SOVIET ATOMIC ENERGY VOL. 58, NO. 3

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000300060003-3
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 71
• Document Creation Date: December 27, 2016
• Document Release Date: March 11, 2013
• Sequence Number: 3
• Publication Date: March 1, 1985
• Content Type: REPORT

Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
ISSN 0038-531X
Russian Original Vol. 58, No. 3, March, 19r7
q?)
September, 1'
SA TEA Z 58(3) 177-24,. ,;185)
SOVIET
ATOMIC
ENERGY
ATOMHAR 3HEFTI411
(ATOMNAYA gNERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
tima
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
SOVIET
ATOMIC
ENERGY
Soviet Atomic Energy is abstracted or in-
dexed in Chemical Abstracts, Chemical
Titles, Pollution Abstracts, Science Re-
search Abstracts, Parts A and 8, Safety
Science Abstracts Journal, Current Con-
tents, Energy Research Abstracts, and
Engineering Index.
Mailed in the USA by Publications
Expediting, Inc., 200 Meacham Ave-
nue, Elmont, NY 11003.
POSTMASTER: Send address changes to
Soviet Atomic Energy, Plenum Publish-
ing Corporation, 233 Spring Street, New
York, NY 10013.
Soviet Atomic Energy is a translation of Atomnaya Energiya, a
publication of the Academy of Sciences of the USSR.
An agreement with the Copyright Agency of the USSR (VAAP)
makes available both advance copies of the Russian journal and
original glossy photographs and artwork. This serves to decrease
the necessary time lag between publication of the original and
publication of the translation and helps to improve the quality
of the latter. The translation began with the first issue of the
Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
Associate Editors: A. I. Artemov, N. N. Ponomarev-Stepnoi,
and N. A. Vlasov
I. A. Arkhangeskii
I. V. Chuvilo
I. Ya. Emeryanov
I. N. Golovin
V. I. ll'ichev
P. L. Kirillov
Yu. I. Koryakin
E. V. Kulov
B. N. Laskorin
V. V. Matveev
A. M. Petras'y_ants
E. P. Ryazantsev
A. S. Shtan
B. A. Sidorenko
Yu. V. Sivintsev
M. F. Troyano
V. A. Tsykanov
E. I. Vorob'ev
V. F. Zelenskii
Copyright ? 1985, Plenum Publishing Corporation. Soviet Atomic Energy partici-
pates,in the Copyright Clearance Center (CCC) Transactional Reporting Service.
The appearance of a code line at the bottom of the first page of an article in this
journal indicates the copyright owner's consent that copies of the article may be
made for personal or internal use. However, this consent is given on the condition
that the copier pay the flat fee of $9.50 per article (no additional per-page fees)
directly to the Copyright Clearance Center, Inc., 27 Congress Street, Salem,
Massachusetts 01970, for all copying not explicitly permitted by Sections 107 or
108 of the U.S. Copyright Law. The CCC is a nonprofit clearinghouse for the pay-
ment of photocopying fees by libraries and other users registered with the CCC.
Therefore, this consent does not extend to other kinds of copying, such as copying
for general distribution, for advertising or promotional purposes, for creating new
collective works, or for resale, nor to the reprinting of figures, tables, and text ex-
cerpts. 0038-531X/85/$09.50
Consultants Bureau journals appear about six months after the publication of the
original Russian issue. For bibliographic accuracy, the English issue published'in
Consultants Bureau carries the same number and date as the original Russian from
which it was translated. For example, a Russian issue published in December will
appear in a Consultants Bureau English translation about the following June, but the
translation issue will carry the December date. When ordering any volume or particu-
lar issue of a Consultants Bureau journal, please specify the date and, where appli-
cable, the volume and issue numbers of the original Russian. The material you will
receive will be a translation of that Russian volume or issue.
Subscription (2 volumes per year)
Vols. 56 & 57: $560 (domestic), $621 (foreign)
Vols. 58 & 59: $645 (domestic), $715 (foreign)
Single Issue: 100
Single Article: $9.50
CONSULTANTS BUREAU, NEW YORK AND LONDON
233 Spring Street
New York, New York 10013
Published monthly. Second-class postage paid at Jamaica, New York 11431.
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved ForRelease2013/03/11 : CIA-RDP10-02196R000300060003-3
SOVIET ATOMIC ENERGY
,
A translation of Atomnaya Energiya
September, 1985
Volume 58, Number 3
March, 1985
CONTENTS
Engl./Russ.
ARTICLES
Effects of a Ballast Zone on the Hydraulic Stability
of a Direct-Flow Steam Generator ? I. I. Belyakov,
M. A. Kvetnyi, and D.A.Loginov 177 155
Circulation Characteristics of a Natural-Circulation
Loop in a Large-Scale Model for a Weakly Boiling Reactor
? N. S. Aliferov, A. S. Babykin, B. F. Balunov,
V. V. Vakhrushev, V. S. Kuul', and E. L. Smirnov 182 159
Corrosion Protection of a Pearlitic Steel in the Stalled
(Shutdown) and Transient (Transitory) Regimes
of a Nuclear Power System ? V. V. Prozorov 186 162
Implicit Method of Solving Mass-Transfer Equations
in the Variables Velocity?Vorticity ? M. P. Leonchuk,
Z. V. Sivak, and Yu. E. Shvetsov 192 166
Trends in the Global Spread of 1291 and Forecasting
the Accumulation Due to Release from Nuclear Fuel
Cycle Facilities ? B. I. Styro, T. N. Nedvetskaite,
and V. I. Filistovich 199 171
Background Limitations in X-Ray Fluorecence Analysis
? V. V. Berdikov, E. A. Zaitsev, and B. S. Iokhin 204 174
Method of Investigation of y-Ray Cascades from the Multiplicity
Spectrum and Low-Energy y-Transitions ? B. V. Danilin,
B. V. Efimov, G. V. Muradyan, F. N. Belyaev,
and V. P. Bolotskii 209 178
Radiative Capture Cross Section of Fast Neutrons
by 197Au, 2361J, and 237NP Nuclei ? A. N. Davletshin,
A. O. Tipunkov, S. V. Tikhonov, and V. A. Tolstikov 216 183
LETTERS TO THE EDITOR
A Mathematical Model for Calculating Stresses in the Microfuel
Elements ? V. S. Eremeev, E. A. Ivanova, V. N. Mikhailov,
A. P. Putilova, and A. S. Chernikov 224 189
Method for the Determination of the Processes of Plural Muon
Catalysis ? V. G. Zinov, L. N. Somov, and V. V. Fillchenkov 226 190
Nonstationary Moderation of Neutrons from a Point Pulsed
Source in a System of Two Media with a Planar Interface
? A. V. Zhemerev 230 192
Conductivity of an Electical Ceramic during Reactor
Irradiation?E. G. Ashirov, Kim Gen Chan, N. S. Kostyukov,
M. I. Muminov, V. N. Sandalov, and Yu. S. Skripnikov 234 195
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
CONTENTS
Use of Weighted Linear Regression Model to Identify Total-
Absorption Peaks during Processing of Complex
y-Ray Spectra ? V. Badulin and T. Petkov
(continued)
Engl./Russ.
237 196
Neutron Absorption Cross Section of 239Pu in the Region
of Resolved Resonances ? V. V. Kolesov and A. A. Luktyanov 239 197
The Russian press date (podpisano k pechati) of this issue was 2/21/1985.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
EFFECT OF A BALLAST ZONE ON THE HYDRAULIC STABILITY
OF A DIRECT-FLOW STEAM GENERATOR
I. I. Belyakov, M. A. Kvetnyi, UDC 621.18:039:532.5
and D. A. Loginov
Hydraulic stability analysis is an important stage in the design of a direct-flow heat
exchanger, in particular a steam generator in a nuclear power plant, as one has to consider
the channels in the heating surface and the characteristic working conditions. Two main forms
of flow instability occur in a boiling channel: static or aperiodic and dynamic or oscilla-
tory [1, 2]. The numerous factors governing the occurrence of unstable modes include the ef-
fects of the mode of heating, about which least is known. The available analytic relationships
resemble most experimental results in corresponding to the conditions of radiative or elec-
trical heating, and if one uses them to evaluate the stability in convective heating, there
may be substantial quantitative or qualitative errors. When heat is transferred by convec-
tion, there is an interaction between the surface temperature and the heat flux, which may,
on the one hand, shift the boundaries for unstable modes and on the other may give rise to
new mechanisms for instability in the system formed by the hot and cool media.
We have performed an analysis of the hydraulic stability in a direct-flow steam generator
heated by liquid sodium, which has shown that puslating states can occur at low loads, which
arise by mechanisms different from known ones and which substantially influence these forms
of instability. Here we consider this phenomenon, which largely determines the choice of
steam-generator working parameters.
The medium in a direct-flow steam generator can be divided into three parts in accordance
with the phase state of the working (cooling) medium: the economizer, the evaporator, and the
steam superheater. The boundaries between the parts shift in accordance with the mode of op-
eration. When the load on the steam generator falls, there are reductions in the flow rates
of the heating medium and the working one and corresponding reductions in the amount of heat
transferred, which means that the economizer and evaporator zones tend to shorten and the
length of the superheating part increases, since the total surface in the heat exchanger re-
mains constant. Above a certain load, part of the surface is, as it were, switched out of the
heat transfer because of temperature reduction in the heating and working media. This part
of the surface has small temperature differences and is called the ballast zone. It usually
lies in the exit section of the superheating part. In a steam generator employing the coun-
tercurrent principle, this form of heating-zone redistribution on load reduction is the most
frequently encountered, but not the only one. A certain combination of the temperatures and
flow rates of the heating and working media can cause a considerable enlargement of the econ-
omizer-evaporator part, while the superheating part shortens. In that case, the ballast zone
lies in the region of transition from the economizer to the evaporator. Although the bounda-
ries of the ballast zone are defined only nominally, calculations show that the main section
of the ballast zone lies in the economizer part. This is evidently due to a marked increase
in the heat-transfer rate in the boiling part. Therefore, this is called the economizer zone.
Figure 1 shows the T?H diagram (T is temperture and H is heating surface), which indi-
cates the limiting possible forms of the heating zones in a direct-flow generator working at
low load (with an extensive ballast zone). To demonstrate when the particular forms occur, we
consider the heat-balance equations for the evaporator-superheater part for a fixed heating-
diagram temperature Tl at the inlet to the generator.
The maximum amount of heat that can be transferred between the media in this part is
(1)
where G is the flow rate of the heating medium and 1 is its enthalpy at T1.
Translated from Atomnaya gnergiya, Vol. 58, No. 3, pp. 155-159, March, 1985. Original
article submitted March 20, 1984.
0038-531X/85/5803-0177$09.50 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
177
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
7; t
7i
1
rf
2 3
Fig. 1. T-H diagram for a steam generator
operting at low power with a.ballast zone
in the superheating part (a) and in the
economizer-evaporator part (b): 1-3)
economizer, evaporator, and superheating
parts correspondingly; 4) ballast zone.
cr
JO
20
10
cr
K2,
JO
20
10
0 I 0
AO 180 320 7;?C 280 360
T,?G
F1-8.2.DePendenceof kr on pressure of
'
the working medium p and heating-medium
temperature at the inlet to the generator
Ti; a) heating medium pressurized water,
MPa: 1) 3; 2) 5; 3) 7; 4) 9; b) heating
medium sodium: 1) 6; 2) 10; 3) 14; 4) 18.
The enthalpy Is is determined from the saturation temperature of the working medium ts,
which is the lower bound to the heating-medium temperature in the evaporator part.
The heat-balance equation for the working medium is
Q=D(ig--C), (2)
where D is the working medium flow rate, while ig and i' are the enthalpies of the medium at
the exit from the generator and of water on the saturation line correspondingly. We equate
the right sides of (1) and (2) to get after algebraic transformation that
178
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
(3)
The temperature of the working medium tg at the exit from the generator corresponding
to ie may be less than Ti; in that case, the temperature of the heating medium tends to ts
in the region of transition from the economizer to the evaporator (near the point i'). This
part will also be thezone of small temperature differences, namely the ballast zone (Fig.
lb). The larger Tl ? tg, the shorter the superheating part, and consequently, the larger
the ballast zone. As the flow rate of the heating medium increases under otherwise con-
stant conditions, tg will tend to T1. The superheating part will then enlarge, and at some
instant one gets another form of the T?H diagram (Fig. la), i.e., the ballast zone transfers
from the economizer part to the superheating one. The transition will corresponds to a cer-
tain limiting ratio of the flow rates of the heating and working media, which is defined by ,
(3), where the condition is t = T1:
where i corresponds to tg = Tl.
It follows from (4) that k]Sr in the general case is dependent on three parameters: the
heating-medium temperature at the inlet, the pressure of the working medium, and to a smaller
extent the pressure of the heating medium. Figure 2 shows the relationship
kV' = f (p, T1),
where p is the pressure of the working medium.
If G/D is less than the critical value, there is an economizer ballast zone, while
otherwise there is a superheating one.
We consider the mode of operation with an economizer ballast zone subject to the con-
dition that themperatare difference at the outlet is T1 ? tg 5?C; if there is a random
rise in T1 by several degrees, kV also alters, and if the condition is initially G/D < ky,
G/D may exceed the critical value after the temperature rise, so the ballast zone transfers
from the economizer part to the superheating one. Therefore, with a given ratio of the flow
rates, the displacement of the ballast zone may be caused by temperature change in the heat-
ing medium at the inlet.
This means that when the generator works at low load with a ratio of the flow rates close
to the critical value, it is possible for the ballast zone to transfer from the superheater
part to the economizer one or vice versa in response to random fluctuations in the working
parameters (flow rates and temperatures of the heating and working media), i.e., the opera-
tion near the point corresponding to the critical ratio with an extended ballast zone is un-
stable. The displacement of the ballast zone leads to alternating coverage of much of the
surface either by two-phase mixture or by superheated steam, as is evident from the forms
of T?H diagram in Fig. 1. This causes fluctuations in the tempertures of the generator
tubes, as well as a nonstationary heat-transfer crisis, and it may lead to the steam?water
mixture being ejected into the collector if the size of the superheating part is small. The
latter is dependent on the dynamic characteristics. It is clear that the economizer ballast
zone will be of pronounced type for a certain finite temperature difference
71--tg )>Atmh, (5)
One can assume nominally that tmin is 3-5?C, so oscillation is possible in the pres-
ence of sign-varying perturbations of finite magnitudes such that (5) is obeyed.
The dynamic characteristics will evidently be determined by the perturbation propaga-
tion rate and perturbation duration. If the effect is caused by changes in flow rate in
the heating or working media, the perturbation propagation rate will be the speed of sound.
The rate of propagation for a temperature perturbation is determined by the transport delay
(with allowance for the axial thermal conduction for liquid metal). Therefore, the dura-
tion of the transient response and the degree of overshoot may differ substantially between
the two cases. As displacement of the ballast zone is related to the conversion of large
volumes of liquid to vapor and vice versa, much of the liquid phase may be in the superheated
state if the perturbation propagation speed is high, and the process will be accompanied by
explosive boiling, which also leads to ejection of the steam?water mixture into the collector.
In a direct-flow generator heated by water under pressure, the ratio of the flow rates
usually substantially exceeds the critical value, so in practice modes of operation involv-
ing economizer ballast length of the superheater part is then substantially reduced, the
kisr =
(GID)cr= (ig - LS),
(4)
179
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved ForRelease2013/03/11 : CIA-RDP10-02196R000300060003-3
ed
706
1
a
0,8 0,9 1,0 1,1 1,2 4 3 . 0 /8 nom
tg
0 LTri
Fig. 3. Effects of ballast-zone displace-
ment on the hydraulic characteristic (a) and
temperature distribution in the working me-
dium along the tube as affected by flow-rate
change (b): dashed line) heating-medium flow
rate G = 1.05 Gnom; 1-6) values of 0.8, 0.9,
1, 1.1, 1.2, and 1.3 times Dnom correspond-
ingly.
pressure difference is reduced, i.e., the hydraulic characteristic has a multivalued region.
Figure 3 shows calculations for a direct-flow generator heated by liquid sodium in which the
heating surface takes the form of spirals (mean winding diameter 0.15 m) for 25% load [4].
The temperature distribution in the working medium shows that there is a flow-rate range for
it (near the critical point) where there is a sharp enlargement in the economizer-evaporator
part of the heating surface (Fig. 3b). As the hydraulic resistance in that state is deter-
mined by the frictional losses, and the contribution from the other components to the pres-
sure difference is small, the shortening in the superheating part leads to a multiple-valued
hydraulic characteristic (Fig. 3a). It is clear that if one evaluates the static stability
on existing recommendations at constant heat uptake, one cannot detect the effects of the
ballast zone on the hydraulic characteristics.
The steeply falling part on the characteristic makes it difficult to employ any design
measures to stabilize the system. For example, when one is choosing throttling devices at
the inlet to the heating-surface channels, the necessary local-resistance coefficient may
be so large that the generator resistance in the nominal state becomes impermissibly great.
In that case, evidently, one should strive not to stabilize the hydraulic characteristic as
a whole but to extend the region of single-valued behavior around the working point (with
the nominal flow rate for the working medium at the given load). It is then necessary to
increase the flow-rate ratio (for example, by altering the flow rate of the heating medium)
to provide a large margin from the critical value. Figure 3a (dashed line) shows calcula-
tions related to increase in the heating-medium flow rate, which show that an increase of 5%
in that rate substantially extends the region of single-valued behavior in the hydraulic
characteristic near the working point.
