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The determination of reactor kinetic parameters in a two-core reactor
Ann. nucl. Energy, Vol. 9, pp. 683 to 687, 1982 Printed in Great Britain
0306-4549/82/110683-05503.00/0 PergamonPressLtd
T E C H N I C A L NOTE THE DETERMINATION
OF R E A C T O R K I N E T I C P A R A M E T E R S
IN A T W O - C O R E R E A C T O R F u Y u ZHENG* a n d W . K. MANSFIELD Nuclear Engineering Department, Queen Mary College, University of London, Mile End Road, London E1 4NS, U.K. (Received 24 M a y 1982)
Abstract--The kinetic parameters, ct the coupling coefficient and f the mean neutron transit time have been determined using a reactor oscillator on the coupled-core of the Queen Mary College research reactor. By using correlation techniques it has proved possible to use detectors small enough to be inserted in the fuel tanks. It is shown that the simplified Baldwin model with one-group diffusion theory is inadequate to describe the kinetic behaviour and the experimentally-determined parameters are dependent upon the positioning of the detectors.
INTRODUCTION Yamane et al. (1980) have reported the experimental determination of the three kinetic parameters ; ~, the reactor coupling coefficient, {, the mean neutron transit time and A, the neutron generation time for a coupled-core reactor. Their analysis is based on the one-group, multiregion theoretical model of Shinkawa et al. (1978). Jeffers (1970) has given a twogroup analysis for an Argonaut type reactor which demonstrates the importance of fast-neutron coupling and throws doubt on the applicability of using only three parameters to describe the coupling. To investigate this effect experiments have been performed using a reactor oscillator perturbing one core and a pair of small thermal-neutron detectors (BF3) which can be located either one in each core or symmetrically disposed in the central reflector. To improve the signal-noise correlation techniques have been used. EXPERIMENTAL MEASUREMENT The Queen Mary College reactor (Shaw, 1972) is a typical Argonaut research reactor having two rectangular fuel tanks, separated by 18" (45.72 cm) of graphite and enclosed in a graphite reflector, see Fig. 1. The reactor oscillator shown in Fig. 2 consists essentially of three sinusoidally-shaped cadmium rotor plates and twelve cadmium stator plates (Vittes, 1977). As a consequence a single rotation of the rotor produces four sinusoidal variations in the area of cadmium exposed to the thermal-neutron flux. The reactivity variation introduced by the oscillator has been determined to be A + B cos wt, where A = 1.367 x 10- 3, B = 1.242 x 10-4 (Ak/k). The oscillator was driven by a d.c. servo motor ( M O T O M A T I C E-
*Present address: Engineering Physics Department, Tsinghua University, Peking, China. 683
650M) and a hysteresis motor (HM16/2) was also driven by suitable gearing to produce a cosinusoidal signal representing this reactivity variation, care being taken to ensure a correct phase relationship. The frequency of the reactivity variation was adjustable in the range 1-200 Hz and was monitored. The reactor oscillator was positioned centrally on the exterior face of the East fuel tank (Core 1) near the mid-core height, see Fig. 2. Two types of thermal-neutron BF 3 detectors were used, the 12EB70/25G and the 5EB40/13, their sensitivities, as proportional counters, are 5.1 and 0.32 cps 1 n V - , respectively. Both types were used in the 'current' mode with E H T voltages of 350 V. The voltage supply was from batteries to minimize 50 Hz main frequency interference. Only the small 5EB40/13 could be inserted in the fuel tanks and it was positioned at the same height as the oscillator. O n e measurement (No. 1) was made with the detectors just inside a central fuel element in each fuel tank, position D 3 and D4 in Fig. 1, the other measurement (No. 2) was taken with the larger detectors placed symmetrically inside the central graphite reflector, position D~ and D z in Fig. 1. The analogue signals proportional to the thermal flux oscillations, An~ and An2, from the pair of detectors, after suitable amplification were recorded on two channels of a multichannel magnetic tape-recorder (AMPEX 1300 F M RECORDER). Simultaneously the output of the hysteresis motor after amplification was also recorded on another channel. O n play back the auto- and cross-correlation of these signals could be evaluated using a computer system. Since the interesting parts of these signals are cosinusoidal the correlation signals are also cosinusoidal and a curve-fitting programme gives an accurate evaluation of signal amplitude and phase, see Figs 3, 4 and 5. The cross-correlation improves the signal-noise ratio by reducing the noise in proportion to the square root of the effective number of data points (Thie, 1963). Both experiments were carried out at a reactor power of 5 W. The fuel loading of both cores were symmetrical.
