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Title: Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods

In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to the low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.
Authors:
ORCiD logo [1] ;  [1] ;  [2]
  1. Idaho National Lab. (INL), Idaho Falls, ID (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Report Number(s):
INL/JOU-16-39124; LA-UR-16-24431
Journal ID: ISSN 0149-1970; PII: S0149197016302220
Grant/Contract Number:
AC07-05ID14517; AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Progress in Nuclear Energy
Additional Journal Information:
Journal Volume: 94; Journal Issue: C; Journal ID: ISSN 0149-1970
Publisher:
Elsevier
Research Org:
Idaho National Lab., Idaho Falls, ID (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org:
USDOE Office of Nuclear Energy (NE)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; high-order numerical methods; stability map; Welander problem; Energy Sciences; Welander problem, high-order numerical methods, stability map
OSTI Identifier:
1369438
Alternate Identifier(s):
OSTI ID: 1410905; OSTI ID: 1458949

Zou, Ling, Zhao, Haihua, and Kim, Seung Jun. Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods. United States: N. p., Web. doi:10.1016/j.pnucene.2016.09.021.
Zou, Ling, Zhao, Haihua, & Kim, Seung Jun. Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods. United States. doi:10.1016/j.pnucene.2016.09.021.
Zou, Ling, Zhao, Haihua, and Kim, Seung Jun. 2016. "Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods". United States. doi:10.1016/j.pnucene.2016.09.021. https://www.osti.gov/servlets/purl/1369438.
@article{osti_1369438,
title = {Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods},
author = {Zou, Ling and Zhao, Haihua and Kim, Seung Jun},
abstractNote = {In this study, the classical Welander’s oscillatory natural circulation problem is investigated using high-order numerical methods. As originally studied by Welander, the fluid motion in a differentially heated fluid loop can exhibit stable, weakly instable, and strongly instable modes. A theoretical stability map has also been originally derived from the stability analysis. Numerical results obtained in this paper show very good agreement with Welander’s theoretical derivations. For stable cases, numerical results from both the high-order and low-order numerical methods agree well with the non-dimensional flow rate analytically derived. The high-order numerical methods give much less numerical errors compared to the low-order methods. For stability analysis, the high-order numerical methods could perfectly predict the stability map, while the low-order numerical methods failed to do so. For all theoretically unstable cases, the low-order methods predicted them to be stable. The result obtained in this paper is a strong evidence to show the benefits of using high-order numerical methods over the low-order ones, when they are applied to simulate natural circulation phenomenon that has already gain increasing interests in many future nuclear reactor designs.},
doi = {10.1016/j.pnucene.2016.09.021},
journal = {Progress in Nuclear Energy},
number = C,
volume = 94,
place = {United States},
year = {2016},
month = {11}
}