A Characteristic Analysis of One‐Dimensional Two‐Fluid Model with Interfacial Area Transport Equation

Xia Wang,Xiaodong Sun

doi:10.1155/2010/476839

Abstract

An interfacial area transport equation (IATE), proposed to dynamically describe the interfacial structure evolution of two‐phase flows, could help improve the predictive capability of the two‐fluid model. The present study aims to investigate the well‐posedness issue of a one‐dimensional two‐fluid model with the IATE (named “two‐fluid‐IATE model” hereafter) using a characteristic analysis. The momentum flux parameters, which take into account the coupling of the volumetric fraction of phase and velocity distributions over the cross‐section of a flow passage, are employed. A necessary condition for the system to achieve hyperbolicity under an adiabatic flow condition is identified. A case study is performed for an adiabatic liquid‐liquid slug flow, which shows that the hyperbolicity of the two‐fluid‐IATE model is guaranteed if appropriate correlations of the momentum flux parameters are applied in the two‐fluid‐IATE model.

Highlights

In modeling of two-phase flows, it is realized that the one-dimensional two-fluid model is widely applied in many computer codes 1, 2
The infinite instability growth rate may exist when two-phase flows are modeled with the twofluid model, which violates the observation that the energy originating from perturbation continuously decays due to the local fluctuations energy cascade and dissipation, resulting in the naturally steady equilibrium of the flow in different flow regimes
This study examines the hyperbolicity property of the one-dimensional incompressible twofluid-IATE model

Summary

Introduction

In modeling of two-phase flows, it is realized that the one-dimensional two-fluid model is widely applied in many computer codes 1, 2. The infinite instability growth rate may exist when two-phase flows are modeled with the twofluid model, which violates the observation that the energy originating from perturbation continuously decays due to the local fluctuations energy cascade and dissipation , resulting in the naturally steady equilibrium of the flow in different flow regimes. These lead to the possibility of the partial differential equations of the two-fluid model being illposed. The characteristic roots of this two-fluid-IATE model are examined graphically under different flow conditions to reveal the effects of the momentum flux parameters on regularizing the two-fluid-IATE model

Governing Equations of the Two-Fluid-IATE Model

Characteristic Analysis

A Case Study

Conclusions