Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

doi:10.1016/j.pnucene.2017.07.008

Title: Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

Abstract

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested with two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form ofmore »« less

Authors:

^[1]; Zhao, Haihua ^[1]; Zhang, Hongbin ^[1]

Idaho National Lab. (INL), Idaho Falls, ID (United States)

Publication Date:: Mon Aug 07 00:00:00 EDT 2017

Research Org.:: Idaho National Lab. (INL), Idaho Falls, ID (United States)

Sponsoring Org.:: USDOE Office of Nuclear Energy (NE)

OSTI Identifier:: 1375246

Alternate Identifier(s):: OSTI ID: 1549808

Report Number(s):: INL/JOU-17-40865
Journal ID: ISSN 0149-1970; PII: S0149197017301750

Grant/Contract Number:: AC07-05ID14517

Resource Type:: Accepted Manuscript

Journal Name:: Progress in Nuclear Energy

Additional Journal Information:: Journal Volume: 100; Journal ID: ISSN 0149-1970

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 22 GENERAL STUDIES OF NUCLEAR REACTORS; Newton-Krylov method; drift-flux model; high-order numerical methods

Citation Formats


                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model.  United States: N. p., 2017. 
Web.  doi:10.1016/j.pnucene.2017.07.008.

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                    Zou, Ling, Zhao, Haihua, & Zhang, Hongbin. Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model.  United States.  https://doi.org/10.1016/j.pnucene.2017.07.008

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                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Mon .  
"Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model".  United States.  https://doi.org/10.1016/j.pnucene.2017.07.008.  https://www.osti.gov/servlets/purl/1375246.

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@article{osti_1375246,

  title        = {Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model},

  author       = {Zou, Ling and Zhao, Haihua and Zhang, Hongbin},

  abstractNote = {This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested with two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).},

  doi          = {10.1016/j.pnucene.2017.07.008},

  journal      = {Progress in Nuclear Energy},

  number       = ,

  volume       = 100,

  place        = {United States},

  year         = {Mon Aug 07 00:00:00 EDT 2017},

  month        = {Mon Aug 07 00:00:00 EDT 2017}

}

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Works referenced in this record:

Development and assessment of system analysis code, TASS/SMR for integral reactor, SMART
journal, March 2012

Chung, Y. J.; Jun, I. S.; Kim, S. H.
Nuclear Engineering and Design, Vol. 244
DOI: 10.1016/j.nucengdes.2011.12.013

Applicability of TASS/SMR using drift flux model for SMART LOCA analysis
journal, September 2013

Chung, Young-Jong; Kim, Soo Hyung; Lee, Gyu Hyeung
Nuclear Engineering and Design, Vol. 262
DOI: 10.1016/j.nucengdes.2013.04.020

A new numerical method for solution of boiling flow using combination of SIMPLE and Jacobian-free Newton-Krylov algorithms
journal, March 2017

Hajizadeh, A.; Kazeminejad, H.; Talebi, S.
Progress in Nuclear Energy, Vol. 95
DOI: 10.1016/j.pnucene.2016.11.005

An advanced new fully implicit numerical method for two-phase flow subchannel analysis based on the Drift Flux Model
journal, October 2017

Hajizadeh, A.; Kazeminejad, H.; Talebi, S.
Annals of Nuclear Energy, Vol. 108
DOI: 10.1016/j.anucene.2017.04.046

Benchmarking a sub-channel program based on a drift-flux model with 8×8 NUPEC BWR rod bundle
journal, August 2013

Hashemi-Tilehnoee, M.; Rahgoshay, M.
Annals of Nuclear Energy, Vol. 58
DOI: 10.1016/j.anucene.2013.03.005

Sub-channel analysis of 8×8 and 9×9 BWR fuel assemblies with different two-phase flow models
journal, December 2013

Hashemi-Tilehnoee, M.; Rahgoshay, M.
Annals of Nuclear Energy, Vol. 62
DOI: 10.1016/j.anucene.2013.06.024

Subchannel analysis in BWR fuel bundles
journal, January 1985

Khan, H. J.; Yi, H. C.
Annals of Nuclear Energy, Vol. 12, Issue 10
DOI: 10.1016/0306-4549(85)90029-5

Jacobian-free Newton–Krylov methods: a survey of approaches and applications
journal, January 2004

Knoll, D. A.; Keyes, D. E.
Journal of Computational Physics, Vol. 193, Issue 2
DOI: 10.1016/j.jcp.2003.08.010

Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
journal, October 2004

Mousseau, V. A.
Journal of Computational Physics, Vol. 200, Issue 1
DOI: 10.1016/j.jcp.2004.03.009

A Fully Implicit Hybrid Solution Method for a Two-Phase Thermal-Hydraulic Model
journal, May 2005

Mousseau, Vincent A.
Journal of Heat Transfer, Vol. 127, Issue 5
DOI: 10.1115/1.1865223

Study on the stability behaviour of two-phase natural circulation systems using a four-equation drift flux model
journal, February 2007

Nayak, A. K.; Dubey, P.; Chavan, D. N.
Nuclear Engineering and Design, Vol. 237, Issue 4
DOI: 10.1016/j.nucengdes.2006.05.009

A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model
journal, January 2012

Talebi, S.; Kazeminejad, H.; Davilu, H.
Nuclear Engineering and Design, Vol. 242
DOI: 10.1016/j.nucengdes.2011.10.038

Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality
journal, December 2011

Wang, Jianhua; Sun, Yuliang; Wang, Jianjun
Nuclear Engineering and Design, Vol. 241, Issue 12
DOI: 10.1016/j.nucengdes.2011.08.074

Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems
journal, September 2015

Zou, Ling; Zhao, Haihua; Zhang, Hongbin
Annals of Nuclear Energy, Vol. 83
DOI: 10.1016/j.anucene.2015.04.016

Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method
journal, January 2016

Zou, Ling; Zhao, Haihua; Zhang, Hongbin
Annals of Nuclear Energy, Vol. 87
DOI: 10.1016/j.anucene.2015.07.033

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark
journal, April 2016

Zou, Ling; Zhao, Haihua; Zhang, Hongbin
Nuclear Engineering and Design, Vol. 300
DOI: 10.1016/j.nucengdes.2016.01.033

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model
journal, April 2016

Zou, Ling; Zhao, Haihua; Zhang, Hongbin
Progress in Nuclear Energy, Vol. 88
DOI: 10.1016/j.pnucene.2015.12.006

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method
journal, April 2016

Zou, Ling; Zhao, Haihua; Zhang, Hongbin
Computers & Fluids, Vol. 129
DOI: 10.1016/j.compfluid.2016.02.008

Numerical study on the Welander oscillatory natural circulation problem using high-order numerical methods
journal, January 2017

Zou, Ling; Zhao, Haihua; Kim, Seung Jun
Progress in Nuclear Energy, Vol. 94
DOI: 10.1016/j.pnucene.2016.09.021

Average Volumetric Concentration in Two-Phase Flow Systems
journal, November 1965

Zuber, N.; Findlay, J. A.
Journal of Heat Transfer, Vol. 87, Issue 4
DOI: 10.1115/1.3689137

Works referencing / citing this record:

A Generalized Reduced-Order Dynamic Model for Two-Phase Flow in Pipes
journal, June 2019

Chaari, Majdi; Fekih, Afef; Seibi, Abdennour C.
Journal of Fluids Engineering, Vol. 141, Issue 10
DOI: 10.1115/1.4043858

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Title: Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

Abstract

Citation Formats

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