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Viscous formulation of the two-fluid model for dispersed two-phase flow in 2-D
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
2005 (English)Report (Other academic)
Place, publisher, year, edition, pages
2005.
Series
Trita-NA, ISSN 0348-2952 ; 0503
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-4940OAI: oai:DiVA.org:kth-4940DiVA: diva2:7143
Note
QC 20101018Available from: 2005-02-16 Created: 2005-02-16 Last updated: 2010-10-18Bibliographically approved
In thesis
1. A numerical study of two-fluid models for dispersed two-phase flow
Open this publication in new window or tab >>A numerical study of two-fluid models for dispersed two-phase flow
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

In this thesis the two-fluid (Eulerian/Eulerian) formulation for dispersed two-phase flow is considered. Closure laws are needed for this type of models. We investigate both empirically based relations, which we refer to as a nongranular model, and relations obtained from kinetic theory of dense gases, which we refer to as a granular model. For the granular model, a granular temperature is introduced, similar to thermodynamic temperature. It is often assumed that the granular energy is in a steady state, such that an algebraic granular model is obtained.

The inviscid non-granular model in one space dimension is known to be conditionally well-posed. On the other hand, the viscous formulation is locally in time well-posed for smooth initial data, but with a medium to high wave number instability. Linearizing the algebraic granular model around constant data gives similar results. In this study we consider a couple of issues.

First, we study the long time behavior of the viscous model in one space dimension, where we rely on numerical experiments, both for the non-granular and the algebraic granular model. We try to regularize the problem by adding second order artificial dissipation to the problem. The simulations suggest that it is not possible to obtain point-wise convergence using this regularization. Introducing a new measure, a concept of 1-D bubbles, gives hope for other convergence than point-wise.

Secondly, we analyse the non-granular formulation in two space dimensions. Similar results concerning well-posedness and instability is obtained as for the non-granular formulation in one space dimension. Investigation of the time scales of the formulation in two space dimension suggests a sever restriction on the time step, such that explicit schemes are impractical.

Finally, our simulation in one space dimension show that peaks or spikes form in finite time and that the solution is highly oscillatory. We introduce a model problem to study the formation and smoothness of these peaks.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. ix, 30 p.
Series
Trita-NA, ISSN 0348-2952 ; 0502
Keyword
Numerical analysis, two-phase flow, two-fluid mode, well-posedness, numerical experiments, Numerisk analys
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-132 (URN)91-7283-964-3 (ISBN)
Public defence
2005-02-22, Kollegiesalen, Valhallavägen 79, Stockholm, 14:00
Opponent
Supervisors
Note
QC 20101018Available from: 2005-02-16 Created: 2005-02-16 Last updated: 2010-10-18Bibliographically approved

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