1. University of Fukui, Japan ○ Akihiro Nimura Shuji Hattori Hiroki Yada
Effect of temperature on cavitation erosion of 9Cr steel in liquid metal
　　　University of Fukui, Japan
　　　　　○ Akihiro Nimura
　　　　　　　Shuji Hattori
　　　　　　　Hiroki Yada
Thank you chairman. My name is Akihiro Nimura, and I’m a student of university of Fukui, Japan. I’ll talk about the “effect of temperature on cavitation erosion of 9Cr steel in liquid metal”.,.

2. Research background
Research on cavitation erosion in liquid metal is very important to confirm the safety of the “Monju”.
But, research on cavitation erosion on liquid metal has been hardly done compared with research in water.
Fast breeder reactor “Monju”.
Cavitation erosion rate at a temperature of 260℃ in sodium was 9 times higher than that in water.
We are afraid that cavitation erosion rate increases at 500℃.
Cavitation erosion in a fast breeder reactor environment has hardly been studied.
This shows the research background of this study. Research on cavitation erosion in liquid metals is very important to confirm the safety of “Monju”. “Monju” is the fast breeder reactor built in Japan.
But, research on cavitation erosion on liquid metal has been hardly done compared with research in water.
Previous, it was found that the cavitation erosion rate at a temperature of 260℃ in sodium was 9 times higher than that in water.
We are afraid cavitation erosion rate increases at 500 degree celsius.
Cavitation erosion in a fast breeder reactor environment has been hardly studied.

3. Previous research
We carried out the cavitation erosion tests in three kinds of lead bismuth ( PbBi ) alloy.
Effect of test temperature is larger than that of metal composition on cavitation erosion.
※ Hattori et al. Wear 267 (2009)
This shows the previous research. We carried out the cavitation erosion test in three kinds of lead bismuth. This figure its result. The blue curves show the mass loss in PbBi-47, red curves in PbBi-68, green curves in PbBi-94, orange curves in deionized water. This test results shows the effect of test temperature is larger than that of metal composition on cavitation erosion.
In the previous research, we clarified that erosion rates in PbBi of relative temperature 14° is 10 to 12 times higher than that in deionized water.
In the previous research, we clarified that erosion rates in PbBi at relative temperature of 14° is times higher than that in deionized water.

4. Problems
Test temperature range is very limited for 75 to 150℃ ( ° of relative temperature ranges)
Erosion rate at high temperatures remains uncertain.
Present test region
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 =
　　　　　　　　　　　　 𝑇𝑒𝑠𝑡 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 −𝐹𝑟𝑒𝑒𝑧𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡 𝐵𝑜𝑖𝑙𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡 −𝐹𝑟𝑒𝑒𝑧𝑖𝑛𝑔 𝑝𝑜𝑖𝑛𝑡 ×100
Objectives
Cavitation erosion tests were carried out at various temperatures.
Effect of the test temperature on the cavitation erosion rates is clarified.
A method for predicting the erosion rate in sodium is proposed using the test results of deionized water and PbBi alloy obtained in this study.
This shows the problems. Test temperature range is a very limited from 75 to 150℃. This figure shows the relation between the relative temperature and erosion rates. The relative temperature was defined as this equation. Test temperature could be changed up to 16 degree. Therefore, erosion rate at high temperatures remains uncertain.
This shows the purposes. Cavitation erosion tests were carried out at various temperatures. Effect of the test temperature on the cavitation erosion rates is clarified. A method for predicting the erosion rate in sodium is proposed using the test results of deionized water and PbBi alloy obtained in this study.

