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Effect of liquid metal composition and hydrodynamic parameters on cavitation erosion
Wear 267 (2009) 2033–2038
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Wear journal homepage: www.elsevier.com/locate/wear
Effect of liquid metal composition and hydrodynamic parameters on cavitation erosion Shuji Hattori a,∗ , Hiroki Yada b , Hiroaki Kurachi a , Kazuyuki Tsukimori b a b
Graduate School of Engineering, University of Fukui, 9-1 Bunkyo 3-Chome, Fukui-shi 910-8507, Japan Japan Atomic Energy Agency, 1 Shiraki, Tsuruga-shi, Fukui 919-1279, Japan
a r t i c l e
i n f o
Article history: Received 9 September 2008 Received in revised form 17 April 2009 Accepted 4 August 2009 Available online 13 August 2009 Keywords: Cavitation erosion Cavitation Liquid metal Hardness Flow velocity Cavitation number
a b s t r a c t Cavitation erosion testing machine for low-temperature melting alloy liquid was developed by using a vibratory apparatus. The erosion tests of SUS304 were carried out in three kinds of lead–bismuth and deionized water. We defined a relative temperature as the percentage between freezing and boiling points. At relative temperature at 14 ◦ C, the erosion rate is 10–12 times in various lead–bismuth alloys, and 2–5 times in sodium, as compared with that in deionized water. When SUS304 was exposed to a cavitation in PbBi, the surface was work hardened 20% harder compared with original surface. In deionized water, SUS304 was work hardened by 5%. Therefore, we can conclude that larger collapse pressure can be estimated to act on the specimen surface in lead–bismuth, as compared with that in water. We discussed the effect of hydrodynamic properties on cavitation erosion in a flowing system. It is considered that the erosion rate in sodium is in proportion to 1st to 6th power of flow velocity similarly to that in mercury. The incipient cavitation number is approximately unity irrespective of test liquids. Furthermore, the relation between MDER and cavitation number is expressed as power low of function with an exponent of 2.5. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Research on cavitation erosion in liquid metals is very important to confirm the safety of fast breeder reactors using sodium coolant and to understand cavitation erosion in the liquid–mercury target system of the neutron spallation source [1]. The effect of cavitation erosion in liquid metals includes liquid properties (temperature, density of the liquid, sound velocity, etc.) and flow properties (flow velocity, cavitation number, etc.). A liquid property is based on characteristics of the liquid itself and is not changed by apparatus such as vibratory and flow systems. Especially, Hattori et al. [2] found that the erosion rates of the cavitating liquid jet method and the vibratory method show similar temperature dependencies after defining a relative temperature. Regarding cavitation erosion in liquid metal, Thiruvengadam et al. examined the temperature dependencies of the erosion rates of pure titanium [3] and SUS316 [4] in sodium using a vibratory apparatus. They reported that the erosion rate of pure titanium has a maximum at 750 ◦ F, and that the erosion rate of SUS316 decreases with increasing temperature. But, they only used the terminal erosion rate of the last stage. Since terminal erosion rates are
∗ Corresponding author. Tel.: +81 776 27 8546; fax: +81 776 27 8546. E-mail address: [email protected] (S. Hattori). 0043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2009.08.002
optional in the ASTM (American Society for Testing and Materials) standard, it has the disadvantage of not comparing well with other test results. Garcia and Hammitt [5] carried out vibratory cavitation erosion test of SUS304 in water, mercury, lithium, and lead–bismuth alloy. They referred to the sodium data by Thiruvengadam, and reported that the erosion rate in sodium at 260 ◦ C is about nine times larger than in water of 18 ◦ C. Moreover, they [5] found that heat transfer controlled collapse occurs only near the boiling point and inertia controlled collapse occurs at temperatures below the boiling point. Young and Johnson [6] carried out vibratory cavitation erosion tests of a cobalt alloy (L-605) in sodium at various pressures and temperatures. They found that the erosion rate increased with increasing pressure, and they obtained a peak for temperature dependence. The peak occurs at the approximate average of freezing and boiling temperatures (as shown in later Fig. 4). However, a detailed study of the temperature effect has not yet been performed. Hattori et al. [7] previously developed a cavitation erosion test apparatus and carried out erosion tests in deionized water and liquid metal. The influence of both liquids on instantaneous MDER (Mean Depth of Erosion Rate) was discussed. Moreover, they discussed the effect of liquid properties and temperature effects on the erosion rate. They previously proposed a new parameter to evaluate the erosion rate in various test liquids, and clarified that in the low relative temperature region an increase in the temperature affects the erosion rate by an increase in the
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S. Hattori et al. / Wear 267 (2009) 2033–2038 Table 4 Mechanical properties of test material.
Table 1 Chemical composition of lead–bismuth mass%.
PbBi-47 PbBi-68 PbBi-94
Bi
Pb
Sn
Cd
In
Tensile strength [MPa]
HB
HV
44.7 50 50
22.6 26.7 28
8.3 13.3 22
5.3 10 –
19.1 – –
672
180
189
Table 2 Physical and mechanical properties of lead–bismuth.
Freezing point [◦ C] Boiling point [◦ C] Density at 20 ◦ C [g/cm3 ] Tensile strength [kPa] Brinell hardness
PbBi-47
PbBi-68
PbBi-94
47 654 8.86 373 12
68 460 9.38 421 9.2
94 560 9.69 530 12.8
vapor pressure, resulting in an increase in the number of cavitation bubbles. Regarding the flow dependence of the erosion rate in liquid metal, Belahadji et al. [8] carried out an erosion test in a venturi tube to obtain a relation between flow velocity and pitting rate (the density of pits per unit surface area and per unit time of exposure) during the flow. They reported that in mercury, the pitting rate is increased with the 6th power of the flow velocity for velocities between 2 and 6 m/s and with the 1st power of the flow velocity for velocities between 6 and 10 m/s. However, they did not discuss the relation between the flow velocity and the pitting rate in water in order to compare it with the experimental results in mercury. Kamiyama and Yamazaki [9] measured incipient cavitation numbers in mercury and in water in venturi tubes. They reported that the incipient cavitation numbers in mercury and in water are almost unity. However, they did not discuss the cavitation number of erosion. In this study, erosion tests were carried out in three kinds of liquid lead–bismuth alloys and in deionized water to discuss the influence of the kind of metal on the erosion rate. The hardness increase of the test specimen by work hardening due to cavitation is also examined. Moreover, the effect of flow velocity and the cavitation number on the erosion rate is discussed. We discuss the effect of the liquid properties with results of a vibratory method obtained in this study and take the effect of the flow properties from references.
