Characteristics and stability analyses of transient one-dimensional two- phase flow equations and their finite difference approximations

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Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded ... continued below

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Pages: 62

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Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W. & Hughes, E.D. January 1, 1975.

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  • Aerojet Nuclear Company
    Publisher Info: Aerojet Nuclear Co., Idaho Falls, Idaho (USA)
    Place of Publication: Idaho Falls, Idaho

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Description

Equation systems describing one-dimensional, transient, two-phase flow with separate continuity, momentum, and energy equations for each phase are classified by use of the method of characteristics. Little attempt is made to justify the physics of these equations. Many of the equation systems possess complex-valued characteristics and hence, according to well-known mathematical theorems, are not well-posed as initial-value problems (IVPs). Real-valued characteristics are necessary but not sufficient to insure well-posedness. In the absence of lower order source or sink terms (potential type flows), which can affect the well-posedness of IVPs, the complex characteristics associated with these two-phase flow equations imply unbounded exponential growth for disturbances of all wavelengths. Analytical and numerical examples show that the ill-posedness of IVPs for the two-phase flow partial differential equations which possess complex characteristics produce unstable numerical schemes. These unstable numerical schemes can produce apparently stable and even accurate results if the growth rate resulting from the complex characteristics remains small throughout the time span of the numerical experiment or if sufficient numerical damping is present for the increment size used. Other examples show that clearly nonphysical numerical instabilities resulting from the complex characteristics can be produced. These latter types of numerical instabilities are shown to be removed by the addition of physically motivated differential terms which eliminate the complex characteristics. (auth)

Physical Description

Pages: 62

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Dep. NTIS

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  • Annual meeting of ASME, Houston, Texas, USA, 30 Nov 1975

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  • Report No.: CONF-751106--13
  • Grant Number: None
  • Office of Scientific & Technical Information Report Number: 4137974
  • Archival Resource Key: ark:/67531/metadc869875

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  • January 1, 1975

Added to The UNT Digital Library

  • Sept. 16, 2016, 12:32 a.m.

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  • Oct. 26, 2017, 3:21 p.m.

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Lyczkowski, R.W.; Gidaspow, D.; Solbrig, C.W. & Hughes, E.D. Characteristics and stability analyses of transient one-dimensional two- phase flow equations and their finite difference approximations, article, January 1, 1975; Idaho Falls, Idaho. (digital.library.unt.edu/ark:/67531/metadc869875/: accessed June 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.