Prediction Of Laminar Flow Over A Back Facing
Step Using New Formula Of Penalty Parameter
Author(s)
Mahmud A. Mehemed Abughalia
Abstract
This paper introduces a numerical solution for flow over a back facing step. In
this study, the continuity equation is replaced by a penalty function and a new
formula of penalty parameter is derived and implemented. The new formula of
penalty parameter is restricted only to the finite element method and the formula
requires the existence of the second derivative of the trial function so that a
rectangular element with exponential trial function is proposed and used.
A laminar flow over a back facing step is chosen as a test model to examine
the numerical solution. The location of the reattachment point is captured
accurately only if the penalty parameter is multiplied by a suitable factor and this
factor depends on the Jacobian.
The current numerical results are validated through a comparison to available
numerical and experimental results for the case of flow over a back facing step.
The tested range of Reynolds number was 200, 400 and 1000 and the ratio
between the step height to the duct height was 0.5. The reattachment point is
tabulated against Reynolds number. The comparison shows that the finite
element solution using the new penalty parameter is closer to the experimental
results than the available numerical results.
Keywords: penalty method, back facing step, finite element, laminar flow, Navier
Stokes equations, numerical solution.
1 Introduction
The Navier Stokes equations govern the physical behavior of most of the fluid
flow applications. Thus they have attracted a great deal of attention by most
engineering fields, chemical, civil, aeronautical, oil and mechanical engineering.
These equations usually are solved numerically and the challenge of the
Keywords
penalty method, back facing step, finite element, laminar flow, NavierStokes equations, numerical solution.
Related Book
Other papers in this volume
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