Spherical standing burning wave with external automatic reactivity control

Neutron kinetics of a nuclear burning wave in moving incompressible neutron-multiplying medium in the presence of nuclear reactions is developed. A spherical reactor is considered, where fuel moves with acceleration to the center of the reactor at a velocity V(r)=VR(R/r)², and the burning wave trave...

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Datum:	2019
Hauptverfasser:	Leleko, Yu.Y., Gann, V.V., Gann, A.V.
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Sprache:	English
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2019
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Physics of radiation damages and effects in solids
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spelling	irk-123456789-1952062023-12-03T17:25:23Z Spherical standing burning wave with external automatic reactivity control Leleko, Yu.Y. Gann, V.V. Gann, A.V. Physics of radiation damages and effects in solids Neutron kinetics of a nuclear burning wave in moving incompressible neutron-multiplying medium in the presence of nuclear reactions is developed. A spherical reactor is considered, where fuel moves with acceleration to the center of the reactor at a velocity V(r)=VR(R/r)², and the burning wave travels radially from the center to periphery. The fuel that came to the origin was unloaded from the reactor, and U-238 was loaded to the peripheral area at the same rate. Comparison of theoretical results with computer simulation using MCNPX code was performed. Була розвинена нейтронна кінетика стоячої хвилі ядерного горіння в нейтронно-розмножуючім середовищі, котре не стискається та є рухомим, при наявності ядерних реакцій. Розглянуто сферичний реактор, в якому хвиля ядерного горіння рухається радіально від центра, а паливо – до центра реактора. Показано, що при підживленні такої системи ²³⁸U в ній може існувати сферична стояча хвиля ядерного горіння. Проведено порівняння теоретичних результатів з даними чисельного моделювання такого реактора з використанням коду MCNPX. Была развита нейтронная кинетика стоячей волны ядерного горения в нейтронно-размножающей среде, которая не сжимается и является подвижной, при наличии ядерных реакций. Рассмотрен сферический реактор, в котором волна ядерного горения движется радиально от центра, а топливо – в центр реактора. Показано, что при подпитке такой системы ²³⁸U в ней может существовать сферическая стоячая волна ядерного горения. Проведено сравнение теоретических результатов с данными численного моделирования такого реактора с использованием кода MCNPX. 2019 Article Spherical standing burning wave with external automatic reactivity control / Yu.Y. Leleko, V.V. Gann, A.V. Gann // Problems of atomic science and technology. — 2019. — № 5. — С. 18-24. — Бібліогр.: 8 назв. — англ. 1562-6016 http://dspace.nbuv.gov.ua/handle/123456789/195206 612.039.517 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Physics of radiation damages and effects in solids Physics of radiation damages and effects in solids
spellingShingle	Physics of radiation damages and effects in solids Physics of radiation damages and effects in solids Leleko, Yu.Y. Gann, V.V. Gann, A.V. Spherical standing burning wave with external automatic reactivity control Вопросы атомной науки и техники
description	Neutron kinetics of a nuclear burning wave in moving incompressible neutron-multiplying medium in the presence of nuclear reactions is developed. A spherical reactor is considered, where fuel moves with acceleration to the center of the reactor at a velocity V(r)=VR(R/r)², and the burning wave travels radially from the center to periphery. The fuel that came to the origin was unloaded from the reactor, and U-238 was loaded to the peripheral area at the same rate. Comparison of theoretical results with computer simulation using MCNPX code was performed.
format	Article
author	Leleko, Yu.Y. Gann, V.V. Gann, A.V.
author_facet	Leleko, Yu.Y. Gann, V.V. Gann, A.V.
author_sort	Leleko, Yu.Y.
