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The viscosity of molten uranium dioxide
JOURNAL
OF NUCLEAR
MATERIALS
50 (1974) 103-106.0
NORTH-HOLLAND
PUBLISHING
COMPANY
LETTERS TO THE EDITORS - LETTRES AUX REDACTEURS THE VISCOSITY OF MOLTEN URANIUM DIOXIDE RE. WOODLEY Hanford Engineering Development Laboratory, WestinghouseHanford Company, Richland, Washington,USA Received 19 September 1973
1. Introduction Certain fuel safety analyses employ a value for the viscosity of the molten oxide fuel. Nelson [I] reported viscosities for molten UO, ranging from 36 to 46 cP, whereas the measurements of Tsai and Olander [2] on this same material yielded values lower than those of Nelson by a factor of 5. This discrepancy in the viscosity of molten UO, is equivalent to as much as a five-fold uncertainty in the flow velocity of an oxide fuel in the event of melting. The present study was therefore initiated to resolve this uncertainty by providing additional measurements on the viscosity of molten UO,.
2. Experimental procedure The viscosity measurements were performed in an oscillating cup viscometer very similar to those employed by other investigators [2,3]. The present apparatus was originally constructed by Nelson [ 1 ] but was modified to provide a more substantial container for the molten UO, and an improved suspension system for the torsional pendulum. Prior to melting, the UO, sample consisted of five pellets weighing a total of 120.2 g. After pressing, the pellets were sintered in pure H, for 4h at 16OO’C.The resultant density was 94.8% of theoretical. A spectrochemical analysis of this material indicated a total impurity content less than 230 ppm. Measurement of the O/U ratio by the Chikalla procedure [4] yielded a value of 2.002. The redesigned cylindrical crucible, with an I.D. of
1.58 cm and a wall thickness of 0.32 cm, was machined from a solid rod of tungsten. Following insertion of the UO, pellets, a tungsten lid was electron-beam welded onto the crucible under vacuum. A support rod was, in turn, attached to the crucible lid by means of a tungsten pin, and this assembly was then rigidly connected to the remainder of the torsional pendulum by means of a bayonet-type mounting. An 11 mil tungsten wire supported the pendulum assembly, with the crucible positioned within the tungsten mesh heating element of a Brew vacuum furnace capable of temperatures near 3000°C. Evacuation of the furnace was accomplished by means of mechanical and diffusion pumps. Because the vacuum connection to the furnace was made through a flexible bellows, no vibration problems were encountered even though the pumps were run continuously. Upon displacement from its equilibrium position, the torsional pendulum performs simple damped harmonic oscillations about its vertical axis. The time-rate of decrease in angular displacement is videotaped and this record subsequently replayed in stop-action mode to determine the logarithmic decrement and the period of oscillation. The logarithmic decrement is obtained by a least-squares procedure from the amplitudes of from 30 to 80 oscillations of the pendulum. The period is determined by timing the same number of oscillations with a stopwatch. The decrement of the tungsten torsion wire was determined at a temperature about 1OO’Cbelow the UO, melting point both before and after each series of measurements. It amounted to about 3% of the total decrement for the pendulum with the UO, molten. The values of the decrement and period thus obtained, together with
104
R.E. Woodley, Viscosity
the moment of inertia of the pendulum, 628.3 g l cm2, the mass of UO,, the inner radius of the crucible, and the measurement temperature, were then employed in a computer program devised by Finucane [S] to calculate the viscosity. Temperature measurements were performed with a ~cro-optics pyrometer calibrated against a tungsten strip lamp to 2300°C and against a carbon arc with neutral filters to a temperature of approximately 3000°C. As in the study of Tsai and Olander [2], the radiation shields of the furnace formed a nearlyblackbody cavity around the sample crucible, which was sighted through a window in the furnace door and a 3 mm diameter hole in the radiation shields. As the above-mentioned investigators also noted, the temperature correction for the furnace window increased during a series of measurements, even though the window was covered by a movable shutter when pyrometer readings were not being made. In the present study, rather than assuming that the window correction varied linearly with the number of temperature measurements, the change for each measurement was weighted by the tungsten vapor pressure at the furnace temperature of that measurement. Over the limited temperature interval studied, the variation in the window correction, ~~0~~ weighted, was nevertheless nearly linear. The temperature correction for the clean window amounted to about 30°C whereas at the completion of a series of measurements the correction was about 45’C.
