layer is at higher temperature. Relatively small temperature gradient in the thermal boundary layer leads to less convective heat transfer from the liquid-vapor interface to liquid and hence, more evaporation occurs. As a consequence, a relatively thick vapor film over the FeCrAl surface is observed. Assuming the laminar heat transfer in the vapor film, the heat transfer coefficient can be estimated based on the thermal conductivity and vapor layer thickness, i.e.

h f b,cond =

kv

(17)

δv

Fig. 10. Quench and boiling curves of FeCrAl specimens at different subcoolings.

Here, the vapor conductivity is determined as that at the atmospheric pressure and the average temperature of vapor layer, i.e. (Tw + Tsat )/2. In the film boiling regime heat transfer coefficient is obtained with



h f b,cond

q − σ εb Tw 4 − Tsat 4 q − qrad = = Tw − Tsat Tw − Tsat



(18)

In Fig. 11 the conductive heat transfer coefficients are compared for the FeCrAl#2 and Zircaloy-4 surfaces. The surface emissivity εb = 0.3 is assumed for both FeCrAl#2 and Zircaloy-4 surfaces while calculating the conductive heat transfer coefficient. Even though the estimation of surface emissivity is crude, it does not show significant effect on the heat transfer coefficient because the radiative heat transfer is relatively insignificant here. We can see that the film boiling heat transfer is less efficient on the FeCrAl surface. On the contrary, Kang et al. [12]’s quenching experiment in saturated water revealed that film boiling heat transfer on Zircaloy-4 surface was less efficient than on the FeCrAl surface. Such contradiction is not surprising because when the liquid is saturated, convective heat transfer between the liquid-vapor interface and liquid is not important any more. The vapor film thicknesses over the FeCrAl#2 and Zircaloy-4 surface calculated based

Fig. 11. Convective heat transfer coefficient in film boiling, FeCrAl#2 and Zircaloy-4 at liquid subcooling of 5 °C.

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

9

Fig. 12. Film thickness over FeCrAl#2 and Zircaloy-4 specimen surface.

Fig. 13. Vapor film formed at the beginning of quench when the subcooling of water bath is 5 °C.

on Eq. (17) are quantitatively compared in Fig. 12. At the subcooling of 5 °C, the initial film thickness is about 250 μm on the Zircaloy-4 surface and about 350 μm on the FeCrAl#2 surface. Such difference can be observed in the high-speed photographs, as shown in Fig. 13. The film thickness decreases steadily on the FeCrAl#2 surface, while on the Zircaloy-4 surface the film thickness decreases rapidly in the beginning, during which heat is transferred to liquid to establish the thermal layer. Difference in vapor film thickness variation provides further evidence on the effect of convective heat transfer between the liquid-vapor interface and liquid. The quench and boiling curves obtained for FeCrAl#2 and Zircaloy-4 are compared in Fig. 14. As large (ρ Cp )w increases quench duration, quenching of FeCrAl#2 occurs much later than that of Zircaloy-4. According to Eq. (16), small (kρ Cp )w of Zircaloy-4 leads to small Tint when liquid-solid contact occurs. Consequently, the liquid spreading starts at relatively high temperature on the Zircaloy-4 surface, i.e. higher TMFB . Duffey and Porthouse [30] gave the analytical solution for quench front speed

u

−1

 D 12 TMF B − T  12 (TMF B − TCHF ) 12 f   = ρw c p,w , Bi  1 (19) 4 hkw

TCHF − T f

and

u−1 =

π ρw c p,w TMF B − T f 2h

TCHF − T f

1−

4

π

Bi 2

TCHF − T f TMF B − T f

 12 , Bi  1

(20)

Fig. 14. Comparison of the quench and boiling curves between FeCrAl and Zircaloy4.

The heat transfer coefficient in the above equations can be estimated with

h=

qCHF TCHF − T f

(21)

According to the boiling curves in Fig. 14b, the heat transfer coefficient is on the magnitude of 103 to 104 W/(m2°C ) which corresponds to Bi > 1. With the high-speed photographs the quench front speed can be calculated with displacement of quench front in a fixed time interval. The first quench front position is recorded about 1s after the quench front arrives at the cylindrical surface, while the second quench front position is recorded 10 s later. The estimated quench front speed does not show remarkable dependence on liquid subcooling. The quench front speed is about 3.5 mm/s on the FeCrAl specimen and about 9 mm/s on the Zircaloy-4 surface. According to Eq. (20), smaller (ρ Cp )w leads to fast propagation of quench front, which is consistent with the experiment observation. Even though the minimum film boiling temperature and the critical heat flux temperature can be directly obtained from the boiling curve, the quench front speed is very sensitive to heat transfer coefficient according to Eq. (20). The heat

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

JID: HMT 10

ARTICLE IN PRESS

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

Fig. 16. Dependence of film thickness on wall superheat and liquid subcooling in film boiling of FeCrAl#2.

