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uranium dioxide surfaces in contact
Journal of Nuclear Materials 92 (1980) 345-348 0 North-Holland Publishing Company
LETTER TO THE EDITORS - LETTRE AUX REDACTEURS EXPERIMENTS CONTACT
ON HEAT FLOW THROUGH ZIRCALOY-2/URANIUM
DIOXIDE SURFACES IN
9.57 mm deep thermocouple holes drilled at 6.35 mm intervals along its length. The test surfaces were prepared by lapping them smooth and flat initially (flatness deviation across any diameter <0.5 pm). The surfaces of pair 1 were later on blasted with microglass beads to get rough but flat surfaces. The surface roughness of this pair of surfaces was comparable to that of commercially available surfaces. Table 1 gives a summary of the surface roughnesses of the test surfaces. In addition to vacuum, tests were also performed in argon and helium environments. The two gases were chosen because of their widely differing thermal conductivities. The thermal conductivities of the test materials are listed in table 2.
1. Introduction The necessarily finite nature of thermal contact conductance is of particular significance in nuclear reactor heat transfer where large fluxes are involved and temperature drops of 80 to 250 deg C have been measured at the fuel/can interface [ 11. The more important factors which influence the thermal conductance of a joint are: (i) the contact pressure, (ii) the surface finishes, arid (iii) the relative thermal properties of the solids and the fluids forming the joint. The present paper outlines the experimental work carried out on contacts formed by uranium dioxide and Zircaloy-2, typical materials of a nuclear fuel element. In particular, the effects of the parameters listed above were investigated. The results are also compared with those of previous experiments wherever possible.
4. Experimental
details
In the experimental rig used the specimens could be assembled in the form of a column which could be
2. Outline of method The axial temperature profile in the temperature field undisturbed by the presence of the interface, of each of a pair of cylindrical specimens in end-to-end contact, is measured and extrapolated to the respective interface. The thermal contact conductance is the average heat flux through the specimens divided by the difference between the extrapolated interface temperatures (fig. 1). The resistance is the reciprocal of conductance.
3. Description
of materials DISTANCE
The uranium dioxide and Zircaloy-2 specimens were each 19.05 mm in diameter and 25.4 mm in length. Each specimen had four 1 mm diameter and
h=x
0
Fig. 1. Thermal contact conductance; definition. 345
C. V. Madhusudana /Experiments
346
on heat flow
Table 3
Table 1
~___._ Pair No.
Pair No.
Surface roughness in pm CLA
Mean interface temperature (“C)
_
1 2
Zircaloy-2
Uranium dioxide
1.50 0.30
1.00 0.55
1 (Rough) 2 (Smooth)
Table 2 Material
Thermal conductivity at 200°C (W/mK)
Ref.
13.82 6.08 0.0291 0.250
121 (31 [41 [41
Zircaloy-2 Uranium dioxide Argon Helium
axially loaded so that a range of contact pressures up to 20 MPa could be obtained .The column was heated at one end by controlled electric resistance heating and the heat was removed at the other end by water flowing in a cooling coil. The whole assembly was enclosed in a vacuum chamber. Full details of the rig can be found in ref. [5]. Prior to each test, the surfaces of the specimens were cleaned and then the specimens assembled with a light load. Chromel-alumel thermocouples were inserted into the specimens which were then lagged with fibreglass insulation enclosed in an aluminium radiation shield. The vacuum chamber was closed and evacuation started. The heater and cooling water were then turned on. An absolute pressure of 6.67 Pa (0.05 Torr) was attained in the vacuum tests. When the system reached steady state, a set of thermocouple outputs with reference to a “cold” junction in a thermostat was read off a digital voltmeter (Solartran LM 1420.2) and recorded. The equilibrium was then disrupted by either increasing the mechanical load or by letting the desired gas into the chamber as required. It may be noted that the latter effect is more drastic. Therefore the system takes a much longer time to regain equilibrium when it is disrupted by the introduction or removal of gas from the chamber, compared to the situation when the mechanical load is increased. Also, preliminary tests indicated that the increase in total conductance with
Vacuum
Argon
Helium
184 185
241 241
180 180
contact pressure is not very pronounced when a fluid is present. These considerations suggest that it is necessary and desirable to conduct only a limited number of tests in a fluid environment. In all of the tests the input power and cooling water temperature were held constant so that the mean interface temperature was reasonably constant for any given environment. Table 3 above lists the average mean interface temperatures obtained on the tests.
