Three Dimensional Pulsatile Non-Newtonian Flow in a Stenotic Vessel

2014 ◽  
pp. 55-64 ◽  
Author(s):  
I. Husain ◽  
C. Langdon ◽  
J. Schwark
Keyword(s):  
Three Dimensional ◽  
Newtonian Flow ◽  
Stenotic Vessel

scholarly journals Exact tensor closures for the three-dimensional Jeffery's equation

2011 ◽  
Vol 680 ◽  
pp. 321-335 ◽  
Author(s):  
STEPHEN MONTGOMERY-SMITH ◽  
WEI HE ◽  
DAVID A. JACK ◽  
DOUGLAS E. SMITH
Keyword(s):  
Fibre Orientation ◽  
Elliptic Integral ◽  
Moment Tensor ◽  
Three Dimensional ◽  
Exact Formula ◽  
Fourth Moment ◽  
Newtonian Flow ◽  
Curve Fit ◽  
Explicit Formulae ◽  
Jeffery’S Equation

This paper presents an exact formula for calculating the fourth-moment tensor from the second-moment tensor for the three-dimensional Jeffery's equation. Although this approach falls within the category of a moment tensor closure, it does not rely upon an approximation, either analytic or curve fit, of the fourth-moment tensor as do previous closures. This closure is orthotropic in the sense of Cintra & Tucker (J. Rheol., vol. 39, 1995, p. 1095), or equivalently, a natural closure in the sense of Verleye & Dupret (Developments in Non-Newtonian Flow, 1993, p. 139). The existence of these explicit formulae has been asserted previously, but as far as the authors know, the explicit forms have yet to be published. The formulae involve elliptic integrals, and are valid whenever fibre orientation was isotropic at some point in time. Finally, this paper presents the fast exact closure, a fast and in principle exact method for solving Jeffery's equation, which does not require approximate closures nor the elliptic integral computation.

The development of asymmetry and period doubling for oscillatory flow in baffled channels

1996 ◽  
Vol 328 ◽  
pp. 19-48 ◽  
Author(s):  
E. P. L. Roberts ◽  
M. R. Mackley
Keyword(s):  
Reynolds Number ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Period Doubling ◽  
Progressive Increase ◽  
Newtonian Flow ◽  
Chaotic Flow ◽  
Spatially Periodic ◽  
Dimensional Simulation ◽  
Time Periodic

We report experimental and numerical observations on the way initially symmetric and time-periodic fluid oscillations in baffled channels develop in complexity. Experiments are carried out in a spatially periodic baffled channel with a sinusoidal oscillatory flow. At modest Reynolds number the observed vortex structure is symmetric and time periodic. At higher values the flow progressively becomes three-dimensional, asymmetric and aperiodic. A two-dimensional simulation of incompressible Newtonian flow is able to follow the flow pattern at modest oscillatory Reynolds number. At higher values we report the development of both asymmetry and a period-doubling cascade leading to a chaotic flow regime. A bifurcation diagram is constructed that can describe the progressive increase in complexity of the flow.

Three-dimensional coating flow of nematic liquid crystal on an inclined substrate

2015 ◽  
Vol 26 (5) ◽  
pp. 647-669 ◽  
Author(s):  
M. A. LAM ◽  
L. J. CUMMINGS ◽  
T.-S. LIN ◽  
L. KONDIC
Keyword(s):  
Free Surface ◽  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Nonlinear Partial Differential Equation ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Linear Stability Theory ◽  
Newtonian Flow ◽  
Surface Evolution ◽  
Coating Flow

We consider a coating flow of nematic liquid crystal (NLC) fluid film on an inclined substrate. Exploiting the small aspect ratio in the geometry of interest, a fourth-order nonlinear partial differential equation is used to model the free surface evolution. Particular attention is paid to the interplay between the bulk elasticity and the anchoring conditions at the substrate and free surface. Previous results have shown that there exist two-dimensional travelling wave solutions that translate down the substrate. In contrast to the analogous Newtonian flow, such solutions may be unstable to streamwise perturbations. Extending well-known results for Newtonian flow, we analyse the stability of the front with respect to transverse perturbations. Using full numerical simulations, we validate the linear stability theory and present examples of downslope flow of nematic liquid crystal in the presence of both transverse and streamwise instabilities.

A Parametric Study on Fatigue Life for Mixed Elastohydrodynamic Lubrication Point Contacts

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Xiao-Liang Yan ◽  
Xiao-Li Wang ◽  
Yu-Yan Zhang
Keyword(s):  
Shear Stress ◽  
Fatigue Life ◽  
Three Dimensional ◽  
Elastohydrodynamic Lubrication ◽  
Point Contacts ◽  
Newtonian Flow ◽  
Lubrication Regimes ◽  
Close Relationship ◽  
Lubrication Characteristics ◽  
Effect Of Surface

The lubrication characteristics and fatigue life are numerically analyzed under full film and mixed lubrication regimes, in which the three-dimensional sinusoidal surfaces with changeable wavelengths in x and y directions are used, the geometry changes of the contact areas are described by the various ellipticity, and the non-Newtonian flow of lubricant is described by the sinh-law rheology model. The results show that the influences of characteristic shear stress, wavelength ratio, and ellipticity on lubrication characteristics and fatigue life are remarkable. The effect of surface topography on lubrication characteristics has a close relationship with speed. Increasing the ellipticity and decreasing wavelength ratio and characteristic shear stress can prolong the fatigue life.