The above results have been obtained from calculations and theoretical analysis of the
hydraulic stability at low power. No special experiments have yet been performed on states
with unstable ballast zones.
180
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
+0 - 275
ou
ba
35
JO
25 ?
270
255
250
255
IP
_
50 100
100
r,sec
Fig. 4. Character of the pulsations in
complete-circuit instability during startup
with an elevated sodium flow rate.
However, in [5] results are given from startup conditions ma direct-flow generator
heated by liquid sodium.
The generator model involved a fl-shaped scheme and was represented by a section con-
sisting of a seven-tube evaporator module where the medium rises and a separate five-tube
superheater section with the working medium descending. In the startup state at constant
pressure (startup 5), general instability in the loop was detected (Fig. 4), which was un-
affected by the degree of throttling in the water flow rate over the range 0.2-5 MPa. Here
the temperature of the medium at the outlet from the superheater tubes tout oscillated in
the range between the saturation temperature and the sodium inlet temperature Tin. Insta-
bility was also found with the following working parameters (average ones): heating-medium
flow rate G and working-medium rate D of 12,700 and 239 kg/h correspondingly, pressure of
working medium 4.2 MPa, sodium temperature at the inlet about 277?C. The data enable one
to determine ky which can be compared with the given flow-rate ratio. The calculations
show that kcr = 56-57, while the ratio of the flow rates during the experiment was 53-55,
i.e., on average it was slightly below the critical value. Featuresof these nonstationary
conditions were that thetemperature of the medium varied fromts and Tin and that the ampli-
tude of the fluctuations was independent ofthe degree of throttling at the inlet, which in-
dicates that the general instability is due to displacement of the ballast zone over the
heating surface. Thermal calculations on a generator with a flow-rate ratio close to criti-
cal showed considerable numericalinstability,which may reflect the unstable position of the
ballast zone under real conditions.
Therefore, when one examines the hydraulic stability at low power, it is necessary to
consider the possible pulsating states 'associated with unstable positioning of the ballast
zone, which may affect known forms of hydrodynamic flow instability. Therefore, particular
attention should be given to choosing the working parameters for startup modes and low loads,
in order to eliminate the economizer ballast zone or restrict its occurrence. It is recom-
mended to choose the flow-rate ratio from the dondition
Cr1.1(ig-n
GID>1.11cD ?
where the generator will work with astable ballast zone in the superheater. The safety
margin in (6) should be chosen to provide an adequate single-valued range in the hydraulic
characteristic near the working point.
(6)
LITERATURE CITED
1. I. I. Morozov and V. A. Gerliga, Stability in Boiling Systems [in Russian], Atomizdat,
Moscow (1969).
2. F. M. Mitenkov and B. I. Motorov, The Mechanisms of Unstable Processes in Thermal and
Nuclear Power Engineering [in Russian], Energoizdat, Moscow (1981).
3. I. I. Belyakov, M. A. Kvetnyi, D. A. Loginov, and S. I. Mochan, "The static instabil-
ity of a direct-flow steam generator with convective heating," At. Energ., 56, No. 5,
317-319 (1984).
181
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
4. L
vi ? tiL 1..C111%. IV ? LI ? ULCUIZ1111.1.1WV J. ? 01..(JgCJV, EMU V ? D. Deromest.nov, uesrgn ways or
improving steam generator reliability by use of modular spiral-design schemes," in:
Papers from the Seminar of Comecom Member Countries on Experiences in Developing and
Operating Fast-Reactor Steam Generators [in Russian], Dmitrovgrad, 18-21 May (1982),
pp. 11-25.
5. G. V. Karetnikov, V. M. Gubanov, A. S. Sokolov, et al., "Recording startup states in a
direct-flow sodium steam generator on a model," ibid., pp. 494-505.
CIRCULATION CHARACTERISTICS OF A NATURAL-CIRCULATION LOOP
IN A LARGE-SCALE MODEL FOR A WEAKLY BOILING REACTOR
N. S. Al'ferov, A. S. Babykin, B. F. Balunov, UDC 621.039.553.34
V. V. Vakhrushev, V. S. Kuul', and E. L. Smirnov
There has recently been research on weakly boiling pressurized-water reactors (x?cuot < 4%)
with natural circulation (NC) in the first loop, which has increased interest in the circula-
tion characteristics of NC loops having near-natural heights, hydraulic-resistance coeffi-
cients for the individual components, and working parameters (Fig. 1). Table 1 gives the
loop characteristics.
The core simulator consisted of 61 uniformly electrically heated pins of diameter 14 mm
and height 3 in, which were located in a six-facedjacketwith an internal dimension under the
keys of 148 mm. The pins were arranged on an equilateral triangle with a pitch of 18.7 mm.
Over the height of the simulator there were uniformly placed five spacing grids of honeycomb
type with relative transmission cross section Fgf/Fco = 0.89.
The coolant parameters at the inlet to the simulator and at the outlet were as follows:
outlet pressure Pc?uot = 1,7-2.3; 3.3-3.8; 4.3-5.0 MPa; water underheating at inlet (Atundq-E=
tn - tg= 20-90?C, and balance weight steam content at outlet xggtfrom -9 to 3.2%.
In the experiements, the simulator power Nco.was varied from 0.4 to 1.8 MW, with q =
50-230 kW/m2, while the measured water circulation speed in the simulator was from 0.3 to 1.2
m/sec
To obtain a wider speed range, some of the experiments were performed with the hydraulic
resistance increased by a factor 40 not only in the rising column but also in the single-phase
TABLE 1. Geometrical Characteristics and
Values of the Reduced Hydraulic Resistance
Coefficient Cre for the NC Loop in the Model
Component
ao
I Cross
section,
103 m5
Hy-
draulic
diam.,
103 -
'2
Core
simulator 3,0
9,35
11,7
9,4
Simulator for rising
part (in-
dividual) 3,5
15,0
63,7
1,28
Simulator for com-
mon rising part 3,7
16,5
145
1,22
Descending part with-
out throttling
washer
2,5
Throttling washer
itwo
orms) 0,005
4,65/2,74
77/59
6,7/21,8
NC loop _
_
?
21,1/36,2
Translated from Atomnaya Energiya, Vol. 58, No. 3, pp. 159-162, March, 1985. Original
article submitted January 17, 1984.
182 0038-531X/85/5803-0182$09.50 (3 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
0
-80
Fig. 1. Design for the experimen-
tal NC loop: 1) condenser; 2) com-
mon rising part simulator; 3)
thermal screen; 4) heat exchanger;
5) simulator for individual rising
part; 6) descending bypass tube;
7) core simulator; 8) interchange-
able throttle washer; 9) plug;
10) overflow window; I) cooling
water inlet; II) air inlet.
a
- 0
;out , kj
'co
kg
eeo 0
? e
0 a, (3a
0 ? ,
-150 -120 -80 -40 0
. out ? kJ
"Co ?
kg
Fig. 2. The (Aphy/Apdy)sp = f(i2gt - io.v.s.b.)
relationship for p = 1.7-5.0 MPa for pw = 100-110
kg/(m2.sec) (a); pw = 410-750 kg/(m2.sec) (b); c,
0. Q, e, 3,0, A p ? ) q = 25-37; 37-50; 50-75; 75-
100; 100-125; 125-150; 150-175; 175-200; 200-225
kW/m2 correspondingly.
(water) part of the NC loop. For this purpose, throttling washers were inserted in the lower
part of the descending branch in the NC loop (Fig. 1, position 8), and also at the inlet and
outlet of the rising prt. Also, the cross section of that part was reduced and the height
was reduced somewhat (to 6.1 m). Then the volume of the through section of the part was re-
duced by a factor 2.81. The experiments were performed in series, in which the through sec-
tion of the throttling washer was varied. The hydraulic-resistance coefficient in the de-
scending branch of the NC loop varied from 280 to 1130 as referred to the cross section of
183
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
,J,
S
g
11 t
X '0 '102
CO
Fig: 3. The G = f(x2gt) relationship for
p = 1.7-2.3 MPa for Nco = 1760 (0);, 1580-
1630 (0); 1430-1560 (3) and 1110-1140 kW
.(A); a-c) calculatiOn for p = 2 MPa, Nco=
1600 kW: a) calculation of [3] and T
[1]; b) T [2, 41 and T [1]; c) T and T
[4].
Fig. 4. The G= f(xTolt): and 0) Nco =
1530 and 1730 kW, p = 3.3-3.8 MPa:C))
Nco = 1730 kW, p = 4.3-5.0 MPa (for symbols
a-c, see Fig. 3, p = 3.5 MPa).
the core simulator (reduced hydraulic resistance coefficient),whichconstituted 61-86% of
the reduced hydraulic resistance coefficient of the entire NC loop:
Care=Fc2o E [(kr
where Ca is the reduced hydraulic-resistance coefficient for the descending branch of the
NC circuit, Poo is the cross sectional area of the core simulator, Afr is the frictional co-
efficient, and Ct is the local hydraulic-resistance coefficient.
This series of experiments was performed with the above ranges in pal.; (Atundg, 411t.
and water circulation speeds of 0.084-0.25 m/sec. With values of xgatelose to zero, there
was a considerable effect on the circulation characteristics from the nonequilibrium scheme,
as recommendations on determining the amount of this had not been thoroughly tested for
these conditions.
Programs for the thermohydraulic calculation of stationary NC characteristics were put
into correspondence with the experimental data. The algorithm was based on recommendations
184
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
ror incorporating the ettects of equilibrium and nonequilibrium steam [1-5]: for the core
simulator (the part generating nonequilibrium steam) we used the recommendations of [2-4],
while for the rising part we calculated the true volume steam content Y by determining the
steam condensation rate in the flow of underheated water by means of [2, 3], while for the
equilibrium two-phase flow was calculated by the method of [5].
The program was written in FORTRAN for the ES-1033 computer.
The experiments with the single-phase coolant (xglit < ?2.5%) gave satisfactory agree-
ment between the driving head (Apdy) and the hydraulic resistance (APhv), where the values
were determined from measurements on the flow rate and temperature. The hydraulic resistance
coefficients were calculated in accordance with the recommendations of [1, 6, 7].
The discrepancies between Apdy and Aphy were not more than t8%, while the error in de-
termining the flow rate was ?3% and there is only a small relative density difference in the
water (Pmax Pmin)/(Pmax + Pmin) = 0.02-0.04, so this is to be taken as satisfactory.
The small density difference for the coolant in the rising and descending parts of the
circuit, as is usual for a single-phase coolant, means that any increase in the flow rate is
closely related to the occurrence of nonequilibrium steam in the rising part. To determine
the onset of vigorous surface boiling (the start of steam-bubble detachment in the flow of
underheated water), we used the formula [6]
)1"8
(1)
where q is the specific heat flux at the heating surface; p, density; w, speed; r, latent
heat of evaportion; v, kinematic viscosity; and dh, hydraulic diameter; a prime relates to
water and two primes to steam, and to check (1) in processing the experimental data for
xout < 0, we used the relationship
co
6-1)34(1(iLut
Ap / sp
dy ,v.s.b. )?
(2)
In determining Aphy and Apdy, we neglected the steam in the coolant flow. Vigorous surface
boiling corresponds to (AphyfAdy)sp > 1, since in this loop the increase in the driving head
for the small steam content in the rising part greatly exceeds the relative increase in the
hydraulicresistance associated with the steam, i.e., Aphy = Apdy for the NC, which may be
written for a two-phase flow as
tp
Aps ?Mptp= Ap-sP -FM P
hy hy dy
fp
and for Mphy > dApVT leads to the inequality
Apg; >
Figure 2 shows the processing results. Formula (1) describes the experimental data ac-
curately throughout the ranges used: p = 1.5-4.0 MPa, q = 25-255 kW/m2, and pw = 85-750 kg/
m2.sec.
When there is steam in the circuit (int > io.v.s.b. ), we obtained satisfactory agree-
ment between the calculations and experiment for the flow rate on calculating y in accord-
ance with the recomendations [2-4] and the inhomogeneity coefficient for the two-phase flow
T from the recommendations of [1] (Figs. 3 and 4). Less satisfactory results were obtained
on calculating T from the recommendations of [4].
LITERATURE CITED
1. The Normative Method of Hydraulic Calculation for Steam Boilers, Vol. 1, Guideline
Statements (TsKTI-VTI) [in Russian], Issue 33, ONTI TsKTI, Leningrad (1973).
2. Yu. S. Molochnikov and G. N. Batashova, in: Advances in Research on Heat Transfer and
Hydraulics for Two-Phase Flows in Power Equipment Components [in Russian], Nauka, Lenin-
grad (1973), pp. 79-96.
3. V. I. Plyutinskii and L. L. Fishgoit, "Derivation of the dynamic equation for the steam
content in steam-generating channels on the boiling of underheated water," At. Energ.,
25, No. 6, 474-479 (1968).
4. V. S. Osmachkin and V. D. Borisov, The Hydraulic Resistance of a Bundle of Heat-Produc-
ing Rods in a Flow of Boilng Water [in Russian], Preprint IA-1957, Moscow (1971).
185
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
K. Declassified and Approved ForRelease2013/03/11 : CIA-RDP10-02196R000300060003-3
5. L. n. linnonenaut L4J, Eq"
6. A. I. Klemin, L. N. Polyanin, and M. M. Strigulin, Thermal and Hydraulic Calculation of
Nuclear Reactors and Heat-Engineering Reliability [in Russian], Atomizdat, Moscow (1980).
7. I. E. Idel'chik, Hydraulic Resistance: Physicomechanical Principles [in Russian], Gos-
energoizdat, Moscow?Leningrad (1954).
CORROSION PROTECTION OF A PEARLITIC STEEL IN THE STALLED
(SHUTDOWN) AND TRANSIENT (TRANSITORY) REGIMES OF A NUCLEAR
POWER SYSTEM
V. V. Prozorov UDC 620.197.2
The time required for preconditioning the nuclear power plant equipment and systems be-
fore putting into operation varies from a few months to a year [1]. All through this period
the equipment is under unfavorable corrosive conditions (poor quality of the supplied water,
variable thermal and hydrodynamic regimes, exposure to atmosphere, etc.). The existing meth-
ods of corrosion protection of the thermal power equipment made from the pearlitic steels
must not be mechanically adopted for the nuclear power units because of the intricacy of con-
struction and the more stringent specifications with regard to the corrosion resistance of
the materials and the quality of the coolant. In recent years there have been publications
[2, 3] indicating high corrosion resistance of the pearlitic steels in high-purity water with
oxygen or hydrogen peroxide dosing at a temperature of nearly 300?C. In such studies it has
been noted that the corrosion rate of this steel in an oxygen-containing flowing water is less
than that of the stainless steels 'in neutral water [4]. However, the unsolved problem of
corrosion in the stalled and the transient regimes sets a limit to the application of the
pearlitic steel as a structural material for the nuclear power systems. The use of corrosion
inhibitors does not completely solve the problem of equipment protection, since their pro-
tective properties become apparent only in a narrow temperature range. Besides this, the
necessity of maintaining a high concentration of these inhibitors leads to an increased time
loss for their removal (extractiOn) from the circuit (loop) before changing over to the sta-
tionary regime because of the procedure of multiple regeneration (restoration) of the filters.
Furthermore, an insufficient concentration of the anodic inhibitors causes pitting corrosion
of the metal. Although prior oxidation decreases the corrosion rate, rupture of the protec-
tive films occurs in the stalled regimes at a low temperature (20-80?C) leading to pit for-
mation [5]. The corrosion rate of an oxidized metal ranges from 1.4 up to 11.4 g/(m2.day) at
80?C [1, 6].
In spite of numerous publications on the effect of the corrosion inhibitors on the metals
in their initial state, there is not enough data on the corrosion behavior of the previously
oxidized steels in the inhibitor solutions. The conducted studies revealed a significant dif-
ference between the corrosion behavior of the oxidized and the unoxidized pearlitic steels in
the inhibitor solutions.
In the present studies on the corrosion of the pearlitic steels in the inhibitor solu-
tions, the "steel 20" specimens were oxidized using:
an ammonium nitrate (5 g/kg) solution at 95?C for a period of 0.5 h at pH = 5.5 and 7.5;
a hydrazine (0.4 g/kg) solution with addition of ammonia to adjust up to pH = 10.5 at
160?C for 16 h; and
an iron nitrate (0.3 g/kg) and hydrogen peroxide (0.05 g/kg) solution at 95?C for 1 h with
periodic (supplementary) additions (0.05 g/kg at 15-min intervals) of hydrogen peroxide
to the solution [7].
The specimens oxidized in the ammonium nitrate solution at pH = 5.5 were subsequently
held in sodium hydroxide solutions (0.16 g/kg) at different temperatures, and also. in an
aqueous coolant that meets the specification OST 25743-79 ("The coolant quality for the nu-
Translated from Atomnaya fnergiya, Vol. 58, No. 3, pp. 162-166, March, 1985. Original
article submitted October 31, 1983.
186 0038-531X/85/5803-0186$09.50 10 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
TABLE 1. Protective Inhibitor-Concentration
(mg/kg) for the Steel 20 in Desalted Water
( X= 0.1-0.3 umho/cm) at 20?C
..-'9
....
.in
...
