Two-Fluid Model Stability, Simulation and Chaos

Abstract

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The Impact of Pore‐Scale Flow Regimes on Upscaling of Immiscible Two‐Phase Flow in Porous Media

“…⟨ f ⟩  i and ⟨ w ⟩  i are the averaged dimensionless interfacial and wall shear stresses of the ith phase in the unit cell. This formulation of the shear stress terms has been inspired by the widely used closures in one-dimensional average models for pipe flow (Bertodano et al, 2017). Such closures are usually formulated in analogy with single-phase flow and only recently have been corrected to describe friction at the fluid-fluid interface and at the solid walls accurately (see .…”

Implementation and Comparison of High-Resolution Spatial Discretization Schemes for Solving Two-Fluid Seven-Equation Two-Pressure Model

“…From the book of De Bertodano et al [1], which is of great reference value for investigating the stability of two-fluid model, the oscillations are caused by the Kelvin-Helmholtz instability (KH). When the relative velocity exceeds the Kelvin-Helmholtz instability criterion, the oscillations occur.…”

“…When the relative velocity exceeds the Kelvin-Helmholtz instability criterion, the oscillations occur. In this book, De Bertodano et al [1] show how the KH instability behaves in horizontal stratified flow for a well-posed fixed-flux model with surface tension compared to an ill-posed one without surface tension. For the well-posed model, the short-wavelength ripples die out and the large wave grows with time while for the ill-posed model the short-wavelength has a larger growth rate and dominates the solution after a short time.…”

Development of temporal and spatial high‐order schemes for two‐fluid seven‐equation two‐pressure model and its applications in two‐phase flow benchmark problems

“…With assumptions of decoupled phasic pressures, approximate incompressible flow, no liquid pressure gradient, no phase change, no wall, and interfacial drag, the analytical solutions of the gas volume fraction and liquid velocity distribution can be derived, similar to the Ransom water faucet problem. 49,50 Based on the aforementioned assumptions, the phasic conservation equations are decoupled so that the volume fraction and liquid velocity distribution can be derived from only liquid mass and momentum conservation equations. Then, the volume fraction distribution and the liquid velocity distribution are derived, as shown in the following:…”