Evaluation of conventional fluid mechanic theory in small channels with singularity
Authors:Sid Ali Si Salah, Abdelwahid Azzi, El Ghalia Filali
Volume 10, Issue 4, Paper No. 100403
Abstract
This study employs numerical simulations using the combined control volume finite element method (CVFEM) to analyze 2D steady, incompressible laminar flow over a microscale backward facing step within a horizontal duct. The investigation focuses on the impact of Reynolds number (Red) and expansion ratio (ER) on flow behavior, aiming to assess the applicability of conventional hydrodynamics at the microscale. The findings reveal that, for an expansion ratio of 2, the flow structure transforms progressively with varying Reynolds numbers in both laminar and transitional flow regimes. Notably, three recirculation zones develop downstream of the step, two along the lower wall and one along the upper wall. The primary recirculation zone’s size expands as Reynolds number increases, contracting when a third recirculation zone emerges on the lower wall (Red ≥ 950). The study successfully matches its numerical predictions with experimental observations from larger-scale backward-facing steps for Reynolds numbers up to 500, maintaining two-dimensional flow characteristics. Furthermore, the computed velocity profiles align closely with experimental outcomes, except for Red = 1000, where the experimental flow shifts to three-dimensionality. The study also examines loss coefficients (Ke), revealing substantially higher values than conventional macro systems for Reynolds numbers above 200. However, for lower Reynolds numbers, the loss coefficient varies accordingly. For expansion ratios of 1.5, 2.0, and 2.5, fluid flow properties such as pressure, Poiseuille number, and friction factors exhibit good agreement with macroscale theory for fully developed laminar flow (Red ≤ 500).
Keywords: microchannel; backward-facing step; Control Volume Finite; Element Method (CVFEM); expansion loss coefficient; friction factor.
100403_ Salah