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On the physical meaning of the fluid velocity measured in BWRs by noise analysis
Ann. nucl. Energy, Vol. 10, No. 5, pp. 233-241, 1983 Printed in Great Britain
0306-4549/83/050233-09503.00/0 Pergamon Press Ltd
O N THE P H Y S I C A L M E A N I N G OF THE F L U I D V E L O C I T Y M E A S U R E D IN BWRs BY NOISE A N A L Y S I S D. Lf,JBBESMEYER
Swiss Federal Institute for Reactor Research, 5303 Wfirenlingen, Switzerland (Received 6 September 1982; accepted in revised form 18 October 1982) Abstract--This paper is dealing with the question of the physical nature of the fluid velocity measured by analysing the noise signals of incore neutron chambers in an operating BWR. It is postulated by phenomenological arguments and proved by measurements that the measured velocity is usually the volumetric fluxj. The advantage of this finding is the fact that it now becomes very easy to determine the mass flux because in addition, only the steam quality x is needed and this can be computed with the enthalpy balance using the axial neutron-flux distribution which can be easily measured. Because in a BWR the instrument tube with the neutron chambers is surrounded by four bundles which may not have equal power distributions and/or may have different mass-flows (and hence, different two-phase flow patterns), the influence of the four bundles on the result of the fluid-velocity measurements may differ with respect to the axial position where the measurement is performed. This means that it is plausible that while in one axial position the volumetric flux in one bundle is measured, in another axial position, the fluid velocity in another bundle is dominant. NOMENCLATURE A d G Gi fs ip j v v~ vs Vw,tcr Vair V x p' p"
Cross-sectional area Detector distance Mass-flow Pseudo-mass-flow of the individual bundle i (equation (6)) Sample frequency Peak index of cross-correlation function Volumetric flux [=(l-C0Vl+~Vs] Measured velocity Velocity of the liquid Velocity of the gas (steam) Volume-flow,. water Volume-flow, air Volume Quality Void fraction Saturation density of liquid Saturation density of steam
INTRODUCTION
When presenting results of fluid-velocity measurements of two-phase flow in BWR bundles by means of cross-correlating the signals of two incore neutron chambers, the following question often arises : "What kind of velocity of the two-phase flow do we really measure?" The right answer to this question is of great interest, especially if the measurements are to be used for code verifications. An answer to this question was given independently by Seifritz and Cioli (1973) and Wach
(1973). They both assumed that the measured fluid velocity was the velocity of the steam (vs). This has also been assumed by many other authors who have presented fluid-velocity measurements in operating BWRs in the past. It is to the credit of Kos/dy and Fahley (1982) that the investigation of the problem was restarted, even if their proposed explanation seems to us to be misleading. Their explanation for the measured velocity is based on the concept of Kinematic Waves first proposed by Lighthill and Whitham (1955) to describe flood movement in long rivers and applied to the problems of two-phase flows by Kanai et al. (1961) and later by Zuber and Staub (1967) who tried to define a propagation velocity of changes of the void fraction. In contrast to Zuber and Staub who derived their relation for the case of the propagation of changes of the void fraction (which is a Macroscopic effect), Koshly and Fahley use the same equation to describe the transport of the density fluctuations due to the heterogeneity of a real two-phase flow (which is a microscopic effect). This concept seems to be questionable because the basic equations (continuity equations) are based on the assumption of a homogenized two-phase flow and therefore, the microscopic features of a real two-phase flow are already 'averaged out' and cannot be reintroduced. By resorting to phenomenological considerations, we shall assume that the velocity measured by noise analysis is usually the volumetric flux j. We shall investigate the validity of this assumption by 233
234
D. Lu BBESMEYER
Comparing it to measurements performed in an excore loop and in an operating BWR. The second part of this paper deals with the question of what kind of velocity information we will get from the four individual bundles surrounding the instrument tube, especially if the individual two-phase flows in the four bundles are different due to different mass fluxes and/or axial power distributions which is usually the case in an operating BWR. PHENOMENOLOGICAL CONSIDERATIONS
The technique of measuring the fluid velocity of a two-phase flow by noise analysis is based on the determination of the transport time of fluid-inherent and consistent flow-patterns between two axiallypositioned detectors. Depending on the type of detector (e.g. local probes like thermocouples which only detect the fluctuations on one "flow-line' or X-ray beams of commercial densitometers which detect density fluctuations along the beam crossing the spool-piece diameter) the result is usually only a somehow spaceand time-averaged value. In the case of neutron-noise measurements in BWRs, mainly considered in this paper, the aforementioned fluid-inherent patterns are the microscopic density fluctuations caused by an axially-movingdensity field. The space average of the transit times of these patterns between the two detectors is an average over the four individual radial velocity distributions (velocity profiles) in the four bundles, which surround the instrument tube. Up to now, it has always been assumed that the space average over the velocity profile in the individual bundles is the area average as defined in all I-D two-phase-flow models. On the other hand, by using computer simulation, it was shown by Lfibbesmeyer (1982) that the average velocity measured by the cross-correlation technique usually does not agree with any mathematically-defined average value of the existing velocity profile. Depending on the profile (ratio of maximum to minimum), the deviation between the measured value and the area-averaged value of the profile may reach 10°;~,. The time average is the average over the Macroscopic velocity fluctuations within the measuring time which is for neutron-noise measurements in the order of 5 min to 1 h. A rigorous mathematical description of a microscopic two-phase flow is still lacking because of the extreme complexity of the problem and particularly because of the stochastic nature of the microscopic phase distribution (Ishii, 1980). Therefore, all twophase-flow models, based on the continuity equations for mass, momentum and energy, describe homogen-
ized flows and totally neglect all kind of microscopic information needed for a rigorous mathematical and physical explanation of noise measurements. Consequently, we must look for a velocity which may describe the transport velocity of the microscopic density fluctuations even if it is derived from the basic continuity equations (homogenized formulation). Referring to the usual 1-D (axial) description of twophase flow where all variables are averaged over the cross section (sometimes indicated by ( )) and consequently, the velocity profiles of the two phases and the void-concentration profile are totally neglected, such a velocity appears to be the volumetric flux.j which is defined by : j : (1 --~)vl+~V ~
(1)
(all variables are cross-section averaged). The volumetric flux j can be interpreted as the velocity of the centre of the volume of the mixture (Zuber and Staub, 1967). Such a volume can be thought of as being "marked' by the microscopic fluctuations of the density of the mixture, since some of its parts contain steam and other parts contain liquid. These fluctuations or 'markers' are 'seen' by the detectors (neutron chambers, light sensors etc.) and their transit time between two downstream mounted detectors is measured by cross-correlating their induced signals. So, it seems plausible that the velocity measured in twophase flows by noise-analysismethods is the velocity of these 'volumes' or the volumetric flux). Summarizing, we propose a simple explanation of what kind of velocity of the investigated two-phase flow we measure when cross-correlating two LPRM signals of a BWR. Although this explanation is restricted to flow-regimes similar to bubbly-flows, where one phase is dispersed in the other (each volume of the mixture should content both steam and liquid subvolumes as 'markers'), it may well explain (or approximate) the kind of velocity measured in BWR bundles by neutronnoise analysis. We shall elaborate more on this point in the next section.
