SOVIET ATOMIC ENERGY - VOL. 34, NO. 6

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP10-02196R000400010006-4
• Release Decision: RIFPUB
• Original Classification: K
• Document Page Count: 93
• Document Creation Date: January 4, 2017
• Document Release Date: September 15, 2013
• Sequence Number: 6
• Publication Date: December 1, 1973
• Content Type: REPORT

?
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Russian Original Vol. 34, No. 6, June, 1973
December, 1973
SATEAZ 34(6) 531-612 (1973)
SOVIET
ATOMIC
ENERGY
ATOMHAH 3HEPikla
(ATOMNAYA il4MIGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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N..
'?
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SOVIET
ATOMIC
ENERGY
?
? Soviet Atomic Energy is a cover-to-cover translation of Atomnaya
Energiya:a pUblication of the Academy of Sciences of the USSR. r
An arrangemeni with. Mzhdunarodnaya Kniga, the SOviet book, _
export agency, makes available both advance cdpies of the Rus-
sian journal and original glossy photographs and artwork. This
serves to decrease the necessary time leg between publication
of the original and Oublication of the trensietion and helps to im-
pr&e the quality of the latter. The translation began with the firSt
issue of the Russian journal.
Editorial Board of Atomnaya Energiya:
Editor: M.,D.,Millionshchikov
Deputy Director
, I. V. Kurchatov institute of Atomic Energy ? '
Academy of Sciences of the USSR"
Moscow, USSR
Associate,Editors: N. A. Kolotiortsov
N: Viasov
A. A. Bochvar
N. A. Dollezhal'
Fursov
I. N. Golovin
V: F. Kalinin
A. K. Krasin
A. I. Leipunskii
-
A. P. Zefirov
r ?
V. V. Matveev
M. G. Meshcheryakov
P. N. Palei
V. B. Shevchenko
D. L. Simonenko
V. I. Smirnov
A. P. Vinogradov
, ? CopyrightC1973 Consultants I3ureau, New York, a division of Plenum Publishing
Corporation, 227 West 17th Street, New York, N.Y. 10611. All rights reserved.
No article contained herein may be Yeproduced for any purpose whatsoever
without permission of the publishers.
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Published monthly. Second-class. postage Paid at Jamaica, New York 11431.
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
December, 1973
Volume 34, Number 6 June, 1973
CONTENTS
Engl./Russ.
Academician Mikhail Dmitrievich Millionschikov
531
426
ARTICLES
On Choosing Methods of Cutting Metals in the Repair of Reactors ? Yu. F. Yurchenko,
V. F. Murav'ev, B. A. Pyatunin, and B. G. Malyavin
532
427
Some Problems in the Operational Safety of Atomic Power Stations using Gas-Cooled
Fast Reactors with a Dissociating Coolant ? G. A. Sharovarov
540
435
Choosing Absorbing-Rod Efficiency for Shielding Against Excessive Power Levels
? A. A. Sarkisov, V. N. Puchkov, and B. A. Melinikov
545
441
Neutron Transport Equation Suitable for Obtaining Approximate Thermalization
Equations ? N. I. Laletin
549
445
Effect of Scattering Anisotropy on the Thermal-Neutron Use Factor ? N. I. Laletin,
N. V. Sultanov, Yu. A. Vlasov, and S. I. Konyaev
555
450
Genesis of Radiogenic Lead Halos in Precambrian Uranium Deposits ? A. V. Tarkhanov
and V. I. Zhykova
561
455
Determination of Stable Neon Isotopes in Radioactive Minerals and Natural Cases
? Yu. A. Shukolyukov, G. Sh. Ashkinadze, and V. B. Sharif-Zade
566
461
Lossless Particle Capture in RF-Acceleration Mode in Proton Synchrotron
? E. A. Myae and P. T. Pashkov
570
465
The REP-5 Heavy-Current Relativistic-Electron Pulse Accelerator, with a Beam
Current of About 50 kA ? G. R. Zablotskaya, B. A. Ivanov, S. A. Kolyubakin,
A. S. Perlin, V. A. Rodichkin, and V. B. Shapiro
577
471
ABSTRACTS
Numerical Solution of the Problem of Optimization of a Heterogeneous Reactor by
Means of Blocked, Burnup Absorbers ? A. V. Voronkov and V. A. Chuyanov
580
475
Analysis of a Pulsed Neutron Experiment by the Moments Method ? D. A. Pankratenko
581
475
An Instrumental-Activation Method for the Determination of Mo, Al, Ca, Mn, Cl, Na,
and K in Soil and Plant Samples ? R. Rustamov, Sh. Khatamov, I. I. Orestova,
and A. A. Kist
582
476
Optimal Placement of a Specimen in Relation to a Detector ? A. N. Silantiev
and I. G. Shkuratova
583
477
LETTERS TO THE EDITOR
Utilization of Metallic Uranium in Power Channel Uranium?Graphite Reactors
? A. D. Zhirnov, A. P. Sirotkin, S. V. Bryunin, V. I. Pushkarev,
and V. I. Runin
584
479
Stability "In the Large" of a Stationary Regime of a Heterogeneous Nuclear Reactor
? V. V. Mikishev and Yu. F. Trunin
587
481
Nuclear-Radiation Detectors Based on High-Purity Germanium ? V. P. Aver tyanova,
M. I. Ginzburg, N. B. Strokan, V. P. Subashieva, and N. I. Tisnek
591
483
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CONTENTS
Determination of Oil?Water Interface Using a 6-8 MeV Electron Beam
? M. M. Dorosh, A. M. Parlag, V. A. Shkoda-U11yanov, I. I. Danilich,
V. M. Mazur, and A. Yu. Urgin
Penetration of Fast Neutrons Through an Axisymmetric Shield ? A. N. Kozhevnikov,
V. A. Khodakov, and A. V. Khrustalev
Energy Balance of Nuclear-Fission Reactions (dt) in the Beam?Target System
(continued)
Engl./Russ.
594 485
597 487
? R. A. Demirkhanov, Yu. V. Kursanov, and L. P. Skripal'
600
490
Average Yield of Prompt Neutrons V in the Fission of U233 by Neutrons with Energies
from Oto 1.4 MeV ? B. Nurpeisov, V. G. Nesterov, L. I. Prokhorova,
and G. N. Smirenkin
603
? 491
INFORMATION: CONFERENCES AND MEETINGS
The Thirty-Third Session of the OIYaI Academic Council ? V. A. Biryukov
605
495
ANNIVERSARIES
Twenty-Fifth Anniversary of the First Soviet Synchrotron ? B. S. Ratner
610
498
The Russian press date (podpisano k pechati) of this issue was 5/28/1973.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
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ACADEMICIAN MIKHAIL DMITRIEVICH MILLIONSCHIKOV
The editorial board and staff of nAtomnaya Energiyan express our deep sorrow on the occasion of the
death of this journal's Editor-in-Chief, Academician Mikhail Dmitrievich Millionschikov, an outstanding
Soviet scientist, the Chairman of the Supreme Soviet of the Russian Soviet Federated Socialist Republic,
the Vice-President of the Academy of Sciences of the USSR, Deputy Director of the I. V. Kurchatov Insti-
tute of Atomic Energy, Hero of Socialist Labor, and laureate of the Lenin and State prizes of the USSR,
who died on the 27th of May, 1973, at the age of 61. We share the bitter loss of the relatives, friends,
and colleagues of the deceased.
Translated from Atomnaya Energiya, Vol. 34, No. 6, p. 426, June, 1973.
1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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ARTICLES
ON CHOOSING METHODS OF CUTTING METALS IN THE
REPAIR OF REACTORS
Yu. F. Yurchenko, V. F. Murav'ev, UDC 621.039.5/68:004.6
B. A. Pyatunin, and B. G. Malyavin
All conceivable reactor repair situations have not as yet been studied in sufficient detail; however, it
is reasonable to assume that the experience which has been gained all over the world in the use of nuclear
power stations will shortly enable mechanisms for the execution of preventive maintenance and emergency
repairs to be incorporated in standard reactor repair equipment. Problems of this kind are even now facing
the designer.
The majority of repair works involve cutting operations and the removal of the reactor construction
elements which are to be replaced. This requires special mechanisms developed for particular repair con-
ditions. The levels of radiation in the repair zones are usually so high that no repair crews can work there.
Sometimes special measures may be taken to reduce the level of radiation in the repair zones. For ex-
ample, filling the vessel of a discharged water-cooled, water-moderated reactor with water after several
years use enables repair work to be carried our fairly safely using special remote-control mechanisms in-
side the vessel. It is therefore of particular interest to discover and develop such effective methods of
cutting metals as will enable reliable remote-control mechanisms to be created, capable of working both
in air and under a layer of water.
For separative cutting in the dismantling of reactor construction elements requiring replacement,
mechanical and gas?electric (plasma) methods of cutting are usually employed. The mechanical cutting
of construction materials is executed with special remote-controlled machinery. The machines are most
frequently designed for one particular operation and are very complicated in design and manufacture. Me-
chanical cutting involves a great deal of mechanical pressure between the tool and the part being cut. This
means that the framework of the mechanism has to be rigid, and the whole thus becomes much heavier.