study, and was converted into the Vickers hardness using a conversion table based on SAE J417b [10]. Fig. 1 shows the vibratory test apparatus for liquid metals which was developed in our previous study [7]. The test apparatus consists of a vibratory apparatus as specified in the ASTM G32-03 standard [11] and a liquid metal reservoir kept at constant temperature. 2.2. Experimental procedure Cavitation erosion tests were carried out with the vibratory specimen method by using a vibratory apparatus. The exposed area of 201 mm2 corresponds to a circular test specimen area with a diameter of 16 mm. The facility was operated at a frequency of 19.5 kHz and a double amplitude of 50 m. The test temperatures were 55, 100 and 150 ◦ C for PbBi-47, 75 ◦ C, 100 and 150 ◦ C for PbBi68, and 100 and 150 ◦ C for PbBi-94. The temperatures of deionized water were 10, 25 and 40 ◦ C. The immersion depth of the specimen was 5 mm at every temperature. Test specimen in liquid metal was removed after every time interval and washed in boiled deionized water. Then, the specimen was washed in acetone with an ultrasonic cleaner and the erosion mass was measured with a precision balance with a sensitivity of 0.01 mg. The cavitation erosion was evaluated in terms of mass loss and instantaneous MDER (Mean Depth of Erosion Rate) of the test specimen. The MDER was defined as the mass loss divided by the material density, the eroded area and the exposure time interval. The tests specimens after testing were cut to measure their Vickers hardness on the cross section with a microhardness testing machine. 3. Experimental results and discussion 3.1. Cavitation test results Fig. 2 shows the mass loss curves in the lead–bismuth alloys and deionized water at each temperature. The data points of PbBi68 were obtained by Hattori et al. [7]. The mass loss passes through an incubation period of low mass loss and then increases linearly at each temperature in the various test liquids. The incubation period
2. Test material and experimental procedures 2.1. Test material and test apparatus Three kinds of low melting point lead–bismuth alloys and deionized water were used as test liquids. The chemical composition and the physical and mechanical properties of the lead–bismuth alloys are listed in Tables 1 and 2, respectively. The numbers for the material identification in Table 1 are the freezing points of the test liquids. The freezing point of lead–bismuth alloys can be widely changed from 20 to 180 ◦ C with the addition of Sn and Cd. The chemical composition and the physical and mechanical properties of the erosion test specimen are listed in Tables 3 and 4, respectively. Since SUS304 stainless steel is used for pipes of sodium in a fast breeder reactor plant, SUS304 was used as test specimen in this study. The Brinell hardness was measured in this Table 3 Chemical composition of test material mass %.
SUS304
C
Si
Mn
P
S
Ni
Cr
0.05
0.33
1.76
0.36
0.22
8.49
18.18
Fig. 1. Vibratory test apparatus.
S. Hattori et al. / Wear 267 (2009) 2033–2038
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Fig. 2. Mass loss curves.
is 1–2 h at all temperatures in deionized water, and at temperatures of up to 100 in three kinds of lead–bismuth alloys. But, it is only half an hour at 150 in the lead–bismuth alloys. Fig. 3 shows the instantaneous MDER (mean depth of erosion rate) curves in the lead–bismuth alloys and deionized water at each temperature. Each curve increases rapidly in the first stage and reaches a constant level. The MDER curves increase gradually in PbBi-47 at 55 ◦ C, and in PbBi-68 at 75 and 100 ◦ C. However, the other curves in the lead–bismuth alloys increase rapidly. The rate of decrease is especially remarkable at 150 ◦ C in the various lead–bismuth alloys. This is because the surface roughness of the test specimen increased and bubbles were trapped at the rough bottom producing a cushioning effect, thus the impact load of the bubble collapse became small. The maximum value of the MDER curves is referred to as MDERmax. The MDERmax is 20–82 m/h in lead–bismuth alloys, and 6–12 m/h in deionized water. The erosion rate in lead–bismuth alloys is higher than that in deionized water as indicated in Fig. 3. Fig. 4 shows the relation between the relative temperature and the MDERmax obtained in our previous study [7] and in this study. We define the relative temperature as the percentage between freezing and boiling points. The relative temperature is given by: Relative temparature =
Test temparature − Freezing point × 100 Boiling point − Freezing point (1)
Hattori et al. [7] reported that the MDERmax in PbBi-68 can be expressed with the relative temperature by a curve as shown in
Fig. 3. Instantaneous MDER curves.
Fig. 4. Relation between relative temperature and MDERmax.
