III. Experiments on fluid viscosity

Mallock, A.

doi:10.1098/rsta.1896.0003

Cited by 96 publications

(29 citation statements)

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“…For a rotating outer cylinder with an inner cylinder at rest, Taylor concluded that the flow was always stable. These results were in contrast with the earlier experiments by Couette (1890) and Mallock (1896).…”

Section: Bagnold's Torque Measurements For Pure Watercontrasting

confidence: 56%

“…Prior to 1954, several studies examined single-phase flow between a rotating outer cylinder and stationary inner cylinder (Couette 1890;Mallock 1896;Wendt 1933;Taylor 1936a, b; see the review by Koschmieder 1993). Although Bagnold did not compare his pure fluid results with these studies, the experimental parameters are similar and a comparison demonstrates the impact of Bagnold's experimental apparatus on his stress measurements.…”

Section: Bagnold's Torque Measurements For Pure Watermentioning

confidence: 80%

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Revisiting the 1954 suspension experiments of R. A. Bagnold

et al. 2002

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In 1954 R. A. Bagnold published his seminal findings on the rheological properties of a liquid-solid suspension. Although this work has been cited extensively over the last fifty years, there has not been a critical review of the experiments. The purpose of this study is to examine the work and to suggest an alternative reason for the experimental findings. The concentric cylinder rheometer was designed to measure simultaneously the shear and normal forces for a wide range of solid concentrations, fluid viscosities and shear rates. As presented by Bagnold, the analysis and experiments demonstrated that the shear and normal forces depended linearly on the shear rate in the 'macroviscous' regime; as the grain-to-grain interactions increased in the 'grain-inertia' regime, the stresses depended on the square of the shear rate and were independent of the fluid viscosity. These results, however, appear to be dictated by the design of the experimental facility. In Bagnold's experiments, the height (h) of the rheometer was relatively short compared to the spacing (t) between the rotating outer and stationary inner cylinder (h/t = 4.6). Since the top and bottom end plates rotated with the outer cylinder, the flow contained two axisymmetric counter-rotating cells in which flow moved outward along the end plates and inward through the central region of the annulus. At higher Reynolds numbers, these cells contributed significantly to the measured torque, as demonstrated by comparing Bagnold's pure-fluid measurements with studies on laminar-to-turbulent transitions that pre-date the 1954 study. By accounting for the torque along the end walls, Bagnold's shear stress measurements can be estimated by modelling the liquid-solid mixture as a Newtonian fluid with a corrected viscosity that depends on the solids concentration. An analysis of the normal stress measurements was problematic because the gross measurements were not reported and could not be obtained.

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Section: Bagnold's Torque Measurements For Pure Watercontrasting

confidence: 56%

Section: Bagnold's Torque Measurements For Pure Watermentioning

confidence: 80%

Revisiting the 1954 suspension experiments of R. A. Bagnold

et al. 2002

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“…It is also worth noting that plane Couette flow is the limiting case of TC when the radius ratio η = 1. Experimental investigations of TC have a long history, dating back to the initial work in the end of the 1800s by Couette (1890) in France, who concentrated on outer cylinder rotation and developed the viscometer and Mallock (1896) in the UK, who also rotated the inner cylinder and found indications of turbulence. Later work by Wendt (1933) and Taylor (1936), greatly expanded on the system, the former measuring torques and velocities for several radius and rotation ratios in the turbulent case, and the latter being the first to mathematically describe the cells which form if the flow is linearly unstable.…”

Section: Optimal Taylor-couette Flow: Radius Ratio Dependencementioning

confidence: 99%

Optimal Taylor–Couette flow: radius ratio dependence

et al. 2014

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Taylor-Couette flow with independently rotating inner (i) & outer (o) cylinders is explored numerically and experimentally to determine the effects of the radius ratio η on the system response. Numerical simulations reach Reynolds numbers of up to Re i = 9.5 · 10 3 and Re o = 5 · 10 3 , corresponding to Taylor numbers of up to T a = 10 8 for four different radius ratios η = r i /r o between 0.5 and 0.909. The experiments, performed in the Twente Turbulent Taylor-Couette (T 3 C) setup, reach Reynolds numbers of up to Re i = 2 · 10 6 and Re o = 1.5 · 10 6 , corresponding to T a = 5 · 10 12 for η = 0.714−0.909. Effective scaling laws for the torque J ω (T a) are found, which for sufficiently large driving T a are independent of the radius ratio η. As previously reported for η = 0.714, optimum transport at a non-zero Rossby number Ro = r i |ω i − ω o |/[2(r o − r i )ω o ] is found in both experiments and numerics. Ro opt is found to depend on the radius ratio and the driving of the system. At a driving in the range between T a ∼ 3 · 10 8 and T a ∼ 10 10 , Ro opt saturates to an asymptotic η-dependent value. Theoretical predictions for the asymptotic value of Ro opt are compared to the experimental results, and found to differ notably. Furthermore, the local angular velocity profiles from experiments and numerics are compared, and a link between a flat bulk profile and optimum transport for all radius ratios is reported.

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“…The history of fluid dynamics in short cylindrical Couette systems extends to the 19th century [7], but our experiment is atypical in several respects. Since the pioneering work by Benjamin [8][9][10], the majority of such work has used a stationary outer cylinder with stationary caps, the main interest being the influence of the short geometry on TCI.…”

Section: Introductionmentioning

confidence: 99%

Circulation in a Short Cylindrical Couette System

Kageyama¹,

Ji²,

Goodman³

2003

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In preparation for an experimental study of magnetorotational instability (MRI) in liquid metal, we explore Couette flows having height comparable to the gap between cylinders, centrifugally stable rotation, and high Reynolds number. Experiments in water are compared with numerical simulations. The flow is very different from that of an ideal, infinitely long Couette system. Simulations show that endcaps corotating with the outer cylinder drive a strong poloidal circulation that redistributes angular momentum. Predicted toroidal flow profiles agree well with experimental measurements. Spin-down times scale with Reynolds number as expected for laminar Ekman circulation; extrapolation from two-dimensional simulations at Re ≤ 3200 agrees remarkably well with experiment at Re ∼ 10 6 . This suggests that turbulence does not dominate the effective viscosity. Further detailed numerical studies reveal a strong radially inward flow near both endcaps.After turning vertically along the inner cylinder, these flows converge at the midplane and depart the boundary in a radial jet. To minimize this circulation in the MRI experiment, endcaps consisting of multiple, differentially rotating rings are proposed. Simulations predict that an adequate approximation to the ideal Couette profile can be obtained with a few rings. * Electronic address: kage@jamstec.go.jp † Electronic address: hji@pppl.gov ‡ Electronic address:

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III. Experiments on fluid viscosity

Cited by 96 publications

References 0 publications

Revisiting the 1954 suspension experiments of R. A. Bagnold

Revisiting the 1954 suspension experiments of R. A. Bagnold

Optimal Taylor–Couette flow: radius ratio dependence

Circulation in a Short Cylindrical Couette System

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