The tool in such mechanisms also has to have at least two motione (to and fro), complicating the kinematics
of the machine.
The use of gas?electric cutting is limited by the thickness of the metal being cut, the dimensional
circumstances in the repair zone, and also the complexity of the technology of repair work under water.
Existing equipment allows steel up to 60 mm thick to be cut under water. Thicker metal can only be cut
if there is space for the plasma jet to pass right through.
As the result of a continuing search for other methods of cutting metals, free from the disadvantages
associated with those just indicated, it was found that the electrical-contact method of cutting was the one
most suitable under the specific conditions of reactor repair. This method involves very little pressure
between the tool and the part being cut, it enables various cutting operations to be carried out with the tool
simply moving forward in the feed direction, the cutting process is stable in both air and water, simple
and inexpensive equipment may be used, and there is a low specific consumption of electrical power (1-4
kW ? h/kg).
In order to compare mechanical drilling with the plasma and electrical-contact cutting of metals,
Table 1 presents some characteristics of the corresponding equipment for driving holes 120 mm in diameter
in stainless steel plates 130 mm thick under a layer of water. The thickness of the platewas chosen from
a consideration of the maximum resistance of a circular drill under optimum boring conditions.
Translated from Atomnaya Energiya, Vol. 34, No. 6, pp. 427-434, June, 1973. Original article
submitted February 1, 1972.
532
Co 1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permtss ion of the publisher. A copy of this article is available from the publisher for $15.00.
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TABLE 1. Some Characteristics of Equipment for Driving Holes in a Steel Plate by Various Methods
Form of cutting
Thickness
of plate,
mm
Form of tool
Cost of tool,
roubles
Cutting
time, min
Cutting force, kg
Weight of equip-
ment (without
supply source),
kg
Cost of equip-
ment, roubles
Drilling
Plasma cutting
Electrical-contact
cuttirm
130
55
130
Circular drill ( 0 130
mm, length of work-
ing part 200 mm)
Plasma bumer
Circular electrode
416
50
2,5
55
2,5
16
Axial 1500, cir-
cumferential 350
?
Up to 5
3100
45
20
3800
6800
1200
Fig. 1. Section of an objectwith a complex
cross section after cutting with a disc elec-
trode, the cutting zone being intensively
water-cooled.
Arrangements for the Electrical-Contact
Cutting of Metals
This method involves the removal of metal from the
part being cut by virtue of the thermal action of powerful
transient arc discharges on its constituent material, these
discharges being excited between electrodes (usually in
mutual contact) attached to ac or dc sources.
Electrical-contact cutting may be executed with either
rotating or nonrotating electrodes. In the first case cutting
may be effected over wide ranges of the electrode voltages
and the specific powers evolved at the electrodes. When
these parameters vary, so do the cutting efficiency and the
quality of the surface cut. For example, cutting by elec-
trical fusion at a voltage of 36 V or over is characterized
by a high value of the specific power evolved at the elec-
trodes and a high cutting efficiency, but a low quality of
the cut surface and a fairly deep zone of thermal influence. This somewhat restricts the use of electrical-
contact cutting in the electrical-fusion mode.
Figure 1 shows a cut through a part of complicated cross section obtained in water by means of a ro-
tating tool electrode (disc) with 24 V on the electrodes. The quality of the surface of the cut is V3.
By using special discs with abrasive electrical-insulating coatings of their lateral surfaces (for ex-
ample, a coating made from aluminum oxide powder) we may improve the quality of the cut surface to V6-
V7. On using such electrode tools for the electrical-contact cutting of hollow parts and tubes under a layer
of water or with intensive water cooling of the cutting zone, we may obtain a high-quality cut surface over
the whole cross section of the part. The cutting efficiency increases by about a factor of ten over that of
conventional mechanical methods.
The foregoing advantages of electrical-contact cutting with a rotating electrode offer excellent pros-
pects for its use in industry [1-3]. However, the use of this type of cutting for the'repair of nuclear reac-
tors involves serious difficulties. This is due to the following circumstances. The weight of the machines
used for electrical-contact cutting with a rotating electrode is as great as that of those used for mechanical
cutting [3]. In the first case the machines have comparatively complex kinematics, which makes remote
control more difficult. Furthermore, the presence of water (as a coolant) greatly increases the power of
the drive motors required for electrode discs rotating at more than 20 m/sec, and requires the installa-
tion of complicated sealing systems to prevent water from passing into the current-taking devices and thus
to ensure their efficient operation.
Hence under the specific conditions of nuclear reactor repair special interest is evoked in electrical-
contact cutting with nonrotating electrodes, which, depending on the shape of the working part of the elec-
trodes, facilitates separative cutting, the cutting of apertures in metal plates and the sides of the vessels,
the removal of broken pins from these, and other operations. The simplicity with which such operations
may be executed enables us to create light, reliable, and inexpensive equipment.
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Fig. 2. Cut through a stainless steel
plate made with a laminar graphite
electrode under a layer of water.
Fig. 3. St. 3 sample with a hole 80 mm in
diameter drilled through it.
Cutting with a nonrotating electrode may only be effected in the mode of electrical fusion.
Figure 2 shows a cut through a stainless steel plate 30 mm thick made with a nonrotating electrode
under a layer of water. The cutting speed was 150-200 mm/min.
Figure 3 shows a St. 3 plate 180 mm thick with a hole bored through it, 80 mm in diameter. The
operation was effected with a tubular graphite electrode under a layer of water.
Materials for Tool Electrodes and Their Wear in
Electrical-Contact Cutting
The intensive action of the powerful arc discharges causes wear of the tool electrode materials, ap-
pearing in the form of electrical erosion. Furthermore, tool electrodes working without intensive cooling
by an external medium experience severe thermal loading. This influences the mechanical strength of non-
rotating electrodes, and reduces the dynamic stability during the operation of rotating electrodes, owing
to thermoplastic deformations. The use of liquid media possessing a fairly high specific heat and thermal
conductivity (for example, ,water and aqueous solutions of chemical compounds) greatly reduces the thermal
stress on the tool electrodes and improves their working conditions.
Apart from electrical erosion, wear on certain electrode materials may also arise from the forma-
tion of volatile oxides and other chemical compounds in gas media. Such materials include molybdenum
and tungsten, which, despite their high thermophysical properties, ,undergo serious wear when used as
electrode material for electrical-contact cutting in air. ,The oxides of these metals, formed at .750-800?C,
sublime very considerably at the same temperatures. The wear on graphite electrodes increases with in-
creasing rate of pumping air through the cutting zone because of the oxidation pf the carbon.
The external medium has hardly any effect on the amount of electrical erosion of the electrode ma-
terials at those currents characterizing electrical-contact cutting with a nonrotating electrode. Tests
showed that the degree of electrical erosion of nonrotating graphite electrodes during electrical-contact
cutting in water, electrolyte solutions, oils, and air (without pumping the latter through the cutting zone)
remained constant. The same effect was noted in [4], in which it was indicated that for high currents in
arc discharges the external medium was displaced from the electrodes by the vapor of the electrode ma-
terials.
The wear of the rotating electrodes also includes a component due to processes taking place as a re-
sult of friction between the tool electrodes and the part being machined in those cases in which cutting is
effected with a low voltage on the electrodes, i.e. , in which the contact mechanism of arc-discharge ex-
citation predominates.
Water-cooled rotating electrodes are usually made from low-carbon steels, brass, copper, or special
cast iron. The use of refractory metals or metalloceramic composites is economically undesirable owing
to the complexity involved in the manufacture of such tools and their high net cost.
Investigations showed that, under optimum cutting conditions, the wear resistance of tools using me-
talloceramic of the VM-70 type (tungsten?copper?nickel) was only 1.3-1.6 times higher than that of cast
iron tools.
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It
Aib
1-1
Fig. 4 Fig.- 5
Fig. 4. Granules formed after the electrical-contact cutting of 18-8 steel under
a layer of water; the granules are collected with a magnet.
Fig. 5. Arrangement of the apparatus for remote-control electrical-contact cut-
ting of an array of tubes: 1) tube being cut; 2) guides; 3) electrode plate; 4) mas-
ter nut; 5) carriage; 6) lead screw; 7) electromechanical drive.
For the reasons just outlined, chief interest lies in nonrotating tool electrodes. These are made of graph-
ites, which have the great advantage that under the thermal action of arc discharges they suffer no fusion
but rather sublime, dissipating far more thermal energy than would occur on melting, and a higher wear
resistance is thus achieved in electrical-contact cutting.
As regards erosion resistance and mechanical strength, pyrolytic graphites are the best; these have
a highly oriented structure and high specific gravity [5]. Pyrolytic graphites may also be used as coatings
for ordinary graphites, increasing the strength of tool electrodes made from such materials and increasing
their cutting efficiency.