title	Spherical standing burning wave with external automatic reactivity control
title_short	Spherical standing burning wave with external automatic reactivity control
title_full	Spherical standing burning wave with external automatic reactivity control
title_fullStr	Spherical standing burning wave with external automatic reactivity control
title_full_unstemmed	Spherical standing burning wave with external automatic reactivity control
title_sort	spherical standing burning wave with external automatic reactivity control
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2019
topic_facet	Physics of radiation damages and effects in solids
url	http://dspace.nbuv.gov.ua/handle/123456789/195206
citation_txt	Spherical standing burning wave with external automatic reactivity control / Yu.Y. Leleko, V.V. Gann, A.V. Gann // Problems of atomic science and technology. — 2019. — № 5. — С. 18-24. — Бібліогр.: 8 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT lelekoyuy sphericalstandingburningwavewithexternalautomaticreactivitycontrol AT gannvv sphericalstandingburningwavewithexternalautomaticreactivitycontrol AT gannav sphericalstandingburningwavewithexternalautomaticreactivitycontrol
first_indexed	2025-07-16T23:04:00Z
last_indexed	2025-07-16T23:04:00Z
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fulltext	ISSN 1562-6016. PASТ. 2019. №5(123), p. 18-24. UDC 612.039.517 SPHERICAL STANDING BURNING WAVE WITH EXTERNAL AUTOMATIC REACTIVITY CONTROL Yu.Y. Leleko, V.V. Gann, A.V. Gann National Science Center “Kharkov Institute of Physics and Technology”, Scientific and Technical Complex “Nuclear Fuel Cycle” Center for Reactor Core Design, Kharkiv, Ukraine E-mail: makswell.com@gmail.com Neutron kinetics of a nuclear burning wave in moving incompressible neutron-multiplying medium in the pres- ence of nuclear reactions is developed. A spherical reactor is considered, where fuel moves with acceleration to the center of the reactor at a velocity V(r)=VR(R/r) 2 , and the burning wave travels radially from the center to periphery. The fuel that came to the origin was unloaded from the reactor, and U-238 was loaded to the peripheral area at the same rate. Comparison of theoretical results with computer simulation using MCNPX code was performed. INTRODUCTION In this article, the theory of nuclear reactor on spher- ical standing burning wave is developed. The neutron kinetics of a nuclear burning wave in a moving neutron- multiplying medium in the presence of nuclear reactions was developed. Computer simulation of moving and standing spherical burning waves in a nuclear reactor was performed using MCNPX code [1]. The reactor core consists of four areas: the outer zone made of U-238, the breading zone where produc- tion of Pu-239 takes place according to the scheme U-238 + n = U-239 → Np-239 → Pu-239, the inner region in which Pu-239 is burning, and central area con- sists of burnt fuel. The fuel moves with acceleration from periphery to the center of the reactor. It is shown that in such a system a spherical standing wave travels radially from the center zone to periphery. The burning wave consists of two regions: the external  breading zone and the internal  burning area. Distributions of the neutron flux, the U-238, Np-239, and Pu-239 iso- tope concentrations and the specific power in the stand- ing spherical burning wave are obtained in this paper. The conditions for existence of spherical standing burn- ing waves are investigated. It is shown that an operation mode of the standing-wave reactor is characterized by two combinations of nuclear cross sections and single function defining the stability boundaries of the stem. Stability region of spherical waves was found to be broader then stability region of one-dimensional travel- ing burning waves in an infinite