SOVIET ATOMIC ENERGY VOL. 56, NO. 1

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• Original Classification: K
• Document Page Count: 71
• Document Creation Date: January 4, 2017
• Document Release Date: September 14, 2013
• Sequence Number: 1
• Publication Date: January 1, 1984
• Content Type: REPORT

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Russian Original Vol. 56, No. 1, January, 1984 _195
July, 1984'
rc
q))
SATEAZ 56(1) 1-64 (1984)
SOVIET
ATOMIC
ENERGY
ATOMHAFI 3HEPrI4F1
(ATOMNAYA ENERGIYA)
TRANSLATED FROM RUSSIAN
CONSULTANTS BUREAU, NEW YORK
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SOVIET Joviet AltOMIC energy is a translation of Atomnaya inergiya,
publication of the Academy of Sciences of ,the USSR.
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Editorial Board of Atomnaya Energiya:
Editor: 0. D. Kazachkovskii
Associate Editors: N. A. Vlasov and N. N. Ponomarev-Stepnoi
Secretary: A. I. Artemov
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Yu. I. Koryakin A. S. Shtan'
E. V. Kulov B. A. Sidorenko
B. N. Laskorin M. F. Troyanov
E. I. Vorob'ev
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SOVIET ATOMIC ENERGY
A translation of Atomnaya Energiya
July, 1984
Volume 56, Number 1 January, 1984
CONTENTS
Engl./Russ.
ARTICLES
High-Temperature Power-Technological Reactor with Solid
Coolant and Radiative Heat Exchange.? A. M. Alekseev,
Yu. M Bulkin, S. I. Vasil'ev, E. S. Gerasimov, N. A. Dollezhal',
I. Ya. Emel'yanov, N.D. Zaichko, Yu. I. Koryakin,
E. K. Nazarov, A. V. Petrushin, S. V. Radchenko, V. P. Smirnov,
V.A. Chernyaev, and I. L. Chikhladze
1
5
Synthesis of a System for Stabilizing Reactor Power and Energy
Distribution on the Basis of Lateral Ionization Chambers
? I. Ya. Emel'yanov, L. N. Podlazov, A. N. Aleksakov,
E. V. Nikolaev, V. M. Panin, and V. D. Rogova
8
11
Analysis of the Statistical Error and Optimization of Correlation
Flow Meters ? B. V. Kebadze
13
15
Analytic Approximation of Neutron Physics Data ? S. A. Badikov,
V. A. Vinogradov, E. V. Gai, and N. S. Rabotnov
19
20
Fracture Rate of 10Kh2M Steel When Water Enters Sodium
in a Counterflow Steam Generator ? V. S. Sroelov, P. P. Bocharin,
A. A. Saigin, and T. I. Vasilevich
26
25
Hydrogen Balance in the INTOR Reactor ? V. A. Sharapov,
A. E. Gorodetskii, A. P. Zakharov, and A. I. Pavlov
30
29
Effect of Uncertainties in Neutron Cross Sections on the Characteristics
of a Thermonuclear Reactor Blanket and Shield ? A. I. Ilyushkin,
I. I. Linge, V. P. Mashkovich, V. K. Sakharov, G. E. Shatalov,
and A. V. Shikin
34
32
Spatial Distributions of Dose Fields in a Water Absorber Bombarded
with High-Energy Nucleons ? A. Ya. Serov, B. S. Sychev,
E. P. Cherevatenko, and S. V. Chernov
39
36
Fused Silica in Ionizing-Radiation Dosimetry ? R. R. Gulamova,
N. A. Kasimov, and M. I. Muminov
44
40
An Application Package for Processing and Analyzing Data
on the Environment and Population Health ? E. I. Vorob'ev,
V. A Kornelyuk, A. S. Kuz'menko, V. Yu. Reznichenko,
and V. L. Shestopalov
48
43
Radionuclide Deflation Effects in a Contaminated Locality
with Intermittent and Steady-State Discharges into the Atmosphere
? K. P. Makhontko
52
47
Use of Proton and.Deuteron Activation Method of Analysis
in the Determination of Elements with Z> 42 ? S. Mukhammedov,
A. Vasidov, and E. Pardaev
56
50
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CONTENTS
(continued)
Engl./Russ.
LETTERS TO THE EDITOR
Results of Measurements of the Neutron Field in the Channels
of the VVER-1000 ? S. S. Lomakin, A. G. Morozov,
G. G. Panfilov, V. P. Kruglov, and G. M. Bakhirev 59 54
Amplitude Characteristic of Pyroelectric Detectors ? V. A. Borisyonok
and E. Z. Novitskii
The Russian press date (podpisano k pechati) of this issue was 12/31/1983.
Publication therefore did not occur prior to this date, but must be assumed
to have taken place reasonably soon thereafter.
61 55
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ARTICLES
HIGH-TEMPERATURE POWER-TECHNOLOGICAL
REACTOR WITH SOLID COOLANT AND RADIATIVE
HEAT EXCHANGE
A. M. Alekseev, Yu. M. Bulkin,
S. I. Vasil'ev, E. S. Gerasimov,
N. A. Dollezhalt, I. Ya. Emel'yanov,
N. D. Zaichko, Yu. I. Koryakin,
E. K. Nazarov, A. V. Petrushin,
S. V. Radchenko, V. P. Smirnov,
V. A. Chernyaev, and I. L. Chikhladze
UDC 621.039.5/6+621.039.524.2
A high-temperature power-technological reactor for carrying out processes based on endothermic chem-
ical reactions usually is associated with a reactor in which helium under pressure is used as the coolant. The
temperature necessary for the efficient conduct of the majority of high-temperature power-technological pro-
cesses amounts to 850-900?C. The direct transfer of heat from the coolant of the core directly into the technolog-
ical process is excluded on the grounds of radiation safety: The populationuses the product obtained as the
result of power-technological processes. Therefore, in such a process the radiation-uncontaminated heat can
be supplied only through some or other system of heat-exchange facilities. This means that the coolant temper-
ature (in this case helium) at the core outlet must be somewhat higher and must attain ?950-1000?C. The prob-
lem of obtaining and, mainly, of transferring into the process coolant at this temperature through a system of
heat-exchange facilities also in the main determines the whole complexity of the construction of a commercial
power-technological reactor.