EXPERIMENTAL VERIFICATION
In what follows, we want to test our previous assumption experimentally by measurements at the air water two-phase-flow test facility FREDLI-II and also, in a rather'semi-experimental'way, by comparing the measurements performed in a BWR at different radial core positions with the results of the computer code COBRA-EIR, which uses the real axial power distributions in the four surrounding bundles given by the plant processor.
Fluid velocity by noise analysis
235
F R E D L I measurements
FREDLI-II
Let us first focus on the measurements at the air water test facility FREDLI-II described earlier (Liibbesmeyer and Leoni, 1980; Liibbesmeyer, 1981). Here, the signals of two light beams (modulated by the interfaces air/water) were cross-correlated to get the transit time and velocity of the investigated two-phase flow. To establish the 'reference', we have measured the inlet volume-flows of the two individual components (air and water) by two turbine flow-meters and the void fraction in the test section by the 'valve method' (i.e. the test section is closed simultaneously by two valves which allows us to determine the part of the volume of the test section which is filled with air). Because of its compressibility, the volume-flow of the air was corrected by using the pressure difference measured between the location of the turbine and location of the light-beam detectors. Knowing the individual volumeflows and the void fraction in the test section, the two individual velocities of the air and the liquid and also the volumetric flux j of the investigated two-phase flow were computed by : vs -
Fair
(2a)
etA
gwater vt - (1 - ~)A j -
Vair+ Vw.,er A
(2b)
20
+
+
+
15
+
+
.a~z+D _
1.0
/-+
o.g
~
x
f
05
, , ~
+ = V e l o c i t y of g o s
t / X
X g O0
x_ = Velocity of liquid [3-- Volumetric flux j 1 05
I I0
Velocity,
I 15
measured
I 2 0
( m s-t)
Fig. 1. Comparison between fluid velocities, measured by cross-correlation and the flow velocitiesv~,vs and j.
hence, cannot be detected. Therefore, in the annularflow regime, all measured velocities are much lower (half the value) than the ones derived by using equations (2). Comparison of B W R measurements with code results
(2c)
Figure 1 shows the comparison for 34 measuring points at void fractions in the range of 5-80% and velocities between 0.2 and 2 m s- 1.The flow-regime was mainly bubbly-flow (including 3 points of the case of bubbles in a standing water column, v = 0); also, a few cases of slug-flows were investigated. The agreement between the volumetric flux (Fl) measured by the turbine flow-meters and the velocity of the two-phase flow determined by cross-correlating the two light-beam signals is extremely good. The [] symbols are clustered around the solid line which is defined by v. . . . . . . d = Vref...... (equations (2a-c), i.e. it is the 'zero-percent error line'. The liquid-velocity points ( x ) are generally below and the gas-velocity points ( + ) generally above this line. Also, some measurements with annular-flows were performed. Here, the agreement for all three velocities (vs, v~ and j) with the velocity determined by crosscorrelation method was worse, mainly due to a greater proportion of the air-flow passing the light-beam spool-piece in the volume enclosed by the water annulus which causes no fluctuations in the signals and
To determine the axial distribution of the volumetric flux as a reference, first the four cross-section-averaged fluxes have been computed for the four individual bundles surrounding the instrument tube using the axial distributions of the two-phase velocities and the void fraction given by the two-phase-flow code COBRAEra. Because the 'measuring system' gives somehow an average of the four bundles, for simplicity, a 'transittime' average was determined by :
1
1 [jl(Z)
j(z) - 4
1 + jz(z) + j ~
1
1 ] + j~
'
(3)
where jl(z) .... are the volumetric fluxes of the four individual bundles 1 4. Figure 2 shows a comparison of measurements performed in a radial position near the centre ofa BWR core with the correspondingj(z). For this comparison, only points where the detector distance is greater than 30 cm were used to reduce the scattering. The measured points are given as squares and the averaged volumetric flux j(z) is plotted as a solid line. The agreement is reasonable, better in the lower than in the upper part of the core. The lower part of the core is
236
D. LLIBBESMEYER BWR
~2 I
t
Io!
channel (El) are very similar to those of the previous measurement and provide us with a strong indication of the fact that the volumetric flux was measured. On the other hand, for the edge-channel measurement, we get different results ( x ). Here, the computed volumetric flux j(z) is some kind of a fit to the rather peculiar 'distribution' of the measured points. Evaluation or measuring errors (which could explain the 'jump' in the axial velocity distribution) can be excluded because some of the points are determined twice or even more. A more plausible explanation for this behaviour will be given in the next section. Also, for the last two measurements, the axial distribution of the steam velocities cannot explain the axial distribution of the measured velocity points. At this point, we should say a few words about the accuracy of the cross-correlation technique itself. Because the 'cross-correlation spool-piece' is a digital one, i.e. the results are only given as discrete points whereas the velocities are registered either as the next higher or the next lower velocity point, the main error of the measurement is usually due to the resolution Rs of the 'digital spool-piece'. The cross-correlation function has its maximum (peak) in one element (ip) of the function array. The next measurable velocity is then related to the array elements i p - I or ip + 1. From this consideration we can derive the resolution of the spool-piece as (Lfibbesmeyer and Ulber, 1977):
m
/ - / / / / "/ / / D /
E
8
/./f~
6
"0
4
2
s/"
N []
/q~ []
. / ' / ~ /~~ / n ~
~
Radial position near the centre of the core
[]
I
I
[
20
40
60
I
l
80
I00
Core height (%)
Fig. 2. Axial velocity distribution (BWR, radial central-core position). that part where a typical bubbly-flow is d o m i n a n t and for which flow-regime the results of COBRAare known to be more accurate than for other flow-regimes. For comparison, the steam velocity is also given in the figure. It can easily be seen that the assumption of measuring the steam velocity by noise analysis is misleading. Figure 3 shows the results of two other measurements in a similar BWR. Here, the measurements were performed at two different radial core positions, one near the centre and the other near the edge of the core. The results of the measurements in the central
Rs
,o9 Position near the centre of the core L~
,,,.IJ £3~mlS;IDD n // []
/
//E/"/D
6
2
/
_
DD
/
~ l _ _ ~ . ~ ~ s i f i o n EJ,n "
I
for ip > 1,
.,'"~7
;WR
E
1
ip-- 1/ip
I.....-Vs
near the edge of the core
~ 7/.
// /
/
I
I
1
20
40
60
Core
height
I
80
I
I00
(%)
Fig. 3. Axial velocity distribution (BWR, radial central- and edge-core position).
(4)
Fluid velocity by noise analysis where ip =
Ld
.
