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

AbstractThe 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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Mathematical study on two-fluid model for flow of K–L fluid in a stenosed artery with porous wall

SN Applied Sciences ◽

10.1007/s42452-021-04399-6 ◽

2021 ◽

Vol 3 (4) ◽

Author(s):

R. Ponalagusamy ◽

Ramakrishna Manchi

Keyword(s):

Theoretical Study ◽

Fluid Model ◽

Porous Wall ◽

Governing Equations ◽

Rate Of Increase ◽

Special Cases ◽

Stenosed Artery ◽

Flow Through ◽

Two Fluid Model ◽

Two Fluid

AbstractThe present communication presents a theoretical study of blood flow through a stenotic artery with a porous wall comprising Brinkman and Darcy layers. The governing equations describing the flow subjected to the boundary conditions have been solved analytically under the low Reynolds number and mild stenosis assumptions. Some special cases of the problem are also presented mathematically. The significant effects of the rheology of blood and porous wall of the artery on physiological flow quantities have been investigated. The results reveal that the wall shear stress at the stenotic throat increases dramatically for the thinner porous wall (i.e. smaller values of the Brinkman and Darcy regions) and the rate of increase is found to be 18.46% while it decreases for the thicker porous wall (i.e. higher values of the Brinkman and Darcy regions) and the rate of decrease is found to be 10.21%. Further, the streamline pattern in the stenotic region has been plotted and discussed.

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Cavitating Flow Simulation in a Closed Pump Sump by Two-Fluid Model and Its PIV Verification

Volume 2: Symposia, Parts A, B, and C ◽

10.1115/fedsm2003-45012 ◽

2003 ◽

Author(s):

Yu Xu ◽

Yulin Wu ◽

Shuhong Liu ◽

Yong Li

Keyword(s):

Fluid Model ◽

Flow Simulation ◽

Cavitating Flow ◽

Governing Equations ◽

Two Phase ◽

Averaged Equations ◽

Flow Through ◽

Pump Sump ◽

Two Fluid Model ◽

Two Fluid

In this paper, the two-fluid model was adopted to analyze the cavitating flow. Based on Boltzmann equation, governing equations for two-phase cavitating flow were obtained by using the microscopic kinetic theory, in which the equation terms for mass and momentum transportations can be obtained directly. Then the RNG k–ε–kg turbulence model, that is RNG k–ε model for the liquid phase and kg model for the cavity phase, was used to close the Reynolds time-averaged equations. According to the governing equations above, the simulation of the two-phase cavitating flow through a closed pump sump has been carried out. The calculated results have been compared with a PIV experiment. Good agreement exhibited.

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Simplification of Ensemble Averaged Two-Phase Flow with Heat and Mass Transfer Equations for Boiling in a Channel

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.273-276.616 ◽

2008 ◽

Vol 273-276 ◽

pp. 616-621

Author(s):

Hikmet Ş. Aybar ◽

Mohsen Sharifpur

Keyword(s):

Two Phase Flow ◽

Fluid Model ◽

Three Dimensional ◽

Phase Flow ◽

Governing Equations ◽

Ensemble Averaging ◽

Two Phase ◽

Transfer Equations ◽

Two Fluid Model ◽

Two Fluid

Generation of vapor and predication of its behavior is an important problem in many industries. In this study, the three dimensional governing equations for turbulence two-phase flow are derived using ensemble averaging two fluid model. The governing equations are simplified by a heuristic approach based on boiling data, and the equations are used to obtain the parameters for each phase along the channel. A computer program is written for the simplified one-dimensional equations, and the results are compared with experimental data.

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A Characteristics-Based Approach to the Numerical Solution of the Two-Fluid Model

Volume 1: Fora, Parts A, B, C, and D ◽

10.1115/fedsm2003-45551 ◽

2003 ◽

Cited By ~ 2

Author(s):

Robert Nourgaliev ◽

Nam Dinh ◽

Theo Theofanous

Keyword(s):

Numerical Solutions ◽

Fluid Model ◽

Main Idea ◽

Effective Field ◽

Field Equations ◽

Two Phase ◽

Widespread Application ◽

Formidable Challenge ◽

Two Fluid Model ◽

Two Fluid

This paper is concerned with numerical solutions of the two-fluid models of two-phase flow. The two-fluid modeling approach is based on the effective-field description of inter-penetrating continua and uses constitutive laws to account for the inter-field interactions. The effective-field balance equations are derived by a homogenization procedure and known to be non-hyperbolic. Despite their importance and widespread application, predictions by such models have been hampered by numerical pitfalls manifested in the formidable challenge to obtain convergent numerical solutions under computational grid refinement. At the root of the problem is the absence of hyperbolicity in the field equations and the resulting ill-posedness. The aim of the present work is to develop a high-order-accurate numerical scheme that is not subject to such limitations. The main idea is to separate conservative and non-conservative parts, by implementing the latter as part of the source term. The conservative part, being effectively hyperbolic, is treated by a characteristics-based method. The scheme performance is examined on a compressible-incompressible two-fluid model. Convergence of numerical solutions to the analytical one is demonstrated on a benchmark (water faucet) problem.

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Applying Multiple Grids to a Multi-Field Model – The Resolution Requirements of Individual Fields in the Two-Fluid Model for 1D Pipe Flow

Journal of Dispersion Science and Technology ◽

10.1080/01932691.2014.987783 ◽

2015 ◽

Vol 36 (10) ◽

pp. 1378-1387 ◽

Cited By ~ 3

Author(s):

A. H. Akselsen ◽

O. J. Nydal

Keyword(s):

Pipe Flow ◽

Field Model ◽

Fluid Model ◽

Two Fluid Model ◽

Multiple Grids ◽

Two Fluid ◽

Resolution Requirements

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Two-Fluid Model Simulation of Thermophoretic Deposition for Fine Particles in a Turbulent Boundary Layer

ASME/JSME 2007 Thermal Engineering Heat Transfer Summer Conference, Volume 2 ◽

10.1115/ht2007-32174 ◽

2007 ◽

Author(s):

Sh. Shahriari ◽

H. Basirat Tabrizi

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Gas Phase ◽

Fine Particles ◽

Model Simulation ◽

Fluid Model ◽

Governing Equations ◽

Diffusion Term ◽

Two Fluid Model ◽

Two Fluid

In this present paper, thermophoretic depositions of fine particles are used in a heated turbulent boundary layer over very small plate via two-fluid model, or Eulerian-Eulerian approach. The Prandtl’s mixing length model of turbulence is used for the closure problem. The governing equations of gas phase are coupled with the governing equations of particle phase in two-way model, while uses the particle diffusion term as another coupling term. The equations are solved numerically by using finite difference method. One can obtain the convergence by numerical calculations much easier than with no diffusion term. A vast amount of information can be extracted for this kind of modeling. The effect of important parameters such as diffusion factor, gravity and thermophoretic force are considered. The cooler temperature of plate results higher particles deposition or concentration on the flat plate. Also, the larger particle size diameters delay the maximum particles deposition further distance away from the plate front edge. The results give the correct physical prediction overall.

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