5. Chemical composition and physical properties of test materials
Test specimen is 9Cr steel which is proposed to be used for pipes in the next-generation fast breeder reactor and stainless steel SUS304 which is used for pipes in the present fast breeder reactor “Monju”.
Material C Si Mn P S Ni Cr Mo V Nb Al HV
9Cr steel
0.09
0.23
0.37
0.02
0.001
0.18
8.82
0.97
0.20
0.07
0.004
180
SUS304
0.05
0.33
1.76
0.036
0.022
8.49
18.2 ―
189
Liquid metal is a low melting-point PbBi alloy which consists of the elements Bi, Pb, Sn, and Cd. Melting temperature is 68℃.
These show the chemical composition and physical property of test materials. The test specimen is 9Cr steel which is proposed to be used for pipes in the next-generation fast breeder reactor and stainless steel SUS304 which is used for pipes in the present fast breeder reactor “Monju”.
This table shows the chemical composition of test material.
Llquid metal is a low melting-point PbBi alloy which consists of the elements Bi, Pb, Sn, and Cd. Melting temperature is 68℃.
This table shows the physical property of PbBi. Bi Pb Sn Cd
PbBi-68 50
26.7
13.3 10
PbBi-68
Freezing point [℃] 68
Boiling point [℃]
575
Density 20℃ [g/cm3]
9.38
100 mm
PbBi

6. Test apparatus and test conditions
Piezo-electric oscillation apparatus
(according to ASTM G32)
Test temperature available : ℃
Vibrational frequency : 20kHz
Peak-to-peak displacement
amplitude : 40μm
Covering gas : Ar
( for the tests at 250 to 400℃)
Amplifying horn
Piezo converter
Specimen
Mantle　heater
Test method
Fig. Whole test apparatus
Cavitation erosion tests were carried out with the vibratory specimen method specified in ASTM G32.
Cavitation erosion was evaluated in terms of mass loss and instantaneous MDER (Mean Depth of Erosion Rate) of the test specimen.
This shows test apparatus and test condition. Test apparatus is a piezo electric oscillation apparatus according to ASTM G32. These pictures shows whole test apparatus and cooling coil. Test temperature is available from 50 to 400℃. Vibrational frequency is 20kHz. Peak-to-peak displacement amplitude is 40μm. Covering gas is Ar for the tests at 250 to 400℃.
This shows the test method. Cavitation erosion tests were carried out with the vibratory specimen method specified in ASTM G32.
Cavitation erosion was evaluated in terms of mass loss and instantaneous MDER (Mean Depth of Erosion Rate) of the test specimen.
Thermocouple
Cooling coil
Fig. Cooling coil

7. Performance of test apparatus
7.9
3.5
8.2℃/min
5.6
Melting
Variation in temperature for heating
Temperature decrease for cooling
Test temperature increased and deceased in a short time.
Test temperature was controlled with cooling air with a tolerance ±3℃.
This shows the performance of test apparatus. This figure shows the variation in temperature for heating. PbBi began to melt after about 5 minutes and reached the highest temperature of 400 °C after 60 minutes.
This figure shows the temperature decrease for cooling. Compressed air flows through the cooling coil. The temperature decreased exponentially. Test temperature increased and decreases in a short time.
This figure shows the variation in temperature during test. Blue plots is with cooling air, pink plots is without cooling air. Test temperature was controlled with a tolerance ±3℃.
Variation in temperature during test

8. Mass loss curves in liquid metal
9Cr steel
SUS304
Incubation period
488
267
515
265
553
490
266
250 69 50
22 mg/h
For 9Cr steel, incubation period were 1 hour at 100℃, 0.3 hour at 250℃ and 300℃, and 0.2 hour at 350℃ and 400℃.
Mass loss rate in the maximum rate stage were about 3 times higher at 100℃, 12 times at 250℃ and 300℃, and 23 times at 350℃ and 400℃ compare with that in deionized water.
Mass loss rates increased with the temperature.
Incubation period of SUS304 is similar to that of 9Cr steel.
This shows the mass loss curves. This figure shows the cumulative mass loss curves of 9Cr steel in PbBi and in deionized water at various temperatures.
For 9Cr steel, incubation period were 1hour at 100℃, 0.3hour at 250, 300℃ and 0.2 hour at 350, 400℃.
These number are mass loss rate in the maximum rate stage. Mass loss rate were about 3times higher at 100℃, 12times at 250, 300℃ and 23 times at 350, 400℃ compare with that in deionized water.
Mass loss rates increased with the temperature.
Incubation period of SUS304 is similar to that of 9Cr steel.

