Particle motions in sheared suspensions XIII. The spin and rotation of disks

1962 ◽  
Vol 12 (1) ◽  
pp. 88-96 ◽  
Author(s):  
H. L. Goldsmith ◽  
S. G. Mason
Keyword(s):  
Couette Flow ◽  
Angular Rotation ◽  
Axis Ratio ◽  
Dissipation Of Energy ◽  
Sheared Suspensions ◽  
Good Agreement

The motions of single disks suspended in a liquid undergoing Couette flow have been studied in detail. The angular rotation and the axial spin of the disks were found to be in good agreement with the theory of Jeffery, provided the equivalent axis ratio re was used instead of the measured axis ratio r. It was found that non-interacting disks move in constant orbits without a tendency to drift into orbits corresponding to a minimum dissipation of energy. Discontinuous changes in orbit were observed to occur following two-body collisions.

Measurements of the viscometric functions for a fluid in steady shear flows

1971 ◽  
Vol 270 (1208) ◽  
pp. 507-556 ◽  
Keyword(s):  
Normal Stress ◽  
Couette Flow ◽  
Direct Method ◽  
Normal Stress Difference ◽  
Optical Measurements ◽  
Measuring Error ◽  
Stress Difference ◽  
Concentric Cylinders ◽  
Plate Apparatus ◽  
Good Agreement

This paper describes a series of experiments in which the three material functions of steady viscometric flows were measured for a given polyisobutene solution. A number of instruments and measuring techniques were used in order to check the experimental method. The shear stress was determined from the torque transmitted by the fluid in a cone-and-plate apparatus and in Couette flow between concentric cylinders. The results obtained from these measurements were in good agreement with each other. The primary normal-stress difference was determined from the normal force acting on the plate of a cone-and-plate apparatus, and from stress-optical measurements on Couette flow between concentric cylinders. These results are in good agreement with each other. Detailed measurements of the distribution f Permanent address: Fluid Mechanics Research Institute, University of Essex, Colchester, Essex. of the normal stress acting on the plate of the cone-and-plate apparatus were made for three cone angles and for two boundary configurations at the rim of the apparatus: from these results a combination of the primary and the secondary normal-stress differences was deduced, thereby making possible the computation of the secondary normal-stress difference. When the normal stress acting on a rigid surface is measured by means of a hole leading to a pressure transducer the results are in error by an amount roughly proportional to the primary normal-stress difference of the fluid (cf. Kaye, Lodge & Vale 1968). In the present experiments this error was determined from measurements of the distribution of the normal stress acting on the plates of a plate-and-plate apparatus, together with the assumption that the error is a function only of the shear rate at the position o the hole in the undisturbed viscometric flow. The values of the measuring error thus obtained are in goo agreement with measurements made in Gouette flow between concentric cylinders. The secondary normal-stress difference, P2, was measured in a number of different ways. From the results it is suggested that the methods of Jackson & Kaye and of Marsh & Pearson may be imprecise and, in particular, may yield incorrect values for P2- A new, direct, method of estimating P2, suggested by Higashitani & Pritchard (1971) and outlined in appendix A, may provide a more convenient means of determining P2.

GRANULAR MEDIA ON A VIBRATING PLATE: A MOLECULAR DYNAMICS SIMULATION

1993 ◽  
Vol 07 (09n10) ◽  
pp. 1779-1788 ◽  
Author(s):  
JASON A.C. GALLAS ◽  
HANS J. HERRMANN ◽  
STEFAN SOKOLOWSKI
Keyword(s):  
Molecular Dynamics ◽  
Molecular Dynamics Simulation ◽  
Granular Materials ◽  
Granular Medium ◽  
Granular Media ◽  
Dynamics Simulation ◽  
Dissipation Of Energy ◽  
Conveyor Belts ◽  
Good Agreement ◽  
Vibrating Plate

When sand or other granular materials are shaken, poured or sheared many intriguing phenomena can be observed. We will model the granular medium by a packing of elastic spheres and simulate it via Molecular Dynamics. Dissipation of energy and shear friction at collisions are included. The onset of fluidization can be determined and is in good agreement with experiments. On a vibrating plate we observe the formation of convection cells due to walls or amplitude modulations. Density and velocity profiles on conveyor belts are measured and the influence of an obstacle discussed. We mention various types of rheology for flow down an inclined chute or through a pipe and outflowing containers.