Fig. 15. Effect of liquid subcooling on quenching behavior of FeCrAl#2.

transfer coefficient estimated with Eq. (21) leads to significant underestimation of quench front speed, which may be attributed to the underprediction of critical heat flux in the IHCP. When the appropriate heat transfer coefficient (from 80 0 0 to 90 0 0 W/(m2°C ), depending on the subcooling) is assumed, the quench front speed can be reasonably predicted. 4.5. Effect of liquid subcooling When liquid subcooling is large, more portion of heat flux are utilized to heat up the subcooled liquid in the film boiling regime. Consequently, evaporation on the liquid-vapor interface is weak and the vapor film is thin in the large-subcooling cases. In Fig. 15 snapshots of FeCrAl#2 quenching at Tsub =5 °C and 20 °C. We can clearly see the thinner vapor film in the case of Tsub =20 °C. According to Eq. (17), difference in film thickness leads to different film boiling heat transfer coefficient. Such effect can be found in the boiling curves, i.e. Fig. 10b and Fig. 14b. We can see that at the same wall superheat the film boiling heat flux is much higher in the high-subcooling cases. The dependence of vapor film thickness on wall superheat is given for the FeCrAl#2 quenching tests in Fig. 16. Here, the vapor film thickness is calculated with Eq. (17) and (18). As the wall superheat decreases, the vapor film attenuates. In the largesubcooling case the film thickness increases right before collapse, i.e. the minimum film boiling point. Since TMFB is relatively high when the subcooling is large, massive evaporation can occur upon liquid-solid contact. In the low-subcooling case the oscillatory film thickness appears which is resulted from the wavy interface, as shown in Fig. 15. At all the liquid subcoolings the vapor film collapses at the similar critical film thickness, δ v, cr ≈150 μm, on the FeCrAl#2 specimen, while on the Zircaloy-4 surface the critical vapor film thickness is lower, δ v, cr ≈110 μm. Since the critical film thickness is not apparently related to the liquid subcooling, we may deduce that the surface condition and/or thermal properties of solid are the key factors determining the critical vapor film thickness. Besides the influence on film boiling heat transfer, liquid subcooling has found to show significant effect on TMFB . Especially,

Dhir et al. [31] regarded liquid subcooling as the only parameter affecting TMFB , while Freud et al. [32] and Ebrahim et al. [14] showed solid thermal properties and dimension, besides liquid subcooling, can affect TMFB . However, it is still a common practice to correlate TMFB as a linear function of liquid subcooling, i.e.

TMF B = ATsub + TMF B,

sat

(22)

Correlating our experimental data in the above form, the coefficient A and minimum film boiling temperature in saturated liquid, TMFB, sat , are given in Table 2. The extrapolated TMFB, sat are similar for the three specimens. Based on the quenching experiment in saturated water, Kang et al. [12] reported similar TMFB, sat (283 °C) for FeCrAl (contact angle 82°), but much higher TMFB, sat (385 °C) for Zircaloy-4 (contact angle 46°). The difference in TMFB, sat is obviously caused by surface wettability. In spite of different contact angle, the coefficients A obtained from FeCrAl#1 and FeCrAl#2 are close. Ebrahim et al. [14] obtained similar coefficient A (A = =10.5) for zirconium cladding. We may conclude that TMFB on Zircaloy-4 cladding is more sensitive to liquid subcooling because of its small (ρ Cp )w . TMFB obtained with the rodlet quenching experiments in the literature, including that from Mori et al. [25], Freud et al. [32], Fu et al. [33], Fudurich [10], Ebrahim et al. [14], together with our experiment data, are used together to evaluate the linear correlations about liquid subcooling. The comparison between the correlations and experiment data are shown in Fig. 17. The coefficients and the prediction errors of linear correlations are given in Table 2. From the error value we can find that none of the correlations shows obvious superiority over the others. Even though TMFB increases apparently with the liquid subcooling, the experiment data scatters in a wide range at the same subcooling. Hence, for the sake of precise prediction, other parameters should be correlated with TMFB . 4.6. Evaluation of TMFB correlations Early in 1960s, Berenson [34] corresponded the minimum heat flux in the film boiling regime to the minimum evaporation rate that can prevent growth of disturbance resulting from the Taylor instability at the liquid-vapor interface and developed the following correlation for minimum heat flux temperature, which is equiv-

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

11

Table 2 Correlation coefficients in Eq. (12) and relative prediction errors. Ref.

