Flow development of Herschel–Bulkley fluids in a sudden three-dimensional square expansion

Burgos, Gilmer R.; Alexandrou, Andreas N.

doi:10.1122/1.550993

Cited by 61 publications

(45 citation statements)

References 21 publications

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“…When the flow is driven by a pressure difference P between the inlet and outlet, a challenge is to identify the critical value of P below which there is no flow and the whole domain is unyielded. It is worth noticing that this type of test problems has motivated one of the few successful three-dimensional viscoplastic flow simulations, namely, the one discussed in Burgos and Alexandrou [1999] for a Herschel-Bulkley flow in a square duct with a 1:2 expansion.…”

Section: A Brief History Of Computational Viscoplasticitymentioning

confidence: 99%

On the Numerical Simulation of Viscoplastic Fluid Flow

Glowinski

Wachs

2011

Handbook of Numerical Analysis

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Section: A Brief History Of Computational Viscoplasticitymentioning

confidence: 99%

On the Numerical Simulation of Viscoplastic Fluid Flow

Glowinski

Wachs

2011

Handbook of Numerical Analysis

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“…In Burgos et al [108], the Herschel-Bulkley model in equation (33) in Table 5 and the approach of the previous papers [105][106][107] is expanded to include the effect of the evolution of microstructure via an equation for t ∂ ∂λ very similar to equation (15) in fact, a way of introducing two relaxation processes as in Quaak [47]). In addition, the yield stress, consistency index K and power law index n are now all assumed to be functions of the volume fraction solid s f and the structural parameter λ .…”

Section: Alexandrou Burgos and Co-workersmentioning

confidence: 99%

“…Burgos and Alexandrou [106] , where H and V are characteristic length and velocity scales), which indicates the importance of the yield stress relative to the inertia forces, and the Reynolds number (see Fig. 31).…”

Section: Alexandrou Burgos and Co-workersmentioning

confidence: 99%

Modelling the Semisolid Processing of Metallic Alloys

Atkinson

2005

ChemInform

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Semi-solid processing of metallic alloys and composites utilises the thixotropic behaviour of materials with non-dendritic microstructure in the semi-solid state. The family of innovative manufacturing methods based on this behaviour has been developing over the last twenty years or so and originates from scientific work at MIT in the early 1970s. Here, a summary is given of:-routes to spheroidal microstructures; types of semi-solid processing; and advantages and disadvantages of these routes.Background rheology and mathematical theories of thixotropy are then covered as precursors to the main focus of the review on transient behaviour of semi-solid alloy slurries and computational modelling. Computational Fluid Dynamics (CFD) can be used to predict die filling. However, some of the reported work has been based on rheological data obtained in steady state experiments, where the semi-solid material has been maintained at a particular shear rate for some time. In reality, in thixoforming, the slurry undergoes a sudden increase in shear rate from rest to 100s -1 or more as it enters the die. This change takes place in less than a second. Hence, measuring the transient rheological response under rapid changes in shear rate is critical to the development of modelling of die filling and successful die design for industrial processing. The modelling can be categorised as one phase or two phase and as finite difference or finite element. Recent work by Alexandrou and co-workers and, separately Modigell and co-workers, has led to the production of maps which, respectively summarise regions of stable/unstable flow and regions of laminar/transient/turbulent fill. These maps are of great potential use for the prediction of appropriate process parameters and avoidance of defects. A novel approach to modelling by Rouff and coworkers involves micro-modelling of the 'active zone' around spheroidal particles.There is little quantitative data on the discrepancies or otherwise between die fill simulations and experimental results (usually obtained through interrupted filling).There are no direct comparisons of the capabilities of various software packages to model the filling of particular geometries accurately. In addition, the modelling depends on rheological data and this is sparse, particularly for the increasingly complex two-phase models. Direct flow visualisation can provide useful insight and avoid the effects of inertia in interrupted filling experiments.

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“…The ideal Bingham-plastic behavior can be approximated by relatively large values of m. The accuracy and effectiveness of the Papanastasiou model have been discussed by several researchers. [26][27][28][29][30][31] Dimensional analysis shows that filling depends on two dimensionless parameters, the Reynolds number and the Bingham number, given by [13] where is the density, U 0 is the average inlet velocity, and H is the inlet height.…”

Section: B the Role Of Yield Stress In Modeling The Rheological Behamentioning

confidence: 99%

Yield behavior of commercial Al-Si alloys in the semisolid state

Pan¹,

Apelian²,

Alexandrou

2004

Metall Mater Trans B

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Systematic experimental work and modeling efforts have been conducted to characterize the yield behavior of commercial aluminum alloys in the semisolid state. In this study, extensive compression experiments were performed to measure the yield stress of semisolid aluminum slurries at high solid fractions (0.5 to 1.0), and a cone penetration method was employed to measure yield stress at low solid fractions (Ͻ0.5). A functional relationship between yield stress and temperature/solid fraction has been established for these alloys. The effect of the processing route on the resultant yield stress of the material in the semisolid state was studied by evaluating commercial A356 billets manufactured via magnetohydrodynamic stirring, grain refining, and UBE's new rheocasting (NRC) processes, respectively. Detailed microstructure observations and image analyses reveal that the difference in yield-stress values among the alloys evaluated is intricately related to the semisolid structure. At a given solid fraction, the yield stress of semisolid slurries depends on microstructural indices (i.e., entrapped-liquid content, shape factor of the alpha phase, and the alpha particle size). In addition, numerical simulation results indicate that the finite yield stress of semisolid metals plays a significant role in determining the flow pattern during die filling. Depending on processing conditions, five distinct filling patterns (shell, disk, mound, bubble, and transition) have been identified and confirmed through experimental observations. Recent simulations demonstrate that the finite yield stress is also responsible for flow instabilities encountered in commercial forming operations, such as "toothpaste behavior." Specifically, most flow instabilities can be avoided by properly controlling processing parameters and the initial semisolid microstructure. A stability map that provides a control guide for semisolid processing has been developed and is presented.

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Flow development of Herschel–Bulkley fluids in a sudden three-dimensional square expansion

Cited by 61 publications

References 21 publications

On the Numerical Simulation of Viscoplastic Fluid Flow

On the Numerical Simulation of Viscoplastic Fluid Flow

Modelling the Semisolid Processing of Metallic Alloys

Yield behavior of commercial Al-Si alloys in the semisolid state

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