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ISSN 1063-7788, Physics of Atomic Nuclei, 2018, Vol. 81, No. 8, pp. 1180–1186. © Pleiades Publishing, Ltd., 2018.
Original Russian Text © E.A. Gomin, V.D. Davidenko, O.V. Davidenko, A.A. Kovalishin, M.N. Laletin, A.K. Pavlov, 2017, published in Voprosy Atomnoi Nauki i Tekhniki.
Seriya: Fizika Yadernykh Reaktorov, 2017, No. 5, pp. 4–11.
DAREUS Software Package for Modeling the Dynamics of Solution
Reactors Using the Monte Carlo Method
E. A. Gomin
a
, V. D. Davidenko
a,
*, O. V. Davidenko
a
, A. A. Kovalishin
a
,
M. N. Laletin
a
, and A. K. Pavlov
a,
**
a
National Research Center Kurchatov Institute, pl. Kurchatova 1, Moscow, 123182 Russia
*e-mail: Davidenk[email protected]
**e-mail: Pavlo[email protected]
Received September 14, 2017
AbstractThe DAREUS software package designed for modeling dynamic processes in the cores of experi-
mental solution reactors is described. The KIR program based on the Monte Carlo method is used in the
package to compute the necessary kinetic parameters. The results of the calculations of some test cases are
given.
Keywords: computation, dynamics, kinetics, solution reactor, Monte Carlo method, supercomputer
DOI: 10.1134/S1063778818080100
INTRODUCTION
The DAREUS software package is designed for
computer simulation of dynamic processes in the
cores of solution reactors and is used at the Kurchatov
Institute for the computational support and computa-
tional modeling of the development of emergency
modes for the Gidra [1, 2] and Argus [1, 2] research
solution reactors.
The Gidra pulsed research reactor (PRR) was
developed and commissioned at the Kurchatov Insti-
tute of Atomic Energy (IAE) (now the National
Research Center Kurchatov Institute) in 1972. It
belongs to the class of self-quenching pulsed reactors,
the power pulse in which is quenched mainly owing to
the negative reactivity effect associated with the for-
mation of radiolytic gas fission fragments along the
tracks. The release of radiolytic gas from the fuel solu-
tion is accompanied by a rapid radiolytic boiling with
a sharp decrease in the fuel density (void reactivity
coefficient).
The reactor is designed to study the nature of radi-
ation defects in various materials in high-intensity
fields of reactor radiation, carry out activation analysis
of short-lived radionuclides, and also conduct
ampoule dynamic tests of fuel rods of various reactors
in the event of an accident with increasing reactivity.
The Argus research reactor (RR) was developed
and commissioned at the IAE in 1981. The reactor
operates at a steady-state power and is designed to f ind
the best physical and technical solutions for the devel-
opment of nuclear physics methods of analysis and
control and for the production of radionuclides for
medical purposes. Neutron activation analysis and
neutron radiography are performed at the Argus reac-
tor.
To date, the nuclear safety of these reactors has
been validated using software tools that make it possi-
ble to calculate the effects and coefficients of reactiv-
ity, other key reactivity characteristics, and the effi-
ciency of the control and protection system (CPS)
using the Monte Carlo method.
The DAREUS software package is the first one
that implements interconnected neutronic, thermo-
hydraulic, and thermomechanical calculations of the
dynamics of solution reactors.
1. DAREUS SOFTWARE PACKAGE
The DAREUS software package includes the KIR
neutronic calculation code [3], the GARD thermohy-
draulic calculation code, and the programming inter-
faces that connect them.
The computational modeling of a dynamic process
using the software package consists in the sequential
operation of the KIR and GARD programs. The total
dynamic process time is divided into a number of
intervals. It is assumed that the physical properties of
the reactor remain unchanged in each interval. Differ-
ent time grids can be used for programs of neutronic
and thermohydraulic calculations.
The KIR program from the DAREUS software
package makes it possible to preliminarily compute a
number of reactor states differing in the density of the
fuel solution, in the temperature of the materials, and
PHYSICS OF ATOMIC NUCLEI Vol. 81 No. 8 2018
DAREUS SOFTWARE PACKAGE 1181
in positions of control elements. To this end, the
DAREUS software package has a special computa-
tional module for determining the functionals
required for the GARD program.
