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Measurement of material buckling as a function of void fraction in a sub-critical assembly
Journal of Nuclear Energu, Vol. 24, pp. 587 to 591. Pergamon Press 1971. Printed in Northern Ireland
MEASUREMENT OF MATERIAL BUCKLING AS A FUNCTION OF VOID FRACTION IN A SUB-CRITICAL ASSEMBLY Department
L. TWUM-DANSO* and P. N. COOPER of Physics, University of Aston in Birmingham, Birmingham 4, England (First received 23 March 1970 and injinai form 11 June 1970)
Abstract-Voids have been introduced into a natural uranium water moderated sub-critical assembly by passing compressed air through the moderator. Changes in material buckling have been measured using foil activation techniques over a range of void fractions from 0 to 9 per cent. Calculations have shown that three group diffusion theory can adequately represent the lattice characteristics provided care is taken in calculation of resonance capture in Ua3* and in calculation of fine structure. The presence of voids can be simply regarded as a decrease in moderator density. 1. SUBCRITICAL
ASSEMBLY
196 NATURAL uranium rods 29.2 mm dia., 813 mm long and weight 10 kg were arranged vertically in a 14 x 14 array on a square pitch of 48.3 mm. Location was by means of aluminium lattice plates at the top and bottom of the core. The rods were clad in aluminium 0.91 mm thick and light water was the moderator. This gave a water to uranium volume ratio of 2.33 and a calculated infinite multiplication factor of 0.89. The core was unreflected in the vertical direction but the horizontal directions were reflected by 100 mm of water on 3 faces and 380 mm of water on the fourth face. A flight tube from a 150 keV SAMES type J accelerator projected through the water on this last face so that the target was close to the core face and central. Neutrons were produced by the D(dn) 3He reaction. A total neutron output of about lo* n see-l was possible and the neutron energy from this reaction is close to the mean energy of fission neutrons. 2. PRODUCTION
OF VOIDS
Several methods for simulating voids have been suggested in the past, such as dilution with heavy water, insertion of magnesium strips, and polystyrene granules (DOWN, 1963). The method adopted here was to blow compressed air through the moderator in order to produce voids throughout the whole core. A similar method has also been used to produce voids in a small section of core only (KLEIJN, 1966). Aluminium tubes were laid along the bottom of the core such that a 12.7 mm hole covered with porous polythene was at the centre of each moderator cell. Two oil-free compressors delivering a total of 940 1 min-l at a pressure of 0.2 kg cm-2 were used, and a maximum void fraction of 9 per cent was obtained. Lower void fractions were obtained with one compressor or by diverting some of the air flow to atmosphere. Bubbles were confined to the active region of the core by aluminium sheets on the vertical faces. Additional holes in the top lattice plate served to let the air escape and were also used to locate foil holders. An average value of void fraction in the core was desired, and this was found by measuring the increase in water height resulting from bubbling. Normally water height was maintained constant by means of an overflow, but this was blocked for * Now with Ghana Atomic Energy Commission, P.O. Box 80, Legon, Accra, Ghana. 587
L. T.-DANSO and P. N.
588
CQOPER
these measurements. A float indicator measured the change in height, and was situated in the reflector suitably shielded from disturbances of the water surface due to bubbling. By this method the void fraction could be found to within an absolute error of f0.5 per cent at all values. Gamma ray attenuation measurements were also attempted to provide a check on uniformity of the voids, but due to the low void fractions involved, meaningful results could not be obtained, thus agreeing with previous work (PERKINS,1961). A further difficulty was caused by the very high background of gamma radiation from the decay of natural uranium. Visual inspection showed a uniform disturbance over the surface of the core, and this rather rough method was sensitive enough to detect when some of the orifices became blocked on one occasion. 3. MEASUREMENT OF MATERIAL BUCKLING Indium foils 0,125 mm thick and 10 mm dia. were used to find the flux distribution in the sub-critical facility by measuring the induced /?-activity resulting from neutron capture in Inli5. The foils were supported on perspex rods and the flux distributions were measured many times along the three principal axes of the core for a range of void fractions. Foil activities were corrected for internal and external flux depression (BOTHE, 1943) (TITTLE, 1951). Half life corrections were made by comparison of activities with a further indium foil irradiated at the same time. Measured flux distributions were fitted by least squares techniques to the following forms :$(X) = A1 eXp (-KX) (30,~) d(z) = A, cos (wpz) + B3 cos (3~s~).
db)
=
4
~0s
(w)
+
B,
~0s
In order to eliminate source and leakage effects the exponential flux form was fitted to measurements taken at points greater than 200 mm from the edges of the active core. Also since the reflector tends to give a rise in neutron flux at the edge of the core no measurements were made closer than 48.3 mm (one lattice pitch) to the core/reflector boundary. For the vertical flux distribution the origin of the fitted curve was also adjusted to improve the fit since there was partial neutron reflection from the concrete pedestal. All measurements were made with bare foils since it had been found by experiment that the epicadmium activation was low and had the same form as the thermal activation. Material buckling was calculated from Bm2 = 0.112+ wz2 -
K’.
