A finite element convergence study for shear‐thinning flow problems

Karagiannis, A.; Mavridis, H.; Hrymak, Andrew N.; Vlachopoulos, J.

doi:10.1002/fld.1650080202

Cited by 16 publications

(6 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Early work on linear viscoelastic flexure of the oceanic lithosphere has already shown that the Maxwell relaxation time can attain the geological timescale [ Beaumont , 1978], De ≫ 0.5; that is, essentially elastic solutions are obtained. Results from laboratory experiments of olivine rheology [ Kohlstedt et al , 1995] confirm this finding and additionally indicate that the Maxwell time is not constant but decreases with increasing strain rate; this produces a shear thinning flow, which is well known in fluid dynamics [ Karagiannis et al , 1988]. This result prompted the development of alternative, solid mechanical approaches, that use idealized nonlinear rheologies such as elastoplastic [ Chery et al , 1991] and full nonlinear elastoviscoplastic formulations [ Regenauer‐Lieb and Yuen , 1998; Albert et al , 2000; Branlund et al , 2001].…”

Section: Resultsmentioning

confidence: 88%

Dynamics of retreating slabs: 1. Insights from two‐dimensional numerical experiments

et al. 2003

View full text Add to dashboard Cite

[1] We use two-dimensional numerical experiments to investigate the long-term dynamics of an oceanic slab. Two problems are addressed: one concerning the influence of rheology on slab dynamics, notably the role of elasticity, and the second dealing with the feedback of slab-mantle interaction to be resolved in part 2. The strategy of our approach is to formulate the simplest setup that allows us to separate the effects of slab rheology (part 1) from the effects of mantle flux (part 2). Therefore, in this paper, we apply forces to the slab using simple analytical functions related to buoyancy and viscous forces in order to isolate the role of rheology on slab dynamics. We analyze parameters for simplified elastic, viscous, and nonlinear viscoelastoplastic single-layer models of slabs and compare them with a stratified thermomechanical viscoelastoplastic slab embedded in a thermal solution. The near-surface behavior of slabs is summarized by assessing the amplitude and wavelength of forebulge uplift for each rheology. In the complete thermomechanical solutions, vastly contrasting styles of slab dynamics and force balance are observed at top and bottom bends. However, we find that slab subduction can be modeled using simplified rheologies characterized by a narrow range of selected benchmark parameters. The best fit linear viscosity ranges between 5 Â 10 22 Pa s and 5 Â 10 23 Pa s. The closeness of the numerical solution to nature can be characterized by a Deborah number >0.5, indicating that elasticity is an important ingredient in subduction.

show abstract

Section: Resultsmentioning

confidence: 88%

Dynamics of retreating slabs: 1. Insights from two‐dimensional numerical experiments

et al. 2003

View full text Add to dashboard Cite

show abstract

“…This policy resulted in a large number of nonlinear iterations, normally 10-17 iterations, especially when the Picard-pathline iteration scheme was used. No convergence acceleration techniques were employed in this study although this could be a very attractive strategy [28] in light of the high cost of the 3-D numerical problems.…”

Section: Contact Line Determinationmentioning

confidence: 99%

“…The contact point (YA, ZA) is then calculated by substitution into the polynomial (25) form leads to divergence of the nonlinear iteration procedure. A stabilizing underrelaxation scheme was employed and the free surface coordinates are calculated as, z = a+ by+ cy2+dy 3 , (28) …”

Section: Ay=~ V--and Az=~ W--u Umentioning

confidence: 99%

Three-dimensional studies on bicomponent extrusion

1990

Self Cite

View full text Add to dashboard Cite

The present work is concerned with the mathematical modelling and numerical simulation of three-dimensional (3-D) bicomponent extrusion. The objective is to provide an understanding of the flow phenomena involved and to investigate their impact on the free surface shape and interface configuration of the extruded article. A finite element algorithm for the 3-D numerical simulation of bicomponent stratified free surface flows is described. The presence of multiple free surfaces (layer interface and external free surfaces) requires special free surface update schemes. The pressure and viscous stress discontinuity due to viscosity mismatch at the interface between the two stratified components is handled with both a double node ( u -v -w -P 1 -P 2 -h l -h 2) formulation and a penalty function ( u -v -w -P -h 1-h2) formulation.The experimentally observed tendency of the less viscous layer to encapsulate the more viscous layer in stratified bicomponent flows of side-by-side configuration is established with the aid of a fully 3-D analysis in agreement with experimental evidence. The direction and degree of encapsulation depend directly on the viscosity ratio of the two melts. For shear thinning melts exhibiting a viscosity crossover point, it is demonstrated that interface curvature reversal may occur if the shearing level is such that the crossover point is exceeded. Extrudate bending and distortion of the bicomponent system because of the viscosity mismatch is shown. For flows in a sheath-core configuration it is shown that the viscosity ratio may have a severe effect on the swelling ratio of the bicomponent system.Modelling of the die section showed that the boundary condition imposed at the fluid/fluid/wall contact point is critical to the accuracy of the overall solution.

show abstract

“…1b) were presented by Skelland (11) , Kozicki and Tiu (12) and Cheremisinoff (13) . Ta-Jo (14) and Karagiannis et al (15) determined the pressure drop-¯ow rate relationship for power-law uids by the Galerkin ®nite-element method, which is applicable to ducts of any geometry. The theory of the steady slow motion of a non-Newtonian¯uid through a slightly tapered tube was proposed by Syoten and Tadayoshi (16) .…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of the Flow of Power-Law Gel Propellants in Converging Injectors

Rahimi

Natan

2000

Propellants Explos. Pyrotech

View full text Add to dashboard Cite

The governing equations of the steady, incompressible, isothermal, laminar flow of a power‐law, shear‐thinning gel propellant in a converging injector were formulated. The equations were transformed to a ψ–ω system, then discretized and solved. A numerical algorithm was developed for the solution of the flowfield. A parametric investigation was conducted to evaluate the effect of the injector geometry and the flow rate on the velocity and viscosity fields, for various gel propellants. In comparison to a straight injector, a convergent one can produce additional decrease in the mean apparent viscosity of the fluid. The mean apparent viscosity decreases significantly with increasing the convergence angle of the injector. In general, increasing the gel flow rate results in a decrease of the mean apparent viscosity of the fluid. Increasing the gellant content of gel propellants results in an increase of the fluid viscosity that decreases when the gel flows through the injector. Gels of different gellant content that flow through the same geometry injector exhibit similar relative reduction in viscosity.

show abstract

A finite element convergence study for shear‐thinning flow problems

Cited by 16 publications

References 15 publications

Dynamics of retreating slabs: 1. Insights from two‐dimensional numerical experiments

Dynamics of retreating slabs: 1. Insights from two‐dimensional numerical experiments

Three-dimensional studies on bicomponent extrusion

Numerical Solution of the Flow of Power-Law Gel Propellants in Converging Injectors

Contact Info

Product

Resources

About