Numerical Simulation of Asymmetric Merging Flow in a Rectangular Channel

TL;DR

This paper numerically investigates the asymmetric flow of viscous fluid in a rectangular channel with a movable splitter plate, using advanced finite-difference methods to analyze flow behavior and compare with symmetric cases.

Contribution

It introduces a numerical approach to study asymmetric splitter plate positions affecting flow in a rectangular channel, extending previous symmetric analyses.

Findings

Flow asymmetry depends on splitter position parameter {}.

Numerical results agree well with symmetric case benchmarks.

The method achieves sixth-order accuracy in solutions.

Abstract

The steady, asymmetric and two-dimensional flow of viscous, incompressible, and Newtonian fluid through a rectangular channel with splitter plate parallel to walls is investigated numerically. In the past, the position of the splitter plate was taken as a centerline of channel but here we consider its different positions which cause the asymmetric behaviour of the flow field. The geometric parameter that controls the position of splitter is defined as splitter position parameter {\alpha}. The plane Poiseuille flow is considered far from upstream and downstream of the splitter. The fourth order method Mancera [11], followed by special finite-method Dennis [5] is used to solve in our purpose. This numerical scheme transforms the governing equations to system of finite-difference equations which are solved by point S.O.R. iterative method. Moreover, the results obtained are further refined and upgraded by Richardson Extrapolation method Jain [18]. This scheme yields the sixth order accurate solution. The results are compared with those of Badr et al [1] for symmetric case (when {\alpha}=0) for velocity, vorticity and skin friction distributions. The comparison is very favourable.