Time-Dependent Simulations of Shear-Thinning Elastic Flows Through Contractions

2001 ◽  
Author(s):  
Paulo J. Oliveira
Keyword(s):  
Steady State ◽  
Unsteady Flow ◽  
Experimental Work ◽  
Shear Thinning ◽  
Time Dependent ◽  
Numerical Work ◽  
Viscoelastic Models ◽  
Vortex Merging ◽  
Constant Viscosity ◽  
Steady State Solutions

Abstract Past numerical work with constant-viscosity viscoelastic fluids through planar contractions has enabled steady-state solutions to be obtained at relatively high Weissenberg numbers (We up to 10). Those solutions for the upper-convected Maxwell and Oldroyd-B models showed steady flow patterns for increasing We with the appearance of lip-vortices, vortex growth, and comer-lip vortex merging, in agreement with recent simulations and some experimental work. When similar simulations were performed with two shear-thinning viscoelastic models, namely the Phan-Thien – Tanner and the Giesekus models, steady state solutions could not be obtained beyond a certain value of We, but the solution was seen to follow a periodic unsteady flow pattern. The present paper reports preliminary numerical results which highlight the formation of the lip vortices through a sequence of time dependent events.

scholarly journals Thermal ignition in a reactive slab with unsymmetric boundary temperatures

1983 ◽  
Vol 24 (3) ◽  
pp. 279-288 ◽  
Author(s):  
K. K. Tam ◽  
P. B. Chapman
Keyword(s):  
Steady State ◽  
Critical Role ◽  
Upper And Lower Solutions ◽  
Lower Solution ◽  
Time Dependent ◽  
Thermal Ignition ◽  
Time Dependent Problem ◽  
Steady State Solutions

AbstractThe problem of thermal ignition in a reactive slab with unsymmetric temperatures equal to 0 and T is considered. Steady state upper and lower solutions are constructed. It is found that T plays a critical role. Results similar to the case with symmetric boundary temperatures are expected when T is small. When T is sufficiently large, there is only one steady state upper or lower solution. The time dependent problem is then considered. Phenomena suggested by studying the upper and lower steady state solutions are confirmed.

Laser Beam-Hygroscopic Aerosol Interactions

1977 ◽  
Vol 99 (2) ◽  
pp. 281-286 ◽  
Author(s):  
G. E. Caledonia ◽  
J. D. Teare
Keyword(s):  
Steady State ◽  
Laser Beam ◽  
Water Droplet ◽  
Atmospheric Aerosol ◽  
Phase Shifts ◽  
Time Dependent ◽  
Small Water ◽  
Steady State Solutions

A model for the prediction of the temperature and vapor fields created about a small water droplet undergoing irradiation by a laser beam has been developed. Time-dependent and steady-state solutions of the model are discussed. Estimates of characteristic phase shifts to be expected in propagating through standard atmospheric aerosol distributions are also presented. While the model is quite general, the calculations are limited to DF laser wavelengths.

scholarly journals Steady-state flow of a shear-thinning liquid in an unbounded pipeline system

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Giovanni P. Galdi ◽  
Carlo R. Grisanti
Keyword(s):  
Steady State ◽  
Cross Section ◽  
Existence And Uniqueness ◽  
Shear Thinning ◽  
Pipeline System ◽  
Constant Cross Section ◽  
Steady State Flow ◽  
Compactness Property ◽  
Newtonian Liquids ◽  
Steady State Solutions

AbstractWe show existence and uniqueness of steady-state solutions to the equations of generalized Newtonian liquids of shear-thinning type in an unbounded region that includes semi-infinite cylinders of constant cross-section (pipeline system). This result is established under the assumption that the datum (flow-rate) is sufficiently small. The main feature of our approach is the proof of a “global compactness” property of the sequence of approximating solutions.

Numerical solutions for the time-dependent viscous flow between two rotating coaxial disks

1965 ◽  
Vol 21 (4) ◽  
pp. 623-633 ◽  
Author(s):  
Carl E. Pearson
Keyword(s):  
Steady State ◽  
Viscous Flow ◽  
Numerical Solutions ◽  
Preceding Paper ◽  
Reynolds Numbers ◽  
Time Dependent ◽  
Main Body ◽  
Rotating Disks ◽  
High Reynolds ◽  
Steady State Solutions