Examples of the measured fluxes with the fitted curves superimposed, measured at 9-l per cent void fraction, are given in Figs. I,2 and 3. These are typical of all the measurements. 4. EXPERIMENTAL RESULTS Since the initial water to uranium volume ratio was about l-5 times the value giving maximum infinite multiplication factor a significant change in the material buckling with void fraction was expected. The measured bucklings and void fractions are given in Tables 1 and 2. Table 1 gives the complete set of results at 9.1 per cent void fraction and Table 2 summarises the complete range of measurements. The quoted
Measurement horizontal
distribution
I-
active
L 011 -30
of material buckling
589
9.1% voids core
I
-20 distance
-10 0 10 20 30 from core centre cm
FIG. 1 .-Horizontal
vertical
distribution
distributioh
<
9.1 per cent voids.
9.1%
active
voids
1 >
core
1.0 -
2 zO.SSO.6
-
=0.4
-
-20.2. E -040 .J -30
-20
-10
distance
from
FIG. 2.-Vertical
axial
0
10
core centre
distribution
distribution
FIG. 3.-Axial
I 30 cm
9.1 per cent voids.
9.1% voids
---active
distance
20
core -
from
core
distribution
centre
cm
91 per cent voids.
40
L. T.-DANSO and P. N. COOPER
590
TABLE1 Bucklingcomponents m-=
Measuredvalues for 9.1% void fraction
Mean Standard error on mean
Q
WZ
KS
12.1 11.8 12.1 11.0 Il.0 11.4
11.3 IO.4 IO.7 9.0 11.6 11.1
43.4 45.1 45.6 43.9
11.6 @2
10.7 0.4
44.5 05
TABLE 2 Void fraction (%) 0 2.5 f 0.5 6.1 f 0.5 9.1 f 0.5
55.8 f 54.3 f 48.7 f 44.5 f
0.4 I.4 0.6 0.5
15.0 f 13.0 * 13.2 + 11.6 rt
0.7 0.5 0.5 0.2
11.1 f 12.0 f 11.0 * 10.7 *
0.2 0.4 0.2 0.4
-29.7 -29.3 -24.6 -22.1
i 0.9 i 1.6 & 0.8 f 0.7
errors in Table 2 are calculated from the spread in individual measurements and are quoted as the standard error on the mean. 5. CALCULATION OF MATERIAL BUCKLING Standard calculation methods, in which voids were included simply by reducing the moderator density, were found to give an adequate representation of the experimental results. A three group diffusion theory approach was adopted. Inter-group boundaries were selected at 180 keV and 0.625 eV. For the fission and slowing down groups the core was regarded as homogeneous and cross-sections obtained from three-group data given by DEUTSCH(1957), were adopted, except for the effective cross-section for Uz3s, which was found from the, effective resonance integral tabulated as a function of surface to mass ratio (ARGONNE, 1963). Geometric shadowing by neighbouring rods was included by use of the Dancoff and Ginsburg correction factor (DANCOFF, 1944). Fast fission was included by means of a fast fission factor taken from tabulations in ANL 5800 (ARGONNE, 1963). The thermal neutron spectrum was assumed to have a Wigner-Wilkins form and cross-sections were taken from the tabulation by Amster (AMZXER,1958). Average fluxes in the fuel and moderator were calculated by the method of Amouyal, Benoist and Horowitz (AMOUYAL,1956). The most sensitive factors in the calculation were found to be the effective crosssection of U238in the resonance region and the thermal neutron flux fine structure. Table (3) summarises the main conclusions from the calculations and Fig. 4 compares the measurements and the calculations. The experimental points have buckling values about 2 rnM2lower than the calculated values, but show the same rate of change over the whole range measured. This indicates that the calculation model used is sufficiently detailed to represent the measured behavior of the system.