Of all the pyrolytical graphites, we may specially mention that of the PGV type, which has advanced
thermophysical and mechanical properties; 1) thermal conductivity ? along the a axis 150-300, along the
c axis 2.5-4.0 m?W/deg; 2) compressive strength ? along the a axis 5-7, along the c axis 25-30 kg/mm2;
3) bending strength ? along the a axis 1-2, along the c axis 25-30 kg/mm2; 4) resistivity ? along the a axis
(1.63-2.0) ? 10-4, along the c axis 0.2-0.3 St ? cm.
Phenomena Accompanying Electrical-Contact Cutting
In developing a technology for repair which involves electrical-contact cutting, allowance should al-
ways be made for phenomena accompanying the cutting process.
As a result of the thermal action of the arc discharges on the electrode material the latter evolve
their own vapors, which emerge from the cutting zone at a high velocity. The intensity of vaporization
depends on the power of the arc discharges, their repetition frequency, and the thermophysical properties
of the electrode materials and the medium.
When the vapors of the electrode materials condense in the gas medium, highly dispersed solid par-
ticles 0.1-20 pin size are created. The particles formed as a result of the cutting of construction materials
having induced radioactivity are propagated into the free gas space in the form of an aerosol cloud. The
particles settling on the wall surfaces of the room and on the equipment constitute radioactive contamina-
tion. These particles adhere firmly to metal, particularly to polished stainless steel, and remain attached
to them [6]. Hence when conducting electrical-contact cutting in air it is essential to provide special suc-
tion systems and corresponding systems of gas purification. Methods of deactivating the equipment must
also be selected.
In order to remove the contaminants formed during electrical-contact cutting, ordinary redox deac-
tivation methods may be used. The volumes of the desorption solutions and the number of deactivation cy-
cles may be reduced if easily-removable coatings are first applied to the surface of the equipment.
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TABLE 2. Examples of Metal-Cutting Operations in Reactor Repair
.o
,... Disc cutting of construction units.
Feed Executed with a rotating electrode and water cooling in the cutting zone.
W. Surface quality V3. Electrode voltage 18-32 V.
-0;
.10 ..
? Finishing of metal surfaces.
0._...?"eg, Feed Executed with a rotating brush electrode and water cooling in the cutting
zone. Surface quality V3-'75. Electrode voltage 10-18 V.
Wate ' idi
V .1
Rotation
4.
\c,
N,.../6
SW
ip
,t
a)
w
Cutting into tubes,, cutting apertures in tubes and sheets.
Executed a rotating tube electrode and water cooling in the cutting
with
411Mzone. Electrode voltage 18-32 V.
s.
Cutting of construction units, face plates, etc.
a,
Executed with a graphite electrode (no rotation) and water cooling of
,
.
the cutting zone, or under a layer of water. Surface quality ? unclassified.
Electrode voltage 36-50 V.
V, "A Broaching of apertures, removal of broken pins.
tmommwstis:
Water Executed with a circular graphite electrode (no rotation), water being
r zAFeed
fed into the inside of the electrode. Quality of machined surface ? unclassi-
w.memrrnmo
fied. Electrode voltage 36-50 V.
,
4, 1111M=11 -a
ate
r
c a)
4)
w
II r
Amr,
+
Hollowing of grooves in parts '
Executed with a graphite electrode having a profiled working part, the
working zone being water cooled, or executed under a layer of water.
Surface quality after machining ? unclassified. Voltage 36-50 V.
In under-water cutting, the electrode vapors condense in the water. In this case colloidal solutions
are formed. Coarse colloidal solutions rapidly coagulate (in 25-30 mm). Fine solutions break up more
slowly. Thus, for example, after leaving the water used for cutting stainless steel to settle for two days
it still contains up to 4 mg/liter of iron oxides and 0.5-0.7 mg/liter of chromium and titanium oxides. The
formation of colloidal solutions turbidizes the water, and this impedes the use of optical observation sys-
tems.
Under-water electrical-contact cutting is accompanied by the evolution of oxygen and hydrogen, formed
by the decomposition of the water. For a thin layer of water above the cutting zone, these gases are in-
tensively evolved and suffer combustion. The possibility of hydrogen accumulating in a certain closed vol-
ume cannot however be ruled out. On immersing the cutting equipment to a depth of 5-6 m these gases
fail to reach the surface of the water. Evacuation of the cutting products from the repair zones is one of
the essential measures required to ensure successful execution of subsequent operations.
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Rotation of
electrode
Turning of head
Fig. 6
I.
Fig. 7
Fig. 6. Mechanism for the electrical-contact cutting of tubes from
within: 1) shaft-rotating motor; 2) current-taking device; 3) hous-
ing of cutting head; 4) screw supports; 5) tube being cut; 6) shaft;
7) electrode.
Fig. 7. Arrangement of apparatus for the electrical-contact broach-
ing of holes in freely-mounted parts: 1) cast iron cube (part to be
broached); 2) plate on which the part is freely mounted; 3) tool elec-
trode; 4) electrically-insulating plate; 5) carriage; 6) guides; 7)
lead screw; 8) electromechanical drive feeding the electrode; 9) stand.
In electrical-contact cutting in air, it is esSential to provide surface protection for equipment sit-
uated around the current zone so as to prevent the adhesion of molten metal, and also to provide for the
subsequent removal of any which does adhere. Demountable screens are used to this end.
The thermophysical properties of the metal being cut and the rate of cooling the molten metal affect
the size and shape of the solidified drops. On cutting in air, the drops of melt merge into a shapeless
mass. On cutting under Water the molten metal becomes granular. During the cutting of stainless steel
under water, hollow granules 0.01-12 mm in size are created. Of these 10-12% are spherical and the rest
are drawn out and geometrically irregular. Up to 60% of the granules acquire magnetic properties arising
as a result of the formation of delta ferrite by the high rate of cooling of the melt in water; magnets may
thus be used to remove them (Fig. 4).
The shape and size of the granules formed in the under-water cutting of aluminum and its alloys dif-
fer considerably from steel. In this case long, drop-like granules with acicular tips are usually formed.
Some granules extend to 15 mm.
Supply Sources
In electrical-contact cutting, supply sources with strict volt?ampere characteristics and fairly high
powers (100 kVA and over) are used; their voltage is regulated within the range 18-50 V.
No special dc or ac sources are produced by industry for electrical-contact machining. Standard-
production armored transformers are therefore employed. These include, for example, dry transformers
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of the OSU-100 type, which may be used in twos or more by parallel connection in the supply source. The
same transformers, furnished with rectifier systems, may be used as dc supply sources; these have some
advantages over ac sources in respect of a reduction of the reactive components of the circuit impedance
and the wear on the tool.
The choice of supply sources with due allowance for the required cutting efficiency is considered in
{7}. The same paper indicates a method of calculating the circuit elements of the supply source for the
electrical-contact cutter.
Use of Electrical-Contact Cutting in the Repair of Reactors
Examples of some technological operations encountered in reactor repairs for which electrical-con-
tact cutting is suitable are presented in Table 2.
In the repair of reactors, cutting operations often have to be executed under cramped conditions so
that traditional cutting methods are difficult or impossible. In such cases electrical-contact cutting with
nonrotating electrodes is particularly effective.
We shall now give a brief description of some mechanisms for electrical-contact cutting in similar
operations.
Cutting of an Array of Tubes. The most typical repair operation is the cutting of an array of tubes.
If the array of tubes is situated in the housing in such a way that the distance between individual tubes and
the walls is insufficient for the operation of ordinary cutting tools, the device illustrated in Fig. 5 is em-
ployed.
A laminar graphite electrode with a length greater than the width of the array of tubes is moved along
guides on a carriage by means of a lead screw, driven by an electromechanical system. The cutting pro-
cess is stabilized and the normal thermal conditions of the cutting electrode kept constant by virtue of feed-
back (introduced into the electrical drive circuit) between the rate of rotation of the de electric drive motor
and the cutting current. In order to avoid rupture of the electrode, a current-limiting relay is also pro-
vided for the current in the core winding of the electric motor driving the electrode; this disconnects the
motor if the current rises too high.
The supply source includes two parallel transformers of the OSU-100/0.5 type each with a power of
100 kVA. The power of the supply source is sufficient for the series or parallel cutting of any tubes made
from the construction materials generally employed in reactor buifding.
;Cutting of Tubes from Inside. In repair work it is often required to cut tubes from inside with the
cutting instrument situated at a considerable distance from its drive point. For cutting tubes with an in-
ternal diameter of 30 mm or over in this way in straight vertical sections an electrical-constant cutting
head may be used (Fig. 6).
The cutting head is furnished with a lamellar electrode made of pyrolytic graphite fixed to a shaft
with a current-collecting device. To the framework of the mechanism an electrical motor for driving the
rotating shaft is attached. The mechanism is placed at the top of the tube and fixed with a screw support.
The shaft carrying the tool electrode is placed eccentrically with respect to the axis of the tube being cut.
