Formulas for Calibration of Rheological Parameters of Bingham Fluid in Couette Rheometer

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Ying-Hsin Wu ◽  
Ko-Fei Liu

We propose simple formulas for calibration of rheological parameters of Bingham fluid using a co-axial cylinder rheometer, in which the inner cylinder rotates at a constant speed, and the outer cylinder is stationary. A critical rotational speed exists due to existence of yield stress. If rotation speed exceeds the critical value, all fluid is fully sheared between the concentric cylinders. Plug flow exists only when rotation speed is less than the critical value. The effects of radius ratio and Bingham number are discussed. The rheometer with radius ratio very close to unity is discussed as a limiting case, and the result confirms previous research. Formulas for calibration are derived using Least Squares and perturbation methods for all values of radius ratio, based on measured rotation speed and torque. Two sets of experimental data are used for verification. The validation shows that the formulas derived here yield reasonable and accurate estimates of rheological parameters.

Author(s):  
P. Castle ◽  
F. R. Mobbs

Since THE Early Work of Taylor (I)†, it has become well known that the Couette flow between an inner, rotating circular cylinder and a concentric, stationary outer cylinder becomes unstable at sufficiently high rotational speeds. The initial instability leads to the formation of a series of toroidal vortices, commonly referred to as Taylor vortices. The vortices occupy approximately square cells, and adjacent pairs are contra-rotating. When the gap d between the cylinders is small compared with the inner cylinder radius R1, the criterion for the onset on the instability is the Taylor number T = Ω1 R1 d3 / v2 where Ω1 is the rotational speed and v the kinematic viscosity of the fluid. A widely accepted critical value is Tc = 1708. Recently Coles (2) has shown the existence of a second instability consisting of travelling circumferential waves superimposed on the Taylor vortices.


2004 ◽  
Vol 67 (11) ◽  
pp. 2410-2415 ◽  
Author(s):  
L. J. FORNEY ◽  
J. A. PIERSON ◽  
Z. YE

A novel reactor is described with flow characteristics that approach that of ideal plug flow but with a residence time that is uncoupled from the hydrodynamics or boundary layer characteristics. The design described consists of an inner cylinder that rotates within a stationary but larger outer cylinder. At low rotation rates, a laminar, hydrodynamic configuration called Taylor-Couette flow is established, which consists of a system of circumferential vortices within the annular fluid gap. The latter constitutes a spatially periodic flow that is the hydrodynamic equivalent to cross flow over a tube bank or lamp array. These vortices provide radial mixing, reduce the boundary layer thickness, and are independent of the axial flow rate and thus the fluid residence time. An additional feature of the rotating design is the repetitive exposure of the fluid parcels to a minimum number of lamps, which substantially reduces the maintenance requirements. Inactivation data for Escherichia coli (ATCC 15597) were recorded in commercial apple and grape juice that are relatively opaque to UV radiation. With initial E. coli concentrations of approximately 106 CFU/ml, Taylor-Couette flow was found to provide a 3- to 5-log improvement in the inactivation efficiency compared with simple channel flow between concentric cylinders.


1994 ◽  
Vol 263 ◽  
pp. 133-150 ◽  
Author(s):  
I. A. Frigaard ◽  
S. D. Howison ◽  
I. J. Sobey

The stability to linearized two-dimensional disturbances of plane Poiseuille flow of a Bingham fluid is considered. Bingham fluids exhibit a yield stress in addition to a plastic viscosity and this description is typically applied to drilling muds. A non-zero yield stress results in an additional parameter, a Bingham number, and it is found that the minimum Reynolds number for linear instability increases almost linearly with increasing Bingham number.


Metals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 127 ◽  
Author(s):  
Yuanxiang Lu ◽  
Zeyi Jiang ◽  
Xinru Zhang ◽  
Jingsong Wang ◽  
Xinxin Zhang

The solid flow plays an important role in blast furnace (BF) ironmaking. In the paper, the descending behavior of solid flow in BFs was investigated by a cold experimental BF model and numerical simulation via the discrete element method (DEM). To eliminate the flat wall effect on the structure of solid flow in lab observations, a cutting method was developed to observe the vertical section of the solid flow by inserting a transparent plate into the experimental BF model. Both the experimental and numerical results indicated that plug flow is the main solid flow pattern in the upper and middle zones of BFs during burden descending. Meanwhile, a slight convergence flow and a deadman zone form at the lower part of the bosh. In addition, the boundary between the plug flow and convergence flow in BFs was determined by analyzing the velocity of the burden in vertical directions and the Wilcox–Swailes coefficient (Uws). The results indicated that the Uws can be defined as a critical value to determine the solid flow patterns. When Uws ≥ 0.65, the plug flow is dominant. When Uws < 0.65, the convergence flow is dominant. The findings may have important implications to understand the structure of the solid flow in BFs.


Fluids ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 95 ◽  
Author(s):  
D. Andrew S. Rees ◽  
Andrew P. Bassom

We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise.