684
Technical Note N
I Core2
CoreI i
Controlrod
18 tt
Graphitereflector
I
East
West
°D~ o
D2
Dj
Tank Neutron
source(~ Water
outlet
line
l Fig. 1. Plan view of reactor core.
DISCUSSION OF RESULTS Adopting the Baldwin formulation (Baldwin, 1957) employed by Jeffers and Humphreys (1969) for a small sinusoidal reactivity oscillation 5k e/wt applied to Core 1, and affecting only Core 1.
Oscilator --.~ East tank
Pl = - c t + b k ¢jwl
d.c. motor ~
P2 =
motor
--~
n I = / ~ 0 - ~ - ~ 1 e jwt n2 = n o + ~ n 2
¢jwt,
where Pl and P2 are the reactivities of the perturbed and unperturbed core, respectively, nt and n 2 are the thermal neutron densities, and a is the coupling coefficient. Substitution in the.Baldwin kinetic equations yields two important equations for the neutron fluctuations An1 and An 2 :
I
Ani 2
q~ = arc tan Fig. 2. Sketch of oscillator.
A 2
+ w~,
(2)
Technical Note
-IO
_x
-
-
~
.
~
No. 2 (mEBTO/ZSG) ~X-~
-20
x~
-I0
x~
x.....,.,x
No.I ( 5 E B 4 0 / 1 5 ) ~x~.x~
X
~"~K"
~
-4o
x
-20
~.x.×.Xx
-3o
.~
685
X-xx ~XxxxD3
-50
× Di
140
D2
-50
-5 0
-60
I
I
I
I I Jill
iOo
I
I
I ~ I IIII
101
I
I 102
Frequency,
I
I
I [ [Ill
IO0
I
I
i01
HZ
I IIIII 102
Frequency,
Hz
Fig. 3. Gain vs frequency in measurement No. 2.
Fig. 4. Gain vs frequency in measurement No. 1.
where 4) is the phase difference between An I and An2, z is the neutron transit time, A is the neutron generation time and/3 is the effective delayed-neutron fraction. The transfer functions are given as follows :
I f / = I 0 cos wt is the input signal from the oscillator, when the correlation measurements were performed at the same amplification, the ratio of the cross- and auto-correlation should be independent of the properties of the correlator. Therefore, one can obtain
/3 An1
Gl(jw) -
(3)
no, 6k
Io
/3 An~
G2(jw) -
C,,(0) = - 2
(4)
no2 6k
Hence 6k
IGllno/Sk cos(wt+ 01)
(5)
6k An z = IG2(jw)l no2 ~ cos(wt + 02).
(6)
An 1 = IGl(jw)l no1 ~
(7)
Can,lma x -
- -
2/3
IG21no2t~k C&n21ma x
-30 ' -40 -50
~
'
"
~X ~ X.~ X...._ " X~ X~X
X
-60
X~
-70
~ ' X X x x •x\
D3
~Xx
~
-80
-90 -IO0 -IlO -120 O.
• I
-1:30 -140 -t50 ll601 -- 170 --180 -- 190 -200
l IO o
l
l
l l llll
l
l
l
l II
i01
Ill 10 2
Frequency,
Hz
Fig. 5. Phase with respect to oscillator vs frequency.
