- Email: [email protected]
Measurement of the void fraction in a channel simulating the HANARO fuel assembly using neutron radiography
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186 www.elsevier.com/locate/nima
Measurement of the void fraction in a channel simulating the HANARO fuel assembly using neutron radiography I.C. Lima,, C.M. Sima, J.E. Chaa, Y.S. Choia, N. Takenakab, Y. Saitoc, B.J. Juna a Korea Atomic Energy Research Institute, Daejeon 305-600, Republic of Korea Department of Mechanical Engineering, Kobe University, Kobe 657-8501, Japan c Kyoto University Research reactor Institute, Kumatori 590-0494, Japan
b
Available online 2 February 2005
Abstract A test section simulating the HANARO fuel channel was constructed and the void fraction was measured by using the high-speed neutron radiography technique. The test was performed at a beam facility of HANARO called Ex-core Neutron-irradiation Facility (ENF). D2O was used as the working liquid and air was used to simulate the void. The measurements were made at various combinations of the liquid flow and gas flow and the result were compared with the predictions of the existing correlations. r 2005 Elsevier B.V. All rights reserved. PACS: 47.55.K Keywords: Void fraction; HANARO ENF; High-speed neutron radiography
1. Introduction The dynamic neutron radiography is a powerful tool for fluid flow visualization as well as the multi-phase flow research [1–3]. This technique can be used to investigate the detailed behavior of neutron-opaque fluid in metallic enclosure. HANARO is an open-tank-in-pool-type research reactor operated by the Korea Atomic Energy Corresponding author. Tel.: +82 42 868 8432;
fax: +82 42 868 8809. E-mail address: [email protected] (I.C. Lim).
Research Institute (KAERI). Its initial criticality was achieved in 1995 and it is now operating at 24 MW. Among the neutron beam utilization facilities in HANARO, the Neutron Radiography Facility (NRF) and the Ex-core Neutron-irradiation Facility (ENF) facility can be used for neutron radiography and they were built in 1997 and 2001, respectively. The ENF facility in HANARO was constructed in 2001 for brain tumor cancer therapy. In the development of this facility, it was recognized that this facility could be well suited for dynamic neutron radiography considering its beam characteristics [4].
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.097
ARTICLE IN PRESS 182
I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
A test section composed of four Fuel Element Simulators (FESs) in a square array simulating the HANARO fuel channel was constructed and the void fraction was measured by using the neutron radiography technique. A high-speed camera was used for the image capture. D2O was used as the working liquid and air was used to simulate the void. The measurements were made at various combinations of the liquid flow and gas flow and the results were compared with the predictions of the existing correlations.
2. ENF facility of HANARO [4] 2.1. Facility description HANARO has seven beam tubes and the IR beam tube is used for the ENF facility. The inside of the shielding room in front of the IR beam exit is as shown in Fig. 1. Its floor area is 4 6 m2 and the height is 3 m. The details for arrangement of the shutter, filter and collimator are shown in Fig. 2. The beam tube nose made from Zr-4 is located at the position of the peak thermal neutron flux in D2O reflector region. A long water cylinder plays the role of beam shutter. By hydraulically moving the water in/out of the water cylinder, it plays the role of the beam shutter. A radiation filter for BNCT should remove fast neutrons and gammas but pass more thermal neutrons. A
Fig. 2. Beam shutter and filter for ENF.
feasibility study on the candidate materials for the filter was performed through computer simulation and the silicon single crystal was chosen for filtering fast neutrons. Its cross-section is high for the fast neutron and low for the thermal neutron. A bismuth single crystal was selected for filtering the gamma radiation, considering that its neutron absorption cross-section is relatively low. To keep the radiation level low, auxiliary shields were added around the radiation filter and polyethylene, borated polyethylene and lead were used. Two exit collimators which are made from PE and 6 Li2CO3 are available and their inside diameters are 15 and 10 cm, respectively.
2.2. Beam characteristics
Fig. 1. A view for the inside of ENF shielding room.