When the supply source and the shaft-rotating motor are connected, the working edge of the electrode
touches the wall of the tube, as a result of which electrical fusion occurs.
After the graphite electrode has rotated through 360? the tube is not completely severed. This is
achieved after rotating the framework of the cutting head through 180?. The cutting may be effected in
either air or water. The fact that there is no pressure between the tool electrode and the part, together
with the fact that the electrode is very light, enables tubes to be cut at a depth of 10-15 m from the site
of the mechanism.
Broaching Holes in Freely-Mounted Parts
Using the mechanism illustrated schematically in Fig. 7, open apertures may be broached in freely-
mounted parts. The mechanism has been used to broach holes 130 mm in diameter in cast iron cubes
freely installed on a steel floor. The depth of the apertures is 280 mm.
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Broaching is effected with a tubular electrode having a diameter 4-5 mm smaller than the diameter
of the opening to be broached, while the length exceeds the thickness of the broached metal by 60 mm. The
electrode is fixed in a movable carriage set in motion by a lead screw. The screw is rotated by an electro-
mechanical drive, the electrical circuit of which incorporates feedback between the current in the core
winding of the dc drive motor feeding the electrode and the current effecting the broaching. All the mecha-
nisms are placed on a firm base. Inside the electrode is a plate of electrically-insulating material pre-
venting it from coming into contact with the core being cut out.
The tool is made of GMZ graphite, the surface of the electrode being coated with pyrographite. As
supply source there is a pair of parallel-connected transformers of the OSU-100/0.5 type with an electrode
voltage of 40-50 V. As the broaching depth increases, the rate of feed of the tool falls from 40 to 5 mm
/min. This is because the conditions for removing the erosion products worsen as the depth of incision in-
creases, despite the fact that water is forced through the inside of the electrode. Using an analogous de-
vice, apertures may be made in the walls of reactor vessels.
CONCLUSIONS
Practice has shown the efficiency and economic viability of the electrical-contact cutting of metals
in the repair of nuclear reactors, particularly cutting with nonrotating electrodes.
The advantages of the electrical-contact method of cutting metals are as follows: simplicity of execu-
tion, low cost of the equipment, and possible application to all metals used in reactor building, whether the
cutting is effected in air or in water.
LITERATURE CITED
1. In Nonstandardized Technological Equipment and Fittings, Catalog No. 2 [in Russian], TsINTINefte-
khimash, Moscow (1971), p. 36.
2. N. S. Kabanov and A. V. Piskunov, Avtomaticheskaya Svarka, No. 4, 11 (1967).
3. D. M. Zmiev and B. V. Kuznetsov, Anodic Mechanical Cutting of Metals in Disc Machines [in Rus-
sian], ENIMS,? Moscow (1970).
4. V. I. Rakhovskii, G. V. Levchenko, and 0. K. Teodorovich, Break Contacts of Electrical Apparatus
[in Russian], Energiya, Moscow (1966).
5. A. S. Fialkov et al., Uspekhi Khimii, 34, No. 1 (1965).
6. A. D. Zimon, Adhesion of Dust and Powders [in Russian], Khimiya, Moscow (1967).
7. A. S. Davydov, in: New Methods of Machining Metals [in Russian], GOSINTI, Moscow (1964).
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SOME PROBLEMS IN THE OPERATIONAL SAFETY OF
ATOMIC POWER STATIONS USING GAS-COOLED
FAST REACTORS WITH A DISSOCIATING COOLANT
G. A. Sharovarov UDC 621.039.58
One of the most important problems in nuclear power generation is the operational safety of atomic
power stations using gas-cooled fast reactors, which are characterized by high thermal stress, low ac-
cumulating capacity in the coolant, and correspondingly short periods of operation before breakdown pro-
cesses develop. Breakdown processes may be divided into two main stages; first, a rise in the tempera-
ture of the fuel and the jacket of the fuel element until the melting point is reached and, second, melting
of the active zone, with displacement of the fuel and the possible formation of a secondary critical mass,
leading to an explosion.
The requirements for absolute safety have been discussed in many recent works on breakdown pro-
cesses in various types of fast-reactor power stations [1-5]. Unfortunately, the general requirements
and the corresponding standards for the investigation of nonstationary breakdown processes in the design
of atomic power stations have not yet been clearly formulated. This is attributable to the fact that the
various atomic power stations investigated differ considerably in their thermodynamic cycles, their flow
circuits, the coolants they use, and other features.
The most important problem in operational safety is to prevent the melting of the active zone, with
possible displacement ,of the fuel, formation of secondary critical mass, and explosion. As is generally
known, this is defined as ultimate failure.
T,?
1000
900
800
700
600
e
\I
?
9
o
Fig. 1
1100
goo
700
500
C=0
0=C
300 0
01
0,2
Fig. 2
Fig. 1. Coolant temperature as a function of time when the heat flow q varies as a step func-
tion: 1) process for equilibrium properties; 2) process for nonequilibrium properties.
Fig. 2. Coolant phase diagram for oxygen (P = const, qv = ?23,000 kcal/m3. sec). The curves
are drawn for a constant value of C = dp40/dT, with C2 > C1 > 0 > ?C3.
?3 Po
Translated from Atomnaya Energiya, Vol. 34, No. 6, pp. 435-439, June, 1973. Original article
submitted November 9, 1972.
540
?
C 1975 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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????11
In order to solve the problem it is essential, above all,
to ensure reliable coolant circulation during a power-station
1,0
breakdown and shutdown cooling of the reactor. In addition,
the reactor design must ensure the necessary temperature
effects and include a highly reliable breakdown-protection
system.
The most dangerous breakdown situations are those
involving a failure of the seal in the primary loop at various
points of the flow circuit, cutting off the flow of the main cir-
culating pumps, the compressors, or the entire power sta-
tion, and also those involving an accidental change in reac-
tivity. In all breakdown situations, it is essential to main-
tain continuous circulation of the coolant through the reactor.
The length of time that continuous circulation is maintained
and the nature of the change in coolant flow for different types
of breakdown are determined primarily by the flow circuits,
the thermodynamic cycle, the design of the reactor, and the
0 2 4 properties of the coolant.
In the present study we shall discuss possible solutions
of these problems for atomic power stations using the dis-
sociating coolant N204. We shall investigate the characteris-
tic factors which are specific to dissociating coolants alone,
since the other difficulties involved in maintaining safe opera-
tion remain the same for all gas-coolant reactors. The most
important feature of atomic power stations using a dissociating coolant is that they use a single-loop conver
sion system and use a gas?liquid thermodynamic cycle in a gas-cooled reactor [5-10].
The main characteristics of nonstationary processes in nuclear power installations using a dissociat-
ing coolant are determined by nonstationary processes in the coolant, which differs in principle from or-
dinary gaseous coolants. Because the thermophysical properties of a dissociating coolant are variable,
the processes in it cannot be regarded as inertialess. For a given pressure and temperature and com-
parable periods of time for the chemical reactions and technological processes, the properties will also
depend on the characteristics of the nonstationary process taking place in the coolant.
For example, Fig. 1 show S that the temperature of a gas in a real nonstationary process varies more
sharply for a change in heat flow than for inertialess chemical reactions.
In Fig. 2 we show the phase diagram for the relative density of oxygen in the dissociating mixture.
The curve C = 0 corresponds to the process with inertialess chemical reactions. The arrows indicate
the direction of the possible process when cooling takes place as a function of the initial state. The amount
of oxygen depends not only on the temperature and pressure but also on the initial conditions and the na-
ture of the nonstationary process. Thus, the dissociating coolant is a dynamic system characterized by
the kinetics of the chemical reactions.
0,5
s-, sec0,5
Fig. 3. Curves showing flow rate, pres-
sure, and temperature of the coolant at
the reactor inlet when the pumps fail:
?) main circulating pumps; ---) pow-
er station.
One of the most dangerous breakdowns in multi-loop atomic power stations using a gaseous or liquid
?metal coolant is loss of power in the main circulating pumps or compressors, since in this case it is ex-
tremely difficult to maintain continuous circulation. Continuity of circulation can be maintained for some
time, at diminishing pressure difference, for a specific quantity of coolant on the high-pressure side. The
use of a gas?liquid thermodynamic cycle with a dissociating coolant is characterized by the large amount
of coolant in the loop in comparison with the flow rate and the considerable drop from maximum to mini-
mum pressure in the loop WM
The ratio of the amount of coolant to the flow rate in the corresponding segment of the loop is deter-
mined by the coefficient
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1,0
0,9
0,8
47
0,6
451 4336
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U,T,A
1,
2
r lk
MIN\
t
2
,
4 *

I
6
1
/
4536
736
4936
1,136
Fig. 5. Variation in fuel-element jacket
temperature when there is a break in a duct
at the reactor outlet: 1) T = 0 sec; 2) 0.5
sec; 3) 1.5 sec; 4) 2 sec; 5) 2.5 sec; 6) 3
sec.