Measurement of material buckling void fraction
591
%
-Is/I
FIG.
4.-Experimental
and theoretical buckling as a function of void fraction. TABLE 3
Void fraction (%)
km
MP (cm”)
BZ (m-3
0
0.890 39.5 -28.6
5
10
0.899 42.6 -24.5
0.910 46.1 -202
The possible effect of asymmetric streaming along the direction of the fuel rods was not included in the calculation model. Agreement with measurements over the void fraction range O-9 per cent justifies this simplification, but for very high values of void fraction the streaming effect will probably become important. 6. CONCLUSIONS The effect of voids in a moderator may be studied by bubbling low pressure com-
pressed air through a core. Such voids would be similar to bulk boiling in a water moderated reactor, but would not simulate the effects of film boiling. A sub-critical core has been shown to be adequate for measurement purposes, and simple foil activation techniques can be made to yield the material buckling. Standard and relatively simple calculation methods have given good agreement with experiment. The presence of voids can be represented adequately for calculation purposes by a reduction in moderator density. An increase in void fraction is similar to a reduction in the water to uranium volume ratio and the results compare reasonably with measurements made on unvoided systems by other workers, notably KOUTS (1955). REFERENCES
A., BENOISTP. and HOROWITZJ. (1956) J. nucl. Energy, 6,19. H. J. (1958) USAEC rep. WAPD-185. ARGONNENAnoNAL LABORATORY(1963) Reactor Physics Constants, USAEC rep. ANL-5800,2nd. edn. AMOUVAL AMSTER
BOTHE, W. (1943) Z. Phys. 120,437. DANCOFF S. M. and GINSBERGM. (1944) USAEC rep. CP-2157. DEUTSCHR. W. (1957) Nucleonics 15, (l), 47. DOWN H. J., DICKIE J. and Fox W. N. (1963) UKAEA rep. AEEW-M 314. KLEIJN H. R. (1966) Proc. Koninklijke Nederlandse Academic van Wetenschappen ser. B, 69. KOUTS H. (1955) Proc. 1st Geneva Conference on the Peaceful Uses of Atomic Energy 5,183. PERKINSH. C., YUSUP M. and LEPPERT G. (1961) Nucl. Sci. Engng 11,304. TITLE C. W. (1951) Nucleonics 8, (6), 5 and 9, (l), 60.
MEASUREMENT OF MATERIAL BUCKLING AS A FUNCTION OF VOID FRACTION IN A SUB-CRITICAL ASSEMBLY Department
L. TWUM-DANSO* and P. N. COOPER of Physics, University of Aston in Birmingham, Birmingham 4, England (First received 23 March 1970 and injinai form 11 June 1970)
Abstract-Voids have been introduced into a natural uranium water moderated sub-critical assembly by passing compressed air through the moderator. Changes in material buckling have been measured using foil activation techniques over a range of void fractions from 0 to 9 per cent. Calculations have shown that three group diffusion theory can adequately represent the lattice characteristics provided care is taken in calculation of resonance capture in Ua3* and in calculation of fine structure. The presence of voids can be simply regarded as a decrease in moderator density. 1. SUBCRITICAL
ASSEMBLY
196 NATURAL uranium rods 29.2 mm dia., 813 mm long and weight 10 kg were arranged vertically in a 14 x 14 array on a square pitch of 48.3 mm. Location was by means of aluminium lattice plates at the top and bottom of the core. The rods were clad in aluminium 0.91 mm thick and light water was the moderator. This gave a water to uranium volume ratio of 2.33 and a calculated infinite multiplication factor of 0.89. The core was unreflected in the vertical direction but the horizontal directions were reflected by 100 mm of water on 3 faces and 380 mm of water on the fourth face. A flight tube from a 150 keV SAMES type J accelerator projected through the water on this last face so that the target was close to the core face and central. Neutrons were produced by the D(dn) 3He reaction. A total neutron output of about lo* n see-l was possible and the neutron energy from this reaction is close to the mean energy of fission neutrons. 2. PRODUCTION
OF VOIDS
Several methods for simulating voids have been suggested in the past, such as dilution with heavy water, insertion of magnesium strips, and polystyrene granules (DOWN, 1963). The method adopted here was to blow compressed air through the moderator in order to produce voids throughout the whole core. A similar method has also been used to produce voids in a small section of core only (KLEIJN, 1966). Aluminium tubes were laid along the bottom of the core such that a 12.7 mm hole covered with porous polythene was at the centre of each moderator cell. Two oil-free compressors delivering a total of 940 1 min-l at a pressure of 0.2 kg cm-2 were used, and a maximum void fraction of 9 per cent was obtained. Lower void fractions were obtained with one compressor or by diverting some of the air flow to atmosphere. Bubbles were confined to the active region of the core by aluminium sheets on the vertical faces. Additional holes in the top lattice plate served to let the air escape and were also used to locate foil holders. An average value of void fraction in the core was desired, and this was found by measuring the increase in water height resulting from bubbling. Normally water height was maintained constant by means of an overflow, but this was blocked for * Now with Ghana Atomic Energy Commission, P.O. Box 80, Legon, Accra, Ghana. 587
