Variable Viscosity Coefficient Research Articles

Flow of a Bingham Fluid Through Circular Pipes with Variable Viscosity Coefficient Along the Pipe Length

Creation of conditions for optimal flow of Bingham media, such as ready-mixed concrete and mortar mixes, in the circular pipeline during delivery by various types of transporting equipment has not been sufficiently studied so far. Purpose: finding patterns of flow of concrete and mortar mixes in different sections of the pipeline, based on the variability of the viscosity coefficient when the medium is flowing through long circular pipes. In calculations of the flow capacity of mortar and concrete pipelines and the required power of the pumping equipment, the properties of concrete and mortar as Bingham media should be taken into account. Dependences for description of the operation process of flow of concrete and mortar mixes through circular pipelines have been found on the basis of the Buckingham equation in the laminar flow mode.Dependences of determination of flow rate and required power with continuous delivery of concrete and mortar mixes in the pipeline, as well in case of alternate inlet pressure variation are presented. Law of variation of μр can be obtained only experimentally, which also results in errors in the computation model.

Effect of Variable Thermal Expansion Coefficient and Nanofluid Properties on Steady Natural Convection in an Enclosure

Steady state natural convection is numerically investigated in an enclosure using variable thermal conductivity, viscosity and thermal expansion coefficient of Al2O3–water nanofluid. This study has been conducted for a wide range of Rayleigh numbers (103≤ Ra ≤ 106), concentrations of nanoparticles (0% ≤ Φ ≤ 7%), enclosure aspect ratios (0.5 ≤ AR ≤ 2) and temperature differences between the cold and the hot walls (1≤ ∆T≤ 30). The main idea in this study is about the effect of temperature on natural convection pattern of nanofluid by changing nanoparticles concentration. Also, changing thermal expansion coefficient with temperature is considerd in this study which will have significant effects on natural convection and has not been considerd before. In low Rayleigh numbers (Ra= 103) and for cavities with AR≥1, the pattern shown in the average Nusselt number versus volume fraction of nanoparticles diagram deteriorates by increasing ∆T. However, for other cases, increasing ∆T has a positive effect on Nu-Φ diagram. The actual Nuselt number curve depicts that dispersing nanoparticles in base fluid deteriorate natural convection heat transfer which is in a good agreement with experimental works.

Dissipative weak solutions to compressible Navier–Stokes–Fokker–Planck systems with variable viscosity coefficients

Motivated by a recent paper by Barrett and Süli (2016) [6], we consider the compressible Navier–Stokes system coupled with a Fokker–Planck type equation describing the motion of polymer molecules in a viscous compressible fluid occupying a bounded spatial domain, with polymer-number-density-dependent viscosity coefficients. The model arises in the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids, where the polymer molecules are idealized as bead-spring chains with finitely extensible nonlinear elastic (FENE) type spring potentials. The motion of the solvent is governed by the unsteady, compressible, barotropic Navier–Stokes system, where the viscosity coefficients in the Newtonian stress tensor depend on the polymer number density. Our goal is to show that the existence theory developed in the case of constant viscosity coefficients can be extended to the case of polymer-number-density-dependent viscosities, provided that certain technical restrictions are imposed, relating the behavior of the viscosity coefficients and the pressure for large values of the solvent density. As a first step in this direction, we prove here the weak sequential stability of the family of dissipative (finite-energy) weak solutions to the system.

A fractional derivative approach to full creep regions in salt rock

Based on the definition of the constant-viscosity Abel dashpot, a new creep element, referred to as the variable-viscosity Abel dashpot, is proposed to characterize damage growth in salt rock samples during creep tests. Ultrasonic testing is employed to determine a formula of the variable viscosity coefficient, indicating that the change of the variable viscosity coefficient with the time meets a negative exponent law. In addition, by replacing the Newtonian dashpot in the classical Nishihara model with the variable-viscosity Abel dashpot, a damage-mechanism-based creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional-derivative creep constitutive model is presented. The parameters of the fractional derivative creep model are determined by the Levenberg–Marquardt method on the basis of the experimental results of creep tests on salt rock. Furthermore, a sensitivity study is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient exponent on creep strain of salt rock. It is indicated that the fractional derivative creep model proposed in the paper provides a precise description of full creep regions in salt rock, i.e., the transient creep region (the primary region), the steady-state creep region (the secondary region) and the accelerated creep region (the tertiary region).

