The Simplified<i>P</i><sub>3</sub>Approximation

Brantley, Patrick S.; Larsen, Edward W.

doi:10.13182/nse134-01

Cited by 143 publications

(75 citation statements)

References 12 publications

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“…However, some studies are being carried out to strengthen the theoretical basis of the SP3 approximation. 7,9) In this study, the finite difference method is used for spatial discretization. The finite difference form of the SP3 equation at the mesh ði; jÞ, the energy group g, is as follows: …”

Section: Simplified P3 (Sp3) Theorymentioning

confidence: 99%

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

Tada

Yamamoto

Yamane

et al. 2008

J. Nucl. Sci. Technol.

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The pin-by-pin fine-mesh core calculation method is considered as a candidate next-generation core calculation method for BWR. In this study, the diffusion and simplified P3 (SP3) theories are applied to the BWR pin-by-pin fine-mesh calculation. The performances of the diffusion and SP3 theories for cell-homogeneous pin-by-pin fine-mesh calculation for BWR are evaluated through comparison with a cell-heterogeneous detailed transport calculation by the method of characteristics (MOC). Two-dimensional, 2 Â 2 multi-assemblies geometry is used to compare the prediction accuracies of the diffusion and SP3 theories. The 2 Â 2 multi-assemblies geometry consists of 9 Â 9 UO 2 fuel assemblies that have two different enrichment splittings. To minimize the cell-homogenization error, the SPH method is applied for the pin-by-pin fine-mesh calculation. The SPH method is a technique that reproduces a result of heterogeneous calculation using that of homogeneous calculation. The calculation results indicated that the diffusion theory shows a discrepancy larger than that of the SP3 theory on the pin-wise fission rate distribution. In contrast to the diffusion theory, the SP3 theory shows a much better accuracy on the pin-wise fission rate distribution. The computation time using the SP3 theory is about 1.5 times longer than that using the diffusion theory. The BWR core analysis consists of various calculations, e.g., the cross section interpolation, neutron flux calculation, thermal hydraulic calculation, and burn-up calculation. The function of the calculation time for the neutron flux calculation is usually less than half in the typical BWR core analysis. Therefore, the difference in the calculation time between the diffusion and SP3 theories would have no significant impact on the calculation time of the BWR core analysis. For these reasons, the SP3 theory is more suitable than the diffusion theory and is expected to have sufficient accuracy for the 2 Â 2 multi-assemblies geometry used in this study, which simulates a typical situation of the actual BWR core.

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Section: Simplified P3 (Sp3) Theorymentioning

confidence: 99%

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

Tada

Yamamoto

Yamane

et al. 2008

J. Nucl. Sci. Technol.

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“…Computational models of light transport including Monte Carlo simulations [13][14][15][16] and numerical implementations of the radiative transport equation [17][18][19][20] are typically too computationally burdensome to be used for applications where rapid analysis is important. Analytical solutions have primarily been restricted to diffusion-theory approximations 21,22 or slightly higher order corrections, [23][24][25][26][27] which are inaccurate near the point-of-entry and when absorption is high or comparable with scattering coefficients. Unfortunately, accurate analytical models of light propagation in tissue near the point-of-entry and for cases where absorption is high or comparable with scattering have been difficult to obtain.…”

Section: Introductionmentioning

confidence: 99%

Phase-function corrected diffusion model for diffuse reflectance of a pencil beam obliquely incident on a semi-infinite turbid medium

Zemp

2013

J. Biomed. Opt

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Abstract. Oblique incidence reflectometry (OIR) is an established technique for the estimation of tissue optical properties. However, a sensing footprint of a few transport mean-free paths is often needed when diffusionregime-based algorithms are used. Smaller-footprint probes require improved light-propagation models and inversion schemes for diffuse reflectance close to the point of entry but might enable micro-endoscopic form factors for clinical assessments of cancers and precancers. The phase-function corrected diffusion theory presented by Vitkin et al. [Nat. Commun. 2, 587 (2011)] to the case of pencil beams obliquely incident on a semi-infinite turbid medium is extended. The model requires minimal computational resources and offers improved accuracy over more traditional diffusion-theory approximations models when validated against Monte Carlo simulations. The computationally efficient nature of the models lends itself to rapid fitting procedures for inverse problems. The analytical model is used in a nonlinear fitting algorithm to demonstrate the recovery of optical properties using a measurement footprint that is significantly smaller than needed in previous diffusion-regime OIR methods. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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“…Considering that diffusion calculation needs many approximation and ordinary transport calculation methods such as MOC or S N method usually takes more computing resources, isotropic SP 3 (simplified P 3 ) method is encouraged to be a middle choice for engineering practice use for whole core pin-by-pin calculation with pin size homogenization [1][2][3][4]. For SP 3 method, neutron transport equation can be transformed into two coupled equations in the same mathematical form as diffusion equation.…”

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confidence: 99%

Development and Verification of an SP3 Code Using Semi-Analytic Nodal Method for Pin-by-Pin Calculation

Tang¹

2017

JPSA

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SP 3 (simplified P 3 ) theory is widely used in LWR (light water reactor) analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP 3 code named STELLA is developed and verified at SNERDI (Shanghai Nuclear Engineering Research and Design Institute). For SP 3 method, neutron transport equation can be transformed into two coupled equations in the same mathematical form as diffusion equation. In this work, SANM (semi-analytic nodal method) is used to solve diffusion-like equation, due to its easy to handle multi-group problem. Whole core nodal boundary net current coupling is used to improve convergence stability in SANM, instead of solving two-node problem. CMFD (coarse-mesh finite difference) acceleration method is employed for 0-th SP 3 equation, which represents the neutron balance relationship. Three benchmarks are used to verify the SP 3 code, STELLA. The first one is a self-defined one dimensional problem, which demonstrates SP 3 method is extremely accurate, due to no academic approximation in one dimensional for SP 3 . The second one is a two dimensional one-group problem cited from Larsen's paper, which is usually used to verify and prove the SP 3 code correct and accurate. And the third one is modified from 2D C5G7-MOX benchmark, whose numerical results indicate that STELLA is accurate and efficient in pin size level, compared to diffusion model.

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The SimplifiedP₃Approximation

Cited by 143 publications

References 12 publications

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

Phase-function corrected diffusion model for diffuse reflectance of a pencil beam obliquely incident on a semi-infinite turbid medium

Development and Verification of an SP3 Code Using Semi-Analytic Nodal Method for Pin-by-Pin Calculation

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The SimplifiedP3Approximation

Cited by 143 publications

References 12 publications

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

Applicability of the Diffusion and Simplified P3 Theories for Pin-by-Pin Geometry of BWR

Phase-function corrected diffusion model for diffuse reflectance of a pencil beam obliquely incident on a semi-infinite turbid medium

Development and Verification of an SP3 Code Using Semi-Analytic Nodal Method for Pin-by-Pin Calculation

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The SimplifiedP₃Approximation