Recent Progress in Rheology

1983 ◽  
Vol 50 (4b) ◽  
pp. 1181-1190 ◽  
Author(s):  
R. I. Tanner
Keyword(s):  
Recent Progress ◽  
Numerical Solutions ◽  
Constitutive Relations ◽  
Complex Flows ◽  
Stress Measurements ◽  
Simple Flows ◽  
Fluid Rheology

Progress in fluid rheology is surveyed, including simple flows useful for stress measurements. The question of how to describe more complex flows is discussed in the light of knowledge of fluid microstructure, and several constitutive relations are exhibited. Finally, the need for numerical solutions to problems is emphasized.

scholarly journals Constitutive relations for compressible granular flow in the inertial regime

2019 ◽  
Vol 874 ◽  
pp. 926-951 ◽  
Author(s):  
D. G. Schaeffer ◽  
T. Barker ◽  
D. Tsuji ◽  
P. Gremaud ◽  
M. Shearer ◽  
...  
Keyword(s):  
Steady State ◽  
Granular Flow ◽  
Numerical Solutions ◽  
Volume Fraction ◽  
Constitutive Relations ◽  
Practical Interest ◽  
Time Dependent ◽  
Direct Result ◽  
Wide Range ◽  
Inertial Regime

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$-rheology that does not suffer from such defects is proposed. In the framework of compressible $I$-dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.

On the Discretization of the Power-Law Hemolysis Model

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Mohammad M. Faghih ◽  
Ahmed Islam ◽  
M. Keith Sharp
Keyword(s):  
Fluid Dynamics ◽  
Power Law ◽  
Velocity Fields ◽  
Radial Expansion ◽  
Complex Flows ◽  
Cfd Simulations ◽  
Large Exponent ◽  
Computer Based ◽  
Computational Fluid Dynamics Cfd ◽  
Simple Flows

Abstract Flow-induced hemolysis remains a concern for blood-contacting devices, and computer-based prediction of hemolysis could facilitate faster and more economical refinement of such devices. While evaluation of convergence of velocity fields obtained by computational fluid dynamics (CFD) simulations has become conventional, convergence of hemolysis calculations is also essential. In this paper, convergence of the power-law hemolysis model is compared for simple flows, including pathlines with exponentially increasing and decreasing stress, in gradually expanding and contracting Couette flows, in a sudden radial expansion and in the Food and Drug Administration (FDA) channel. In the exponential cases, convergence along a pathline required from one to tens of thousands of timesteps, depending on the exponent. Greater timesteps were required for rapidly increasing (large exponent) stress and for rapidly decreasing (small exponent) stress. Example pathlines in the Couette flows could be fit with exponential curves, and convergence behavior followed the trends identified from the exponential cases. More complex flows, such as in the radial expansion and the FDA channel, increase the likelihood of encountering problematic pathlines. For the exponential cases, comparison of converged hemolysis values with analytical solutions demonstrated that the error of the converged solution may exceed 10% for both rapidly decreasing and rapidly increasing stress.

Dependence of the Coefficient of Friction on the Sliding Conditions in the High Velocity Range

1999 ◽  
Vol 121 (1) ◽  
pp. 35-41 ◽  
Author(s):  
A. Molinari ◽  
Y. Estrin ◽  
S. Mercier
Keyword(s):  
Coefficient Of Friction ◽  
High Velocity ◽  
Numerical Solutions ◽  
Constitutive Relations ◽  
Shear Banding ◽  
Normal Pressure ◽  
Adiabatic Shear ◽  
Velocity Range ◽  
Adiabatic Shear Banding ◽  
The Coefficient Of Friction

The velocity, normal pressure, and slider size dependence of the coefficient of dry friction of metals in the range of high sliding velocities (V ≥ 1 m/s) is investigated theoretically. Failure of the adhesive junctions by adiabatic shear banding is considered as the underlying process. The concept of asperity shearing by the adiabatic shear banding mechanism represents a new approach to unlubricated high velocity friction. Analytical solutions of a coupled thermomechanical problem are given for two constitutive relations. Numerical solutions for steel-on-steel friction showing a decrease of the coefficient of friction with the sliding velocity for different normal pressures are presented. The model is considered to be adequate in the velocity range of 1–10 m/s where friction enhanced oxidation or surface melting are believed not to interfere with the asperity shearing process.

Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes

2003 ◽  
Vol 2 (2) ◽  
pp. 175-192 ◽  
Author(s):  
John A. Ekaterinaris
Keyword(s):  
Numerical Solutions ◽  
Sound Propagation ◽  
Finite Difference Methods ◽  
High Order ◽  
Curvilinear Coordinates ◽  
Compressible Turbulence ◽  
Test Problems ◽  
Complex Flows ◽  
Time Marching ◽  
Implicit And Explicit

High-order accurate, finite-difference methods, such as the compact centered schemes with spectral-type or characteristic-based filters and the weighted essentially non-oscillatory (WENO) schemes, which are used in high resolution CFD solutions and for DNS or LES of compressible turbulence, are applied to aeroacoustics. Implicit and explicit schemes are used for time marching. The accuracy of the numerical solutions is evaluated for test problems. It is found that these methods are appropriate for sound propagation in complex flows that require use of curvilinear coordinates. Therefore they are applicable for the prediction of sound generation from both smooth subsonic flows, and transonic or supersonic flows with discontinuities.

On Numerical Simulations of Complex Flows of Viscoplastic Materials

2000 ◽  
Author(s):  
Paulo R. Souza Mendes ◽  
Mônica F. Naccache ◽  
Harry T. M. Vinagre
Keyword(s):  
Flow Visualization ◽  
Flow Pattern ◽  
Numerical Solutions ◽  
Momentum Balance ◽  
Complex Flows ◽  
Large Expansion ◽  
Liquid Model ◽  
Axisymmetric Channel ◽  
Visualization Experiments ◽  
The One

Abstract The performance of a typical numerical simulation for complex flows of viscoplastic materials was examined. The inertialess flow of viscoplastic materials through an axisymmetric channel formed by an abrupt expansion followed by a contraction was employed with this purpose. Flow visualization experiments were performed with a well characterized Carbopol aqueous solution. Numerical solutions of the mass and momentum balance equations were obtained, using the Generalized Newtonian Liquid model with a biviscosity function. The flow visualization results showed that the flow pattern is essentially Newtonian for large expansion lengths. For smaller expansion lengths, however, flow is observed only in an inner axisymmetric region whose diameter is approximately the same as the one of the inlet and outlet tubes. Outside this region the flow is stagnant, and a slip interface between these two regions seems to occur. The corresponding numerical solution was not capable of predicting the observed flow pattern.

Time-dependent kinematic dynamos with stationary flows

1989 ◽  
Vol 425 (1869) ◽  
pp. 407-429 ◽  
Keyword(s):  
Reynolds Number ◽  
Numerical Solutions ◽  
Magnetic Reynolds Number ◽  
Velocity Models ◽  
Stationary Flows ◽  
Induction Equation ◽  
Steady Solutions ◽  
Simple Flows ◽  
Magnetic Induction Equation ◽  
Stationary Velocity

Numerical solutions to the magnetic induction equation in a sphere have been obtained for a number of stationary velocity models. By searching for non-steady magnetic fields and in some circumstances showing that all magnetic field modes decay, the inability of several earlier researchers to find convergent steady solutions is explained. Results of previous authors are generally confirmed, but also extended to cover non-steady fields, different values of magnetic Reynolds number and other parameters, and higher truncation limits. Some non-decaying fields are found where only decaying or non-convergent results have previously been reported. Two flows ∊ s 0 2 + t 0 2 and ∊ s 0 2 + t 0 1 , each consisting of two very simple axisymmetric rolls are seen to sustain growing fields provided that (i) the magnetic Reynolds number R and the poloidal to toroidal flow ratio ∊ are of appropriate magnitudes, and (ii) the meridional s 0 2 flow is directed inwards along the equatorial plane and out towards the poles. An even simpler axisymmetric single roll flow ∊ s 0 1 + t 0 1 is also seen to support growing fields for appropriate ∊ and R . These simple flows dispel the somewhat prevalent belief that dynamo maintenance relies on the supporting flow being complex, and having length scale significantly less than that of the conducting fluid volume.

scholarly journals A Continuum Model for Complex Flows of Shear Thickening Colloidal Solutions

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 21
Author(s):  
Joseph Green ◽  
Daniel Ryckman ◽  
Michael Cromer
Keyword(s):  
Continuum Model ◽  
Full Range ◽  
Shear Thickening ◽  
Free Path Length ◽  
Mean Free Path ◽  
Colloidal Solutions ◽  
Complex Flow ◽  
Complex Flows ◽  
Theoretical Understanding ◽  
Simple Flows