Fig. 4. The data points of PbBi-47 can be approximated by the curve of PbBi-68 [7], but the data points of PbBi-94 are fitted by another curve with a lower gradient. The test results in sodium by Young et al. [6] and Thiruvengadam et al. [4] are also plotted in Fig. 4. At a relative temperature of 14 ◦ C, the erosion rate is 10–12 times in lead–bismuth alloys, and 2–5 times in sodium, as compared with that in water. Wilson et al. [12] showed that the erosion rate in various liquids increases exponentially with the acoustic impedance L CL . L is the liquid density and CL is the sound velocity in the liquid. Therefore, the erosion rate in liquid metals was evaluated in terms of the acoustic impedance L CL. The symbols * are the test results in heptane, butyl alcohol, aniline, anisole, benzene, ethylene glycol, trichloroethane, carbon tetrachloride, ethylene dibromide and bromoholm which were carried out by Wilson et al. [12]. The data in mercury are taken from Garcia and Hammitt [5]. The data in sodium are close to Wilson’s result. But, the erosion rates in lead–bismuth alloy and mercury with high density could not be evaluated. The authors [7] previously reported that liquid metal including mercury with high acoustic impedance can be evaluated using the Rayleigh-Plesset equation [13] and the water hammer equation, which applies to both liquid metals and liquids. 1 √ ((1/L CL ) + (1/S CS )) L
(2)
where S is the material density of the solid and CS is the velocity of sound. The MDERmax in Fig. 5 shows a nearly straight line in a double logarithmic scale using this parameter regardless of the kind of test liquids. Cavitation bubble collapse creates impact loads acting on the specimen surface. It is conceivable that a severe cavitation condition can produce heavy plastic deformation and a work hardened layer. Fig. 6(a) and (b) shows photographs of the cross section of a test specimen on which an erosion test was carried out in PbBi-68 at 100 ◦ C for 8 h and in deionized water at 40 ◦ C for 10 h. In PbBi, the deep erosion pits are formed like worm holes. On the other hand, many small pits are observed in deionized water. The Vickers hardness was measured over the cross section inward from the bottom of the erosion pits on the tested specimen. Fig. 7 shows the relation between the distance from bottom of the eroded surface and the Vickers hardness. The hardness was measured on the cross section of the eroded specimen in various PbBi metals at 100 ◦ C and deionized water at 40 ◦ C. The hardness was measured also on the specimen immersed in PbBi-68 for
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S. Hattori et al. / Wear 267 (2009) 2033–2038
√ Fig. 5. Relation between 1/((1/L CL ) + (1/S CS )) L and MDERmax.
Fig. 8. Relation between flow velocity and erosion rate.
3.2. Influence of flow velocity and cavitation number Cavitation occurs in actual piping systems as flowing cavitation. The effect of flow velocity and cavitation number on the erosion rate is discussed based on the reference survey. The cavitation number is a parameter of the cavitation condition, and is given by the following equation =
p − pv pd − pv = d pu − pd 1/2V 2
(3)
where pu , pd , pv , and V are upstream pressure, downstream pressure, vapor pressure, liquid density and flow velocity, respectively. Fig. 6. Photographs of erosion cross sections. (a) PbBi-68, 100 ◦ C, 8 h. (b) Deionized water, 40 ◦ C, 10 h.
10 h without cavitation. The eroded specimens in all lead–bismuth alloys were work hardened to 30 m from the specimen surface and the hardness near the specimen surface increased by about 20% compared with that of the matrix. The specimen in deionized water was work hardened to 20 m in depth from the surface and the hardness increase due to cavitation was about 5%. Therefore, we can conclude that a larger collapse pressure acted on the specimen surface in PbBi, as compared with that in deionized water.
3.3. Influence of flow velocity Belahadji et al. [8] carried out the erosion tests in a venturi tube for SUS316 stainless steel specimens which were positioned downstream from a throat. The erosion pit diameters were measured in an observation region of 0.142 mm × 0.201 mm in a 512 × 512 size image with a magnification of 40, which were photographs taken by a CCD camera and recorded and processed by a micro computer. Fig. 8 shows the relation between the flow velocity and the pitting rate for pits of a diameter of 20 m or more in mercury [8] and in water calculated by the present authors. In water, the pitting rate increases with the 6th power of the flow velocity between 15 and 50 m/s. Moreover, in the mercury, the pitting rate increased as in water with the 6th power of the flow velocity between 2 and 6 m/s and with the 1st power of the flow velocity between 6 and 10 m/s. We interpret the abrupt change in slope with the flow velocity to be a “saturation” phenomenon proposed by Lecoffre et al. [14]. The pitting rates of 1 pit/cm2 /s with water and mercury were compared. The flow velocity was about 20 m/s in water, while it was about 5 m/s in mercury. We think that the pits occurred in mercury after cavitation erosion test at low velocity due to the high liquid density of mercury. 3.4. Influence of cavitation number Figs. 9 and 10 show the relation between the flow velocity and the incipient cavitation number in mercury and in water, respectively, which was measured in a venturi tube by Kamiyama and Yamazaki [9]. They defined the cavitation number as =
Fig. 7. Relation between distance from bottom of eroded surface and hardness.
p1 − pv 1/2V02
(4)
S. Hattori et al. / Wear 267 (2009) 2033–2038
2037
Fig. 9. Incipient cavitation number of mercury [9]. Fig. 11. Relation between cavitation number and MDER [15].
where p1 , pv , and v0 are the upstream pressure, the vapor pressure (1.80 × 10−7 MPa at 20 ◦ C), the liquid density and the mean flow velocity in the throat. The cavi,1 and the cavi,2 in Fig. 10 show the cavitation at the throat and at the downstream location, respectively. The incipient cavitation number is approximately unity irrespective of the test liquids. On the other hand, cavitation inception occurs at flow velocities of between 4.5 and 8 m/s in mercury and at velocities of between 16 and 28 m/s in water. The relation of the pitting rate in Fig. 8 seems very reasonable both in mercury obtained by Belahadji et al. and in water calculated by us, because the velocity of 5 m/s in mercury and that of 20 m/s in water at a pitting rate of 1 pit/cm2 /s in Fig. 8 correspond to the velocity range of 4–8 m/s in mercury and 15–28 m/s in water in Figs. 9 and 10, respectively. Since the cavitation erosion tests are carried out at a constant amplitude and frequency with a vibratory apparatus, the cavitation condition is thought to be fixed during the test. When the test results of the vibratory method are compared with those of the flowing method, the vibratory results correspond to the results under constant flow conditions such as the constant flow velocity. From Fig. 5, the erosion rate in mercury is six times that of water at a relative temperature of 14 ◦ C. Since it was reported [9] that the MDER in the maximum rate stage is in proportional to the pitting rate in the incubation stage, the test result of the vibratory method was plotted at a flow velocity of 25 m/s, when the pitting rate in mercury is six times that in water. The erosion rate is expected to increase with the 1st power of the flow velocity in lead–bismuth, which has almost the same physical properties (liquid density and sound velocity) as those of mercury. Since the physical properties of sodium are between mercury and water, the velocity dependence of the erosion rate is assumed to be somewhere between the first and the sixth power. However, the detailed dependence will be investigated in the near future. As mentioned above, Kamiyama et al. [9] reported that the incipient cavitation number i is nearly unity at flow velocities of 5–7 m/s in mercury with a venturi tube and at 15–30 m/s in water.