7 csec
Fig. 4. Curves showing the flow rate,
pressure, and temperature of the cool-
ant at the reactor inlet for a burst duct
at the reactor outlet; ?) break in main
vapor duct, with Fell = (1/6)F0;
break in one branch of a six-branch va-
por duct.
which indicates the length of time the segment could
maintain a nominal coolant flow rate. The difference
between the maximum and minimum pressure values
results in natural flow of the coolant between the high-
pressure and low-pressure sides. Relatively low flow
velocities in the dissociating coolant in the liquid phase
will result in large values of the coefficient Km. In in-
dividual segments, according to the data of the Nuclear
Energy Institute of the Academy of Sciences of the Byelo-
russian SSR, this length of time that the coolant continues
to flow after the pump stops may vary from 20 to 6.0 sec,
depending on the design and the parameters of the cycle.
For gas-cooled loops with other coolants, this co-
efficient is much lower. In a two-loop conversion sys-
tem the difference between the maximum and minimum
pressure values in the first loop depends only on the hy-
draulic resistances and has a low value, which cannot
maintain the necessary coolant circulation. In a single-
loop conversion system this difference depends on the
pressure ratio in the thermodynamic cycle. When the
coolant used is helium, this values varies from 2 to 7
[6]. In a gas-liquid cycle with a dissociating coolant
the pressure ratio is about 70 when the difference be-
tween the pressures ranges up to 160 atm.
The following basic assumptions were made in the
investigation of breakdown situations: the gas in the loop
expands polytropically; the fuel and the jacket of the fuel element have a temperature equal to the value
obtained by averaging over the radius; the processes in each volume correspond to equilibrium properties;
the characteristics of the turbines conform to Fluegelts equations; and the reactor kinetics are charac-
terized by a concentrated model with six groups of delayed neutrons.
We can see from Fig. 3 how the flow rate, pressure, and temperature of the dissociating coolant at
the reactor inlet vary when the main circulating pumps fail (there is no overshoot of the pumps, and vapor
is formed only as a result of the heat contained in the coolant). When the whole station loses power, the
vapor goes past the turbines into the condenser.
Owing to the accumulation of gas on the high-pressure side, continuous circulation is 'maintained for
a fairly long time, affording an opportunity for action to restore the power or shut down the reactor and
organize the shutdown cooling process.
Let us consider a breakdown in which there is a break in the main vapor duct with an effective cross
section equal to the area of one branch on the segment between the reactor and the high-pressure turbine.
The variation of the coolant flow rate, temperature, and pressure at the reactor inlet is shown for two
cases of this kind of breakdown in Fig. 4. The coolant flow rate sharply increases at first, after which it
diminishes as time increases. The reactor control systems maintain constant power, and the breakdown
protection system is not yet activated. In Fig. 5 we show how the fuel-element jacket temperature varies
along the zone. The maximum temperature drop is about 10%.
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Fig. 6. Diagram of shutdown
cooling system; 1) reactor;
2) regenerator; 3) condenser;
V-4 4) pump; 5) tank of liquid
coolant.
A study of the power variation resulting from the temperature effects following a failure of the auto-
matic power-regulating system showed that when the value N = 1.15 No is reached, the breakdown-protec-
tion system will be activated, with a delay of 0.5 sec. The variation in jacket temperature vertically along
the zone does not exceed the allowable values.
Thus, when there is a break in the main vapor duct at the reactor outlet, the accumulation of gas on
the high-pressure side may maintain continuous circulation, affording an opportunity to take steps to shut
down the reactor and initiate the process of shutdown cooling. The greatest danger in such a breakdown
may result from the substantially increased pressure drop in the structural elements of the reactor due to
the increase in hydraulic resistances when the coolant flow rate is high.
A break in the main vapor duct at the reactor inlet is a very serious kind of breakdown. Depending
on the cross-sectional area of the break, the forward circulation may be reduced and reverse circulation
may take place. There may be points with zero coolant flow in the gas passages. When there is reverse
circulation, the coolant stops at the instant the break takes place, after which it flows in the reverse direc-
tion owing to the accumulation of gas in the segment between the reactor and the high-pressure turbine.
The gas in the high-pressure cavity'flows out in two directions at the same time; through the reactor and
through the high-pressure turbine into the regenerator, after which it passes through the low-pressure
turbine into the condenser.
In order to estimate the properties of reactor self-regulation when there is a sudden variation in
reactivity, we compared it with a sodium-cooled reactor. To obtain an equal power-excursion value, we
must introduce twice as much reactivity into the reactor using the dissociating coolant.
The density effect makes very little change in transient regimes. Even when the coolant is complete-
ly removed and the regulating system fails, the power excursion does not exceed the allowable values.
The special physicochemical and thermophysical properties of N204, whose boiling point lies in the
operating-temperature range, makes it possible to use the coolant in the liquid phase for shutdown cooling
of a gas-cooled reactor [11]. A special system is provided for emergency shutdown cooling. The initial
(emergency) cooling of the reactor, as was shown, can be carried out by means of the main loop, after
which the shutdown cooling system is connected.
In Fig. 6 we show a diagram of the shutdown cooling system, which is a closed gas?liquid loop con-
nected to the reactor in parallel with the main loop. While the power station is in operation, the coolant
passes through the shutdown cooling system by way of the shutoff valve V-3, heating the heat-exchange ap-
paratus and the ducts. The coolant passes from the reactor to the regenerator and is then condensed; it
enters the regenerator by way of valve V-4, bypassing the pump and is discharged to the condenser of the
main loop.
When there is a breakdown, the heat is initially removed by the main loop owing to the coolant flow-
ing through it. Then, by means of the breakdown-protection system, shutdown cooling takes place; for
this purpose valves V-1 and V-2 are opened and the main loop is disconnected. The shutdown cooling sys-
tem operates on a gas?liquid cycle. After reducing the pressure and temperature of the coolant, there is
a change to liquid circulation. For this purpose, valve V-5 is opened and the liquid frdm the tank enters
the loop. The shutdown cooling system is fed by an independent source of electric power.
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It should be noted that an emergency shutdown cooling system using a liquid product can be used in
ordinary operation.
On the basis of the foregoing, we may state the following conclusions.
1. The special properties of a flow circuit and a thermodynamic cycle using a dissociating coolant
make it possible to maintain continuity of circulation and ensure both initial cooling of the reactor and shut-
down cooling after the breakdown-protection system has been activated.
2. The special physicochemical properties of dissociating coolants make it possible to use the cool-
ant in the lquid phase for shutdown cooling of a gas-cooled reactor.
k.?) 3. In order to prevent any deformation and rupture of structural elements of the reactor, means
should be provided for limiting the flow rate of the coolant coming out of the maximum-pressure region.
4. For single-loop atomic power stations with a dissociating coolant, it is desirable to use a special
emergency shutdown cooling system.
LITERATURE CITED
1. D. Okrent et al. (United States), Third Geneva Conference (1964), Report No. 267.
2. W. J. McCarthy Jr. et al. (United States), Third Geneva Conference (1964), Report No. 284.
3. K. Grattion et al. (Netherlands), Fourth Geneva Conference (1971), Report No. 023.
4. 0. M. Kovalevich, in: Status and Prospects of Work Designed to Develop Atomic Power Stations with
Fast Reactors, Vol. II [in Russiani, SEV Symposium, Obninsk (1967), p. 344.
5. Yu. E. Bagdasarov et al., Technological Problems of Fast Reactors [in Russian], Atomizdat, Mos-
cow (1969).
6. A. K. Krasin, Reactors of Atomic Power Stations [in Russian], Izd-vo Nauka i Tekhnika, Minsk
(1971).
7. V. B. Nesterenko, Proceedings of the All-Union Conference on Dissociating Gases as Coolants and
Working Fluids of Power Installations [in Russian], Izd-vo Nauka i Tekhnika, Minsk (1970),, p. 11.
8. Thermodynamic and Transfer Properties of Chemically Reacting Gaseous Systems [in Russian],
A. K. Krasin and V. B. Nesterenko (editors), Izd-vo Nauka i Tekhnika, Minsk, Part I (1967); Part
11 (1971).
9. V. B. Nesterenko, Physicotechnological Foundations of the Use of Dissociating Gases as Coolants
and Working Fluids at Atomic Power Stations [in Russian], Izd-vo Nauka i Tekhnika, Minsk (1971).
10. V. B. Nesterenko et al., Izv. AN BSSR, Seriya Fiz. -Energ. Nauk, 3, 5 (1971).
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CHOOSING ABSORBING-ROD EFFICIENCY FOR
SHIELDING AGAINST EXCESSIVE POWER LEVELS
A. A. Sarkisov, V. N. Puchkov, UDC 621.039.566.8
and B. A. Mel'nikov
Most of the emergency shielding (ES) algorithms in use specify reactor shutdown when an excessive
power level is signalled. This has two extremely undesirable effects; 1) significant thermal stresses
arise in the core structural elements; this has a negative effect on their reliability; 2) restarting the re-
actor takes a great deal of time which significantly decreases the installation's adjustability.