The possibility of overcoming such a high-temperature barrier undoubtedly is increased by finding alter-
native concepts for reactors of this designation. We note, that at one time the economic competitiveness of
electric power reactors was mainly promoted by alternative reactor concepts, extending the feasibility of uti-
lizing coolant with a temperature of ?300?C, at which the majority of light-water reactors operate for the pro-
duction of electric power.
In this paper, a graphite reactor is described in which the principle of heat transfer by radiative heat-ex-
change from a solid coolant is used (GROTT). It is proposed to utilize in the nuclear-chemical assembly of the
production plant, ammonia as the principal source of high-temperature heat for the steam catalytic conversion
of methane.
Construction of the Reactor Facility [1]. The reactor vessel is made of sheet carbon steel in the form of
a leaktight ring-shaped box of rectangular cross section. The cover and the base are flat. The vessel is filled
with an inert gas (helium) at a pressure close to atmospheric. In one of the sector spaces of the vessel, occu-
pying approximately 1/10th of the volume of the annular graphite brickwork, the core is located. In the remain-
ing space, the plant of the technological zone is located (Fig. 1).
The core moderator is made of graphite blocks, collected in rows of curved stacks (Fig. 2), which are
installed concentrically one to the other with a specified pitch over the radius. Above, below, outside, and in-
side face, the core is surrounded by the reflector, also assembled from graphite blocks. In the longitudinal di-
rection of the core, the curved stacks of the fixed moderator become the brickwork of the so-called neutron
cutoff, consisting of graphite blocks with a high-temperature absorbing material. Between the rows of the mod-
erator brickwork, also concentrically with the gaps relative to it, are installed the ring-shaped masonry of the
solid coolant, assembled from graphite blocks with a high-temperature nuclear fuel in the form of microparti-
des with a multilayered graphite cladding. The masonry of the solid coolant is installed on individual support-
ing annular rotating platforms, made of separate steel curved sections and joined together in a ring with special
tie rods. The design of the tie rods ensures, on the one hand, joining of these sections into a single annular
rotating platform without free play and, on the other hand, preservation of the originally fixed diameter of the
Translated from Atomnaya Energiya, Vol. 56, No. 1, pp. 5-10, January, 1984. Original article submitted
April 27, 1983.
0038-531X/84/5601-0001$08.50 (g) 1984 Plenum Publishing Corporation
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14 15 18
17
18
Fig. 1. Fig. 2
Fig. 1. Reactor facility with solid coolant: 1) reactor vessel; 2) solid coolant brickwork; 3)
core reflector; 4) core moderator brickwork; 5) brickwork of the neutron cutoff zone; 6) thermal
shield; 7) thermal insulation; 8) radiation shield; 9) unloading-loading manhole; 10) control and
safety rod slave mechanism; 11) evaporative channel; 12) evaporative zone group collector; 13)
drum-separator; 14) steam-gEs channel; 15) group collector of the steam-gas mixture; 16)
steam-gas mixer; 17) distributing collector; 18) conversion channel; 19) conversion zone group
collector; 20) composite collector; 21) bearing-rotatable platform; 22) solid coolant actuator;
23) supporting roller; 24) centering roller.
Fig. 2. Diagram of an annular element of the reactor facility: 1) ring-shaped masonry of the
mobile solid coolant; 2) masonry of the fixed graphite-moderator of the core; 3) control and
safety rods; 4) masonry of the neutron cutoff zone; 5) technological zone (heat-exchanger).
platform (and, consequently, of the coolant brickwork) over the whole range of their working temperature. Each
annular platform is supported on rollers and driving wheels installed on the bottom of the vessel. The driving
wheels are connected through a leaktight magnetic coupling with individual electric drives. The magnetic cou-
plings are located in cuttings through the bottom of the vessel, and the electric drives are disposed in the sub-
reactor compartment. The technological channels are located in the technological zone in the gaps between the
rows of the solid coolant masonry. They are also arranged in concentric rows and are grouped according to
purpose.
In accordance with the possible variations of the layout of the reactor facility, the channels for the steam
catalytic conversion of natural gas (methane), evaporative and superheat channels, channels for heating up the
steam-gas mixture, etc. can be located in the technological zone of the reactor. All the channels are structur-
ally designed according to the Field scheme, and the heads of the channels are sealed to the upper flanges of the
cuttings through the cover of the vessel. Each group of channels, serving some or other purpose, is joined
through headers with the inlet and outlet main lines from the corresponding technological plant of the facility.
The reactor vessel is shielded from inside from the high temperature with a thermal insulator. The cover
of the reactor vessel is filled with a material which shields the compartments located above it from the radia-
tive emission. The cover is cooled with water by coils laid in it.
The rods of the reactor control and safety system are arranged in vertical openings of the moderator
brickwork, and the rod actuators are brought out at the cap of the radiator.
The principal characteristics of the reactor for a chemical combine with a production of -1 million tons
of ammonia per annum are as follows:
Thermal power, MW
-500
Nuclear fuel charge per run with nuclear fuel enriched to 10%in 235U, tons
-25
Running time of facility before recharging fuel and replacement of conversion tubes, years
-40
Solid coolant in the form of ring-shaped bricks:
number of ring-shaped bricks
12
diameter of central ring, m
24
2
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height of active part of ring, m
4
peripheral velocity of ring, m/ sec
0.5
maximum temperature, ?C
-1350
average change of temperature during one revolution (cycle) of the ring, ?C
100
number of cycles per running time
2 .106
Reactor vessel:
height, m
9.5
outside diameter, m
32
inside diameter, m
16
pressure of gas medium inside vessel, MPa
0.095
Reactor Operation [2]. Continuous rotational motion of the supporting annular rotating platforms, with
the masonry of graphite blocks installed on them, is effected with electric drives due to the friction coupling of
the driving wheels with the bearing surfaces of the platforms. As a result of this, every part of the ring of a
graphite brick fulfilling the role of coolant passes through the core, the neutron cutoff zone, and the technolog-
ical zone. In the core, the nuclear fuel contained in the graphite blocks enters into a chain fission reaction, is
heated up, and heats up the graphite. During transit through the core, the graphite is heated up by approximately
100?C on the average, and reaches the maximum temperature, for example 1350?C, sufficient for the efficient
transfer of heat by radiative heat emission.
