LIII.<i>Viscous flow through pipes with cores</i>

We study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle's dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a "leaky" piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle's motion as functions of the particle's position and dimensions. When the particle is short, a superpositionbased algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory. We study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle's dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a ''leaky'' piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle's motion as functions of the particle's position and dimensions. When the particle is short, a superposition-based algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory.

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“…Piercy et al 9 derived an analytical solution for the flow field in an eccentric annulus. Their solution is reproduced in White.…”

Section: Compared Their Experimental Datamentioning

confidence: 99%

On the translation of a cylinder in a long tube

Liu

Bau

2004

Physics of Fluids

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show abstract

“…Table 4.6. In addition to the validation with experimental results, simulation results are compared with analytical (Piercy et al, 1933) and numerical (Fang et al, 1999) results for eccentric annuli reported in the literature. The results are presented in Section 5.…”

Section: Cfd Verificationmentioning

confidence: 99%

“…Table 2.1 presents the hydraulic parameter as a function of dimensionless eccentricity, power law index and diameter ratio obtained by Fang et al (1999). Results in parenthesis are from Piercy et al (1933) …”

Section: Figure 22 Eccentric Annulus In Bipolar Coordinatesmentioning

confidence: 99%

“…For Newtonian fluids, Piercy et al (1933) analytically determined the relationship between flowrate and pressure loss in eccentric annuli (Eqn. 2.4).…”

Section: Eccentric Annular Flowmentioning

confidence: 99%

“…3.29) developed for Newtonian fluids (Piercy et al 1933). The fRe values reported by Fang et al (1999) for eccentric annulus are for diameter ratios of 0.2, 0.5 and 0.8, eccentricities from 0 to 0.8, and power-law fluids from = 0.2 to 1 (Fig.…”

Section: Comparison Of Cfd Model With Analytical and Numerical Solutionsmentioning

confidence: 99%

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