Material

A

TMFB,

This work

FeCrAl#1 FeCrAl#2 Zircaloy-4 316SS Zr-702 Inconel-600 Zircaloy-4 Brass

8.48 8.6 10.4 9.7 10.5 7 7.5 6.7

234.4 274.4 265.3 276 307 256 240 177

Ebrahim et al. [14] Mori et al. [25] Fu et al. [33]

sat

1 N

N  i=1

|

22.7% 17.1% 18.5% 17.6% 19.5% 20.2% 22.5% 37.8%

exp cal TMF −TMF B,i B,i exp TMF B,i

 |

1 N

N  i=1

|

cal −T exp TMF B,i MF B,i exp TMF B,i

2

|

26.3% 21.8% 23.9% 22.7% 25.1% 23.9% 26.1% 40.2%

Fig. 17. Comparison between linear correlation of minimum film boiling temperature based on liquid subcooling and experiment data.

alent to the minimum film boiling temperature. B TMF B = Tsat

 12   13     23  ρg h f g g ρ f − ρg σ μ     + 0.127 kg ρ f + ρg g ρ f − ρg g ρ f − ρg (23)

Later, the correlations of minimum film boiling temperature are based on Berenson’s correlation. Henry [35] considered the effect of transient contacting and the microlayer evaporation and proposed the following correlation.

⎡

H B TMF B − TMF B B TMF − Tf B

= +0.42⎣

⎤0.6 (kρ c p ) f hfg  B ⎦ (kρ c p )w c p,w TMF − Tsat B

(24)

Peterson and Bajorek [36] optimized the coefficients in the above correlation based on their experiment data and obtained



(kρ c p ) f  B  = 0.239 (kρ c p )w TMF B − T∞ P B Tmin − TMF B

0.25  

hfg

B c p,w TMF − Tsat B

0.832

Fig. 18. Comparison between correlations and experiment data.

 (25)

Henry correlation, i.e. Eq. (24), and Peterson-Bajorek correlation, i.e. Eq. (25), are compared with the experimental data in Fig. 18. We can see that both correlations can prescribe the effect of solid thermal properties, but fail to predict the subcooling effect. Among the same set of data large subcooling leads to high TMFB . In general, Henry correlation overpredicts TMFB in the low-subcooling cases,

but underpredicts it at large subcoolings. Peterson-Bajorek correlation overpredicts almost all the data sets, except some largesubcooling points. Realizing the fact that the subcooling effect is not sufficiently accounted for with the correlations based on Berenson correlation, we may adopt the concept of critical film thickness, as we discussed in the Section 4.5. The critical vapor film thickness can be determined with the surface condition and solid thermal proper-

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

ARTICLE IN PRESS

JID: HMT 12

[m5G;November 29, 2019;13:0]

J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

ties, i.e.

δv,cr = f (θ , Ra , ρw , kw , Cp,w )

Acknowledgment

(26)

The corresponding heat transfer coefficient can be obtained with Eq. (17). The film boiling heat transfer coefficient can be calculated with the correlation, e.g. Nishio and Ohtake [24] which can be written in the following generalized form

h f b = h f b (Tsub , Tw , ρv /ρl , μv /μl , . . .)

(27)

Hence, the minimum film boiling temperature can be determined by solving

kv = h f b (Tsub , Tw , ρv /ρl , μv /μl , . . .) f (θ , Ra , ρw , kw , C p,w )

The authors would like to express their acknowledgement to the National Natural Science Foundation of China for their funding for this work (Project No. 51676120). Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ijheatmasstransfer. 2019.119131. References

(28)