Dispersion in a Non-Linear Non-Darcy Flow of a Variable Viscosity Liquid

An infinite horizontally extended sparcely packed chemically inert porous channel flow of a Newtonian liquid is considered. The walls of the channels are assumed to be at different temperatures so that the viscosity of the fluid varies across the channel. A dimensionless variable viscosity coefficient is introduced in the Darcy–Forchheimer- Brinkman model, along with the Darcy number, Forchheimer number and the Brinkman number. A series solution is obtained for the Darcy-Forchheimer-Brinkman equation using the differential transform method (DTM). Using this solution for the fully developed flow velocity and the convective diffusion equation, the influence of the variable viscosity coefficient and the Darcy, Brinkman and Forchheimer numbers on the all-time valid dispersion coefficient is analyzed. An increase the variable viscosity parameter is to increase the dispersion coefficient while an increase in all the other parameters will decrease the dispersion coefficient. The Light hill, Taylor-Aris and Taylor dispersion coefficients are obtained as the limiting cases of the generalized dispersion coefficient.

基于分数阶导数的盐岩流变本构模型

A modeling approach to the creep behavior of natural rock salt is of special interest for many underground engineering such as underground storage of natural gas and crude oil, and a permanent repository of CO2 and radioactive and toxic wastes. Based on the definition of fractional derivative, the Abel dashpot with a constant viscosity coefficient is generalized to an Abel dashpot with a variable viscosity coefficient, referred to as a new time-dependent element. By replacing a Newtonian dashpot in the classical Nishihara model with the fractional derivative Abel dashpot of a variable viscosity coefficient, a new creep constitutive model is proposed on the basis of time-based fractional derivative. The analytic solution for the fractional derivative creep constitutive model is given theoretically. Moreover, a computer-controlled creep set-up is employed to measure creep strain of a salt rock sample under the condition of uniaxial compression, taking from the Chuwang Well No.1, Jianghan Oilfield, Hubei Province. The parameters of the fractional derivative creep model are determined by fitting to the experimental results of time-dependent deformation of salt rock. In addition, a sensitivity study for the analytic solution of the time-based fractional derivative model is carried out, showing the effects of stress level, fractional derivative order and viscosity coefficient on a creep strain of salt rock. Furthermore, it is shown that the time-based fractional derivative model in the paper can be simplified to the classical Nishihara model in the special case. It is indicated that the fractional derivative creep model proposed in the paper gives a precise description of the three stages of creep especially the tertiary stage, i.e., an unsteady state period.

The Discrete Duality Finite Volume Method for Stokes Equations on Three-Dimensional Polyhedral Meshes

We develop a discrete duality finite volume method for the three-dimensional steady Stokes problem with a variable viscosity coefficient on polyhedral meshes. Under very general assumptions on the mesh, which may admit nonconforming polyhedrons, we prove the stability and well-posedness of the scheme. We also prove the convergence of the numerical approximation to the velocity, velocity gradient, and pressure and derive a priori estimates for the corresponding approximation error. Final numerical experiments confirm the theoretical predictions.

2A2-I07 MRブレーキを用いた可変粘性係数による人工筋肉マニピュレータの位置及び振動制御(アクチュエータの機構と制御)

2A2-I07 MRブレーキを用いた可変粘性係数による人工筋肉マニピュレータの位置及び振動制御(アクチュエータの機構と制御)

Large eddy simulation using a new set of sixth order schemes for compressible viscous terms

A set of conservative sixth order central differencing schemes is suggested for compressible flows with variable viscosity coefficient. This new set of central differencing schemes has the stencil width matching that of the seventh order weighted essentially non-oscillatory scheme (WENO). This feature is important to maintain the compactness of the seventh order WENO scheme and facilitate boundary condition treatment. As an application example, a large eddy simulation (LES) is conducted for a cylinder flow using the seventh order WENO scheme for the convective terms and the new set of sixth order central differencing scheme for the viscous terms. The results are compared with those from other research groups and those obtained using the fifth order WENO scheme and fourth order central differencing.

CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY

In this paper, we consider the compressible Navier–Stokes equation with density-dependent viscosity coefficients and a term of capillarity introduced formally by van der Waals in Ref. 51. This model includes at the same time the barotropic Navier–Stokes equations with variable viscosity coefficients, shallow-water system and the model introduced by Rohde in Ref. 46.We first study the well-posedness of the model in critical regularity spaces with respect to the scaling of the associated equations. In a functional setting as close as possible to the physical energy spaces, we prove global existence of solutions close to a stable equilibrium, and local in time existence of solutions with general initial data. Uniqueness is also obtained.

Acquired Clustering Properties and Solution of Certain Saddle Point Systems

Many mathematical models involve flow equations characterized by nonconstant viscosity, and a Stokes-type problem with variable viscosity coefficient arises. Appropriate block diagonal preconditioners for the resulting algebraic saddle point linear system produce well-clustered spectra, except for a few interior isolated eigenvalues which may tend to approach zero. These outliers affect the convergence of Krylov subspace system solvers, causing a possibly long stagnation phase. In this paper we characterize the influence of the spectral properties of the preconditioner on the final spectrum of the saddle point matrix by providing accurate spectral intervals depending on the involved operators. Moreover, we suggest that the stagnation phase may be completely eliminated by means of an augmentation procedure, where approximate spectral eigenspace information can be injected. We show that the modifications to the original code are minimal and can be easily implemented. Numerical experiments confirm our findings.