9. Eroded specimen surfaces
9Cr steel
9Cr steel
In water
In PbBi
5mm
In deionized water of 25℃
In PbBi of 400℃
In deionized water, the test surface has an uneroded ring region.
In PbBi, the test surface is eroded over the whole surface.
The difference in surface profile is due to the difference in the mobility of vapor bubbles. μm
15.6mm
Specimen surface of before test
This shows the eroded specimen surface. These photographs show the eroded surface in deionized water and PbBi.
In deionized water, the test surface has an uneroded ring region.
In PbBi, the surface was eroded over the whole surface, and does not show any uneroded region.
The difference in surface profile is due to the difference in the mobility of vapor bubbles in deionized water and in liquid metal such as those simple figure shows.
Uneroded region
In deionized water at 400℃ 9Cr steel after 5 hours
In PbBi at 400℃ 9Cr steel after 2 hours

10. Mean depth of erosion rate and temperature
𝑀𝑒𝑎𝑛 𝐷𝑒𝑝𝑡ℎ 𝑜𝑓 𝐸𝑟𝑜𝑠𝑖𝑜𝑛 𝑅𝑎𝑡𝑒= 𝑀𝑎𝑠𝑠 𝑙𝑜𝑠𝑠 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙𝑠 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 ×𝐸𝑟𝑜𝑑𝑒𝑑 𝑎𝑟𝑒𝑎 ×𝐸𝑥𝑝𝑜𝑠𝑢𝑟𝑒 𝑡𝑖𝑚𝑒 𝑖𝑛𝑡𝑒𝑟𝑣𝑎𝑙
( 𝑀𝐷𝐸𝑅 )
6.6％
3.3％
4.3％
6.1％
1 – 2 %
MDERmax of 9Cr steel and SUS304 changes similarly.
In deionized water, each increase of 1℃ increases the erosion rate by 1 to 2 % at near 25℃.
In PbBi, each increases 1°in relative temperature increased the erosion rate in PbBi by % at °and by % at °.
The increasing ratio in PbBi was almost 3 times higher.
This shows the Mean Depth of Erosion Rate. This figurer shows the relation between relative temperature and MDERmax. Mean depth of erosion rate is defined this equation. MDERmax is maximum of MDER. MDERmax of 9Cr steel and SUS304 changes similarly. The value in this figure show the increasing ratio of the erosion rate. ASTM G32 explain the ratio. In deionized water, each increase of 1℃ increased the erosion rate by 1 to 2 % at near 25℃. In PbBi, each increases 1°in relative temperature increased the erosion rate in PbBi by 3 to 4 % at 10 to 40° and by 6 to 7 % at 40 to 50°.The increasing ratio of the erosion rate with the temperature in PbBi was almost 3 times higher.

11. Prediction method of erosion rate in sodium : Basic idea
𝑎= 𝜌 𝐿 𝐶 𝐿 𝜌 𝑆 𝐶 𝑆 𝜌 𝐿
𝑀𝐷𝐸𝑅𝑚𝑎𝑥=𝑘 𝑎 𝑛
ρ: Density, C: Sound velocity, S: Solid, L: Liquid
[ 𝑘𝑔 𝑚 𝑠 ]
Liquid 𝒂
PbBi
120,000
Deionized water
45,000
Sodium
69,000
※ Hattori et al.　Wear 265 (2008)
MDERmax can be evaluated in various liquids and liquid metals by using the this parameter.
MDERmax can be expressed with a power law as a function of 𝑎. The lower equation can be obtained.
We predicted the erosion rate by using this equation.
This shows the prediction method of erosion rate in sodium basic idea. This figure shows the relation between MDERmax of various liquids and this parameter. MDERmax can be evaluated similarly to those in the other liquids and liquid metals by using this parameter. And the MDERmax can be expressed with a power law as a function of a. The lower equation can be obtained. We predicted the erosion rate by using this equation.