The most challenging work in deriving a correlation based on Eq. (28) is to correlate the critical film thickness with the surface properties, which demands a large experiment matrix to investigate the effect of each parameter. 5. Conclusion Quench experiments were carried out with the FeCrAl and Zircaloy-4 rodlet at atmospheric pressure to investigate the effect of solid thermal properties, liquid subcooling and surface condition on transient pool boiling. A high-speed camera is employed to record quenching phenomenon. Based on the measured temperature and the solution of one-dimensional inverse heat conduction problem, the boiling heat transfer during quench is investigated. The main conclusions are as follows: (1) Quenching of FeCrAl alloy is not affected by surface oxidation, while surface oxidation of Zircaloy-4 increases the minimum film boiling temperature, TMFB , but decreases the critical heat flux due to small (ρ kCp )w of the oxide layer. (2) Surface roughness on the polished level does not affect TMFB in an appreciable way. However, TMFB is sensitive to the contact angle because the better wettability promotes liquid spreading once the liquid-solid contact starts. (3) Due to its large (ρ Cp )w , quench front speed is relatively low and quenching duration for FeCrAl alloy is relatively long, compared with Zircaloy-4. Large (ρ kCp )w of FeCrAl leads to thick vapor film in the film boiling regime when the liquid is subcooled and consequently, less efficient film boiling heat transfer. (4) Liquid subcooling effect is stronger for Zircaloy-4 due to its small (ρ Cp )w . Henry and Peterson- Bajorek correlation for TMFB do not properly account for the effect of liquid subcooling. (5) The critical vapor film thickness is found before the film collapse. The critical thickness is independent of liquid subcooling in the range of 5◦ C ≤ Tsub ≤ 20◦ C. However, it is affected by the solid thermal properties and surface conditions. Based on the critical vapor film thickness, a new approach for prediction of TMFB is proposed. Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted. CRediT authorship contribution statement Jinbiao Xiong: Conceptualization, Methodology, Writing - original draft, Writing - review & editing, Project administration, Funding acquisition.

[1] G. Liang, I. Mudawar, Review of pool boiling enhancement by surface modification, Int. J. Heat Mass Transfer 128 (2019) 892–933. [2] S.K.R. Chowdhury, R.H.S. Winterton, Surface effects in pool boiling, Int. J. Heat Mass Transfer 28 (10) (1985) 1881–1889. [3] H. Kim, et al., Nanoparticle deposition effects on the minimum heat flux point and quench front speed during quenching in water-based alumina nanofluids, Int. J. Heat Mass Transfer 53 (7) (2010) 1542–1553. [4] J.-Q. Li, et al., Enhanced pool boiling heat transfer during quenching of water on superhydrophilic porous surfaces: effects of the surface wickability, Int. J. Heat Mass Transfer 125 (2018) 494–505. [5] C. Kruse, et al., Extraordinary shifts of the leidenfrost temperature from multiscale micro/nanostructured surfaces, Langmuir 29 (31) (2013) 9798–9806. [6] J. Sinha, Effects of surface roughness, oxidation level, and liquid subcooling on the minimum film boiling temperature, Exp. Heat Transfer 16 (1) (2003) 45–60. [7] C.Y. Lee, S. Kim, Parametric investigation on transient boiling heat transfer of metal rod cooled rapidly in water pool, Nucl. Eng. Des. 313 (2017) 118–128. [8] T. Yamada, et al., Film boiling heat transfer around a vertical finite-length cylinder with a convex hemispherical bottom, Heat Transfer Asian Res. 39 (3) (2010) 166–177. [9] H. Yeom, et al., Transient pool boiling heat transfer of oxidized and roughened Zircaloy-4 surfaces during water quenching, Int. J. Heat Mass Transfer 120 (2018) 435–446. [10] V.D. Fudurich, in: Effect of Liquid Subcooling, Initial Surface Temperature, and Surface Properties on the Minimum Film Boiling Temperature in College of Engineering, The Pennsylvania State University, 2016, p. 80. [11] C.Y. Lee, T.H. Chun, W.K. In, Effect of change in surface condition induced by oxidation on transient pool boiling heat transfer of vertical stainless steel and copper rodlets, Int. J. Heat Mass Transfer 79 (2014) 397–407. [12] J.Y. Kang, et al., Quenching of candidate materials for accident tolerant fuel– cladding in LWRs, Ann. Nucl. Energy 112 (2018) 794–807. [13] J.Y. Kang, et al., Film boiling heat transfer on a completely wettable surface with atmospheric saturated distilled water quenching, Int. J. Heat Mass Transfer 93 (2016) 67–74. [14] S.A. Ebrahim, et al., Parametric investigation of film boiling heat transfer on the quenching of vertical rods in water pool, Appl. Therm. Eng. 140 (2018) 139–146. [15] S.J. Zinkle, et al., Accident tolerant fuels for LWRs: A perspective, J. Nucl. Mater. 448 (1) (2014) 374–379. [16] K.A. Terrani, Accident tolerant fuel cladding development: promise, status, and challenges, J. Nucl. Mater. 501 (2018) 13–30. [17] R.B. Rebak, Alloy Selection for Accident Tolerant Fuel Cladding in Commercial Light Water Reactors, Metallurg. Mater. Trans. E 2 (4) (2015) 197–207. [18] M. Snead, et al., Technology Implementation Plan ATF FeCrAl Cladding for LWR Application, Oak Ridge National Laboratory, May 2014 ORNL/TM-2014-3532014. [19] A. Seshadri, K. Shirvan, Quenching heat transfer analysis of accident tolerant coated fuel cladding, Nucl. Eng. Des. 338 (2018) 5–15. [20] Z. Wang, et al., Experimental investigation on the Leidenfrost phenomenon of droplet impact on heated silicon carbide surfaces, Int. J. Heat Mass Transfer 128 (2019) 1206–1217. [21] Z. Wang, et al., Investigation on effect of surface properties on droplet impact cooling of cladding surfaces, Nuclear Eng. Technol. (2019). [22] K.-G. Lee, W.-K. In, H.-G. Kim, Quenching experiment on Cr-alloy-coated cladding for accident-tolerant fuel in water pool under low and high subcooling conditions, Nucl. Eng. Des. 347 (2019) 10–19. [23] J.V. Beck, B. Blackwell, C.R.S. Clair Jr, Inverse Heat Conduction: Ill-Posed Problems, James Beck, 1985. [24] S. Nishio, H. Ohtake, Vapor-film-unit model and heat transfer correlation for natural-convection film boiling with wave motion under subcooled conditions, Int. J. Heat Mass Transfer 36 (10) (1993) 2541–2552. [25] M. Mori, et al., Transient cooling process of fuel rod in reactivity initiated accident, J. Nucl. Sci. Technol. 17 (6) (1980) 413–424. [26] D. Pan, et al., Formation and stability of oxide layer in FeCrAl fuel cladding material under high-temperature steam, J. Alloys Compd. 684 (2016) 549–555. [27] A.F. Ali, et al., Surface wettability and pool boiling critical heat flux of accident tolerant fuel cladding-FeCrAl alloys, Nucl. Eng. Des. 338 (2018) 218–231. [28] J.D. Bernardin, I. Mudawar, The Leidenfrost point: experimental study and assessment of existing models, J. Heat Transfer 121 (4) (1999) 894–903.