The moving fuel version, in contrast from the fixed fuel version (also possible in GROTT) is accepted
because it provides a lower temperature to which the fuel must be heated up during operation of the reactor,
and also because of the tendency to reduce its recharging to a minimum. The period between rechargings in
this case coincides with the service lifetime of the conversion technological tubes of -90-100 .103 h, i.e., approxi-
imately 10-11 years. The disposal of the fuel over the whole annular circuit of movement of the solid coolant
ensures the necessary running time of the reactor.
In the neutron cutoff zone, the chain reaction in the nuclear fuel and the subsequent heating up of the graph-
ite during rotation of the annular rotating platforms cease. In the technological zone, the heated graphite trans-
fers the heat accumulated in it by means of radiative emission to the walls of the technological channels, along
which the working medium is moving, and the graphite itself is cooled (Fig. 3).
Fig. 3
1 2 3 4 5 6 7 8 910V
Fig. 4
Fig. 3. Diagram of the movement of the working medium through the technolog-
ical zones of the reactor facility: 1) evaporative channel; 2) drum-separator;
3) feed water; 4) saturated steam (in the steam superheater); 5) steam-water
mixture; 6) steam-gas channel; 7) superheated steam (from the steam super-
heater); 8) steam-gas mixer; 9) natural gas after sulfur purification; 10) dis-
tributive collector; 11) composite collector; 12) conversion product offtake; 13)
grouped collector; 14) conversion channel; 15) solid coolant brickwork.
Fig. 4. Distribution of the optimum velocities of motion of the ring of solid
coolant with Tmax =1450?C and with a conversion tube temperature Tt =850?C.
3
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The feed water, at a temperature of 300?C and a pressure of 10.65 MPa, is fed into the evaporative chan-
nels; there it is partially evaporated and then directed into the drum-separator, where the saturated steam is
separated from the water. The returned water is mixed with the feed water and again enters the evaporative
channels, the saturated steam is directed into the steam superheater of the technological part of the facility,
where it is superheated up to 482?C, and then it is mixed with methane. The steam-gas mixture at 4 MPa and
370?C is directed from the mixer into the channels of the steam-gas mixture preheater, whence it enters the
distributing collectors of the conversion zone. The temperature of the steam-gas mixture reaches 525?C.
From the distributive collectors the heated steam-gas mixture is directed into the steam conversion channels
In which a catalyst is located. The products of the catalytic conversion of natural gas at 835?C enter the com-
posite collector and then go onto the second conversion stage. The wall temperature of the conversion channels,
made from centrifugal cast tubes (an alloy of the type 45Kh25N2062), which are used in the tubular furnaces of
ammonia production, does not exceed the permissible limits of 950?C.
In the structural layout of the reactor facility being considered, the graphite structures, technological
channels, and the thermal insulation of the reactor vessel are located in the high-temperature zone (-1000?C).
The actuator mechanisms and equipment, and also the supporting ring-shaped rotating platforms of the solid
coolant masonry, are taken out into the low-temperature zone (150-200?C), i.e., they are located close to the
bottom of the reactor vessel cooled by water. The electrical part of the actuators are brought out from the re-
actor vessel into the servicing compartment. This considerably facilitates the working and servicing conditions
of the running part of the reactor.
The satisfactory specific heat, excellent thermal conductivity, and high degree of blackness with the nec-
essary fire resistance makes efficient the use of graphite as a coolant in the conditions of heat transfer by radi-
ative heat exchange at 1000?C achieved in GROTT.
The use of graphite as the coolant in a high-temperature power-technological reactor has many advantages,
the principal ones of which are the following:
1. The inert gas medium filling the reactor vessel can have any arbitrarily low pressure, right down to
vacuum, which:
allows the use for the reactor facility of a low-pressure steel vessel, the construction of which has been
assimilated into Soviet reactor construction (for example, the vessel of the RBMK type of channel reac-
tor);
significantly reduces leakage of the gaseous inert medium and radioactive fission products from the reac-
tor vessel;
considerably facilitates the assurance of radiation safety in the case of accidental depressurization of the
reactor vessel;
makes it possible to have a pressure gradient between the working medium of the technological circuit
and the gas medium filling the inside volume of the reactor vessel, directed from the reactor, and this
excludes the entry of radioactive fission products into the technological circuits.
2. The proposed methods of moving the solid coolant ensure its return to the reactor core for repeated
heating up at high temperature, which eliminates nonproductive heat losses, due to the necessity for reducing
the coolant temperature (when using convective heat exchange), and rids of the solution of the complex problem
of designing a system of heat-exchanger equipments and gas blowers for carrying away the heat from the core
and transferring it at a permissible temperature to the technological process.
3. Engineering solutions, verified in the production of ammonia in the chemical industry, can be used.
Neutron-Physics Characteristics of GROTT. We shall mention the most significant of them [2, 3, 4]. One
of the most valuable qualities of the high-temperature route on the whole is the possibility of extending the nu-
clear power fuel base by the use of the 232Th-233U cycle. As is well known, the formation of the intermediate
product 233Pa with a long half-life T1/2=27 days and a thermal neutron absorption cross section ?a43 b is ex-
tremely important. The buildup of 233Pa is proportional to the power level, and the capture by it of a neutron
leads to a double loss: 233Pa is lost - the potential nucleus of 233U after decay with intensity XpaNpa, and also
a neutron which, with a finite probability, could form a 233U nucleus. The necessity for reducing capture leads
to a limitation of the specific power of HTGR and, consequently, to a large core size. This creates difficulties
when designing reactor systems of this type with a high unit capacity.