.c
Specimens
machined
oxidized in
ammonium
nitrate so-
lution at a
pH:
-
oxidized by
hydrazine-am-
moniac
method
oxidized in a
solution of
iron nitrate an
hydrogen per-
okide
NaNO2
NaOH
NH4OH
K2Cr04
Na2CO3
Na411407
Na2HPO4
N114\703
(C2H5)3N
(C2115)2NH
K4EFe(CN)21
50
110
115
70
2200
2000
2500
1200
800
700
1800
5 0,3
10 3
13 4
2311 230
600 500
1400 1200
1210 1100
250 200
100 60
80 40
700 700
0,1
8
15
200
450
1100
1000
180
55
40
700
0,02
0,1
0,15
90
300
800
500
8)
15
10
500
TABLE 2. Protective Inhibitor-Concentration
(mg/kg) for the Steel 20, Oxidized in Ammonium
Nitrate Solution and Held under Different
Conditions, in Desalted Water (x= 0.1-0.3
'mho/cm) at 20?C
Oxidized specimens
Inhibitor
NaNO2
Na011
NH4oH
Hold in NaOH solution
(0.16 enter) for a pe-
riod of 1000 h at a
temp., ''C:
20
0,5
4
4
60
0,2
3
3
200
0,03
0,7 ,
0,8
270
0,001
0,3
0,5
Hold in the aqueous cool-
ant at the Leningrad
NPP at a temp..
160 (8950 h) '
0,4
3
3
270 (8030 h)
0,2
2
2
TABLE 3. Protective Inhibitor-Concentration
(mg/kg) for the Steel 20 in Desalted Water
(x= 0.1-0.3 'mho/cm) at Different Tempera-
tures
Inhibitor
Surface
condition
Temp., ?C
20
50
100
150
200
250
300
NaNO2
Not oxidized
50
2011400
Oxidized in
5
7
12
18
25
40
45
NH4NO3
NaOH
- Not oxidized
110
170
230
?
?
?
Oxidized in
10
15
35
75
105
115
105
NH4NO3
187
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
SOO
400
< 300
c.; 200
100
cri
0 20 40 60 BO
Aggressive-ion concn., mg/liter
Fig. 1. Dependence of the protective
concentration of sodium nitrite on the
aggressive-ion concentration for the
steel 20 at 20?C: 1, 3, 4) unoxidized
specimens; 2, 5, 6) specimens oxidized
in ammonium nitrate solution: x)
Na2SO4;0) NaCl; 40) NaNO3. The area
above the respective curves represents
the protective zone (total suppression
of corrosion), and the area below the
curves represents corrosion zone (cor-
rosive failure of specimens).
100
04
?
w 03
2 0,2
=
0
8 g/
--2
' II
0 1 2 .1
NaNO2 concn., mg/liter
Fig. 2. Effect of sodium nitrite con-
centration on the corrosion rate of the
oxidized steel 20 in desalted water at
20?C for 100 days: oxidized by the hy-
drazine-ammoniac method (1), in ammonium
nitrate solution at pH = 7.5 (2) and
pH = 5.5 (3).
clear power plants with the RBMK type reactors, and the methods of ensuring and controlling
the quality") in a deaerator at 160?C for a period of 8950 h and in a circuit of multistage
forced circulation (at 270?C) for 8030 h, and the specimens were then subjected to the cor-
rosion tests. We determined the corrosion rate of the specimens in the solutions over a pe-
riod of 100 days and the minimum protective inhibitor-concentration at which complete sup-
pression of corrosion isachieved (i.e., at which there is no change in the specimen weight
and the iron content in the solution does not increase). In order to determine the minimum
188
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
TABLE 4. Corrosion Rate of the Steel 20,
Oxidized in Ammonium Nitrate Solution (pH=
5.5), in Desalted Water ( x= 0.5-0.8 pmho/
cm) and NaNO2 Solutions at 60?C for 10 Days
Inhibitor
concn.,
mg/ liter
Flqwrate,
m/sec
General cor.-4
rosion rate,
g/(m2. day)
Nature of
corrosion
0
0
0,51
Pitting
0
1-3
0,22
Pitting
1
0
0,44
Pitting
1
1--3
0,04
Uniform
5
0
0,32
Pitting
5
1-3
,2Na0H+1/202?N2,
the excess amount of the liberated oxygen can lead to a more complete conversion (rearrange-
ment) of magnetite into hematite which does not have a spinel structure, and in pure form,
it does not possess the protective properties. Thus, in case sodium nitrite is used, there
is an upper limit of concentration (70 mg/kg) above which one cannot achieve complete sup-
pression of corrosion of an oxidized steel at a tempeiature exceeding 100?C. Hematite forms
even when the specimens are held in NaOH solution if there is a considerable amount of oxy-
gen in the system.
At a temperature above 100?C the upper limit of protective concentration of sodium hy-
droxide was found to be 200 mg/kg. Corrosion reappears at higher concentrations. The in-
teraction of the oxide films with the alkali produces dissolvable ferrites. In this case,
the dissolution process assumes a localized character.
Thus, when the oxidized steel is held in the inhibitor solutions, complex physicochemi-
cal processes occur which change the structure and the phase constitution of the oxide films,
and thereby, affect their protecting ability. It follows from the data presented here that
the protective inhibitor concentration depends on the method of passivation, the temperature,
the quality of desalted water, the flow rate, and the duration of holding the steel in the
solution. The significant reduction in the protective concentration of the dissolvable ni-
trites and hydroxides and the widened temperature range in which these inhibitors exhibit
protective properties permit us to recommend them for protecting the previously oxidized
power-equipment in the stalled and the transient regimes. As the nuclear power system at-
tains the stationary state, the oxide films become dense (thick) and water becomes free from
aggressive ions, owing to which the inhibitor can be withdrawn from the circuit (when there
is total suppression of corrosion), and at this stage, it is advisable to introduce specific
doses of oxygen or hydrogen peroxide into the system. When the nuclear power system is shut
down for maintenance, it is essential to add the corrosion inhibitor again for avoiding the
rupture of oxide films under the stalled conditions. In this case, the inhibitor concentra-
tion required for complete suppression of corrosion, even under the conditions of depres-
surization and saturation of the system with oxygen and carbon dioxide, can be considerably
reduced as compared to the concentration required for the corrosion protection of a nonpassi-
vated metal.
The choice of the inhibitors depends on the specific service conditions of the equip-
ment: the ionizing radiation, tightness of the system, the reactor type, the temperature,
the presence of other structural materials in the system, etc.
Among the examined methods of oxidizing the pearlitic steel, using ammonium nitrate so-
lution is not the best because of the formation of a significant quantity of insoluble ferric
oxide lepidocrocite compounds which contaminate the circuit during the process of condition-
ing the equipment. The hydrazine-ammoniac oxidation method requires a high temperature
(above 140?C). Hydrazine hydrate is fire hazardous and toxic. Treating the pearlitic steel
with iron nitrate and hydrogen peroxide solution does not suffer from these shortcomings
and the oxide films formed possess better protective properties.
190
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
The given technologicalsolutionformed the main postinstallation chemical treatment of
the internalsurfaces of thecondensate supply channel of the fourth block of the Chernobyl'sk
Nuclear Power Plant. The equipment and the channel piping (surface area greater than 5000
m2 and volume 1200 m3) made from the pearlitic steel were treated with nitric acid solution
of 60 mg/kg concentration at 95?C for 4 h (during this treatment iron nitrate forms in the
system). Thereafter, we introduced hyrogen peroxide (5 mg/kg) into the circuit and continued
the treatment for 1 h at the same temperature. After water treatment in the ion-exchange
filters until an electrical conductivity of 0.6-0.7 pmho/cm is obtained, sodium nitrite was
added to the system up to a concentration of 16-18 mg/kg. On treating with nitric acid and
hydrogen peroxide, dense black-colored oxide layer, strongly adhering to the metal, formed
on the internal surfaces of the equipment of the condensate supply channel. Analysis of
the phase constitution using nuclear 1-resonance spectrometry (NGRS) established that this
layer totally consists of magnetite. Subsequent conservation of the channel surfaces by so-
dium nitrite was found to be effective. The circuit was emptied after 6 days. During this
period the iron concentration in water, measured at all the sampling points of the channel,
remained at the original level. During the postinstallation start-up period, it took only
18 h to obtain the specified quality indices of the coolant when operating at 150-260 MW.
Thus, we can recommend prior oxidation and the subsequent use of desalted water with
dissolvable nitrite and hydroxide additions for working out the corrosion protection tech-
nology in the stalled and the transient regimes of the equipment of the nuclear power sys-
tems made from a pearlitic class steel. Such a technology permits wider application of this
steel in lieu of the scarce and costly austenitic stainless steels of the 18-10 type.
LITERATURE CITED
1. P. G. Krutikov nd V. M. Sedov, Water-Chemical Treatments during the Start-up of Nuclear
Power Plants [in Russian], Energoizdat, Moscow (1981).
2. K. A. Nesmeyanova, E. B. Matskevich, and V. G. Kasatkina, in: Proceedings of the III
Internat. Congress on Corrosion of Metals [Russian translation], Vol. IV, Mir, Moscow
(1966), p. 278.
3. Ya. N. Kolotyrkin et al., in: Corrosion of Rector Materials [in Russian], Atomizdat,
Moscow (1960), p. 29.
4. E. P. Anan'ev, Nuclear Systems in Energetics [in Russian], Atomizdat, Moscow (1978).
5. V. N. Belous, A. I. Gromova, and V. V. Gerasimov, Nuclear Science and Technology, Re-
actor Physics and Engineering Series [in Russian], Issue 3 (3) (1978), p. 43.
6. V. N. Belous, A. I. Gromova, V. V. Gerasimov, et al., ibid., p. 51.
7. V. V. Prozorov, Inventor's ,Certificate No. 1027284, Byull. Izobret., No. 25, 105 (1983).
8. R. Biernat and R. Robins, Electrochem. Acta, 17, 1261 (1972).
9. P. A. Akol'zin, Corrosion of Metals in Steam Generators [in Russian], Leningrad (1957).
191
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
IMPLICIT METHOD OF SOLVING MASS-TRANSFER EQUATIONS
IN THE VARIABLES VELOCITY-VORTICITY
M. P. Leonchuk, Z. V. Sivak, UDC 532.54
and Yu. E. Shvetsov
In the theortical investigation of heat and mass transfer in a nuclear reactor there has
recently been steadily increasing use of the porous-body model [1-3]. The efficiency of this
approach is especially apparent in calculating the fields of the heat-carrier velocity and
temperature in geometrically complex objects consisting of several elements differing in their
hydraulic and thermophysical properties. The motion of a viscous incompressible liquid in an
anisotropic porous body is described by the continuity equation
d04710 ?0
Oxj
and the equation of motion [1]
ow?), IA7 I OP , 0
VV - = - - - VY V W
Oxi ""
Ot Oxi m p axm ? oxi
where t, m = 1, 2, 3 (summation is performed over t).
In the particular case when liquid flow in an unenclosed volume is considered with a
porosity of the medium E = 1 and there are no volume forces, i.e., Ame = 0, this system of
equations transforms to the Navier-Stokes system of equations, numerical solution of which
is associated with a series of well-known difficulties. However, if volume friction forces
predominate over viscous and inertial forces, the structure of the solution of Eqs. (1) and
(2) is considerably simplified. In the limiting case, the steady problem may be reduced to
the solution of a single quasiliner equation of parabolic type. Numerical solution of this
problem is possible, as a rule, using fewer iteration than for the Navier-Stokes problem.
However, the problem of constructing a more effective algorithm remains pressing in this case
too.
One widespread approach to solving the system of fluid-dynamic equations is to pass to
new functions: the current function ly and the vorticity w. The principal advantage of meth-
ods based on the use of these functions is that the continuity equation is automatically sat-
isfied at each step of the iterative process at internal points of the calculation region. In
a series of problems, this ensures a benefit in terms of the rate of convergence. However,
solving the problem in (IP, w) variables entails specifying boundary conditions for the vor-
ticity at a solid wall absent in the physical formulation of the problem. The rate of conver-
gence of thenumerical method is found to depend on themethod of specifyingtheboundary con-
dition for the vorticity and the accuracy of its approximation (4]. This deficiency is elim-
inated by numerical methods of solving the system of Navier-Stokes equations in the "natural"
variables velocity-pressure. In addition, in solving three-dimensional problems in the nat-
ural variables, it is required to solve fewer differential equations. Finally, they are more
simply generalized to the case of inhomogeneous calculation regions. The method of solving
the equations of the porous-body model in the variables velocity-vorticity which is outlined
below combines the advantages of both approaches. The method has a high rate of convergence
thanks to the precise satisfaction of the continuity equation at each iteration and has prac-
tically absolute stability, since it is based on the use of implicit difference approxima-
tions of the equations being solved.
In r-z geometry, after introducing the vorticity
Ou Ov
Eqs. (1) and (2) may be reduced to the form
(3)
Translated from Atomnaya gnergiya, Vol. 58, No. 3, pp. 166-170, March, 1985. Original
article submitted July 22, 1984.
192 0038-531X/85/5803-0192$09.50 0 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
dry dry
dz -1- dz
= 0*;
Ow 1 OM , duo) 02(0 \1
Ot ?r or ? dz (Arv) + v {4)7 (--.-1 ?":)
r.
ihs2 If'
The diagonal components Ar and Az of the tensor of volume frictional forces are not equal
in the general case, and depend on the velocity vector; the other components are assumed to
be zero. On the external contour r of the calculation region (R0 < r .< RI, 0 < z < H),
the radial v and axial u velocity components
vir==vr(r, z): ulr-ur(r, z) (6)
or else their derivatives are specified. The initial conditions are also specified for veloc-
ity components
(4)
(5)
/6_0==u0(r, z); vit=0==wr, z),
and then the initial conditions for w are calculated using Eq. (3).
To obtain the difference analog of the system in Eqs. (3)-(5), the
overlaid with a basic grid with integer indices i and k (i = 0, 1, ...,
and two auxiliary grids with semiinteger values of one of the indices i
(7)
calculation region is
I; k = 0, 1, K)
+ 1/2 or k t 1/2
(Fig. 1). In the general case, the steps of the basic grid over the radius Ari+1/2 and over
the height zk+1/2 depend on the coordinate. Values of the vorticity are assigned to points
of thevelocity components1 / 2it u and vik+1/2
auxiliary grid.
to the cell of the basic grid, a different form of the
of the basic grid wik, and the values
culated at points of the corresonding
? Integrating Eq. (4) with respect
continuity equation is obtained
are cal-
? 2Azh_1/2
Ui- 1/2k = 1/2 k- 2 2 (riVi k- 1/2 ? ri-ivi- 1 k-1/2)7
Ti ? Ti_
where i = 1, 2, .., I; k = 1, 2, ..., K.
The subsequent calculations demand an .expression for the axial velocity component
next point on the radius
i+1/2 k =
2Az1_1/2 ?i
2 2 (r1+1.9+1 h-112?r1v1 k-1/2)?
ri+i ?ri
(8)
at the
(9)
The superscript j denotes that the value of the given quantity is taken at the preceding itera-
tion. For the sake of simplicity, the index (j + 1) is omitted; i = 0, 1, 2, ..., I - 1;
k = 1, 2, ..., K.
The difference expression for Eq. (3) defining the vorticity
region is written in the following form, with vik+1/2 isolated:
,
vi h+1/2 V{ k- 1/2, A4 ? (un-1/2 k k)
Ar
Azh (Azh+1/2 ? Azk _ 1/2)12;
Ari = (Ar1+1/2 Ar 1/2)12,
.= 1, 2, ...,/--1; k= 1, 2, ...,/C--1.
In determining the vorticity at the boundaries of the region the first-order approxima-
tion at a halfstep from the boundary is used. For example, when z = 0
at internal
points of the
(10)
Iii+1/ 2 0 u'i - 1/2
= 0
2 (vi 112-010
(NO
Ari Azin '
1, 2, ..., 1 ? 1.
Within the framework of the method outlined, the accuracy of
boundaries of the region may be increased to second order without
of the algorithm if Eq. (11) for the vorticity is replaced by the
8v10---9Vi 1/2 ?')i 3/2 U1-1-1/2 0 ?Ili -1/2 0
(NO =
3Az112
*To simplify the calculations, e = const and v = const is assumed
the approximation at the
significant complication
expression
here and below.
193
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
__
I
If.I
_ t _
? lk
'
Zli?
(AiGle
Ve-lk- 4 1/4.1k1
/(-
?41
Fig. 1. Calculation grid.
Analogous relationsdetermine the vorticity in cells adjacent to the other boundaries.
For a difference representation of the vorticity-transfer equation, Eq. (5) is inte-
grated in the vicinity (ri_i/2 < r < ri.1.1/2; zk_1/2 < z < zki-1/2) of each internal point
over the element drdz. After calculating the integrals, a conservative difference scheme with
a near-second-order approximation with respect to the spatial variable is obtained:
wth-4, II) [tot-1 All 1 I j rik-i V
At Ari + i/2 k VI-1/2
Azh k+1/2 coik+i it- 1/2
WM ] = -- X
Ari
Ow): +1i I kij? wa
ri+1cui+1 h riwik r to) ih ? ri-toi_I k v h+1 11+11
inri+1/2 Ar_ 112r_112 1 +i_112 Azh 1 Azh+1/2 1/2 )
-I- I (Ai Viri ?A' .1
2? 1/2 12V1 k- 112} ? ?
zi+112,12i+1/2 1/2
.1/24. (12)
Here the mean velocity values are determined by linear interpolation over four adjacent
values of the corresponding velocities from the preceding step of the iteration (for exam-
ple, vi+1/2k is determined in terms of vii-ik?1/2). This means linearization of the vortic-
ity-transfer equation at each step of the iterative process. The upper value in the square
brackets is taken when the mean velocity preceding the brackets is positive and the lower
value when this mean velocity is negative.