medium. A state dia- gram of such a reactor has been obtained. Concept of the traveling wave nuclear reactor (TWR) is one of the brilliant ideas of 20-th century. It suggests using depleted uranium (or thorium) as fuel and promises to supply inexhaustible source of energy worldwide. This idea was proposed by S.M. Feinberg, realized in theory by L.P. Feoktistov [2] and developed in many publications (see bibliography in [3]), in which several ways of its practical implementation were sug- gested. One of the most promising designs of TWR is a fast reactor, which is able to work in maneuverable mode [3, 6]. Mathematical modeling of TWR using MCNPX code was performed in [4, 7, 8]. Computer simulation of reactor on standing and traveling spherical burning wave has been carried out in present article. The computer model of the reactor using the MCNPX code is a ball of 2 m radius filled with ura- nium dioxide fuel. In the traveling spherical wave mode, nuclear burning begins in the central zone of the core enriched with uranium. When concentration of Pu-239 in U-238 becomes high enough due to breeding mecha- nism according to the scheme U-238 + n = U-239 → Np-239 → Pu-239, a spherical burning wave appears; then it breaks away from the ignition region and contin- uously moves to the edges of the core during ~ 150 years. In our model at a power of 240 MW, the burning wave velocity was 0.5 cm/year. The mode of a standing spherical burning wave (SWR) was achieved by selecting the values of fuel speed and reactor power. Radial distributions of neutron flux, power density and the concentrations of Pu-239 and U-238 in the spherical standing burning wave were obtained using MCNPX code. A comparison of theoretical results with the data of numerical simulation has been carried out. Possibility of using depleted uranium as a nuclear fuel in reactors on spherical burning wave is confirmed. 1. NEUTRON KINETICS EQUATION IN MOVING NEUTRON-MULTIPLYING MEDIUM Let us consider nuclear burning wave in incompress- ible uranium-based medium, which moves to the center of the reactor at velocity V(r) = VR(R/r) 2 , where VR is speed of fuel at periphery of the reactor at r = R. The simplest description of neutron kinetics and burning of nuclear fuel can be obtained using the coor- dinate system x ', y ', z ', in which the fuel is stationary: 1 ˆ ( ) v f aD S t         ; (1) 8 8 8a n n t       , 9 9 89 8 89 n n n t        , 9 9 9 9 89 a n n n t        , 9 92c f n n t      , (2) where ( ', )r t is neutron flow; v is speed of neutrons; n8 ( ', )r t is concentration of 238 U; 9 ( ', )n r t is concen- tration of 239 Np; 9 ( ', )n r t is concentration of 239 Pu; ( ', )cn r t is concentration of fission products; D̂  neu- tron transport operator; 99 nff   macroscopic cross-section of fission and ccaaa nnn   9988  macroscopic neutron absorption cross section. S  term describing the reactor operating controls; 89  transmutation cross-section of 238 U to 239 Pu; 89  time of the decay in chain 239 U  239 Np  239 Pu; 9f  fission cross-section of 239 Pu;  the number of fission neutrons; 8a and 9a  neutron absorption cross- sections for nuclei 238 U and 239 Pu; c is neutron ab- sorption cross-section for fission products. To simplify we put 8a = 9a = a . Boundary conditions have to be added to Eqs. (1) and (2): Ψ(∞, t) = 0, Ψ'(0, t) = 0, n9(∞, t) = 0, 9 ~n (∞, t) = 0, nc(∞, t) = 0, n8(∞, t) = n8(0). (3) We need to find a time-independent solution of equations (1) in the form of a spherical standing wave Ψ(r), n8 (r), n9(r). Consider the movement of fuel mate- rials rather slow: 89 V<<L, where L is the characteristic size of the burning region, then Eqs. (1), (2) can be in- terpreted as quasi-stationary (v=∞). The operator D̂ we choose in diffusion approximation. The boundary conditions (3) look as follows: Ψ(∞) = 0, Ψ'(0) = 0, n9(∞) = 0, nc(∞) = 0, n8(∞) =n0. (4) 2. THEORY OF SPHERICAL NUCLEAR BURNING WAVE Equation for fluence Now, instead of the r coordinate we will introduce a new variable 2 2 ( ') ( ) ' ( ') ' ' ( ') a a Rr r r r dr r r dr V r V R           , which is proportional to fluence F(x) and ranges from 0 to a maximum value of 0 maxaF  . Let us choose the function S(x) describing the automatic control on excess reactivity ρ as:  fS  . After these changes Eqs. (1) and (2) become: 2 2 4 2 4 (1 ) 0 2 a f a R D r V R                 , (5) 8 8 n d dn   , (6) 9898 9 / nn d dn a   , (7) af c n d dn   /2 9 , (8)   dQRVP faR /4 2 , (9) 9nff  , (10) ccaa nnn  )( 98 , (11) where Q is nuclei 239 Pu fission energy release. The boundary conditions (4) for the functions Ψ(φ), n8(φ), 9 ~n (φ), n9(φ) look as follows: 0 9 8 0(0) 0; '( ) 0; (0) 0; (0) 0; (0) ,cn n n n       (12) where 0 (0)  is the maximum neutron fluence. Equation for neutron flux density Equations (6) - (8) can be solved:   enn 08 )( ,   enn a 0899 /)( , 2 89 0( ) 2 / [1 (1 ) ]c f an n e         , (13) where 0n is concentration of U-238 in the initial mate- rial, and equation (5) becomes: 4 2 2 4 0 8989 2 ( ) 2 (1 2 ) 2 2 (1 ) , a R f a a D d r d e n V d R d e e                                        (14) where 3 89 /c f a     is a parameter, which determines the speed of breeding in the system. System excess reactivity calculation Integrating equation (14) over φ taking into account the boundary condition Ψ(0) = 0, we obtain: 4 2 2 4 0 ( ) ( ) 2 a R D r d f n V R d       , (15) where ( ) 2 (1 2 )( 1)f e         8989 2 2 (1 ) [1 (1 ) ] f a a e                     . Substituting φ = φ0 in (15) and using the boundary conditions (12), we obtain the equation for the system excess reactivity ρ: 0( ) 0f   . (16) Solving Eq. (16) we obtain expression for excess re- activity, which is necessary for the existence of a sta- tionary solution:   2 0 89 a f c q        (17) where 0 0 0 0 0 2 (1 2 )( 1) 1 (1 ) e q e              , and 891 2 f a a c               . (18) Eq. (17) and (18) relate excess reactivity ρ to the maximum fluence in unloaded fuel φ0. This value lies in the range 0 ≤ φ0 ≤ χ, where χ is the maximum fluence in the flat burning wave [4] (Eq. (19) and Fig. 1): 22 22 )1(2]1)1[( )1(           ee ee . (19) 0 2 4 6 8 10 12 14 0 1 2 3   Fig. 1. Dependence χ(β) Neutron field calculation Substituting (17) to (15) we obtain: 4 2 1 02 4 0 ( ) ( , ), 2 a R D r d f q n V R d       (20) where 1 0 0 0( , ) 2 (1 2 )( 1)f q q e q e           . The function 1 0( , )f q has the following analytical properties [7, 8]: 1 0(0, ) 0f q  , 1 0 0( , ) 0f q  ; it be- comes zero at the ends of the range 00   . Substituting expression 2 R a V R d r dr            in equation (20) and introducing new dimensionless varia- bles 2 0 0R a D D n V R n R     ; 0( ) /an D r  , we get the system of equations: 2 1( ) / d f d       , (21) 2d d      (22) with boundary conditions 0( ) 0, (0) , ( ) .        (23) Set 0 in the interval 0< 0 < χ and solve equations (21), (22) with boundary conditions (23) by the shooting method: choose a value 0 and start from 0  with initial conditions 0(0)  and (0)   ; we ob- tain solutions ( )  and ( )  diverging at   . We select 0 so that the region of divergence was as far as possible. Returning to the variables r, φ(r), and Ψ(r), we find the radial dependences of the neutron fluence φ(r), and flux )(r , as well as the concentration profiles of plu- tonium )( 0899 )(/)( r a ernrn   , (24) uranium )( 08 )( renrn  and fission products  2 ( ) 89 0( ) 2 / [1 1 ( ) ]r c f an r n r e        . (25) We also get the expression for power: fP Q dV    02 2 0 89 04 / [1 (1 ) ]R f aQV R n e          . (26) The speed of fuel movement is proportional to the power of the reactor. The burning wave profile remains unchanged. The main result of theory is that spherical standing- burning wave can be described with tree parameters: two combinations of nuclear cross sections c, β and neu- tron fluence φ0 in unloaded fuel. Fig. 2 shows an example for radial profiles of the neutron flux in standing burning waves for material pa- rameter β = 1 (when χ = 2 – the maximal value of φ0) and different values of the parameter φ0. 