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.

Computed Synovial Fluid Flow in a Simple Knee Joint Model

Abstract: Prediction of shear stress induced by the fluid flow on knee joint cells is the main aim of this study. Oscillatory flow of a Newtonian synovial fluid is examined in two-dimensional joint geometries. The experimental model is a fluid driven shear loader test rig, which features a finite plate oscillating at 1Hz, that is 1mm over a stationary cell culture surface. Oscillating Couette flow in the thin gap is generated by the finite span plate. An incompressible two-dimensional transient and laminar CFD model is developed using the STAR-CD® code. The infinite oscillating plate Couette flow solutions (Stoke’s Second Problem with a finite gap) are reviewed and used in the grid sensitivity and validation tests of the computational finite oscillating plate model. The resulting flow features and vorticity convection are discussed and shear stress induced on the stationary plate due to an oscillating finite plate is compared with its infinite counterpart. As an extension, the effect of articular cartilage curvature is studied in a topologically equivalent model with and without menisci.Copyright © 2003 by ASME

Modelling with viscous and viscoplastic materials under combining and separating flow configurations

Abstract: Combining and separating incompressible flow of Newtonian and inelastic Herschel–Bulkley fluids is studied numerically employing a semi-implicit Taylor–Galerkin pressure-correction algorithm, where steady solutions are obtained through a transient finite element procedure. The influence of inertia and fluid rheology is analysed on flow patterns, velocity fields and pressure drops for various flow configurations, with fixed geometric gap width that stimulates the merging and splitting in the flow. For Newtonian fluids and at larger levels of inertia, the appearance of vortices was observed, with an increase in velocity differences and pressure drops across the channel. In this case, the numerical procedure was verified with good agreement against previous numerical and experimental observations. To extend the consideration to non-Newtonian inelastic materials, the material rheological characteristics were approximated with the use of the Herschel–Bulkley fluid model, incorporating the Ostwald–de Waele power-law model and viscoplastic yield stress. Findings for unyielded power-law fluids reveal slight increase in the size of the vortices as power index (m) was decreased. Variation of the consistency index (k) shows strong influence on the streamline patterns with a rapid increase in the vortex formation as k was decreased. For Bingham model solutions, devoid of shear-thinning and increasing yield stress, a higher value of Reynolds number is required for equivalent levels of vortex formation; also one observes the appearance of yielded and unyielded regions. Under Herschel–Bulkley modelling, there was little change noted in the kinematics, but some was apparent in rheological response. Once more, observations reveal the tendency to eliminate vortices at larger yield stress levels, with the appearance of unyielded regions.

Comparison of potential flow and viscous fluid models in gap resonance

Abstract: This work presents numerical simulation results of wave motion in narrow gaps subjected to incident water waves using both potential theory flow model and viscous fluid model, including single narrow gap separated by twin bodies and double narrow gaps between three identical bodies. The numerical results of variation of wave height in the narrow gaps with incident wave frequencies are compared with available experimental data. The numerical results and comparisons indicated that both potential flow model and viscous fluid model are able to predict the resonant frequency. However, it was found that potential flow model significantly over-predict the wave height in narrow gaps at frequencies near the resonant frequency. It was revealed that the viscous effect/or energy dissipation plays an important role in limiting the wave height in narrow gaps at resonance. The mechanism of fluid forces on structures is also investigated based on the numerical simulations using the viscous fluid model.

The law of velocity distribution of bingham fluid's flowing in the encircle pipe

Abstract: In this article,combinating Bingham fluid's constitutive equation with momentum equation,the velocity distribution of Bingham fluid's flowing in the encircle pipe is obtained by means of dimension analysis,which is under the condition of laminar flowing.Moreover the effects of some parameters such as yield stress and pressure gradient on the velocity profile have been discussed:the difference of velocity distribution between Bingham fluid and Newtonian fluid increases with yield stress,the width of flow nucleus also increases with yield stress;as pressure gradient is smaller and the velocity profile becomes flatter,it means the width of flow nucleus increases.

Chapter 3 – Biological Study on Pulsatile Flow of Herschel-Bulkley Fluid in Tapered Blood Vessels

Abstract: This chapter investigates the effect of pulsatility on flow through a tapered artery. Blood has been represented by a non-Newtonian fluid obeying the Herschel-Bulkley equation. Using the Reynolds number as the perturbation parameter, a perturbation technique is adopted to solve the resulting quasi-steady, nonlinear, coupled, implicit system of differential equations. It is observed that the wall shear stress and flow resistance increase with increasing values of the taper angle and the axial distance. The present approach generally has validity over many mathematical models developed by others, and it may be applied to any mathematical model by taking into account any type of rheological property of blood. The obtained velocity profiles have been compared with the experimental data, and it is observed that blood behaves like a Herschel-Bulkley fluid rather than Power-law, Bingham, or Newtonian fluid. Finally, some biorheological applications of the present model have briefly been discussed.