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131

JID: HMT

ARTICLE IN PRESS J. Xiong, Z. Wang and P. Xiong et al. / International Journal of Heat and Mass Transfer xxx (xxxx) xxx

[29] H. Kim, et al., On the effect of surface roughness height, wettability, and nanoporosity on Leidenfrost phenomena, Appl. Phys. Lett. 98 (8) (2011) 083121. [30] R.B. Duffey, D.T.C. Porthouse, The physics of rewetting in water reactor emergency core cooling, Nucl. Eng. Des. 25 (3) (1973) 379–394. [31] V. Dhir, G. Purohit, Subcooled film-boiling heat transfer from spheres, Nucl. Eng. Des. 47 (1) (1978) 49–66. [32] R. Freud, R. Harari, E. Sher, Collapsing criteria for vapor film around solid spheres as a fundamental stage leading to vapor explosion, Nucl. Eng. Des. 239 (4) (2009) 722–727.

[m5G;November 29, 2019;13:0] 13

[33] B.-R. Fu, et al., Quenching characteristics of a continuously-heated rod in natural sea water, Int. J. Heat Mass Transfer 95 (2016) 206–213. [34] P.J. Berenson, Film-boiling heat transfer from a horizontal surface, J. Heat Transfer 83 (3) (1961) 351–356. [35] R.E. Henry, A correlation for the minimum film boiling temperature, AIChE Symp., Ser., 70, 1974. [36] Peterson, L.J. and S.M. Bajorek, Experimental investigation of minimum film boiling temperature for vertical cylinders at elevated pressure. 2002(35979): p. 883-892.

Please cite this article as: J. Xiong, Z. Wang and P. Xiong et al., Experimental investigation on transient boiling heat transfer during quenching of fuel cladding surfaces, International Journal of Heat and Mass Transfer, https://doi.org/10.1016/j.ijheatmasstransfer.2019. 119131