0
Fundamental Issues and Canonical Flows

The Shear-Driven Fluid Motion Using Oscillating Boundaries

[+] Author and Article Information
Md. Shakhawath Hossain

Department of Mechanical Engineering,  University of Saskatchewan, 57 Campus Drive, Saskatoon, SK S7N 5A9, Canada

Nihad E. Daidzic1

AAR Aerospace Consulting, L.L.C., P.O. Box 208, Saint Peter, MN 56082–0208aaraerospace@cs.com;

1

Corresponding author.

J. Fluids Eng 134(5), 051203 (May 07, 2012) (13 pages) doi:10.1115/1.4006362 History: Received January 02, 2012; Revised March 10, 2012; Published May 03, 2012; Online May 07, 2012

A classical Stokes’ second problem has been known for a long time and represents one of the few exact solutions of nonlinear Navier-Stokes equations. However, oscillatory flow in a semi-infinite domain of Newtonian fluid under harmonic boundary excitation only leads to fluid wind-milling back and forth in close wall vicinity. In this study, we are presenting the mathematical model and the numerical simulations of the Newtonian fluid and the shear-thinning non-Newtonian blood-mimicking fluid flow. Positive flow rates were obtained by periodic yet nonharmonic oscillatory motion of one or two infinite boundary flat walls. The oscillatory flows in semi-infinite or finite 2D geometry with sawtooth or periodic rectified-sine boundary conditions are presented. Rheological human blood models used were: Power-Law, Sisko, Carreau, and Herschel-Bulkley. A one-dimensional time-dependent nonlinear coupled conservative diffusion-type boundary layer equations for mass, linear momentum, and energy were solved using the finite-differences method with finite-volume discretization. It was possible to test the accuracy of the in-house developed computational programs with the few isothermal flow analytical solutions and with the celebrated classical Stokes’ first and second problems. Positive flow rates were achieved in various configurations and in absence of the adverse pressure gradients. Body forces, such as gravity, were neglected. The calculations utilizing in-phase sawtooth and rectified-sine wall excitations resulted in respectable net flow which stabilizes and becomes quasi-steady, starting from rest, after three to ten periods depending on the fluid rheology. It was assumed that rapid return stroke of the wall actuator resulted in total wall slip while forward wall motion existed with no-slip boundary condition. Shear “driving” and “driven” fluid regions were identified. The shear-thinning fluid rheology delivered many interesting results, such as pluglike flow. Constructive interference of diffusive penetration layers from multiple flat surfaces could be used as practical pumping mechanism in micro-scales.

Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

General 2D flow geometry with two oscillating boundaries apart by distance h.

Grahic Jump Location
Figure 2

Graph of the sawtooth oscillations

Grahic Jump Location
Figure 3

Graph of the unit full-wave rectified-sine oscillations

Grahic Jump Location
Figure 4

Newtonian and non-Newtonian time-invariant fluids. (a) The change of shear-stress versus shear-rate. (b) Apparent dynamic viscosity monotonically decreases with increasing shear-rate for shear-thinning fluids.

Grahic Jump Location
Figure 5

(a) Finite (control) volumes and grid point cluster for 1D diffusion problem (b) Finite difference nodal points for one-dimensional spatial diffusion problem

Grahic Jump Location
Figure 6

Analytical and computational nondimensional velocity distributions for 2D planar geometry (h = 5 mm) using Newtonian fluid (water) with in-phase sawtooth (ramp) oscillation of both walls with period of two seconds and constant acceleration of 0.01 m/s2

Grahic Jump Location
Figure 7

Transient oscillatory dimensionless velocity profiles of water with cosine harmonic excitation of f = 0.5 Hz and U = 0.01 m/s of single boundary in the semi-infinite domain

Grahic Jump Location
Figure 8

Developed steady-state velocity profiles at various times for cosine harmonic oscillation at f = 0.5 Hz and U = 0.01 m/s of single wall in the semi-infinite domain and water as working fluid

Grahic Jump Location
Figure 9

Velocity profiles during first-period in a thin 5 mm 2D-channel with sawtooth oscillation of a single wall at f = 0.05 Hz and constant acceleration, b = 0.01 m/s2

Grahic Jump Location
Figure 10

Dimensionless velocity profiles for water and several non-Newtonian blood models for sawtooth excitation of a single wall at f = 0.5 Hz and b = 0.01 m/s2

Grahic Jump Location
Figure 11

Dimensionless velocity distributions with water as a working fluid and in-phase sawtooth excitations of both boundaries at f = 0.5 Hz and b = 0.01 m/s2

Grahic Jump Location
Figure 12

Averaged dimensionless velocity distributions in a thin 2D-channel for water and several non-Newtonian fluids with in-phase sawtooth oscillation of both walls at f = 0.5 Hz and b = 0.01 m/s2

Grahic Jump Location
Figure 13

Average dimensionless velocity profile for changing Power-Law index “n.” In-phase sawtooth excitations of both boundaries were utilized.

Grahic Jump Location
Figure 14

Velocity distributions during the first period in thin 2D-channel using water with the in-phase full-wave rectified-sine oscillations of both walls at f = 0.5 Hz and maximum wall speed of U = 0.01 m/s

Grahic Jump Location
Figure 15

First-period averaged velocity profiles for water and several non-Newtonian blood models with rectified-sine oscillation of both walls

Grahic Jump Location
Figure 16

Variation of WSS for water and three non-Newtonian blood models due to harmonic sine oscillation of the single boundary (Stokes’ second problem)

Grahic Jump Location
Figure 17

Variation of the WSS for water and three non-Newtonian fluids due to nonharmonic full-wave rectified-sine excitation of both flat boundaries

Grahic Jump Location
Figure 18

Velocity distribution in a thin 5 mm planar channel using water for a second period of in-phase sawtooth excitation of both walls. The constant acceleration is b = 0.01 m/s2 and the period is two seconds.

Grahic Jump Location
Figure 19

Period-averaged velocity distributions for the first ten periods utilizing water with the in-phase sawtooth oscillation at both walls at f = 0.5 Hz and b = 0.01 m/s2

Grahic Jump Location
Figure 20

Steady-state average velocity distributions utilizing sawtooth excitations of both walls at f = 0.5 Hz and b = 0.01 m/s2

Grahic Jump Location
Figure 21

Steady-state average velocity distributions utilizing rectified-sine excitations of both walls at f = 0.5 Hz and U = 0.01 m/s

Grahic Jump Location
Figure 22

The effect of the channel height h on the velocity profile for rectified-sine excitations of both walls

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In