3. Experimenta results and discussion Two series of viscosity measurements were performed with the same encapsulated UO, sample. The measurements of Series I cover the temperature range 2870 to 2985”C, whereas those of Series 2, which were performed at a later date, cover the temperature interval 2885 to 3030°C. Ordinarily, three measurements were made at each temperature. All of the viscosities obtained may be found in table 1, where the results are presented in chronological sequence. The two low viscosity values, Runs 2 and 3 of Series 1, are believed to be erroneous and due to partial resolidification of the molten UO, at a temperature which is near the UO, melting point, 2865°C [6]. This type of behavior was not observed at any temperature above 2870-2875°C. In general, the present viscosities con-
of rnaltenuranium dioxide Table 1 The
Run
viscosityof molten uraniumdioxide.
Tern’ (“0
Density a)
Viscosity
(g/cm3 1
(CPI
Series I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2870 2875 2815 2920 2920 2920 2985 2985 2985 2940 2940 2945 2905 2910 2910 2890 2890 2890
10.35 9.72 9.26 10.60 10.55 10.66 10.43 10.39 10.36 10.47 IO.48 10.48 IO.51 10.55 10.54 10.42 IO.38 IO.40
2.693 2.682 2.682 2.667 2.657 2.655 2.660 2.665 2.667 2.660 2.663 2.660 2.663 2.663 2.660 2.663 2.662 2.665
8.74 8.73 8.73 8.69 8.69 8.69 8.63 8.63 8.63 8.67 8.67 8.67 8.70 8.70 8.70 8.72 8.72 8.72
4.25 3.65 3.26 4.41 4.34 4.44 4.20 4.17 4.15 4.26 4.28 4.27 4.32 4.36 4.34 4.24 4.20 4.23
10.35 10.45 10.43 10.36 10.39 10.38 10.20 10.27 10.23 10.21 10.18 10.16 10.21 10.19 10.19 10.28 10.24 10.22 10.28 LO.22 10.28
2.663 2.643 2.663 2.663 2.657 2.663 2.663 2.663 2.663 2.663 2.663 2.666 2.663 2.666 2.663 2.666 2.649 2.671 2.671 2.671 2.674
8.72 8.72 8.72 8.69 8.68 8.69 8.63 8.63 8.63 8.60 8.60 8.59 8.62 8.62 8.62 8.67 8.67 8.67 8.70 8.70 8.70
4.18 4.28 4.25 4.17 4.18 4.19 3.99 4.05 4.02 3.98 3.95 3.94 3.99 3.98 3.97 4.09 4.06 4.04 4.12 4.06 4.13
Series 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1.5 16 17 18 19 20 21 - -
2885 2885 2890 2925 2935 2925 2990 2990 2990 3025 3025 3030 3000 3000 3000 2945 2940 2945 2905 2905 290.5
a) Based on the density function p = 8.?4/[ I + 0.000105 (T-
286513
,
with Tin deg C. This function was derived from the data of Christensen [8], but it was assumed that the liquid density, 8.74 g/cm3, was obtained at 2865’C rather than at 28OO”C, the apparent melting point as determined by Christensen.
R E. Woodley, Viscosity of molten uranium dioxide
0
105
0
SERIES 1
- 4.2 rl(CP) -4.1
- 4.0
- 3.9 1.351 ' 3.00
I 3.05
I
I
3.10
3.15
I, 3.20
d/T (OKI
Fig. 1. Viscosity of molten UO2 as a function of temperature.
