On the approximate Riemann solver for the two-phase two-fluid six equation model and application to real system

Guojun Hu, Tomasz Kozlowski

Research output: Contribution to journalArticle

Abstract

A new method is proposed to solve the two-phase two-fluid six-equation model. A Roe-type numerical flux is formulated based on a very structured Jacobian matrix. The Jacobian matrix with arbitrary equation of state is formulated and simplified with the help of a few auxiliary variables, e.g. isentropic speed of sound. Because the Jacobian matrix is very structured, the eigenvalue and eigenvector can be obtained analytically. An explicit Roe-type numerical solver is constructed based on the analytical eigenvalue and eigenvector. A critical feature of the method is that the formulation of the solver does not depend on the form of the equation of state. The proposed method is applicable to realistic two-phase problems. It is applied to the BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Considering simplified physical models, the solutions are in very good agreement with those from both existing codes and experiment data. The numerical solver using analytical eigenvalue and eigenvector is shown to be stable and robust.

Original languageEnglish (US)
Pages (from-to)415-422
Number of pages8
JournalNuclear Engineering and Design
Volume341
DOIs
StatePublished - Jan 2019

Fingerprint

Jacobian matrices
eigenvalue
Eigenvalues and eigenfunctions
eigenvectors
eigenvalues
Equations of state
equation of state
matrix
Fluids
fluid
fluids
equations of state
Acoustic wave velocity
bundles
mesh
Fluxes
formulations
acoustics
method
experiment

Keywords

  • BFBT
  • Reactor safety
  • Riemann solver
  • Two-phase flow

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Nuclear Energy and Engineering
  • Materials Science(all)
  • Safety, Risk, Reliability and Quality
  • Waste Management and Disposal
  • Mechanical Engineering

Cite this

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abstract = "A new method is proposed to solve the two-phase two-fluid six-equation model. A Roe-type numerical flux is formulated based on a very structured Jacobian matrix. The Jacobian matrix with arbitrary equation of state is formulated and simplified with the help of a few auxiliary variables, e.g. isentropic speed of sound. Because the Jacobian matrix is very structured, the eigenvalue and eigenvector can be obtained analytically. An explicit Roe-type numerical solver is constructed based on the analytical eigenvalue and eigenvector. A critical feature of the method is that the formulation of the solver does not depend on the form of the equation of state. The proposed method is applicable to realistic two-phase problems. It is applied to the BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Considering simplified physical models, the solutions are in very good agreement with those from both existing codes and experiment data. The numerical solver using analytical eigenvalue and eigenvector is shown to be stable and robust.",
keywords = "BFBT, Reactor safety, Riemann solver, Two-phase flow",
author = "Guojun Hu and Tomasz Kozlowski",
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AU - Hu, Guojun

AU - Kozlowski, Tomasz

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N2 - A new method is proposed to solve the two-phase two-fluid six-equation model. A Roe-type numerical flux is formulated based on a very structured Jacobian matrix. The Jacobian matrix with arbitrary equation of state is formulated and simplified with the help of a few auxiliary variables, e.g. isentropic speed of sound. Because the Jacobian matrix is very structured, the eigenvalue and eigenvector can be obtained analytically. An explicit Roe-type numerical solver is constructed based on the analytical eigenvalue and eigenvector. A critical feature of the method is that the formulation of the solver does not depend on the form of the equation of state. The proposed method is applicable to realistic two-phase problems. It is applied to the BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Considering simplified physical models, the solutions are in very good agreement with those from both existing codes and experiment data. The numerical solver using analytical eigenvalue and eigenvector is shown to be stable and robust.

AB - A new method is proposed to solve the two-phase two-fluid six-equation model. A Roe-type numerical flux is formulated based on a very structured Jacobian matrix. The Jacobian matrix with arbitrary equation of state is formulated and simplified with the help of a few auxiliary variables, e.g. isentropic speed of sound. Because the Jacobian matrix is very structured, the eigenvalue and eigenvector can be obtained analytically. An explicit Roe-type numerical solver is constructed based on the analytical eigenvalue and eigenvector. A critical feature of the method is that the formulation of the solver does not depend on the form of the equation of state. The proposed method is applicable to realistic two-phase problems. It is applied to the BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Considering simplified physical models, the solutions are in very good agreement with those from both existing codes and experiment data. The numerical solver using analytical eigenvalue and eigenvector is shown to be stable and robust.

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