5. Results and discussion Accuracy. In each case, straight lines were fitted to thermocouple outputs and the interface temperatures obtained by extrapolation of the straight lines in each specimen. The heat flux in each specimen was calculated using the corresponding temperature gradient and the average value of the thermal conductivity over the range of specimen temperatures. It was estimated that the interface temperatures were probably accurate to 5% in vacuum, 10% in argon and 15% in helium. The heat fluxes in the two specimens agreed to lo%, 15% and 20% in vacuum, argon and helium, respectively, According to law of combination of errors, therefore, the overall accuracy in conductance would be 1 l%, 18%, and 15% in vacuum, argon and helium, respectively. It may be mentioned that a rigorous statistical analysis of errors is not feasible because of the small number of temperature readings. Tests in vacuum. The variations of conductance with pressure for pairs 1 and 2 in vacuum are shown plotted on a log-log basis in fig. 2. The graphs are linear, showing that a relationship of the type h 0: pn exists, with n = 0.64 for rough surfaces and n = 0.5 for smooth ones (h is the thermal contact conductance and p the contact pressure). The values of n are in reasonable agreement with earlier experimental
C. V. Madhusudana /Experiments
1022 03
00 1
30
IO p (4
Fig. 2. Comparison of the performance surfaces in vacuum.
341
on heat flow
I
5
10 P (MR)
i
-40
Fig. 4. Conductance versus contact pressure - pair of smooth surfaces.
of the two pairs of
values of n = 0.66 [6], and IZ= 0.41 [7]. (The results
of ref. [6] were not plotted on a log-log basis and had to be replotted for the present purpose.) However, the value of n is considerably less than theoretically predicted values of 0.94 [S] , and 0.956 [9]. The values of conductance for smooth surfaces throughout the pressure range are at least 30% higher than corresponding values for rough surfaces. This suggests that the finishes of available surfaces could be improved to obtain better performance. Tests in gaseous environments. The results for vacuum are compared with the results in argon and helium in figs. 3 and 4. For both pairs of surfaces, it is evident that the conductance values in gaseous media are considerably higher than the corresponding
values in vacuum. Table 4, below, lists the increase in conductance, due to the presence of gases, at the lowest and highest contact pressures obtained in the tests. It can be seen that, at high contact pressures, the improvement due to argon becomes less noticeable. The improvement due to helium persists at high contact pressures also. This is in accordance with previously observed trends [IO]. Comparison with previous work. The only available work for direct comparison was that of Ross and Stoute [ 111 whose pair 7 of tested specimens had very similar characteristics to pair 1 of the present tests. The conductance values reported by them are plotted on fig. 2 and it can be seen that they agree well with the present results.
Table 4 Pair No.
Percentage increase in conductance over vacuum value, at contact pressure of 0.89 MPa
0
0
5
Fig. 3. Conductance surfaces.
P&
1s
20.13 MPa
Argon
Helium
Argon
Helium
435 352
856 765
17 4
48 68
20
versus contact pressure - pair of rough
1 (Rough) 2 (Smooth)
348
C. V. Madhusudana /Experiments
6. Conclusions The following conclusions summarize the results of present experimental investigations: (i) The thermal contact conductance of flat Zircaloy_2/uranium dioxide surfaces in vacuum varies as a simple power of contact pressure. The values of the index are in the same range as those of previous experimental work on other materials. (ii) In general, the smooth surfaces shown higher conductances, indicating that there is an incentive to improve the surface finish of practical surfaces. (iii) The presence of a gas of good conductivity can significantly improve the thermal conductance even at high contact pressures. (iv) The results show fair agreement with comparable previous test results.
Acknowledgements The experiments were conducted at Monash University during the author’s tenure as a research scholar. The Australian Atomic Energy Commission supported
Received 22 April 1980
on heat flow
the projects and supplied the materials required for the specimens. Thanks are hereby offered to both these organisations for their support.
References [l] W.W. Plotnikoff and G.A. Tingate, Australian Atomic Energy Commission Research Establishment, private communication (1970). [2] B.J. Seddon,TRG Report 108 (R) (UKAEA, 1962). [ 31 IAEA Technical Report No. 59 (1966). [4] W.M. Rohsenow and J.P. Hartnett, Handbook of Heat Transfer (McGraw-Hill, New York, 1973). [5] A. Williams, in: Proc. 3rd Intern. Heat Transfer Conf., Chicago, Vol. IV (AIChE, New York, 1966) pp. 109117. [6] V.A. Mal’kov, Heat Transfer-Soviet Res. 2 (1970) 24. [7] M. Necati Ozisik and D. Hughes, Paper No. 66-WA/HT54 (ASME, New York, 1966). [8] B.B. Mikic, Intern. J. Heat Mass Transfer 17 (1974) 205. [9] V.M. Popov, Power Eng. 14 (1976) 158. [lo] C.V. Madhusudana, Intern. J. Heat Mass Transfer 18 (1975) 989. [ll] A.M. Ross and R.L. Stoute, Report No. CRFD-1075 (Atomic Energy of Canade Limited, Ontario, 1962).
