Steady-State Flow of Two Viscous Immiscible Incompressible Fluids in a Plane Channel

Abstract

Numerical investigation is performed of the problem on stratified flow of two viscous incompressible fluids in a horizontal (and slightly inclined to the horizontal) plane-parallel channel. An algorithm is developed for the determination of the interface between fluids. The control volume approach and the SIMPLER algorithm are used to obtain the results. The following characteristic quantities are determined and analyzed in all versions of calculations for the water-oil system: flow field, pressure, fluid interface, friction on the channel walls, velocity profiles in the channel cross sections.

A new interface‐capturing discretization scheme for numerical solution of the volume fraction equation in two‐phase flows

“…The validation cases were likewise chosen to highlight the ability of the new scheme to accurately resolve the interface, and include oil-water flow in a 2-D channel [21], and free-surface air-water flow in a 2-D channel with a contoured bottom [22]. Comparison with available reference data shows that the new scheme performs at least as well as existing methods in predicting the overall location of the interface, while demonstrating the ability to minimize diffusion of the interface without evidencing any non-physical wrinkling.…”

“…faces for which volumetric flow rate is out of the cell) to obtain the terms in the numerator and denominator of Equation (21). The limited value of the weight factor in each cell is then computed by determining the maximum value of W for which the following boundedness criteria are satisfied.…”

“…This case was recently investigated numerically by Zubkov et al [21] using an interface reconstruction VOF algorithm in combination with a very fine (801×101 cells) structured mesh. Two sets of simulations were performed, with the channel oriented at +2 • and −2 • , with respect to horizontal.…”

“…The computational domain and meshes used in the present work are shown in Figure 19, with the channel height (H ) as indicated. The overall computational domain extended from x = 0 to x = 20H, as in [21]. For the volume fraction equation, the primary phase was water ( = 0) and the secondary phase was oil ( = 1).…”

“…The key point is that the new discretization scheme yields results for volume fraction similar to those shown in the previous section when coupled to the continuity and momentum equations. The computed volume fraction distribution is compared with the reference results [21] in Figure 21, which contains plots of volume fraction versus normalized y-coordinate at a measurement location corresponding to x/H = 0.5. Four separate plots are presented corresponding to the four different meshes used.…”