In solving the difference system in Fqs. (8), (10), and (12), the following method of
longitudinal?transverse "fitting" is employed. In fitting along the coodinate z, the vari-
ables of the preceding layer k ? 1 are expressed in terms of the variables v and w of the
following layer k, and in fitting along the coordinate r, the variables of the precedinglayer
i ? 1 are expressed in terms of the variables u and w of the following layer i. The sequence
of calculations is outlined for the example of fitting along z for a fixed layer with respect
to the radius ri. Suppose in the k-th layer
U1_ 2 h- 1 = A(1h)V1 h - 1/2 ? B11 (13)1)(0ik
UH-1/2 k- 1 = 24(2k)Vi k -1/2 + B(21')Wik Dr; (14)
vi h_3/2 = 24(31')V i k - / 2 + /334)(0i h D(31i); (15)
toi h-I = A(4h)Vi k- 1/2 ? ?B(41')Wi k g4k), (16)
where i = 1, 2, ..., I ? 1; k = 1, 2, ..., K ? 1.
The values of the "fitting" coefficients Az, Bi, DR, (It = 1-4) are determined for the
following (k + 1)-th layer. To this end, the explicit dependence on / ui+1,2..-1 is first elim-
inated using the fitting relations in Eqs. (13) and (14). Then it is found that
194
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/1,1 : CIA-RDP10-02196R000300060003-3
-where
(17)
k= A2v1 k-112+ B2Wik -I- D2, (18)
k =1, 2, ..., K.
ff Ilzh-inri
; Bi==e;
2 2
ri?ri_i
(k)
DI.= DI +24zh_iari?
vi_th- 1/2;
2 2
ri?ri-1
242 = il(20 + 2A2k _ ii2ri B =, Le;
71+ i ? r? ; 2
D ?(k)
2 ?D 2 INzIt_inr41 j
ri2?i _ r2i Vi+1 k- 1/2.
Note that, when z = H(k = K), it should be assumed in these formulas that Azk = A
-Zk_ 1/2/2 in
accordance with the definition of the vorticity for the boundary cell.
New expressions for up. 1/2k are substituted into the equation for the vorticity and it
is solved for vik..,12:
V1 h-112 = a3v1 /1+1/2 +153(Oih d3
k=1, 2, ..., K;
(23? (A2 ? A1) ; b3
d3 ?(D1?D2)
;
(19)
Using Eq. (19), the expression for the velocities up I/2k is transformed to the form
U1_ 1/2 h =aivi 4+1/2 bi(Oih + di
k='1, 2, ...,K;
ui+112h=a2v1 4+1/2 -I- bzwih ? dz,
where
(20)
(21)
ac=ilias; 1,1=A11)3+B1; d1=Di+A1d3;
a2 ,42a2; b2==.112N-I-B2; d2=D2drit2d3.
Further, in the vorticity-transfer Eq. (12), Eq. (16) for wik_l of the preceding step is first
substituted, followed by the expression for wi_ik and
141-- 1/2k Ui-312 k V i-1 4+1/2 vi- 1 k-1/2 .
k
Ar 6.2h
ui+3/2 k?vi+112 4 vi+1 k+1/2 ?ui+1 4-1/2
(0i+t h Ari.44 Azh
deriving from Eq. (10) for the vorticity. Finally, the velocities vik_1/2, ui+1/2k are elim-
inated from the resulting equation using Eqs. (19)-(21) and it is solved for wik to give
finally the fitting relation for the vorticity in the (k + 1)-th layer:
D14+0,... h+, n(440
k+ m ,
k..1, 2, ...,1C--1.
Expressions for the coefficients in Eq. (22) may be found in [5], where the give method
is outlined in detail. The other fitting factors in the (k + 1)-th layer are determined by
substituting Eq. (22) for wik into the corresponding Eqs. (19)-(21). Then, for example, the
coefficients of the fitting relation determining ui_//2k are found to be
AT+"?a1 + biAS,h+"; /A!'" b1B(4"+";
Dr" =di 4 biA"+".
(22)
Thus, if the fitting factors 01, JJ) D" in the k-th layer are known, successive use of the
above formulas permits the calculation of /W+0Ah+0014"-0 in the (k + 1)-th layer, then in
the (k + 2)-th layer, etc. The initial values of the fitting factors when z = 0 are calcu-
lated from the corresponding boundary conditions
195
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
t
tift
of /Witt t
o ti I fittt
titttiftt t.
? trfttfttfttft
tOtttlittttg
?frttttttitttf
,,,,ottfttfttft
,,,,,offtttttfttt
? ttfttittti
? H ot 01 Hitt
A
AAt tk t tt tit t
? tOttltilltt? f
t ttt t tt t
W I 'In t.
? ..,.x11 tit tt tf'
\WWI
44""0111 ft
ft
'
A? 4,144'711/
?0,?,/ifttfttf
? oonAl, fit
A4A.40,400ttit
A"A0ifftttfttft
##,,Alftttfttftl
fff#0,,ftttttttt
444,,4tfOttfttft
ffifffttttiltt
n.n1ffftftittitt
...#fftftitttfttt
A.ffdfOttiltttt
Afif#4ftttilttft
/44,4,44,01111M
4444400ftttiti
twriftttittilt
ftltIttlt
???otttttittt
?
tftttttt
Ro ?
"
Fig. 2 Fig. 3
Fig. 2. -Velocity field in the unenclosed
cylinder with an obstacle at the inlet and
outlet (Ar = 0, Az = 0).
Fig. 3. Velocity field in the active zone
with obstacles at the cylinder inlet and
outlet (Ar ? Az >> 0).
200 400 600
Fig. 4. Establishing the so-
lution: 1) (u, v, 0 method;
2) (u, v, p) method.
B1= O; D(11) = 111? 1/ 2 0;
= 0; DV) U1-1-1/2 0;
B(31)=0; D= v,;
2 ;B(41),=0; DV )=111-1-1/2 01/2 0 , 20io
Azi/2 Ari MAz1/2 ?
At the upper boundary with z = H, the velocity is known from the boundary conditions.
The boundary value of the vorticity wik may be found from Eq. (20), taking ui_if 2k = ui-2/2K
and vik+1/2 = va according to the formula
?d1)/b1.
196
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved ForRelease2013/03/11 : CIA-RDP10-02196R000300060003-3
-0 -42 0 42 0,4, 45 48
Fig. 5. Horizontal-velocity profile in the
central vertical cross section of a cavity
with Re = 400: the continuous curve corre-
sponds to the data of [8], uniform grid
57 x 57, nonuniform grid 29 x 29 and the
data of [9], uniform grid 41 x 41; the
crosses to [10], finite-element method (FEM),
grid 15 x 15; the circles to [11], FEM, grid
51 x 51; the filled circles to [12], grid
40 x 40; triangles to the (u, v, w) method,
grid 31 x 31.
L/11
0,5
0,2
41
50 100 500 1000 Re
Fig. 6. Dependence of the vortex
height at an upstream point of
the cavity on the Reynolds num-
ber: filled circles correspond
to the experimental data of [13]
and crosses to the results of
calculation by the (u, v,
method.
After inverse fitting according to Eqs. (13)-(16), the vorticity and radial velocity
component at the i-th radius are determined, as well as the axial velocity component at the
radii i + 1/2 and i ? 1/2. This means that the velocity component u is actually calculated
twice at each internal point: first as ui+1/ 2k at the i-th radius and secondly as ui_, /2k
at the (i + 1)-th radius. All the velocity values appearing in Eq. (8) belong to the next
iteration, i.e., Eq. (8) is a purely implicit relation. Hence, after repeated calculation
of the velocity ui_1/2k, the continuity equation for the corresponding cell is solved ac-
curately. The solution of Eqs. (10) and (12) for the vorticity is iterative.
The formulas given for the fitting factors are used in the layers i = 1, 2, 3, ...,
I ? 1. For the layer i = 1 with which the calculation begins, it must be taken into account
that wi_i is calculated for the corresponding halfcell, taking account of boundary conditions
according to formulas of the type in Eq. (11) but for the boundary r = R,. For the last
fitting layer i = I ? 1, the vorticity wi+lk is determined taking account of the boundary
conditions for r = RI.
The fitting in the radialdirection is organized analogously. But in this case the
variables vi_1k_1/2, vi_
11E+1/2, Wi-lk, ui-3/2k of the preceding (i ? 1)-th layer are ex-
pressed in terms of the parameters ui_ 1/2k and wik of the next layer i. Crossed fitting is
continued until an iterative process with specified accuracy is established.
197
mmommommomm Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Numerical experiments snow tnat tne stacility or tne given metric)?, is practically dUSU-
lute. In particular, the integration step is varied over the range 10-8 5 At 5 1. The con-
vergence rate of the iterative process decreases with increase in Reynolds number. However,
the formally stable solutions are obtained with an arbitrary Reynolds number, for example, for
an ideal liquid. At sufficiently large frictional coefficients, the rate of convergence is
approximately an order of magnitude larger than for the Navier-Stokes problem. This is a
consequence of the simpler structure of flow in the presence of volume frictional forces.
Whereas when Ar = 0 and Az = 0 there are vortex zones behind the obstacle at the inlet
and in front of the obstacle at the cylinder outlet (Fig. 2), when Ar and Az are sufficiently
large (Fig. 3), the flow pattern becomes close to potential flow.
The advantage of this method in solving problems on friction in comparison with the im-
plicit methods formulated in the variables velocity-pressure [6] is obvious from Fig. 4, where
the dependence of the accuracy C = - log (uJ - e) on the number of iterations in both meth-
ods in solving the same problem for liquid flow in a cylindrical region with obstacles at the
inlet and outlet is shown. It follows from Fig. 4 that in the (u, v, 0 method the relaxation
of the perturbation introduced by the initial data occurs considerably more rapidly. This is
especially significant when high accuracy of the solution is not required. In particular,
almost an order of magnitude fewer iterations are required to obtain a solution with an error
of 0.1% in the given sample for the (u, v, 0.method.
The difference in convergence rate for the two methods becomes less considerable for
the Navier-Stokes problem. Also in this case, however, the (u, v, w) method allows a solu-
tion of specified accuracy to be obtained 2-3 times faster. The accuracy of the method is
checked in solving a series of test problems for the Navier-Stokes equations (Ar = 0, Az = 0):
flow in a tube with sudden expansion at Re = 0-200, liquid flow in a square cavity with Re =
100-1000, longitudinal flow around a cylinder and a disk with Re = 40-1000. The theoreti-
cal data are in good agreement with experimental data and the results of other authors; see
[7] for more details. The accuracy of the (u, v, w) method may be judged from a comparison of
the results of solving a typical test problem for liquid flow in a square cavity by the method
here proposed with theoretical [8-12] and experimental [13] literature data (Figs. 5 and 6).
Note, in conclusion, that the methodhere proposed may also be formulated solely in "ve-
locity" variables, without explicit use of the vorticity. It is sufficient to eliminate the
vorticity from Eq. (12) using Eq. (10) and to transform the fitting relations to the form
where the velocities / ui.f.1/20.1
and vik+3/2.
vik-1/2 being determined may be expressed in terms of vik.1.1/2
LITERATURE CITED
1. M. K. Gorchakov, V. M. Koshcheev, A. G. Kolmakov, and Yu. S. Yur'ev, Teplcfiz. Vys.
Temp., 14, No. 4, 866 (1976).
2. M. P. Leonchuk, N. S. Smirnova, and Yu. E. Shvetsov, At. Energ., 52, No. 3, 187 (1982).
3. H. Domanus et al., Nucl. Eng. Des., 62, 81 (1980).
4. P. J. Roache, Computational Fluid Dynamics, Hermosa,(1976).
5. M. P. Leonchuk, Z. V. Sivak, Yu. E. Shvetsov, Preprint FEI-1434 [in Russian], Obninsk (1983) .
6. M. P. Leonchuk and Yu. E. Shvetsov, Preprint FEI-1100 [in Russian], Obninsk (1980).
7. M. P. Leonchuk, Z. V. Sivak, and Yu. E. Shvetsov, Preprint FEI-1433 [in Russian], Obninsk
(1983).
8. K. Gkhia, V. Klignki, and Dzh. Khodzh, Raket. Tekh. Kosmon., 17, No. 3, 89-92 (1979).
9. O. R. Burggraf, in: Collection of Reviews and Translations of Foreign PeriodicalLitera-
ture, Mechanics [Russian translation], Mir, Moscow (1966), No. 6(100), pp. 51-90.
10. A. G. Daikovskii, V. I. Polezhaev, and A. I. Fedoseev, in: Numerical Methods of Con-
tinuum Mechanics [in Russian], Vol. 11, No. 1, Novosibirsk (1980), p. 37.
11. V. I. Kopchenov, A. I. Kraiko, and M. P. Levin, Zh. Vychisl. Mat. Mat. Fiz., 22, No. 6,
1457-1467 (1982).
12. S. Ozawa, J. Phys. Soc. Jpn., 38, No. 3, 889-895 (1975).
13. F. Pan and A. Acrivos, J. Fluid Mech., 28, No. 4, 643-655 (1967).
198
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
TRENDS IN THE GLOBAL SPREAD OF 1291 AND FORECASTING
THE ACCUMULATION DUE TO RELEASE FROM NUCLEAR
FUEL CYCLE FACILITIES
B. I. Styro, T. N. Nedvetskaite, UDC 551.464.6:551.510.7
and V. I. Filistovich
Research on man-made environmental pollution is a major task in current science. It
has recently been found that certain radionuclides accumulating in the environment may affect
geophysical processes [1], whose changes may affect man. These nuclides include not only the
radioactive noble gases but also 1291, whose half-life is about 10 years. This nuclide
continuously accumulates in the environment from the operations of fuel processing facilities
(FPF) throughout the world. Here we consider this accumulation and forecast the possible
increase, which provides specifications for systems for restricting the entry of 1291 into the
environment.
One assumes that the geochemical circulation of 129I follows the same laws as that for
stable 1271 [2, 3]. No allowance is made for isotopic fractionation because we lack any in-,
formation on the process.
In researching th 1271 mass balance, it was assumed that there are no additional sources
of it and there are only transitions from one sphere to another, where the fluxes should be
equal. With regard to the 1291 balance, however, there are additional sources and sinks in
each pool: the spontaneous fission of 238U [4], the formation of 1291 by the interaction of
cosmic radiation with atmospheric xenon [5], and radioactive decay.
We have introduced nine pools in examining the iodine circulation (Fig. 1). The symbols
are: Ci, the 1291 concentrations in the steady state in the individual pools, the constants
for passage from one pool to another, the constants pi for passage from one pool to all
the others, the rates of formation Qi of 1291 in the individual pools, and the decay con-
stant A. Then in accordance with the scheme of Fig. 1, we have the following system of equa-
tions for the global equilibrium distribution of 1291 in the environment:
Qa = NCI ? [131C3;
Q2 = I12C2 1112CI 1152C5;
Q3= R3C 3 ? 1113C 3C4 ?1-183C 6 ?
1183C 8 -1133C6; (1)
Q = 114C4 -1124C2 -1154C5;
Q5 [15C5 -1145C4;
Q6 = 1-16C6 -1136C3 N?76C7;
Q7 = PIC 7 ? PVC 6;
Q 8 = 118C 8 ? I148C 4;
Q9 119C 9 ? 1149C 4.
The overall transfer coefficients for the individual pools take the values
+1112 ? P13, 112 + 112i +1124,
113 - + /131 + 1136, 1-14 = + 1143 +1145 + F148 + 11467
115 + P'52 + 1154, 116 = + 1163 +11677
N-7-7 2t. 118 = +83, 11'9 -= + 143.
(2)
Translated from Atomnaya fnergiya, Vol. 58, No. 3, pp. 171-174, March, 1985. Original
article submitted May 10, 1984.
0038-531X/85/5803-0199$09.50 ? 1985 Plenum Publishing Corporation 199
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
/, 44 .10" f, 2 .10" .
yr' 2 vr.'
Atm, dyer
land,
iTe./0.18
2,310' 44101 J,S?10I? 1 8.70f
r- '
r" r 8,1.1r fri yr'
r'
Atm, over
oceans,
8,410-Eg
3
Ocean mixing
layer,
44.107 g
414r
r
6
Deep ocean
layers,
8,1. 104.8
2,2.10
yr_
4040-7
7
Oceanic
sediments,
7,J? 105g
7.10 2 I
yr I 5
5,2.10'5 IT130,13Cied,
Yri 40.70-76
SurfSurface1,1.10 3gLi
Surface
soil layer,
40.10-6
r"
1,8
Intermediate
layers in earth,
5,o70 g
2, 8 .1077
r4
1,5.104,
Yr'
H 9
in tile
layers
earth,
.9,6'1048
41.70-7
yr
Fig'. 1. Scheme for the global biogeo,77
chemical.circulation of 1291 (1-9 are
the pools).
0
b,03
102
4'
A-
112
,4 loo
1945 195
II
1955
1950 1.965 1.970 1975 1980
Year
Fig. 2. Rates of 1291 influx due to nu-
clear tests.
The values of the pij were taken as for stable iodine [2, 31. System (1) was solved
numerically, and Fig. 1 gives the results.
Here it should be borne in mind that the earth's crust contains 240 TBq of 1291 [6],
but only about 6 TBq is involved in the circulation. The man-made 1291 perturbs the sta-
tionary distribution and began to enter the environment in 1945. In [7], the irregular
fluctuations in the entry of 1291 due to nuclear tests were smoothed by a method as used here.
