New analysis of non‐newtonian turbulent flowndashyield‐power‐law fluids

Thomas, A. D.; Wilson, Kenneth

doi:10.1002/cjce.5450650221

Cited by 53 publications

(25 citation statements)

References 2 publications

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“…For a generalised Newtonian fluid, it is not possible in general to determine the mean velocity a priori. Correlations proposed in [10] for power law fluids and in [11] for Herschel-Bulkley fluids, provide estimates that are within 5-10% of the predicted values for all simulations here. For the Carreau-Yasuda model, a reasonable estimate (also within 10%) was achieved by using the infinite-shear viscosity, g 1 in the Blasius correlation.…”

Section: Generalised Reynolds Numbersupporting

confidence: 58%

“…384 data planes) in the axial direction, with a domain length of 5pD. A nominal bulk flow generalised Reynolds number of 7500 was chosen and the resulting parameter estimation (based on correlations in [10] and [11]) for the simulations considered here are shown in Table 3. The actual predicted mean velocity (W) defines the predicted generalised Reynolds number.…”

Section: Turbulent Pipe Flowmentioning

confidence: 99%

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Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

Rudman

Blackburn

2006

Applied Mathematical Modelling

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A spectral element-Fourier method (SEM) for Direct Numerical Simulation (DNS) of the turbulent flow of non-Newtonian fluids is described and the particular requirements for non-Newtonian rheology are discussed. The method is implemented in parallel using the MPI message passing kernel, and execution times scale somewhat less than linearly with the number of CPUs, however this is more than compensated by the improved simulation turn around times. The method is applied to the case of turbulent pipe flow, where simulation results for a shear-thinning (power law) fluid are compared to those of a yield stress (Herschel-Bulkley) fluid at the same generalised Reynolds number. It is seen that the yield stress significantly dampens turbulence intensities in the core of the flow where the quasi-laminar flow region there co-exists with a transitional wall zone. An additional simulation of the flow of blood in a channel is undertaken using a Carreau-Yasuda rheology model, and results compared to those of the one-equation Spalart-Allmaras RANS (Reynolds-Averaged NavierStokes) model. Agreement between the mean flow velocity profile predictions is seen to be good. Use of a DNS technique to study turbulence in non-Newtonian fluids shows great promise in understanding transition and turbulence in shear thinning, non-Newtonian flows.

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Section: Generalised Reynolds Numbersupporting

confidence: 58%

Section: Turbulent Pipe Flowmentioning

confidence: 99%

Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

Rudman

Blackburn

2006

Applied Mathematical Modelling

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“…Although the τ y value was low, n was also low, indicating a stronger non-Newtonian behaviour [11,12]. One notices that as Re R increased, the accuracy of RSM2 with ψ 1 increased, whereas that of κ-with ψ 1 was reduced.…”

Section: Observationsmentioning

confidence: 95%

“…Heywood and Cheng [8] provide a review of known expressions for the laminar flow of Herschel-Bulkley fluids through circular horizontal pipes.) Akin to Equation (12), expressions that relate the wall stress to the flow velocity for the turbulent flow of Herschel-Bulkley fluids have also been proposed. Heywood and Cheng [8] mention that such expressions are correlations of experimental data and are not fully theoretical.…”

Section: Herschel-bulkley Fluidsmentioning

confidence: 99%

“…Further, Wilson and Thomas [11] proposed a correlation based on the relation between the dissipative small-scale turbulent eddies and the thickness of the viscous boundary layer. This was extended to Herschel-Bulkley fluids [12] and compared against experiments by Slatter [13]. Slatter [13] reported that the correlation by Thomas and Wilson [12] is accurate in the early turbulent regime but diverges when the shear stress (or the flow velocity) increases, leading to more turbulence.…”

Section: Herschel-bulkley Fluidsmentioning

confidence: 99%

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A Wall Boundary Condition for the Simulation of a Turbulent Non-Newtonian Domestic Slurry in Pipes