C.V. Madhusudana Department of Mechanical Engineering, The University of New South Wales, Broken Hill, Australia
LETTER TO THE EDITORS - LETTRE AUX REDACTEURS EXPERIMENTS CONTACT
ON HEAT FLOW THROUGH ZIRCALOY-2/URANIUM
DIOXIDE SURFACES IN
9.57 mm deep thermocouple holes drilled at 6.35 mm intervals along its length. The test surfaces were prepared by lapping them smooth and flat initially (flatness deviation across any diameter <0.5 pm). The surfaces of pair 1 were later on blasted with microglass beads to get rough but flat surfaces. The surface roughness of this pair of surfaces was comparable to that of commercially available surfaces. Table 1 gives a summary of the surface roughnesses of the test surfaces. In addition to vacuum, tests were also performed in argon and helium environments. The two gases were chosen because of their widely differing thermal conductivities. The thermal conductivities of the test materials are listed in table 2.
1. Introduction The necessarily finite nature of thermal contact conductance is of particular significance in nuclear reactor heat transfer where large fluxes are involved and temperature drops of 80 to 250 deg C have been measured at the fuel/can interface [ 11. The more important factors which influence the thermal conductance of a joint are: (i) the contact pressure, (ii) the surface finishes, arid (iii) the relative thermal properties of the solids and the fluids forming the joint. The present paper outlines the experimental work carried out on contacts formed by uranium dioxide and Zircaloy-2, typical materials of a nuclear fuel element. In particular, the effects of the parameters listed above were investigated. The results are also compared with those of previous experiments wherever possible.
4. Experimental
details
In the experimental rig used the specimens could be assembled in the form of a column which could be
2. Outline of method The axial temperature profile in the temperature field undisturbed by the presence of the interface, of each of a pair of cylindrical specimens in end-to-end contact, is measured and extrapolated to the respective interface. The thermal contact conductance is the average heat flux through the specimens divided by the difference between the extrapolated interface temperatures (fig. 1). The resistance is the reciprocal of conductance.
3. Description
of materials DISTANCE
The uranium dioxide and Zircaloy-2 specimens were each 19.05 mm in diameter and 25.4 mm in length. Each specimen had four 1 mm diameter and
h=x
0
Fig. 1. Thermal contact conductance; definition. 345
C. V. Madhusudana /Experiments
346
on heat flow
Table 3
Table 1
~___._ Pair No.
Pair No.
Surface roughness in pm CLA
Mean interface temperature (“C)
_
1 2
Zircaloy-2
Uranium dioxide
1.50 0.30
1.00 0.55
1 (Rough) 2 (Smooth)
Table 2 Material
Thermal conductivity at 200°C (W/mK)
Ref.
13.82 6.08 0.0291 0.250
121 (31 [41 [41
Zircaloy-2 Uranium dioxide Argon Helium
axially loaded so that a range of contact pressures up to 20 MPa could be obtained .The column was heated at one end by controlled electric resistance heating and the heat was removed at the other end by water flowing in a cooling coil. The whole assembly was enclosed in a vacuum chamber. Full details of the rig can be found in ref. [5]. Prior to each test, the surfaces of the specimens were cleaned and then the specimens assembled with a light load. Chromel-alumel thermocouples were inserted into the specimens which were then lagged with fibreglass insulation enclosed in an aluminium radiation shield. The vacuum chamber was closed and evacuation started. The heater and cooling water were then turned on. An absolute pressure of 6.67 Pa (0.05 Torr) was attained in the vacuum tests. When the system reached steady state, a set of thermocouple outputs with reference to a “cold” junction in a thermostat was read off a digital voltmeter (Solartran LM 1420.2) and recorded. The equilibrium was then disrupted by either increasing the mechanical load or by letting the desired gas into the chamber as required. It may be noted that the latter effect is more drastic. Therefore the system takes a much longer time to regain equilibrium when it is disrupted by the introduction or removal of gas from the chamber, compared to the situation when the mechanical load is increased. Also, preliminary tests indicated that the increase in total conductance with
Vacuum
Argon
Helium
184 185
241 241
180 180
contact pressure is not very pronounced when a fluid is present. These considerations suggest that it is necessary and desirable to conduct only a limited number of tests in a fluid environment. In all of the tests the input power and cooling water temperature were held constant so that the mean interface temperature was reasonably constant for any given environment. Table 3 above lists the average mean interface temperatures obtained on the tests.
