New analytical solutions to the two-phase water faucet problem

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

doi:10.1016/j.pnucene.2016.05.013

Title: New analytical solutions to the two-phase water faucet problem

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Abstract

Here, the one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With certain simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for the purposes of code assessment, benchmark and numerical verifications. In our previous study, the Ransom’s solutions were used for the mesh convergence study of a high-resolution spatial discretization scheme. It was found that, at the steady state, an anticipated second-order spatial accuracy could not be achieved, when compared to the existing Ransom’s analytical solutions. A further investigation showed that the existing analytical solutions do not actually satisfy the commonly used two-fluid single-pressure two-phase flow equations. In this work, we present a new set of analytical solutions of the water faucet problem at the steady state, considering the gas phase density’s effect on pressure distribution. This new set of analytical solutions are used for mesh convergence studies, from which anticipated second-order of accuracy is achieved for the 2nd order spatial discretization scheme. In addition, extendedmore »« less

Authors:

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

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

Publication Date:: Fri Jun 17 00:00:00 EDT 2016

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

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

OSTI Identifier:: 1363780

Alternate Identifier(s):: OSTI ID: 1341208

Report Number(s):: INL/JOU-16-37695
Journal ID: ISSN 0149-1970; PII: S0149197016301202

Grant/Contract Number:: AC07-05ID14517

Resource Type:: Accepted Manuscript

Journal Name:: Progress in Nuclear Energy

Additional Journal Information:: Journal Volume: 91; Journal Issue: C; Journal ID: ISSN 0149-1970

Publisher:: Elsevier

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; analytical solutions; numerical verifications; two-phase flow; water faucet problem

Citation Formats


                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. New analytical solutions to the two-phase water faucet problem.  United States: N. p., 2016. 
Web.  doi:10.1016/j.pnucene.2016.05.013.

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                    Zou, Ling, Zhao, Haihua, & Zhang, Hongbin. New analytical solutions to the two-phase water faucet problem.  United States.  https://doi.org/10.1016/j.pnucene.2016.05.013

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                    Zou, Ling, Zhao, Haihua, and Zhang, Hongbin. Fri .  
"New analytical solutions to the two-phase water faucet problem".  United States.  https://doi.org/10.1016/j.pnucene.2016.05.013.  https://www.osti.gov/servlets/purl/1363780.

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@article{osti_1363780,

  title        = {New analytical solutions to the two-phase water faucet problem},

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

  abstractNote = {Here, the one-dimensional water faucet problem is one of the classical benchmark problems originally proposed by Ransom to study the two-fluid two-phase flow model. With certain simplifications, such as massless gas phase and no wall and interfacial frictions, analytical solutions had been previously obtained for the transient liquid velocity and void fraction distribution. The water faucet problem and its analytical solutions have been widely used for the purposes of code assessment, benchmark and numerical verifications. In our previous study, the Ransom’s solutions were used for the mesh convergence study of a high-resolution spatial discretization scheme. It was found that, at the steady state, an anticipated second-order spatial accuracy could not be achieved, when compared to the existing Ransom’s analytical solutions. A further investigation showed that the existing analytical solutions do not actually satisfy the commonly used two-fluid single-pressure two-phase flow equations. In this work, we present a new set of analytical solutions of the water faucet problem at the steady state, considering the gas phase density’s effect on pressure distribution. This new set of analytical solutions are used for mesh convergence studies, from which anticipated second-order of accuracy is achieved for the 2nd order spatial discretization scheme. In addition, extended Ransom’s transient solutions for the gas phase velocity and pressure are derived, with the assumption of decoupled liquid and gas pressures. Numerical verifications on the extended Ransom’s solutions are also presented.},

  doi          = {10.1016/j.pnucene.2016.05.013},

  journal      = {Progress in Nuclear Energy},

  number       = C,

  volume       = 91,

  place        = {United States},

  year         = {Fri Jun 17 00:00:00 EDT 2016},

  month        = {Fri Jun 17 00:00:00 EDT 2016}

}

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