L. T.-DANSO and P. N.
588
CQOPER
these measurements. A float indicator measured the change in height, and was situated in the reflector suitably shielded from disturbances of the water surface due to bubbling. By this method the void fraction could be found to within an absolute error of f0.5 per cent at all values. Gamma ray attenuation measurements were also attempted to provide a check on uniformity of the voids, but due to the low void fractions involved, meaningful results could not be obtained, thus agreeing with previous work (PERKINS,1961). A further difficulty was caused by the very high background of gamma radiation from the decay of natural uranium. Visual inspection showed a uniform disturbance over the surface of the core, and this rather rough method was sensitive enough to detect when some of the orifices became blocked on one occasion. 3. MEASUREMENT OF MATERIAL BUCKLING Indium foils 0,125 mm thick and 10 mm dia. were used to find the flux distribution in the sub-critical facility by measuring the induced /?-activity resulting from neutron capture in Inli5. The foils were supported on perspex rods and the flux distributions were measured many times along the three principal axes of the core for a range of void fractions. Foil activities were corrected for internal and external flux depression (BOTHE, 1943) (TITTLE, 1951). Half life corrections were made by comparison of activities with a further indium foil irradiated at the same time. Measured flux distributions were fitted by least squares techniques to the following forms :$(X) = A1 eXp (-KX) (30,~) d(z) = A, cos (wpz) + B3 cos (3~s~).
db)
=
4
~0s
(w)
+
B,
~0s
In order to eliminate source and leakage effects the exponential flux form was fitted to measurements taken at points greater than 200 mm from the edges of the active core. Also since the reflector tends to give a rise in neutron flux at the edge of the core no measurements were made closer than 48.3 mm (one lattice pitch) to the core/reflector boundary. For the vertical flux distribution the origin of the fitted curve was also adjusted to improve the fit since there was partial neutron reflection from the concrete pedestal. All measurements were made with bare foils since it had been found by experiment that the epicadmium activation was low and had the same form as the thermal activation. Material buckling was calculated from Bm2 = 0.112+ wz2 -
K’.
Examples of the measured fluxes with the fitted curves superimposed, measured at 9-l per cent void fraction, are given in Figs. I,2 and 3. These are typical of all the measurements. 4. EXPERIMENTAL RESULTS Since the initial water to uranium volume ratio was about l-5 times the value giving maximum infinite multiplication factor a significant change in the material buckling with void fraction was expected. The measured bucklings and void fractions are given in Tables 1 and 2. Table 1 gives the complete set of results at 9.1 per cent void fraction and Table 2 summarises the complete range of measurements. The quoted
Measurement horizontal
distribution
I-
active
L 011 -30
of material buckling
589
9.1% voids core
I
-20 distance
-10 0 10 20 30 from core centre cm
FIG. 1 .-Horizontal
vertical
distribution
distributioh
<
9.1 per cent voids.
9.1%
active
voids
1 >
core
1.0 -
2 zO.SSO.6
-
=0.4
-
-20.2. E -040 .J -30
-20
-10
distance
from
FIG. 2.-Vertical
axial
0
10
core centre
distribution
distribution
FIG. 3.-Axial
I 30 cm
9.1 per cent voids.
9.1% voids
---active
distance
20
core -
from
core
distribution
centre
cm
91 per cent voids.