Three-dimensional Numerical Simulation of Non-isothermal and Non-Newtonian Flow in Twin Screw Extruders

2000 ◽  
Vol 2000 (0) ◽  
pp. 151
Author(s):  
Masaru Miyazaki ◽  
Masatomo Yamaura ◽  
Tetsuyuki Takayama ◽  
Shinichi Kihara ◽  
Kazumori Funatsu
Keyword(s):  
Numerical Simulation ◽  
Three Dimensional ◽  
Newtonian Flow ◽  
Twin Screw Extruders ◽  
Twin Screw ◽  
Screw Extruders

Implementation of a Cavitation Algorithm into a Procedure for the Prediction of Non-Newtonian Flow in Hydrodynamic Journal Bearings

1987 ◽  
Vol 201 (6) ◽  
pp. 449-456
Author(s):  
P D Williams ◽  
G R Symmons
Keyword(s):  
Effective Viscosity ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Journal Bearings ◽  
Navier Stokes ◽  
Newtonian Flow ◽  
Film Rupture ◽  
Navier Stokes Equations ◽  
Finite Breadth ◽  
Newtonian Liquids

A procedure for solving the Navier–Stokes equations for the steady, three-dimensional, cavitated flow of non-Newtonian liquids within finite-breadth journal bearings is described. The method uses a finite difference approach, together with a technique known as SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) which has now become well established in the field of computational fluid dynamics. The concept of ‘effective viscosity’ to describe the non-linear dependence of shear stress on shear rate is used to predict the performance of bearings having a single axial inlet groove situated at the position of maximum clearance between the shaft and housing. The implementation of a cavitation algorithm into the equation set allows the loci of film rupture and reformation in the vicinity of the supply groove and elsewhere to be traced, these having a particularly important influence on the predicted lubricant flowrate. Results are obtained for a range of non-linearity factors and lead to the conclusion that all the important indicators of bearing performance can be determined using the technique described.

Study of the Phan-Thien–Tanner Equation of Viscoelastic Blood Non- Newtonian Flow in a Pipe-Shaped Artery under an Emotion-Induced Pressure Gradient

2012 ◽  
Vol 67 (10-11) ◽  
pp. 628-632
Author(s):  
Karem Boubaker ◽  
Yasir Khan
Keyword(s):  
Fluid Flow ◽  
Pressure Gradient ◽  
Three Dimensional ◽  
Unsteady State ◽  
Newtonian Flow ◽  
Shooting Technique ◽  
Radial Profiles ◽  
Boubaker Polynomials ◽  
Newtonian Method ◽  
Expansion Scheme

In this paper, a three-dimensional, unsteady state non-Newtonian fluid flow in a pipe-shaped artery of viscoelastic blood is considered in the presence of emotion-induced pressure gradient. The results have been expressed in terms of radial profiles of both axial velocity and viscosity and were presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of some parameters on the dynamics are analyzed.

Remarks on Unsteady Newtonian Flow Theory

1976 ◽  
Vol 27 (1) ◽  
pp. 66-74 ◽  
Author(s):  
G E Mahood ◽  
W H Hui
Keyword(s):  
Dynamic Stability ◽  
Centrifugal Force ◽  
Dynamic Theory ◽  
Three Dimensional ◽  
Newtonian Flow ◽  
Stability Derivatives ◽  
Impact Theory ◽  
High Mach ◽  
Derivatives Of ◽  
Double Limit

SummaryUnsteady high Mach number flows past oscillating cones and oscillating wedges are studied according to Newtonian impact theory, with and without centrifugal force corrections. It is found that, contrary to existing theories, the centrifugal force contribution in unsteady flow is significant and not negligible; for example, it contributes one-half to the dynamic stability derivatives of an oscillating wedge and one-third to that of an oscillating cone. It is also shown that in both cases the dynamic stability derivatives calculated by Newtonian impact theory with centrifugal force correction agree exactly with those obtained by gas-dynamic theory in the double limit γ → 1 and M∞ → ∞, independently. These conclusions are expected to hold for more general three-dimensional unsteady Newtonian flow when the Newtonian shock layer is attached.

Pulsatile Non-Newtonian Flow Characteristics in a Three-Dimensional Human Carotid Bifurcation Model

1991 ◽  
Vol 113 (4) ◽  
pp. 464-475 ◽  
Author(s):  
K. Perktold ◽  
M. Resch ◽  
H. Florian
Keyword(s):  
Shear Stress ◽  
Carotid Sinus ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Outer Wall ◽  
Maximum Diameter ◽  
Newtonian Flow ◽  
Pulse Cycle ◽  
Flow Phenomena ◽  
Human Carotid

Numerical analysis of flow phenomena and wall shear stresses in the human carotid artery bifurcation has been carried out using a three-dimensional geometrical model. The primary aim of this study is the detailed discussion of non-Newtonian flow velocity and wall shear stress during the pulse cycle. A comparison of non-Newtonian and Newtonian results is also presented. The applied non-Newtonian behavior of blood is based on measured dynamic viscosity. In the foreground of discussion are the flow characteristics in the carotid sinus. The investigation shows complex flow patterns especially in the carotid sinus where flow separation occurs at the outer wall throughout the systolic deceleration phase. The changing sign of the velocity near the outer sinus wall results in oscillating shear stress during the pulse cycle. At the outer wall of the sinus at maximum diameter level the shear stress ranges from −1.92 N/m2 to 1.22 N/m2 with a time-averaged value of 0.04 N/m2. At the inner wall of the sinus at maximum diameter level the shear stress range is from 1.16 N/m2 to 4.18 N/m2 with a mean of 1.97 N/m2. The comparison of non-Newtonian and Newtonian results indicates unchanged flow phenomena and rather minor differences in the basic flow characteristics.

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