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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

doi:10.1016/j.anucene.2015.07.033

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

Abstract

This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. The Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.

Authors:

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

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

Publication Date:: Wed Aug 24 00:00:00 EDT 2016

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

Sponsoring Org.:: USDOE

OSTI Identifier:: 1303303

Alternate Identifier(s):: OSTI ID: 1396942

Report Number(s):: INL/JOU-15-35253
Journal ID: ISSN 0306-4549; PII: S0306454915003977; TRN: US1700088

Grant/Contract Number:: AC07-05ID14517

Resource Type:: Accepted Manuscript

Journal Name:: Annals of Nuclear Energy (Oxford)

Additional Journal Information:: Journal Name: Annals of Nuclear Energy (Oxford); Journal Volume: 87; Journal Issue: P2; Journal ID: ISSN 0306-4549

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; 97 MATHEMATICS AND COMPUTING; drift flux model; Jacobian-free Newton–Krylov method; verification; validation

Citation Formats


                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method.  United States: N. p., 2016. 
Web.  doi:10.1016/j.anucene.2015.07.033.

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                    Zou, Ling, Zhao, Haihua, & Zhang, Hongbin. Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method.  United States.  https://doi.org/10.1016/j.anucene.2015.07.033

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                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Wed .  
"Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method".  United States.  https://doi.org/10.1016/j.anucene.2015.07.033.  https://www.osti.gov/servlets/purl/1303303.

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@article{osti_1303303,

  title        = {Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method},

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

  abstractNote = {This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. The Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.},

  doi          = {10.1016/j.anucene.2015.07.033},

  journal      = {Annals of Nuclear Energy (Oxford)},

  number       = P2,

  volume       = 87,

  place        = {United States},

  year         = {Wed Aug 24 00:00:00 EDT 2016},

  month        = {Wed Aug 24 00:00:00 EDT 2016}

}

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Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
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Works referencing / citing this record:

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow
journal, July 2018

Hajizadeh, A.; Kazeminejad, H.; Talebi, S.
Nuclear Science and Techniques, Vol. 29, Issue 8
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Title: Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

Abstract

Citation Formats

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

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Subchannel analysis in BWR fuel bundles journal, January 1985

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

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

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Erratum to: “One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase flow regimes” [International Journal of Heat and Mass Transfer 46 (2003) 4935–4948]
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Subchannel analysis in BWR fuel bundles
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Void Fractions in Subcooled Flow Boiling
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Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
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A Fully Implicit Hybrid Solution Method for a Two-Phase Thermal-Hydraulic Model
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Study on the stability behaviour of two-phase natural circulation systems using a four-equation drift flux model
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A numerical technique for analysis of transient two-phase flow in a vertical tube using the Drift Flux Model
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Numerical study of nuclear coupled two-phase flow instability in natural circulation system under low pressure and low quality
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