The incipient cavitation numbers in liquid metal and in water are considered to be almost the same. Therefore, we discuss the relations between the MDER and the cavitation number which were obtained in water. Fig. 11 is the relation between the cavitation number and the erosion rate at constant velocities in water within a venturi facility obtained by Hattori et al. [15]. The cavitation number used in this study substitutes the downstream pressure pd for p1 in the numerator of Eq. (3). When the cavitation number decreases, the erosion rate increases and reaches a maximum value, followed by a gradual decrease. When the downstream pressure increases and leads to a higher the cavitation number, the number and the mean diameter of the bubbles decrease. On the other hand, when the downstream pressure decreases, the erosion damage disperses. In this study, the effect of the cavitation number on the erosion was discussed quantitatively based on experimental data. The erosion was confined from the cavitation damage inception to its peak. The cavitation number of the incipient damage id was defined as the intercept of the cavitation number axis with the extension of MDER– curve. The id is 1.0 for 49 m/s and 1.2 for 36.3 m/s, respectively. Therefore, the MDER can be expressed by the following equation.
MDER = ˛(id − )2.5
id = 1.0 id = 1.2
˛ = 119 ˛ = 12
(49 m/s) (36.3 m/s)
(5)
where ˛ is a constant. This agrees with the Mean Depth of Deformation Rate (MDDR) [16] to increase with the 2.5th power of the function (1 − /id ) obtained from the theoretical analysis of a cavitating vortex proposed by Lecoffre [17]. It also agrees with an increase in the pitting rate with the 2.5th power of ( id –) according to the relation between the pitting rate and the cavitating number in valves obtained by Tullis et al. [18]. Therefore, the relation between the MDER and the cavitation number is expressed by the power law of Eq. (4) with an exponent of 2.5. 4. Conclusions
Fig. 10. Incipient cavitation number of water [9].
In this study, erosion tests were carried out in lead–bismuth alloys and we discussed differences in the erosion rate with the variation of the kind of metal. Furthermore, we discussed the effect of the flow velocity and the cavitation number on cavitation erosion in liquid metals with a reference survey. We reach the following conclusions. We defined a relative temperature as the percentage between freezing and boiling points. At a relative temperature of 14 ◦ C, the erosion rate is 10–12 times in various lead–bismuth alloys, and 2–5 times in sodium, as compared with that in deionized water. When SUS304 was exposed to cavitation in PbBi, the surface was work hardened by 20% harder compared with that of the substrate. SUS304 was work hardened by 5% in deionized water.
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S. Hattori et al. / Wear 267 (2009) 2033–2038
The erosion rate is expected to increase with the 1st power of the flow velocity in lead–bismuth, which has almost the same physical properties (liquid density and sound velocity) as those of mercury. Since the physical properties of sodium are between that of mercury and water, the velocity dependence of the erosion rate in sodium is assumed to be between the first to the sixth power. The incipient cavitation number is approximately unity irrespective of the test liquids. Furthermore, the relation between the MDER and the cavitation number is expressed as power law function of ( id –) with an exponent of 2.5 (id : the cavitation number of incipient damage). References [1] M. Futakawa, T. Naoe, C. Tsai, H. Kogawa, S. Ishikawa, Y. Ikeda, H. Soyama, H. Date, GS-11-006 Cav2003, Osaka, Japan, November 1–4, 2003. [2] S. Hattori, Y. Goto, T. Fukuyama, Influence of temperature on erosion by a cavitating liquid jet, Wear 260 (2006) 1217–1223. [3] Preiser, H.S., Thiruvengadam, A., Couchman, C.E., NASACR-54071, TPR-235-1, HYDRONAUTICS, Incorporated, Laurel, Maryland, April 1964.
[4] Thiruvengadam, A., Preiser, H.S., Rudy, S.L., NASACR-54459, TPR467-3, HYDRONAUTICS, Incorporated, Laurel, Maryland, 30 June 1965. [5] R. Garcia, F.G. Hammitt, Trans. ASME, J. Basic Eng. (1967) 753–763. [6] S.G. Young, J.R. Johnston, ASTM STEP 474, American Society for Testing and Materials, 1970, pp. 67–108. [7] S. Hattori, F. Inoue, K. Watashi, T. Hashimoto, Effect of liquid parameters on cavitation erosion in liquid metals, Wear (2008). [8] B. Belahadji, J.P. Frank, J.M. Michel, J. Fluids Eng. 113 (December) (1991) 700–706. [9] S. Kamiyama, T. Yamasaki, The effect of magnetic field on cavitation in mercury flow. The Memoirs of the Institute of High Speed Mechanics, vol. 36, no. 344, ¯ Tohoku University, Sendai, Japan, 1975, pp. 1–16. [10] SAE J417b, Handbook of Japanese Industrial Standards, 2002, pp. 1283–1286. [11] ASTM Designation G32-03, Annual Book of ASTM Standards, 2003, pp. 106–119. [12] R.W. Wilson, R. Graham, Cavitation of metal surfaces in contact with lubricants, in: Conf. Lubrication and Wear, IME, London, 1957, pp. 707–712. [13] L. Rayleigh, On the Pressure developed in a Liquid during the Collapse of a Spherical Cavity, Phil. Mag. S. 6, 34 (200) (1917) 94–98. [14] Y. Leccoffre, CAVITATION Bubble Trackers, 1999, p. 288. [15] S. Hattori, B.-H. Sun, F.G. Hamiitt, Wear 103 (1985) 119–131. [16] H. Kato, Cavitation, 1999, p. 195 (Maki-shoten). [17] Y. Lecoffre, A. Archer, A method to evaluate cavitation erosion in valves, in: Third International Symposium on Cavitation, Grenoble, France, April, 1998. [18] Tullis, P.J., Cavitation Guide for Control Valves, NUREG/CR-6031, May, vol. 21, 1993, pp. 1–106.