It is known that most cases of triggering the shielding when excessive power is signalled are caused
by reactivity release when the control system malfunctions or by errors made by personnel.
In several cases when the reactivity release is caused by moving the controls it is possible when the
power is exceeded to a certain extent to stop the action of the source of disturbance by inserting an inter-
lock into the absorber control circuit. Then, to end the emergency situation, instead of shutting down the
reactor, one can rapidly insert into the core absorbing rods whose efficiency is equal to the magnitude of
the released reactivity. Functionally, these duties can be given, for instance, to the reserve regulator
which is constantly in "hot" reserve. In this variant, the emergency shielding rods must play the role of
an insurance unit. For this purpose, their triggering level must be increased a bit.
The main problem of this study consisted of determining the minimum efficiency for absorbing-rods
which would provide reliable reactor shielding during reactivity disturbances in all cases when these rods
are triggered simultaneously with stopping the effect of the source of disturbance. The study was made
using the IR-100 reactor and an electronic model of reactor kinetics made on an MN-14 analog computer.
While the experiment was performed on the IR-100, an absorbing rod was located in the central ex-
perimental channel; it was moved out of the core by a special servomechanism at various cons6nt speeds.
The rod was moved in the range where its differential efficiency is practically constant. Removal of the
rod began at a certain steady-state power level No = 0.5 Np = const, and ended when the ES was triggered
by a signal that the prescribed power Np had been exceeded by a factor of 2. The prescribed power level
was kept constant in all modes. The rate of reactivity release was varied within the limits (8-32) .10-5
sec-1.
As a result of the experiments, we obtained a family of curves determining the variation in relative
reactor power as a function of the rate of reactivity release and the time. Since in all cases po = 0 and the
reactivity increases linearly, at any moment of time the magnitude of the released reactivity is pt. Thus,
the dependences we obtain can be given in the form p = f(p, N/No) (see Fig. 1).
By comparing the curves given in Fig. 1 it follows that at low rates of reactivity release the magnitude
p corresponding to the given value of N/No depends significantly on the reactivity-release rate. As p in-
creases, this dependence approaches a saturation point, and becomes weaker. In connection with this, we
continued the study on an electronic model of reactor kinetics, which allowed us to increase the reactivity-
release rate to 68 ? 10-4 sec-1.
When the process was described mathematically, the space distribution of neutrons in the core was
disregarded and a one-group representation of the neutron spectrum was taken to be correct. The admis-
sibility of such a simplification when studying transition processes with prolonged reactivity discontinuities
Translated from Atomnaya nergiya, Vol. 34, No. 6, pp. 441-444, June, 1973. Original article
submitted July 14, 1972.
C 1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
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p, x 104
21
19
17
15
f3
11
2
4
7
10
f,2
1,4 1,6
Fig. 1
1,8
N/No
28
24
20
16
12
8
4
0
2
4
6' ;
7
0
10
1,4 ,1,6
Fig. 2
1,8 N/No
Fig. 1. Dependence of the reactivity p released up to the time when the power increases
by a factor of N/No, on the rate of reactivity release .1) (sec-1): 1) 32 ? 10-5; 2) 28 ? 10-5; 3)
24 ? 10-5; 4) 20 ? 10-5; 5) 16 ? 10-5; 6) 12 ? 10-5; 7) 8 ? 10-5.
Fig. 2. Dependence of p released up to the time -when the power increases by a factor of
N/No on the rate of reactivity release 16 (sec-1): 0) limit; 1) 68 ? 10-4; 2) 56 ? 10-4; 3) 44
? 10-4; 4) 32 '10-4; 5) 20 ? 10-4; 6) 8 ? 10-4; 7) 2 ? 10-4.
up to Ap = 6 ? 10-3 has been shown in [1]. The differential equations have been recorded for all six groups
of delayed neutrons, whose parameters were chosen in accordance with the recommendations in [2] (i3
= 0.0064).
The mean lifetime of prompt neutrons was taken to be 5 ? 10-5 sec. We did not simulate the inverse
temperature relation, since we studied emergency regimes caused by releasing reactivity through remov-
ing regulating units from the core. Under such conditions, the reactivity temperature effect would only
ameliorate the emergency situation by decreasing the reactivity-release rate.
The results obtained from the model were analyzed using the same method as the experimental data.
The curves shown in Fig. 2 also support the fact that, beginning with certain large values of p, the mag-
nitude of the reactivity released up to the time when the threshold value N/No is reached is practically in-
dependent of the rate of reactivity release and is determined only by the value of N/No. This indicates that
at the limit the dependence p = f(p, N/No) simplifies to a relationship of the form p = f(N/N0), which is of
greatest interest.
We can show that when we examine transient processes having durations no greater than 0.1 sec, when
Np = No = const, and the triggering setting of the emergency-shielding system does not exceed 200-250% of
No, then the limiting dependence in which we are interested has the form
P=0 (1?No/N). (1)
This dependence characterizes the maximum reactivity which under the above indicated conditions can be
released at the time the threshold power value is attained; it is shown in Fig. 2 as a limiting curve in-
dicated by 0.
Thus, in the simplest case, when Np = No = const and pi) = 0, the efficiency of absorbing rods needed
to compensate excess reactivity in the emergency situation under consideration can be determined from Eq.
(1).
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p,x(o4
20
15
10
0
....
'
.... .... .....--.
---
-
/
......"
/
/
/,
/
/
/
?..--.?
I
...?
//'''
..-
.... ...-
...? ?
1
4 8 12
Fig. 3
16 p, x10
Axto4
26
22
18
Fig. 4
Fig. 3. Dependence of reactivity p released when I = 5 ?.10-3 sec-1 and po = 0 to the
time of introducing the reserve regulator, on the vafue of p and the triggering setting:
1) ARR 0.2; 2) 0.4; 3) 0.6.
Fig. 4. Dependence of the reactivity p released when Srp = 5 ? 10-3 sec-1 and po = 12
? 10-4 up to the time the reserve regulator is introduced, on the value of I; and the trig-
gering setting; 1) Aim = 0.2; 2) 0.4; 3) 0.6.
However, in practice there may occur more complicated emergency situations in which the reactivity
release when the power increases by a factor of N/No exceeds the value obtained from Eq. (1). For exam-
ple, if the above-studied emergency regime caused by releasing reactivity linearly is not limited by the
condition No = const, then when N > 0, the necessary absorbing-rod efficiency will be somewhat higher
than when Ip = const. Here, the maximum reactivity, release when the reserve-regulator rods are in-
serted will be greater, the greater the rate of increase of the prescribed power level.
To determine the absorbing-rod efficiency needed to compensate excess reactivity in the emergency
system studied we can approximate the initial dependences N/No = go(j), t) by a function of the type
N/No=exp (krtn). (2)
The values of the coefficients, k, m, and n are determined from the composition and structure of the core
6
as functions of /3, l*, and E Pitt.
The efficiency of the reserve-regulator rods is defined as the product p.t, where t is the time from
the start of the emergency process until the insertion of the rods, which can be found from the relation-
ship
Npo+ t
elt.PM ? A RR
NPo
(3)
Here, ARR is the setting for inserting the reserve-regulator rods.
The calculations using the method described were made in accordance with the modeled reactor.
Here, the rate of power increase was taken to be 0.5% per second in the calculations. In Fig. 3, the solid
curves show the results of calculations for three values of ARR with Np = 5 ? 10-3 sec-1. For comparison,
we show by dashed lines on the same figure the dependences p = f(p, N/No) when Np = const.
The emergency situation examined can be made more rigorous if we assume that at the time the im-
balance between N and Np appeared the reactivity was nonzero (po 0), but corresponded to some value
causing reactor excursion with maximum allowable period. In this case, the necessary reserve-regulator-
rod efficiency can be determined from
RR=Po-Ff;t? (4)
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imivo
1,2
f,
48
46
0,4
0,2
)6-510-4
0
2
4
7 8 t, sec
Fig. 5. Transient processes when absorbing rods having ef-
ficiencies 20.10-3 (curve 1) and 1.1 ? 10-3 (curve 2) are .ac-
tuated.
The time t from the start of the mismatch between the prescribed and actual power levels, as in the pre-
vious case, can be found from Eq. (3), but the values of the coefficients k, m, and n in Eq. (2) must, in
this case, be changed according to the initial reactivity /30. Besides this, the values of No and Npo are here
taken not at the start of the transient process, but at the instant Np is exceeded.
Figure 4 shows results of calculating the maximum values of reactivity released to the time when the
power increases to (N/N0)* equal to 1.2, 1.4, and 1.6, when Np = 5 ? 10-3 sec-1 and po = 12 ? 10-4. All cal-
culations were made in accordance with the modeled reactor.
Comparison of the curves in Figs. 3 and 4 shows that the greatest reactivity can be released when po
corresponds to the maximum allowable period and the given powerin the transient process increases at a
maximal rate. However, in this case even when (N/No)* = 1.6, the necessary reserve-regulator rod ef-
ficiency is only 2.88 ? 10-3. This allows us to conclude that, to eliminate the studied emergency situations
caused by release of reactivity, we can effectively use relatively "light" absorbing rods.