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In GROTT, the concentration of radioactive products, including 233Pa, because of the fuel circulation is
reduced with respect to the length of the movement channels: overall and through the core, i.e., by approxi-
mately a factor of 10. This circumstance can be utilized in two ways: either to increase the specific power,
or the breeding factor for the same specific power.
Similarly, 233Pa is reduced (in the same ratio, i.e., approximately by a factor of 10) and the concentration
of precursors 138Xe and 148Sm-138I and 148Pm, respectively. In the case of 138Xe, this leads to a reduction of its
concentration by a factor of -2.5, a reduction of the neutron poison capture in 135Xe and, consequently, to an
additional increase of the breeding factor, a reduction of the steady-state poisoning from - 5 to 3%, which causes
an increase of the running time by - 10% and facilitates control of the reactor.
In the case of movement of the solid coolant with the fuel along the core, its burnup takes place on the
average along the line of movement in the neutron flux. This effect, which can be called self-recharging, leads
to an increase of the running time by -.15% by comparison with the case of the nonmoving fuel.
There are no rigid thermophysical limitations on the thickness of the graphite zone (with and without the
fuel) in the solid coolant in GROTT. This gives the possibility of achieving large-scale heterogeneity, which is
optimum with respect to neutron physics and which contributes to the achievement of an economically feasible
aim -the use of a low-enrichment fuel.
The fuel is disposed over the whole coolant movement circuit, which means that the synchronous charging
and running time of the reactor is increased. This might be supposed to be a drawback of the GROTT; however,
if one bears in mind the prospect of increasing the unit capacity, and also the specific energy intensity of the
core, then this characteristic makes it possible to choose the optimum duration of the running time. In contrast
from this case, frequent fuel charging of the reactor with nonmoving fuel would cause considerable deviations
of the parameters from the optimum values.
Among the less important, but characteristic features of GROTT, the following are included:
In the outer technological part there is a powerful y-emission from fission products, which can be used
for carrying out radiation-chemical processes. In particular, in the conversion of natural gas using the GROTT
with a capacity of 500 MW, the reacting mixture in the conversion tubes with a diameter of 90 x 130 mm absorbs
the energy of the y-field equal to 1.5 ? 1018 eV.
A considerable fraction of the delayed neutrons are carried away into the outer part. With a core size
along the line of movement of - 5-8 m and a velocity of movement of the ring of - 0.5 m/sec, the neutron re-
moval amounts to - 30-40%. This, taking account of the strong negative temperature coefficient of reactivity
inherent in GROTT, does not create difficulties in the reactor control. In addition, in the outer part there is a
certain undesirable submultiplication of neutrons. These effects, as calculations show, are insignificant.
Optimization calculations are interesting, for example, to find the distribution of the linear velocity of mo-
tion of the ring, which will ensure an identical maximum temperature at the outlet from the core (Fig. 4).
The calculations showed that the power distribution, the power itself, and its nonuniformity do not vary in
the case of the optimization method considered, although the velocity of motion of the rings can vary consider-
ably, for example by a factor of 5 or more. Physically, this is explained simply: The peripheral rings for
"pulling? the temperature at the core outlet up to Tmax (they are moving in lower neutron fluxes) must be mov-
ing more slowly. Therefore, they carry away less heat, i.e., ATv is found to be constant. This factor can be
used conveniently for generating a uniform temperature field in the heat exchange zone when carrying out tech-
nological processes.
Figure 5 shows the power distribution W along the rings at 1-rn height of the solid coolant with different
nonuniformity Wk, for a reactor power Wn and a thickness of the fuel layer H=1 cm and H=3 cm, with a veloc-
ity of motion of the ring of 0.5 m/sec.
Thermotechnical Characteristics of GROTT. At the basis of the thermotechnical processes taking place
in the reactor, there lie well-studied processes of thermal conductivity, heat transfer by thermal radiation, and
convective heat exchange in the technological channels. The necessity for the joint consideration of these pro-
cesses, the intrinsic heterogeneity of the heat-transfer system, the multiple linking of the heat-transfer scheme,
and the limited possibilities of the computer do not allow the well-known mathematical methods to be used for
solving this problem without any simplifications of the model of the heat-transfer system. Therefore, a combi-
nation of procedures was developed for the thermotechnical calculation of GROTT. In particular, the method of
calculation of the multiring system is based on the partial homogenization of the structure of the moving graphite
5
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VC
1350
10
MVO
1300 MOO
4 1100
911111111 900 1150
23 4 56 7 89 0 2 0,3 44 45 48 ,m/sec
Fig. 5 Fig. 6
Fig. 5. Power distribution of the rings of solid (read-
ings of rings from central): 1) H=1 cm; Tt =850?C,
Wk =0.767, W430 MW; 2) 1 cm, 550?C, 0.772, 590 MW,
respectively; 3) 3 cm, 850?C, 0.770, 690 MW, respectively;
4) 3 cm, 550?C, 0.774, 820 MW, respectively.
Fig. 6. Effect of velocity of rotation of the middle ring
on the maximum fuel temperature.
ring with the fuel elements. The homogenization principle was also used when considering the radiative heat
exchange between the graphite ring and the series of technological channels (introduction of the average heat
fluxes, coefficient of light irradiance, temperature of the surface of the technological channels, etc.).
The major part of the accumulated heat within the confines of the core after one revolution of the rings is
in the fuel (70-80%). Therefore, the use of the principle of moving sources of heat release, distributed uni-
formly over the volume and moving, improves the heat transfer to the solid coolant.
The size of the core is determined from neutron-physical calculations. The low specific power, generated
by the low heat-transfer coefficient by radiation (50-300 W/m2) leads to a considerable size for the heat ex-
changer and the facility as a whole: The diameter of the middle ring amounts to 25 m.
It follows from Fig. 6 that with increase of vn, preheating of the coolant is decreased, which leads to a
reduction of Tmaxf. The same relationship is observed also for the thickness of the graphite ring (5. However,
for 6 > 100-150 mm, the value of Tmaxf remains constant. This is explained by the fact that with a large thick-
ness the middle of the graphite ring participates in the transfer of heat. Variations of v and (5 only insignifi-
cantly affect the length of the heat-exchanger.
