Research Article 
Corresponding author: Denis A. Plotnikov ( pda1995@gmail.com ) Academic editor: Yury Kazansky
© 2023 Denis A. Plotnikov, Aleksey L. Lobarev, Ivan N. Krivoshein, Pavel B. Kuznetsov, Anastasia N. Ivanyuta.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Plotnikov DA, Lobarev AL, Krivoshein IN, Kuznetsov PB, Ivanyuta AN (2023) A spatial dynamic model of the SHELFM reactor facility with fuel and coolant temperature feedbacks. Nuclear Energy and Technology 9(1): 7176. https://doi.org/10.3897/nucet.9.102912

The evolution of nuclear power is inseparably linked with the development of breakthrough solutions in the field of economic development of new territories. A pressing issue in this connection nowadays is generation of power for remote and hardtoreach areas with decentralized power supply. To resolve this issue, JSC NIKIET is developing a version of the SHELFM modular watercooled watermoderated reactor facility as a source of power for offshore installations, including the Arctic coast areas, as well as localities with practically no power and transport infrastructure. One of the stages in justifying the safety of the reactor facility operation is to investigate the behavior of the reactor facility in dynamic transient modes at various power levels. To this end, a spatial dynamic model has been developed for the reactor facility with fuel and coolant temperature feedbacks. The dynamic model development process is a complex task that includes both preparation of constants for subsequent calculations and generation of the reactor neutronic and thermophysical models. The paper describes the development stages of the SHELFM reactor facility spatial dynamic model and the results of coupled neutronic and thermophysical calculations for transients using the developed dynamic model of the reactor. Shim rod movement in the cold and hot states of the SHELFM reactor facility is considered as transients.
pressurized watercooled watermoderated reactor, dynamics, feedbacks, simulation
Recent years have seen a growing interest worldwide in developing and using small nuclear power plants (SNPP). SNPPs offer an efficient substitute for the existing hydrocarbonbased power supply systems in remote hardtoreach areas in Russia (
Highly reliable, safe and ecofriendly reactor facilities have been developed by now at JSC NIKIET reaching different design stages (
As part of the SHELFM project, it was required to justify computationally the safety of the reactor facility operation during transients at different power levels. A spatial dynamic reactor model with fuel and coolant temperature feedbacks was developed to this end.
The dynamic model development process involved the following stages: preparation of a twogroup library of macroconstants using an MCUfamily code (
To analyze the SHELFM transients, a twogroup library of macroscopic crosssections and diffusion coefficients was formed depending both on the position of the shim rods and on the values of the fuel and coolant temperature in the computational cell of interest. To this end, a precision reactor model was developed in an MCUfamily code with the MDB650 neutron data library to be used for design of thermal reactors. This code allows precision neutronic Monte Carlo calculations with solving the gaskinetic neutron transport equation and describing continuously the neutron spectrum.
The SHELFM precision model is a 3D computational reactor model which describes heterogeneously all core and side reflector components. The end reflector is defined in the model homogeneously. The fuel in the computational model is divided axially into 10 material zones. To record the functionalities, the FA is broken down into 18 layers, including three bottom reflector layers, ten layers at the core level, and five top reflector layers. A portion of the SHELFM computational model prepared in the MCU code is shown in Fig.
To generate the twogroup library of macroconstants in the prepared computational model, the positions of the shim rods and the fuel and coolant temperature and nuclear concentration values was varied among respective computational cells. The calculation of the coolant nuclear concentrations took into account the dependence of the coolant (light water) density on the coolant temperature at the same pressure as the reactor primary circuit pressure. This dependence is presented in Fig.
A matrix of the macroconstant values was formed in each computational cell based on the neutronic calculation results. The least square method was further used to calculate quartic polynomials depending on the fuel and coolant temperature. The obtained polynomials were normalized against the macroconstant values that corresponded to the fuel and coolant temperature, equal to 300 K, which fits the reactor cold state.
The so obtained twogroup macroconstant library was used at further stages of developing the dynamic spatial model of the reactor facility.
The prepared twogroup library of macroscopic crosssections and diffusion coefficients was used to generate the SHELFM model in the FACT code. The model represents a set of 19 calculation cell types divided axially into 18 layers (ten layers for the core, and eight layers for the bottom and top end reflectors). The cells were divided according to type depending on the number and type of the surrounding shim rods and on the type of the FAs in the cell under consideration. In the considered model, the shim rods were arranged as three banks, including a peripheral shim rod bank (PSG), a middle shim rod bank (MSB), and a central shim rod bank (CSB).
A map of the SHELFM computational model in the FACT code is shown in Fig.
Cell numbers  Cell types 

