Application of Differential Sensitivity Theory to a Neutronic/Thermal-Hydraulic Reactor Safety Code

Parks, C.V.; Maudlin, P.J.

doi:10.13182/nt81-a32752

Cited by 14 publications

(18 citation statements)

References 8 publications

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“…There are several alternative theoretical approaches to the adjoint-based sensitivity analysis. The prominent methods are the variational method, [9,11,18,19] the perturbation method [10,13,14], and the differential method [22,23]. The variational method is implemented in PERSENT as it only requires the use of a single method to obtain the sensitivities for all of the response parameters of interest.…”

Section: Sensitivity Functionalmentioning

confidence: 99%

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

Adams

Smith

2018

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The nodal diffusion method is one of the most widely used approaches in modern reactor analysis. In the nodal diffusion method, a coarse multi-group set of "homogenized" parameters is constructed such that the complex geometry of a reactor core along with the energy dependence of neutron and gamma ray cross sections in a nuclear reactor are conserved in the simpler geometry. The homogenization is typically done on a fuel assembly level as is the case in the DIF3D code developed at Argonne National Laboratory. The nodal methodology is used primarily to predict fuel cycle behavior of nuclear systems of which there is a substantial amount of validation in the literature. Another use of the nodal method is to obtain reactivity coefficients and kinetics parameters for use in a safety analysis of a given nuclear reactor. While there are many ways to obtain reactivity worth and kinetics parameters, the work presented in this manuscript is unique as it provides the user with the ability to compute reactivity worths, kinetics parameters, and cross section sensitivities with a Cartesian and hexagonal geometry based transport code.This manuscript serves as a single manual for two separate codes: VARI3D and PERSENT. The VARI3D code (VARiational 3D) is based upon the classic finite difference diffusion theory solver available in DIF3D. The PERSENT code (PERturbation and SENitivity for Transport) is based upon the variational nodal method employed in DIF3D termed VARIANT. The VARIANT solver was added to DIF3D in 1995 and has seen continued development and use for the last 18 years. Because VARI3D primarily uses deprecated coding practices, rather than incorporate the perturbation and sensitivity treatments for transport within VARI3D, a new coding development was built using modern Fortran coding. The primary purpose of this manual is to describe the theory behind PERSENT (and by convenience, that of VARI3D) and discuss the input and output of PERSENT along with giving potential users an idea of how to use it. While this manuscript does describe the input and output of VARI3D, the PERSENT code is intended to be the replacement capability of VARI3D as PERSENT can generate nearly identical (if not superior) diffusion theory results.In this manuscript, the relevant aspects of generalized perturbation theory that are relevant to both VARI3D and PERSENT are covered. The input and output of VARI3D is displayed by excerpting several of the example problems. Similarly, the input and output of PERSENT is displayed along with tips on how best to use the code. Note that the input and output of the inhomogeneous solver wrapped around DIF3D (DIF3D_IFS) is also discussed as it is needed to carry out some of the sensitivities in PERSENT such as reaction rate ratios.This manuscript describes several perturbation theory problems and sensitivity problems and the results computed using PERSENT. From these sections, potential users should find that PERSENT provides not only the typical tables of numbers desired in perturbation and sensitivity ana...

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Section: Sensitivity Functionalmentioning

confidence: 99%

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

Adams

Smith

2018

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“…(11-13) with Eq. (11-11) and solving for s^ function of a: (11)(12)(13)(14)(15)(16) where the subscript d denotes drag-controlled deformation. Using this constant-structure deformation form in Eq.…”

Section: -11)mentioning

confidence: 99%

“…6 for more details concerning the formulation of Eqs. (11)(12)(13) through (11)(12)(13)(14)(15)(16).…”

Section: -11)mentioning

confidence: 99%

Implementation and assessment of the mechanical-threshold-stress model using the EPIC2 and PINON computer codes

Maudlin¹,

Davidson²,

Henninger³

1990

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“…We began (2) by applying an equation-based sensitivity technique used successfully in the early eighties that was applied to reactor-safety thermalhydraulics problems (3,4), which is called Differential Sensitivity Theory (DST) (5,6). The methodology is as follows: the system of partial differential equations (the forward or physical PDEs) is assembled, and differentiated with respect to the model parameters of interest; the adjoint equations are then determined using the innerproduct rules of Hilbert spaces (5); and finally, the resulting adjoint PDEs are solved using straightforward numerical operators.…”

Section: Introductionmentioning

confidence: 99%

Sensitivities for Taylor-Test Model Parameters

Henninger¹

2002

AIP Conference Proceedings

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Abstract. The Taylor-Cylinder test has long been used to calibrate equation-of-state and materialstrength models. The process consists of impacting a cylinder of material on a rigid anvil and adjusting the model parameters to predict the resultant shape. Here we discuss the use of Automatic Differentiation (AD) of an Eulerian hydrodynamics model to provide sensitivities that are used as a gradient in the parameter fitting process. We apply AD in the forward and adjoint modes. For comparison, the gradient is also determined by finite differences. We find that adjoint methods provide the most efficient use of computational resources when there are 9 or more parameters.

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Application of Differential Sensitivity Theory to a Neutronic/Thermal-Hydraulic Reactor Safety Code

Cited by 14 publications

References 8 publications

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

VARI3D & PERSENT: Perturbation and Sensitivity Analysis

Implementation and assessment of the mechanical-threshold-stress model using the EPIC2 and PINON computer codes

Sensitivities for Taylor-Test Model Parameters

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