The nature of the steady-state viscous flow between two large rotating disks has often been discussed, usually qualitatively, in the literature. Using a version of the numerical method described in the preceding paper (Pearson 1965), digital computer solutions for the time-dependent case are obtained (steady-state solutions are then obtainable as limiting cases for large times). Solutions are given for impulsively started disks, and for counter-rotating disks. Of interest is the fact that, at high Reynolds numbers, the solution for the latter problem is unsymmetrical; moreover, the main body of the fluid rotates at a higher angular velocity than that of either disk.

scholarly journals Numerical Modeling of a Short-Dwell Coater for Bio-Based Coating Applications

Coatings ◽  
2020 ◽  
Vol 11 (1) ◽  
pp. 13
Author(s):  
Ebrahim Gozali ◽  
Lars Järnström ◽  
Konstantinos Papadikis ◽  
Alamin Idris
Keyword(s):  
Shear Thinning ◽  
Deborah Number ◽  
Coating Material ◽  
Cfd Simulations ◽  
Viscous Forces ◽  
Viscoelastic Models ◽  
Critical Issues ◽  
Constant Viscosity ◽  
Coated Surface ◽  
Computational Fluid Dynamics Cfd

Computational fluid dynamics (CFD) simulations were used for the evaluation of critical issues associated with coating processes with the aim of developing and optimizing this important industrial technology. Four different models, namely, the constant viscosity, shear thinning, Oldroyd-B viscoelastic, and Giesekus models, were analyzed and compared in a short-dwell coater (SDC) using a bio-based coating material. The simulation results showed that the primary vortex formations predicted by the viscoelastic models were highly dependent on the flow Deborah number, resulting in uneven stress distribution over the coated surface. For the viscoelastic models, the dominance of elastic forces over viscous forces gave rise to significant normal stress difference, primarily along the surface of the substrate paper. The shear-thinning phenomena predicted by the Giesekus model, however, tended to relax the stress development in contrast to the Oldroyd-B model. The observations indicate that a reduced coating velocity or modification of the coating material with a reduced relaxation time constant can significantly enhance the uniformity and thickness of the coating over the coated surface under controlled conditions.

scholarly journals The solution of Problems Involving the Melting and Freezing of Finite Slabs by a Method due to Portnov

1964 ◽  
Vol 14 (2) ◽  
pp. 109-128 ◽  
Author(s):  
F. Jackson
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Temperature Distribution ◽  
Heat Fluxes ◽  
Poisson Integral ◽  
Time Dependent ◽  
Arbitrary Time ◽  
Infinite Slab ◽  
The Face ◽  
Steady State Solutions

In a recent paper (1) Portnov used a form of Poisson integral to find the exact solution for the temperature distribution in a freezing semi-infinite slab occupying the region x > 0, and having an arbitrary time dependent temperature applied at the face x = 0. Previously, Boley (2) had used a method based on Duhamel's theorem to find solutions for problems involving melting, in both finite and semi-finite regions, caused by time dependent heat fluxes. Steady-state solutions have been investigated by Landau (3), Masters (4) and others (5).

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current

1968 ◽  
Vol 2 (1) ◽  
pp. 51-57 ◽  
Author(s):  
R. C. Hewson-Browne ◽  
D. N. Burghes
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Time History ◽  
Time Dependent ◽  
Two Dimensional ◽  
Dimensional Problem ◽  
Line Current ◽  
History Of ◽  
Steady State Solutions ◽  
The Magnetic Field

This paper concerns the time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current. The two-dimensional problem is formulated and solved with two particular classes of solutions being given; namely, the steady-state solutions and the time-history of the interaction with a cloud of flux.

scholarly journals Comments on “The Interaction of an Eastward-Flowing Current and an Island: Sub- and Supercritical Flow”

2016 ◽  
Vol 46 (7) ◽  
pp. 2263-2265 ◽  
Author(s):  
Peter G. Baines ◽  
Roger L. Hughes
Keyword(s):  
Steady State ◽  
Numerical Model ◽  
Rossby Wave ◽  
Rossby Waves ◽  
Wave Theory ◽  
Time Dependent ◽  
Physical Oceanography ◽  
Upstream Side ◽  
Steady State Solutions ◽  
Upstream Waves

AbstractIn regards to the recent paper by Pedlosky and Spall (Journal of Physical Oceanography, November 2015), this comment maintains that the steady-state solutions of Rossby waves in a uniform eastward current past an island have waves on the upstream side that are not caused by the island because of inappropriate boundary conditions and the assumed form of the solution. The solutions are interesting but are not the solutions to the problem as posed in their paper. Similar upstream waves in a time-dependent numerical model are also inconsistent with linear Rossby wave theory, though the reasons for their presence are uncertain.

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