LAMINAR FLOW THROUGH A DOUBLE ELBOW GEOMETRY WITH
LATTICE BOLTZMANN NUMERICAL METHOD
N. M. Akmal, C. S. N. Azwadi and M. S. Zuhairi
Faculty of Mechanical Engineering,
Universiti Teknologi Malaysia,
81200 Skudai, Johor
akmaln@uthm.edu.my
azwadi@fkm.utm.my
Abstract
This paper presents a lattice Boltzmann method for the
simulation of laminar flow through double elbow
geometry. The lattice Boltzmann method was built up
on the D2Q9 model and the single relaxation time
called the lattice-BGK method. The dependence of
reattachment length on the Reynolds number is
determined. Results show that the flow was found to be
strongly dependent on Reynolds number and two-
dimensional behavior for Reynolds numbers below
approximately 400. Comparable results were obtained
between the present approach and those from a
Navier-Stokes solver.
Keywords: Double elbow geometry, laminar fluid flow,
lattice Boltzmann method
1. Introduction
The lattice Boltzmann model (LBM) has
increasingly been accepted as a viable alternative
approach to the well-known finite difference, finite
element, and finite volume techniques for solving the
Navier-Stokes equations [1, 2, 3]. Unlike any other
well-known computational methods, LB scheme treats
the fluid behavior at the microscopic level and brings
together its information to predict the macroscopic
behavior of fluid flow. This provides the opportunity to
go deeper into the particles community and understand
how the interaction between them would affect the
macroscopic parameters of fluid flow. Another
important improvement to enhance the computational
efficiency is the implementation of the Bhatnagar
Gross Krook collision operator (BGK) approximation
(single relaxation time approximation) for the collision
function [4]. Even under the simplifications provided
using BGK, LBM has demonstrated its ability to
simulate flows in porous media [1], immiscible fluids
[5] and magneto-hydrodynamics [6].
Historically LBM was derived from the lattice gas
automata (LGA) method [7]. Consequently, the LBM
inherits some features from its precursor, the LGA
method. The dynamics of distribution function
evolving on a lattice space consists of two main steps;
collision, particle at the same site collide according to a
set of hard sphere particle collisions rules; and
streaming, particle move to the nearest node in the
direction of its velocities. However, instead of using
Boolean representation of particle in LGA, LBM uses
real numbers represent the local ensemble-averaged
particle distribution function, and only kinetic
equations for the distribution function are solved. The
number of discrete velocities determines the lattice
structure of LBM models. In other words, the
discretization of physical space is coupled with the
discretization of momentum space. As a result,
computational in LBM is only restricted with uniform
lattice structure and second order accuracy in space
and time [8].
In this study, we used LBM to investigate the
velocity profile and flow characteristics of a fluid
flowing through double elbow geometry. This
geometry is commonly found in piping systems,
involving high accelerations and decelerations when
the fluid is flowing at high speeds. The reattachment
length after elbows is studied to determine the location
of the fully developed profile after flow separation.
Pressure gauges, flow meters, anemometers and other
auxiliary devices are usually installed outside of the
separated region to avoid the flow instabilities that
could commonly occur. Pressure loss, low flow rate,
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Proceedings of the International Graduate on Engineering and Science (IGCES'08)
23 - 24 December © 2008 IGCES
Mechanical Engineering