On the secondary instabilities of transient growth in Couette flow

2017 ◽  
Vol 813 ◽  
pp. 528-557 ◽  
Author(s):  
Michael Karp ◽  
Jacob Cohen
Keyword(s):  
Couette Flow ◽  
Initial Energy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Transient Growth ◽  
Vortical Structures ◽  
Inflection Points ◽  
Theoretical Predictions ◽  
Secondary Instabilities ◽  
Good Agreement

The secondary instability of linear transient growth (TG) in Couette flow is explored theoretically, utilizing an analytical representation of the TG based on four modes and their nonlinear interactions. The evolution of the secondary disturbance is derived using the multiple time scales method. The theoretical predictions are compared with direct numerical simulations and very good agreement with respect to the growth of the disturbance energy and associated vortical structures is observed, up to the final stage just before the breakdown to turbulence. The theoretical model enables us to perform a full parametric study, including TG symmetry type, various wavenumbers, initial energy, TG nonlinearity and Reynolds number, to find all possible routes to transition and the optimal parameters for each type of the secondary disturbance. It is found that the most dangerous secondary disturbances are associated with spanwise wavenumbers which generate the strongest inflection points, i.e. those having maximal shear, rather than with those maximizing the energy gain during the TG phase.

scholarly journals Heat transport in Rayleigh–Bénard convection and angular momentum transport in Taylor–Couette flow: a comparative study

2017 ◽  
Vol 375 (2089) ◽  
pp. 20160079 ◽  
Author(s):  
Hannes J. Brauckmann ◽  
Bruno Eckhardt ◽  
Jörg Schumacher
Keyword(s):  
Angular Momentum ◽  
Couette Flow ◽  
Nusselt Numbers ◽  
Bénard Convection ◽  
Benard Convection ◽  
Taylor Couette ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard ◽  
Good Agreement ◽  
Taylor Couette Flow

Rayleigh–Bénard convection and Taylor–Couette flow are two canonical flows that have many properties in common. We here compare the two flows in detail for parameter values where the Nusselt numbers, i.e. the thermal transport and the angular momentum transport normalized by the corresponding laminar values, coincide. We study turbulent Rayleigh–Bénard convection in air at Rayleigh number Ra =10 7 and Taylor–Couette flow at shear Reynolds number Re S =2×10 4 for two different mean rotation rates but the same Nusselt numbers. For individual pairwise related fields and convective currents, we compare the probability density functions normalized by the corresponding root mean square values and taken at different distances from the wall. We find one rotation number for which there is very good agreement between the mean profiles of the two corresponding quantities temperature and angular momentum. Similarly, there is good agreement between the fluctuations in temperature and velocity components. For the heat and angular momentum currents, there are differences in the fluctuations outside the boundary layers that increase with overall rotation and can be related to differences in the flow structures in the boundary layer and in the bulk. The study extends the similarities between the two flows from global quantities to local quantities and reveals the effects of rotation on the transport. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

scholarly journals Relationship between temperature and apparent shape of pristine ice crystals derived from polarimetric cloud radar observations during the ACCEPT campaign

2016 ◽  
Vol 9 (8) ◽  
pp. 3739-3754 ◽  
Author(s):  
Alexander Myagkov ◽  
Patric Seifert ◽  
Ulla Wandinger ◽  
Johannes Bühl ◽  
Ronny Engelmann
Keyword(s):  
Free Fall ◽  
Crystal Shape ◽  
Ice Crystal ◽  
Ambient Conditions ◽  
Axis Ratio ◽  
Microwave Scattering ◽  
Cloud Radar ◽  
Ice Particles ◽  
Rapid Changes ◽  
Good Agreement

