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TECHNICAL PAPERS

# Influence of Wall Proximity on the Lift and Drag of a Particle in an Oscillatory Flow

[+] Author and Article Information
Paul F. Fischer, Gary K. Leaf

Mathematics and Computer Science Division,  Argonne National Laboratory,Argonne, IL 60439

Juan M. Restrepo1

Department of Mathematics and Department of Physics,  University of Arizona, Tucson, AZ 85721restrepo@math.arizona.edu

Not to be confused with Stokes boundary layer solution to oscillatory bounded flows.

1

Corresponding author. Telephone: (520) 621-4367, Fax: (520) 621-8322.

J. Fluids Eng 127(3), 583-594 (Dec 04, 2004) (12 pages) doi:10.1115/1.1905647 History: Received May 14, 2004; Revised December 04, 2004

## Abstract

We report on the lift and drag forces on a stationary sphere subjected to a wall-bounded oscillatory flow. We show how these forces depend on two parameters, namely, the distance between the particle and the bounding wall, and on the frequency of the oscillatory flow. The forces were obtained from numerical solutions of the unsteady incompressible Navier–Stokes equations. For the range of parameters considered, a spectral analysis found that the forces depended on a small number of degrees of freedom. The drag force manifested little change in character as the parameters varied. On the other hand, the lift force varied significantly: We found that the lift force can have a positive as well as a negative time-averaged value, with an intermediate range of external forcing periods in which enhanced positive lift is possible. Furthermore, we determined that this force exhibits a viscous-dominated and a pressure-dominated range of parameters.

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## Figures

Figure 1

Drag histories for ϵ=0.5; (a) τ=10, (b) τ=40, (c) τ=120, and (d) τ=260

Figure 2

Pressure and viscous contributions to the drag histories for ϵ=0.5; (a) τ=10, (b) τ=40, (c) τ=120, and (d) τ=260

Figure 3

CDM as a function of gap ϵ and period τ

Figure 4

CDM, CDM,p, and CDM,ν for ϵ=0.125. Also plotted are Eqs. 8,9

Figure 5

Lift histories for ϵ=0.5; (a) τ=10, (b) τ=40, (c) τ=120, and (d) τ=260

Figure 6

Pressure and viscous contributions to the lift histories for ϵ=0.5; (a) τ=10, (b) τ=40, (c) τ=120, and (d) τ=260

Figure 7

(a) CLM, (b) CLm, (c) and (d) CLA as a function of gap ϵ and period τ; (d) shows small τ details of CLA

Figure 8

CLA (solid), average of the viscous component of the lift (diamonds), average of the pressure component of the lift (stars); as a function of τ, for (a) ϵ=0.250, (b) ϵ=0.375, (c) ϵ=0.425, (d) ϵ=0.500, and (e) ϵ=0.750. Note scales.

Figure 9

Boundary line in (ϵ,τ)-space for the pressure and the viscous dominated regimes for the average lift CLA. The calculated points have been connected by straight lines.

Figure 10

Lift for a sphere in a plane Couette flow, ϵ=0.5, for a Re*=DU*∕ν in the range of Re*=10−4–101

Figure 11

Spectrum of CL(t;τ,ϵ) for ϵ=0.500; (a) τ=10, (b) τ=40, (c) τ=120, and (d) τ=260. Amplitude scaled to CL.

Figure 12

Phase relationship between the pressure and viscous components of the average lift CLA, for ϵ=0.5; (a) τ=10, (b) τ=40, (c) τ=120, and (d) τ=260. Shown here is the superposition of 6.5 periods of data, including the initial transient data.

Figure 13

Vorticity magnitude, velocity profiles, and phase portrait at t∕τ=0.375, 0.500, 0.625, 0.750, 0.875, and 0.975 for ϵ=0.5, τ=40

Figure 14

Vorticity magnitude, velocity profiles, and phase portrait at t∕τ=0.375, 0.500, 0.625, 0.750, 0.875, and 0.975 for ϵ=1.0, τ=40

Figure 15

Vorticity magnitude, velocity profiles, and phase portrait at t∕τ=0.500, 0.600, 0.700, 0.800, 0.900, and 1.000 for ϵ=0.5, τ=120

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