This makes it possible to significantly reduce the
calculated dynamic process modeling time, and, if
necessary, the bank of computed states of the reactor
can be quite easily supplemented.
Apparently, this approach is optimal for the com-
putational studies of specific solution reactors, in par-
ticular, the Argus RR.
2. GARD PROGRAM
The most important problem in analyzing the
dynamics of solution RRs is to formulate a complete
system of equations for the dynamics of RRs that link
up heterogeneous transient processes of neutron,
molecular, thermomechanical, thermodynamic, and
hydrodynamic phenomena [4]. An extensive list of
original works in this field is given in the cited paper.
Specific features of the dynamics of solution RRs
are largely determined by the phenomenon of radio-
lytic boiling of the core, which requires a correct
description of the mechanism of formation (nucle-
ation) of bubble nuclei in the core solution, the pro-
cess of transport of radiolytic gas and heat, and the
general behavior of vapor-gas bubbles under steady
and unsteady pressures and temperatures.
The regular and most widespread model of the
mechanism of formation of bubbles by ionizing parti-
cles is generalized in the bubble chamber theory [4]. In
this model, a charged particle passing through water
creates a thermal track, a region of high temperature
along the trajectory of this particle. The thermal track
rapidly expands causing a pressure wave and then
decays into discrete regions of water vapor and radio-
lytic gas under the influence of surface tension. In the
superheated water or water supersaturated with gas,
these gas microbubbles can be centers of further
increase in the gas phase volume.
The GARD program is specially designed for mod-
eling thermomechanical and hydrodynamic processes
in solution reactors, including pulsed ones, in both the
nominal and emergency modes.
The solution of the system of equations for the
dynamics of solution reactors mentioned above is
implemented in it. The program consists of a set of
computational modules describing the heterogeneous
transient processes of the physical phenomena listed
above, which are characteristic of solution reactors.
The GARD program sequentially calls the neces-
sary calculation modules on the basis of the pre-
defined thermohydraulic reactor model. In this case, a
complete and mutually consistent system of equations
of dynamics is formed, after solution of which new
thermophysical functionals are transferred to the KIR
program for further neutronic calculation. These
functionals include the temperature of the structural
materials of the reactor and the density of the core
solution. Note that, when the density of the core solu-
tion changes, its volume also changes, which leads to a
change in the fill level. This change is taken into
account in the neutronic calculation of the next state
of the reactor in order to obtain the reactivity value.
In the current version of the GARD program, in
addition to the standard modules specific to reactors
of any type, computational modules are implemented
in which the following physical processes are simu-
lated:
1. Formation of bubbles of radiolytic gas in solution
as a result of the interaction of fission fragments with
water molecules.
2. Diffusion of radiolytic gas from bubbles into the
core solution.
3. Motion (ascent) of bubbles and release of radio-
lytic gas into the cavity above the core.
4. Change in the pressure in the cavity above the
reactor owing to the release of radiolytic gas from the
core and change in the fill level because of changes in
the density of the core solution.
5. Processes of heat exchange in the core taking
into account the heat removal through different chan-
nels: gas discharge and heat exchange with the vessel
and water coolant of circuit I.
6. Processes of heat and mass transfer in circuit II
and change in the level in the volume compensator of
circuit II.
7. Processes of heat exchange in the vessel and the
reflector.
Computational modules of the GARD program
make it possible to adequately describe the physical
processes in the solution reactor, in particular, the
processes associated with the introduction of positive
reactivity (burst).
3. KIR PROGRAM
The KIR program [3] is designed to solve the inho-
mogeneous stationary and nonstationary equations
and the homogeneous neutron transport equation by
analogous Monte Carlo methods based on the calcu-
lated nuclear data in systems with three-dimensional
geometry.
In the KIR program, the nonstationary neutron
transport equation is solved by the Monte Carlo
method with the time dependences of the positions of
the control elements and the densities and tempera-
tures of the materials of the structural elements.