Abstract. This paper presents first quantitative estimations of apparent ice particle shape at the top of liquid-topped clouds. Analyzed ice particles were formed under mixed-phase conditions in the presence of supercooled water and in the temperature range from −20 to −3 °C. The estimation is based on polarizability ratios of ice particles measured by a Ka-band cloud radar MIRA-35 with hybrid polarimetric configuration. Polarizability ratio is a function of the geometrical axis ratio and the dielectric properties of the observed hydrometeors. For this study, 22 cases observed during the ACCEPT (Analysis of the Composition of Clouds with Extended Polarization Techniques) field campaign were used. Polarizability ratios retrieved for cloud layers with the cloud-top temperatures of  ∼ −5,  ∼ −8,  ∼ −15, and  ∼ −20 °C were 1.6, 0.9, 0.6, and 0.9, respectively. Such values correspond to prolate, quasi-isotropic, oblate, and quasi-isotropic particles, respectively. Data from a free-fall chamber were used for the comparison. A good agreement of detected apparent shapes with well-known shape–temperature dependencies observed in laboratories was found. Polarizability ratios used for the analysis were estimated for areas located close to the cloud top, where aggregation and riming processes do not strongly affect ice particles. We concluded that, in microwave scattering models, ice particles detected in these areas can be assumed to have pristine shapes. It was also found that even slight variations of ambient conditions at the cloud top with temperatures warmer than  ∼ −5 °C can lead to rapid changes of ice crystal shape.

scholarly journals Shapes and Fall Speeds of Freezing and Frozen Raindrops

2020 ◽  
Vol 21 (6) ◽  
pp. 1311-1331
Author(s):  
Kalimur Rahman ◽  
Firat Y. Testik
Keyword(s):  
Drag Coefficient ◽  
High Speed ◽  
Drop Size ◽  
Equivalent Diameter ◽  
Field Observations ◽  
Axis Ratio ◽  
Shape Model ◽  
The Mean ◽  
Distinct Features ◽  
Good Agreement

AbstractThis study investigates the shapes and fall speeds of freezing and frozen raindrops through field observations using an instrument called the high-speed optical disdrometer (HOD) that we developed recently. Our field observations showed that while the shapes of all of the observed freezing raindrops and a portion of the frozen raindrops (39% of the frozen raindrops that are larger than 1.0 mm in volume equivalent diameter D) resemble the shapes of warm raindrops, majority of frozen raindrops (61% of the frozen raindrops with D > 1.0 mm) exhibited a distinct feature such as a spicule, bulge, cavity, or aggregation. Field observations of axis ratios (i.e., ratio of the vertical to horizontal chord) and fall speeds were compared with the predictions of available models. Separate empirical axis ratio parameterizations were developed for the freezing and frozen raindrops using the HOD field observations and extensions to an available shape model were also incorporated. For the fall speeds of freezing and frozen raindrops, field observations demonstrated a good agreement with the predictions of the available parameterizations. Frozen raindrops showed a larger scatter of fall speeds around the mean fall speed of a given drop size than those of the freezing raindrops due to the shape variety among the frozen raindrops with the aforementioned distinct features. The drag coefficients for the observed hydrometeors were compared with the predictions of the available drag coefficient models. Separate “drag coefficient–Reynolds number” relationships for freezing and frozen raindrops were developed.

scholarly journals Application of HPM to Find Analytical Solution of Coette Flow with Variable Viscosity