Although according to thermotechnical considerations it is desirable to increase the velocity of movement,
and also the height of the ring, their final choice is dictated by the neutron-physics characteristics of the core
and the mechanical stability of the rotating graphite brickwork.
The following thermotechnical characteristics of the facility and its technological part were obtained by
the method of calculation of the multiring system for the starting data:
Length of core together with the neutron cutoff bricks, m 11
Thickness of graphite ring, m 0.25
Angular frequency of rotation of graphite rings, r/min 0.36
Intensity of internal heat release sources, referred to the fuel volume, W/m3 1.29 .107
Coefficient of nonuniformity of heat release:
along the core radius 1.16
over the height of the core 1.12
Maximum permissible wall temperature of the technological channel, ?C 950
The temperature and the thermal fluxes in Table 1 are given for the middle ring in cross section over the
height, where the fuel temperature reaches the maximum value.
The calculations of the temperature fields in the moving brickwork, based on the homogenized model, were
refined by taking into account the heterogeneous disposition of the fuel. The maximum temperature of the fuel
elements and graphite amounted to 1365 and 1315?C, respectively, and the maximum nonuniformity of the fuel
element and graphite temperature was 85 and 124?C. A comparison of the calculations by the procedures with
a heterogeneous disposition of the fuel and with a homogenized fuel layer showed that consideration of the het-
erogeneous disposition leads to an increase of the maximum fuel temperature by 40?C.
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TABLE 1. Thermotechnical Characteristics
of the Zones of the Technological Part of the
Facility
Parameter
Reactor zone
evap-
ora-
tive
pre -
heater
(gas
mixt.)
conver-
sion
Power of zone, MW
248
37,4
196,6
Av. thermal flux,
kW/m2
150
65
53
Length of zone, m
25
5
37
Pressure of medium, MPa
11
4
4
Temp. of substance at inlet
(outlet) to zone
300(314)
370 (525)
525(830)
1389
ii
.1340
bo
4320
1300 1300
E.
1280 10 20 40 50 1280
sec 0 5
10 15 20
i; min
Fig. 7. Change of maximum temperature of
fuel (1) and graphite (2) in a small (a) and
large (b) time after shutdown of the reactor.
The nonuniformity of the heat-transfer coefficient by radiation around the perimeter of the technological
channel can cause nonuniformity of the temperature in it. The radiative heat exchange in the system of bodies
(graphite ring ? row of technological channels) was calculated by dividing the system of bodies into sections.
For each section the equation of the radiative heat exchange with the adjacent sections was written. Thus, the
problem was reduced to the solution of a system of linear equations relative to the temperature of the sections.
The maximum temperature nonuniformity over the perimeter of the conversion tubes, located in the worst
temperature conditions, on the outside surface amounts to 24?C and on the inside surface ?14?C. The reactor
with a solid coolant has a large thermal inertia. This facilitates obtaining the necessary rate of heating up and
cooling of the reactor units both in the case of planned startups and shutdowns, transition from one power level
to another, and also in emergency situations.
Using the method of calculating the nonsteady thermal conductivity in a region with arbitrary geometry,
a calculation was performed of the heating-up of the graphite brickwork for the case when the heat is not re-
moved from the masonry. This situation can arise in the case, for example, of an accidential stoppage of the
rotation of the annular brickwork of graphite blocks. The temperature field in this brickwork at the instant of
its passing the edge of the core is assumed as the initial distribution. It was supposed that the graphite rings
are stopped instantaneously. Figure 7 shows the behavior in time of the maximum temperature of the fuel and
graphite. At first, the fuel temperature falls because of the outflow of heat into the graphite. Over 15 min, it is
equalized in the graphite masonry, and then it starts to increase, over 5 h it reaches the initial maximum value,
and over 10-12 h it reaches the maximum permissible of 1400?C. Hence, it follows that there is a large time
reserve (10-12 h) for carrying out the various measures to eliminate the consequences of an emergency shut-
down of the rings.
The slow rate of heating up of the graphite masonry due to residual heat release can be used for organiz-
ing the reactor cooling process by means of a small number of revolutions of the graphite rings (the time be-
tween the first and second revolutions of the graphite rings amounts to 13 days).
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The computational thermophysical investigations carried out, experiments and test-rig tests of one of the
possible variants of the GROTT concept, confirmed the technical feasibility and the efficiency of high-tempera-
ture heat transfer from the nuclear fuel to the technological users.
LITERATURE CITED
1. N. A. Dollezhall, N. D. Zaichko, and A. M. Alekseev, At. Energ., 43 No. 6, 432 (1977).
2. I. L. Chikhladze, Problems of Nuclear Science and Technology. Series Atomic-Hydrogen Power Genera-
tion and Technology [in Russian], Issue 2 (1979), p. 101.
3. V. T. Zhukov, R. P. Fedorenko, and I. L. Chikhladze, Thermal Problem for a Nuclear Reactor with Solid
Coolant. Preprint of the Institute of Applied Mathematics, Academy of Sciences of the USSR [in Russian],
No. 51 (1981).
4. I. Ya. Emeliyanov, V. T. Zhukov, and I. L. Chikhladze, Problems of Nuclear Science and Technology.
Series of Atomic-Hydrogen Power Generation [in Russian], Issue 2(12) (1982), p. 29.
SYNTHESIS OF A SYSTEM FOR STABILIZING REACTOR
POWER AND ENERGY DISTRIBUTION ON THE BASIS
OF LATERAL IONIZATION CHAMBERS
I. Ya. Emel'yanov, L. N. Podlazov,
A. N. Aleksakov, E. V. Nikolaev,
V. M. Panin, and V. D. Rogova
UDC 621.039.515
A current task with the power reactors in nuclear power stations is to upgrade the stability and working
parameters by upgrading the automatic controls [1]. One way of improving reactor stability is to use branched
automatic stabilization systems for the power distribution. The current approach of designing such systems
involves introducing a certain number of local automatic controls (LAC) working with signals from transducers
within the reactor and uniformly distributed over the core [1, 2]. However, it has been shown [3-5] that it is
possible to improve the stabilizing performance of an automatic control by optimizing the spatial structure of
the control system by using the asymmetry of the neutron-balance operator [6, 7]. It has been suggested [4] that
the asymmetry principle should be combined with zone control in constructing a power-distribution stabilization
system. This suggestion was extended in [5], where it was shown that the optimum location for the rods and
transducers as regards stabilizing performance is characterized by placing the rods closer to the center of the
reactor and the transducers at the periphery. As a result, it became clear that a high-performance stabiliza-
tion system can be based not only on transducers within the reactor but also on lateral ionization chambers
(LIC). Such a structure is technically attractive because of the higher reliability and wide dynamic range of
LIC by comparison with transducers within the reactor.