12. Prediction method of erosion rate in sodium
: Procedure
Select a temperature to obtain the MDERmax in deionized water and in PbBi.
k and n are obtained.
MDERmax in sodium is obtained using the value 𝒂 of sodium.
Prediction curve of MDERmax is obtained as a function of relative temperature.
Young’s test results in sodium (green points) agree with the prediction curve. ②
𝑴𝑫𝑬𝑹𝒎𝒂𝒙=𝒌 𝒂 𝒏 ④ ③ ①
This shows the prediction method of the erosion rate in sodium procedure. We discuss the prediction method of the erosion rate of 9Cr steel in sodium by using the test result in this study.
This shows the prediction method. First, Select a temperature to obtain the MDERmax in deionized water and in PbBi. Second, k and n are obtained. Third, MDERmax in sodium is obtained using the value 𝑎 of sodium. Fourth, Prediction curve of MDERmax is obtained as a function of relative temperature. Last, Young’s test results in sodium agree with the prediction curve. This shows the prediction curve. And erosion rate curve in sodium is located halfway from the rates between PbBi and deionized water.
Prediction erosion rate curve in sodium is located halfway from the rates between PbBi and deionized water.

13. Conclusions Acknowledgement
Performance test of newly developed apparatus showed that test temperature increased and deceased in a short time and test temperature was controlled with a tolerance of ± 3℃.
Each increase of 1°relative temperature increased the erosion rate in PbBi by % and the increasing ratio in PbBi is almost 3 times higher than that in deionized water
Erosion rate in sodium was estimated to be located halfway from the rates between lead bismuth and deionized water.
Acknowledgement
This shows the conclusions.
The present study includes the FY2010 result of the “Core R&D program for commercialization of the fast breeder reactor by utilizing Monju” entrusted to the University of Fukui by the Ministry of Education, Culture, Sports, Science and Technology of Japan (MEXT).

14. In deionized water at 25℃
In PbBi at 100℃ (Relative temperature 8°)

15. Influence of liquid on erosion rate
Rayleigh-Plesset Equation
moving velocity of the bubble wall
(1)
ρL ：liquid density ［kg/m3］ c L　:sound velocity of liquid ［m/s］ γ :surface tension ［N/m］　 P∞：downstream pressure [Pa]　Pv： vapor pressure [Pa]　 R0：initial value of the bubble radius [m] R： instantaneous value of the bubble radius [m]
pressure p of a water hammer
(2)
ρS　：solid density［kg/m3］ c S　：sound velocity of liquid［m/s］
This shows influence of liquid on erosion rate.
When a bubble collapses under inertia control conditions, the moving velocity of the bubble wall is given by the Rayleigh-Plesset equation.
Please pay attention to a denominator in √ having ρ L.
On the other hand, the pressure p of a water hammer is given by this equation.
Generally, acoustic impedance of solid is larger than that of liquid, and is given by this equation.
This shows the relation between mass loss and acoustic impedance by Wilson.
The mass loss in various liquids increases exponentially with acoustic impedanceρLCL
Therefore, erosion rate in liquid metal was evaluated in terms of acoustic impedance in the next figure.
ρsCs　>>　ρLCL
p=ρLCLV
by Wilson

16. Relative temperature at 14℃
Influence of liquid on erosion rate
Relative temperature at 14℃
The erosion rate in PbBi alloy and mercury is far from the curve. We discuss a new parameter.
New parameter based on Eq.(1) and (2)
(3)

17. Liquid Density [kg/m3] Sound velocity [m/s] Acoustic impedance
[g/mm2s]
1 ( 1 𝜌 𝐿 𝐶 𝐿 𝜌 𝑆 𝐶 𝑆 ) 𝜌 𝐿 [ 𝑘𝑔 𝑚 𝑠 ]
PbBi
10,200
1,690
17,300
120,000
Sodium
891
2,440
2,180
69,000
Deionized water
998
1,490
1,480
45,000
9Cr steel（specimen）
7,630
5,250
40,000 ―