The influx yj in year i was converted to an influx rate q(t) in g/yr at a time t by means of
a sum of Gaussian functions: q(0 =.(1/1/27(a) Eyiexp {--(t --1M242a2)} with its maximum
in the middle of yearti. The parameter a was taken as 1/6 year, as in [7]. Figure 2 shows
the graph for this function. In the case of our value of a, the sum of Gaussian functions
in q(t) can be replaced by a Gaussian function for each year qi(t), with the assumption that
the discharge in year i does not make a substantial contribution to subsequent years.
It was further assumed that the 1291 formed by nuclear tests enters pool 10 in the
earth's stratosphere, which is not shown in Fig. 1, with a half-deposition time from this
pool of about one year. Then the 1291 enters the troposphere, with a half-deposition time
of 15 days.
200
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Aooroved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
705
to'
10?
a
7
b
jegge0",/j
777
c
6 -
7 ...
_
,
0
9 g
6
, 6
6 if
6' 85
5 OP' i
6 41 6
111????-
6
,f ( lir 5
5 OA\ .. 'a
OH
J
it
0
1
l'i\
-..
.,..-
-
V104\1\1111t. 1
: 110 i 1 i I 10
10 10
; I
10
1.90
1980
1010
195'0
1950
2020
195'0
7
1950
2010 Year
7
5
1000 2020
Fig. 3 Time course of the 1291 distributions in
the lines are those of the pools in Fig. 1): a) due to natural processes and nu-
clear tests; b, d) due to natural processes, nuclear explosions, and the operation
of FPF provided that current level is maintained for the purification coefficient
and the entry of 1291 into the environment in accordance with the first and second
models correspondingly; c, e) the same as in the previous case but on increasing
the purification coefficient in accordance with Fig. 4 for the first and second
models correspondingly.
87 /0
Year
individual
19110
I__ /0 -
020 2060
pools (the numbers on
Then the 1291 distribution in the environment can be determined by solving a system of
differential equations:
dCi
dt t I 114'2 1-1,31C 3 0 7081) 1C10 Q1;
dC2
R12C1 V2C2 IA52C5 +U 2,92/110.2C10 + Q2;
dt
d
Rift? p,C, 1.1.43C4 tt,,C6 + iC9 4- Q3;
dt.
201
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
dC4
112C2? [14C 4+ 105 Q4;
dc5 (3)
Tri =1145C4-11/2C5 + Q5;
dC6
de =1136C 8-116C 6+1-146C7+ Q6;
dC7
de = i-1037C 6? RiC7-+ Q7;
dC8 dC,
de ? 1-118'r 4 ? 115C5 + Q9; de = PVC 4-119C o + Q9;
Itio.i) C10-f q (t) -1- Q10.
dt
The initial 1291 content in each pool was taken as the amount obtained by solving (1).
The solution to (3) was obtained by the fourth-order Runge-Kutta method with a BESM-6. In
the case of the nuclear tests, the time course of the 1291 distribution in each of the pools
was as shown in Fig. 3a. It is evident that the 1291 quite rapidly reaches the earth's sur-
face and enters the ocean mixing layer, and then enters the biosphere (pool 5). It is also
evident that the 1291 contents in the atmosphere and ocean mixing layer decrease rapidly,
whereas the soil and biosphere retain the accumulated 1291 much longer, which is due to the
smaller values of the transition constants. There is a certain tendency for the 1291 con-
tents to increase in the deep ocean layers, while the levels in the oceanic sediments and in
the middle and deep layers of the earth vary only very slowly. Also, the amounts of 1291 in
the biosphere and soil exceed the natural stationary 1291 levels by more than an order of
magnitude.
To calculate the global 1291 distribution due to FPF, we solved (3) withallowance for
the rate of entry of 1291 from FPF. The calculations were performed for two extrelle cases:
the first model for discharges entering the ocean mixing layer 25 times the discharges en-
tering the atmosphere [8], while the second model has the corresponding ratio of 90 [9].
The incorporation of 1291 into the circulation is shown in parts b and d of Fig. 3 on
the assumption that the purification coefficient in future remains at the current level.
These calculations show that on entry to the atmosphere (second model), the 1291 concentra-
tion in pools 4 and 5 during the next decade will be larger by an order of magnitude or more
than for passage to the ocean mixing layer (first model). This is because 1291 spends a
long time in the deep-ocean layers. If the FPF work under these conditions, the 1291 con-
centrations in the atmosphere, ocean mixing layer, soil, and deep-ocean layers (pools 1-6)
increase exponentially. The 1291 concentration in the biosphere in the year 2000 will ex-
ceed the natural level by four or five orders of magnitude for the first and second models
correspondingly.
This raises the questions of how far the purification coefficient should be increased
at FPF to keep the changes in 1291 concentration in the environment within an order of mag-
nitude. Figure 4 indicates these recommendations. The data of [2] have been used here.
In the first case, the purification coefficient should attain 0.8-1.104 by the year 2000,
while in the second it should be larger by an order of magnitude. Figure 4 also indicates
the amounts of 1291 entering the environment if the purification alters in accordance with
the first and second models. Figure 3c (first model) and Fig. 3e (second model) show the
1291 distributions occurring with time-varying purification coefficient as obtained by solv-
202
Purification coeff.
log
?JD
lo
vs10-
a,Fig. 4. Recommended increase in
the purification coefficient
(solid line) and corresponding
ma-
course of the rate of entry of
1291 into the environment (dashed
701 line)? for the first model (a)
and the second one (b).
102
1950 2000 20,4
Year
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
ing (3). There is a minimum due to the reduced entry of 1291 from FPF in 1990 in connection
with the supposed improvement in the purification system.
These calculations show that 1291 entering the environment Ls dispersed in accordance
with the laws of iodine circulation. Therefore, to avoid accumulation in any medium or near
FPF it is necessary that this rate of entry should be less than or equal to the natural dis-
sipation rate.
In the current level of purification, the 1291 entering the environment by the year 2000
will virtually all be present in the mixing layer and deep layers of the ocean together with
the soil and biosphere. As indicated previously, the levels in the earth's biosphere will
increase by 4-5 orders of magnitude. For this reason, it is necessary to improve FPF puri-
fication plants in order that by the year 2000 the purification coefficient should attain
1.10 or 1.105 when most of the 1291 enters the ocean mixing layer or the atmosphere corre-
spondingly.
In relation to the problem of storing 1291, it should be borne in mind that it is a mi-
grating global nuclide, and the disposal of it in the oceans, as suggested in [10], may cause
considerable accumulation in other pools (in the ocean mixing layer, atmosphere, and soil)
and entry into the earth's biosphere.
LITERATURE CITED
1. B. I. Styro, D. V. Butkus, and K. K. Zemkayus, in: Atmospheric Physics, Vol. 7, Prob-
lems in Researching Atmospheric Pollution [in Russian], Mokslas, Vilnius (1981), p. 164.
D: Kocher and J. Till, Trans. Am. Nucl. Soc., 33, 1957 (1979).
3. D. Kocher, in: Environmental Migration of Long-Lived Radionuclides, IAEA, Vienna (1982),
1;.. 669.
4. E. V. Sobotovich, E. N. Bartnitskii, 0. V. Tsyn', and L. V. Kononenko, Handbook on Iso-
tope Geochemistry [in Russian], Energoizdat, Moscow (1982), p. 241.
5. V. I. Filistovich, T. N. Nedvetskaite, and V. Yu. Luyanas, in: Atmospheric Physics,
Vol. 9, Local and Global Impurities in the Atmosphere [in Russian], Mosklas, Vilnius
(1984), p. 171.
6. C. Keller, Naturwissenschaft Rundsch., 30, No. 8, 293 (1977).
7. G. Kilough, Health Phys., 38, No. 3, 269 (1980).
8. I. Ya. Vasilenko and Yu. I. Moskalev, "Biosphere contaminationwith 129I," At. Energ.,
52, No:, 3; 155-158 (1982). ,
9. J. Russel and P. Hahn, Radiol. Health Data Rep., 12, No. 4, 189 (1971).
10. "Radioiodine removal in nuclear facilities. Methods and techniques for normal and emer-
gency situations," in: Techn. Rep. Ser. No. 201, IAEA, Vienna (1980), p. 98.
203
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
BACKGROUND LIMITATIONS IN X-RAY FLUORESCENCE ANALYSIS
V. V. Berdikov, E. A. Zaitsev, UDC 543.426
and B. S. Iokhin
For the x-ray fluorescence analysis of solutions formed in the technological processes
of the nuclear fuel cycle, a method of preliminary selection was developed for the content of
heavy elements [1, 2] according to the radiation energy of the sample, by means of a cylin-
drical pyrographite Bragg reflector, located between the sample and an Si(Li) detector. This
method allows the background created by scattered perturbing radiation to be reduced. Limits
of detection 1,0.15 ppm were achieved for uranium and neighboring elements in solution with
quasimonochromatic excitation of a transmission x-ray tube with a 25-W power; the loading of
the spectrometric channel for this amounted toless than 300 sec".
This paper reports on the attempts to reduce the limits of detection, due to the use of
a powerful tube for excitation. Values were obtained for the limits of detection of 1,10-8.
In addition to the background components discussedearlier [1], two further effects were
found to be significant in the background generation: bremsstrahlung of photoelectrons in
the sample and Compton scattering by the bound electrons in it.
Experimental Facility. The layout of the facility is shown in Fig. 1. The scattering
chamber is similar to that which was described in detailed earlier [1, 3]. The maximum of
the transmission function of the scattering chamber (Fig. 2) is tuned to an energy of 14.0
keV for the optimum recording of the La-lines of Th, U, Np, and Pu. Excitation is provided
by a BKhV-7 x-ray tube (50 kV, 70 mA) with a cylindrical Pd-anode and with water cooling.
The average angle 00 between the primary and secondary beams in the facility amounts to 90?
or 113?. In the latter case (see Fig. 1), the average distance anode-sample is equal to
36 mm. An anode of Pd instead of Ag [1] was chosen because of the lower transmission effi-
ciency of scattered Ka radiation of the anode through the chamber in the second order of re-
flection. In order to record the fluorescent radiation, an Si(Li) detector with an area of
25 mm2 and with a resolution of 300 eV (at the ULa 13.6-keV line) used. In orderto reduce
the detector background in the spectrometric channel, a discriminator is introduced with re-
spect to the front of the pulse rise (DFR) which prohibits recording if the duration of the
leading front of the pulse with preamplifier exceeds 150 nsec. It was shown in [4] that the
DFR provides a sixfold reduction of the steady detector "tail" of the photopeak, without loss
in the counting rate of the peak.
Limits of Detection. The measurements were conducted with aqueous solutions containing
uranium to the amount of a few ppm. The limit of detection was determined as the mass frac-
tion corresponding to the area of the peak p = 233.02, where p and b correspond to the time
of measurement of 1 h. The background b was measured on a pure sample (cell with water) in
an energy window with a width of 2.6 x (PShPV of the ULa peak).
Just as in [1], the curves of the ULa count rate, the ratios of peak/background and the
limit of detection versus the thickness of the palladium filter (f) and the diameter of the
inlet collimator of the chamber (d) were plotted. The main part of the backgrond comprises
the residual bremsstrahlung of the tube. Its contribution becomes negligible with f = 350 pm
(see Fig. 2). But in this case, because of the large loss in the count rate, the limit of
detection increases by a factor of two. Losses in intensity in the general case can be com-
pensated with a more powerful excitation source (a tube with a rotating anode with a power of
'?,105 W or synchrotron radiation).
Four Components of the Background above the Analytical Peak. The data givenhereabout
the background were obtained with the following conditions: tube operating regime 40 kV, 50
mA; f = 350 pm, d = 6 mm, 00 = 90* (unless otherwise stated). The total background below the
ULa peak amounts to B = 1.8 sec". The contribution of the residual bremsstrahlung of the
tube (Bt) in this case is estimated from the value of Bt with filtration f = 200 pm by multi-
Translated from Atomnaya fnergiya, Vol. 58, No. 3, pp. 174-178, March, 1985. Original
article submitted May 22, 1984.
204 0038-531X/85/5803-0204$09.50 ID 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
H14
Fig. 1. Diagram of the experimental facility:
1) Si(Li) detector; 2) screen (W); 3) scat-
tering chamber; 4) collimator (W); 5) cell; 6)
Pd-filter; 7) cylindrical Pd-anode; 8) X-ray
tube; 9) cylindrical pyrographite Bragg re-
flector; 10) preamplifier; 12) analog?digital
converter (ADC); 14) minicomputer.
100 200 250 000 050
Channel number
+00
Fig. 2. Spectrum obtained during measurement
of a uranium solution (Cu = 6.6 ppm) in the
case of intense filtration of the exciting
beam (f = 350 pm); the time of collection
600 sec. The dashed line is the transmission
function of the scattering chamber (only the
first order of reflection is shown).
plying by the factor exp(--ppAx), which gives Bt = 0.01 sec-I. Another component of the back-
ground (Bx), related with the residual x-factor of the detector, is determined by the part of
the spectrum with almost uniform background (in the 10-keV range): Bx = 0.3 sec-I. Thus,
we obtain Bx + Bt 90?. Moreover, Oeff can vary with time. This effect is due to the nonuniform and,
probably, unstable distribution of the electron beam over the cylindrical surface of the tube
anode.
(9)
The calculated and measured background ratios are given in Table 1 for an aqueous solu-
tion of uranium (Cu = 1 ppm). Ratios of B/Ju from 1.2 to 1.6 were observed for the total
background (the relative statistical errors did not exceed 8%). These variations can be ex-
plained by the above-mentioned effect. The calculated Bc/Ju ratios are given for two values
of Oeff: Oeff = 105', corresponding to a uniform distribution of the electron beam, and
eeff = 115? illustrates the increase of Bc for a small increase of Oeff. Taking account of
the indeterminacy of certain parameters and constants used in the calculation (wULIII'eff'
etc.), it can be concluded that the agreement between the calculated and experimental data
in Table 1 is satisfactory. In order to verify this, additional experiments were carried
out. Firstly, the increase of By/Ju was measured for rotation of the tube axis, shown in
Fig. 1 (00 = 113'). Ratios of By/Ju from 1.6 to 2.3 were observed, i.e., the average in-
crement amounted to 0.75 (expected was 0.7).
A second series of measurements was carried out with solutions differing strongly from
water with respect to macrocomposition. It can be seen from formulas (2) and (8) that the
background components B and He depend on the effective Z number of the sample. The contri-
butions to Bc are additive for the different elements in the sample, but when calculating
B averaging must be carried out separately:
B (T z) (Z),
(10)
as the processes of photoelectric absorption and bremsstrahlung generation are independent.
The results of the measurements, and also the calculated values for solutions containing
large amounts of Cs, Fe, and Co (and several ppm of U), are given in Table 2. The tendency
to increase of By/Ju with increase of Z is confirmed. The discrepancies between calcula-
tion and experiment probably can be explained by the rough assumptions in the method of mo-
mentum approximation used for the calculation of B.
Thus, the four mechanisms of background generation considered apparently are sufficient
for explaining the background in the noncrystal version with quasimonochromatic excitation.
The components Bp and Ec are determined by processes in the sample itself, and therefore im-
pose a limitation on the peak/background ratio which can be achieved for given mtrix of a
"thick" sample. The component Bc, in principle, can be reduced either by means of polarized
beams for excitation (but this is associated with loss of intensity by three to four orders)
or by means of a reduction of the angle of take-off. However, the component Be depends weakly
on 0 and is not related with polarization. Consequently, the limits of detection in reality
can be improved only by an increase of the intensity of the exciting beam. Values on the
order of 2.10-8 can be achieved, obviously, for the analysis of heavy elements in a light ma-
trix, if a tube with a power of '?,108 W is used for excitation, with a rotating anode and with
an anode?sample distance at 30-40 mm.
Thus, the method of preliminary selection with respect to the energy of the emission
from the sample ensures the highest peak/background ratio in the case of noncrystal x-ray
fluorescence analysis of thick samples. These maximally attainable ratios are determined by
processes in the sample itself, and can be estimated by the method described above. With
the use for excitation of commercially manufactured x-ray tubes with a power of a few kW, the
heavy elements in light materials with a content on the order of 10-8 can be analyzed. It
208
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
may be supposed thatthere will be a similar situation in the case of noncrystal analysis of
elements with average and, possibly, low Z number and also in the crystal-diffraction ver-
sion of x-ray fluorescence analysis.
LITERATURE CITED
1. V. Berdikov, 0. Grigorlev, and B. Iokhin, Nucl. Instrum. Methods, 155, 313 (1978).
2. V. Berdikov, O. Grigoreev, and B. Iokhin, J. Radioanal. Chem., 68, 181 (1982).
3. V. Berdikov, O. Grigoriev, and B. Iokhin, J. Radioanal. Chem., 58, 123 (1980).
4. V. V. Berdikov, E. A. Zaitsev, B. S. Iokhin, Preprint of theV. G. Khlopin Radium Insti-
tute, RI-166 [in Russian], Leningrad (1983).
5. F. Goulding and J. Jaklevic, Nucl. Instrum. Methods, 142, 323 (1977).
6. A. Compton and S. Alison, X-Ray Beams, Theory and Experiment [Russian translation],
Gostekhizdat, Leningrad?Moscow (1941).
