Rotational Effect on Viscous Fluid Flow through Rectangular Rotating Straight Duct

Nazmul Islam

doi:10.11648/j.ajam.20180605.12

Abstract

In this paper, a numerical study has been done for fully developed laminar flow of an incompressible viscous fluid through a rotating straight duct with rectangular cross-section. The duct is rotated at a constant angular velocity around the vertical axis. The flow depends on the pressure driven parameter and the rotational parameter along with aspect ratio. The dimensionless non-linear equations are solved by using Spectral method where Chebyshev polynomial is adopted as a key tool. The calculations are carried out for different rotational parameter with a fixed aspect ratio at a constant pressure gradient parameter. The effect of rotational parameter has been observed for axial and secondary flows from the obtained results, which are shown in two dimensional contours and surface plots for axial flow whereas, two dimensional streamline plot, surface plot and vector plot for secondary flow. The asymmetry structure is seen in the axial flow pattern while the double vortex configuration is seen in the secondary flow structure, for all rotational parameter. However, the double vortex pattern in the secondary flow configuration is slightly compressed against the upper and lower walls of the duct for small rotational parameter, but it is highly compressed against the upper and lower walls for high rotational speed.

Highlights

Viscous fluid is a fluid which has the property of viscosity and which offers resistance to flow
The fully developed flow of viscous fluid has been investigated in a rotating straight duct with rectangular crosssection for a constant aspect ratio 2
The fully developed laminar flow of viscous incompressible fluid has been investigated through a rotating straight duct for the different values of rotational parameter with a fixed aspect ratio and pressure driven parameter

Summary

Introduction

Viscous fluid is a fluid which has the property of viscosity and which offers resistance to flow. Due to the property viscosity, one layer of fluid resists the adjacent layer of fluid; as a result, we can see the parabolic velocity profile for the flow in a straight tube, involving the maximum fluid velocity along the centerline or tube axis. Flow of a Newtonian fluid through an axi-symmetric straight pipe was first studied independently by Hagen and Poiseuille in the early 1800's. Zhang et al [20] studied numerically the force dependent and time dependent transition of secondary flow in a rotating straight channel numerically by lattice Boltzmann method. The effects of rotation on the steady viscous fluid flow through a rotating straight duct with rectangular crosssection at a constant aspect ratio 2 is studied here numerically. The flow is governed by the Navier-Stokes equation along with continuity equation that can be written in the following vector form:

Governing Equations

Numerical Calculation Techniques

Results and Discussions

Conclusion