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Effect of liquid metal composition and hydrodynamic parameters on cavitation erosion Shuji Hattori a,∗ , Hiroki Yada b , Hiroaki Kurachi a , Kazuyuki Tsukimori b a b
Graduate School of Engineering, University of Fukui, 9-1 Bunkyo 3-Chome, Fukui-shi 910-8507, Japan Japan Atomic Energy Agency, 1 Shiraki, Tsuruga-shi, Fukui 919-1279, Japan
a r t i c l e
i n f o
Article history: Received 9 September 2008 Received in revised form 17 April 2009 Accepted 4 August 2009 Available online 13 August 2009 Keywords: Cavitation erosion Cavitation Liquid metal Hardness Flow velocity Cavitation number
a b s t r a c t Cavitation erosion testing machine for low-temperature melting alloy liquid was developed by using a vibratory apparatus. The erosion tests of SUS304 were carried out in three kinds of lead–bismuth and deionized water. We defined a relative temperature as the percentage between freezing and boiling points. At relative temperature at 14 ◦ C, the erosion rate is 10–12 times in various lead–bismuth alloys, and 2–5 times in sodium, as compared with that in deionized water. When SUS304 was exposed to a cavitation in PbBi, the surface was work hardened 20% harder compared with original surface. In deionized water, SUS304 was work hardened by 5%. Therefore, we can conclude that larger collapse pressure can be estimated to act on the specimen surface in lead–bismuth, as compared with that in water. We discussed the effect of hydrodynamic properties on cavitation erosion in a flowing system. It is considered that the erosion rate in sodium is in proportion to 1st to 6th power of flow velocity similarly to that in mercury. The incipient cavitation number is approximately unity irrespective of test liquids. Furthermore, the relation between MDER and cavitation number is expressed as power low of function with an exponent of 2.5. © 2009 Elsevier B.V. All rights reserved.
1. Introduction Research on cavitation erosion in liquid metals is very important to confirm the safety of fast breeder reactors using sodium coolant and to understand cavitation erosion in the liquid–mercury target system of the neutron spallation source [1]. The effect of cavitation erosion in liquid metals includes liquid properties (temperature, density of the liquid, sound velocity, etc.) and flow properties (flow velocity, cavitation number, etc.). A liquid property is based on characteristics of the liquid itself and is not changed by apparatus such as vibratory and flow systems. Especially, Hattori et al. [2] found that the erosion rates of the cavitating liquid jet method and the vibratory method show similar temperature dependencies after defining a relative temperature. Regarding cavitation erosion in liquid metal, Thiruvengadam et al. examined the temperature dependencies of the erosion rates of pure titanium [3] and SUS316 [4] in sodium using a vibratory apparatus. They reported that the erosion rate of pure titanium has a maximum at 750 ◦ F, and that the erosion rate of SUS316 decreases with increasing temperature. But, they only used the terminal erosion rate of the last stage. Since terminal erosion rates are
∗ Corresponding author. Tel.: +81 776 27 8546; fax: +81 776 27 8546. E-mail address: [email protected] (S. Hattori). 0043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2009.08.002
optional in the ASTM (American Society for Testing and Materials) standard, it has the disadvantage of not comparing well with other test results. Garcia and Hammitt [5] carried out vibratory cavitation erosion test of SUS304 in water, mercury, lithium, and lead–bismuth alloy. They referred to the sodium data by Thiruvengadam, and reported that the erosion rate in sodium at 260 ◦ C is about nine times larger than in water of 18 ◦ C. Moreover, they [5] found that heat transfer controlled collapse occurs only near the boiling point and inertia controlled collapse occurs at temperatures below the boiling point. Young and Johnson [6] carried out vibratory cavitation erosion tests of a cobalt alloy (L-605) in sodium at various pressures and temperatures. They found that the erosion rate increased with increasing pressure, and they obtained a peak for temperature dependence. The peak occurs at the approximate average of freezing and boiling temperatures (as shown in later Fig. 4). However, a detailed study of the temperature effect has not yet been performed. Hattori et al. [7] previously developed a cavitation erosion test apparatus and carried out erosion tests in deionized water and liquid metal. The influence of both liquids on instantaneous MDER (Mean Depth of Erosion Rate) was discussed. Moreover, they discussed the effect of liquid properties and temperature effects on the erosion rate. They previously proposed a new parameter to evaluate the erosion rate in various test liquids, and clarified that in the low relative temperature region an increase in the temperature affects the erosion rate by an increase in the
2034
S. Hattori et al. / Wear 267 (2009) 2033–2038 Table 4 Mechanical properties of test material.
Table 1 Chemical composition of lead–bismuth mass%.
PbBi-47 PbBi-68 PbBi-94
Bi
Pb
Sn
Cd
In
Tensile strength [MPa]
HB
HV
44.7 50 50
22.6 26.7 28
8.3 13.3 22
5.3 10 –
19.1 – –
672
180
189
Table 2 Physical and mechanical properties of lead–bismuth.