7. P. Eizenberger and P. Platzman, Phys. Rev., A2, 415 (1970).
8. V. A. Bushuev and R. N. Kuzimin, Usp. Fiz. Nauk, 122, 81 (1977).
METHOD OF INVESTIGATION OF y-RAY CASCADES FROM THE MULTIPLICITY
SPECTRUM AND LOW-ENERGY y-TRANSITIONS
B. V. Danilin, B. V. Efimov,
G. V. Muradyan, F. N. Belyaev,
and V. P. Bolotskii
UDC 539.17 + 539.122
The study of 1-ray cascades that arise during the resonance capture of neutrons is of
great interest for the investigation of the properties of nuclear levels. If the cascade
does not pass through an isomeric state, it can be considered as a process that distinguishes
a certain generality of properties of the nuclear levels through which it passes. The study
of a large number of neutron resonances, therefore, makes it possible to compare their quan-
tum characteristics with different types of 1-ray cascades. For a complete examination of a
1-ray cascade it is necessary to establish its passage throughall the intermediate levels.
The solution of this problem in the general case involves a large number of technical diffi-
culties. It thus becomes necessary to use methods of investigation that give only partial
information.
The principal feature of cascades in an (n, 1) reaction is a considerable change in its
nature on passing from the neutron-capturing state to the ground state. The density of the
nuclear levels drops and their structure becomes simpler in the process. As the cascade begins
there area large number of ways in which it can proceed while toward the end it is contracted
abruptly. This allows the cascade to be divided arbitrarily into two stages, initial and
final. In thefirst approximation, in the initial stage a 1-ray cascade is characterized by
the number of 1-ray quanta emitted (their multiplicity) and their average energy. The spe-
cific levels through which the cascade passes are less significant. It is more important
to know in how many stages the nucleus released the excitation energy and changed its moment
and parity. The range of levels of thefinal stage can be chosen so that when a cascade enters
it the further fate of the cascade can already be predicted in the main. Thus, the multiplic-
ity of 1-ray quanta in the initial stage and the level from which the final stage begins can
characterize the cascade.
For the experimental execution of the program it was natural to use multisectional 41T-
detectors, based on NaI crystals, which are applied in the study of (n, 1) and (n, 0 reac-
tions [1]. They can be used directly to study the initial stage of the cascade. In our pro-
gram such a detector had to be supplemented withone more, making it possible to establish
the final stage. From the methodological point of view the final stage can be isolated
easily if it contains 1-ray quanta of lower energy than the first stage does. In this case
we can use a thin detector that can effectively detect the low-energy 1-ray quanta of the
final stage and freely transmit the 1-ray quanta of the initial stage. This treatment is
applicable to nuclei that have intense low-energy transitions at the end of the cascade. A
Translated from Atomnaya Energiya, Vol. 58, No. 3, pp. 178-183, March, 1985. Original
article submitted March 16, 1984.
0038-531X/85/5803-0209$09.50 ? 1985 Plenum Publishing Corporation 209
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
?
B 7", 2"
1 ,r-Tn-h 1 rrr -TIT111*- - yrr- 1 :III
11 III it 11 11
4 1 1 /11 111 11
III, !Ii? 1 1 111 111
11 I
I /11 1 1 111 111
111 111 11 HII
1 11 111 1111 II II '
P III I
ci
II III
i III 4
tl It41 ..Iti.11 ..f4I 4_ toivr", ,0 _ 11...JI.1__I itt. +.
1 1
1 1111111111111ilirillal? 1
H
H
I
11
III I 1'37" H I -
1 ik'l rl III II
1111111111111121111111111111111111 I
imursorirwixitimummy Immo!!!
21
1"C,d
a b c
Fig. 1. Classification of y-ray cascades on the
example of 158Gd compound-nuclei. Cascades that
include levels of the rotational band of the ground
state (I) pass simultaneously through a series of
collective excitations (y-vibrational, Kir ? 0+,
etc.). Cascades that do not include the rota-
tional band of the ground state (II) most prob-
ably bypass these bands as well. On the right
(a, b, c) we show the classification of y-ray
cascades of our experiment. III denotes the
boundary of the region of known levels.
Fig. 2. Detector arrangement: 1)
boron polyethylene; 2) lead; 3) speci-
men; 4) detector of low-energy y-ray
quanta; 5) slit collimator.
typical example of such transitions is that of intense E2 transitions in the fundamental 4+ ?
2+_ 0+ rotational band for even-even deformed nuclei (Fig. 1). Most y-transitions from the
vibrational and other collective bands that lie in the region Ex = 0.5-2 MeV pass through
these levels. Detection of 4+ ? 2+ ? 0+ transitions with an energy of 70-200 keV will de-
note passage of the cascade through these bands and the absence of these transitions will in-
dicate with a considerable degree of probability that, the cascade had bypassed the collec-
tive bands. The compound nuclei 156GaA,
158Gd, 62Dy, "Dy, 168Er, 172yb, 174yb, 178Hf,
180Hf, , 184"wand "'Os are suitable for study by the indicated method and are formed in an
(n, y) reaction.
General Scheme of the Experiment. In the experiment y-ray cascades in an (n, y) reac-
tion are studied on the basis of the number of y-ray transitions and the characteristic of
the passage of the cascade through chosen levels in its final stage,usingthe time-of-flight
technique. The Fakel linear electron accelerator serves as a pulsed source of neutrons.
The path length is 45 m and the time resolution is 2.2 nsec/m.
The setup consists of the following main elements:
210
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
0,5 Epts,46V
Fig. 3. Efficiency of detec-
tion of 1-ray quanta (with
discrimination of the total
energy) in the detector for
low-energy 1-ray quanta, mea-
sured with the aid of standard
1-ray sources: 1) geometric
efficiency; 2) 1-ray transi-
tions measured in 1560d.
a 12-section 1-ray detector based on Nal crystals, dubbed "Romashka";
a spectrometric detector of low-energy 1-ray quanta, with a high detection efficiency
for an energy of up to 200 keV;
electronic equipment to receive signals from the detectors and carry out the preliminary
processing of the signals prior to transmission to a computer;
an SM-4 computer which sorts and stores the data input from the detector system.
For each detected (n, y) reaction event the computer records the neutron time of flight
T, the multiplicity K of coincidences onsignalsofy-rayquantain the "Romashka" detector, as
well as information obtained from the spectrometric detector about the detection of 1-ray
quanta in the final stage of the cascade, viz., the amplitude characteristic A. From these
data for cascades with a specified type of end we can get the relative intensity (per neutron
capture) and the spectrum of multiplicity of the emitted 1-ray quanta. These data form an
ensemble over the neutron resonances studied.
Detector Arrangement and Its Characteristics. The detector arrangement in the operating
position on a neutron beam is shown in Fig. 2. The design and main properties of the Romashka
detector were described in [2]. The twelve sections of the detector are scanned by an FEU-110
photomultiplier. During traditional use the two blocks are in tight contact with each other
and the neutron beam passes along their axis. In our case, we changed the geometry so as to
place a spectrometric detector of low-energy 1-ray quanta in the internal cavity. The blocks
were moved apart by 2.5 cm and the neutral beam was passed through the slit so formed. This
resulted in a loss of efficiency by the detector, viz., its geometric efficiency de-
creased from 0.96 to 0.87. The probability of detection of 1-ray quanta with an energy of
%1.2 MeV lay within the limits 0.82-0.85. It was determined by measurement of the complete
spectrum of "Co quanta, carried out for the total signal from all 12 sections.
The spectrometric detector of low-energy 1-ray quanta consists of two scintillation
blocks with NaI(T1) crystals of diameter 63 mm and height 20 mm and an FEU-110 photomulti-
plier. On the specimen side the crystals are covered with a thin layer of MgO and an alu-
minum foil of thickness 0.1 mm. The specimen is placed between the scintillation blocks.
Its design ensures a yield of low-energy y rays and allows a few grams of the substance to
be used. The size of the crystals was chosen so that 1-ray quanta with an energy of less
than 200 keV would be detected with a high efficiency while high-energy quanta from the cas-
cade, which should pass freely through the detector and be detected in Romashka, would be
detected with a low efficiency. On the basis of measurements with calibrated sources of
1-ray quanta we obtained the dependence of the detector efficiency on Ey for total absorption
of the energy of they-ray quantum (Fig. 3). The efficiency was 36 and 46%, respectively, for
1-ray quanta corresponding to 44. ? 24 and 24 ? 04 transitions in 1560d.
The spectrometric characteristics of the detector of low-energy 1-ray quanta are given
in Fig. 4 (the spectra shown were measured with the aid of several standard 1-ray sources).
The resolution of the detector varies from 30 to 15% in the range from 60 to 280 keV. Such
a resolution is sufficient, e.g., for the study of 44 ? 24 and 24 ? 04 transitions in the
fundamental rotational bands of '56,158Gd.
211
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
2'
- 2
a
100
200
E keV
300
Fig. 4. Spectra of standard y-ray
sources, obtained on the detector of low-
energy y-ray quanta: a) 24IAm, resolu-
tion 31.3%; b) 57Co, resolution 20.5%;
c) 139Ce, resolution 19.6%; d) 203Hg,
resolution 15%; 1) x-ray peak; 2) escape
peak.
500
400
a)
300
0= 200
100
50 100 150
Analyzer channels
Fig. 5. Spectra obtained on the detector
of low-energy y-ray quanta for the 155Gd
(n, y) reaction (---) and 157Gd (n, y) re-
action (---). The columns beneath the
peaks indicate the calculated intensities
of the y-ray lines.
In the energy range up to 160 keV the "escape" peak, which is a satellite to the main
peak and appears in 24IAm and 57Co spectra, is of major importance. This peak is connected
with the escape, from the surface layer of the Nal crystal, of an x-ray quantum when the
K-shell, which is ionized by the y-ray quanta under study, is occupied by L electrons.
Figure 5 shows the y-ray spectrum in the energy range up to 300 MeV measured for 155Gd
(n, y) and 157Gd (n, y) reactions in coincidence with the detector Romashka. These spectra
are characterized by a peak at 43.3 keV caused by the x-ray quanta that are formed as a re-
sult of the internal conversion for the 4+ ? ? 0+ transitions. The internal conversion
coefficient for the 4+ ? 2+ transition is 15-20% while for the 2+ ? 0+ transition it is 60-
212
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
1D12
Fig. 6. Schematic of electronics.,
70%. It must be pointed out that the ratio of the areas of the peaks, determined by subtract-
ing the smoothed base beneath them, in the spectra in Fig. 5 coincides with the estimates
obtained with the aid of the known intensities of the 1-ray transitions 13], the detection
efficiency, the internal conversion coefficients [4], and the probability of the escape of
1-ray quanta from the specimens. The bases beneath the peaks are caused by the Compton
scattering of high-energy 1-ray quanta from the capture of neutrons in structural materials.
Experiments and estimates showed that the main contribution to the base (1.->-50%) is made by
the first component. The contributions of the other components is smaller and depends on
the specific conditions.
In order to select the cascades that pass through the separate lower-lying states of the
nucleus and to suppress the background of the (n, 1) reaction events studied we made the se-
lection on the basis of the following criteria:
1) the existence of a coincidence between the signals in Romashka and in the detector
of low-energy 1-ray quanta;
2) discrimination of an energy Ey 60 keV in one section of the detector Romashka;
3) discrimination, in all the sections of Romashka, of a totalenergy Ez above the thresh-
old established within the limits 0.5-1.5 MeV;
4) correspondence between the total amplitude (from both scintillation blocks) from the
detector of low-energy 1-ray quanta and the energy of the distinguished lower transitions.
The existence of coincidences between the two detectors is the main factor in the sup-
pression of the background in the arrangement. Because a low threshold ET was used the co-
incidences made it possible to increase the detection efficiency and also to do without the
shielding usually employed to absorb the neutrons scattered by the specimen. The influ-
ence of the coincidences leads to a sharp reduction of the background to about 1.5 MeV in the
region of Ey.
Beam-Collimation System and Detector Shielding. The collimation system ensures that
the beam from the entire area of the moderator is convergedto an 8 x 1-cm cross section in
the region of the specimen. This is accomplished by the application of four collimators in
the evacuated tube of the neutron guide and regulated-slit collimator set up in front of the
detector Romashka. The four collimators are filled with boric acid, boron carbide, and iron
shot. The regulated-slit collimator is made of thin-walled steel boxes filled with boron
carbide.
Lead "shadow" shielding of diameter 50 mm and length 400 mm, set up in front of the tar-
get of the accelerator, protects the detector from the 1-ray quanta that are formed in the
uranium target of the accelerator.
A boron carbide filter, which effectively absorbs neutrons of less than 2 eV, is used to
eliminate the influence of "recycled" neutrons.
LDeclassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
213
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
ri
20
15
?
0
a
2
11
22
_112
12222
_22221
1,22,22,
08 1,0 1,2R 0,7 0,9 1,1 1,3 R
Fig. 7. Resonance distribution of in-
tensities of cascades passing through
the 2+ state (a) and the 4+ state (b).
The values of the spins 1 and 2 for the
resonances in which they were determined
are indicated and the relative values of
R are normalized so that their average
is 1.
Electronics. The schematic of the electronics is shown in Fig. 6. It ensures that the
conditions for the detection of (n, y) reaction events are satisfied.
Signals from the sections of Romashka are fed into integral discriminators ID i (i = 1,
2, 3, ..., 12) and simultaneously to a linear adder Al. The operation thresholds of the dis-
criminators are set at the same level, corresponding to Ey 6O keV. The amplitudes of the
signals at the inputs of adder Al are also set at one level with the aid of regulators in-
tegrated into them. Pulses from the output of adder Al travel to an integral discrimina-
tor ID on which a threshold EE is set. The pulses thus generated serve as control pulses
for a number of circuit elements.
The values of the coincidence multiplicity in Romashka are generated by a circuit called
a coincidence multiplicity encoder (CME). The same circuit also generates (for single sig-
nals) the codes of the numbers of thesections in Romashaka that are used to monitor the op-
eration of the detector. Signals are fed into the encoder from the discriminators ID. The
encoder is triggered by control pulses from the ID. The coincidence multiplicity or sec-
tion number codes enter the computer input.
Pulses from the detector of low-energy y-ray quanta enter the circuit of the linear
adder A2. The addition of signals from the scintillation blocks of the detector lead to a
loss of information about the place of detection of y-ray quanta and about their number but
does make it possible to establish the arrival of a cascade at the 4+ or 2+ level of the
fundamental rotational band. The signals are selected according to amplitude by three dif-
ferential discriminators DD that are designed for the range of amplitudes of pulses from the
y-ray transitions under study and the range of the background for higher energies. The dif-
ferential discriminators operate in coincidence with the control signals from the discrim-
inator ID. After passing through the shaper S2 the signals from the differential discrim-
inators enter the computer as an amplitude attribute A.
In order to reduce the consequences from the initial burst of y-ray quanta in the ac-
celerator target all the amplification channels and the scintillation blocks of the detector
of low-energy -'-ray quanta are blocked for the duration of the burst (inhibit pulses IP in
the schematic of Fig. 6).
214
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
0,3
1 2 1 5 6 /
Coincidence multiplicity
Fig. 8.. Coincidence multi-
plicity spectra, averaged
over the resonances, for the
155Gd (n, y) reaction.
Program for Data Acquisition and Recording on an SM-4 Computer. A stream of events of
different types passes through theSM-4 computer during the experiment. The tasks of the pro-
gram is to isolate the necessary events and to sort them and record them in the computer
memory.
The code of an event includes the time of flight T of the neutron, the amplitude at-
tribute A, and the multiplicity K of coincidences of pulses in Romashka. The maximum number
of channels in which encoding occurs is 16,384 for T, up to 5 for A, and up to 12 for K. The
necessarymemorycapacity thus comes to 960K, which is much larger than the internal memory
of the SM-4 computer. This was decreased by reducing the 16,384 time channels to 256 time
channels, correspnding to selected neutron resonances. The range of multiplicities of coin-
cidences was also reduced to eight (seven values of the multiplicity of coincidences and one
value corresponding to the total effect for multiplicities of 8 to 12). This reduction was
subtantiated by the fact that the effects for K ;?, 7 were already small. As a result the ne-
cessary capacity of the internal memory was reduced to 16K. The conditions for the selection
of events thus were: 16,384 ;% T > 0, 5 -..;= A > 0, and 12 K > 0. Events that did not sat-
isfy these conditions were discarded.
The complete spectrum consists of regions that correspond to different A, each of which
contains eight subspectra that correspond to different K. A 256-channel time spectrum is
contained in each subspectrum. A control time spectrum 4096 channels long, located in the
most informative region of the neutron flight time, is also formed.
After the experiment the information is rewritten onto magnetic tape for subsequent pro-
cessing on another computer.
Study of y-Ray Cascades of 155Gd Neutron Resonances. The capabilities of the method
were tested during the study of y-ray cascades on neutron resonances of the '"Gd (n, y) re-
action [5]. Intense E2 transitions between 4+, 24". and 0+ levels in the fundamental rota-
tional band served as the y-ray transitions by which the y-ray cascades under study were dis-
tinguished. Results were obtained for 64 neutron resonances in the energy range up to 220
eV. The experimental data made it possible to obtain the following information for each of
the resonances studied: intensity of the y-ray cascades passing through 4+ and 2+ states
(in relative numbers of y-ray cascades per neutron capture) and coincidence multiplicity
spectra. The intensity I (4+) of the y-ray cascades formed two groups, the average values
for which differed by a factor of 1.3. At the same time the intensities I (2+) grouped
around one average value (Fig. 7).