2021 ◽  
Vol 53 (6) ◽  
pp. 065502
Author(s):  
Ming C Lee ◽  
Huan J Keh

Abstract The steady rotation of a slip spherical particle about a diameter lying along the longitudinal axis of a slip circular tube filled with an incompressible Newtonian fluid at low Reynolds numbers is analyzed. To solve the Stokes equations for the fluid flow, the solution is constituted by the summation of general solutions in both cylindrical and spherical coordinates. The boundary conditions are implemented first along the tube wall via the Fourier cosine transform and then over the particle surface through a collocation method. Results of the resisting torque acting on the particle are obtained for various values of the relevant dimensionless parameters. The effect of the confining tube on the axisymmetric rotation of the particle with slip surfaces is interesting. The torque increases monotonically with an increase in the stickiness of the tube wall, keeping the other parameters unchanged. When the stickiness of the tube wall is greater than a critical value, the torque is greater than that on the particle in an unbounded identical fluid and increases with increases in the stickiness of the particle surface and particle-to-tube radius ratio. When the stickiness of the tube wall is less than the critical value, conversely, the torque is smaller than that on the unconfined particle and decreases with increases in the particle stickiness and radius ratio.


1965 ◽  
Vol 5 (01) ◽  
pp. 6-14 ◽  
Author(s):  
R.F. Burdyn

Abstract The inadequate use of centrifugation to economically recover solids from weighted drilling fluids reflects the need for better equipment and techniques for this purpose. Laboratory studies in the development of an improved separator are described in which an operating equation is derived and tested. Results show that the concentric cylinder geometry employed effectively separates barite from a suspension and that the operating equation provides a good approximation for scale-up. Introduction Our current drilling technology frequently requires a high-density drilling fluid obtained by addition of barite. In the course of drilling, formation solids which are too fine to be removed either by screening or settling become suspended in the drilling fluid and gradually the volume of solids in the mud increases. The volume fraction of solids must be limited (if a satisfactory set of rheological parameters are to be maintained). A centrifugal separator provides an economical way of accomplishing this. The barite recovery process can be considered as a separation of two solids. One, the light solids, composed of formation and added solids, has a specific gravity of 2.6 to 2.7; the other, barite, has a specific gravity of 4.2 to 4.3. This density difference, plus the fact that the average light-solids particle size is much smaller than the average barite particle size, permits separation by a centrifuge. In drilling fluids some of the coarse particles of the light-solids-range will settle faster than fine particles of the barite-particle range. As a result a complete separation of the two species is not possible. Since the object of the process is not merely recovering the maximum amount of barite but includes as well removing the maximum amount of light solids, an optimum barite recovery efficiency exists. From a practical standpoint this optimum cannot be determined in the field for each drilling fluid system, and in practice the separation is less than optimum, with some sacrifice of barite. Drilling technology has included centrifugal separators for barite recovery for more than a decade. Results have been reported by a number of investigators indicating that the process is practical and economical. The decision to use a centrifuge is based on economics in which direct cost savings and the indirect benefits in rig time derived from improvement of the drilling fluid are important factors. One would expect that centrifugal separation of barite from drilling fluids would significantly affect barite consumption; however, this is not the case. The Minerals Yearbook shows an annual domestic barite consumption in the drilling industry of nearly I million tons. By rough estimate there are perhaps 80 separators presently in field use. Assuming half of these in use at any one time, operating an, average of four hours per day, at recovery rates averaging 3,000 lb of barite per hour, total annual recovery is about 90,000 tons. This is less than 10 per cent of the total barite used. I conservatively estimate that barite consumption in drilling operations can be reduced by 30 per cent through greater utilization of centrifugal separators. To encourage more wide- spread acceptance of centrifugal separators in the drilling industry, improved equipment and techniques would be very desirable. The present paper, covering theory and results obtained from a laboratory model, is the first in a series on the development of an improved mud separator for field use. THE CONCENTRIC CYLINDER GEOMETRY AS A SEPARATING DEVICE Consider the geometry shown in Fig. 1, consisting of two concentric cylinders separated by an annular space. These are arranged so that the outer cylinder is fixed and the inner one can be rotated about its axis on shafts sealed against the ends of the outer cylinder. SPEJ P. 6ˆ


2005 ◽  
Vol 73 (1) ◽  
pp. 108-111 ◽  
Author(s):  
A. A. Rashaida ◽  
D. J. Bergstrom ◽  
R. J. Sumner

In the present investigation, an analytical numerical solution is presented for the mass transfer from a rotating disk to a Bingham fluid for the case of laminar boundary layer flow. The analytical approach includes the coupled effects of steady disk rotation and non-Newtonian fluid properties on the mass transfer rate. A dimensionless expression for the wall mass transfer rate based on the Sherwood number, Sh, is obtained in terms of the system parameters (Reynolds number, Rep, and Schmidt number, Scp) which depend on the dimensionless yield stress or Bingham number, By. The analytical relation indicates that an increase in By (up to the limit By⩽1) leads to a slight increase in the wall mass transfer rate, and thereafter, for By>1, the mass transfer rate is reduced.


Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 154
Author(s):  
Alessandra Borrelli ◽  
Giulia Giantesio ◽  
Maria Cristina Patria

In this paper, we describe our study of the mixed convection of a Boussinesquian Bingham fluid in a vertical channel in the absence and presence of an external uniform magnetic field normal to the walls. The velocity, the induced magnetic field, and the temperature are analytically obtained. A detailed analysis is conducted to determine the plug regions in relation to the values of the Bingham number, the buoyancy parameter, and the Hartmann number. In particular, the velocity decreases as the Bingham number increases. Detailed considerations are drawn for the occurrence of the reverse flow phenomenon. Moreover, a selected set of diagrams illustrating the influence of various parameters involved in the problem is presented and discussed.


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