Energy-consistent formulation of the pressure-free two-fluid model
Autor: | Jurriaan F. H. Buist, Benjamin Sanderse, Svetlana Dubinkina, Cornelis W. Oosterlee, Ruud A. W. M. Henkes |
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Přispěvatelé: | Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands, Mathematics |
Jazyk: | angličtina |
Rok vydání: | 2022 |
Předmět: |
pressure-free model
two-phase pipe flow Finite volume method Applied Mathematics Mechanical Engineering Computational Mechanics finite volume method Energy-conserving discretization Computer Science Applications incompressible flow constraint Mechanics of Materials energy-conserving discretization Two-phase pipe flow SDG 7 - Affordable and Clean Energy Incompressible flow constraint Pressure-free model |
Zdroj: | Buist, J F H, Sanderse, B, Dubinkina, S, Oosterlee, C W & Henkes, R A W M 2023, ' Energy-consistent formulation of the pressure-free two-fluid model ', International Journal for Numerical Methods in Fluids, vol. 95, no. 5, pp. 869-898 . https://doi.org/10.1002/fld.5168 International Journal for Numerical Methods in Fluids International Journal for Numerical Methods in Fluids, 95(5) International Journal for Numerical Methods in Fluids, 95(5), 869-898. John Wiley and Sons Ltd |
ISSN: | 0271-2091 |
Popis: | The pressure-free two-fluid model (PFTFM) is a recent reformulation of the one-dimensional two-fluid model (TFM) for stratified incompressible flow in ducts (including pipes and channels), in which the pressure is eliminated through intricate use of the volume constraint. The disadvantage of the PFTFM was that the volumetric flow rate had to be specified as an input, even though it is an unknown quantity in case of periodic boundary conditions. In this work, we derive an expression for the volumetric flow rate that is based on the demand for energy (and momentum) conservation. This leads to PFTFM solutions that match those of the TFM, justifying the validity and necessity of the derived choice of volumetric flow rate. Furthermore, we extend an energy-conserving spatial discretization of the TFM, in the form of a finite volume scheme, to the PFTFM. We propose a discretization of the volumetric flow rate that yields discrete momentum and energy conservation. The discretization is extended with an energy-conserving discretization of the source terms related to gravity acting in the streamwise direction. Our numerical experiments confirm that the discrete energy is conserved for different problem settings, including sloshing in an inclined closed tank, and a traveling wave in a periodic domain. The PFTFM solutions and the volumetric flow rates match the TFM solutions, with reduced computation time, and with exact momentum and energy conservation. |
Databáze: | OpenAIRE |
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