Here we consider the engineering synthesis of a zone-asymmetric stabilization system for the radial and
azimuthal power distributions that also provides overall power regulation by means of LIC. A difference from
[5] is that a criterion is used for minimum spatial dispersion in the neutron-flux deviations in tracking reactiv-
ity perturbations:
t) dr,
where cp(r, t) is the dimensionless neutron-flux deviation from the stationary value.
The control system is synthesized by the method of [8], according to which the synthesis is divided into
two stages. In the first stage, one analyzes the system viability at constant (nominal) power under conditions of
instability in the power distribution and with technological perturbations. The second stage includes examining
the operation in emergency situations requiring rapid controlled power reduction.
Translated from Atomnaya Energiya, Vol. 56, No. 1, pp. 11-15, January, 1984. Original article submitted
February 16, 1983; revision submitted May 11, 1983.
8
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TABLE 1. Optimum Values of the Rod-Location
Radius and Angle of Rotation Relative to the
Chambers for Three, Four, and Five Regula-
tors: the Values of R Are Given as Fractions
of the Extrapolated Core Radius
3
.4
5
0,38
0,37
0,38
11.101
109
- 8 I TJ
0,3 0,35 0. R
Fig. 1. Dependence of the
dispersion of the location
radius of the rods in the
LAC?LIC system with
various angles of displace-
ment of a rod relative to a
transducer for three regu-
lators: 1) 7 =0*; 2) y =15?;
3) y =22'; 4) y =30?.
In the first stage, the control system is synthesized on the basis of a linear two-dimensional model for the
spatial neutron kinetics [8]. The neutron flux is described by a linearized diffusion equation with allowance for
one group of delayed neutrons and two power feedbacks (fast and slow) in the form of first-order links. The
rapid power feedback incorporates effects from the fuel temperature and steam content, while the slow one is
related to the graphite temperature and xenon poisoning. The control is provided by rods at discrete points
following a relay law. Galerkinis method [9] is used. The calculations incorporated 17 harmonics of the form
(r, 0) = (--c-?
fito I cosj0 '
rl f sin /0
where J(z) is a Bessel function of the first kind and ai are the solutions to the equation J(z) = 0. The number
of harmonics was chosen on the basis of attaining an adequate accuracy.
A serious problem arises over choosing the form of the perturbation, since this substantially influences
the results. Real perturbations vary in spatial form and occur with different rates. To select a representative
set of perturbations, one needs information on the perturbations characteristic of a given reactor, whose fea-
tures are related to ones in the technological scheme and the detailed specifications for power control for a
reactor working in a power system. The most reliable source of such data comes from experience in reactor
operation. At present, statistical data are lacking on the actual frequencies and intensities for perturbations of
various spatial forms in existing reactors; and it is even more difficult to obtain such information for reactors
under design. To overcome this uncertainty and to synthesize a system having sufficient practical performance,
we use an approach based on a time-stepped perturbation uniformly distributed over the amplitudes of all the
harmonics incorporated into the solution:
Akp= E (r) 1(t).
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Fig. 2. Spatial form of the inherent motion for the power distribution in a reactor fitted with
an LAC?LIC system: a-c) three, four, and five regulators correspondingly; 0) rod in LAC?
LIC system; A) transducer in LAC?LIC system; I 1--- ) line of equal deviation in the
energy distribution from the initial state in %.
The optimum control-rod disposition is found from the condition for minimum D at the instant when the
relay zone-asymmetric regulator system has tracked the initial perturbation and is going over to a sliding mode
of operation. Figure 1 shows the dependence of D on the rod location radius R for various angles of displace-
ment of the rod relative to the transducer y for three rod-transducerpairs (the curves for larger number of
regulators are similar to these). There is a pronounced minimum of each curve in Fig. 1. Table 1 gives the
optimum values of R and' for three, four, and five regulators. As the number of regulators increases, the
angle of displacement of a rod relative to a transducer decreases, as does the significance for optimizing the
response to a perturbation. There is a minimum in D as R varies because the system does not bring the mean
power back to the initial value on taking up the unbalance in the regulator channels in the insensitive zone on
tracking the perturbation when the rods are displaced closer to the transducers, to the edge of the core.
Conversely, displacing the rods towards the center of the core causes mean-power overshoot.
Different results are obtained as regards the angle y between the rod and transducer on synthesizing the
system from the criterion for minimum in the maximal real part of the root of the characteristic equation for
the dynamics of the radial and azimuthal energy distribution [5] and from the criterion for minimum spatial
dispersion. One gets a smaller angle if one incorporates into the synthesis not only the stability but also the
transient response.
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These results have been obtained from a linear reactor model. It is necessary to use a nonlinear two-
dimensional digital model in a detailed examination of the viability of the LAC -LIC system under conditions of
emergency controlled power reduction. The reason arises from the characteristic difficulties encountered in
performing tests on power-station reactors: There are nonstationary states related to extensive changes in the
parameters, which are particularly difficult for the automatic control, and which are extremely undesirable to
produce artificially for experimental purposes, since they involve large loads of all the main equipment. How-
ever, it is necessary to be completely convinced that the automatic system will perform its functions reliably
in a real emergency. The only possibility is to synthesize a system with allowance for all the states that have
to be provided for with a model that accurately reproduces these states. Such a model has been realized with a
BESM-6 computer. The model equations contained 540 nodes and described the nonstationary neutron-physics
processes in the diffusion approximation, the core thermodynamics, including convective heat transfer and the
formation of steam, the changes in xenon and iodine concentrations, and the operation of the control systems on
the basis of the characteristics of the control apparatus and effecters. The calculated and experimental values
were compared for RBMK-1000 reactors, particularly in order to check the adequacy of the model, and the
agreement was good [8].