5. Results and discussion Accuracy. In each case, straight lines were fitted to thermocouple outputs and the interface temperatures obtained by extrapolation of the straight lines in each specimen. The heat flux in each specimen was calculated using the corresponding temperature gradient and the average value of the thermal conductivity over the range of specimen temperatures. It was estimated that the interface temperatures were probably accurate to 5% in vacuum, 10% in argon and 15% in helium. The heat fluxes in the two specimens agreed to lo%, 15% and 20% in vacuum, argon and helium, respectively, According to law of combination of errors, therefore, the overall accuracy in conductance would be 1 l%, 18%, and 15% in vacuum, argon and helium, respectively. It may be mentioned that a rigorous statistical analysis of errors is not feasible because of the small number of temperature readings. Tests in vacuum. The variations of conductance with pressure for pairs 1 and 2 in vacuum are shown plotted on a log-log basis in fig. 2. The graphs are linear, showing that a relationship of the type h 0: pn exists, with n = 0.64 for rough surfaces and n = 0.5 for smooth ones (h is the thermal contact conductance and p the contact pressure). The values of n are in reasonable agreement with earlier experimental
C. V. Madhusudana /Experiments
1022 03
00 1
30
IO p (4
Fig. 2. Comparison of the performance surfaces in vacuum.
341
on heat flow
I
5
10 P (MR)
i
-40
Fig. 4. Conductance versus contact pressure - pair of smooth surfaces.
of the two pairs of
values of n = 0.66 [6], and IZ= 0.41 [7]. (The results
of ref. [6] were not plotted on a log-log basis and had to be replotted for the present purpose.) However, the value of n is considerably less than theoretically predicted values of 0.94 [S] , and 0.956 [9]. The values of conductance for smooth surfaces throughout the pressure range are at least 30% higher than corresponding values for rough surfaces. This suggests that the finishes of available surfaces could be improved to obtain better performance. Tests in gaseous environments. The results for vacuum are compared with the results in argon and helium in figs. 3 and 4. For both pairs of surfaces, it is evident that the conductance values in gaseous media are considerably higher than the corresponding
values in vacuum. Table 4, below, lists the increase in conductance, due to the presence of gases, at the lowest and highest contact pressures obtained in the tests. It can be seen that, at high contact pressures, the improvement due to argon becomes less noticeable. The improvement due to helium persists at high contact pressures also. This is in accordance with previously observed trends [IO]. Comparison with previous work. The only available work for direct comparison was that of Ross and Stoute [ 111 whose pair 7 of tested specimens had very similar characteristics to pair 1 of the present tests. The conductance values reported by them are plotted on fig. 2 and it can be seen that they agree well with the present results.
Table 4 Pair No.
Percentage increase in conductance over vacuum value, at contact pressure of 0.89 MPa
0
0
5
Fig. 3. Conductance surfaces.
P&
1s
20.13 MPa
Argon
Helium
Argon
Helium
435 352
856 765
17 4
48 68
20
versus contact pressure - pair of rough
1 (Rough) 2 (Smooth)
348
C. V. Madhusudana /Experiments
6. Conclusions The following conclusions summarize the results of present experimental investigations: (i) The thermal contact conductance of flat Zircaloy_2/uranium dioxide surfaces in vacuum varies as a simple power of contact pressure. The values of the index are in the same range as those of previous experimental work on other materials. (ii) In general, the smooth surfaces shown higher conductances, indicating that there is an incentive to improve the surface finish of practical surfaces. (iii) The presence of a gas of good conductivity can significantly improve the thermal conductance even at high contact pressures. (iv) The results show fair agreement with comparable previous test results.
Acknowledgements The experiments were conducted at Monash University during the author’s tenure as a research scholar. The Australian Atomic Energy Commission supported
Received 22 April 1980
on heat flow
the projects and supplied the materials required for the specimens. Thanks are hereby offered to both these organisations for their support.
References [l] W.W. Plotnikoff and G.A. Tingate, Australian Atomic Energy Commission Research Establishment, private communication (1970). [2] B.J. Seddon,TRG Report 108 (R) (UKAEA, 1962). [ 31 IAEA Technical Report No. 59 (1966). [4] W.M. Rohsenow and J.P. Hartnett, Handbook of Heat Transfer (McGraw-Hill, New York, 1973). [5] A. Williams, in: Proc. 3rd Intern. Heat Transfer Conf., Chicago, Vol. IV (AIChE, New York, 1966) pp. 109117. [6] V.A. Mal’kov, Heat Transfer-Soviet Res. 2 (1970) 24. [7] M. Necati Ozisik and D. Hughes, Paper No. 66-WA/HT54 (ASME, New York, 1966). [8] B.B. Mikic, Intern. J. Heat Mass Transfer 17 (1974) 205. [9] V.M. Popov, Power Eng. 14 (1976) 158. [lo] C.V. Madhusudana, Intern. J. Heat Mass Transfer 18 (1975) 989. [ll] A.M. Ross and R.L. Stoute, Report No. CRFD-1075 (Atomic Energy of Canade Limited, Ontario, 1962).
C.V. Madhusudana Department of Mechanical Engineering, The University of New South Wales, Broken Hill, Australia