0 5 10 15 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 0.045  0 =0.3  0 =0.5  0 =1  0 =1.3  0 =1.5  0 =1.7    Fig. 2. Radial dependences of the neutron flux ψ(ζ) in standing waves, χ = 2 The maximum of neutron flux in the burning wave (see Fig. 2) moves away from the center of the core when φ0 increases and goes to infinity at φ0 = χ. Fig. 3 shows dependence the power of the standing burning wave on the fluence φ0 at χ = 1. The fundamen- tal difference between a spherical standing-wave reactor and a one-dimension traveling-wave reactor is that its power can be physically limited by choosing a suffi- ciently small parameter φ0 and small dimensions of the core. Spherical standing-wave differs from a traveling burning wave Feoktistov’s type, in which the power and neutron fluxes are much more than modern structural materials can allow. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 P   Fig. 3. Dependence of power of the standing burning wave on the fluence φ0 with χ = 1 0 1 2 3 0.0 0.1 0.2 Pu-239 Fissium    C o n c e n tr a ti o n , P u -2 3 9 , fi s s iu m   Fig. 4. Dependences of Pu-239 concentrations and fis- sion products on the radius 0 1 2 3 0.7 0.8 0.9 1.0 1.1    C o n c e n tr a ti o n , U -2 3 8   Fig. 5. Dependence of U-238 concentration on the radi- us in the standing burning wave Figs. 4,5 show the dependences of the concentra- tions of Pu-239, U-238 and fission products on the radi- us in the standing burning wave of a spherical shape. From Fig. 5 one can see that in the standing burning wave with the specified parameters, the uranium isotope U-238 burns out by 18%, and in the spent fuel there are still ~ 6% Pu-239. 3. ANALYSIS OF STABILITY THE SPHERICAL BURNING WAVE In Fig. 6 the family of phase trajectories ψ(φ) for different values of φ0 is shown. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 0.00 0.05  0 =0.1  0 =0.3  0 =0.5  0 =1  0 =1.3  0 =1.5  0 =1.7  0 =1.8    Fig. 6. Dependence ψ(φ) for a some values of φ0 at χ = 2 A necessary condition for stability of a standing burning wave is the positivity of the values of φ and ψ along the trajectory of the solution ( )  and ( )  . Thus, the entire trajectory of the dependence φ(ψ) should lie in the first quadrant. As can be seen in Fig. 6 this condition is valid. Calculation of the minimum value of the parame- ter with the scope of the solution The condition ρ ≥ 0 for the existence of a standing spherical wave gives a relation: c ≥ q0(β, φ0). (27) Relation (27) determines сmin(φ0)  the minimum value of с, for which a stationary solution still exists for a given value of φ0. The dependence сmin(φ0) has the form: 0 0 0 min 0 0 2 (1 2 )( 1) ( , ) . 1 (1 ) e c e                (28) The dependence сmin(φ0, β) calculated using (28) for the value β = 1 is shown in Fig. 7. The wave exists in the open region of the graph. The dependence сmin(φ0, β) has a minimum, indicated in the graph as cmm(β), which is located below the line q(β) corresponding to a plane burning wave. One can see from Fig. 7 that a standing spherical burning wave is more stable than a plane burn- ing wave, and two times lower fluency φ0 is required for existence of a standing wave. 