The stabilizing behavior is characterized by the times involved in the residual deformations in the power
distribution during prolonged operation in the steady state. The viability of the LAC -LIC system in a stabili-
zation mode was examined with this model. The reactivity coefficients were as follows in the calculations:
ao, =0.02025; a T =-0.9 .10-5 1/?C; a c =5.5 ? 10-5 1/?C (these correspond approximately to the states of the re-
actors in the first and second units of Leningrad Nuclear Power Station at the present time). The purpose of
the calculation was to identify the spatial form of the inherent motion in the energy distribution together with
the time characteristics under conditions of prolonged maintenance of stationary power by the LAC LIC system
in the absence of other controls. Pulsed reactivity perturbations to the initial state were introduced at the start
of calculations (two or three rods were displaced by about ?0.5 m in the intervals between the regulators). Over
a sufficiently long interval, the traces of the initial perturbation die away and one identifies the inherent distri-
bution motion.
The results show that the period of rising amplitude in the inherent motion for the LAC -LIC system with
three regulators is about 30 min. Figure 2a shows the spatial form of this motion. The motion in a reactor with
four regulators is determined in the main by the second azimuthal harmonic, and the period is about 50 min
(Fig. 2b). A five-zone LAC-LIC system has even better stabilizing performance, but as with three regulators,
it is difficult to identify the predominance of any one harmonic (Fig. 2c). The period was estimated as several
hours, i.e., the LAC-LIC system with five regulators is close in performance to the seven-zone LAC system
with transducers within the reactor [2].
It was found that there was no objection to increasing the number of LAC further on the basis of a study of
the performance of the LAC-LIC system for stabilizing the distribution in the steady state and also from an
analysis of the response of the system to perturbations. However, calculations on the period of the residual mo-
tion indicate that there will be no increase in stabilizing performance from using more than seven LAC. A sys-
tem consisting of seven regulators completely stabilizes the radial and azimuthal distributions with the above
reactivity coefficients. Figure 3 shows the dependence of the residual-deformation time constant on the number
of regulators in the LAC-LIC system.
Nevertheless, improved overall performance is produced in the rods included in the power control, and
this is favorable from the viewpoint of emergency power reduction in individual parts of the main equipment. Of
course, all the requirements of the nuclear safety rules are met. Final choice of the LAC -LIC system struc-
ture is based not only on the calculations but also on the requirement for maximum possible simplicity in real-
ization. In the present case, the structure of the automatic-control system on the RBMK-1000 allows very sim-
ple transfer to an LAC -LIC system, since the signal from each of the chambers is processed by an individual
amplifier, in which it is simultaneously subtracted from the power-transducer signal [9]. The RBMK-1000 is
fitted with two automatic controls (main and reserve) with four chambers in each, which are located virtually
uniformly in azimuth [9]. Under these conditions, it is clear that one should implement an LAC-LIC system
with eight individual regulators.
The operation of an eight-zone LAC -LIC system under nonstationary conditions was considered by refer-
ence to emergency power reduction on emergency shutdown in the main circulation pump (MCP) in one of the
circulation loops. When the MCP shuts down, the circulation rate in one half of the reactor decreases and the
steam content increases, and on account of the steam effect on the reactivity a perturbation is produced in this
half that can cause an increase in the neutron power. To provide normal conditions for fuel-pin cooling under
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14, 16, s
110
6
^ f,
? 2
0
0
I I
0 1 2 .7 4 1 N
Fig. 3
00
tS
SO
1,0 V
SOO
0#00
100
0
et;
tt, 0
20
/ 1
40 810
2
80
?
?t, sec
Fig. 4
Fig. 3. Dependence of the residual-deformation time constant Tree on the
number of regulators N: 41) value of Tree in the presence of automatic con-
trol (r o).
Fig. 4. Transience in MCP shutdown mode: a) behavior of the neutron
power f and nonuniformity coefficient for the radial distribution Kr: 1) 3;
2) Kr; ? ? ?) setting; b) rod position in LAC ?LIC system in left half L3
and right half 147 of reactor: 1) Ls; 2) L7; o and d) unbalance in the LAC?
LIC system channel in the left half 6408 and the right half 607 of the reac-
tor correspondingly; ? ?) boundary of the insensitive zone.
such a situation one has to reduce the power at a rate cif 2%/sec to the level of 60% of the nominal value, while
maintaining the energy distribution unchanged. Figure 4 shows the transience in this state as obtained with the
nonlinear digital spatial dynamic model. Parts c and d of Fig. 4 give the unbalances in the LAC?LIC system
channels in different halves of the reactor. The unbalance in the channel in the half with the switch-off MCP
rapidly but briefly passes outside the limits of the insensitivity zone. The unbalances in the LAC?LIC channels
in the opposite half remain virtually within this zone throughout the transient response. The LAC LIC system
copes successfully with this perturbation and provides a power reduction uniform over the reactor. The per-
formance of the control rods in the LAC ?LIC system in this state is sufficient: The rods remain t in the working
range throughout the transient response.
This study of synthesis of a zone-unsymmetrial system has shown that it is possible to produce a highly
effective system for stabilizing the power distribution on the basis of LIC, which have high reliability and a
wide dynamic range. Increasing the number of regulators to more than seven or eight is undesirable, since be-
yond this limit there is virtually no more increase in the stabilization performance. A five-zone LAC?LIC
system is comparable in stabilizing performance with a seven-zone LAC as regards the residual-deformation
growth time. Synthesis of an LAC?LIC system provides a system corresponding to the set of practical spec-
ifications.
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LITERATURE CITED
1. I. Ya. Emelvyanov et al., At. Energ., 49 No. 6, 357 (1980).
2. I. Ya. Emeltyanov et al., Nuclear Science and Engineering, Series Reactor Physics and Engineering
[in Russian], Issue 1(5), 3 (1979).
