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.

Flow of a viscoelastic fluid between two rotating circular cylinders subject to suction or injection

Abstract: The steady flow of an Oldroyd-B fluid between two porous concentric circular cylinders is studied. The equation of motion and the constitutive equations form a system of non-linear ODEs that is solved numerically, and in a few cases the numerical results are compared with a known analytical solution. We consider the effect of the non-Newtonian nature of the fluid on the drag and on the boundary layer structure near the walls. Numerical computations show the effect of the non-Newtonian quantities on the velocity and on the shear stress as the dimensionless parameters are varied. © by 1997 John Wiley & Sons, Ltd.

Taylor-Couette flow of an Oldroyd-B fluid in a circular cylinder subject to a time-dependent rotation

Abstract: The velocity and the shear stress, corresponding to the unsteady flow of an Oldroyd-B fluid in an infinite circular cylinder subject to a timedependent couple, are established by means of the Hankel transform. The similar solutions for Maxwell, Second grade and Newtonian fluids can be obtained as limiting cases of general solutions. Finally, the influence of the material parameters on the velocity profile and the shear stress is spotlighted by means of graphical illustrations.

A new approach to modelling viscoelastic flow

Abstract: By adapting the free Lagrangian approach (M.J. Fritts and J.P. Boris, J. Comput. Phys, 31 (1979) 173), a new numerical simulation technique for modelling viscoelastic fluid flow has been developed. Using a comoving Voronoi mesh, the method is able to track the details of fluid behaviours, e.g. deformation and stream line. The primary results include a Johnson-Segalman fluid and a single-integral Doi-Edwards fluid in a simple planar channel, and a Giesekus-Leonov fluid and an Oldroyd-B fluid in a planar 4:1 abrupt contraction at modestly high Weissenberg number. A free-surface flow is also considered.

Flow of yield stress and Carreau fluids through rough-walled rock fractures: Prediction and experiments

Abstract: Many natural phenomena in geophysics and hydrogeology involve the flow of non-Newtonian fluids through natural rough-walled fractures. Therefore, there is considerable interest in predicting the pressure drop generated by complex flow in these media under a given set of boundary conditions. However, this task is markedly more challenging than the Newtonian case given the coupling of geometrical and rheological parameters in the flow law. The main contribution of this paper is to propose a simple method to predict the flow of commonly used Carreau and yield stress fluids through fractures. To do so, an expression relating the “in-situ” shear viscosity of the fluid to the bulk shear-viscosity parameters is obtained. Then, this “in-situ” viscosity is entered in the macroscopic laws to predict the flow rate-pressure gradient relations. Experiments with yield stress and Carreau fluids in two replicas of natural fractures covering a wide range of injection flow rates are presented and compared to the predictions of the proposed method. Our results show that the use of a constant shift parameter to relate “in-situ” and bulk shear viscosity is no longer valid in the presence of a yield stress or a plateau viscosity. Consequently, properly representing the dependence of the shift parameter on the flow rate is crucial to obtain accurate predictions. The proposed method predicts the pressure drop in a rough-walled fracture at a given injection flow rate by only using the shear rheology of the fluid, the hydraulic aperture of the fracture and the inertial coefficients as inputs.