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An improved semi-implicit direct kinetics method for transient analysis of nuclear reactors

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Abstract

Semi-implicit direct kinetics (SIDK) is an innovative method for the temporal discretization of neutronic equations proposed by J. Banfield. The key approximation of the SIDK method is to substitute a time-averaged quantity for the fission source term in the delayed neutron differential equations. Hence, these equations are decoupled from prompt neutron equations and an explicit analytical representation of precursor groups is obtained, which leads to a significant reduction in computational cost. As the fission source is not known in a time step, the original study suggested using a constant quantity pertaining to the previous time step for this purpose, and a reduction in the size of the time step was proposed to lessen the imposed errors. However, this remedy notably diminishes the main advantage of the SIDK method. We discerned that if the original method is properly introduced into the algorithm of the point-implicit solver along with some modifications, the mentioned drawbacks will be mitigated adequately. To test this idea, a novel multi-group, multi-dimensional diffusion code using the finite-volume method and a point-implicit solver is developed which works in both transient and steady states. In addition to the SIDK, two other kinetic methods, i.e., direct kinetics and higher-order backward discretization, are programmed into the diffusion code for comparison with the proposed model. The final code is tested at different conditions of two well-known transient benchmark problems. Results indicate that while the accuracy of the improved SIDK is closely comparable with the best available kinetic methods, it reduces the total time required for computation by up to 24%.

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Abbreviations

SIDK:

Semi-implicit direct kinetics

FVM:

Finite-volume method

HOBD:

Higher-order backward discretization

α :

Heat-up conversion factor

β :

Fission neutron fraction of a delayed neutron precursor group

γ :

Thermal feedback constant

λ :

Decay constant of a delayed neutron precursor group

ν :

Average number of neutrons released per fission

ϕ :

Neutron flux

χ :

Fission neutron energy spectrum

Σa :

Macroscopic absorption cross section

Σf :

Macroscopic fission cross section

Σg′→g :

Macroscopic scattering cross section from energy group g′ to g

ΣR :

Macroscopic removal cross section

A f :

Surface area vector of a face enclosing the target numerical cell

C :

Concentration of delayed neutron precursor

Ce:

Total number of numerical cells

D :

Neutron diffusion coefficient

G :

Total number of neutron energy groups

k eff :

Effective multiplication factor

M :

Total number of delayed neutron precursor groups

N f :

Total number of faces enclosing each cell

P :

Power density

t :

Time

T :

Temperature

v :

Velocity

V :

Volume

f :

Counter of faces enclosing each numerical cell

g :

Counter of neutron energy group

i :

Counter of numerical cells

k :

Counter of time steps

m :

Counter of delayed neutron precursor group

n :

Counter of numerical iterations

o :

Indicator of being an initial quantity

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Authors and Affiliations

  1. School of Nuclear Reactors and Safety, Nuclear Science and Technology Research Institute, End of North Karegar Ave., Tehran, 14359-836, Iran

    Roozbeh Vadi & Kamran Sepanloo

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  1. Roozbeh Vadi
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  2. Kamran Sepanloo
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Correspondence to Roozbeh Vadi.

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Vadi, R., Sepanloo, K. An improved semi-implicit direct kinetics method for transient analysis of nuclear reactors. NUCL SCI TECH 30, 162 (2019). https://doi.org/10.1007/s41365-019-0690-3

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