I
l
(8)
(9)
686
Technical Note
Then
,201
Ca,,Imax IGII nolg)k R1 = Cn(0) io]~
(10)
R2 = Can2lmax __ IG~I nolJk Cll(0) I0~
(11)
I00
90 ,~ 8o 70
"e" 6o
Hence
50 40 30
(12)
2O 10
(~ = 0 2 - - 0 1 .
(13)
Figure 6 shows that the linear relationship between the square of the ratio of the amplitude and the square of the frequency for the two measurements (equation (1)) holds for frequencies up to about 100 Hz for both measurements. Figure 7 shows the variation of the phase difference with the frequency (equation (2)). Using equations (1) and (2), the kinetic parameters can be obtained. For measurement No. 1, ct///= 3.07 $, A = 156 #s a n d f = (6.28 _+ 1.57) × 10 - a s a n d for measurement No.2,ct//~ = 3.80 $, A = 106/~s and f = (8.0+3.1) × 10 -5 s. If Yamane et al.'s (1980) kinetic equations are used, two
10o
i0 ~
i0 z
Frequency,
Fig. 7. The phase difference between the two detectors vs the frequency.
equations for ~ and z can be obtained = Re{2- l[q(jw) - ~(jw)]}
(14)
= -[we<] -1 I m { 2 - 1 [ n ( j w ) - ~ ( j w ) ] } ,
(15)
150
120 I10
I00
90
N
80
70
o
o
6O
50 40
,o
2O I0
~x~X~X ~x~ I 1.0
Hz
I 2.0 ( Frequencyl z
[ 3.0 ,
X I0 4
i. 4.0
(Hz) 2
Fig. 6. The square of the ratio of the amplitude vs the square of the frequency.
Technical Note
687
where tl(jw) = [ G l (jw ) _ G 2(jw)]-1
(16)
~(jw) =- [Gl(jw) + G2(jw)] - i
(17)
The values ofct derived from equation (14) were 4.50 and 6.05 $ for measurements Nos 1 and 2, respectively. Figures 8 and 9 show that values ofz cannot be determined unambiguously. For measurement No. 2 z appears to be negative! Whilst for measurement No. 1 negative values of z are obtained f o r f < 3 Hz. Above 100 Hz the mean value is approx. (6.77+ 1.37)x 10 4 s. Re-analysing Yamane et al.'s experimental results showed that for f < 40 Hz negative r's could also be obtained. A possible explanation of this effect has been suggested by Jeffers using his two-group diffusion theory (Jeffers, 1970). He shows that the 'fast' neutrons become increasingly important to the coupling between the cores at high frequencies. This is because of the greater attenuation of the thermal-neutron flux oscillation and the spectrum hardening as one moves away from the oscillator, especially for the higher frequencies (see Figs 2 and 3 in Jeffers, 1970). Jeffers suggests that the rapid decrease in the phase lag of the thermal-neutron oscillation near Core 2 at high frequencies leads to negative values of r if measurements are taken in the central reflector. Jeffers' theoretical computation shows that the values ofct as well as T obtained are dependent upon where the detectors are placed (see Figs 9 and 10 in Jeffers, 1970). From these experimental results, it has been found that the value of a in measurement No. 2 is larger than that in measurement No. 1. Whereas the value of f i n measurement No. 2 is much smaller than in No. 1. This bears out the predictions of Jeffers' calculation. In contrast Zikides (1973) has used the 'noise' technique on the same reactor with detectors in positions DI and D2 and also on the exterior faces of the fuel tanks. He finds that the values o f ? are 5.60 x 10 -4 and 5.49 x 10 -4 s, respectively. In the 'noise' technique the perturbations are stochastic and are uniformly distributed over the cores. As a consequence the asymmetrical effects of thermal-neutron attenuation and spectrum hardening do not arise except as second-order effects.
p'~.
/ ./. . . . .
<~.~. ~ . . ~ ...o..o.,,.,.,=,:,--
/ -o
A/
/:
No. 2
-7o9 / / )~
10 -3
_AN \.
6.28x
-
I0 -4
10-4
No.
