Abstract
Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations. In this paper we discuss the development of such methods in addition to species transport for liquid fueled molten salt reactors (MSRs). Conventional nuclear reactors work with fixed fuel assemblies in which fission products and fissile material do not transport throughout the core. Liquid fueled molten salt reactors work in a much different way, allowing for material to transport throughout the primary reactor loop. Because of this, fission product transport must be taken into account. The set of partial differential equations that apply are discretized into systems of first order ordinary differential equations (ODEs). The exact solution to the set of ODEs is herein being estimated using the matrix exponential method known as the Chebychev Rational Approximation Method (CRAM).
Highlights
Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations
In liquid fueled molten salt reactors, the fuel and fission products are allowed to flow around the primary loop, requiring that species transport be taken into account
If these methods are utilized very small time steps must be taken to reach high levels of accuracy, leading to increased computational time. Depletion codes such as ORIGEN have implemented highly accurate matrix exponential methods to calculate fission product distributions [1]. These same methods are being implemented into a c++ software environment to model depletion and transport of fission products, which are generally grouped into delayed neutron precursor groups
Summary
Matrix exponential methods have long been utilized for isotopic depletion in nuclear fuel calculations. Traditional time discretization methods used for scalar data transport cannot achieve the level of accuracy required for nuclear analysis of fission products. If these methods are utilized very small time steps must be taken to reach high levels of accuracy, leading to increased computational time. Depletion codes such as ORIGEN have implemented highly accurate matrix exponential methods to calculate fission product distributions [1]. These same methods are being implemented into a c++ software environment to model depletion and transport of fission products, which are generally grouped into delayed neutron precursor groups
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