firm the results of Tsai and Olander as opposed to the high values obtained by Nelson. The temperature dependence of the UO, viscosity is illustrated in fig. 1. The solid line is the least-squares fit to the data of Series 2, which covered a somewhat greater temperature range and showed less scatter than the results of Series 1. The dashed line is constrained to the slope established by the viscosities of Series 2 but has an intercept computed using all of the experimental points, which exhibit a standard deviation from the dashed line of + 0.10 cP. At a given temperature, the viscosity difference between the two lines is only about 0.06 cP. The activation energy obtained from the Series 2 data is 9.18 f 2.18 kcal/mol. The error limit was obtained from the standard deviation of the slope at the 95% confidence level, i.e., k2.093 (I for the 21 measurements of Series 2. Although the temperature intervals are similar, the viscosity data obtained in the present study do not show the scatter exhibited by the data of Tsai and Olander, but are confined to a relatively narrow viscosity range. This is primarily a reflection of the consistent values obtained for the logarithmic decrement, as may be noted from the decay constants listed in
table 1. The decay constant is the quotient of the de crement and the period. Of the experimentally determined quantities, only the decrement has a significant effect on the viscosity. The viscosity is relatively insensitive to small errors in the temperature and the period. For example, comparing Runs 7 and 8 of Series 2, it is seen that a 0.68% variation in the decay constant (or decrement), all other quantities being equal, results in a 1.5% variation in the viscosity. On the other hand, when the temperature, acting through the density of the molten UO, and the thermal expansion of the tungsten crucible, is increased by 20°C, the calculated viscosity is only lowered by 0.24% or about 0.01 cP. Because our temperature measurements are believed to be accurate to within 20°C or probably less, the present viscosity values are relatively unaffected by temperature errors. The maximum difference noted in two consecutive measurements of the period was 0.4 set for 35 complete oscillations of the pendulum. This is equivalent to a variation of about 0.01 set in the period which, in turn, affects the viscosity by only about 0.5% or 0.02 cP. No corrections to the viscosity values have been made to account for the fact that the free liquid sur-
106
R.E. Woodley, Viscosity of molten uranium dioxide
face is nonplanar [7]. Tsai and Olander 121, who used t~~ten crucibles of about the same radius as the present crucible, found that the formation of a meniscus increased the height of liquid in contact with the crucible wall by about 5%. Thus, the maximum error in the present viscosity values due to this effect would be only about 0.2 cP. The solution of tungsten in the molten IJO, could conceivably alter the U02 viscosity, however, there is no way to evaluate the extent of any viscosity variation due to tungsten contamination. It has been reported [6] that stoichiometric UO, at its melting point dissolves only about 0.25 wt% tungsten. In the present study, the tungsten solubility averaged about 0.19 wt %. It, thus, appears unlikely that a significant change in the UO, viscosity would be effected in this manner.
4. Conciusions The viscosity of uranium dioxide has been measured with an oscillating cup viscometer from just above the melting point to a temperature of 303Ok Over this temperature interval, the viscosity follows the relationship q(cP) = 0.988 exp (4620/T) with Tin deg K. A median viscosity of 4.2 CPis exhibited. The present results confirm the magnitude of the viscosity values measured by Tsai and Olander as opposed to the higher values obtained by Nelson.
Acknowledgement The author is grateful to O.D. Slagle and W.J. Woods both experienced in the use of the oscillating cup viscometer, for their many helpful suggestions and their assistance in the design and construe tion of the modified crucible and pendulum suspension. The experimental meas~ements were ably performed by G.I.,. Jones to whom special thanks are due.
RefeHnces [1] R.P. Nelson, Battelle-Northwest(USA) Report, BNWL1279 (1970) 2.4; this study is alsobriefly describedby J.L. Bates, C.E. McNeilly and J.J. Rasmussen, Materials Science Research 5 (1971) 11. [2] H.C. Tsai and D.R. Olander, J. Nucl. Mater. 44 (1972) 83. [ 31 L.J. Wittenberg, D. Ofte and D.F. Curtiss, J. Chem. Phys. 48 (1968) 3253. [4] C.E. McNeilly and T.D. Chikalla, J. Nucl. Mater. 39 (1971) 77. [S] J.S. Finucane, University of California Radiation Laboratory (USA) Report, UCRL-16988 (1969). [6] R.E. Latta and R.E. Fryxell, J. Nucl. Mater. 35 (1970) 195. f7] H.R Thresh, ASM Trans. 55 (1962) 790. [8] J.A. Christensen, J. Amer. Cer. Sot. 46 (1963) 607.