(4a)
U
This affects only a scattering of the individual measuring points around the 'real' velocity curve and not the trend of a measurement. According to equation (4), the resolution depends on the sample frequency (fs) of the AD conversion, the distance between the detectors (d) and the measured velocity v. For BWR measurements,f~ is usually 128 Hz. Hence, the worst case is the one in which the detectors are closest to each other and the velocity is high (in our case 0.35 m and 6.7 m s - 1 respectively). For this case Rs becomes 15°~o, which is +1 m s I. In most of the measurements, the distance between the detectors was higher ; hence, the resolution for most of the cases is less than 10",,. The FREDLI measurements (light-beam spoolpiece) are much more accurate. With a sample frequency of 1280 Hz and a detector distance of 0.04 m, we obtain for the worst case (v = 2 m s- 1), a resolution of around 4°J~,.
THE I N F L U E N C E OF T H E FLOW-PATTERN IN THE FOUR S U R R O U N D I N G BUNDLES ON THE MEASURED VELOCITY
Determination of the mass-flow The great advantage of the finding that what is measured by noise analysis is the volumetric flux is the fact that it opens the possibility of determining the mass-flow G which is in general the most interesting quantity from the practical point of view. If we make use of the relation G
G
j(z) = x(z~p,, + [1 -x(z)]--, p'
(5)
where x(z) = axial quality distribution, the mass-flow is only a function of the quality and the volumetric flux because the densities in the case of BWR applications can be assumed constant (saturation densities, which are only functions of the system pressure). While usually the main problem of a mass-flow measurement in two-phase flow is the determination of the void fraction a (which can only be evaluated from the steam quality by using empirical correlations), the steam quality itself is a quantity which can easily be evaluated from an enthalpy balance by measuring the axial heat-flux distribution (by measuring the neutronflux distribution). This latter measurement can often be done with relatively high accuracy by the processing system of the power plant.
237
For the two axial velocity distributions of the second set of BWR measurements, the axial quality distributions, as given by the process computer of the power plant, were available. Using these distributions, the 'axial mass-flow distributions' were determined. Negative qualities (subcooled boiling region) have been set equal to zero to avoid any use of empirical correlations as given by subcooled boiling models. The qualities of the four surrounding bundles are linear averages (assuming for simplicity that only the twophase-flow conditions of these four bundles determine the fluid velocity measured by neutron-noise analysis). Above, the mass-flow is given in inverted comas ; this is due to the fact that the mass-flow should be axially constant and any deviation from this would indicate a kind of error. Hence, this is a very sensitive test for the accuracy of the measurement. Figure 4 shows the results of such a 'test'. Let us first look at the central-core position (I-q).For less than 20°:0 core height, the scattering of the points is rather high. This is the subcooled void region where the quality was set equal to zero and consequently, the results are uncertain. For core heights higher than 20~o, the measured points are distributed around the thick solid line which marks the average mass-flow of the four bundles given by the process computer of the plant (the values of the individualbundles are close together). One could say that the points are scattered around a line with a small negative slope; we shall try to give an explanation to this in due course. For the edge-position measurements ( x ) the 'jump' can be seen again. Whereas the agreement with the average mass-flow is now worse(thin solid line), for core heights lower than 50~o, a relatively good agreement is achieved with a mass-flow average (G,d~e.3)formed with similar mass-flows of three of the four bundles. For core heights higher than 50~o, the measured points are nearer to the mass-flow of one of the four bundles (G,d~,.1). The mass-flow of that bundle has only half the value of each of the other three as given by the process computer of the plant. This is an interesting observation because as far as the neutron detector is concerned, it indicates a kind of 'change of the bundle importance' in the four-bundleset surrounding the instrument tube. The two-phase flow in this bundle set is assumed to influence mainly the results of noise-analysis velocity measurements at a certain radial core position of a BWR.
Bundle importance We shall now focus more on the 'bundle importance' and compute the four 'pseudo-mass-flows' of the individualbundles, G1-G4, by combining the measured volumetric-flux distribution with the individual axial
238
D. Lf.]BBESMEYER 25
Edge IX~Sition ~
[]
2O x
XX [] X [] DD~DD
I 5 --
[] 10
Ged~e
X× Gedge, 3 []
[]
Q~
[] D~DD• x
[]
Dx
x x
--
n
D~IOD
I 20
0
centre
DDD x x ~x
X X Gedge , I
Centre position
05
/
×
] 40
I 60
Core
l 80
I lO0
heigh~ (°,/.)
Fig. 4. Mass-flow determined for ditlerent ¢ore heights.
quality distributions in the four bundles determined by the process computer of the plant : f)'f;'j(z)
~;' = Ei~ X6t]~;; + xi~ip' where value),
i6/
j(z)= measured volumetric flux (averaged x~(z) = individual steam quality distribution.
Because the pseudo-mass-flows are not the real individual mass-flows, the deviation of these massflows from the reference values may give an indication as to which of the four bundles is the most important one (as far as the detector is concerned) at a certain axial core height. Figure 5 shows the results for the radial core position near the centre of the core. Because two of the four pseudo-mass-flows are very similar, only one was plotted ([]). For clarity, all values which were higher than 1650 kg m - 1 s - 1 or smaller than 1350 kg m - 1 s were disregarded ; to indicate this 'elimination', largescale symbols are given for the suppressed mass-flows in the region where they occur. For relative core heights less than 40%, the disregarded values are always higher than the mass-flow given by the process computer ( ) and are only values from the "[2' and the ' + ' bundles. In the upper part of the core (core height higher than 65%), some A values are lower than the above given limits. It can easily be seen that for core heights less than 40%, the bundle indicated with a A is the dominant one because the pseudo-mass-flow of that bundle gives the
"right' mass-flow, i.e. the mass-flow given from the plant processor. By looking now at the axial quality distribution in the lbur bundles (small plot), we can find the reason for this effect. Compared with the other three bundles, the quality in this bundle has twice the value of the quality in the other bundles. This indicates a much more established two-phase flow with more 'noise sources' in it and as a consequence, a dominant role of these noise sources over the noise sources of the other three bundles. Things change when core heights greater than 50% are considered. Here, the two '[2' bundles and the ' + ' bundle become dominant. Looking again for the quality distribution, we observe a similar shape for these three bundles. Although the ' / V bundle has still a higher steam content, the void fraction in the other is now high enough (steam quality higher than 5% which means a void fraction of approx. 45%) to provide a sufficient number of noise sources. Near the core exit, the' +" bundle (which is the bundle with the lowest exit quality) becomes dominant. This is an indication that the 'density of noise sources' in a two-phase flow decreases again with higher steam contents, a fact which has been observed earlier by the author in his light-beam experiments, where the highest RMS values of the signals have been found with bubbly-flows. Summarizing our findings for the 'centre-core' position, we can say that we have established the fact that the importance of the individual bundles in the bundle set surrounding the instrument tube is usually
Fluid velocity by noise analysis
239
BWR 50
_ 20
i
25 o
n
10 5
I
1
0
50
×
Core height
"
I00
(%)
20
+D A
[]
+
+
1.5
0 ,,
10
A~_a-_/__A u
A
I
I
I
I
I
20
40
60
80
IQO
Core
h e i g h t (%)
Fig. 5. Pseudo-mass-flowand quality distribution for a central-core position.
