Herschel–Bulkley fluid

About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.

Sensitivity Analysis of a Wall Boundary Condition for the Turbulent Pipe Flow of Herschel–Bulkley Fluids

Abstract: This article follows from a previous study by the authors on the computational fluid dynamics-based analysis of Herschel-Bulkley fluids in a pipe-bounded turbulent flow. The study aims to propose a numerical method that could support engineering processes involving the design and implementation of a waste water transport system, for concentrated domestic slurry. Concentrated domestic slurry results from the reduction in the amount of water used in domestic activities (and also the separation of black and grey water). This primarily saves water and also increases the concentration of nutrients and biomass in the slurry, facilitating efficient recovery. Experiments revealed that upon concentration, domestic slurry flows as a non-Newtonian fluid of the Herschel-Bulkley type. An analytical solution for the laminar transport of such a fluid is available in literature. However, a similar solution for the turbulent transport of a Herschel-Bulkley fluid is unavailable, which prompted the development of an appropriate wall function to aid the analysis of such flows. The wall function (called ψ1 hereafter) was developed using Launder and Spalding's standard wall function as a guide and was validated against a range of experimental test-cases, with positive results.ψ1 is assessed for its sensitivity to rheological parameters, namely the yield stress, the fluid consistency index and the behaviour index and their impact on the accuracy with which ψ1 can correctly quantify the pressure loss through a pipe. This is done while simulating the flow of concentrated domestic slurry using the Reynolds-Averaged Navier-Stokes (RANS) approach for turbulent flows. This serves to establish an operational envelope in terms of the rheological parameters and the average flow velocity within which ψ1 is a must for accuracy. One observes that, regardless of the fluid behaviour index, ψ1 is necessary to ensure accuracy with RANS models only in flow regimes where the wall shear stress is comparable to the yield stress within an order of magnitude. This is also the regime within which the concentrated slurry analysed as part of this research flows, making ψ1 a requirement. In addition, when the wall shear stress exceeds the yield stress by more than one order (either due to an inherent lower yield stress or a high flow velocity), the regular Newtonian wall function proposed by Launder and Spalding is sufficient for an accurate estimate of the pressure loss, owing to the relative reduction in non-Newtonian viscosity as compared to the turbulent viscosity.

A solvable weak-potential model of a non-Newtonian fluid

Abstract: A theoretical model is developed for a non-Newtonian fluid of spherical molecules interacting with a weak potential. The Kirkwood-Smoluchowski equation for planar Couette flow reduces in leading order in potential strength to a shear-diffusion equation with an inhomogeneous source term. The pressure tensor elements are calculated and, for a Gaussian potential, reduce to one-dimensional integrals which are evaluated numerically. The model reproduces several qualitative features of non-Newtonian liquids and the computer simulations of Evans and Hanley. These features include shear thinning, shear dilatancy, normal pressure differences, and dependence on shear rate to a half-integer power.

Numerical Modeling of Non-Newtonian Flow in Viscous Micropump

Abstract: Non-Newtonian fluid can be encountered in many applications of Microdevices. In this study, two-dimensional non-Newtonian simulations of viscous micropump were performed. The viscous micropump consists of a rotating cylinder located eccentrically inside a microchannel. When the cylinder rotates, a net force is transferred to the fluid due to the unequal shear stresses on the upper and lower surfaces of the cylinder, thus causing the fluid to displace. Navier Stokes equations and modified Bingham model have been used to describe the fluid flow. Parameters as viscosity and stress used in the model are based on experimental data. It was found that Reynolds number is a predominant parameter on the variation of bulk velocity as a function of eccentricity. The stress and bulk velocity decrease with increasing the eccentricity at low Reynolds number. The changes in non-Newtonian fluid structure are related to Reynolds number, eccentricity and channel height. The pumping performance of non-Newtonian fluid is increasing with global pressure gradient and decreasing with the channel height.

Effects of heat and chemical reaction on Jeffrey fluid model with stenosis

Abstract: In this article, we have studied a non-Newtonian fluid model for blood flow through a tapered artery with a stenosis by assuming blood as Jeffrey fluid. Heat and mass transfer phenomena have been taken into account by giving temperature 0 and concentration 0 to the upper wall of the arteries, while at the centre we have considered symmetry condition for both temperature and concentration. Perturbation method is used to solve the resulting equations. The effects of non-Newtonian nature of blood on velocity profile, temperature field and concentration, wall shear stress, shearing stress at the stenosis throat, and impedance of the artery are discussed. The results for Newtonian fluid are obtained as a special case from this model. Trapping phenomena have been discussed at the end of this article.