A low Reynolds number turbulence closure for viscoelastic fluids

Pinho, F.T.; Li, C.F.; Younis, Bassam A.; Sureshkumar, R.

doi:10.1016/j.jnnfm.2008.02.008

Cited by 55 publications

(95 citation statements)

References 49 publications

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“…On the other hand, to solve Equation (15), one also needs a closure for the term η γ ij mentioned as the fluctuating-viscosity stress tensor in literature [20,21]. Known closures include those proposed by Pinho et al [21] and Leighton et al [22]; the latter was based on a priori direct numerical simulation.…”

Section: Computational Fluid Dynamics (Cfd) and Non-newtonian Fluidsmentioning

confidence: 99%

“…Known closures include those proposed by Pinho et al [21] and Leighton et al [22]; the latter was based on a priori direct numerical simulation. However, the validation of such closures is restricted to very low Reynolds numbers, as direct numerical simulation is computationally intensive [23].…”

Section: Computational Fluid Dynamics (Cfd) and Non-newtonian 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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Section: Computational Fluid Dynamics (Cfd) and Non-newtonian Fluidsmentioning

confidence: 99%

Section: Computational Fluid Dynamics (Cfd) and Non-newtonian Fluidsmentioning

confidence: 99%

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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“…Moreover, modeling approaches for viscoelastic turbulent flows have to be developed and these are essentially of RANS (Reynolds-averaged Navier-Stokes) techniques and of LES (large-eddy simulation). DNS studies on these issues are ongoing (Kawamoto et al, 2010;Pinho et al, 2008;Tsukahara et al, 2011c) and the observations in these works will be valuable for those studying such complicated flows using RANS and LES.…”

Section: Resultsmentioning

confidence: 99%

Turbulent Heat Transfer in Drag-Reducing Channel Flow of Viscoelastic Fluid

Tsukahara¹,

Kawaguchi²

2011

Evaporation, Condensation and Heat Transfer

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“…No hypotheses are necessary on the dependence of the turbulent dissipation rate on the fluctuating part of the rate of deformation tensor, as required in [15], neither a particular statistical distribution of the average viscosity, as required in [16]. The present procedure allows to obtain a new transport equation of ε in a conservative form, more general than that obtained previously in the literature.…”

Section: Introductionmentioning

confidence: 84%

“…A procedure based on the DNS predictions of the budgets of momentum and viscoelastic shear stress is developed to evaluate the mean velocity profile. A RANS model is employed using the FENE-P constitutive relationship to describe the rheology of polymer-induced turbulent drag reduction [15]. Correlations among flow and polymer conformation variables are identified by analyzing recent DNS results of dilute polymer solutions.…”

Section: Introductionmentioning

confidence: 99%

Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids

Gori

Boghi

2011

International Communications in Heat and Mass Transfer

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A new equation for the dissipation rate of turbulent kinetic energy is derived exactly in conservative form for a Generalized Newtonian Fluid (GNF). The transport equations for mass, momentum, and turbulent kinetic energy are written along to the transport equation for the shear rate. A new transport equation for the apparent viscosity is derived assuming the viscosity as dependent only on the shear rate. The assumption is of incompressible two-dimensional GNF flow.

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A low Reynolds number turbulence closure for viscoelastic fluids

Cited by 55 publications

References 49 publications

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

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

Turbulent Heat Transfer in Drag-Reducing Channel Flow of Viscoelastic Fluid

Two new differential equations of turbulent dissipation rate and apparent viscosity for non-newtonian fluids

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