not the same. The influence of the two-phase flow in these bundles on the 'formation' of the resulting noise signal (weighting) depends on the axial position and normally changes with core height. This explains the observation that the average mass-flow (Fig. 4) has a small negative slope. The influence of the bundle importance can be observed in a much more pronounced way for bundle sets where the four bundles have significantly different mass-flows as it is the case at the chosen position on the radial edge of the core. The results of the pseudo-massflows for such a position are shown in Fig. 6. For clarity again, 'outlying' values are disregarded and only their positions are indicated by their corresponding largescale symbols. As can be seen from Fig. 6, only two of the four bundles of the bundle set ('•' and ' + ' bundles) seem to form the noise signal because the points of the pseudo-mass-flows for the other two bundles ( x and A bundles) lie completely outside the region of the reference mass-flows given by the plant's process computer. This may be due to the relatively low steam content of the latter two bundles, which does not reach steam qualities higher than 5~o. This 5 ~ steam quality boundary we have observed earlier in the previous case. This is the steam content which seems to be necessary for a significantcontribution of the individual bundle to the total 'signal noise generation' if there are bundles with higher steam content in the vicinity. Therefore, the
measured mass-flow is determined by the mass-flows of only two bundles, the [] and the + bundle. Because their axial steam quality distribution is similar, their pseudo-mass-flows are also similar. On the other hand, the 'reference mass-flows' in the two bundles differ by a factor of two. In the lower part of the core (core height less than 50%), the pseudo-mass-flows correspond to the reference of the [] bundle and in the upper part of the core with the reference of the + bundle. This means that there is a change in the importance of the two bundles in the axial middle of the core, probably due to different two-phase flow-patterns. Up to now, we can only speculate on this point which cannot be proved. Second perturbation
A further question is that of the physical nature of the observed 'second perturbation' found by some authors in the upper part ofa BWR core (e.g. Koshly et al., 1977 ; Behringer and Crowe, 1981 ; Federico et al., 1981). The first explanation of this effect was given by Kos~ly et al. (1977) and further investigated by Miteff (1981) who assumed the second perturbation to be due to the interface waves of a classical annular-flow whereas the 'main perturbation' is the velocity of the entrained water droplets in the steam core. This explanation seems to be rather simplistic since the detectors 'see' inside a bundle set of four bundles with 64 pins each. Federico et al. (1981) deny this 'annular-flow'
240
D . LUBBESMEYER
BWR
3.0
>,
E
=os
2.5
o AX 0
50
I x _.-..
2.0
X
'~'~'-'-" ~ ~'~'~ E
I00
C o r e height (%)
I 5
-
I 0
-
[]
x
L~
I
O5 0
I
I
I
20
40
60
Core
I
J IOO
80
(%)
height
F i g . 6. Pseudo-mass-flow and quality distribution for an edge-core position.
explanation but they do not give their own explanation and they assume a more 'global' effect related to the bthaviour of the core as a whole. Another explanation was recently given by L0bbcsmeyer (1981) who assumed that the second perturbation (second transit time) is due to a velocity profile in the bundles. This explanation is based on
measurements in a simple air-water loop by lightscattering techniques. It was proved later by computer simulations with artificial signals (Liibbesmeyer, 1982). With the above findings of the bundle importance, another explanation seems plausible, namely that the second transit time is due to two bundles with nearly the same 'importance' but different individual mass-flows.
2.5 25
%
:>~
2.0
~
~E
io
I o
x ..-. Ivl 04
15
0
40
60
80
ioo
Core htigi~t 1%) + O A
1.5
+
-tO
+o
I.O frO
+ 1:3
+ C]
[] I'1 A
A
A
.,.,
A 0.5 40
I 50
l 60
Core height F i g . 7. P s e u d o - m a s s - f l o w
t 70
[ 80
i 90
I I00
(%)
distribution determined for the second perturbation (central-core p o s i t i o n ) .
Fluid velocity by noise analysis To investigate this assumption, the pseudo-massflows of the 'second perturbations' at the position near the centre of the core were computed and plotted in Fig. 7. As one can see, the second perturbation exists only in the upper third of the core. The pseudo-mass-flows are much lower than 'postulated' by the mass-flow given by the process computer of the plant as a reference so that for this position, the 'importance explanation' for the second perturbation can be excluded. On the other hand, for the edge position where some second transit-time points occur in the vicinity of the 'velocity step', this explanation is probably valid because the second transit time always gives the 'opposite velocity' (i.e. for a high first transit time, the second transit time has the values of the lower 'branch' of the axial 'mass-flow distribution' and vice versa).
241
influenced by the usually different two-phase-flow characteristics in the bundles around the detector. This means that the velocity measured in BWRs by means of neutron-noise analysis are usually non-uniformly weiohted averages of the individual velocities in the four surrounding bundles (or even more bundles). Normally, this weighting function is unknown. It depends on the two-phase flow-pattern in the surrounding bundles which is a function of the radial and axial core position. Acknowledoements--The author would like to express his t hanks to Dr G. Th. Analytis for severalimportant suggestions and also for reading the manuscript and correcting my English.
REFERENCES
CONCLUSIONS The aim of this paper has been to investigate the nature of the velocity measured by neutron-noise analysis at certain radial positions of a BWR core. It was found that the measured fluid velocity can be associated with the volumetric flux j. Although this finding could not be proved in an exact mathematical way it is plausible and allows us to determine easily the mass-flow G by using the quality distribution given by the process computer of the power plant, a value which can be computed to a relatively high accuracy. By evaluating the 'pseudo-mass-flows' of the four bundles surrounding one instrument tube, it has been shown that the results of fluid-velocity measurements in a BWR core by neutron-noise analysis are mainly
Federico A. Galli C., Parmeggiani C., Ragona R. and Tosi V, (1981) Paper VIII. 3. SMORN-III, Tokyo. ishii M. (1980) Trans. Am. nucl. 5oc. 34, 273. K anai T., Kawai T. and Aoki R. (1961) J. atom. Eneroy $oc. 3,
168. Kos~tlyG. and Fahley J. M. (1982) Report EPR1-NP-2401. Kos~dy G., Kosti~ Lj., Miteff L., Varadi G. and Behringer K. (1977) Report EIR-328. Lighthill M. J. and Whitham G. B.(1955) Proc. R. Soc. Lond, A 229, 281. Liibbesmeyer D. (1981) Paper 1.2, SMORN-II1, Tokyo. Liibbesmeyer D. (1982) Report EIR-473. Lfibbesmeyer D. and Leoni B. (1980) Report EIR-400. Lfibbesmeyer D. and Ulber M. (1977) Atom Wirtsch. 22, 271. Miteff L. (1981 ) Report E1R-431. Seifritz W. and Cioli F. (1973) Trans Am. nucl. Soc. 17, 451. Wach D. (1973)Atom Wirtsch. 18, 580. Zuber N. and Staub F. W. (1967) Nucl. Sci. Enqny 30, 268.