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0 2 4 6 8 10 q 0 (  )   c mm ()   c q() Fig. 7. Dependence of сmin(φ0, β) on φ0 with β=1,(χ= 2) State diagram of a reactor on the standing spheri- cal burning wave The dependence of cmm(β) is shown in Fig. 8 with dotted line. It represents the lower limit of parameter c for standing burning wave stability in a spherical reac- tor. For comparison, the lower limit of c for a plane burning wave stability in an infinite medium q(β) [4] is shown in the same graph. 0 1 2 3 4 0 2 4 6 8 10 12 14 c mm ()  c q() Fig. 8. State diagram of the reactor on a standing spherical burning wave The state diagram of a reactor on a standing spheri- cal burning wave is shown in Fig. 8. In the pink shaded region there are no standing waves, in the region shaded in yellow the spherical standing waves exist only for some values of φ0. In the open region of the Fig. 8 the waves exist for any values of φ0. 4. COMPUTER SIMULATION OF SPHERICAL TRAVELLING BURNING WAVE Computer model of STBW is a sphere with radius R =2 m, filled with uranium dioxide based fuel, which is divided into spherical layers with thickness of 5 cm. In order to reach criticality an igniter containing enriched uranium was located in the central part of the reactor core. Due to transmutation under fast neutron irradia- tion the 238 U isotope converts to 239 Pu according to the chain: 238 U + n = 239 U  239 Np  239 Pu. When concen- tration of 239 Pu in the fuel reaches high level, spherical burning wave appears; it breaks away from the central area and moves to the edges of the active zone during 30 years. In this model the speed of the burning wave is ~0.5 cm/year at 240 MW power (see Figs. 9 and 10 in which radial distributions of neutron flux and power are shown). 0 10 20 30 40 50 60 70 80 90 100 110 120 130 0.0 2.0x10 14 4.0x10 14 6.0x10 14 8.0x10 14 1.0x10 15 1.2x10 15 1.4x10 15 0 years 5 years 10 years 20 years 30 years F lu x , n /c m 2 /s r, cm Fig. 9. Radial dependences of the neutron flux density in a traveling spherical burning wave for period of 30 years 0 20 40 60 80 100 120 140 0.00 0.02 0.04 0.06 0.08 0.10 0.12 Spherical travelling nuclear burning wave 0 years 5 years 10 years 15 years 20 years 25 years 30 years P o w e r fr a c ti o n ,  r = 5 c m r, cm SWRSh8, 30 years, Power 240 MW Fig. 10. Radial distribution of power fraction of the layers in the traveling spherical burning wave during 30 years at 240 MW power 5. COMPUTER SIMULATION OF SPHERICAL STANDING BURNING WAVE In SWR model fuel is moving towards the burning wave at the same speed, that ensures the stationarity of breading and burning processes in the reactor. The re- sults of computer simulation of a standing nuclear burn- ing wave during 20 years are shown in Fig. 11. It shows that parameters of the model ensure stationary of the spherical nuclear burning wave when reactor is fed with depleted uranium. Figs. 11–13 show dependences of power density and concentrations of Pu-239 and U-238 on the radius, which were obtained using MCNPX computer simulation of the spherical standing burning wave. They are in qualitative agreement with the theo- retical results (see Figs. 3–5). 0 10 20 30 40 50 60 70 80 90 100 110 120 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0 years 5 years 10 years 15 years 20 years P o w e r fr a c ti o n ,  r = 5 c m r, cm SWRS, 20 years, Power 240 MW Spherical standing nuclear burning wave Fig. 11. Radial distribution of power fraction of the layers in a standing spherical burning wave over a period of 20 years 0 10 20 30 40 50 60 70 80 90 100 110 120 0 1 2 3 4 5 6 7 8 9 10 Pu-239 C o n c e n tr a ti o n , % r, cm SWRS, 20 years, Power 240 MW Spherical standing nuclear burning wave Fig. 12. Dependence of Pu-239 concentration on the radius in the standing burning wave 0 10 20 30 40 50 60 70 80 90 100 110 120 0 10 20 30 40 50 60 70 80 90 100 110 U-238 Pu-239 C o n c e n tr a ti o n , % r, cm SWRS, 20 years, Power 240 MW Spherical standing nuclear burning