The neutron flux, L/D ratio, Cd ratio and n=g ratio at the various locations in the ENF shielding room are given in Table 1. The neutron fluxes and Cd ratios were measured by using the gold wire activation method. The n=g ratios were obtained by the simulations using MCNP4B. The L/D ratios were obtained by using the geometric information. If the Si filter is cooled by liquid nitrogen, the neutron flux increases by 40%.
ARTICLE IN PRESS I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
183
Table 1 Neutron beam characteristics of ENF beam in HANARO at 24 MW operation Distance from beam exit (m) 2
Flux (n/cm s) n=g ratio (n/mR cm2) L/D ratio Cd ratio
0
1.05
2
3.57
8.34E8 1.48E8 38.5 104
3.34E8 — 47.3 160
2.58E8 — 55.2 —
1.30E8 1.10E8 68 —
R/ T
1256
L/ T
Fig. 3. Cross-section of test section.
3. HANARO fuel channel test (Hex Bolt, Nut, S/ W)
3.1. Test section and test loop HANARO uses two types of fuel assemblies: 36element assembly and 18-element assembly. A test section composed of the four FESs was built, which simulates a part of the 18-element assembly. The cross-section of the test section is in Fig. 3 and the overall view of the test section is in Fig. 4. The maximum path length of the neutron beam through the test section is 24.05 mm. The part of the test section facing the neutron beam was made of Al and the FESs were made of Al as well. At about every quarter of the test section in vertical direction, a spacer in Fig. 5 is located. Fig. 6 is the schematic diagram of the test loop with the NR setup. A pump circulated D2O and the air from the test section outlet was vent to the outside of the test section. A mass flow meter was used for the liquid flow rate measurement and rotor meters were used for the airflow rate measurement.
(Bolt, S/ W)
(STS 304)
3
32 (
)
Fig. 4. Overall view of the test section.
3.2. Imaging system The list of optical devices used for the test is in Table 2. The HG-LE camera adopt CMOS sensor and the special resolution of 752 752 is available when the frame rate is less than 1500 fps.
ARTICLE IN PRESS I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
184
between the test section and the converter was 7.1 cm. A neutron image covers the region of 26.8 to 117.8 mm from the top spacer. The images were taken at the various combinations of liquid and air flow rates. In addition, a series of tests was performed with three spacers and another series was performed with only the bottom spacer. The camera frame rate was 1000 fps and the gate time of the image intensifier was 650 ms. The gain of the image intensifier was maintained at its minimum value, which is 1.7E4 lm/m2/lx.
4. Void fraction calculation Fig. 5. A spacer used for the test.
Monitor
irr
GG ¼ Cfth expfST dT g þ G 0
or
Neutron Beam
M
Converter
Separator
The local void fraction was calculated by using the S-scaling method [5]. The image gray level of the test section filled with gas GG ; liquid G L and two-phase mixture GM are expressed by
Mass Flow meter
Test Section
Collimator High Speed Camera
Grid Spacer
Image Processor
Pressure Regulator
G0 ¼ GS þ GD
ð1Þ
GL ¼ Cfth expfSL dL ST dT g þ G 0
(2)
GM ¼ Cfth expfSL dML ST dT g þ G 0 .
(3)
Converter Lens
a¼1
Air Filter
Table 2 List of optical devices used for the test
Here, C, fth ; S and d mean the gain, the incident neutron flux, the total macroscopic cross-section for thermal neutrons, and the object thickness, respectively. The subscripts L, T and ML denote the liquid single phase, the test section and the liquid phase in the two-phase mixture, respectively. The offset term G 0 includes the dark current of the imaging system GD and the gray level due to scattered neutrons GS. Then, the void fraction a at a point can be determined from Eqs. (1)–(3) as
Magnetic Gear Pump Filter
Bubble Generator
Rotor meter
Compressed Air
D2O (Tap water)
Fig. 6. Schematic diagram of the test loop with NR setup.
Image intensifier Relay lens Camera
NE426 type Nikon 105 mm Telegraphic lens Hamamatsu C6598+booster Hamamatsu A4539 Redlake HG-LE
3.3. Test method The test section was located at the position of 239 cm from the beam exit and the distance
dML ln ½G L G0 =G M G 0
¼ ln ½G L G 0 =G G G0
dL
(4)
where G0 ¼
G L G G expðSL dL Þ . 1 expðSL dL Þ
The void fraction obtained from this equation is the line average void fraction and the area averaged void fraction should be obtained by integrating the line average void fraction weighted with the beam path length.