0306-4549/83/050233-09503.00/0 Pergamon Press Ltd
O N THE P H Y S I C A L M E A N I N G OF THE F L U I D V E L O C I T Y M E A S U R E D IN BWRs BY NOISE A N A L Y S I S D. Lf,JBBESMEYER
Swiss Federal Institute for Reactor Research, 5303 Wfirenlingen, Switzerland (Received 6 September 1982; accepted in revised form 18 October 1982) Abstract--This paper is dealing with the question of the physical nature of the fluid velocity measured by analysing the noise signals of incore neutron chambers in an operating BWR. It is postulated by phenomenological arguments and proved by measurements that the measured velocity is usually the volumetric fluxj. The advantage of this finding is the fact that it now becomes very easy to determine the mass flux because in addition, only the steam quality x is needed and this can be computed with the enthalpy balance using the axial neutron-flux distribution which can be easily measured. Because in a BWR the instrument tube with the neutron chambers is surrounded by four bundles which may not have equal power distributions and/or may have different mass-flows (and hence, different two-phase flow patterns), the influence of the four bundles on the result of the fluid-velocity measurements may differ with respect to the axial position where the measurement is performed. This means that it is plausible that while in one axial position the volumetric flux in one bundle is measured, in another axial position, the fluid velocity in another bundle is dominant. NOMENCLATURE A d G Gi fs ip j v v~ vs Vw,tcr Vair V x p' p"
Cross-sectional area Detector distance Mass-flow Pseudo-mass-flow of the individual bundle i (equation (6)) Sample frequency Peak index of cross-correlation function Volumetric flux [=(l-C0Vl+~Vs] Measured velocity Velocity of the liquid Velocity of the gas (steam) Volume-flow,. water Volume-flow, air Volume Quality Void fraction Saturation density of liquid Saturation density of steam
INTRODUCTION
When presenting results of fluid-velocity measurements of two-phase flow in BWR bundles by means of cross-correlating the signals of two incore neutron chambers, the following question often arises : "What kind of velocity of the two-phase flow do we really measure?" The right answer to this question is of great interest, especially if the measurements are to be used for code verifications. An answer to this question was given independently by Seifritz and Cioli (1973) and Wach
(1973). They both assumed that the measured fluid velocity was the velocity of the steam (vs). This has also been assumed by many other authors who have presented fluid-velocity measurements in operating BWRs in the past. It is to the credit of Kos/dy and Fahley (1982) that the investigation of the problem was restarted, even if their proposed explanation seems to us to be misleading. Their explanation for the measured velocity is based on the concept of Kinematic Waves first proposed by Lighthill and Whitham (1955) to describe flood movement in long rivers and applied to the problems of two-phase flows by Kanai et al. (1961) and later by Zuber and Staub (1967) who tried to define a propagation velocity of changes of the void fraction. In contrast to Zuber and Staub who derived their relation for the case of the propagation of changes of the void fraction (which is a Macroscopic effect), Koshly and Fahley use the same equation to describe the transport of the density fluctuations due to the heterogeneity of a real two-phase flow (which is a microscopic effect). This concept seems to be questionable because the basic equations (continuity equations) are based on the assumption of a homogenized two-phase flow and therefore, the microscopic features of a real two-phase flow are already 'averaged out' and cannot be reintroduced. By resorting to phenomenological considerations, we shall assume that the velocity measured by noise analysis is usually the volumetric flux j. We shall investigate the validity of this assumption by 233
234
D. Lu BBESMEYER
Comparing it to measurements performed in an excore loop and in an operating BWR. The second part of this paper deals with the question of what kind of velocity information we will get from the four individual bundles surrounding the instrument tube, especially if the individual two-phase flows in the four bundles are different due to different mass fluxes and/or axial power distributions which is usually the case in an operating BWR. PHENOMENOLOGICAL CONSIDERATIONS
The technique of measuring the fluid velocity of a two-phase flow by noise analysis is based on the determination of the transport time of fluid-inherent and consistent flow-patterns between two axiallypositioned detectors. Depending on the type of detector (e.g. local probes like thermocouples which only detect the fluctuations on one "flow-line' or X-ray beams of commercial densitometers which detect density fluctuations along the beam crossing the spool-piece diameter) the result is usually only a somehow spaceand time-averaged value. In the case of neutron-noise measurements in BWRs, mainly considered in this paper, the aforementioned fluid-inherent patterns are the microscopic density fluctuations caused by an axially-movingdensity field. The space average of the transit times of these patterns between the two detectors is an average over the four individual radial velocity distributions (velocity profiles) in the four bundles, which surround the instrument tube. Up to now, it has always been assumed that the space average over the velocity profile in the individual bundles is the area average as defined in all I-D two-phase-flow models. On the other hand, by using computer simulation, it was shown by Lfibbesmeyer (1982) that the average velocity measured by the cross-correlation technique usually does not agree with any mathematically-defined average value of the existing velocity profile. Depending on the profile (ratio of maximum to minimum), the deviation between the measured value and the area-averaged value of the profile may reach 10°;~,. The time average is the average over the Macroscopic velocity fluctuations within the measuring time which is for neutron-noise measurements in the order of 5 min to 1 h. A rigorous mathematical description of a microscopic two-phase flow is still lacking because of the extreme complexity of the problem and particularly because of the stochastic nature of the microscopic phase distribution (Ishii, 1980). Therefore, all twophase-flow models, based on the continuity equations for mass, momentum and energy, describe homogen-
ized flows and totally neglect all kind of microscopic information needed for a rigorous mathematical and physical explanation of noise measurements. Consequently, we must look for a velocity which may describe the transport velocity of the microscopic density fluctuations even if it is derived from the basic continuity equations (homogenized formulation). Referring to the usual 1-D (axial) description of twophase flow where all variables are averaged over the cross section (sometimes indicated by ( )) and consequently, the velocity profiles of the two phases and the void-concentration profile are totally neglected, such a velocity appears to be the volumetric flux.j which is defined by : j : (1 --~)vl+~V ~
(1)
(all variables are cross-section averaged). The volumetric flux j can be interpreted as the velocity of the centre of the volume of the mixture (Zuber and Staub, 1967). Such a volume can be thought of as being "marked' by the microscopic fluctuations of the density of the mixture, since some of its parts contain steam and other parts contain liquid. These fluctuations or 'markers' are 'seen' by the detectors (neutron chambers, light sensors etc.) and their transit time between two downstream mounted detectors is measured by cross-correlating their induced signals. So, it seems plausible that the velocity measured in twophase flows by noise-analysismethods is the velocity of these 'volumes' or the volumetric flux). Summarizing, we propose a simple explanation of what kind of velocity of the investigated two-phase flow we measure when cross-correlating two LPRM signals of a BWR. Although this explanation is restricted to flow-regimes similar to bubbly-flows, where one phase is dispersed in the other (each volume of the mixture should content both steam and liquid subvolumes as 'markers'), it may well explain (or approximate) the kind of velocity measured in BWR bundles by neutronnoise analysis. We shall elaborate more on this point in the next section.