To illustrate the advantages of the suggested reactor-shielding method during reactivity disturbances,
we made two series of calculations on an electronic model. In both cases, from the initial state po = 0 re-
activity was released at rates of 10-4, 5 ? 10-4, and 5 ? 10-3 sec-1. However, in the first variant, when the
prescribed power level was exceeded by 20%, "heavy" emergency shielding rods were actuated, having a
total "weight" of 20 ? 10-3; the second variant used "light" absorbing rods whose efficiency was 1.1 ? 10-3,
determined from Eq. (1).
It is clear from Fig. 5 that in the emergency regimes examined, the use of "light" absorbing rods in-
stead of the traditional system of shutting down the reactor allows one to ensure reliable shielding of the -
reactor from accidentally exceeding the prescribed power level while minimizing thermal stresses. Be-
sides this, triggering of the reserve regulator in this case practically does not interfere with the prescribed
working regime of the power station.
LITERATURE CITED
1. I. I. Sidorova, Analog Modeling in Nuclear Technology [in Russian], Atomizdat, Moscow (1969).
2. G. Keepin et al., Phys. Rev. , 107, 1044 (1957).
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NEUTRON TRANSPORT EQUATION SUITABLE FOR
OBTAINING APPROXIMATE THIRMALIZATION
EQUATIONS
N. I. Laletin UDC 539.125.52:621.039.51.12
It often proves useful to convert an equation describing some physical process into an equivalent equa-
tion which, in some specific sense, is more convenient. The usual procedure for such a conversation is as
follows. The operator A of the original equation Af = St is divided into a sum of two A = Ao + B. If there
exists an operator Ao-i reciprocal (inverse) to Ao, then for the unknown function f we have an equation
1= A-0-1 S ?
Examples of this kind of transformation include the following; in quantum mechanics, the derivation of the
integral form of SchrOdinger's equation from the differential form [1]; in the theory of neutron transport,
the derivation of the Wigner?Weinberg?Corngold?Orlov equation [3-4] and the Peierls equation [2] from
the Boltzmann relationship. This kind of transformation will be useful if we make a successful choice of
Ao, i.e., essentially if we choose an operator reasonably characteristic of the group of problems evoking
our particular interest.
When considering the thermalization of neutrons this type of transformation requires a certain modi-
fication. We have to s?tart by choosing a characteristic solution, and in this regard cannot dispense with
physical considerations.
Let us consider the very simple problem of the energy spectrum of the slow neutrons arising from a
monoenergetic, spatially-uniform source in an infinite homogeneous medium '[5]. The equation for this
case takes the form
[Ea (e) ? Es (e)] (I) (e) =Es (e' ?)- e) CD (e') de' +6 ?e').
(1)
Here E = E/kT is the energy E of the neutrons in units of kT, where T is the temperature of the medium
and k is Boltzmann's constant, 43(e) is the neutron flux of energy e, Ea(e) and Es(e) are the macroscopic
neutron absorption and inelastic scattering cross sections, Es(el e) is the scattering cross section of a
neutron with energy e' in the range close to the energy E, 6(x) is the Dirac 6-function, ei is the energy of
the source neutrons. We shall consider that
Let us rewrite Eq. (1):
el >>1.
dQ ? E a (e) CD (0-6 (e? et),
de ?
(2)
where we have introduced the nomenclature
e
Q (6) = .c de" ). de'Es (e' e") (I) (e') ? .c de" ). de'Es (e' e") (e'). (3)
o e
We see from the foregoing equation that Q(e) is the generalized slowing-down density for the case in which
the nuclei are moving. It is natural to call Q(e) the current along the energy axis.
Translated from Atomnaya nergiya, Vol. 34, No. 6, pp. 445-449, June, 1973. Original article
submitted April 17, 1972.
0 1973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available frcm the publisher for $15.00.
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As auxiliary functions for the transformation of Eq. (2) we take the solution to the equation
(18
One solution corresponding to Q(e) 0 is the equilibrium distribution M(e) = ee-6. Another solution will
be the function for which Q(6) = const 0 (without reducing generality we may take the constant as 1).
Let us denote this solution by 1(e) and present the basic information relating to it which will be needed
for the future.
In the slowing-down range (c>> 1) I (e) will transform into the well-known Fermi spectrum I(e) 1
A0E5e. Here is the logarithmic mean of the energy loss in a collision with a stationary nucleus. Gen-
erally speaking, the function I(e) may be divided into two parts: 1(e) = ? (o(e)/Es(0) + Ir(6), where Ir(e)
is the regular component of the solution. This component is accurately defined apart from the addition of
a Maxwell function with an arbitrary factor. It is therefore more convenient to deal with the function
i (8) [ir (8)/M (6)]*
Making allowance for the behavior of i(e) at e >> 1 we introduce the new function
00
Z (e) = ee i (e')e-c' de'.
C
Then i(e) = z(e) ? (d/d6)z(e).
Since in the limiting cases of the gas model (m = 1 and m >> 1 where m is the mass number of the
slowing-down nucleus) the function z(e) may be expressed by a unique formula [6]
zg.i-n(8)=bzscom co'
it is reasonable in the general case-to express z(e) in the form
1+ t (e)
z(6) = bEs (OM (6) ?
It is easy to show that t(e) satisfies an integral equation of the second kind which may be solved nu-
merically by standard methods. Hence t(e) 0 for a gas with m = 1 while for a gas with m >> 1 this func-
tion only differs appreciably from zero for e <
We note that in the expression for z(c) the quantity t(E) enters in the combination 0E5(e)/[1 + t(e)1.
Let us introduce the quantity (6) = /[i+ t(c)J. We may assume that this in some way characterizes the
width of the distribution of singly-scattered neutrons having an energy e before collision.
Using the two characteristic solutions of M(E) and I(e) at our disposal we may transform the original
kinetic equation (1). In the formal procedure under consideration, the first step-is that of separating out
an operator Ao determined by the characteristic solutions. In the present case a suitable operator will be
A0f= (e' ?)-e) f (e') de' ?Es (e) f (e).
However, there is no continuous reciprocal operator A-01 in the class of functions satisfying the natural
physical requirements, since there is no solution to the equation
DO
(6' f (8' ) de' ? Es (e) f (s) = ? 6(6 ? ei).
Physically this is readily understandable, being due to the fact that there can be no steady-state neutron
distribution in an infinite nonabsorbing medium with a constantly acting source. However, a solution exists
for the equation
550
CO
.c Es (e' 8) f (e') de' ? Es (6) f (8) =
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(4)
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and this will be used later. This solution is defined apart from the addition of a Maxwell function with an
arbitrary factor. Apart from obvious physical considerations we may use a formal mathematical argument
Is a verification of the existence of a solution to Eq. (4). It is well known that, if a homogeneous equation
Aof = 0 has a nontrivial solution, the corresponding inhomogeneous equation Aof = cp will only have a solu-
tion if the right-hand side of the equation'yo(x) is orthogonal to the solution of the conjugate homogeneous
equation Ate- = 0. Since in the present case the solution of the conjugate equation
00
A+ f+
is constant, it is required that the integral of the right-hand side of Eq. (4) should vanish, and this is in-
deed the case.
In order to simplify the calculations we may put et ? 00 into Eq. (4), although this will not reduce the
generality of the consideration. The solution of the equation so obtained we call G(e/eo). Since the left-
hand side of Eq. (4) is the quantity dQ/de, it is easy to show that Q = 0 for e < eo and Q = 1 for e > E. We
then proceed as follows. On considering the energy range e < eo, we may reasonably assume that, if the
neutron sink situated at e = oin the problem is displaced in the direction of infinite energies, then this
will only make an appreciable difference to the solution in the energy range of present interest in the im-
mediate vicinity of e = Co, i.e. , the chief component of the solution G(e/ei) for E < eo will be the Maxwell
function M(e). An analogous discussion when considering the range e > eo strongly suggests that the chief
component of the solution will in this case be I(E). Guided by these considerations, we express G(e/e0) in
the form
G (8/8?) g (e/e0) 6 (8-60) I Ci (so) M (8), 8< so;
8 (e) 2a (8) + C2 (60) M (0+ I (8), 680-
(5)
After requiring that the equation Ci(eo)M(eo) = C2(e0)M(e0)+ 1(e0) should be satisfied, we are left with only
one arbitrary function. We rewrite the expression for G(e/e0)
{0, e6o.
Equation (5) signifies that, instead of the unknown function G(e/e0), we have introduced the unknown function
g(e/60). The usefulness of this change depends on how valid are the considerations serving as a basis for
Eq. (5).
Substituting (5a) into (4) and making a number of transformations, we obtain an equation for g(e/eo)
00
g (6'/2) 188'-) 8) de' g (e18) = S (s/so)?
The expression for S(e/?0) takes the form
0.