Freezing point [◦ C] Boiling point [◦ C] Density at 20 ◦ C [g/cm3 ] Tensile strength [kPa] Brinell hardness
PbBi-47
PbBi-68
PbBi-94
47 654 8.86 373 12
68 460 9.38 421 9.2
94 560 9.69 530 12.8
vapor pressure, resulting in an increase in the number of cavitation bubbles. Regarding the flow dependence of the erosion rate in liquid metal, Belahadji et al. [8] carried out an erosion test in a venturi tube to obtain a relation between flow velocity and pitting rate (the density of pits per unit surface area and per unit time of exposure) during the flow. They reported that in mercury, the pitting rate is increased with the 6th power of the flow velocity for velocities between 2 and 6 m/s and with the 1st power of the flow velocity for velocities between 6 and 10 m/s. However, they did not discuss the relation between the flow velocity and the pitting rate in water in order to compare it with the experimental results in mercury. Kamiyama and Yamazaki [9] measured incipient cavitation numbers in mercury and in water in venturi tubes. They reported that the incipient cavitation numbers in mercury and in water are almost unity. However, they did not discuss the cavitation number of erosion. In this study, erosion tests were carried out in three kinds of liquid lead–bismuth alloys and in deionized water to discuss the influence of the kind of metal on the erosion rate. The hardness increase of the test specimen by work hardening due to cavitation is also examined. Moreover, the effect of flow velocity and the cavitation number on the erosion rate is discussed. We discuss the effect of the liquid properties with results of a vibratory method obtained in this study and take the effect of the flow properties from references.
study, and was converted into the Vickers hardness using a conversion table based on SAE J417b [10]. Fig. 1 shows the vibratory test apparatus for liquid metals which was developed in our previous study [7]. The test apparatus consists of a vibratory apparatus as specified in the ASTM G32-03 standard [11] and a liquid metal reservoir kept at constant temperature. 2.2. Experimental procedure Cavitation erosion tests were carried out with the vibratory specimen method by using a vibratory apparatus. The exposed area of 201 mm2 corresponds to a circular test specimen area with a diameter of 16 mm. The facility was operated at a frequency of 19.5 kHz and a double amplitude of 50 m. The test temperatures were 55, 100 and 150 ◦ C for PbBi-47, 75 ◦ C, 100 and 150 ◦ C for PbBi68, and 100 and 150 ◦ C for PbBi-94. The temperatures of deionized water were 10, 25 and 40 ◦ C. The immersion depth of the specimen was 5 mm at every temperature. Test specimen in liquid metal was removed after every time interval and washed in boiled deionized water. Then, the specimen was washed in acetone with an ultrasonic cleaner and the erosion mass was measured with a precision balance with a sensitivity of 0.01 mg. The cavitation erosion was evaluated in terms of mass loss and instantaneous MDER (Mean Depth of Erosion Rate) of the test specimen. The MDER was defined as the mass loss divided by the material density, the eroded area and the exposure time interval. The tests specimens after testing were cut to measure their Vickers hardness on the cross section with a microhardness testing machine. 3. Experimental results and discussion 3.1. Cavitation test results Fig. 2 shows the mass loss curves in the lead–bismuth alloys and deionized water at each temperature. The data points of PbBi68 were obtained by Hattori et al. [7]. The mass loss passes through an incubation period of low mass loss and then increases linearly at each temperature in the various test liquids. The incubation period
2. Test material and experimental procedures 2.1. Test material and test apparatus Three kinds of low melting point lead–bismuth alloys and deionized water were used as test liquids. The chemical composition and the physical and mechanical properties of the lead–bismuth alloys are listed in Tables 1 and 2, respectively. The numbers for the material identification in Table 1 are the freezing points of the test liquids. The freezing point of lead–bismuth alloys can be widely changed from 20 to 180 ◦ C with the addition of Sn and Cd. The chemical composition and the physical and mechanical properties of the erosion test specimen are listed in Tables 3 and 4, respectively. Since SUS304 stainless steel is used for pipes of sodium in a fast breeder reactor plant, SUS304 was used as test specimen in this study. The Brinell hardness was measured in this Table 3 Chemical composition of test material mass %.
SUS304
C
Si
Mn
P
S
Ni
Cr
0.05
0.33
1.76
0.36
0.22
8.49
18.18
Fig. 1. Vibratory test apparatus.
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Fig. 2. Mass loss curves.
is 1–2 h at all temperatures in deionized water, and at temperatures of up to 100 in three kinds of lead–bismuth alloys. But, it is only half an hour at 150 in the lead–bismuth alloys. Fig. 3 shows the instantaneous MDER (mean depth of erosion rate) curves in the lead–bismuth alloys and deionized water at each temperature. Each curve increases rapidly in the first stage and reaches a constant level. The MDER curves increase gradually in PbBi-47 at 55 ◦ C, and in PbBi-68 at 75 and 100 ◦ C. However, the other curves in the lead–bismuth alloys increase rapidly. The rate of decrease is especially remarkable at 150 ◦ C in the various lead–bismuth alloys. This is because the surface roughness of the test specimen increased and bubbles were trapped at the rough bottom producing a cushioning effect, thus the impact load of the bubble collapse became small. The maximum value of the MDER curves is referred to as MDERmax. The MDERmax is 20–82 m/h in lead–bismuth alloys, and 6–12 m/h in deionized water. The erosion rate in lead–bismuth alloys is higher than that in deionized water as indicated in Fig. 3. Fig. 4 shows the relation between the relative temperature and the MDERmax obtained in our previous study [7] and in this study. We define the relative temperature as the percentage between freezing and boiling points. The relative temperature is given by: Relative temparature =
Test temparature − Freezing point × 100 Boiling point − Freezing point (1)
Hattori et al. [7] reported that the MDERmax in PbBi-68 can be expressed with the relative temperature by a curve as shown in
Fig. 3. Instantaneous MDER curves.
Fig. 4. Relation between relative temperature and MDERmax.