40
L. T.-DANSO and P. N. COOPER
590
TABLE1 Bucklingcomponents m-=
Measuredvalues for 9.1% void fraction
Mean Standard error on mean
Q
WZ
KS
12.1 11.8 12.1 11.0 Il.0 11.4
11.3 IO.4 IO.7 9.0 11.6 11.1
43.4 45.1 45.6 43.9
11.6 @2
10.7 0.4
44.5 05
TABLE 2 Void fraction (%) 0 2.5 f 0.5 6.1 f 0.5 9.1 f 0.5
55.8 f 54.3 f 48.7 f 44.5 f
0.4 I.4 0.6 0.5
15.0 f 13.0 * 13.2 + 11.6 rt
0.7 0.5 0.5 0.2
11.1 f 12.0 f 11.0 * 10.7 *
0.2 0.4 0.2 0.4
-29.7 -29.3 -24.6 -22.1
i 0.9 i 1.6 & 0.8 f 0.7
errors in Table 2 are calculated from the spread in individual measurements and are quoted as the standard error on the mean. 5. CALCULATION OF MATERIAL BUCKLING Standard calculation methods, in which voids were included simply by reducing the moderator density, were found to give an adequate representation of the experimental results. A three group diffusion theory approach was adopted. Inter-group boundaries were selected at 180 keV and 0.625 eV. For the fission and slowing down groups the core was regarded as homogeneous and cross-sections obtained from three-group data given by DEUTSCH(1957), were adopted, except for the effective cross-section for Uz3s, which was found from the, effective resonance integral tabulated as a function of surface to mass ratio (ARGONNE, 1963). Geometric shadowing by neighbouring rods was included by use of the Dancoff and Ginsburg correction factor (DANCOFF, 1944). Fast fission was included by means of a fast fission factor taken from tabulations in ANL 5800 (ARGONNE, 1963). The thermal neutron spectrum was assumed to have a Wigner-Wilkins form and cross-sections were taken from the tabulation by Amster (AMZXER,1958). Average fluxes in the fuel and moderator were calculated by the method of Amouyal, Benoist and Horowitz (AMOUYAL,1956). The most sensitive factors in the calculation were found to be the effective crosssection of U238in the resonance region and the thermal neutron flux fine structure. Table (3) summarises the main conclusions from the calculations and Fig. 4 compares the measurements and the calculations. The experimental points have buckling values about 2 rnM2lower than the calculated values, but show the same rate of change over the whole range measured. This indicates that the calculation model used is sufficiently detailed to represent the measured behavior of the system.
Measurement of material buckling void fraction
591
%
-Is/I
FIG.
4.-Experimental
and theoretical buckling as a function of void fraction. TABLE 3
Void fraction (%)
km
MP (cm”)
BZ (m-3
0
0.890 39.5 -28.6
5
10
0.899 42.6 -24.5
0.910 46.1 -202
The possible effect of asymmetric streaming along the direction of the fuel rods was not included in the calculation model. Agreement with measurements over the void fraction range O-9 per cent justifies this simplification, but for very high values of void fraction the streaming effect will probably become important. 6. CONCLUSIONS The effect of voids in a moderator may be studied by bubbling low pressure com-
pressed air through a core. Such voids would be similar to bulk boiling in a water moderated reactor, but would not simulate the effects of film boiling. A sub-critical core has been shown to be adequate for measurement purposes, and simple foil activation techniques can be made to yield the material buckling. Standard and relatively simple calculation methods have given good agreement with experiment. The presence of voids can be represented adequately for calculation purposes by a reduction in moderator density. An increase in void fraction is similar to a reduction in the water to uranium volume ratio and the results compare reasonably with measurements made on unvoided systems by other workers, notably KOUTS (1955). REFERENCES
A., BENOISTP. and HOROWITZJ. (1956) J. nucl. Energy, 6,19. H. J. (1958) USAEC rep. WAPD-185. ARGONNENAnoNAL LABORATORY(1963) Reactor Physics Constants, USAEC rep. ANL-5800,2nd. edn. AMOUVAL AMSTER
BOTHE, W. (1943) Z. Phys. 120,437. DANCOFF S. M. and GINSBERGM. (1944) USAEC rep. CP-2157. DEUTSCHR. W. (1957) Nucleonics 15, (l), 47. DOWN H. J., DICKIE J. and Fox W. N. (1963) UKAEA rep. AEEW-M 314. KLEIJN H. R. (1966) Proc. Koninklijke Nederlandse Academic van Wetenschappen ser. B, 69. KOUTS H. (1955) Proc. 1st Geneva Conference on the Peaceful Uses of Atomic Energy 5,183. PERKINSH. C., YUSUP M. and LEPPERT G. (1961) Nucl. Sci. Engng 11,304. TITLE C. W. (1951) Nucleonics 8, (6), 5 and 9, (l), 60.