Prediction of the rate of cross-flow ultrafiltration of colloids with concentration-dependent diffusion coefficient and viscosity — theory and experiment

The influence of the physicochemical conditions on the permeation rate in cross-flow ultrafiltration of a colloidal suspension has been investigated. A numerical solution of the coupled Navier–Stokes, continuity and convective diffusion equations has been used to model the concentration polarisation and hence predict the rate of cross-flow ultrafiltration. A 2-D finite difference solution based on the Thomas algorithm and coded in FORTRAN has been developed. The model may be applied to flat sheet modules (with one or two porous walls) and is easily adapted to tubular modules. The model is versatile and can be run with constant or variable properties. The model takes into account the effects of the variation of the three key properties of osmotic pressure, diffusion coefficient and viscosity throughout the module. Determination of these three key physical properties was based on a fundamental calculation of the colloidal interactions between particles which accounts for multiparticle electrostatic interactions, dispersion forces and configurational entropic effects. These descriptions of colloidal interactions were used to develop an a priori model, with no adjustable parameters, that allows quantitative prediction of the properties of a colloidal dispersion as a function of pH (and hence colloid surface properties), colloid size, ionic strength and colloid concentration. The model results have been compared to experimentally measured data for the proteins bovine serum albumin and recombinant human lactoferrin. Good agreement between theoretical predictions and experimental cross-flow ultrafiltration data has been obtained. The results of these calculations show that, contrary to the usual assumption, the effects of variable viscosity and variable diffusion coefficient are both significant and comparable in magnitude. The numerical description of the cross-flow filtration model developed is completely general and allows for the future incorporation of any theoretical description for key solution properties.

A simple notation for differential vector expressions in orthogonal curvilinear coordinates

SUMMARY We present a simple notation for performing differential vector operations in orthogonal curvilinear coordinates, and for easily obtaining partial differential expressions in terms of the physical components. We express nth-order tensors as the summed products of the physical components and nth-order polyads of unit vectors (an extension of Gibbs dyadic notation convenient for a summation convention). By defining a gradient operator with partial derivatives balanced by the inverse scale factors, differential vector (or tensor) operations in orthogonal coordinates do not require the covariant/contravariant notation. Our primary focus is on spherical-polar coordinates, but we also derive formulae which may be applied to arbitrary orthogonal coordinate systems. The simpler case of cylindrical-polar coordinates is briefly discussed. We also offer a compact form for the gradient and divergence of general second-order tensors in orthogonal curvilinear coordinates, which are generally unavailable in standard handbooks. We show how our notation relates to that of tensor analysis/differentiaI geometry. As the analysis is not restricted to Euclidean geometry, our notation may be extended to Riemannian surfaces, such as spherical surfaces, so long as an orthogonal coordinate system is utilized. We discuss the Navier-Stokes equation for the case of spatially variable viscosity coefficients.

Mixed-Layer Shear Generated by Wind Stress in the Central Equatorial Pacific

Abstract Sixteen months of wind and current profile observations in the central equatorial Pacific show the response of the upper-ocean shear to local wind forcing. The shear at the ocean surface is significantly correlated with the wind stress in direction but not in magnitude, implying that the vertical eddy viscosity coefficient is proportional to the square of the wind speed or to the stress. Using this variable eddy viscosity coefficient in Stommel's model of the Equatorial Undercurrent, we calculate shears in the mixed layer that compare well with the observations. The flow is downwind on the equator and tends toward and Ekman spiral off the equator.

Rock dilatancy in uniaxial tests

Rock Dilatancy in Uniaxial Tests A procedure to find an elastic/viscoplastic constitutive equation able to describe rock dilatancy in uniaxial unconfined creep tests is given starting from experimental data. The influence of the loading rate on the rock dilatancy can also be described with this model. It is shown that a creep of the volume takes place during tests and that this volume creep has the following property: the volume strain is oscillating before ariving at its final stable value. This property is described by the proposed mathematical model using a variable viscosity coefficient which may change sign. According to the model the volume creep takes place during loading only.

Dispersion through a flowing fluid with variable viscosity and diffusion coefficient

In the study of dispersion of a solute through a flowing fluid it is shown that, for a given mean velocity, the Taylor diffusion coefficient decreases as the viscosity or the thickness of the peripheral layer decreases and as the molecular diffusion coefficient of this layer increases.