Fig. 4. The data points of PbBi-47 can be approximated by the curve of PbBi-68 [7], but the data points of PbBi-94 are fitted by another curve with a lower gradient. The test results in sodium by Young et al. [6] and Thiruvengadam et al. [4] are also plotted in Fig. 4. At a relative temperature of 14 ◦ C, the erosion rate is 10–12 times in lead–bismuth alloys, and 2–5 times in sodium, as compared with that in water. Wilson et al. [12] showed that the erosion rate in various liquids increases exponentially with the acoustic impedance L CL . L is the liquid density and CL is the sound velocity in the liquid. Therefore, the erosion rate in liquid metals was evaluated in terms of the acoustic impedance L CL. The symbols * are the test results in heptane, butyl alcohol, aniline, anisole, benzene, ethylene glycol, trichloroethane, carbon tetrachloride, ethylene dibromide and bromoholm which were carried out by Wilson et al. [12]. The data in mercury are taken from Garcia and Hammitt [5]. The data in sodium are close to Wilson’s result. But, the erosion rates in lead–bismuth alloy and mercury with high density could not be evaluated. The authors [7] previously reported that liquid metal including mercury with high acoustic impedance can be evaluated using the Rayleigh-Plesset equation [13] and the water hammer equation, which applies to both liquid metals and liquids. 1 √ ((1/L CL ) + (1/S CS )) L
(2)
where S is the material density of the solid and CS is the velocity of sound. The MDERmax in Fig. 5 shows a nearly straight line in a double logarithmic scale using this parameter regardless of the kind of test liquids. Cavitation bubble collapse creates impact loads acting on the specimen surface. It is conceivable that a severe cavitation condition can produce heavy plastic deformation and a work hardened layer. Fig. 6(a) and (b) shows photographs of the cross section of a test specimen on which an erosion test was carried out in PbBi-68 at 100 ◦ C for 8 h and in deionized water at 40 ◦ C for 10 h. In PbBi, the deep erosion pits are formed like worm holes. On the other hand, many small pits are observed in deionized water. The Vickers hardness was measured over the cross section inward from the bottom of the erosion pits on the tested specimen. Fig. 7 shows the relation between the distance from bottom of the eroded surface and the Vickers hardness. The hardness was measured on the cross section of the eroded specimen in various PbBi metals at 100 ◦ C and deionized water at 40 ◦ C. The hardness was measured also on the specimen immersed in PbBi-68 for
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√ Fig. 5. Relation between 1/((1/L CL ) + (1/S CS )) L and MDERmax.
Fig. 8. Relation between flow velocity and erosion rate.
3.2. Influence of flow velocity and cavitation number Cavitation occurs in actual piping systems as flowing cavitation. The effect of flow velocity and cavitation number on the erosion rate is discussed based on the reference survey. The cavitation number is a parameter of the cavitation condition, and is given by the following equation =
p − pv pd − pv = d pu − pd 1/2V 2
(3)
where pu , pd , pv , and V are upstream pressure, downstream pressure, vapor pressure, liquid density and flow velocity, respectively. Fig. 6. Photographs of erosion cross sections. (a) PbBi-68, 100 ◦ C, 8 h. (b) Deionized water, 40 ◦ C, 10 h.
10 h without cavitation. The eroded specimens in all lead–bismuth alloys were work hardened to 30 m from the specimen surface and the hardness near the specimen surface increased by about 20% compared with that of the matrix. The specimen in deionized water was work hardened to 20 m in depth from the surface and the hardness increase due to cavitation was about 5%. Therefore, we can conclude that a larger collapse pressure acted on the specimen surface in PbBi, as compared with that in deionized water.
3.3. Influence of flow velocity Belahadji et al. [8] carried out the erosion tests in a venturi tube for SUS316 stainless steel specimens which were positioned downstream from a throat. The erosion pit diameters were measured in an observation region of 0.142 mm × 0.201 mm in a 512 × 512 size image with a magnification of 40, which were photographs taken by a CCD camera and recorded and processed by a micro computer. Fig. 8 shows the relation between the flow velocity and the pitting rate for pits of a diameter of 20 m or more in mercury [8] and in water calculated by the present authors. In water, the pitting rate increases with the 6th power of the flow velocity between 15 and 50 m/s. Moreover, in the mercury, the pitting rate increased as in water with the 6th power of the flow velocity between 2 and 6 m/s and with the 1st power of the flow velocity between 6 and 10 m/s. We interpret the abrupt change in slope with the flow velocity to be a “saturation” phenomenon proposed by Lecoffre et al. [14]. The pitting rates of 1 pit/cm2 /s with water and mercury were compared. The flow velocity was about 20 m/s in water, while it was about 5 m/s in mercury. We think that the pits occurred in mercury after cavitation erosion test at low velocity due to the high liquid density of mercury. 3.4. Influence of cavitation number Figs. 9 and 10 show the relation between the flow velocity and the incipient cavitation number in mercury and in water, respectively, which was measured in a venturi tube by Kamiyama and Yamazaki [9]. They defined the cavitation number as =
Fig. 7. Relation between distance from bottom of eroded surface and hardness.
p1 − pv 1/2V02
(4)
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Fig. 9. Incipient cavitation number of mercury [9]. Fig. 11. Relation between cavitation number and MDER [15].
where p1 , pv , and v0 are the upstream pressure, the vapor pressure (1.80 × 10−7 MPa at 20 ◦ C), the liquid density and the mean flow velocity in the throat. The cavi,1 and the cavi,2 in Fig. 10 show the cavitation at the throat and at the downstream location, respectively. The incipient cavitation number is approximately unity irrespective of the test liquids. On the other hand, cavitation inception occurs at flow velocities of between 4.5 and 8 m/s in mercury and at velocities of between 16 and 28 m/s in water. The relation of the pitting rate in Fig. 8 seems very reasonable both in mercury obtained by Belahadji et al. and in water calculated by us, because the velocity of 5 m/s in mercury and that of 20 m/s in water at a pitting rate of 1 pit/cm2 /s in Fig. 8 correspond to the velocity range of 4–8 m/s in mercury and 15–28 m/s in water in Figs. 9 and 10, respectively. Since the cavitation erosion tests are carried out at a constant amplitude and frequency with a vibratory apparatus, the cavitation condition is thought to be fixed during the test. When the test results of the vibratory method are compared with those of the flowing method, the vibratory results correspond to the results under constant flow conditions such as the constant flow velocity. From Fig. 5, the erosion rate in mercury is six times that of water at a relative temperature of 14 ◦ C. Since it was reported [9] that the MDER in the maximum rate stage is in proportional to the pitting rate in the incubation stage, the test result of the vibratory method was plotted at a flow velocity of 25 m/s, when the pitting rate in mercury is six times that in water. The erosion rate is expected to increase with the 1st power of the flow velocity in lead–bismuth, which has almost the same physical properties (liquid density and sound velocity) as those of mercury. Since the physical properties of sodium are between mercury and water, the velocity dependence of the erosion rate is assumed to be somewhere between the first and the sixth power. However, the detailed dependence will be investigated in the near future. As mentioned above, Kamiyama et al. [9] reported that the incipient cavitation number i is nearly unity at flow velocities of 5–7 m/s in mercury with a venturi tube and at 15–30 m/s in water.
