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Title: Hyperbolic two-pressure models for two-phase flow

Abstract

For some time it has been known that many of the two-phase flow models lead to ill-posed Cauchy problems because they have complex characteristic values. A necessary condition (at least in the linear case) for the Cauchy problem to be well-posed is that it be stable in the sense of von Neumann. For systems of partial differential equations of first order, stability in the sense of von Neumann is essentially equivalent to the condition that the model be hyperbolic (all real characteristic values and complete set of characteristic vectors). Herein models are developed which have real characteristic values for all physically acceptable stgates (state space) and except for a set of measure zero have a complete set of characteristic vectors in state space. Therefore, these models are hyperbolic a.e. (almost everywhere) in state space. Also, they are stable in the sense of von Neumann a.e. in state space even without inclusion of viscosity terms. The models discussed herein are developed for the case of two-phase separated planar flow and include transverse momentum considerations. These models are referred to as ''two-pressure'' models because each phase is assumed to exist at an average pressure different from the average pressure in the othermore » phase; the pressure fields are related through momentum considerations. Numerical results on a steady-state problem show good agreement with existing steady-state results. Numerical results on a transient problem agree with a single-pressure model until the onset of numerical instability in the single-pressure model. Compared to the single-pressure (hydrostatic) model, the two-pressure model approximates additional physical features and is shown to be viable approach for the case of separated flow.« less

Authors:
;
Publication Date:
Research Org.:
EG and G Idaho, Inc., Idaho Falls, Idaho 83415
OSTI Identifier:
5133421
DOE Contract Number:  
AC07-76ID01570
Resource Type:
Journal Article
Journal Name:
J. Comput. Phys.; (United States)
Additional Journal Information:
Journal Volume: 53:1
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; TWO-PHASE FLOW; MATHEMATICAL MODELS; BOUNDARY CONDITIONS; ONE-DIMENSIONAL CALCULATIONS; STEADY-STATE CONDITIONS; TRANSVERSE MOMENTUM; FLUID FLOW; LINEAR MOMENTUM; 420400* - Engineering- Heat Transfer & Fluid Flow; 640410 - Fluid Physics- General Fluid Dynamics

Citation Formats

Ransom, V H, and Hicks, D L. Hyperbolic two-pressure models for two-phase flow. United States: N. p., 1984. Web. doi:10.1016/0021-9991(84)90056-1.
Ransom, V H, & Hicks, D L. Hyperbolic two-pressure models for two-phase flow. United States. https://doi.org/10.1016/0021-9991(84)90056-1
Ransom, V H, and Hicks, D L. 1984. "Hyperbolic two-pressure models for two-phase flow". United States. https://doi.org/10.1016/0021-9991(84)90056-1.
@article{osti_5133421,
title = {Hyperbolic two-pressure models for two-phase flow},
author = {Ransom, V H and Hicks, D L},
abstractNote = {For some time it has been known that many of the two-phase flow models lead to ill-posed Cauchy problems because they have complex characteristic values. A necessary condition (at least in the linear case) for the Cauchy problem to be well-posed is that it be stable in the sense of von Neumann. For systems of partial differential equations of first order, stability in the sense of von Neumann is essentially equivalent to the condition that the model be hyperbolic (all real characteristic values and complete set of characteristic vectors). Herein models are developed which have real characteristic values for all physically acceptable stgates (state space) and except for a set of measure zero have a complete set of characteristic vectors in state space. Therefore, these models are hyperbolic a.e. (almost everywhere) in state space. Also, they are stable in the sense of von Neumann a.e. in state space even without inclusion of viscosity terms. The models discussed herein are developed for the case of two-phase separated planar flow and include transverse momentum considerations. These models are referred to as ''two-pressure'' models because each phase is assumed to exist at an average pressure different from the average pressure in the other phase; the pressure fields are related through momentum considerations. Numerical results on a steady-state problem show good agreement with existing steady-state results. Numerical results on a transient problem agree with a single-pressure model until the onset of numerical instability in the single-pressure model. Compared to the single-pressure (hydrostatic) model, the two-pressure model approximates additional physical features and is shown to be viable approach for the case of separated flow.},
doi = {10.1016/0021-9991(84)90056-1},
url = {https://www.osti.gov/biblio/5133421}, journal = {J. Comput. Phys.; (United States)},
number = ,
volume = 53:1,
place = {United States},
year = {Sun Jan 01 00:00:00 EST 1984},
month = {Sun Jan 01 00:00:00 EST 1984}
}