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.

Modeling and Optimization of Non-Linear Herschel-Bulkley Fluid Model Based Magnetorheological Valve Geometry

Abstract: Rheological fluids find great relevance in various engineering applications. Among them, magnetorheological (MR) fluid has become popular due to its controllable rheological characteristics. It has been found that non-linear Herschel-Bulkley (H-B) fluid model is the most suitable model for characterizing MR fluids as it is able to capture shear-thinning and shear-thickening phenomena at high shear rates; the popular linear Bingham fluid model lacks this. This inadequacy of Bingham model leads to a linear approximation of hysteresis curves generated as damping force versus velocity plots and hence tends to underestimate or overestimate the behavior depending on the MR fluid used. In previous literature, authors have modeled and optimized MR valve geometry of semi-active dampers for multiple objective functions using Bingham model. In the present study, the valve is modeled using H-B fluid model and the optimization problem establishes geometric parameters of volume-constrained MR valve by minimizing multiple objective functions based on H-B fluid model; such work has not been reported till now. The proposed optimization aims at (i) maximizing dynamic range and (ii) minimizing inductive time constant with the constraints stated below. The formulation of objective functions is based on the analytical solution of a magnetic circuit such that there is a constraint on geometry for keeping magnetic flux density less than saturation limits of the valve material. All the parameters associated with H-B model of a commercially available MR fluid are determined as a function of magnetic flux density. Since there are multiple objective functions, one can go for Pareto optimal points. Therefore, for solving this multiobjective optimization problem, genetic algorithm is used for finding Pareto fronts in MATLAB® environment. Finally, the performance of the optimally designed MR valve is studied.

Diffusion Equation for Fluid Flow in Porous Rocks

Abstract: The multiphase flow in porous media is a subject of great complexities with a long rich history in the field of fluid mechanics. This is a subject with important technical applications, most notably in oil recovery from petroleum reservoirs and so on. The single-phase fluid flow through a porous medium is well characterized by Darcy’s law. In the petroleum industry and in other technical applications, transport is modeled by postulating a multiphase generalization of the Darcy’s law . In this connection, distinct pressures are defined for each constituent phase with the difference known as capillary pressure, determined by the interfacial tension, micro pore geometry and surface chemistry of the solid medium. For flow rates, relative permeability is defined that relates the volume flow rate of each fluid to its pressure gradient. In the present paper, there is a derivation and analysis about the diffusion equation for the fluid flow in porous rocks and some important results have been founded. The permeability is a function of rock type that varies with stress, temperature etc., and does not depend on the fluid. The effect of the fluid on the flow rate is accounted for by the term of viscosity. The numerical value of permeability for a given rock depends on the size of the pores in the rock as well as on the degree of interconnectivity of the void space. The pressure pulses obey the diffusion equation not the wave equation. Then they travel at a speed which continually decreases with time rather than travelling at a constant speed. The results shown in this paper are much useful in earth sciences and petroleum industry.

Unsteady flow of incompressible electrically conducting second grade fluid through a composite medium in a rotating parallel plate channel bounded by a porous bed

Abstract: In this paper, we consider the unsteady flow of an incompressible electrically conducting second grade fluid in a rigidly rotating parallel plate channel bounded below by a sparsely packed porous bed. The flow in nonporous region is governed by the equation of motion derived using the constitutive equation for the stress in compressible second order fluid, while the Brinkman’s model equation has been used for the momentum equation in the porous bed. In the undisturbed state both the fluid and the plates are in rigid rotation with same angular velocity about the normal to the plates and at t >0 the fluid is driven by the constant pressure gradient-parallel to the channel wall and in addition, the lower plate perform non-torsional oscillation in its own plane. Exact solution of the velocity in the clean fluid and the porous medium consists of steady state and transient state. The time required for the transient state to decay is evaluated and the ultimate quasi steady state solution has been derived analytically and its behaviour is computationally discussed with reference to the governing parameter. The shear stress on the boundary is obtained analytically and its behaviour is computationally discussed.

An Analysis of the Flow of a Newtonian Fluid between Two Moving Parallel Plates

Abstract: We consider flow of an incompressible Newtonian fluid produced by two parallel plates, moving towards and away from each other with constant velocity. Inverse solutions of the equations of motion are obtained by assuming certain forms of the stream function. Analytical expressions for the stream function, fluid velocity components, and fluid pressure are derived.