EXPERIMENTAL VERIFICATION
In what follows, we want to test our previous assumption experimentally by measurements at the air water two-phase-flow test facility FREDLI-II and also, in a rather'semi-experimental'way, by comparing the measurements performed in a BWR at different radial core positions with the results of the computer code COBRA-EIR, which uses the real axial power distributions in the four surrounding bundles given by the plant processor.
Fluid velocity by noise analysis
235
F R E D L I measurements
FREDLI-II
Let us first focus on the measurements at the air water test facility FREDLI-II described earlier (Liibbesmeyer and Leoni, 1980; Liibbesmeyer, 1981). Here, the signals of two light beams (modulated by the interfaces air/water) were cross-correlated to get the transit time and velocity of the investigated two-phase flow. To establish the 'reference', we have measured the inlet volume-flows of the two individual components (air and water) by two turbine flow-meters and the void fraction in the test section by the 'valve method' (i.e. the test section is closed simultaneously by two valves which allows us to determine the part of the volume of the test section which is filled with air). Because of its compressibility, the volume-flow of the air was corrected by using the pressure difference measured between the location of the turbine and location of the light-beam detectors. Knowing the individual volumeflows and the void fraction in the test section, the two individual velocities of the air and the liquid and also the volumetric flux j of the investigated two-phase flow were computed by : vs -
Fair
(2a)
etA
gwater vt - (1 - ~)A j -
Vair+ Vw.,er A
(2b)
20
+
+
+
15
+
+
.a~z+D _
1.0
/-+
o.g
~
x
f
05
, , ~
+ = V e l o c i t y of g o s
t / X
X g O0
x_ = Velocity of liquid [3-- Volumetric flux j 1 05
I I0
Velocity,
I 15
measured
I 2 0
( m s-t)
Fig. 1. Comparison between fluid velocities, measured by cross-correlation and the flow velocitiesv~,vs and j.
hence, cannot be detected. Therefore, in the annularflow regime, all measured velocities are much lower (half the value) than the ones derived by using equations (2). Comparison of B W R measurements with code results
(2c)
Figure 1 shows the comparison for 34 measuring points at void fractions in the range of 5-80% and velocities between 0.2 and 2 m s- 1.The flow-regime was mainly bubbly-flow (including 3 points of the case of bubbles in a standing water column, v = 0); also, a few cases of slug-flows were investigated. The agreement between the volumetric flux (Fl) measured by the turbine flow-meters and the velocity of the two-phase flow determined by cross-correlating the two light-beam signals is extremely good. The [] symbols are clustered around the solid line which is defined by v. . . . . . . d = Vref...... (equations (2a-c), i.e. it is the 'zero-percent error line'. The liquid-velocity points ( x ) are generally below and the gas-velocity points ( + ) generally above this line. Also, some measurements with annular-flows were performed. Here, the agreement for all three velocities (vs, v~ and j) with the velocity determined by crosscorrelation method was worse, mainly due to a greater proportion of the air-flow passing the light-beam spool-piece in the volume enclosed by the water annulus which causes no fluctuations in the signals and
To determine the axial distribution of the volumetric flux as a reference, first the four cross-section-averaged fluxes have been computed for the four individual bundles surrounding the instrument tube using the axial distributions of the two-phase velocities and the void fraction given by the two-phase-flow code COBRAEra. Because the 'measuring system' gives somehow an average of the four bundles, for simplicity, a 'transittime' average was determined by :
1
1 [jl(Z)
j(z) - 4
1 + jz(z) + j ~
1
1 ] + j~
'
(3)
where jl(z) .... are the volumetric fluxes of the four individual bundles 1 4. Figure 2 shows a comparison of measurements performed in a radial position near the centre ofa BWR core with the correspondingj(z). For this comparison, only points where the detector distance is greater than 30 cm were used to reduce the scattering. The measured points are given as squares and the averaged volumetric flux j(z) is plotted as a solid line. The agreement is reasonable, better in the lower than in the upper part of the core. The lower part of the core is
236
D. LLIBBESMEYER BWR
~2 I
t
Io!
channel (El) are very similar to those of the previous measurement and provide us with a strong indication of the fact that the volumetric flux was measured. On the other hand, for the edge-channel measurement, we get different results ( x ). Here, the computed volumetric flux j(z) is some kind of a fit to the rather peculiar 'distribution' of the measured points. Evaluation or measuring errors (which could explain the 'jump' in the axial velocity distribution) can be excluded because some of the points are determined twice or even more. A more plausible explanation for this behaviour will be given in the next section. Also, for the last two measurements, the axial distribution of the steam velocities cannot explain the axial distribution of the measured velocity points. At this point, we should say a few words about the accuracy of the cross-correlation technique itself. Because the 'cross-correlation spool-piece' is a digital one, i.e. the results are only given as discrete points whereas the velocities are registered either as the next higher or the next lower velocity point, the main error of the measurement is usually due to the resolution Rs of the 'digital spool-piece'. The cross-correlation function has its maximum (peak) in one element (ip) of the function array. The next measurable velocity is then related to the array elements i p - I or ip + 1. From this consideration we can derive the resolution of the spool-piece as (Lfibbesmeyer and Ulber, 1977):
m
/ - / / / / "/ / / D /
E
8
/./f~
6
"0
4
2
s/"
N []
/q~ []
. / ' / ~ /~~ / n ~
~
Radial position near the centre of the core
[]
I
I
[
20
40
60
I
l
80
I00
Core height (%)
Fig. 2. Axial velocity distribution (BWR, radial central-core position). that part where a typical bubbly-flow is d o m i n a n t and for which flow-regime the results of COBRAare known to be more accurate than for other flow-regimes. For comparison, the steam velocity is also given in the figure. It can easily be seen that the assumption of measuring the steam velocity by noise analysis is misleading. Figure 3 shows the results of two other measurements in a similar BWR. Here, the measurements were performed at two different radial core positions, one near the centre and the other near the edge of the core. The results of the measurements in the central
Rs
,o9 Position near the centre of the core L~
,,,.IJ £3~mlS;IDD n // []
/
//E/"/D
6
2
/
_
DD
/
~ l _ _ ~ . ~ ~ s i f i o n EJ,n "
I
for ip > 1,
.,'"~7
;WR
E
1
ip-- 1/ip
I.....-Vs
near the edge of the core
~ 7/.
// /
/
I
I
1
20
40
60
Core
height
I
80
I
I00
(%)
Fig. 3. Axial velocity distribution (BWR, radial central- and edge-core position).
(4)
Fluid velocity by noise analysis where ip =
Ld
.