10-5 i0 0
i0 F
Frequency,
i0 2
Hz
Fig. 9. Neutron transit time vs frequency using Jeffers and Humphreys' (1969) analysis. CONCLUSIONS The experimental results obtained are consistent with the predictions made by Jeffers that at higher frequencies (above 100 Hz) fast-neutron coupling is indeed significant and a single mean neutron transit time is inappropriate when used in conjunction with the Baldwin model. As a consequence differing values of the reactor coupling coefficient and the neutron transit time are obtained according to the positioning of the detectors when the core is perturbed asymmetrically. Likewise 'negative' transit times can be obtained if the detectors are located inside the central reflector. For frequencies below 100 Hz the linearity of Fig. 6 suggests that only thermal-neutron effects are significant and the phenomenon may be described by the Baldwin model.
' ~ .,,....
~/
'_0
-\
Acknowledgements--The authors wish to thank Drs J. Shaw and A. D. Ross, Mr W. K. To and the staffof the Queen Mary College research reactor for their help with these experiments.
No. I
/
!°x: jNo
] FOt
J 102 Frequency,
I 2xlO z
Hz
Fig. 8. Neutron transit time vs frequency using Yamane et al.'s (1980) analysis.
REFERENCES
Baldwin G. C. (1957) Nucl. Sci. Engng 6, 320. Jeffers D. E. (1970) Atomkerneneryie 16, 23; 129. Jeffers D. E. and Humphreys E. (1969) Nucleonik 12, 284. Shaw J. (1972) General Specification of the Queen Mary College Research Reactor. Operating Report No. 1/5, 5th edn, London. Shinkawa M. et al. (1978) Nucl. Sci. Engng 67, 19. Thie J. A. (1963) Reactor Noise. Rowman & Littlefield, New York. Vittes P. (1977) Master Thesis, Department of Nuclear Engineering, Queen Mary College, University of London. Yamane Y. et al. (1980) Nucl. Sci. Engng 76, 232. Zikides C. (1973) Ph.D. Thesis, Department of Nuclear Engineering, Queen Mary College, University of London.
0306-4549/82/110683-05503.00/0 PergamonPressLtd
T E C H N I C A L NOTE THE DETERMINATION
OF R E A C T O R K I N E T I C P A R A M E T E R S
IN A T W O - C O R E R E A C T O R F u Y u ZHENG* a n d W . K. MANSFIELD Nuclear Engineering Department, Queen Mary College, University of London, Mile End Road, London E1 4NS, U.K. (Received 24 M a y 1982)
Abstract--The kinetic parameters, ct the coupling coefficient and f the mean neutron transit time have been determined using a reactor oscillator on the coupled-core of the Queen Mary College research reactor. By using correlation techniques it has proved possible to use detectors small enough to be inserted in the fuel tanks. It is shown that the simplified Baldwin model with one-group diffusion theory is inadequate to describe the kinetic behaviour and the experimentally-determined parameters are dependent upon the positioning of the detectors.
