Abstract
The flow in tubes with periodically varying cross-section has many interests due to its various practical applications such as it can be used as particle separation devices. In this paper, we have examined the oscillatory flow of a viscous incompressible fluid in a sinusoidal periodic tube at low Reynolds number. The numerical study is undertaken to examine fluid movement at different cross-sections for different time. The boundary element method (BEM) has been formulated for the infinite sinusoidal periodic tube to solve the governing equations for obtaining components of surface force on the tube wall. We have calculated the axial and radial velocities at different cross-sections for different time and compared them. We find that the behaviors of the velocity curves for different cross-sections remain the same for the same phase of time over the oscillation. On the contrary, the behavior of the velocity curves become different for different phase of time. For the tube geometry, the axial velocity at the converging and diverging regions are the same while the radial velocity at these regions are the same in magnitudes but in opposite direction. In addition, the radial velocity is maximum in the half way between the tube axis and the tube wall, and it is minimum on the tube axis and on the tube wall. The obtained velocity indicates that the net fluid movement after each complete oscillation is zero, which is an assumption to separate particles in such periodic tube.
Highlights
The study of flow in tubes with periodic variations has attracted much attention of researchers due to its various physiological and engineering applications
Nishimura et al [11] conducted an experiment about the flow characteristics in wavy-walled channels for steady flow and indicated that the diverse flow structures in this geometry depended on both oscillatory Reynolds number and Strouhal number
We have investigated the oscillatory creeping flow of viscous incompressible fluid through an axi-symmetric sinusoidal periodic tube to find the characteristics of the velocity and movement of fluid particle at different cross-sections and at different time
Summary
The study of flow in tubes with periodic variations has attracted much attention of researchers due to its various physiological and engineering applications. Nishimura et al [11] conducted an experiment about the flow characteristics in wavy-walled channels for steady flow and indicated that the diverse flow structures in this geometry depended on both oscillatory Reynolds number and Strouhal number. Lee et al [14] discussed the mass transfer enhancement in an axisymmetric wavy channel for pulsatile laminar flow Their numerical results indicated that the optimal Strouhal number increases as the Reynolds number and the channel wavelength decreasing. We have investigated the oscillatory creeping flow of viscous incompressible fluid through an axi-symmetric sinusoidal periodic tube to find the characteristics of the velocity and movement of fluid particle at different cross-sections and at different time. We have used the boundary element technique to solve the governing equations and to find the effect of oscillating flow on velocity in axi-symmetric sinusoidal tube, and to reexamine the assumption that there is no net fluid movement after a complete oscillatory flow which is a postulate that use in particle separation technique
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