1–4  Reflector cells 
5–19  FA cells (the number is defined by the FA type and the quantity of the shim rods around the FA) 
The cell numbers are defined both by the FA type (for fuel cells) and by the rods of one of the shim banks residing (taken into account) in the computational cell. Thus, for example, the computational cell that represents a reflector and does not contain any shim rods is numbered 1, and the computational cell that represents a reflector surrounded by three PSB rods is numbered 4.
The FACT code is an adaptation of the FACT BR code for the SHELFM reactor facility (
To check if the reactor model was defined correctly, the FACT code was used to calculate the reactor steady states prepared with the fuel and coolant temperature values equal to 300 K (reactor cold state). The reactor steady states match particular positions of the peripheral (PSB), middle (MSB) and central (CSB) shim rods. The adequacy of the model definition was checked using relative deviations of the K_{eff} values and the rootmeansquare (RMS) power deviations between the calculation results for the MCU and FACT steady states calculated using the power values in each computational fuel cell (FA).
The obtained deviations are presented in Table
State number  Insertion depth, cm  K_{eff} ^{MCU}  K_{eff}^{FACT}  Relative K_{eff} deviations (FACTMCU), %  RMS power deviations, %  

PSB  MSB  CSB  EP  
1  0  0  0  0  1.262  1.263  0.05  2.1 
2  87  0  0  0  1.213  1.210  0.26  4.4 
3  0  87  0  0  1.153  1.154  0.07  3.0 
4  0  0  87  0  1.225  1.230  0.35  4.8 
5  0  0  0  92  1.238  1.238  0.04  4.2 
6  87  87  87  0  0.990  0.992  0.22  2.7 
7  87  87  87  92  0.976  0.976  0.02  3.9 
To simulate thermophysical processes, a thermophysical software module called IVIS was used, designed to simulate and justify computationally the behavior of a single multilayer cylindrical object, including a fuel element with different fuel types and gas and liquidmetal layers flown over by liquidmetal coolant or pressurized water. The IVIS thermophysical module was developed based on the IVISBR thermophysical module (
No hydraulic processes have been calculated. The coolant flow through the FA was assumed to be constant and did not vary in the simulated transients. The SHELFM thermophysical parameters were calculated for the condition of no coolant boiling.
The IVIS calculation results are the fuel and coolant temperature values in the computational cells of the SHELFM model. The obtained temperature values were used to calculate twogroup macroscopic crosssections and diffusion coefficients. The calculations did not include the power density in the reflector, so the temperatures in the reflector’s bottom layers are constant and equal to the reactor core inlet coolant temperature, and do not vary in the transient, as the reflector’s top layers assume the core outlet coolant temperature values.
The shim rod movement in the reactor critical state (starting state) in the reactor cold and hot states is considered as the demonstration of the coupled neutronic and thermophysical calculation results for transients.
A transient is calculated in two stages. The calculation’s stage 1 is to establish the reactor steady state. In the process of recalculating the neutron flux density, the fuel and coolant temperatures are recalculated, and the macroscopic crosssections and diffusion coefficients are respectively recalculated in each computational cell. The transient is simulated at the second stage.
Six groups of delayed neutrons are used to simulate transients. Table
Emitter group number  Fraction of delayed neutrons  Delayed neutron emitter decay constant, s^{1} 

1  2.56×10^{4}  0.012 
2  1.46×10^{3}  0.033 
3  1.306×10^{3}  0.121 
4  2.843×10^{3}  0.303 
5  9.37×10^{4}  0.849 
6  2.02×10^{4}  2.85 
Table
Parameter  Value 

Fuel temperature, K  590 
Core inlet coolant temperature, K  544 
Reactor power, MW  35.2 
K_{eff}  0.9988 
PSB rod position, cm  53 
MSB rod position, cm  65 
CSB rod position, cm  78 
To demonstrate the operation of the IVIS code, the maximum fuel temperature, the maximum coolant temperature, and the maximum fuel element temperature drop reached in the process of establishing the steadystate temperature field in the reactor in the course of the steadystate calculation are presented in Table
Parameter  Value 

Maximum fuel temperature, K  659.9 К 
Maximum coolant temperature, K  584.6 К 
Maximum fuel element temperature drop, K  140.08 К 
After the reactor steady state is established, the transient is simulated. The transient was simulated as follows:
The transient is shown in the diagrams of the change in reactivity (Fig.
To check the serviceability of the prepared SHELFM model at different power levels, the transient was also calculated for the reactor’s cold state. The reactor cold state matches the reactor power equal to 1.0 MW. The transient simulation process in the event of the reactor cold state was similar to that in the event of the reactor hot state. A description of the starting state in the event of the SHELFM cold state is presented in Table
Parameter  Value 

Fuel temperature, K  300 
Core inlet coolant temperature, K  300 
Reactor power, MW  1.0 
K _{eff}  0.9999 
PSB rod position, cm  68 
MSB rod position, cm  82 
CSB rod position, cm  68 
The transient was simulated as follows in the event of the cold state:
The transient is shown in the diagrams for the change in reactivity (Fig.
As the result of the study, a technology has been implemented in the FACT code to calculate the SHELFM reactor facility transients using a spatial dynamic model of the reactor with fuel and coolant temperature feedbacks.
Coupled neutronic and thermophysical calculations were undertaken for the SHELFM transients involving the shim rod movement in the reactor cold and hot state. Simulation results are shown for the transients under investigation.
Therefore, the obtained spatial dynamic model of the SHELFM reactor facility makes it possible to analyze the reactor behavior in transients at different power levels.
Further activities will aim at improving the SHELFM model, developing thermalhydraulic and thermomechanical model of the reactor, and integrating respective software modules into the FACT code.