Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel–Bulkley fluids

Huilgol, R. R.; You, Zhenjiang

doi:10.1016/j.jnnfm.2005.04.004

Cited by 113 publications

(90 citation statements)

References 48 publications

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“…e minimum stress value required for initiation of the molten feedstock flow is termed as yield stress [25]. In our study, the Casson model [26] was used to calculate the yield stress values of feedstocks with different binder contents at temperatures ranging from 130 to 170°C, and the results are shown in Figure 4.…”

Section: Rheological Properties Shear Rate Dependence Of the Feedstomentioning

confidence: 99%

Development of Hypereutectic AlSi Alloy Powder Injection Molding Feedstocks by Rheological Analysis

Han

2018

Advances in Materials Science and Engineering

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e comprehensive properties of a feedstock have a critical influence on the powder injection molding process. Proper feedstock with homogeneous structure, favorable flow characteristic, and moldability is the prerequisite for obtaining a final part with excellent comprehensive properties. e objective of the present work was to develop an optimal feedstock for fabrication of hypereutectic AlSi (20 wt.%) alloy parts by the powder injection molding technique. For this purpose, micron-sized hypereutectic AlSi (20 wt.%) alloy powder was mixed with different amounts of a binder which consisted of 35 wt.% high-density polyethylene, 62 wt.% carnauba wax, and 3 wt.% stearic acid. e binder contents of the feedstocks were in the range from 13 wt.% to 21 wt.%. e influences of binder content, shear rate, and temperature on the rheological behaviors of feedstocks have been investigated via a capillary rheometer. e feedstock with 21 wt.% binder exhibited a variable flow behavior and was culled. e rest of the feedstocks showed a pseudoplastic behavior. Comprehensive analysis of rheological parameters such as the flow behavior index, yield stress, flow activation energy, and the general moldability index, the feedstock with 17 wt.% binder exhibited the best rheological performance and favorable moldability. e molded part with 17 wt.% binder had constant density, good shape retention, and stiffness as well as homogeneous distribution of the powder and binder. After solvent debinding, the debound item showed a homogeneous porous structure which is suitable for the subsequent thermal debinding and sintering processes.

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Section: Rheological Properties Shear Rate Dependence Of the Feedstomentioning

confidence: 99%

Development of Hypereutectic AlSi Alloy Powder Injection Molding Feedstocks by Rheological Analysis

Han

2018

Advances in Materials Science and Engineering

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“…We consider a family of numerical flux functions which define a well-balanced finite volume solver. System (24) can be seen as a semi-discretization in time of a parabolic system, which for r = 0 degenerates into an hyperbolic system with source terms. Following [12], in order to obtain a well-balanced finite volume method, the numerical flux φ, approaching the flux function F (W ) at x i+1/2 , must depend on the definition of the source terms.…”

Section: Some Remarks On the Treatment Of Wet/dry Frontsmentioning

confidence: 99%

“…[33], [37,36], [24], [35], [25]) is that they use decomposition-coordination methods to solve the variational inequality associated to constitutive laws with a so-called plastic threshold (the most simple and iconic one being the Bingham model). This kind of approach takes its roots in the seminal works of Duvaut-Lions [15] and the series of papers of Glowinski and coworkers (see the recent book [22] for a detailed review), initiated at the end of the seventies and anchored in the Augmented Lagrangian formalism.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

Fernández-Nieto

Gallardo

Vigneaux

2014

Journal of Computational Physics

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This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated to the yield threshold: finitevolume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of well-balancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

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“…[34], [38,37], [25], [36], [26]) is that they use decomposition-coordination methods to solve the variational inequality associated to constitutive laws with a so-called plastic threshold (the most simple and iconic one being the Bingham model). This kind of approach takes its roots in the seminal works of Duvaut-Lions [15] and the series of papers of Glowinski and coworkers (see the recent book [23] for a detailed review), initiated at the end of the seventies and anchored in the Augmented Lagrangian formalism.…”

Section: Introductionmentioning

confidence: 99%

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

Fernández-Nieto

Gallardo

Vigneaux

2018

Journal of Computational Physics

View full text Add to dashboard Cite

This paper deals with the numerical resolution of a shallow water viscoplastic flow model. Viscoplastic materials are characterized by the existence of a yield stress: below a certain critical threshold in the imposed stress, there is no deformation and the material behaves like a rigid solid, but when that yield value is exceeded, the material flows like a fluid. In the context of avalanches, it means that after going down a slope, the material can stop and its free surface has a non trivial shape, as opposed to the case of water (Newtonian fluid). The model involves variational inequalities associated to the yield threshold: finite-volume schemes are used together with duality methods (namely Augmented Lagrangian and Bermúdez-Moreno) to discretize the problem. To be able to accurately simulate the stopping behaviour of the avalanche, new schemes need to be designed, involving the classical notion of wellbalancing. In the present context, it needs to be extended to take into account the viscoplastic nature of the material as well as general bottoms with wet/dry fronts which are encountered in geophysical geometries. We derived such schemes and numerical experiments are presented to show their performances.

show abstract

Application of the augmented Lagrangian method to steady pipe flows of Bingham, Casson and Herschel–Bulkley fluids

Cited by 113 publications

References 48 publications

Development of Hypereutectic AlSi Alloy Powder Injection Molding Feedstocks by Rheological Analysis

Development of Hypereutectic AlSi Alloy Powder Injection Molding Feedstocks by Rheological Analysis

Efficient numerical schemes for viscoplastic avalanches. Part 1: The 1D case

Efficient numerical schemes for viscoplastic avalanches. Part 2: The 2D case

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