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SPECIAL SECTION ON THE FLUID MECHANICS AND RHEOLOGY OF NONLINEAR MATERIALS AT THE MACRO, MICRO AND NANO SCALE

# Swirling Flow of a Viscoelastic Fluid in a Cylindrical Casing

[+] Author and Article Information
Motoyuki Itoh

Department of Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555, Japan

Masahiro Suzuki, Takahiro Moroi

Toyota Industries Corporation, Kariya, Japan

J. Fluids Eng 128(1), 88-94 (Oct 04, 2005) (7 pages) doi:10.1115/1.2136925 History: Received July 27, 2004; Revised October 04, 2005

## Abstract

The swirling flow of a viscoelastic fluid in a cylindrical casing is investigated experimentally, using aqueous solutions of 0.05–$1.0wt.%$ polyacrylamide as the working fluid. The velocity measurements are made using laser Doppler anemometer. The aspect ratios $H∕R$ ($H$: axial length of cylindrical casing; $R$: radius of rotating disk) investigated are 2.0, 1.0, and 0.3. The Reynolds numbers $Re0$ based on the zero shear viscosity and the disk-tip velocity are between 0.36 and 50. The velocity measurements are mainly conducted for the circumferential velocity component. The experimental velocity data are compared to the velocity profiles obtained by numerical simulations using Giesekus model and power-law model. It is revealed that at any aspect ratios tested the dimensionless circumferential velocity component $Vθ′$ decreases with increasing Weissenberg number We. Both the Giesekus and power-law models could predict the retardation of circumferential velocity fairly well at small We. The extent of the inverse flow region, where the fluid rotates in the direction opposite to the rotating disk, is clarified in detail.

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## Figures

Figure 11

Velocity distributions for 1.0wt.% PAA solution (Re0=0.36,We=13.7,H∕R=1.0): (a) radial component Vr′, (b) circumferential component Vθ′, (c) axial component Vz′, and (d) axial component Vz′

Figure 8

Profiles of circumferential velocity component (Re0=50,H∕R=2.0): (a) r∕R=0.5 and (b) r∕R=0.8

Figure 7

Profiles of circumferential velocity component (Re0=5.8,H∕R=2.0): (a) r∕R=0.5 and (b) r∕R=0.8

Figure 12

Secondary flow in the meridional section (1.0wt.% PAA solution, Re0=0.36,We=13.7,H∕R=1.0)

Figure 14

Structure of unsteady flow region (0.3wt.%,Re0=5.8,We=10.8,H∕R=2.0)

Figure 10

Profiles of circumferential velocity component (Re0=50,H∕R=0.3): (a) r∕R=0.5 and (b) r∕R=0.8

Figure 9

Profiles of circumferential velocity component (Re0=10,H∕R=0.3): (a) r∕R=0.5 and (b) r∕R=0.8

Figure 15

Structure of reverse flow region (1.0wt.%,Re0=0.36,We=13.7,H∕R=2.0)

Figure 13

Comparison of velocity profiles between experiments and numerical simulations (H∕R=1.0): (a) Re0=10,We=0.048,r∕R=0.5 and (b) Re0=50,We=0.24,r∕R=0.8

Figure 6

Secondary flow patterns for a small aspect ratio H∕R=0.3: (a) typical secondary flow patterns and (b) secondary flow patterns for various E0 and Re0

Figure 5

Secondary flow patterns for a large aspect ratio H∕R=2.0: (a) typical secondary flow patterns and (b) secondary flow patterns for various E0 and Re0

Figure 4

Relaxation time λG

Figure 3

Rheological characteristics of the working fluid: (a) shear viscosity and (b) first normal stress difference

Figure 2

Disk and cylinder system

Figure 1

Experimental apparatus

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