The influence of interfacial pressure forces on the character of two-phase flow model equations

Stuhmiller, James H.

doi:10.1016/0301-9322(77)90029-5

Cited by 255 publications

(128 citation statements)

References 1 publication

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“…The first attempts to restore hyperbolicity 3.1. Interfacial pressure The first chronological attempt to restore hyperbolicity was based on the concept of mean interfacial pressure (Stuhmiller 1977). Discarding the velocity fluctuations (K d = K c = 0), assuming the equality of the two bulk pressures (p d = p c = p) and defining p as the mean pressure on the interfaces, the momentum balances appear as in (2.2) with…”

Section: Conservation Of Energymentioning

confidence: 99%

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On the quest for a hyperbolic effective-field model of disperse flows

2013

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The cornerstone of multiphase flow applications in engineering practice is a scientific construct that translates the basic laws of fluid mechanics into a set of governing equations for effective interpenetrating continua, the effective-field (or two-fluid) model. Over more than half a century of development this model has taken many forms but all of them fail in a way that was known from the very beginning: mathematical ill-posedness. The aim of this paper is to refocus awareness of this problem from a unified fundamental perspective that clarifies the manner in which such failures took place and to suggest the means for a final closure.

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Section: Conservation Of Energymentioning

confidence: 99%

“…The hyperbolicity of that set of equations was investigated in Stuhmiller (1977) for non-compressible mixtures and in Ndjinga (2007) and Chang et al (2007) for compressible ones. For non-compressible mixtures Stuhmiller (1977) found the hyperbolicity condition…”

Section: Conservation Of Energymentioning

confidence: 99%

On the quest for a hyperbolic effective-field model of disperse flows

2013

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“…This would generally lead to a lack of existence of stable mathematical solutions to the model, as well as loss of stability of our numerical methods. To avoid such a highly undesirable situation, we follow in the footsteps of much of the existing literature [6,7,27,30] and choose the regularization term introduced by Stuhmiller [37]: …”

Section: The Interface Pressure Termmentioning

confidence: 99%

On the effect of temperature and velocity relaxation in two-phase flow models

Ferrer¹,

Flåtten²,

Munkejord³

2011

ESAIM: M2AN

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Abstract.We study a two-phase pipe flow model with relaxation terms in the momentum and energy equations, driving the model towards dynamic and thermal equilibrium. These equilibrium states are characterized by the velocities and temperatures being equal in each phase. For each of these relaxation processes, we consider the limits of zero and infinite relaxation times. By expanding on previously established results, we derive a formulation of the mixture sound velocity for the thermally relaxed model. This allows us to directly prove a subcharacteristic condition; each level of equilibrium assumption imposed reduces the propagation velocity of pressure waves. Furthermore, we show that each relaxation procedure reduces the mixture sound velocity with a factor that is independent of whether the other relaxation procedure has already been performed. Numerical simulations indicate that thermal relaxation in the two-fluid model has negligible impact on mass transport dynamics. However, the velocity difference of sonic propagation in the thermally relaxed and unrelaxed two-fluid models may significantly affect practical simulations.Mathematics Subject Classification. 76T10, 65M08, 35L60.

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“…The derivations and results given in this section have been obtained previously [3,4]. These results are reproduced here for the sake of completeness.…”

Section: Review Of Eigenvalues Of Isothermal Incompressible Two-fluidmentioning

confidence: 83%

“…Moreover, for these flows, inclusion of a correction term in the two-fluid model results in a model which is hyperbolic. This term can be derived exactly for these flows [4]. For the compressible flows, one of the approaches is to use the abovementioned correction term (sometimes in conjunction with a virtual mass term) [5].…”

Section: Introductionmentioning

confidence: 99%

Effect of Compressibility on Hyperbolicity and Choke Flow Criterion of the Two-phase Two-fluid Model

Singh¹,

Mousseau²

2008

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The influence of interfacial pressure forces on the character of two-phase flow model equations

Cited by 255 publications

References 1 publication

On the quest for a hyperbolic effective-field model of disperse flows

On the quest for a hyperbolic effective-field model of disperse flows

On the effect of temperature and velocity relaxation in two-phase flow models

Effect of Compressibility on Hyperbolicity and Choke Flow Criterion of the Two-phase Two-fluid Model

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