wave Fig. 13. Dependence of the concentrations of U-238 and Pu-239 on the radius in the standing burning wave CONCLUSION • Standing nuclear burning wave can exist not only in one-dimensional geometry, but in systems with cy- lindrical and spherical symmetries as well. • Phenomenological theory of standing spherical nu- clear burning wave was developed • Existence of a standing spherical nuclear burning wave was proved for a reactor with fuel continuously moving toward the center. • State diagram of such a reactor was proposed and the boundaries of the standing wave existence were de- fined. • Mathematical modeling of reactor on spherical standing burning wave was carried out using MCNPX code, and obtained numerical results are in agreement with results of the phenomenological theory. REFERENCES 1. MCNPX User’s Manual Version 2.5.0, April. 2005 LA-CP-05-0369 2. L.P. Feoktistov. Neutron-fission wave // Rep. Academy Sciences of the USSR. 1989, v. 309, p. 864- 867. 3. T. Ellis, R. Petroski. Traveling-Wave Reactors: A Truly Sustainable and Full-Scale Resource for Global Energy Needs // Proceedings of ICAPP ’10, San Diego, CA, USA, June 13-17, 2010, 10189 p. 4. V.V. Gann, A.V. Gann. Benchmark on traveling wave fast reactor with negative reactivity feedback ob- tained with MCNPX code // 4 International Conference “Current Problems in Nuclear Physics and Atomic En- ergy” (NPAE-Kyiv 2012), September 37, 2012, Kyiv, Ukraine. Proceedings Part II, p. 421-425. 5. Yu.Y. Leleko, V.V. Gann, A.V. Gann. Computer Simulation of Stationary Burning Wave Reactor // 4th International Conference “Computer modelling in high- tech” (CMHT-Kharkov 2016), May 2631, 2016, Khar- kov, Ukraine, p. 206 6. TERRAPOWER, LLC Traveling Wave Reactor Develop Program Overview // http://dx.doi.org/10.5516/NET.02.2013.520 7. Yu.Y. Leleko, V.V. Gann, A.V. Gann. Nuclear reactor on cylindrical standing burning wave with an external negative reactivity feedback // Problems of Atomic Science and Technology. 2017, № 2(108), p. 138-143. 8. V.V.Gann, Yu.Y.Leleko, A.V.Gann Computer simulation of nuclear reactor on cylindrical standing burning wave // Proceedings of NUCLEAR 2017 the 10th International Conference on Sustainable Develop- ment through Nuclear Research and Education, Pitesti, 2017, May 2426, p. 161-168. Article received 07.11.2018 http://dx.doi.org/10.5516/NET.02.2013.520 СФЕРИЧЕСКАЯ СТОЯЧАЯ ВОЛНА ЯДЕРНОГО ГОРЕНИЯ С ВНЕШНИМ АВТОМАТИЧЕСКИМ КОНТРОЛЕМ РЕАКТИВНОСТИ Ю.Я. Лелеко, В.В. Ганн, А.В. Ганн Была развита нейтронная кинетика стоячей волны ядерного горения в нейтронно-размножающей среде, которая не сжимается и является подвижной, при наличии ядерных реакций. Рассмотрен сферический реак- тор, в котором волна ядерного горения движется радиально от центра, а топливо – в центр реактора. Пока- зано, что при подпитке такой системы 238 U в ней может существовать сферическая стоячая волна ядерного горения. Проведено сравнение теоретических результатов с данными численного моделирования такого ре- актора с использованием кода MCNPX. СФЕРИЧНА СТОЯЧА ХВИЛЯ ЯДЕРНОГО ГОРІННЯ З ЗОВНІШНІМ АВТОМАТИЧНИМ КОНТРОЛЕМ РЕАКТИВНОСТІ Ю.Я. Лелеко, В.В. Ганн, А.В. Ганн Була розвинена нейтронна кінетика стоячої хвилі ядерного горіння в нейтронно-розмножуючім середо- вищі, котре не стискається та є рухомим, при наявності ядерних реакцій. Розглянуто сферичний реактор, в якому хвиля ядерного горіння рухається радіально від центра, а паливо – до центра реактора. Показано, що при підживленні такої системи 238 U в ній може існувати сферична стояча хвиля ядерного горіння. Проведено порівняння теоретичних результатів з даними чисельного моделювання такого реактора з використанням коду MCNPX.

Spherical standing burning wave with external automatic reactivity control

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