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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

doi:10.1016/j.nucengdes.2016.01.033

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

Journal Article · Wed Mar 09 00:00:00 EST 2016 · Nuclear Engineering and Design

DOI:https://doi.org/10.1016/j.nucengdes.2016.01.033· OSTI ID:1303302

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

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

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3D code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.

Research Organization:: Idaho National Laboratory, Idaho Falls, ID (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC07-05ID14517

OSTI ID:: 1303302

Alternate ID(s):: OSTI ID: 1359682
OSTI ID: 22561506

Report Number(s):: INL/JOU--15-36898; PII: S0029549316000534

Journal Information:: Nuclear Engineering and Design, Journal Name: Nuclear Engineering and Design Journal Issue: C Vol. 300; ISSN 0029-5493

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (13)

A Jacobian-free Newton-Krylov method for thermalhydraulics simulations: A JFNK METHOD FOR THERMALHYDRAULICS SIMULATIONS Ashrafizadeh, A.; Devaud, C. B.; Aydemir, N. U. International Journal for Numerical Methods in Fluids, Vol. 77, Issue 10 https://doi.org/10.1002/fld.3999	journal	January 2015
Modelling of Two-Phase Flow with Second-Order Accurate Scheme Tiselj, Iztok; Petelin, Stojan Journal of Computational Physics, Vol. 136, Issue 2 https://doi.org/10.1006/jcph.1997.5778	journal	September 1997
The physical closure laws in the CATHARE code Bestion, D. Nuclear Engineering and Design, Vol. 124, Issue 3 https://doi.org/10.1016/0029-5493(90)90294-8	journal	December 1990
Notes on the implementation of a fully-implicit numerical scheme for a two-phase three-field flow model Frepoli, Cesare; Mahaffy, John H.; Ohkawa, Katsuhiro Nuclear Engineering and Design, Vol. 225, Issue 2-3 https://doi.org/10.1016/S0029-5493(03)00159-6	journal	November 2003
Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems Zou, Ling; Zhao, Haihua; Zhang, Hongbin Annals of Nuclear Energy, Vol. 83 https://doi.org/10.1016/j.anucene.2015.04.016	journal	September 2015
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 Annals of Nuclear Energy, Vol. 87 https://doi.org/10.1016/j.anucene.2015.07.033	journal	January 2016
Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method Zou, Ling; Zhao, Haihua; Zhang, Hongbin Computers & Fluids, Vol. 129 https://doi.org/10.1016/j.compfluid.2016.02.008	journal	April 2016
Jacobian-free Newton–Krylov methods: a survey of approaches and applications Knoll, D. A.; Keyes, D. E. Journal of Computational Physics, Vol. 193, Issue 2 https://doi.org/10.1016/j.jcp.2003.08.010	journal	January 2004
Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction Mousseau, V. A. Journal of Computational Physics, Vol. 200, Issue 1 https://doi.org/10.1016/j.jcp.2004.03.009	journal	October 2004
Improvement of the one-dimensional dissolved-solute convection equation using the QUICKEST–ULTIMATE algorithm Bertolotto, D.; Manera, A.; Macián-Juan, R. Nuclear Engineering and Design, Vol. 241, Issue 1 https://doi.org/10.1016/j.nucengdes.2010.10.021	journal	January 2011
Implementation and assessment of high-resolution numerical methods in TRACE Wang, Dean; Mahaffy, John H.; Staudenmeier, Joseph Nuclear Engineering and Design, Vol. 263 https://doi.org/10.1016/j.nucengdes.2013.05.015	journal	October 2013
Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model Zou, Ling; Zhao, Haihua; Zhang, Hongbin Progress in Nuclear Energy, Vol. 88 https://doi.org/10.1016/j.pnucene.2015.12.006	journal	April 2016
Accurate Solution of the Nonlinear Partial Differential Equations from Thermal Hydraulics: Thermal Hydraulics Mousseau, Vincent A. Nuclear Technology, Vol. 158, Issue 1 https://doi.org/10.13182/NT07-A3822	journal	April 2007

Cited By (1)

Development of temporal and spatial high-order schemes for two-fluid seven-equation two-pressure model and its applications in two-phase flow benchmark problems Chao, Fei; Liu, Dong; Shan, Jianqiang International Journal for Numerical Methods in Fluids, Vol. 88, Issue 4 https://doi.org/10.1002/fld.4515	journal	June 2018

Similar Records

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

Journal Article · Tue Aug 23 20:00:00 EDT 2016 · Annals of Nuclear Energy (Oxford) · OSTI ID:1303303

Newton-Krylov Method in Applications of Solving Two-phase Problems using Drift Flux Model

Conference · Fri Apr 01 00:00:00 EDT 2016 · OSTI ID:1482983

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 Article · Fri Apr 01 00:00:00 EDT 2016 · Computers and Fluids · OSTI ID:1372906

Related Subjects

42 ENGINEERING
97 MATHEMATICS AND COMPUTING
Jacobian-free Newton-Krylov method
fully implicit method
high-resolution spatial scheme
two-fluid model
validation

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

Citation Formats

References (13)

Cited By (1)

Similar Records

Related Subjects