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.

Simulation and Analysis of a Drilling Fluid Using a Herschel-Bulkley Model

Abstract: In the study, a drilling fluid with known properties is analyzed and simulated in the laminar regime through a pipe with dimensions of 1.5m in length and 0.02m in diameter. The purpose of the conducted analysis is to demonstrate the advantages of the Herschel-Bulkley model currently used in the oil and gas industry for analyzing non-Newtonian drilling fluids. For comparison, the analysis is also performed using more simple models for nonNewtonian fluids such as the Bingham Plastic model and the Power Law model and for a Newtonian fluid (water). In addition to analytical models, computations are conducted using commercial computational fluid dynamics software: Star-CCM+ and Solidworks Flow Simulation. The comparison of the model results are mainly considered in the pipe entrance region, because this flow area is of importance for drilling processes. The differences between the fluid models is largely apparent in this region.

A Perturbation Approach to the Analysis of a Casson Model Fluid

Abstract: The rheological behaviour of non-Newtonian fluids with yield stress has been extensively studied, but the task of constructing analytic solutions of the governing equations has proved extremely difficult. The so-called Casson fluid is a known to display a yield stress; and, moreover, its behaviour is described by a relatively simple two-parameter constitutive equation. This model has several applications, of which the modelling of blood flow is the most significant. This study examines the case of helical flow of a Casson fluid between coaxial cylinders with given constant rotation of the inner cylinder and axial flow rate. Such helical flow constitutes one of the simplest three-dimensional flows for which an analytic solution might be sought. For the particular case where the intercylindrical gap width is small, a perturbation approach based on a scaled version of the gap width as a perturbation parameter is applied to yield expressions for describing the fluid flow, together with the fundamental relationship linking the angular velocity of the inner cylinder, the torque experienced there, and the given axial flow rate. The accuracy of these expressions will be tested by comparison with solutions generated numerically.

Nonsteady flow of viscous fluid in a tube of triangular cross-section

Abstract: By superposing of one-dimensional solutions an exact solution is obtained for the nonsteady two-dimensional problem of the motion of an incompressible viscous fluid in a rigid tube whose cross-section is a regular triangle. The fluid is driven by a time-dependent pressure gradient. The fluid particles may have a nonuniform initial velocity distribution over the tube cross-section. Solutions are obtained in the form of series for the cases in which the fluid is accelerated from rest by a varying pressure gradient and also in the stationary oscillating regime under the action of a periodically pulsating pressure gradient.

Flow of a fractional Oldroyd-B fluid over a plane wall that applies a time-dependent shear to the fluid

Abstract: The unsteady flow of an incompressible Oldroyd-B fluid with fractional derivatives induced by a plane wall that applies a time-dependent shear stress fta to the fluid is studied using Fourier sine and Laplace transforms. Exact solutions for velocity and shear stress distributions are found in integral and series form in terms of generalized G functions. They are presented as a sum between the corresponding Newtonian solutions and non-Newtonian contributions and reduce to Newtonian solutions if relaxation and retardation times tend to zero. The solutions for fractional second grade and Maxwell fluids, as well as those for ordinary fluids, are obtained as limiting cases of general solutions. Finally, some special cases are considered and known solutions from the literature are recovered. An important relation with the first problem of Stokes is brought to light. The influence of fractional parameters on the fluid motion, as well as a comparison between models, is graphically illustrated.

Exact Solutions Of Different Motions Of Non Newtonian Fluids With / Without Fractional Derivatives

Abstract: In the present thesis, we will present the analytical studies of some fluid flow models. We wish to analyze two main scenarios, one of which deals with non-fractional (ordinary) models and the other with fractional models for the flow of non-Newtonian fluids.We use classical computational techniques capable of accurately operating in order to obtain exact analytical solutions. Our studies include Couette flows of a Maxwell fluid under slip conditions between the fluid and walls.The motion of the bottom plate is assumed to be a rectilinear translation in its plane while, the upper plate is at rest.Two particular cases, namely translation with constant velocity and sinusoidal oscillations of the bottom plate are considered. Next, unsteady motions of Oldroyd–B fluids over an infinite plate between two side walls will be investigated. The motion of the fluid is due to the bottom plate that applies two types of shears to fluid. Extending our studies, we look at the unsteady magnetohydrodynamic (MHD) flow of fractional Oldroyd B fluid between two side walls perpendicular to a plate. Expressions of the obtained solutions are presented in a series form in terms of the generalized G functions.Finally, the unsteady flow of an Oldroyd B fluid with fractional derivative model between two infinite coaxial circular cylinders is studied. The motion of the fluid is produced by the inner cylinder that, at time t = 0+, applies a time dependent longitudinal shear stress to the fluid. Expressions of the obtained results are presented in a series form in terms of the generalized G and R functions. In all the flow models, we obtained the exact analytical solutions for motions with technical relevance, both for the velocity field and the shear stress(es).These solutions corresponding to some flows in which either velocity or the shear stress is given on the boundary are established for different kinds of non-Newtonian fluids as well as for fractional models.The exact analytical solutions that have been presented in all the fluid flow models satisfy all imposed initial and boundary conditions. Further on, the flow properties of models and the comparison to other models are highlighted with graphical illustrations