OF NUCLEAR
MATERIALS
50 (1974) 103-106.0
NORTH-HOLLAND
PUBLISHING
COMPANY
LETTERS TO THE EDITORS - LETTRES AUX REDACTEURS THE VISCOSITY OF MOLTEN URANIUM DIOXIDE RE. WOODLEY Hanford Engineering Development Laboratory, WestinghouseHanford Company, Richland, Washington,USA Received 19 September 1973
1. Introduction Certain fuel safety analyses employ a value for the viscosity of the molten oxide fuel. Nelson [I] reported viscosities for molten UO, ranging from 36 to 46 cP, whereas the measurements of Tsai and Olander [2] on this same material yielded values lower than those of Nelson by a factor of 5. This discrepancy in the viscosity of molten UO, is equivalent to as much as a five-fold uncertainty in the flow velocity of an oxide fuel in the event of melting. The present study was therefore initiated to resolve this uncertainty by providing additional measurements on the viscosity of molten UO,.
2. Experimental procedure The viscosity measurements were performed in an oscillating cup viscometer very similar to those employed by other investigators [2,3]. The present apparatus was originally constructed by Nelson [ 1 ] but was modified to provide a more substantial container for the molten UO, and an improved suspension system for the torsional pendulum. Prior to melting, the UO, sample consisted of five pellets weighing a total of 120.2 g. After pressing, the pellets were sintered in pure H, for 4h at 16OO’C.The resultant density was 94.8% of theoretical. A spectrochemical analysis of this material indicated a total impurity content less than 230 ppm. Measurement of the O/U ratio by the Chikalla procedure [4] yielded a value of 2.002. The redesigned cylindrical crucible, with an I.D. of
1.58 cm and a wall thickness of 0.32 cm, was machined from a solid rod of tungsten. Following insertion of the UO, pellets, a tungsten lid was electron-beam welded onto the crucible under vacuum. A support rod was, in turn, attached to the crucible lid by means of a tungsten pin, and this assembly was then rigidly connected to the remainder of the torsional pendulum by means of a bayonet-type mounting. An 11 mil tungsten wire supported the pendulum assembly, with the crucible positioned within the tungsten mesh heating element of a Brew vacuum furnace capable of temperatures near 3000°C. Evacuation of the furnace was accomplished by means of mechanical and diffusion pumps. Because the vacuum connection to the furnace was made through a flexible bellows, no vibration problems were encountered even though the pumps were run continuously. Upon displacement from its equilibrium position, the torsional pendulum performs simple damped harmonic oscillations about its vertical axis. The time-rate of decrease in angular displacement is videotaped and this record subsequently replayed in stop-action mode to determine the logarithmic decrement and the period of oscillation. The logarithmic decrement is obtained by a least-squares procedure from the amplitudes of from 30 to 80 oscillations of the pendulum. The period is determined by timing the same number of oscillations with a stopwatch. The decrement of the tungsten torsion wire was determined at a temperature about 1OO’Cbelow the UO, melting point both before and after each series of measurements. It amounted to about 3% of the total decrement for the pendulum with the UO, molten. The values of the decrement and period thus obtained, together with
104
R.E. Woodley, Viscosity
the moment of inertia of the pendulum, 628.3 g l cm2, the mass of UO,, the inner radius of the crucible, and the measurement temperature, were then employed in a computer program devised by Finucane [S] to calculate the viscosity. Temperature measurements were performed with a ~cro-optics pyrometer calibrated against a tungsten strip lamp to 2300°C and against a carbon arc with neutral filters to a temperature of approximately 3000°C. As in the study of Tsai and Olander [2], the radiation shields of the furnace formed a nearlyblackbody cavity around the sample crucible, which was sighted through a window in the furnace door and a 3 mm diameter hole in the radiation shields. As the above-mentioned investigators also noted, the temperature correction for the furnace window increased during a series of measurements, even though the window was covered by a movable shutter when pyrometer readings were not being made. In the present study, rather than assuming that the window correction varied linearly with the number of temperature measurements, the change for each measurement was weighted by the tungsten vapor pressure at the furnace temperature of that measurement. Over the limited temperature interval studied, the variation in the window correction, ~~0~~ weighted, was nevertheless nearly linear. The temperature correction for the clean window amounted to about 30°C whereas at the completion of a series of measurements the correction was about 45’C.