ARTICLE IN PRESS I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
5. Instantaneous void fraction images Fig. 7 shows several instantaneously processed void fraction images for the test with three spacers and Fig. 8 those for the test without middle and top spacers. For these tests, the liquid velocity was
185
0.3 m/s and the air velocity was 0.82 m/s. The images were clear enough to discern flow patterns.
6. Void fraction data In Fig. 9, j G =a are plotted against j for data from the tests with three spacers. Here, jG is the gas phase velocity and j is the summation of gas phase velocity and liquid phase velocity. Fig. 10 is the same graph for the test without top and middle spacers. The area averaged void fraction data were obtained for the two series of test; one with all spacers and the other without middle and top spacers. The experimental results were compared with the prediction of the Zuber correlations [6]. The Zuber correlation applicable to the whole flow pattern is a¼
jG
Co j þ 1:41 sgðrL rG Þ=r2L
1=4 .
(5)
Here, s; g and r are surface tension, gravitational acceleration and density, respectively. Co is 1.13. The Zuber correlation for slug flow pattern is Fig. 7. Instantaneous processed void fraction images (j L ¼ 0:3 m=s; j G ¼ 0:82 m=s; with three spacers). (a) 0 s, (b) 250 ms, (c) 500 ms, (d) 750 ms.
Fig. 8. Instantaneous processed void fraction images (j L ¼ 0:3 m=s; j G ¼ 0:82 m=s; without top and middle spacers). (a) 0 s, (b) 250 ms, (c) 500 ms, (d) 750 ms.
a¼
jG
1=2 . Co j þ 0:345 gDðrL rG Þ r2L
(6)
Fig. 9. Comparison of measure void fraction with the predicted values (tests with three spacers).
ARTICLE IN PRESS 186
I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
the high-speed dynamic neutron radiography technique. From the test, the followings were found: 1. The neutron flux at the ENF facility of HANARO was high enough to obtain clear images at 1000 fps. 2. When the top and middle spacers do not exist, the bubbles coalesce easier and the bubble size becomes longer and larger. 3. The Zuber correlation gives the better prediction of void fraction when three spacers exist. 4. The Zuber correlation for slug flow gives the better prediction of void fraction when the middle and top spacers do not exist. Fig. 10. Comparison of measured void fraction with the predicted values (tests without bottom and middle spacers).
Here, D is the pipe diameter and the hydraulic diameter of the test section was used for this analysis. In Fig. 9, it can be found that the Zuber correlation fits the experimental data very well. In Fig. 10, j G =a are plotted against j for data from the tests without top and middle spacers. In this figure, it can be found that the Zuber correlation for slug flow fits the experimental data better. When the top and middle spacers do not exist, the bubbles coalesce easier and the bubble size becomes longer and larger. This is believed to be the reason why the Zuber correlation for slug flow gives better prediction.
7. Conclusion The void fraction for the channel simulating the HANARO fuel channel was measured by using
Acknowledgments The authors would like to thank KISTEP (Korea Institute of S&T Evaluation and Planning) for supporting the project to perform this joint research between Korea and Japan. The authors also appreciate Syncron Co. for offering a HG-LE high-speed camera and technical assistance.
References [1] J.T. Lindsay, et al., in: J.P. Barton (Ed.), Proceedings of the Fourth World Conference On Neutron Radiography, Gordon & Breach Science Publishers., San Francisco, 10–16 May 1992. [2] K. Mishima, et al., Nucl. Instr. and Meth. A 424 (1999) 66. [3] I.C. Lim, KAERI Report, KAERI/RR-2094/2001, 2001. [4] I.C. Lim, Key Engineering Materials 270–273 (2004) 1343. [5] Y. Saito, et al., Proceedings of NURETH-10, Seoul, Korea, 5–9 October 2003. [6] N. Zuber, J.A. Findlay, J. Heat Transfer 87 (1965) 45.
Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186 www.elsevier.com/locate/nima
Measurement of the void fraction in a channel simulating the HANARO fuel assembly using neutron radiography I.C. Lima,, C.M. Sima, J.E. Chaa, Y.S. Choia, N. Takenakab, Y. Saitoc, B.J. Juna a Korea Atomic Energy Research Institute, Daejeon 305-600, Republic of Korea Department of Mechanical Engineering, Kobe University, Kobe 657-8501, Japan c Kyoto University Research reactor Institute, Kumatori 590-0494, Japan
b
Available online 2 February 2005
Abstract A test section simulating the HANARO fuel channel was constructed and the void fraction was measured by using the high-speed neutron radiography technique. The test was performed at a beam facility of HANARO called Ex-core Neutron-irradiation Facility (ENF). D2O was used as the working liquid and air was used to simulate the void. The measurements were made at various combinations of the liquid flow and gas flow and the result were compared with the predictions of the existing correlations. r 2005 Elsevier B.V. All rights reserved. PACS: 47.55.K Keywords: Void fraction; HANARO ENF; High-speed neutron radiography
1. Introduction The dynamic neutron radiography is a powerful tool for fluid flow visualization as well as the multi-phase flow research [1–3]. This technique can be used to investigate the detailed behavior of neutron-opaque fluid in metallic enclosure. HANARO is an open-tank-in-pool-type research reactor operated by the Korea Atomic Energy Corresponding author. Tel.: +82 42 868 8432;
fax: +82 42 868 8809. E-mail address: [email protected] (I.C. Lim).
Research Institute (KAERI). Its initial criticality was achieved in 1995 and it is now operating at 24 MW. Among the neutron beam utilization facilities in HANARO, the Neutron Radiography Facility (NRF) and the Ex-core Neutron-irradiation Facility (ENF) facility can be used for neutron radiography and they were built in 1997 and 2001, respectively. The ENF facility in HANARO was constructed in 2001 for brain tumor cancer therapy. In the development of this facility, it was recognized that this facility could be well suited for dynamic neutron radiography considering its beam characteristics [4].
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.097
ARTICLE IN PRESS 182
I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
A test section composed of four Fuel Element Simulators (FESs) in a square array simulating the HANARO fuel channel was constructed and the void fraction was measured by using the neutron radiography technique. A high-speed camera was used for the image capture. D2O was used as the working liquid and air was used to simulate the void. The measurements were made at various combinations of the liquid flow and gas flow and the results were compared with the predictions of the existing correlations.
2. ENF facility of HANARO [4] 2.1. Facility description HANARO has seven beam tubes and the IR beam tube is used for the ENF facility. The inside of the shielding room in front of the IR beam exit is as shown in Fig. 1. Its floor area is 4 6 m2 and the height is 3 m. The details for arrangement of the shutter, filter and collimator are shown in Fig. 2. The beam tube nose made from Zr-4 is located at the position of the peak thermal neutron flux in D2O reflector region. A long water cylinder plays the role of beam shutter. By hydraulically moving the water in/out of the water cylinder, it plays the role of the beam shutter. A radiation filter for BNCT should remove fast neutrons and gammas but pass more thermal neutrons. A
Fig. 2. Beam shutter and filter for ENF.
feasibility study on the candidate materials for the filter was performed through computer simulation and the silicon single crystal was chosen for filtering fast neutrons. Its cross-section is high for the fast neutron and low for the thermal neutron. A bismuth single crystal was selected for filtering the gamma radiation, considering that its neutron absorption cross-section is relatively low. To keep the radiation level low, auxiliary shields were added around the radiation filter and polyethylene, borated polyethylene and lead were used. Two exit collimators which are made from PE and 6 Li2CO3 are available and their inside diameters are 15 and 10 cm, respectively.
2.2. Beam characteristics
Fig. 1. A view for the inside of ENF shielding room.
The neutron flux, L/D ratio, Cd ratio and n=g ratio at the various locations in the ENF shielding room are given in Table 1. The neutron fluxes and Cd ratios were measured by using the gold wire activation method. The n=g ratios were obtained by the simulations using MCNP4B. The L/D ratios were obtained by using the geometric information. If the Si filter is cooled by liquid nitrogen, the neutron flux increases by 40%.