The incipient cavitation numbers in liquid metal and in water are considered to be almost the same. Therefore, we discuss the relations between the MDER and the cavitation number which were obtained in water. Fig. 11 is the relation between the cavitation number and the erosion rate at constant velocities in water within a venturi facility obtained by Hattori et al. [15]. The cavitation number used in this study substitutes the downstream pressure pd for p1 in the numerator of Eq. (3). When the cavitation number decreases, the erosion rate increases and reaches a maximum value, followed by a gradual decrease. When the downstream pressure increases and leads to a higher the cavitation number, the number and the mean diameter of the bubbles decrease. On the other hand, when the downstream pressure decreases, the erosion damage disperses. In this study, the effect of the cavitation number on the erosion was discussed quantitatively based on experimental data. The erosion was confined from the cavitation damage inception to its peak. The cavitation number of the incipient damage id was defined as the intercept of the cavitation number axis with the extension of MDER– curve. The id is 1.0 for 49 m/s and 1.2 for 36.3 m/s, respectively. Therefore, the MDER can be expressed by the following equation.
MDER = ˛(id − )2.5
id = 1.0 id = 1.2
˛ = 119 ˛ = 12
(49 m/s) (36.3 m/s)
(5)
where ˛ is a constant. This agrees with the Mean Depth of Deformation Rate (MDDR) [16] to increase with the 2.5th power of the function (1 − /id ) obtained from the theoretical analysis of a cavitating vortex proposed by Lecoffre [17]. It also agrees with an increase in the pitting rate with the 2.5th power of ( id –) according to the relation between the pitting rate and the cavitating number in valves obtained by Tullis et al. [18]. Therefore, the relation between the MDER and the cavitation number is expressed by the power law of Eq. (4) with an exponent of 2.5. 4. Conclusions
Fig. 10. Incipient cavitation number of water [9].
In this study, erosion tests were carried out in lead–bismuth alloys and we discussed differences in the erosion rate with the variation of the kind of metal. Furthermore, we discussed the effect of the flow velocity and the cavitation number on cavitation erosion in liquid metals with a reference survey. We reach the following conclusions. We defined a relative temperature as the percentage between freezing and boiling points. At a relative temperature of 14 ◦ C, the erosion rate is 10–12 times in various lead–bismuth alloys, and 2–5 times in sodium, as compared with that in deionized water. When SUS304 was exposed to cavitation in PbBi, the surface was work hardened by 20% harder compared with that of the substrate. SUS304 was work hardened by 5% in deionized water.
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The erosion rate is expected to increase with the 1st power of the flow velocity in lead–bismuth, which has almost the same physical properties (liquid density and sound velocity) as those of mercury. Since the physical properties of sodium are between that of mercury and water, the velocity dependence of the erosion rate in sodium is assumed to be between the first to the sixth power. The incipient cavitation number is approximately unity irrespective of the test liquids. Furthermore, the relation between the MDER and the cavitation number is expressed as power law function of ( id –) with an exponent of 2.5 (id : the cavitation number of incipient damage). References [1] M. Futakawa, T. Naoe, C. Tsai, H. Kogawa, S. Ishikawa, Y. Ikeda, H. Soyama, H. Date, GS-11-006 Cav2003, Osaka, Japan, November 1–4, 2003. [2] S. Hattori, Y. Goto, T. Fukuyama, Influence of temperature on erosion by a cavitating liquid jet, Wear 260 (2006) 1217–1223. [3] Preiser, H.S., Thiruvengadam, A., Couchman, C.E., NASACR-54071, TPR-235-1, HYDRONAUTICS, Incorporated, Laurel, Maryland, April 1964.
[4] Thiruvengadam, A., Preiser, H.S., Rudy, S.L., NASACR-54459, TPR467-3, HYDRONAUTICS, Incorporated, Laurel, Maryland, 30 June 1965. [5] R. Garcia, F.G. Hammitt, Trans. ASME, J. Basic Eng. (1967) 753–763. [6] S.G. Young, J.R. Johnston, ASTM STEP 474, American Society for Testing and Materials, 1970, pp. 67–108. [7] S. Hattori, F. Inoue, K. Watashi, T. Hashimoto, Effect of liquid parameters on cavitation erosion in liquid metals, Wear (2008). [8] B. Belahadji, J.P. Frank, J.M. Michel, J. Fluids Eng. 113 (December) (1991) 700–706. [9] S. Kamiyama, T. Yamasaki, The effect of magnetic field on cavitation in mercury flow. The Memoirs of the Institute of High Speed Mechanics, vol. 36, no. 344, ¯ Tohoku University, Sendai, Japan, 1975, pp. 1–16. [10] SAE J417b, Handbook of Japanese Industrial Standards, 2002, pp. 1283–1286. [11] ASTM Designation G32-03, Annual Book of ASTM Standards, 2003, pp. 106–119. [12] R.W. Wilson, R. Graham, Cavitation of metal surfaces in contact with lubricants, in: Conf. Lubrication and Wear, IME, London, 1957, pp. 707–712. [13] L. Rayleigh, On the Pressure developed in a Liquid during the Collapse of a Spherical Cavity, Phil. Mag. S. 6, 34 (200) (1917) 94–98. [14] Y. Leccoffre, CAVITATION Bubble Trackers, 1999, p. 288. [15] S. Hattori, B.-H. Sun, F.G. Hamiitt, Wear 103 (1985) 119–131. [16] H. Kato, Cavitation, 1999, p. 195 (Maki-shoten). [17] Y. Lecoffre, A. Archer, A method to evaluate cavitation erosion in valves, in: Third International Symposium on Cavitation, Grenoble, France, April, 1998. [18] Tullis, P.J., Cavitation Guide for Control Valves, NUREG/CR-6031, May, vol. 21, 1993, pp. 1–106.