3. Experimenta results and discussion Two series of viscosity measurements were performed with the same encapsulated UO, sample. The measurements of Series I cover the temperature range 2870 to 2985”C, whereas those of Series 2, which were performed at a later date, cover the temperature interval 2885 to 3030°C. Ordinarily, three measurements were made at each temperature. All of the viscosities obtained may be found in table 1, where the results are presented in chronological sequence. The two low viscosity values, Runs 2 and 3 of Series 1, are believed to be erroneous and due to partial resolidification of the molten UO, at a temperature which is near the UO, melting point, 2865°C [6]. This type of behavior was not observed at any temperature above 2870-2875°C. In general, the present viscosities con-
of rnaltenuranium dioxide Table 1 The
Run
viscosityof molten uraniumdioxide.
Tern’ (“0
Density a)
Viscosity
(g/cm3 1
(CPI
Series I 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
2870 2875 2815 2920 2920 2920 2985 2985 2985 2940 2940 2945 2905 2910 2910 2890 2890 2890
10.35 9.72 9.26 10.60 10.55 10.66 10.43 10.39 10.36 10.47 IO.48 10.48 IO.51 10.55 10.54 10.42 IO.38 IO.40
2.693 2.682 2.682 2.667 2.657 2.655 2.660 2.665 2.667 2.660 2.663 2.660 2.663 2.663 2.660 2.663 2.662 2.665
8.74 8.73 8.73 8.69 8.69 8.69 8.63 8.63 8.63 8.67 8.67 8.67 8.70 8.70 8.70 8.72 8.72 8.72
4.25 3.65 3.26 4.41 4.34 4.44 4.20 4.17 4.15 4.26 4.28 4.27 4.32 4.36 4.34 4.24 4.20 4.23
10.35 10.45 10.43 10.36 10.39 10.38 10.20 10.27 10.23 10.21 10.18 10.16 10.21 10.19 10.19 10.28 10.24 10.22 10.28 LO.22 10.28
2.663 2.643 2.663 2.663 2.657 2.663 2.663 2.663 2.663 2.663 2.663 2.666 2.663 2.666 2.663 2.666 2.649 2.671 2.671 2.671 2.674
8.72 8.72 8.72 8.69 8.68 8.69 8.63 8.63 8.63 8.60 8.60 8.59 8.62 8.62 8.62 8.67 8.67 8.67 8.70 8.70 8.70
4.18 4.28 4.25 4.17 4.18 4.19 3.99 4.05 4.02 3.98 3.95 3.94 3.99 3.98 3.97 4.09 4.06 4.04 4.12 4.06 4.13
Series 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1.5 16 17 18 19 20 21 - -
2885 2885 2890 2925 2935 2925 2990 2990 2990 3025 3025 3030 3000 3000 3000 2945 2940 2945 2905 2905 290.5
a) Based on the density function p = 8.?4/[ I + 0.000105 (T-
286513
,
with Tin deg C. This function was derived from the data of Christensen [8], but it was assumed that the liquid density, 8.74 g/cm3, was obtained at 2865’C rather than at 28OO”C, the apparent melting point as determined by Christensen.
R E. Woodley, Viscosity of molten uranium dioxide
0
105
0
SERIES 1
- 4.2 rl(CP) -4.1
- 4.0
- 3.9 1.351 ' 3.00
I 3.05
I
I
3.10
3.15
I, 3.20
d/T (OKI
Fig. 1. Viscosity of molten UO2 as a function of temperature.