2015 ◽  
Vol 9 (1) ◽  
pp. 5-8 ◽  
Author(s):  
Alireza Azimi ◽  
Mohammadreza Azimi ◽  
Amirhossein Javanfar
Keyword(s):  
Analytical Solution ◽  
Couette Flow ◽  
Nonlinear Problem ◽  
Variable Viscosity ◽  
Mathematical Formulation ◽  
Exact Method ◽  
Analytical Results ◽  
Solution Accuracy ◽  
Good Agreement

Abstract In this paper, the couette flow of fluid with variable viscosity is studied analytically by using Homotopy Pertubation Method (HPM). At first the basic idea of Homotopy Pertubation Method (HPM) is presented. The mathematical formulation and application of HPM to nonlinear problem are presented in section three. In order to check the validity of solution the analytical results are compared with exact ones for various numerical cases. The good agreement between exact method and Homotopy Pertubation Method has been assures us about the solution accuracy.

On the competition between centrifugal and shear instability in spiral Couette flow

2000 ◽  
Vol 402 ◽  
pp. 33-56 ◽  
Author(s):  
A. MESEGUER ◽  
F. MARQUES
Keyword(s):  
Couette Flow ◽  
Shear Instability ◽  
Critical Surface ◽  
Neutral Stability ◽  
Zeroth Order ◽  
Coaxial Cylinders ◽  
Centrifugal Instability ◽  
Wide Range ◽  
Experimental Parameters ◽  
Good Agreement

The linear stability of a fluid confined between two coaxial cylinders rotating independently and with axial sliding (spiral Couette flow) is examined. A wide range of experimental parameters has been explored, including two different radius ratios. Zeroth-order discontinuities are found in the critical surface; they are explained as a result of the competition between the centrifugal and shear instability mechanisms, which appears only in the co-rotating case, close to the rigid-body rotation region. In the counter-rotating case, the centrifugal instability is dominant. Due to the competition, the neutral stability curves develop islands of instability, which considerably lower the instability threshold. Specific and robust numerical methods to handle these geometrical complexities are developed. The results are in very good agreement with the experimental data available, and with previous computations.

scholarly journals Single-Layer Circularly Polarized Wide Band Reflectarray Antenna with High Aperture Efficiency

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Xinyu Da ◽  
Jialiang Wu ◽  
Jing Zhao ◽  
Lin Baoqin ◽  
Kai Wu
Keyword(s):  
Phase Response Curve ◽  
Low Cost ◽  
Single Layer ◽  
Wide Band ◽  
Center Frequency ◽  
Angular Rotation ◽  
Circularly Polarized ◽  
Aperture Efficiency ◽  
Rotation Technique ◽  
Good Agreement

A circularly polarized broadband low-cost reflectarray in Ku-band is presented using a novel single-layer subwavelength phase-shifting element. The proposed subwavelength element consists of the concentric split ring and the crossed bowtie. The linear reflected phase response curve with 360° phase coverage is obtained. For experimental verification, an array of 25 × 25 reflectarray prototype has been designed and manufactured by employing the angular rotation technique. The measurements are in good agreement with the simulations. The measured gain at the center frequency of 12.5 GHz is 26.6 dBi, corresponding to the aperture efficiency of 52.5%, and the 1 dB gain bandwidth is 26.4%.

Influence of the Aspect Ratio on the Stability of Pseudoplastic Fluids Between Rotating Cylinders

2012 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Gap Effect ◽  
Critical Conditions ◽  
Taylor Vortices ◽  
Circular Couette Flow ◽  
Centrifugal Instability ◽  
Toroidal Vortices ◽  
The Stability ◽  
Pseudoplastic Fluids ◽  
Good Agreement

Pseudoplastic circular Couette flow in annulus is investigated in finite gap. The onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and detecting the critical conditions. The obtained governing equations were solved by the spectral method. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, known as Taylor vortices. A range of parameters is found in which the combination of shear thinning and gap effect leads to destabilizing the vortex structure indicated as the point of Hopf bifurcation. Comparison with existing measurements on pseudoplastic circular Couette flow results in good agreement.

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