Mehta

Radhakrishnan

Lier

et al. 2018

Water

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Abstract:The concentration (using a lesser amount of water) of domestic slurry promotes resource recovery (nutrients and biomass) while saving water. This article is aimed at developing numerical methods to support engineering processes such as the design and implementation of sewerage for concentrated domestic slurry. The current industrial standard for computational fluid dynamics-based analyses of turbulent flows is Reynolds-averaged Navier-Stokes (RANS) modelling. This is assisted by the wall function approach proposed by Launder and Spalding, which permits the use of under-refined grids near wall boundaries while simulating a wall-bounded flow. Most RANS models combined with wall functions have been successfully validated for turbulent flows of Newtonian fluids. However, our experiments suggest that concentrated domestic slurry shows a Herschel-Bulkley-type non-Newtonian behaviour. Attempts have been made to derive wall functions and turbulence closures for non-Newtonian fluids; however, the resulting laws or equations are either inconsistent across experiments or lack relevant experimental support. Pertinent to this study, laws or equations reported in literature are restricted to a class of non-Newtonian fluids called power law fluids, which, as compared to Herschel-Bulkley fluids, yield at any amount of applied stress. An equivalent law for Herschel-Bulkley fluids that require a minimum-yield stress to flow is yet to be reported in literature. This article presents a theoretically derived (with necessary approximations) law of the wall for Herschel-Bulkley fluids and implements it in a RANS solver using a specified shear approach. This results in a more accurate prediction of the wall shear stress experienced by a circular pipe with a turbulent Herschel-Bulkley fluid flowing through it. The numerical results are compared against data from our experiments and those reported in literature for a range of Reynolds numbers and rheological parameters that are relevant to the prediction of pressure losses in a sewerage transporting non-Newtonian domestic slurry. Nonetheless, the application of this boundary condition could be extended to areas such as chemical and food engineering, wherein turbulent non-Newtonian flows can be found.

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Hybrid rheological model for non‐Newtonian turbulent pipe flow

Wilson

Thomas²

2010

Can J Chem Eng

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Many slurry rheograms do not follow the Bingham model, but are curved (convex upwards) at low-strain rates. Alternate models such as the yield-power law (YPL), provide a good fit to the low-strain rate data, but they tend to underestimate apparent viscosities at high-strain rates. The current paper considers a hybrid rheological model consisting of a cubic-spline fit to the low-strain rate data merging into a Bingham linear model above a limiting strain rate. This model predicts turbulent flow well, depending only on the area difference between the Bingham rheogram and the cubic spline.Un bon nombre de rhéogrammes de boues liquides ne suivent pas le modèle de Bingham mais sont incurvés (convexes vers le haut) aux faibles vitesses de dilatation. Des modèles de remplacement tels que la loi rendement-puissance offrent une bonne correspondance avec les données de faibles vitesses de dilatation mais elles tendentà sous-estimer les viscosités apparentes aux vitesses de dilatationélevées. L'article présent considère un modèle rhéologique hybride composé d'une spline cubique adapté aux données de faibles vitesses de dilatation, ce systèmeétant fusionné avec un modèle linéaire de Bingham au-dessus d'une vitesse de dilatation limite. Ce modèle bien lesécoulements turbulents, dépendant uniquement de la différence de surface entre le rhéogramme de Bingham et la spline cubique. Keywords: non-Newtonian turbulent flow, rheology PROBLEMS WITH RHEOLOGICAL MODEL SELECTIONI n calculating pressure drops in pipelines carrying nonNewtonian fluids, it is often necessary to extrapolate to values of shear stress considerably in excess of those on the rheogram. Although rheograms are very often curved (convex upward) at low-strain (or shear) rates, they often tend to approximate straight lines at high-strain rates as is illustrated later in Figure 1. The Wilson-Thomas prediction method for turbulent flow of Bingham plastic fluids, first published in 1985, has been extended recently to prediction of the transition velocity (Wilson and Thomas, 2006) and from smooth to rough walled pipes (Thomas and Wilson, 2007). These previous analyses are based on an assumed true Bingham rheogram with a yield stress and a linear section of slope equal to the plastic viscosity. That is, they do not allow for the curved sections of the rheograms at low-strain rates. Whilst alternate models, such as the YPL, provide a good fit to the low-strain rate data they tend to physically unrealistic apparent viscosities (often less than water at high-strain rates).In turbulent pipe flow, the effect of fluid viscosity is confined to a thin sub-layer, which extends from the wall to a distance ı given by:where and are viscosity and density, respectively, and U* is the shear velocity at the wall. In the main flow (y > ı), momentum transfer takes place by turbulent mixing, which is an inertial process rather than a viscous one. It follows that the velocity profile in the main flow is logarithmic, as opposed to the linear

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New analysis of non‐newtonian turbulent flowndashyield‐power‐law fluids

Cited by 53 publications

References 2 publications

Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

Direct numerical simulation of turbulent non-Newtonian flow using a spectral element method

A Wall Boundary Condition for the Simulation of a Turbulent Non-Newtonian Domestic Slurry in Pipes

Hybrid rheological model for non‐Newtonian turbulent pipe flow

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