INTRODUCTION Yamane et al. (1980) have reported the experimental determination of the three kinetic parameters ; ~, the reactor coupling coefficient, {, the mean neutron transit time and A, the neutron generation time for a coupled-core reactor. Their analysis is based on the one-group, multiregion theoretical model of Shinkawa et al. (1978). Jeffers (1970) has given a twogroup analysis for an Argonaut type reactor which demonstrates the importance of fast-neutron coupling and throws doubt on the applicability of using only three parameters to describe the coupling. To investigate this effect experiments have been performed using a reactor oscillator perturbing one core and a pair of small thermal-neutron detectors (BF3) which can be located either one in each core or symmetrically disposed in the central reflector. To improve the signal-noise correlation techniques have been used. EXPERIMENTAL MEASUREMENT The Queen Mary College reactor (Shaw, 1972) is a typical Argonaut research reactor having two rectangular fuel tanks, separated by 18" (45.72 cm) of graphite and enclosed in a graphite reflector, see Fig. 1. The reactor oscillator shown in Fig. 2 consists essentially of three sinusoidally-shaped cadmium rotor plates and twelve cadmium stator plates (Vittes, 1977). As a consequence a single rotation of the rotor produces four sinusoidal variations in the area of cadmium exposed to the thermal-neutron flux. The reactivity variation introduced by the oscillator has been determined to be A + B cos wt, where A = 1.367 x 10- 3, B = 1.242 x 10-4 (Ak/k). The oscillator was driven by a d.c. servo motor ( M O T O M A T I C E-
*Present address: Engineering Physics Department, Tsinghua University, Peking, China. 683
650M) and a hysteresis motor (HM16/2) was also driven by suitable gearing to produce a cosinusoidal signal representing this reactivity variation, care being taken to ensure a correct phase relationship. The frequency of the reactivity variation was adjustable in the range 1-200 Hz and was monitored. The reactor oscillator was positioned centrally on the exterior face of the East fuel tank (Core 1) near the mid-core height, see Fig. 2. Two types of thermal-neutron BF 3 detectors were used, the 12EB70/25G and the 5EB40/13, their sensitivities, as proportional counters, are 5.1 and 0.32 cps 1 n V - , respectively. Both types were used in the 'current' mode with E H T voltages of 350 V. The voltage supply was from batteries to minimize 50 Hz main frequency interference. Only the small 5EB40/13 could be inserted in the fuel tanks and it was positioned at the same height as the oscillator. O n e measurement (No. 1) was made with the detectors just inside a central fuel element in each fuel tank, position D 3 and D4 in Fig. 1, the other measurement (No. 2) was taken with the larger detectors placed symmetrically inside the central graphite reflector, position D~ and D z in Fig. 1. The analogue signals proportional to the thermal flux oscillations, An~ and An2, from the pair of detectors, after suitable amplification were recorded on two channels of a multichannel magnetic tape-recorder (AMPEX 1300 F M RECORDER). Simultaneously the output of the hysteresis motor after amplification was also recorded on another channel. O n play back the auto- and cross-correlation of these signals could be evaluated using a computer system. Since the interesting parts of these signals are cosinusoidal the correlation signals are also cosinusoidal and a curve-fitting programme gives an accurate evaluation of signal amplitude and phase, see Figs 3, 4 and 5. The cross-correlation improves the signal-noise ratio by reducing the noise in proportion to the square root of the effective number of data points (Thie, 1963). Both experiments were carried out at a reactor power of 5 W. The fuel loading of both cores were symmetrical.
684
Technical Note N
I Core2
CoreI i
Controlrod
18 tt
Graphitereflector
I
East
West
°D~ o
D2
Dj
Tank Neutron
source(~ Water
outlet
line
l Fig. 1. Plan view of reactor core.
DISCUSSION OF RESULTS Adopting the Baldwin formulation (Baldwin, 1957) employed by Jeffers and Humphreys (1969) for a small sinusoidal reactivity oscillation 5k e/wt applied to Core 1, and affecting only Core 1.
Oscilator --.~ East tank
Pl = - c t + b k ¢jwl
d.c. motor ~
P2 =
motor
--~
n I = / ~ 0 - ~ - ~ 1 e jwt n2 = n o + ~ n 2
¢jwt,
where Pl and P2 are the reactivities of the perturbed and unperturbed core, respectively, nt and n 2 are the thermal neutron densities, and a is the coupling coefficient. Substitution in the.Baldwin kinetic equations yields two important equations for the neutron fluctuations An1 and An 2 :
I
Ani 2
q~ = arc tan Fig. 2. Sketch of oscillator.
A 2
+ w~,
(2)
Technical Note
-IO
_x
-
-
~
.