(4a)
U
This affects only a scattering of the individual measuring points around the 'real' velocity curve and not the trend of a measurement. According to equation (4), the resolution depends on the sample frequency (fs) of the AD conversion, the distance between the detectors (d) and the measured velocity v. For BWR measurements,f~ is usually 128 Hz. Hence, the worst case is the one in which the detectors are closest to each other and the velocity is high (in our case 0.35 m and 6.7 m s - 1 respectively). For this case Rs becomes 15°~o, which is +1 m s I. In most of the measurements, the distance between the detectors was higher ; hence, the resolution for most of the cases is less than 10",,. The FREDLI measurements (light-beam spoolpiece) are much more accurate. With a sample frequency of 1280 Hz and a detector distance of 0.04 m, we obtain for the worst case (v = 2 m s- 1), a resolution of around 4°J~,.
THE I N F L U E N C E OF T H E FLOW-PATTERN IN THE FOUR S U R R O U N D I N G BUNDLES ON THE MEASURED VELOCITY
Determination of the mass-flow The great advantage of the finding that what is measured by noise analysis is the volumetric flux is the fact that it opens the possibility of determining the mass-flow G which is in general the most interesting quantity from the practical point of view. If we make use of the relation G
G
j(z) = x(z~p,, + [1 -x(z)]--, p'
(5)
where x(z) = axial quality distribution, the mass-flow is only a function of the quality and the volumetric flux because the densities in the case of BWR applications can be assumed constant (saturation densities, which are only functions of the system pressure). While usually the main problem of a mass-flow measurement in two-phase flow is the determination of the void fraction a (which can only be evaluated from the steam quality by using empirical correlations), the steam quality itself is a quantity which can easily be evaluated from an enthalpy balance by measuring the axial heat-flux distribution (by measuring the neutronflux distribution). This latter measurement can often be done with relatively high accuracy by the processing system of the power plant.
237
For the two axial velocity distributions of the second set of BWR measurements, the axial quality distributions, as given by the process computer of the power plant, were available. Using these distributions, the 'axial mass-flow distributions' were determined. Negative qualities (subcooled boiling region) have been set equal to zero to avoid any use of empirical correlations as given by subcooled boiling models. The qualities of the four surrounding bundles are linear averages (assuming for simplicity that only the twophase-flow conditions of these four bundles determine the fluid velocity measured by neutron-noise analysis). Above, the mass-flow is given in inverted comas ; this is due to the fact that the mass-flow should be axially constant and any deviation from this would indicate a kind of error. Hence, this is a very sensitive test for the accuracy of the measurement. Figure 4 shows the results of such a 'test'. Let us first look at the central-core position (I-q).For less than 20°:0 core height, the scattering of the points is rather high. This is the subcooled void region where the quality was set equal to zero and consequently, the results are uncertain. For core heights higher than 20~o, the measured points are distributed around the thick solid line which marks the average mass-flow of the four bundles given by the process computer of the plant (the values of the individualbundles are close together). One could say that the points are scattered around a line with a small negative slope; we shall try to give an explanation to this in due course. For the edge-position measurements ( x ) the 'jump' can be seen again. Whereas the agreement with the average mass-flow is now worse(thin solid line), for core heights lower than 50~o, a relatively good agreement is achieved with a mass-flow average (G,d~e.3)formed with similar mass-flows of three of the four bundles. For core heights higher than 50~o, the measured points are nearer to the mass-flow of one of the four bundles (G,d~,.1). The mass-flow of that bundle has only half the value of each of the other three as given by the process computer of the plant. This is an interesting observation because as far as the neutron detector is concerned, it indicates a kind of 'change of the bundle importance' in the four-bundleset surrounding the instrument tube. The two-phase flow in this bundle set is assumed to influence mainly the results of noise-analysis velocity measurements at a certain radial core position of a BWR.
Bundle importance We shall now focus more on the 'bundle importance' and compute the four 'pseudo-mass-flows' of the individualbundles, G1-G4, by combining the measured volumetric-flux distribution with the individual axial
238
D. Lf.]BBESMEYER 25
Edge IX~Sition ~
[]
2O x
XX [] X [] DD~DD
I 5 --
[] 10
Ged~e
X× Gedge, 3 []
[]
Q~
[] D~DD• x
[]
Dx
x x
--
n
D~IOD
I 20
0
centre
DDD x x ~x
X X Gedge , I
Centre position
05
/
×
] 40
I 60
Core
l 80
I lO0
heigh~ (°,/.)
Fig. 4. Mass-flow determined for ditlerent ¢ore heights.
quality distributions in the four bundles determined by the process computer of the plant : f)'f;'j(z)
~;' = Ei~ X6t]~;; + xi~ip' where value),
i6/
j(z)= measured volumetric flux (averaged x~(z) = individual steam quality distribution.
Because the pseudo-mass-flows are not the real individual mass-flows, the deviation of these massflows from the reference values may give an indication as to which of the four bundles is the most important one (as far as the detector is concerned) at a certain axial core height. Figure 5 shows the results for the radial core position near the centre of the core. Because two of the four pseudo-mass-flows are very similar, only one was plotted ([]). For clarity, all values which were higher than 1650 kg m - 1 s - 1 or smaller than 1350 kg m - 1 s were disregarded ; to indicate this 'elimination', largescale symbols are given for the suppressed mass-flows in the region where they occur. For relative core heights less than 40%, the disregarded values are always higher than the mass-flow given by the process computer ( ) and are only values from the "[2' and the ' + ' bundles. In the upper part of the core (core height higher than 65%), some A values are lower than the above given limits. It can easily be seen that for core heights less than 40%, the bundle indicated with a A is the dominant one because the pseudo-mass-flow of that bundle gives the
"right' mass-flow, i.e. the mass-flow given from the plant processor. By looking now at the axial quality distribution in the lbur bundles (small plot), we can find the reason for this effect. Compared with the other three bundles, the quality in this bundle has twice the value of the quality in the other bundles. This indicates a much more established two-phase flow with more 'noise sources' in it and as a consequence, a dominant role of these noise sources over the noise sources of the other three bundles. Things change when core heights greater than 50% are considered. Here, the two '[2' bundles and the ' + ' bundle become dominant. Looking again for the quality distribution, we observe a similar shape for these three bundles. Although the ' / V bundle has still a higher steam content, the void fraction in the other is now high enough (steam quality higher than 5% which means a void fraction of approx. 45%) to provide a sufficient number of noise sources. Near the core exit, the' +" bundle (which is the bundle with the lowest exit quality) becomes dominant. This is an indication that the 'density of noise sources' in a two-phase flow decreases again with higher steam contents, a fact which has been observed earlier by the author in his light-beam experiments, where the highest RMS values of the signals have been found with bubbly-flows. Summarizing our findings for the 'centre-core' position, we can say that we have established the fact that the importance of the individual bundles in the bundle set surrounding the instrument tube is usually
Fluid velocity by noise analysis
239
BWR 50
_ 20
i
25 o
n
10 5
I
1
0
50
×
Core height
"
I00
(%)
20
+D A
[]
+
+
1.5
0 ,,
10
A~_a-_/__A u
A
I
I
I
I
I
20
40
60
80
IQO
Core
h e i g h t (%)
Fig. 5. Pseudo-mass-flowand quality distribution for a central-core position.