3. A. M. Afanas' ev and B. Z. Torlin, At. Energ., 43, No. 4, 243 (1977).
4. I. Ya. Emellyanov et al., ibid., 46, No. 2, 82 (1979) .
5. I. Ya. Emel'yanov et al., ibid., 47, No. 6, 370 (1979).
6. D. Wiberg,, Nucl. Sci. Eng, 27, 600 (1967).
7. I. S. Postnikov and E. F. Sabaev, At. Energ., 26, No. 1, 56 (1969).
8. I. Ya. Emel' yanov et al., ibid, 53, No. 5, 301 (1982).
9. I. Ya. Emeliyanov et al., ibid., 48, No. 6, 360 (1980).
ANALYSIS OF THE STATISTICAL ERROR
AND OPTIMIZATION OF CORRELATION FLOW METERS
B. V. Kebadze UDC 681.12:621.039.534
Correlation methods are used increasingly to measure the coolant flow rate in nuclear power plants,
making use of different kinds of inhomogeneities in the flow and employing appropriate sensors [1-6]. The shift
of the maximum of the cross correlation function (CCF) along the time axis is the directly measurable param-
eter in this case. An important advantage of the correlation method is that it is not sensitive to a change in the
conversion ratios of the sensors. One drawback of the method is the relatively long measuring time due to the
need to carry out statistical processing of random signals. The error caused by the statistical scatter of the
positions of the correlation maximum along the time axis is considered in this paper. This error appears re-
gardless of the form of coolant and sensor, depends on the frequency properties and degree of correlation of
the signals, and determines the measuring time necessary to obtain the required accuracy; from the practical
point of view it is important to make a substantiated reduction of this time.
Derivation of Relations for the Estimation of the Statistical Error. Unlike the case of the amplitude error,
which has been discussed in detail in [7], methods for the estimation of the time error in correlation measure-
ments have not been developed adequately. The computational relation obtained in one paper on this subject [2]
is applicable only to a partial form of statistical characteristics. The correlated nature of the amplitude errors
Is obtained in the form of a functional dependence on the total amplitude error of the CCF.
At the same time, it is not difficult to show that for completely correlated signals the time error of the
position of the maximum is insignificant and easily removed for any large amplitude error. As an example, we
consider identical signals x(t) = y(t) which are not shifted_ in time. When cyclical notation is used for the real-
ization of a random process determined by the condition x(t + T)=x(t), the following relation is satisfied:
1
[X2 - X (t) X (t dt = ?2T 5 ix (t) _x +.012 dt fit (0)- o
0 0
Here ft(0) and R(T) are estimates of the correlation function (CF). Thus, in this case R(T) has a maximum
at r ;--0 without regard for the dependence on the amplitude error of the estimate. The absence of a shift along
the time axis is due mainly to the fact that the amplitude errors at close points of the CF are not independent
but are cross-correlated. This subsequently allows the shape of the correlation peak in the absence of uncor-
related noise to be assumed to be approximately constant, only random variations of the amplitude being taken
into account. Similar discussions can be carried out for the case of pure delay between completely correlated
identical signals.
Uncorrelated noise is the main source of error in the time shift. It is clear from the above that we must
separate the components of the signal and the correlation functions into correlated (CC) and uncorrelated (UC)
components. The following arguments can serve as the physical basis for this separation. The nearly identical
signals from the sensors arise when flow inhomogeneities (of temperature, the velocity profile) pass through
the sensors. As follows from the experiment in [3, 5], these inhomogeneities are due mainly to the existence
Translated from Atomnaya Energiya, Vol. 56, No. 1, pp. 15-20, January, 1984. Original article submitted
May 10, 1982.
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of large-scale hydrodynamic formations (vortices) in the flow; the stability of these formations under displace-
ment over a considerable distance (L > D, where D is the diameter of the tubing) and the fact that they maintain
their spatial orientation are conducive to the formation of identical signals (the correlated component). There
are also obstacles to this. Thus, with displacement with the flow some "smearing" of inhomogeneities occurs,
as manifested in the damping of high frequencies in the signals. The use of filtration with allowance for the
frequency variations during the transfer of perturbations makes it possible to reduce the difference of the sig-
nals and to increase the fraction of the correlated component. At the same time, the complex nature of the tur-
bulent motion leads to the appearance of uncorrelated components. The probability exists that a vortex, de-
tected by the first sensor, will break up before reaching the second sensor; new perturbations, which affect only
the second sensor, are formed in the segment between the sensors. For vortices recorded by both sensors
there exists a statistical scatter of the trajectories, displacement time, and spatial orientation. Local small-
scale fluctuations within the confines of each sensor and the noise of the measuring ions within the confines of
each sensor and the noise of the measuring channels are additional sources of uncorrelated noise. Thus, the
signals of the sensors are represented as
= s (t T max) + n2 (t),
where the noise sources n1(t) and n2(t), which are uncorrelated with the value of s(t) and s(t? rmax) because
for the nonideal coincidence of s(t) and s(t ? T ) because the filters incompletely compensate for the fre-
quency distortions. When the uncorrelated nature of s(t), ni(t), and n2(t) is taken into account the autocorrela-
tion and cross-correlation functions of the x and y signals can be represented as
R. (T) = (T) 4- R N (S);
Ry (I) ?=, R a (1) RN2(t); (2)
(1)
Further derivation follows? mainly from [8]:
1. Using the well-known expression from [7] for the variance of the estimate of the CCF of random pro-
cesses with a normal distribution law,
1
?lin= T j R. (a) R y (g) Rxy (g+ T) Rys(t
taking Eq. (2) into account, and assuming that the length of realization is sufficient for the uncorrelated com-
ponents of the CCF to vanish, we separate the components of the error of the correlated and uncorrelated com-
ponents of the CCF: --0
(An= (T6c CrtiC = + (E -FT ?Tmax) R, (t-T+ 'rm.)] dE +
+ 4- s [Ra R R e(I) RN, (V+ RN I (I) RN, (l)] d.
The value of a2 can be estimated as
CC
(3)
aCc