The measured coincidence multiplicity spectra gave the following picture. Their changes
from resonance to resonance turned out to be small and did not reveal a tendency toward group-
ing. Figure 8 presents the experimental spectra averaged over all the resonances studied for
cascades that passed through the 2+ state (11) and the 4+ state (A). The average values of
the numbers of y-ray quanta in the first stage of a cascade can be estimated to be close to
three.
The experimental data are consistent with the results of computer simulation (by the
Monte Carlo method) of cascades in the 155Gd (n, y) reaction. The calculations were per-
215
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
formed on a model based on generally accepted assumptions [6-10]. The calculated intensities
I (4+) formed two separate groups, corresponding to resonance spins of 1- and 2- with aver-
age values in a ratio of 1.46, which is in agreement with the experiment. The calculated
values of I (2+) also formed two groups for two spin systems of resonances but with average
values in a ratio of 1.05. For this value of the ratio the experimental fluctuations can
easily lead to mixing of the two groups. Comparison of our data with the known values of
the spins [11] indicates that for 16 of the 23 resonances the observed grouping of intens-
ities of cascades can be attributed to the spin dependence. For the other seven resonances
there is a distinct deviation, whose cause is not yet clear.
The example of measurements described here indicates that the method developed for the
study of y-ray cascades can yield interesting physical results.
In conclusion, the authors wish to thank V. F. Gerasimov and A. N. Pastukhov for col-
laboration and assistance in the automation of the experiments.
LITERATURE CITED
1. G. V. Muradyan, At. Energ., 59, No. 6, 394 (1981).
2. Yu V. Adamchuk et al., in: Neutron Physics [in Russian], Part 3, TsNII-atominforma,
Moscow (1977), p. 113.
3. Nuclear Data Tables, A5, No. 1, 162 (1968).
4. Atomic Data and Nuclear Data Tables, 21, Nos. 2-3 (1978).
5. V. V. Danilin et al., Neutron Physics [in Russian], Part 3, TsNII-atominforma, Moscow
(1983), p. 25.
6. W. Ponitz, Z. Physik, 197, 262 (1966).
7. D. Sperber, Nucl. Phys., A90, 665 (1967).
8. C.Coceva et al., Nucl. Phys., A117, 586 (1968).
9. R. Clark and D. Gill, Nucl. Phys., A213, 349 (1974).
10. E. Nerdy et al., Nucl. Phys., A237, 419 (1975).
11. Neutron Cross Sections, BNL-325, Vol. 1 (4th ed.) (1981).
RADIATIVE CAPTURE CROSS SECTION OF FAST NEUTRONS BY 167AU,
236U AND 237Np NUCLEI
A. N. Davletshin, A. 0. Tipunkov, UDC 539.125.5
S. V. Tikhonov, and V. A. Tolstikov
Introduction. The necessity for investigating the radiative capture reactions of fast
neutrons, studied by us, is determined mainly by the requirements of nucler power generation
based on fast reactors. In the buildup chains of 232U, 236PU, and 238Pu, a knowledge of the
amount of which is important for the conditions of reprocessing the recycled fuel of fast
reactors, an,y of fast neutrons for 236U and 237Np plays an important role. The require-
ments on the accuracy of the estimated values of these cross sections are given in Table 1.
Obviously, it should be assumed that information about the errors of the estimated
values of these cross sections is not sufficiently accurate, since the estimates are made on
the results of one or two experimental works, the data of which do not agree between them-
selves.
233U. In the range 0.3-3.0 MeV, the data of [1,. 2] obtained by the activation method
gave poor agreement between themselves. For En < 20 keV, there are the data of [3], obtained
by the time of flight method. Finally, work was published recently [41, carried out by the
method of moderation time in lead, the results of which relate to the range En < 50 keV.
237Np. The energy range >0.2 MeV was investigated in [5, 6], the results of which dis-
agree by 20-250%. For En < 0.2 MeV, data of unpublished papers by M. Hofman (1971) and P.
Weston (1979), differing by a factor of 2 approximately, are given in graphical form in [7].
Translated from Atomnaya gnergiya, Vol. 58, No. 3, pp. 183-188, March, 1985. Original
article submitted June 18, 1984.
216 0038-531X/85/5803-0216$09.50 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
TABLE 1. Required and Achieved Errors in
the Estimated Values of the Radiative Cap-
ture Cross Sections
Error, ID
Nuclide
Energy
range,
re-
at-
Application
keyquired
tamed
197Au
200-500
2
6,1
Nuclear
500-1000
2
4,1
standard
1000-2500
2
20
299U
500-5000
4
40
Fuel
cycle
znpip
500-5000
10
40
Fuel
cycle
This brief review shows that at the present time there is not a sufficient number of
published results for obtaining reliable estimated data about the radiative capture cross
sections of neutrons by 2360 and 237Np. An experimental estimate of the errors of the one-
group radiative capture cross section of 236U and 237Np by averaging over a fast reactor
spectrum amounts to ?40% [8].
The ono, cross section of 197Au is used as a nuclear standard in measurements of the
neutron cross sections of other nuclei. For En > 0.1 MeV the cross section obtained in ex-
periments with moderate resolution depends quite smoothly on En and is known with satisfac-
tory accuracy, and therefore its measurement is a good verification of the procedure used.
On the other hand, the errors of the estimated values of this cross section [9] are con-
siderably greater than rquired. Moreover, analysis shows that data about the errors must be
assumed to be insufficiently substantiated and, consequently, additional information about
alio, (En) for 197Au will prove to be useful. These circumstances also have led to the ap-
pearance of the present paper.
Measurement Procedure. The cross sections of the reactions 236U (n, y) 237U and 237Np
(n, y)238Np are measured by the activation method. The experiment was conducted in such a
way that during the irradiation of the uranium (or neptunium) sample the neutron flux was
measured simultaneously by the reactions I97AU (n, y)198Au (disk sample) and 'H (n, n)11.1
(proportional counter). It is clear that in this experiment there existed the possibility
of determining the ono, cross section for 197Au relative to the an,p cross section. The ac-
tivity of the irradiated sample was measured by the accompanying y-radiation in a Ge(Li)
detector.
The radiative neutron capture cross section ono, measured relative to the a n,p cross
section, was determined from the relation
(E n)
Ny (X, 1) NeGe o, IP n1? (1)
Crn, v s Gs n P
Here En is the averge energy of tne irradiating neutrons; Nx, number of events recorded
by the Ge(Li) detector; f(A, t), a factor taking account of the time of irradiation of the
sample, the measurement of the induced activity and the decay constant [11]; Ay, a correc-
tion for the activity by scattered neutrons; n, recording efficiency by the Ge(Li) .detector
of the corresponding y-quanta; Nin, number of interactions in the proportional counter dur-
ing irradiation of the sample [10]; N and G, number of nuclei and the geometric factors for
the counter and sample; an,p (En), elastic scattering cross section of the neutrons by pro-
tons [9].
The geometric factors for the counterand sample have identical form:
G ? Na (En)?
(2)
In this expression, v is the absolute efficiency of the corresponding detector for the case
of a disk isotropic source of neutrons; a (En) = an,p (En) [an,y (En)] for the counter (sam-
ple), and their values are taken from any estimate. In both cases the values of v were cal-
culated by the Monte Carlo method for a disk isotropic neutron source and a cylindrical uni-
form detector, located coaxially at a certain distance from one another.
217
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
48
41
200 00 600 800 Ell, keV
Fig. 1. Dependence of the cor-
rection Ay on the neutron energy
for samples of U308 (1), Au (2)
and Np02 (3)
The radiative neutron capture cross sections an,x measured relative to the '''Au ano,
cross section were determined from the relation
i
e;, v (Es,) [N v NA v f 1 j [N v Nily1 t 1 stx iTist a;Sit, y (.8, n) , (3)
I
I
where the suffix x refers to the sample being investigated, and the suffix at to the standard
(sample of 197Au); the values of an y?(En) are taken from [9] and are averaged over the energy
range of the irradiating neutrons (0-100 keV). The other symbols have the same meaning as in
expression (1).
Irradiation of Samples. Activity Measurement. Irradiation of the samples was conducted
on the KG-2.5 accelerator, using the T (p, n) 'He and 'Li (p, n) 'Be reactions. The target
was water-cooled. The sample under investigation and the standard were positioned close to -
one another at a distance of 4 cm from the target in a cadmium container. The samples of
1J308 and Np02 powder were packed into stainless-steel containers. The neutron flux density
at the center of the samples amounted to (4-8).10' cm-2.sec-', and the mass of the gold,
uranium, and neptunium samples was 1 g, 1 g and 0.57 g, respectively.
A cylindrical proportional counter [12], just like the samples, was located coaxially
with the accelerator proton beam. The front end of the counter was located at a distance of
70 cm from the target (neutron source). The counter housing was made of stainless steel
and the end sections had the form of hemispheres. The internal volume was equal to 180.5
cm3, the filling was pure hydrogen and the gas pressure was 1.235.10 Pa. During irradia-
tion (12-20 h), the area of the recoil proton spectrum amounted to (2-4).10' pulses. The
number of interactions of neutrons with protons was determined from the relation [10]:
N
Ar (x)
ill--eGOTdAcW (4)
Here N (x) is the area of the measured spectrum of the recoil protons with threshold
x = Ep/En, where Ep is the energy of the recoil protons; e (x), corresponding area of the
normalized recoil proton spectrum, calculated by the Monte Carlo method; Td, correction for
the "dead" time of the spectrometric channel; AE (x), correction to the recoil proton spec-
trum for the effect of scattered neutrons. This correction is measured experimentally and
its value varies appreciably, depending on the value of x; in the range x = 0.2-1.0, the
correction amounts to approximately 1.0-0.9. The effect of neutrons scattered at the walls
of the room, the structure of the target holder, the sample and its holder, the structure of
the counter, and in the air [11] is taken into consideration in it.
The induced activity was measured with respect to the line Ex = 208 keV for 237U(T1/2 =
6.75 days), with respect to the line Ex = 412 keV for '98Au (TI/2 = 2.7 days) and with re-
spect to the line Ex = 984 keV for '''Np (TI/2 = 2.12days). We note one special feature
of the measurement of the 238Np activity in the sample of Np02: it is necessary to take
special measures to eliminate overloading of the spectrometric channel by the intense back-
ground emission of the sample. For this purpose, a filter with a thickness of 0.7 cm of mer-
cury was used, for which the y-quanta absorption curve has a discontinuity close to the en-
218
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
ergy of the background y-quanta of maximum intensity. In addition, in order to reduce the
loading of the amplitude?digital converter, the threshold for the analysis of the spectrum
was set at the level of 770 keV.
The total correction Ay is introduced into the measured values of the activity in ac-
cordance with expressions (l) and (3), by which account is taken of the effects leading to
an additional increase or decrease of the sample activity with respect to the main isotropic
neutron source. The effects leading to an increase of activity are: scattering of neutrons
at the walls of the room, in the sample, in the containers (cadmium and stainless steel), in
the target holder (stainless steel and water), in the sample holder, and in the other sample
being irradiated simultaneously. The effect of nonisotropicity of the neutron source was
taken into account: as the samples are located at a distance of 4 cm from the target, this
effect leads to a reduction of activity, by 4-5%. The correction for the target holder (4-
16% of the induced activity) is measured when carrying out the experiments described. The
other corrections are measured in experiments [13] similar to those described in the present
paper. The corrections for scattering in the samples are calculated by the Monte Carlo method.
Figure 1 shows the correction Ay for samples of Au, U308 and Np02 as a function of the
neutron energy. The errors of the corrections vary from 2.7 to 1.8% with increase of the
neutron energy. Attention should be paid to the significantly different energy dependences
of the corrections for the samples of Au and Np02, despite the similar energy dependences of
an,y for 197Au and 237Np in the range of neutron energies investigated. This is due first
and foremost to the difference in the energy dependences of the corrections for the target
holder for the gold and neptunium samples. The energy of the neutrons scattered in the
water-cooled target holder is appreciably less than the energy of the primary neutrons en-
tering the sample. The energy dependence of the corrections is determined by the energy
curve of the an,y (E) cross section in both the energy range being investigated and in the
energy range of the scattered neutrons. For the gold and neptunium samples, the dependences
of the corrections on the neutron scattering in the sample holder are found to be signifi-
cantly different. On the other hand, despite the fact that the energy curve of the an,y (E)
cross section for 2380 and '97Au in the energy range investigated is different, these correc-
tions have an identical energy curve although they are different in value. The examples
considered show that taking account of the scattered neutrons, especially when their spectra
differ significantly from the spectrum of the primary neutrons, is a complex problem. It can
only be solved by measuring the additional activity or by performing the appropriate calcu-
lations by the Monte Carlo method for a realistic configuration of the experimental facility.
In view of the complex relation between the values of the activity induced by the primary
and scattered neutrons, approximate estimates or experiments may give inaccurate results.
Measurements of the Ge(Li)-Detector Efficiency. In order to calculate the cross sec-
tions by relations (1) and (3), it is nessary to know the values of the recording efficiency
for y-quanta, or their ratio, for samples of different configuration and mass, located non-
identically relative to the Ge(Li)-detector crystal. The method used for calibration of the
detector with respect to efficiency did not require quantitative data about the decay schemes
and quantum yields of the radiations.
'97Au. The efficiency n was determined from the ratio of the activity values of sam-
ples with identical specific activity, which were obtained with fission spectrUm neutrons:
Am
aM
11=
(5)
The activity A of a sample with mass M, identical to the samples used for irradition in the
accelerator, was measured in the Ge(Li) detector. The absolute activity a of a foil with 1
mass m was determined bythe4ff8?y coincidence method. A value of n = 3.05.10-2 ? 1.5% was
obtained.
237Np. The ratio of the recording efficiencystinx was determined in the following
n
way. Samples of Au and Np02, which were used in the accelerator experiments, were obtained
with thermal neutrons. Irradiation of the samples was conducted separately and the flux was
monitored with gold foils. The activity of the samples was measurd with a Ge(Li) detector
and nstinx
was determined from the ratio
ilst1113: AoKT ) stI '01A; )
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
(6)
219
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
TABLE Z. Results o? cross section measuremencs LOZ U, mp, auu AU
Neutron
energy,
keV
an, v 23 U, nib
?
an, v 237Np, nib
o 197Aus
n, y
nib, rel. to
?n, p
Ref. cross section
rel. to
Li ... MaA.
...
rel to
0
n. p
rel to
.
0no,
na lgTAu
rel. to
a n,p ?
rel. to on,y
197Aus nib
an, p. b
166+37
168+35
174+30
206+26
240+24
354+41
459+36
472+38
483+38
551+51
718+44
890+43
897+31
1046+45
1146+38
223+10,7
213+10,7
208+10,7
205+7,1
194+7,1
174+6,9
153+6,8
-
-
161+5,1
177+5,1.
163+5,1
-
149+7,7
126+7,7
-
254+4,1
251+4,1
-
-
188+3,8
-
_.
-
158+3,0
-
178+3,5
178+3,5
-
153+3,6
132+3,6
-
---
791+11,9
751+8,8
687+8,8
555+8,8
-
374+8,7
383+8,7
326+7,4
217+7,4
159+7,3
-
? -
119+7,7
106+7,7
-
-
-
-
594+6,9
-
403+0,8
403+6,8
326+6,8
214+6,8
175+6,8
171+0,8
119+6,8
110+6,8
-
300+4,1
295+4,1
-
-
194+3,7
192+3,7
151+3,6
145+3,6
122+3,0
125+3,6
96,4+3,5
93,2+3,5
, 94,3+3,5
-
82,8+3,5
80,9+3,5
80,9+3,5
80,9+3,5
253,1+10
251,5+10
247,1+10
245,5+6,1
234,4+6,1
179,6+6,1
142,7+6,1
140,4+6,1
138,0+6,1
124,7+4,1
99,0+4,1
85,8+4,1
-
-
81,3+7
77,8+7
-
10,45+1
10,29+1
-
-
7,36+1
-
6,33+1
6,25+1
5,84+1
5,08+1
4,53+1
4,51+1
4,16+1
3,97+1
Note. The error is given in percentages.
200 4.00 600 800
keV
Fig. 2. Radiative neutron capture
cross section of 'Au: *) experiment
(with irradiation with samples of
U308; -E) experiment (with irradia-
tion with samples of Np02), ---)
ENDF/BV estimate [9].
where A is the activity of the simple, corrected for activation by epicadium neutrons; K, a
correction for self-screening of the thermal neutron flux in the sample; aT, activation cross
section by thermal neutrons. Values of the cross sections aT (237Np) = 181 ? 9 b [7],
fiT (297Au) = 98.8 ? 0.3 b [14] were used. As a result nst/nx
= 49.75 ? 5.5% was obtained.
The recording efficiency n was calculated from the measured values of nst/nx and nst
(nst is the recording efficiency for samples of Au). The value of n determined from these
data is 6.13-10 ? 5.7%.
236U. The recording efficiency was found from the ratio of the values of the activity
of known volumes of a solution in which the concentration of 237U is identical:
220
Av
11.=. aV
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
(7)
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
In order to determine the absolute activity a of the volume v, the 470?y coincidence
method was used. A solution of 237U in HNO3 depositedon plastic film, metallized with gold,
was used. The thickness of the film was q,10 pg/cm2 and the thickness of the active layer was
q4.0 pg/cm2. The coincidence of the 237U 0-particles with y-quantawithEy= 208 keV and the
ICC-quanta of 237Np with Ey = 103 keV was investigated. This version of the method for deter-
mining the absolute activity of 237U was used for the first time. Almost coincident values
of the absolute activity were obtained.