Colloidal shear thickening fluids (STFs) have applications ranging from commercial use to those of interest to the army and law enforcement, and the oil industry. The theoretical understanding of the flow of these particulate suspensions has predominantly been focused through detailed particle simulations. While these simulations are able to accurately capture and predict the behavior of suspensions in simple flows, they are not tractable for more complex flows such as those occurring in applications. The model presented in this work, a modification of an earlier constitutive model by Stickel et al. J. Rheol. 2006, 50, 379–413, describes the evolution of a structure tensor, which is related to the particle mean free-path length. The model contains few adjustable parameters, includes nonlinear terms in the structure, and is able to predict the full range of rheological behavior including shear and extensional thickening (continuous and discontinuous). In order to demonstrate its capability for complex flow simulations, we compare the results of simulations of the model in a simple one-dimensional channel flow versus a full two-dimensional simulation. Ultimately, the model presented is a continuum model shown to predict shear and extensional thickening, as observed in experiment, with a connection to the physical microstructure, and has the capability of helping understand the behavior of STFs in complex flows.

Application of Turbulence Models to Separated Flow Over Rough Surfaces

1995 ◽  
Vol 117 (2) ◽  
pp. 234-241 ◽  
Author(s):  
V. C. Patel ◽  
J. Y. Yoon
Keyword(s):  
Sand Dune ◽  
Numerical Solutions ◽  
Turbulence Models ◽  
Separated Flow ◽  
Complex Flows ◽  
Flow Equations ◽  
Wide Range ◽  
Wall Flow ◽  
Extensive Experimental Data ◽  
Moody Diagram

Principal results of classical experiments on the effects of sandgrain roughness are briefly reviewed, along with various models that have been proposed to account for these effects in numerical solutions of the fluid-flow equations. Two models that resolve the near-wall flow are applied to the flow in a two-dimensional, rough-wall channel. Comparisons with analytical results embodied in the well-known Moody diagram show that the k–ω model of Wilcox performs remarkably well over a wide range of roughness values, while a modified two-layer k–ε based model requires further refinement. The k–ω model is applied to water flow over a fixed sand dune for which extensive experimental data are available. The solutions are found to be in agreement with data, including the flow in the separation eddy and its recovery after reattachment. The results suggest that this modeling approach may be extended to other types of surface roughness, and to more complex flows.

scholarly journals On Magnetohydrodynamic Flow of Viscoelastic Nanofluids with Homogeneous–Heterogeneous Reactions

Coatings ◽  
2020 ◽  
Vol 10 (1) ◽  
pp. 55 ◽  
Author(s):  
Metib Alghamdi
Keyword(s):  
Nonlinear Systems ◽  
Mass Transport ◽  
Transport Process ◽  
Numerical Solutions ◽  
Constitutive Relations ◽  
Viscous Fluids ◽  
Heterogeneous Reactions ◽  
Second Grade ◽  
Heat And Mass Transport ◽  
Mass Transport Process

This article explores magnetohydrodynamic stretched flow of viscoelastic nanofluids with heterogeneous–homogeneous reactions. Attention in modeling has been specially focused to constitutive relations of viscoelastic fluids. The heat and mass transport process is explored by thermophoresis and Brownian dispersion. Resulting nonlinear systems are computed for numerical solutions. Findings for temperature, concentration, concentration rate, skin-friction, local Nusselt and Sherwood numbers are analyzed for both second grade and elastico-viscous fluids.

Discretization Error Estimation in Transient Flow Simulations

2016 ◽  
Author(s):  
Ismail B. Celik ◽  
Zhiyuan Ma ◽  
Sofiane Benyahia
Keyword(s):  
Error Estimation ◽  
Transient Flow ◽  
Burgers Equation ◽  
Steady Flows ◽  
Reasonable Accuracy ◽  
Complex Flows ◽  
Two Phase ◽  
Flow Simulations ◽  
Transient Error ◽  
Simple Flows

Most methods presented in the literature for estimation of discretization errors focus primarily on steady flows. The transport of error in strongly transient flow has not been adequately addressed. Issues related to transient error calculations are discussed and some methods that are viable for such applications are proposed. Examples are presented on simple flows such as transient Burgers equation followed by applications to more complex flows, e.g. two-phase gas-solid flow relevant fluidized beds. It is demonstrated that error estimation can be made with reasonable accuracy using a combination of various methods.

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