~
No. 2 (mEBTO/ZSG) ~X-~
-20
x~
-I0
x~
x.....,.,x
No.I ( 5 E B 4 0 / 1 5 ) ~x~.x~
X
~"~K"
~
-4o
x
-20
~.x.×.Xx
-3o
.~
685
X-xx ~XxxxD3
-50
× Di
140
D2
-50
-5 0
-60
I
I
I
I I Jill
iOo
I
I
I ~ I IIII
101
I
I 102
Frequency,
I
I
I [ [Ill
IO0
I
I
i01
HZ
I IIIII 102
Frequency,
Hz
Fig. 3. Gain vs frequency in measurement No. 2.
Fig. 4. Gain vs frequency in measurement No. 1.
where 4) is the phase difference between An I and An2, z is the neutron transit time, A is the neutron generation time and/3 is the effective delayed-neutron fraction. The transfer functions are given as follows :
I f / = I 0 cos wt is the input signal from the oscillator, when the correlation measurements were performed at the same amplification, the ratio of the cross- and auto-correlation should be independent of the properties of the correlator. Therefore, one can obtain
/3 An1
Gl(jw) -
(3)
no, 6k
Io
/3 An~
G2(jw) -
C,,(0) = - 2
(4)
no2 6k
Hence 6k
IGllno/Sk cos(wt+ 01)
(5)
6k An z = IG2(jw)l no2 ~ cos(wt + 02).
(6)
An 1 = IGl(jw)l no1 ~
(7)
Can,lma x -
- -
2/3
IG21no2t~k C&n21ma x
-30 ' -40 -50
~
'
"
~X ~ X.~ X...._ " X~ X~X
X
-60
X~
-70
~ ' X X x x •x\
D3
~Xx
~
-80
-90 -IO0 -IlO -120 O.
• I
-1:30 -140 -t50 ll601 -- 170 --180 -- 190 -200
l IO o
l
l
l l llll
l
l
l
l II
i01
Ill 10 2
Frequency,
Hz
Fig. 5. Phase with respect to oscillator vs frequency.
I
l
(8)
(9)
686
Technical Note
Then
,201
Ca,,Imax IGII nolg)k R1 = Cn(0) io]~
(10)
R2 = Can2lmax __ IG~I nolJk Cll(0) I0~
(11)
I00
90 ,~ 8o 70
"e" 6o
Hence
50 40 30
(12)
2O 10
(~ = 0 2 - - 0 1 .
(13)
Figure 6 shows that the linear relationship between the square of the ratio of the amplitude and the square of the frequency for the two measurements (equation (1)) holds for frequencies up to about 100 Hz for both measurements. Figure 7 shows the variation of the phase difference with the frequency (equation (2)). Using equations (1) and (2), the kinetic parameters can be obtained. For measurement No. 1, ct///= 3.07 $, A = 156 #s a n d f = (6.28 _+ 1.57) × 10 - a s a n d for measurement No.2,ct//~ = 3.80 $, A = 106/~s and f = (8.0+3.1) × 10 -5 s. If Yamane et al.'s (1980) kinetic equations are used, two
10o
i0 ~
i0 z
Frequency,
Fig. 7. The phase difference between the two detectors vs the frequency.
equations for ~ and z can be obtained = Re{2- l[q(jw) - ~(jw)]}
(14)
= -[we<] -1 I m { 2 - 1 [ n ( j w ) - ~ ( j w ) ] } ,
(15)
150
120 I10
I00
90
N
80
70
o
o
6O
50 40
,o
2O I0
~x~X~X ~x~ I 1.0
Hz
I 2.0 ( Frequencyl z
[ 3.0 ,
X I0 4
i. 4.0
(Hz) 2
Fig. 6. The square of the ratio of the amplitude vs the square of the frequency.