Delayed neutrons are taken into account (those whose
precursors accumulated by the beginning of the simu-
lated time process and those that are formed during
the process). Note that, in addition to the standard set
of neutron flux functionals, the program makes it pos-
sible to calculate the effective fraction of delayed neu-
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GOMIN et al.
trons and the effective lifetime of fission neutrons tak-
ing into account the importance function.
4. DAREUS SOFTWARE PACKAGE TEST
The DAREUS software package was verified with
respect to modeling the dynamics of solution reactors.
The results of modeling the dynamic processes are
presented below in order to illustrate the DAREUS
software package performance.
4.1. Gidra Reactor
The Gidra PRR belongs to the class of self-
quenching PRRs, the power pulse in which is
quenched mainly owing to the negative reactivity
effect associated with the formation of radiolytic gas
fission fragments along the tracks. The release of radi-
olytic gas from the fuel solution is accompanied by a
rapid radiolytic boiling with a sharp decrease in the
fuel density.
The core vessel is a steel cylinder with a hemispher-
ical bottom.
The internal diameter of the core vessel is 38.6 cm,
the height of the solution is 42 cm, and the working
volume is 40 L. The fuel is an aqueous solution of ura-
nyl sulfate UO
2
SO
4
enriched to 90%
235
U. The reactor
has no reflector. The longitudinal and cross sections of
the core of the Gidra PRR are shown in Figs. 1 and 2.
The results of the calculations of dynamic pro-
cesses associated with the introduction of positive
reactivity due to the booster rod ejection using the
DAREUS software package are presented. They are
given in Fig. 3 in comparison with the experimental
data.
Let us consider the results of the calculations of
dynamic processes in the Gidra PRR in the case of the
introduction of positive reactivity in the interval of 1–
6 β
eff
. The results show that the differences between
the calculated and experimental values of energy
release at the time of the burst do not exceed 25% with
the introduction of positive reactivity in the interval of
1.5–4.5 β
eff
. A physical change in the process takes
place in the interval of 4.5–6 β
eff
: the increased energy
release creates inertial pressure of the solution (also on
the vessel lid) accompanied by the expansion of the
Fig. 1. Longitudinal section of the Gidra reactor and the positions of actuators. A group of actuators of reactivity compensators
is raised to an intermediate position.
Peripheral
channel
Fuel
solution
Central
channel
Vessel
Graphite column
portion
PHYSICS OF ATOMIC NUCLEI Vol. 81 No. 8 2018
DAREUS SOFTWARE PACKAGE 1183
solution. At the point corresponding to 4.5 β
eff
, the
calculated curve should change the inclination angle
and become steeper. The absence of this inflection
increases the difference between calculations and
measurements, which amounts to about 40% in the
interval of 4.5–6 β
eff
.
The results of the verification of the DAREUS
software package based on the data of pulsed experi-
ments conducted on the Gidra PRR made it possible
to conclude that the method of computational model-
ing of the processes occurring in the fuel solution and
associated with the formation and transport of bubbles
Fig. 2. Cross section of the Gidra reactor. The graphite column is partially shown.
Central
experimental
channel
Reactivity
compensator
Booster rod
Graphite column
Vessel
Experimental
channel
Fig. 3. Experimental and calculated maximum energy releases at the time of the burst depending on the initial reactivity jump
(KNK-57 is the neutron compensation chamber and PM is the photomultiplier).
20
40
60
80
100
120
KNK-57
PM
Calculation
1 2 3 4 5 6 70
Reactivity, β
e
Maximum energy release, MJ
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PHYSICS OF ATOMIC NUCLEI Vol. 81 No. 8 2018
GOMIN et al.
of radiolytic gas gives an acceptable calculated accu-
racy of the pulse power estimate.
4.2. Argus Reactor
The Argus RR operates at a steady-state power. By
design, it is very similar to the Gidra PRR.
The core vessel is a steel cylinder with a hemispher-
ical bottom.
The DAREUS software package was verified using
the experimental data obtained on the Argus RR with
highly enriched fuel (90%). The internal diameter of
the reactor vessel (core diameter) is 30.5 cm, the
height of the solution is 45 cm, and the working vol-
ume is 26 L. The fuel is an aqueous solution of uranyl
sulfate (UO
2
SO
4
). The reactor has a graphite reflector.