ARTICLE IN PRESS I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
183
Table 1 Neutron beam characteristics of ENF beam in HANARO at 24 MW operation Distance from beam exit (m) 2
Flux (n/cm s) n=g ratio (n/mR cm2) L/D ratio Cd ratio
0
1.05
2
3.57
8.34E8 1.48E8 38.5 104
3.34E8 — 47.3 160
2.58E8 — 55.2 —
1.30E8 1.10E8 68 —
R/ T
1256
L/ T
Fig. 3. Cross-section of test section.
3. HANARO fuel channel test (Hex Bolt, Nut, S/ W)
3.1. Test section and test loop HANARO uses two types of fuel assemblies: 36element assembly and 18-element assembly. A test section composed of the four FESs was built, which simulates a part of the 18-element assembly. The cross-section of the test section is in Fig. 3 and the overall view of the test section is in Fig. 4. The maximum path length of the neutron beam through the test section is 24.05 mm. The part of the test section facing the neutron beam was made of Al and the FESs were made of Al as well. At about every quarter of the test section in vertical direction, a spacer in Fig. 5 is located. Fig. 6 is the schematic diagram of the test loop with the NR setup. A pump circulated D2O and the air from the test section outlet was vent to the outside of the test section. A mass flow meter was used for the liquid flow rate measurement and rotor meters were used for the airflow rate measurement.
(Bolt, S/ W)
(STS 304)
3
32 (
)
Fig. 4. Overall view of the test section.
3.2. Imaging system The list of optical devices used for the test is in Table 2. The HG-LE camera adopt CMOS sensor and the special resolution of 752 752 is available when the frame rate is less than 1500 fps.
ARTICLE IN PRESS I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
184
between the test section and the converter was 7.1 cm. A neutron image covers the region of 26.8 to 117.8 mm from the top spacer. The images were taken at the various combinations of liquid and air flow rates. In addition, a series of tests was performed with three spacers and another series was performed with only the bottom spacer. The camera frame rate was 1000 fps and the gate time of the image intensifier was 650 ms. The gain of the image intensifier was maintained at its minimum value, which is 1.7E4 lm/m2/lx.
4. Void fraction calculation Fig. 5. A spacer used for the test.
Monitor
irr
GG ¼ Cfth expfST dT g þ G 0
or
Neutron Beam
M
Converter
Separator
The local void fraction was calculated by using the S-scaling method [5]. The image gray level of the test section filled with gas GG ; liquid G L and two-phase mixture GM are expressed by
Mass Flow meter
Test Section
Collimator High Speed Camera
Grid Spacer
Image Processor
Pressure Regulator
G0 ¼ GS þ GD
ð1Þ
GL ¼ Cfth expfSL dL ST dT g þ G 0
(2)
GM ¼ Cfth expfSL dML ST dT g þ G 0 .
(3)
Converter Lens
a¼1
Air Filter
Table 2 List of optical devices used for the test
Here, C, fth ; S and d mean the gain, the incident neutron flux, the total macroscopic cross-section for thermal neutrons, and the object thickness, respectively. The subscripts L, T and ML denote the liquid single phase, the test section and the liquid phase in the two-phase mixture, respectively. The offset term G 0 includes the dark current of the imaging system GD and the gray level due to scattered neutrons GS. Then, the void fraction a at a point can be determined from Eqs. (1)–(3) as
Magnetic Gear Pump Filter
Bubble Generator
Rotor meter
Compressed Air
D2O (Tap water)
Fig. 6. Schematic diagram of the test loop with NR setup.
Image intensifier Relay lens Camera
NE426 type Nikon 105 mm Telegraphic lens Hamamatsu C6598+booster Hamamatsu A4539 Redlake HG-LE
3.3. Test method The test section was located at the position of 239 cm from the beam exit and the distance
dML ln ½G L G0 =G M G 0
¼ ln ½G L G 0 =G G G0
dL
(4)
where G0 ¼
G L G G expðSL dL Þ . 1 expðSL dL Þ
The void fraction obtained from this equation is the line average void fraction and the area averaged void fraction should be obtained by integrating the line average void fraction weighted with the beam path length.