not the same. The influence of the two-phase flow in these bundles on the 'formation' of the resulting noise signal (weighting) depends on the axial position and normally changes with core height. This explains the observation that the average mass-flow (Fig. 4) has a small negative slope. The influence of the bundle importance can be observed in a much more pronounced way for bundle sets where the four bundles have significantly different mass-flows as it is the case at the chosen position on the radial edge of the core. The results of the pseudo-massflows for such a position are shown in Fig. 6. For clarity again, 'outlying' values are disregarded and only their positions are indicated by their corresponding largescale symbols. As can be seen from Fig. 6, only two of the four bundles of the bundle set ('•' and ' + ' bundles) seem to form the noise signal because the points of the pseudo-mass-flows for the other two bundles ( x and A bundles) lie completely outside the region of the reference mass-flows given by the plant's process computer. This may be due to the relatively low steam content of the latter two bundles, which does not reach steam qualities higher than 5~o. This 5 ~ steam quality boundary we have observed earlier in the previous case. This is the steam content which seems to be necessary for a significantcontribution of the individual bundle to the total 'signal noise generation' if there are bundles with higher steam content in the vicinity. Therefore, the
measured mass-flow is determined by the mass-flows of only two bundles, the [] and the + bundle. Because their axial steam quality distribution is similar, their pseudo-mass-flows are also similar. On the other hand, the 'reference mass-flows' in the two bundles differ by a factor of two. In the lower part of the core (core height less than 50%), the pseudo-mass-flows correspond to the reference of the [] bundle and in the upper part of the core with the reference of the + bundle. This means that there is a change in the importance of the two bundles in the axial middle of the core, probably due to different two-phase flow-patterns. Up to now, we can only speculate on this point which cannot be proved. Second perturbation
A further question is that of the physical nature of the observed 'second perturbation' found by some authors in the upper part ofa BWR core (e.g. Koshly et al., 1977 ; Behringer and Crowe, 1981 ; Federico et al., 1981). The first explanation of this effect was given by Kos~ly et al. (1977) and further investigated by Miteff (1981) who assumed the second perturbation to be due to the interface waves of a classical annular-flow whereas the 'main perturbation' is the velocity of the entrained water droplets in the steam core. This explanation seems to be rather simplistic since the detectors 'see' inside a bundle set of four bundles with 64 pins each. Federico et al. (1981) deny this 'annular-flow'
240
D . LUBBESMEYER
BWR
3.0
>,
E
=os
2.5
o AX 0
50
I x _.-..
2.0
X
'~'~'-'-" ~ ~'~'~ E
I00
C o r e height (%)
I 5
-
I 0
-
[]
x
L~
I
O5 0
I
I
I
20
40
60
Core
I
J IOO
80
(%)
height
F i g . 6. Pseudo-mass-flow and quality distribution for an edge-core position.
explanation but they do not give their own explanation and they assume a more 'global' effect related to the bthaviour of the core as a whole. Another explanation was recently given by L0bbcsmeyer (1981) who assumed that the second perturbation (second transit time) is due to a velocity profile in the bundles. This explanation is based on
measurements in a simple air-water loop by lightscattering techniques. It was proved later by computer simulations with artificial signals (Liibbesmeyer, 1982). With the above findings of the bundle importance, another explanation seems plausible, namely that the second transit time is due to two bundles with nearly the same 'importance' but different individual mass-flows.
2.5 25
%
:>~
2.0
~
~E
io
I o
x ..-. Ivl 04
15
0
40
60
80
ioo
Core htigi~t 1%) + O A
1.5
+
-tO
+o
I.O frO
+ 1:3
+ C]
[] I'1 A
A
A
.,.,
A 0.5 40
I 50
l 60
Core height F i g . 7. P s e u d o - m a s s - f l o w
t 70
[ 80
i 90
I I00
(%)
distribution determined for the second perturbation (central-core p o s i t i o n ) .
Fluid velocity by noise analysis To investigate this assumption, the pseudo-massflows of the 'second perturbations' at the position near the centre of the core were computed and plotted in Fig. 7. As one can see, the second perturbation exists only in the upper third of the core. The pseudo-mass-flows are much lower than 'postulated' by the mass-flow given by the process computer of the plant as a reference so that for this position, the 'importance explanation' for the second perturbation can be excluded. On the other hand, for the edge position where some second transit-time points occur in the vicinity of the 'velocity step', this explanation is probably valid because the second transit time always gives the 'opposite velocity' (i.e. for a high first transit time, the second transit time has the values of the lower 'branch' of the axial 'mass-flow distribution' and vice versa).
241
influenced by the usually different two-phase-flow characteristics in the bundles around the detector. This means that the velocity measured in BWRs by means of neutron-noise analysis are usually non-uniformly weiohted averages of the individual velocities in the four surrounding bundles (or even more bundles). Normally, this weighting function is unknown. It depends on the two-phase flow-pattern in the surrounding bundles which is a function of the radial and axial core position. Acknowledoements--The author would like to express his t hanks to Dr G. Th. Analytis for severalimportant suggestions and also for reading the manuscript and correcting my English.
REFERENCES
CONCLUSIONS The aim of this paper has been to investigate the nature of the velocity measured by neutron-noise analysis at certain radial positions of a BWR core. It was found that the measured fluid velocity can be associated with the volumetric flux j. Although this finding could not be proved in an exact mathematical way it is plausible and allows us to determine easily the mass-flow G by using the quality distribution given by the process computer of the power plant, a value which can be computed to a relatively high accuracy. By evaluating the 'pseudo-mass-flows' of the four bundles surrounding one instrument tube, it has been shown that the results of fluid-velocity measurements in a BWR core by neutron-noise analysis are mainly
Federico A. Galli C., Parmeggiani C., Ragona R. and Tosi V, (1981) Paper VIII. 3. SMORN-III, Tokyo. ishii M. (1980) Trans. Am. nucl. 5oc. 34, 273. K anai T., Kawai T. and Aoki R. (1961) J. atom. Eneroy $oc. 3,
168. Kos~tlyG. and Fahley J. M. (1982) Report EPR1-NP-2401. Kos~dy G., Kosti~ Lj., Miteff L., Varadi G. and Behringer K. (1977) Report EIR-328. Lighthill M. J. and Whitham G. B.(1955) Proc. R. Soc. Lond, A 229, 281. Liibbesmeyer D. (1981) Paper 1.2, SMORN-II1, Tokyo. Liibbesmeyer D. (1982) Report EIR-473. Lfibbesmeyer D. and Leoni B. (1980) Report EIR-400. Lfibbesmeyer D. and Ulber M. (1977) Atom Wirtsch. 22, 271. Miteff L. (1981 ) Report E1R-431. Seifritz W. and Cioli F. (1973) Trans Am. nucl. Soc. 17, 451. Wach D. (1973)Atom Wirtsch. 18, 580. Zuber N. and Staub F. W. (1967) Nucl. Sci. Enqny 30, 268.