Technical Note
687
where tl(jw) = [ G l (jw ) _ G 2(jw)]-1
(16)
~(jw) =- [Gl(jw) + G2(jw)] - i
(17)
The values ofct derived from equation (14) were 4.50 and 6.05 $ for measurements Nos 1 and 2, respectively. Figures 8 and 9 show that values ofz cannot be determined unambiguously. For measurement No. 2 z appears to be negative! Whilst for measurement No. 1 negative values of z are obtained f o r f < 3 Hz. Above 100 Hz the mean value is approx. (6.77+ 1.37)x 10 4 s. Re-analysing Yamane et al.'s experimental results showed that for f < 40 Hz negative r's could also be obtained. A possible explanation of this effect has been suggested by Jeffers using his two-group diffusion theory (Jeffers, 1970). He shows that the 'fast' neutrons become increasingly important to the coupling between the cores at high frequencies. This is because of the greater attenuation of the thermal-neutron flux oscillation and the spectrum hardening as one moves away from the oscillator, especially for the higher frequencies (see Figs 2 and 3 in Jeffers, 1970). Jeffers suggests that the rapid decrease in the phase lag of the thermal-neutron oscillation near Core 2 at high frequencies leads to negative values of r if measurements are taken in the central reflector. Jeffers' theoretical computation shows that the values ofct as well as T obtained are dependent upon where the detectors are placed (see Figs 9 and 10 in Jeffers, 1970). From these experimental results, it has been found that the value of a in measurement No. 2 is larger than that in measurement No. 1. Whereas the value of f i n measurement No. 2 is much smaller than in No. 1. This bears out the predictions of Jeffers' calculation. In contrast Zikides (1973) has used the 'noise' technique on the same reactor with detectors in positions DI and D2 and also on the exterior faces of the fuel tanks. He finds that the values o f ? are 5.60 x 10 -4 and 5.49 x 10 -4 s, respectively. In the 'noise' technique the perturbations are stochastic and are uniformly distributed over the cores. As a consequence the asymmetrical effects of thermal-neutron attenuation and spectrum hardening do not arise except as second-order effects.
p'~.
/ ./. . . . .
<~.~. ~ . . ~ ...o..o.,,.,.,=,:,--
/ -o
A/
/:
No. 2
-7o9 / / )~
10 -3
_AN \.
6.28x
-
I0 -4
10-4
No.
10-5 i0 0
i0 F
Frequency,
i0 2
Hz
Fig. 9. Neutron transit time vs frequency using Jeffers and Humphreys' (1969) analysis. CONCLUSIONS The experimental results obtained are consistent with the predictions made by Jeffers that at higher frequencies (above 100 Hz) fast-neutron coupling is indeed significant and a single mean neutron transit time is inappropriate when used in conjunction with the Baldwin model. As a consequence differing values of the reactor coupling coefficient and the neutron transit time are obtained according to the positioning of the detectors when the core is perturbed asymmetrically. Likewise 'negative' transit times can be obtained if the detectors are located inside the central reflector. For frequencies below 100 Hz the linearity of Fig. 6 suggests that only thermal-neutron effects are significant and the phenomenon may be described by the Baldwin model.
' ~ .,,....
~/
'_0
-\
Acknowledgements--The authors wish to thank Drs J. Shaw and A. D. Ross, Mr W. K. To and the staffof the Queen Mary College research reactor for their help with these experiments.
No. I
/
!°x: jNo
] FOt
J 102 Frequency,
I 2xlO z
Hz
Fig. 8. Neutron transit time vs frequency using Yamane et al.'s (1980) analysis.
REFERENCES
Baldwin G. C. (1957) Nucl. Sci. Engng 6, 320. Jeffers D. E. (1970) Atomkerneneryie 16, 23; 129. Jeffers D. E. and Humphreys E. (1969) Nucleonik 12, 284. Shaw J. (1972) General Specification of the Queen Mary College Research Reactor. Operating Report No. 1/5, 5th edn, London. Shinkawa M. et al. (1978) Nucl. Sci. Engng 67, 19. Thie J. A. (1963) Reactor Noise. Rowman & Littlefield, New York. Vittes P. (1977) Master Thesis, Department of Nuclear Engineering, Queen Mary College, University of London. Yamane Y. et al. (1980) Nucl. Sci. Engng 76, 232. Zikides C. (1973) Ph.D. Thesis, Department of Nuclear Engineering, Queen Mary College, University of London.