ARTICLE IN PRESS I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
5. Instantaneous void fraction images Fig. 7 shows several instantaneously processed void fraction images for the test with three spacers and Fig. 8 those for the test without middle and top spacers. For these tests, the liquid velocity was
185
0.3 m/s and the air velocity was 0.82 m/s. The images were clear enough to discern flow patterns.
6. Void fraction data In Fig. 9, j G =a are plotted against j for data from the tests with three spacers. Here, jG is the gas phase velocity and j is the summation of gas phase velocity and liquid phase velocity. Fig. 10 is the same graph for the test without top and middle spacers. The area averaged void fraction data were obtained for the two series of test; one with all spacers and the other without middle and top spacers. The experimental results were compared with the prediction of the Zuber correlations [6]. The Zuber correlation applicable to the whole flow pattern is a¼
jG
Co j þ 1:41 sgðrL rG Þ=r2L
1=4 .
(5)
Here, s; g and r are surface tension, gravitational acceleration and density, respectively. Co is 1.13. The Zuber correlation for slug flow pattern is Fig. 7. Instantaneous processed void fraction images (j L ¼ 0:3 m=s; j G ¼ 0:82 m=s; with three spacers). (a) 0 s, (b) 250 ms, (c) 500 ms, (d) 750 ms.
Fig. 8. Instantaneous processed void fraction images (j L ¼ 0:3 m=s; j G ¼ 0:82 m=s; without top and middle spacers). (a) 0 s, (b) 250 ms, (c) 500 ms, (d) 750 ms.
a¼
jG
1=2 . Co j þ 0:345 gDðrL rG Þ r2L
(6)
Fig. 9. Comparison of measure void fraction with the predicted values (tests with three spacers).
ARTICLE IN PRESS 186
I.C. Lim et al. / Nuclear Instruments and Methods in Physics Research A 542 (2005) 181–186
the high-speed dynamic neutron radiography technique. From the test, the followings were found: 1. The neutron flux at the ENF facility of HANARO was high enough to obtain clear images at 1000 fps. 2. When the top and middle spacers do not exist, the bubbles coalesce easier and the bubble size becomes longer and larger. 3. The Zuber correlation gives the better prediction of void fraction when three spacers exist. 4. The Zuber correlation for slug flow gives the better prediction of void fraction when the middle and top spacers do not exist. Fig. 10. Comparison of measured void fraction with the predicted values (tests without bottom and middle spacers).
Here, D is the pipe diameter and the hydraulic diameter of the test section was used for this analysis. In Fig. 9, it can be found that the Zuber correlation fits the experimental data very well. In Fig. 10, j G =a are plotted against j for data from the tests without top and middle spacers. In this figure, it can be found that the Zuber correlation for slug flow fits the experimental data better. When the top and middle spacers do not exist, the bubbles coalesce easier and the bubble size becomes longer and larger. This is believed to be the reason why the Zuber correlation for slug flow gives better prediction.
7. Conclusion The void fraction for the channel simulating the HANARO fuel channel was measured by using
Acknowledgments The authors would like to thank KISTEP (Korea Institute of S&T Evaluation and Planning) for supporting the project to perform this joint research between Korea and Japan. The authors also appreciate Syncron Co. for offering a HG-LE high-speed camera and technical assistance.
References [1] J.T. Lindsay, et al., in: J.P. Barton (Ed.), Proceedings of the Fourth World Conference On Neutron Radiography, Gordon & Breach Science Publishers., San Francisco, 10–16 May 1992. [2] K. Mishima, et al., Nucl. Instr. and Meth. A 424 (1999) 66. [3] I.C. Lim, KAERI Report, KAERI/RR-2094/2001, 2001. [4] I.C. Lim, Key Engineering Materials 270–273 (2004) 1343. [5] Y. Saito, et al., Proceedings of NURETH-10, Seoul, Korea, 5–9 October 2003. [6] N. Zuber, J.A. Findlay, J. Heat Transfer 87 (1965) 45.