(6)
.f p (e)
co
s (6/80) _ ; (,Bo ? E) X Es (e' --).- e) de' , e< eo;
Es (80) 1 1
[ m 1 t,8 ) s
b ,co), m (8, ) ___ I (8,)]
t o
I X Es (e' ??- 8) de', 8 > eo.
It is easy to see that S(e/e0) is an alternating function only differing from zero in a narrow range of energies
L close to the value eo (in the region of the energy transferred by a neutron in a single collision). The in-
tegral of S(e/e0) with respect to e equals zero
S (e/e0) de -= O.
The function g(e/e0) is not determined uniquely by Eq. (6). In order to avoid the indeterminacy, we
transform Eq. (6) by means of (5a), assuming C(e0) = const = C in the latter.
We obtain an equation
CO
g (8/80) ? S (6'/8) g (6/8') de' = h (818).
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Here
h (?/Eo) = ?S (8/80) + Es (8)M (8) S (e/e0) i (8") de" d8'.
b e?
The function g(6/60) so defined is alternating, the interval over which it deviates appreciably from zero
being similar to the corresponding interval for S(6/60). For e>> 1 we have
g (8/80) [1(71 ?70-1 PA ( ) X (80 ?
where PA(x) is the Placzek function [4], x(x) = (, 0, x 1/m and Ea(1)/0E0 1 have to be satisfied.
If in Eq. (10) we put
1
z (e) ? 4Es (?) m (8) Ii (8) = z (8) ? z (e)1 ;
/3 (8) = (1 erf me
+ ;
V 111118
11 (ell)) = To = 1 1 a (ln ct)2CL?
nz \ 2
2 (1? ago ' )
we obtain an equation incorporating three limiting cases: the Wigner?Wilkins equation for m = 1 and the
Wilkins and Corngold equations for m ?1. This equation, which was earlier proposed in [6], should thus
give reasonable results for a gas of any arbitrary mass.
If the functions i(e) and y(e) are chosen so that, in a medium of low absorption behaving as 1/Arc, the
approximate equation should give a solution as close as possible to the solution of the exact equation, we
obtain the equation of the "generalized heavy-gas model" [10, 11] and that of the "secondary" model [11].
Furthermore, Eq. (10) enables us to derive formulas providing a more reliable determination of the func-
tions i(e) and y(e) than those of [10, 11].
Of the two functions entering into the approximate equations under consideration, the principal part
is, of course, played by the function i(E) for all energies 6, and especially for e >> 1, where its role be-
comes dominant. In media with not too strong an absorption, however, the function y(e) only affects the
behavior of the solution for 6 1, when the Maxwell component of the solution plays the major part. The
weak dependence of the neutron spectra on the function y(e) in media with an absorption cross section vary-
ing as 1//6 is demonstrated by the results of the calculations in [10, 12]. However, if the absorption varies
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in a resonance manner, the role of the function y(E) becomes more important. This may be seen from the
corresponding curves of [11, 121.
These considerations served as a basis for the proposition that the thermalization of neutrons in wa-
ter should be described by means of a two-constant model [12]. In choosing the function (E)Es(E) = const
allowance was made for the fact (noted by many research workers) that the neutron spectra in water with an
absorber varying as 1/1,re were excellently described by the "heavy-gas" model. The function y(E) was in-
troduced so that the model should also satisfactorily describe thermalization in water with a resonance ab-
sorber. Since all the "interesting" resonances in the absorption cross sections lie in the range E >> 1, the
simplest relationship y(e) = yo = 1 was chosen. As we have just shown, this simple model gives a com-
pletely acceptable accuracy.
In conclusion, we note that there is no difficulty in carrying out a transformation similar to the one
of the present analysis for an equation with the spatial dependence of [7].
LITERATURE CITED
1. D. Schiff, Quantum Mechanics [Russian translation], IL, Moscow (1957).
2. B. Davison, Theory of Neutron Transport [Russian translation], Atomizdat, Moscow (1960).
3. N. Corngold, Proc. Phys. Soc., A70, 793 (1957).
4. A. Weinberg and E. Wigner, Physical Theory of Nuclear Reactors [Russian translation], IL, Mos-
cow (1961).
5. N. I. Laletin, Preprint IA-2146 (1971).
6. N. I. Laletin, At. Energ., 14, 458 (1963).
7. N. I. Laletin, Preprint IAE-2145 (1971).
8. E. Cohen (USA), First Geneva Conference (1955), Paper No. R/611.
9. N. Corngold, Ann. Phys., 6, 368 (1959).
10. H. Pitcher, AEEW-M-350 (1963).
11. M. Cadilhac et al., BNL-719 (c-32), Vol. 2 (1962), p. 439; in: Thermalization of Neutrons [Rus-
sian translation], Atomizdat, Moscow (1964); M. Cadilhac et al. (France), Third Geneva Conference
(1964), Paper No. R/73.
12. N. I. Laletin, At. Energ., 17, 193 (1964).
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EFFECT OF SCATTERING
THERMAL-NEUTRON USE
N. I. Laletin, N. V.
Yu. A. Vlasov, and
ANISOTROPY ON THE
FACTOR
Sultanov, UDC 621.039:512.4
S. I. Konyaev
In calculating the use factor of the thermal neutrons in a heterogeneous reactor, anisotropic scatter-
ing is usually taken into account in only a very coarse manner. The transport approximation [1] is nearly
always used, and only sometimes the linearly-anisotropic approximation [1, 2]. In these approximations
the zeroth and first angular moments of the scattering indicatrix are correctly taken into account, but the
higher moments are distorted. In the transport approximation all the angular moments with numbers n a-2
are regarded as being equal to the first angular moment, while in the linearly-anisotropic approximation
they are put equal to zero.
The general opinion to the effect that such a distortion would not lead to any serious errors in the
thermal-neutron use factor was recently questioned [3]. When calculating certain two-zone plane cells,
Eccleston and McCormick [3] observed that allowance for the second angular moment of the scattering in-
dicatrix led to a change in the disadvantage factor comparable in magnitude with the corresponding change
associated with the first angular moment. In addition to this, both changes were of the same sign.
If these conclusions [3] are valid, then in calculating uranium?water cells it is extremely vital to al-
low for the second angular moment of the scattering indicatrix. We note that for many of the methods em-
ployed this implies serious complication of the computing process.
The validity of the results presented in [3], however, arouses serious misgivings. It was in fact
shown in [4, 5]* that
01-00?EarnVrn= C oll'I,P,16/77.VIn
(1)
Here 00 and 01 are the thermal-neutron use factors on the isotropic and linearly-anisotropic approxima-
tions respectivelyt; lam is the absorption cross section in the moderator; Vm is the volume of the mod-
erator; Egi)n is the first angular moment of the scattering cross section in the moderator; ?I/K0 and 14
111
are the first angular moments of the neutron distribution function in the moderator calculated on the iso-
tropic (iIrRo) and linearly-anisotropic (4,4) approximations.
By AP(ri) we understand 2n + 1-component vectors with components *(),k In KI)P111(rli,4) eik(PdC2,
while 11411)?1,n) is their scalar product (here P(o) are associated Legendre polynomials with the usual nor-
malization
If we slightly transform the equations of [4] we obtain
0,-01 ?EamVm5Esm 011)11), 2 di'. (2)
v.
*The change in the thermal-neutron use factor 60 is simply related to the corresponding change in the dis-
advantage factor 6d:
tTwo-zone cells are here under consideration, scattering always being regarded as isotropic in the fuel.
Translated from Atomnaya Energiya, Vol. 34, No. 6, pp. 450-454, June, 1973. Original article
submitted August 22, 1972.
C /973 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York,
N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without
permission of the publisher. A copy of this article is available from the publisher for $15.00.
555
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TABLE 1. Discrete Value of vc,
ineff
0 1 2 3
Transport
approxima-
tion*
2,06
6,33192
6,33192
10,87639
7,68370
10,88836
7,68501
10,88836
10,88836
3,71085
5,22654
*The calculations on the transport approximation involve replacing
Es by E s (1 -7).
TABLE 2. Rate of Convergence of GN
GN
GI
G3
Gb
07
Gii
G13
d
1,0902
1,1442
1,1572
1,1611
1,1625
1,1630
1,1635
(1,1631)*
The brackets indicate a calculation in which the integral in (3) was
computed by a 27-point quadrature formula of the Gauss type.
Here 02 is the thermal-neutron use factor calculated on an approximation in which the three first terms are
left in the Legendre-polynomial expansion of the scattering indicatrix in the moderator, 2) is the second
angular moment of the scattering cross section in the moderator, xi, f??, 2 is the second angular moment of
the distribution function in the approximation under consideration.
It follows from Eqs. (1) and (2) that the following relationships must be satisfied for the results of
[3] to be valid:
and
13r,g JC iriV, 077;2, dr 5E2,1)% 041(,1), 2 06*
Vm V.
llf.;,;011T,), 2 dr x';
x'-x
^ dv for x