firm the results of Tsai and Olander as opposed to the high values obtained by Nelson. The temperature dependence of the UO, viscosity is illustrated in fig. 1. The solid line is the least-squares fit to the data of Series 2, which covered a somewhat greater temperature range and showed less scatter than the results of Series 1. The dashed line is constrained to the slope established by the viscosities of Series 2 but has an intercept computed using all of the experimental points, which exhibit a standard deviation from the dashed line of + 0.10 cP. At a given temperature, the viscosity difference between the two lines is only about 0.06 cP. The activation energy obtained from the Series 2 data is 9.18 f 2.18 kcal/mol. The error limit was obtained from the standard deviation of the slope at the 95% confidence level, i.e., k2.093 (I for the 21 measurements of Series 2. Although the temperature intervals are similar, the viscosity data obtained in the present study do not show the scatter exhibited by the data of Tsai and Olander, but are confined to a relatively narrow viscosity range. This is primarily a reflection of the consistent values obtained for the logarithmic decrement, as may be noted from the decay constants listed in
table 1. The decay constant is the quotient of the de crement and the period. Of the experimentally determined quantities, only the decrement has a significant effect on the viscosity. The viscosity is relatively insensitive to small errors in the temperature and the period. For example, comparing Runs 7 and 8 of Series 2, it is seen that a 0.68% variation in the decay constant (or decrement), all other quantities being equal, results in a 1.5% variation in the viscosity. On the other hand, when the temperature, acting through the density of the molten UO, and the thermal expansion of the tungsten crucible, is increased by 20°C, the calculated viscosity is only lowered by 0.24% or about 0.01 cP. Because our temperature measurements are believed to be accurate to within 20°C or probably less, the present viscosity values are relatively unaffected by temperature errors. The maximum difference noted in two consecutive measurements of the period was 0.4 set for 35 complete oscillations of the pendulum. This is equivalent to a variation of about 0.01 set in the period which, in turn, affects the viscosity by only about 0.5% or 0.02 cP. No corrections to the viscosity values have been made to account for the fact that the free liquid sur-
106
R.E. Woodley, Viscosity of molten uranium dioxide
face is nonplanar [7]. Tsai and Olander 121, who used t~~ten crucibles of about the same radius as the present crucible, found that the formation of a meniscus increased the height of liquid in contact with the crucible wall by about 5%. Thus, the maximum error in the present viscosity values due to this effect would be only about 0.2 cP. The solution of tungsten in the molten IJO, could conceivably alter the U02 viscosity, however, there is no way to evaluate the extent of any viscosity variation due to tungsten contamination. It has been reported [6] that stoichiometric UO, at its melting point dissolves only about 0.25 wt% tungsten. In the present study, the tungsten solubility averaged about 0.19 wt %. It, thus, appears unlikely that a significant change in the UO, viscosity would be effected in this manner.
4. Conciusions The viscosity of uranium dioxide has been measured with an oscillating cup viscometer from just above the melting point to a temperature of 303Ok Over this temperature interval, the viscosity follows the relationship q(cP) = 0.988 exp (4620/T) with Tin deg K. A median viscosity of 4.2 CPis exhibited. The present results confirm the magnitude of the viscosity values measured by Tsai and Olander as opposed to the higher values obtained by Nelson.
Acknowledgement The author is grateful to O.D. Slagle and W.J. Woods both experienced in the use of the oscillating cup viscometer, for their many helpful suggestions and their assistance in the design and construe tion of the modified crucible and pendulum suspension. The experimental meas~ements were ably performed by G.I.,. Jones to whom special thanks are due.
RefeHnces [1] R.P. Nelson, Battelle-Northwest(USA) Report, BNWL1279 (1970) 2.4; this study is alsobriefly describedby J.L. Bates, C.E. McNeilly and J.J. Rasmussen, Materials Science Research 5 (1971) 11. [2] H.C. Tsai and D.R. Olander, J. Nucl. Mater. 44 (1972) 83. [ 31 L.J. Wittenberg, D. Ofte and D.F. Curtiss, J. Chem. Phys. 48 (1968) 3253. [4] C.E. McNeilly and T.D. Chikalla, J. Nucl. Mater. 39 (1971) 77. [S] J.S. Finucane, University of California Radiation Laboratory (USA) Report, UCRL-16988 (1969). [6] R.E. Latta and R.E. Fryxell, J. Nucl. Mater. 35 (1970) 195. f7] H.R Thresh, ASM Trans. 55 (1962) 790. [8] J.A. Christensen, J. Amer. Cer. Sot. 46 (1963) 607.