A sample, the activity of which was measured in the Ge(Li) detector, was prepared from
238U in the form of U308 contained in the dry residue of a solution with 23217 with a volume
V. It was placed in the same container inwhichthere was a sampleof 236Uin theformofU308,
having been irradiated in the accelerator. As a result of the measurements made, r = 1.40.
10-2 ? 1.6%.
The ratio of the recording efficiency values nstinx was determined by two methods. The
first method is similar to that used for the neptunium samples. For this, the values of the
.,?
thermal cross sections a (236u/
T = 5.2 ? 0.3 b and aT (197Au) = 98.8 ? 0.3 b [14] were used.
In the second method nstinx was calculated from the independently measured values of nst and
nx (see above). In this case nstinx = 2.18 ? 2.2%. When processing the experimental data,
the latter value was used, as, for this method, possible systematic errors are less random.
Measurements Results. Table 2 gives the values of the radiative neutron capture cross
sections for the nuclei 236U and 237Np, measured relative to an,p and an,/ for 197Au, and for
nuclei of '97Au relative to an,p. The spread ofthe energy values shown in the table is the
spread of the energies of the outgoing neutrons from the target at an angle of 00. The refer-
ence values of the 197Au an,p cross sections are averaged over the corresponding range of
neutron energies of the cross section, and an,p are obtained by interpolation for the aver-
age value of the neutron energy.
The errors of the measured cross sections given in Table 2 are obtained by quadratic sum-
mation of the errors of the quantities in expressions (1) or (3): ?Ny for the gold, uranium,
and neptunium samples are equal to 0.7, 1.4, and 2%, respectively; ?N1n = 2.0, 6Nc = 1.1,
6N5 = 0.1, 6Gc = 0.3, and 6G5 = 0.6%. For the other parametes, the error values are given
earlier in the text.
Discussion of Results. Conclusions. 197Au. The measured values of a 197Au and
the total errors for certain energy values are shown in Fig. 2. They agree satisfactorily
with the ENDF/BV estimate within the limits of error, with the exception of individual values.
This can be taken as proof of the absence of significant systematic errors in the measurement
procedure for the cross sections an,y 236U and 237Np. The spread of the cross section values,
obtained for identical energies in independent series of measurements, shows that the esti-
mates of the random errors given above for 6N1 and ON are completely objective.
The energy En = 200 keV delimits the regions in which the procedures for obtaining the
estimated data were different. If account is taken of the coincidence of our results with
the ENDF/BV estimate for other neutron energy values, then the marked difference between the
measured cross section value and the estimated value for En = 168 keV, in our opinion, con-
firms that the estimate of the cross section in the vicinity of this energy value has been
performed unsatisfactorily.
2'6U. Figure 3 shows the existing experimental data, the estimated data, and the results
of a theoretical calculation for the an,y cross section of 236U, for the range of energies
studied. Our experimental data, measured relative to an,y for 197Au and an,p, agree well
between themselves. Differences appear only to the same degree as our measured values of
a n,y for '97Au differ from the ENDF/BV estimate (see Fig. 2). The values of the cross sec-
tions obtained by us are a factor of 1.6-2 less than the estimated values, which were deter-
mined on the basis of the results of [1, 21.
For the purpose of analyzing the complicated situation, calculations were performed of
the cross sections based on the statistical theory of nuclear reactions described in detail
in [15]. For this, values of the distance between levels Dobs (see Fig. 3) were used, which
are close to the recent estimates of the experimental data: 15 ? 1 eV [16] and 16.2 ? 0.8
eV [17]. Satsisfactory agreement was obtained with our results and also with the results of
[4] forEn > Ao, Attu [4]?
(2)
*Henceforth we shall use the generally accepted notation: A0 = 4.55.10 sec-1 is the muon
decay rate, A
-ttp is the formation rate of ttp molecules, and wt t is the probability of a muon
sticking to a helium nucleus in reaction (1).
Translated from Atomnaya fnergiya, Vol. 58, No. 3, pp. 190-192, March, 1985. Original
article submitted January 3, 1983.
226
0038-531X/85/5803-0226$09.50 C) 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Under real experimental cOnditions the products of muon catalysis reactions are detec-
ted with an efficiency E < 1. It can be shown easily thatthe time distribution of all (i.e.,
obtained without the introduction of auxiliary selection criteria) detected catalysis events
will have the form
dnexP dt =Xttp,8 exp 1?(Xo-FmttXttiL) tl,
and their yield ("experimental multiplicity") is
;Texp attg/(Xo+mtAttt2),
(4)
(5)
i.e., theycoincide with "physical" expressions (2) and (3) to within thenormalizing factor.
As can be seen from expressions (4) and (5), their use in analysis of the experimental
data allows only the products wtt AAttp and eAttp to be found, i.e., the detection efficiency
must be known for the independent deteimination of wtt and At. Direct determination of E
is an extremely complex problem. As a rule, in such cases the efficiency is calculated by
the Monte Carlo method with allowance for the parameters of the process under study and the
geometry of the experimental setup. For reaction (1) such calculations are further compli-
cated by the factthat the neutron energy spectrum is extended in nature. Moreover, the in-
formation about the form of the neutron energy distribution from expression (1) is inde-
terminate because of contradictory information about the contribution of the (nn) and (na)
interactions in the final state [5].
It seems obvious that the yield and time distribution of all the neutrons byno means
reflect the total information about the process of successive muon catalysis. Additional
measurements can be made of the time distribution of the "first," "second," etc., neutrons
and their yield or the yield of single, double, etc., neutrons. It turns out that if such addi-
tional information is used it becomes unnecessary to have a prior knowledge of e (it can be
found from the experimental data). In this case in order to determine wtt and Attp inde-
pendently it is sufficient to use only data about the yield and the time distribution of the
"first" detected neutrons and about the yield of "second" detected neutrons.
The scheme of the successive muon catalysis of reaction (1) is given in Fig. 1. A muon
liberated in reaction (1) forms a tp atom "instantaneously"(>X0 kud and then forms a ttp
molecule at the rate Att. By Ni we denote the number of tp atoms that survive until the
i-th fusion reaction event. The functions satisfy the systems of equations
dl V Idt -= ?X1)11;
dN 2Idt --XN 2+ (1 -----0u) 1N 1;
.DIV;Idt ? 2t1 ? tott)ktt,LN
where A E Ao Attu-
The solution of this problem for the boundary condition N2 (0) = 1 has the form
N1(0,,R1--coup,u,14-1-0-1e:1/(j--1)1
Since the reaction (1) proceeds at the rate 40.0,u,?Xo the time distribution of neutrons
from the i-th fusion reaction event is
ft (t).?dizildt?kttANi (1)--
? --- %It (1? tutt)i-] 0-1 (Hi --1)! (6)
The yield of neutrons from the i-th event is
n = f (t) dt (1 t -1 -(240.14i ? (7)
0
With the aid of expression (7) we can also get a relation for the yield of single,
double, etc., reactions:
(4-1-ceuXtt0)/ki+1. (8)
It can be easily shown that the time distribution of all events coincides with expres-
sion (2), and the yield of all fusion reaction events
00 CO
n= 2 ni= n (t) dl t---=kttnno-1- ottk in)
227
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
? A - A
)tim
N,
6111'703 4iit A
Fig. 1. Scheme of successive moun cata-
lysis of the ttp fusion reaction.
coincides with expression (3).
Next we take into account the final detection efficiency e < 1. In this case it becomes
possible that.the neutron from the i-th catalysis event will be detected first on condition
that the neutrons from the preceding i reaction-events will not be detected. When this
is taken into account the time distribution of the first detected neutrons can be represented
as a sum
ixP ()=th (0+0 (8/2(t)-1-(1-8) [Pia (t)+ ...1) e [fi (t)+(1 - 8) /2 (t) -8)21? . . .] = 8 (1 (t).
(9)
On substituting expression (6) for f(t) into Eq. (9), we get an explicit formula for
this time distribution:
f 3!XP (I) =at' exp -14+(e+cott-8)tt)Xttul t).
The yield of the first detected neutrons is
exp ' exp
nj = ? 1 i (t) dt ? -=
(10)
eXttg/IX2+ (e-I-fott -e(ott)kt 411. (11)
This expression can be obtained with the aid of formula (9) if in it we replace f(t) by ni
in accordance with relation (8).
When deriving an expression for the yield of second detected reaction events, we must take
into account the fact that neutrons from the pairs of catalysis events
(1, 2), (1, 3) ... (1, i); (2, 3), (2,4), ...,(2, i);
can be detected. Therefore, the yield is
exp
n2 = s2n2 +82 (1-e) n3+... +82 (1 -e)i-2ni + ? ? ? +
+82(1_8) n3+... =82 [n2+2 (1-0 n2+3 (1 -)2N +
+ + (i -1) (1 -8)i-2ni + ...] = 82 (1 -wit) X
Oo
X 041002 E 10 ?80 ? Wit) (i
=82Altp, ?(Ott)/1k0+ (8+ (Ott ?Mit) kttp.19.
We note that expression (12) can be derived with the aid of a expression analogous to
(8) for i = 1,
(12)
exp exp exp
n, -n, =n (1),
(13)
where nexP (1) is the yield of singly detected events. In actual fact, the formula for the
yield of m events can be written as
nexp
= n ()PT,
where PT is the binomial probability of detection of m events out of i events,
and CT are the binomial coefficients.
228
Pln=crein(1?-8)i-nt,
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
(14)
(15)
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
When into formula (14) we substitute for n(i) from (8) and for PT from (15), we get
nexp (m) en(1? wit)m-1
For m = 1 we have
(X0-1-0:Aitn)WilL
(16)
[10-1-(8-1-cott?ecott)Xttgr"
n elqp (1)?
eXttu (AT+ cottXtm)
I)0-1-(8-Fmtt ?mu) ktiu12
Substituting expressions (17) and (11) into formula (13), we get Eq. (12) for 2 ?
nexp
Expressions (10)-(12) and (16) are entirely sufficient for use in the analysis of ex-
perimental data for the purpose of independently determiningwtt and Attu. It seems most
appropriate to use the following algorithm.
1. From analysis of the time distribution (10) ofthefirst detected events we deter-
(17)
mine
areAcfOondhe?switp44,.
2. Using the measured values of a, nTxP, and nFP with theaid of the relation nTxP
(Ao wttAttp)/a = T
(1) = n!xp _ nexp, we get
n" 2
3. From the relation
ko-F(01tXttti?
1 _ xp (n ?xp ),
we determine wtt.
4. Substituting this value into the expression for the already known value of b =
Ao wttAttp, we find Attu.
Thus, the desired wtt and Attu can be found with use of the detection efficiency.
Clearly, the efficiency itself can also be obtained on the basis of the analysis carried out
and this is of interest in itself. Comparing this value with the corresponding calculations
in which different assumptions are made as to the nature of the energy distribution of neu-
trons from the t + t reaction, we can obtain information about the contribution of (nn) and
(na) interactions in the final state.
It must be pointed out that a necessary condition for the correct determination of wtt
and Attu in process (1) is that the neutron detection threshold be set properly for each
detector; the energy threshold should be below the minimum possible value (from the kine-
matics of the reaction t + t -> "He + 2n) of the total energy of two neutrons.
The expressions (10)-(12) and (16) obtained here can easily be generalized to muon
catalysis in pure deuterium. A general comment is that these expressions can be used effec-
tively in the analysis of experimental data only if the experimental multiplicity nexp > 1,
i.e., as follows from formula (5) , with eXttp/A0 >, 1 (the value of wtt is small) or for deu-
terium with EAddu/A0 1. For muon catalysis of reaction (1) this condition can be observed
for liquid tritium, where Attu 3.106 sec-' [3], or gaseous tritium at a pressure P 10"
kPa.
The authors express their thanks to V. M. Bystritskii and A. D. Konin for useful dis-
cussions.
LITERATURE CITED
1. Ya. B. Zel'dovich and S. S. Gershtein, Usp. Fiz. Nauk, 71, 580 (1960); S. S. Gerstein
and L. I. Ponomarev, in: Muon Physics, B. Hughes and C. Wu (eds.), Vol. III, New York
(1975), P. 141.
2. S. I. Vinitskii, L. I. Ponomarev, I. V. Puzynin,
(1978); S. S. Gerstein and L. I. Ponomarev, Phys.
3. S. S. Gershtein, Yu. V. Petrov, L. I. Ponomarev,
(1980).
4. L. I.
et al.,
Lett.,
et al.,
Zh. Eksp. Teor. Fiz.,
72B, 80 (1977).
74,
78,
849
2099
Zh. Eksp. Teor. Fiz.,
Ponomarev, in: Proceedings Sixth International Conference on Atomic Physics,
Plenum Publ., New York (1978), p. 182.
5. B. Kuhn, A. Kumpf, S. Parzhitsky, and S. Tesh, Nucl. Phys., A183, 640 (1972); R. Larose-
Poutisson, and H. Jeremie, Nucl. Phys., A218, 559 (1974).
229
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
NONSTATIONARY MODERATION OF NEUTRONS FROM A POINT PULSED
SOURCE IN A SYSTEM OF TWO MEDIA WITH A PLANAR INTERFACE
A. V. Zhemerev UDC 621.039.512.4
Nonstationary moderation of neutrons in homogeneous and weakly inhomogeneous media has
been investigated fairly well [1-4]. During the solution ofa number of problems of great
scientific and practical interest, it becomes necessary to determine the nonstationary dis-
tribution function in inhomogeneous media, in particular in a system of two different media
in contact with each otheeiong a planar interface. This problem has not been studied in
sufficient detail. Thus, the nonstationary distribution function of neutrons from planar and
point sources was investted in [5] on the assumption that in each medium the Mean free
path of neutrons is inverOtly proportional to their velocity. The nonstationary moderation
of neutrons with an energYAndependent mean free path was considered in [6], but only for a
planar source.
In this work on the basis of an age approximation we study the nonstationary distribu-
tion function of neutrons from a point pulsed isotropic source in a system consisting of two
different media with a Planar interface. It is assumed that the neutrons are moderated only
as a result of elastic collisions, the neutron mean free path in each medium does not depend
on the energy, and no absorption of neutrons occurs.
The Boltzmann kinetic equation for neutrons moderated as a result of elastic collisions
with nuclei of the medium in the absence of absorption can be written in the age approxima-
tion as [7]
1 OF (u, r, t) 12 OF (u r t)
AF (u, r, t) , , S (u, r, ),
Ot 3 Ou
where F(14, la (u, r, 0 is the density of neutron collisions; N (u,r,Orirdu , number of neu-
trons at the time t in the interval (r,rd-dr;u,u+d0;u--In(E01E), lethargy; E, energy of the
moderated neutrons; E0, maximum energy of the neutrons of the source; v, neutron velocity; 2,,
neutron mean free path up to elastic collision; E, average change in the lethargy as a re-
sult of a separate elastic collision; p, mean cosine of the angle of elastic scattering of
neutrons in the laboratory coordinate system; and S(u,r, 0, a function that characterizes
the space?energy and time distributions of the neutron sources. For a point isotropic mono-
energetic instantaneous source of neutrons we have
S (u, r, 0=6 (r) (u) 6 (t). (2)
Suppose that neutron moderation occurs in a system of two different media with the plane
z = 0 as their interface and the neutron source (2) is on the z axis, perpendicular to the
interface of the two media. Then Eq. (1) in a cylindrical coordinate system can be written
as
/2 OF 2 102F2 1 0 oF, t
oo Ot 3(1--2) 0z2 p of) ( P )/ 5 2 ?0Fu2 = 6, 2xtp (p) 8 (z Zo) 8 (u) (t), z > 0;
02F1 H 1 L _OF1
u OFi
1?
e vo at aF,
3 (1? ) Oz2 p op r op )) ?7=0, z < 0,
(3)
(4)
where v, is the initial neutron velocity. In writing Eqs. (3) and (4) we assume that the
first medium with the higher moderating power is at z < 0 while the neutron source is in the
other medium or on the interface (z, 0).
The solution of Eqs. (3) and (4) should be determined from the conditions of boundedness
at infinity
Translated from Atomnaya fnergiya, Vol. 58, No. 3, pp. 192-194, March, 1985. Original
article submitted October 1, 1984.
230 0038-531X/85/5803-0230$09.50 ? 1985 Plenum Publishing Corporation
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
Declassified and Approved For Release 2013/03/11 : CIA-RDP10-02196R000300060003-3
F1 (u, z, p, 1) 0 for z -co;
F2 (U, Z, p, t) 0 for z oo;
F1, 2 (U, Z, p, t) 0 for p 00;
as well as from the conditions of continuity of the neutron flux and current across the in-
terface [71
(5)
Making a change of variables,
OP', 4P
litFi=l2F =
2; - 2 for 2-0.
1-11.1 Oz 102
-ttz
tea
; Z
12
113('-712) 2z;
/2
p;
.2
(6)
(7)
T-2 (e2 1) t', (8)
Eqs. (3) and (4) can be represented in the following form (henceforth we omit the primes in
t', z, p'),
o2F2 ( OF ) OF2
2
= Si 6A-.)) 6 (z- - zo) 6 (u) 6 (r), z > 0; (9)
az2 p op du p
where
g2
7 kp 0%1)1 0, z 0;
Ozzau
(I ab) e pF g2 7zy ,,f-X21" 1 0, z