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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.


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TL;DR: In this paper, the Lagrangian approach for the solution of viscoelastic constitutive equation using the co-deformational frame of reference with a possibility of analytically solving the equation along the particles trajectories was designed, making use of finite element algorithms generally regarded as advantageous for tackling the problem.
Abstract: A new numerical scheme for simulation of viscoelastic fluid flows was designed, making use of finite element algorithms generally regarded as advantageous for tackling the problem. This includes the Lagrangian approach for the solution of viscoelastic constitutive equation using the co-deformational frame of reference with a possibility of analytically solving the equation along the particles trajectories, which in turn allowed eluding the solution of any system of linear equations for the stress. Then, the full ellipticity of the momentum conservation equation was utilised thanks to a possibility of accurate determination of the stress tensor independently of the velocity field at the current stage of computation. The needed independent stress was calculated at each time step on the basis of the past deformation history, which in turn was determined on the basis of the past velocity fields, all incorporated into a modified Euler time stepping algorithm. Owing to explicit inclusion of the full viscous term from the viscoelastic model into the momentum conservation equation, no stress splitting was necessary. The trajectory feet tracking was done accurately using a semi-analytic solution of the displacement gradient evolution equation and a weak formulation of the kinematics equation, the latter at the expense of solving an extra symmetric system of linear equations. The error expressed in the form of the Sobolev norms was determined using a comparison with available analytical solution for UCM fluid in the transient regime or numerically obtained steady-state stress values for the PTT fluid in Couette flow. The implementation of the PTT fluid model was done by modifying the relative displacement gradient tensor so that a new convective frame was defined. The stability of the algorithm was assessed using the well-known benchmark problem of a sphere sedimenting in a tube with viscoelastic fluid. The stable numerical results were obtained at high Weissenberg numbers, with the limit of convergence Wi=6.6, exceeding any previously reported values. The robustness of the code was proven by simulation of the Weissenberg effect (the rod-climbing phenomenon) with the use of PTT fluid.

22 citations

Journal ArticleDOI
TL;DR: In this paper, the authors generalize the Saffman model to the case of a Bingham fluid, where the porous medium is assumed to be statistically homogeneous and isotropic.
Abstract: The study of the flow of a Newtonian fluid in a porous medium and the dispersion of markers has been the subject of numerous works after Taylor and Saffman. Characteristics of the flow of a non-Newtonian fluid have not been investigated as much. We attempt to generalize the Saffman modelling to the case of a Bingham fluid. The porous medium is assumed to be statistically homogeneous and isotropic. Dispersion is completely described by a lateral and a longitudinal dispersion coefficient. Pores are represented by monodispersed capillary tubes with an isotropic angular distribution.

22 citations

Journal ArticleDOI
TL;DR: The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically in this article.
Abstract: The steady flow of non-Newtonian Herschel-Bulkley fluids over a one-to-two axisymmetric sudden expansion was studied numerically Finite difference numerical solutions of the governing continuity and fully-elliptic momentum equations were obtained within the laminar flow regime for a range of Reynolds numbers, yield numbers, and power-law index values The Reynolds number, based on the upstream pipe diameter and bulk velocity, was varied between 50 and 200, while the yield number was varied between 0 and 2 The power-law index values mapped the 06-12 range, allowing for the investigation of both shear-thinning and shear-thickening effects Two distinct flow regimes are identified One is associated with a combination of low yield numbers, high Reynolds numbers, and high power-law indexes, and exhibits a recirculating flow region at the step corner which is similar to that seen in Newtonian flows The other flow regime, however, is characterized by a dead-zone behind the step corner, and is obtained for a combination of high yield numbers, low Reynolds numbers, and low power-law indexes

22 citations

Journal ArticleDOI
S. Goldstein1
01 Jan 1936
TL;DR: In this paper, the stability of a viscous fluid flow in which the undisturbed velocity is parallel to the axis of x and its magnitude U is a function of y only (x, y, z being rectangular Cartesian co-ordinates), and if we assume that any possible disturbance may be analysed into a number (usually infinite) of principal disturbances, each of which involves the time only through a single exponential factor, then it has been proved by Squire, by supposing the disturbance analysed also into constituents which are simple harmonic functions of X and z, and considering only
Abstract: If we consider, by the method of small oscillations, the stability of a viscous fluid flow in which the undisturbed velocity is parallel to the axis of x and its magnitude U is a function of y only (x, y, z being rectangular Cartesian co-ordinates), and if we assume that any possible disturbance may be analysed into a number (usually infinite) of principal disturbances, each of which involves the time only through a single exponential factor, then it has been proved by Squire, by supposing the disturbance analysed also into constituents which are simple harmonic functions of x and z, and considering only a single constituent, that if instability occurs at all, it will occur for the lowest Reynolds number for a disturbance which is two-dimensional, in the x, y plane. Hence only two-dimensional disturbances need be considered. The velocity components in the disturbed motion will be denoted by (U + u, v). Since only infinitesimal disturbances are considered, all terms in the equations of motion which are quadratic in u and v are neglected. When u and v are taken to be functions of y multiplied by ei(αx−βi), the equation of continuity becomesand the result of eliminating the pressure in the equations of motion then gives the following equation for v, where ν is the kinematic viscosity of the fluid:

22 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202341
202295
202117
202022
201920
201836