The coolant of circuit I is distilled water. The longitu-
dinal and cross sections of the Argus core are shown in
Figs. 4 and 5.
The results of the DAREUS software package cal-
culations of the parameters of the RR Argus after the
shutdown of distillate circulation in the reactor cool-
ing system (RCS) (RCS pump shutdown) are pre-
sented. The experiment was carried out at a steady-
state reactor power of 20 kW. The temperature of the
fuel solution was about 80°C. As a result of the pump
shutoff, heat removal through the heat exchanger was
stopped. The temperature of the fuel solution and the
distillate in the coil started to rise. The temperature
increase added negative reactivity to the reactor, which
led to a drop in reactor power. For some time, the tem-
perature of the fuel solution stabilized around 100°C
owing to heat removal through the reactor vessel.
Fig. 4. Longitudinal cross section of the Argus reactor and position of the CPS actuator (A). A group of actuators of the safety
system (SS) is shown in an intermediate position.
Cavity over
solution
Coil tube
Fuel
solution
Lid
Vessel
Gap
Graphite
reflector
PHYSICS OF ATOMIC NUCLEI Vol. 81 No. 8 2018
DAREUS SOFTWARE PACKAGE 1185
Approximately 5 min after the pump shutoff, it was
switched on again. After some time, the reactor power
returned to the level of 20 kW (the automatic power
control system (APCS) was also turned on). The tem-
perature of the fuel solution also returned to the level
of 80°C.
When modeling this process using the DAREUS
software package, the reactor was brought to a power
of 20 kW, and after stabilization of the reactor param-
eters, the distillate circulation in the cooling system
was shut off. The RCS was turned on after about
6min.
Fig. 5. Cross section of the Argus reactor.
SS
Cooling
coil
VC
Central
channel
External
regulating rods
Fig. 6. Dependence of the reactor power on time when the RCS of circuit I is switched off and then switched on. The solid line
denotes experimental power values and the dotted line shows power values calculated using the DAREUS software package.
5
10
15
20
25
5 10 15 20 250
Time, min
Power, kW
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GOMIN et al.
A comparison of the experimental and calculated
reactor power for the enabled and disabled RCS pump
is shown in Fig. 6. A comparison of the experimental
and calculated temperatures of the fuel solution are
given in Fig. 7.
CONCLUSIONS
The DAREUS software package designed for com-
puter modeling of dynamic processes in the cores of
Gidra and Argus solution RRs of the Kurchatov Insti-
tute complex of solution reactors is described.
The DAREUS software package implements inter-
connected neutronic, thermohydraulic, and thermo-
mechanical calculations of the dynamics of solution
reactors.
The DAREUS software package includes the KIR
neutronic calculation code based on the Monte Carlo
method, the GARD thermohydraulic calculation
code, and the programming interfaces that connect
them. The description of the codes is given.
The DAREUS software package performance is
illustrated by the results of the computational model-
ing and experimental data for two dynamic processes.
Their comparison demonstrates the efficiency of the
DAREUS software package.
REFERENCES
1. High-Temperature Nuclear Power Engineering. Unique
Developments and Experimental Base of the Kurchatov
Institute, Ed. by N. N. Ponomarev-Stepnoi (IzdAt,
Moscow, 2008) [in Russian].
2. Research Nuclear Facilities of the CIS Member States,
Ed. by M. K. Vinogradov and V. N. Fedulin (Gelios
ARV, Moscow, 2016) [in Russian].
3. E. A. Gomin, V. D. Davidenko, A. S. Zinchenko, and
I. K. Kharchenko, Vopr. At. Nauki Tekh., Ser.: Fiz.
Tekh. Yad. Reakt., No. 5, 4 (2016).
4. V. F. Kolesov, Aperiodic Pulsed Reactors (RFYaTs-
VNIIEF, Sarov, 1999) [in Russian].
Translated by O. Pismenov
Fig. 7. Dependence of the temperature of the fuel solution of the reactor on time when the APCS and pump of the RCS of circuit I
are switched off and then switched on (the solid line denotes the experimental temperature values and the dotted line shows the tem-
perature values calculated using the DAREUS software package).