Fluid Mechanics of Viscoplasticity

Huilgol, R. R.

doi:10.1007/978-3-662-45617-0

Cited by 49 publications

(31 citation statements)

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“…Since in the present case, even a larger value of M = 10 7 has been used, the present results are expected to be free from such numerical artefacts. The relative merits and demerits of the socalled exact methods vis-à-vis those of the regularization approximations have been highlighted, amongst others, by Glowinski and Wachs [23], Huilgol [36] and others [33]. In summary, since the numerical predictions based on the exponential regularization scheme for a sphere and (Table 5).…”

Section: Streamlines and Isotherm Contoursmentioning

confidence: 93%

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Baranwal

Chhabra

2016

Heat Transfer Engineering

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In this study, laminar natural convection heat transfer to Bingham plastic fluids from two differentially heated isothermal cylinders confined in a square enclosure (with isothermal walls) has been investigated numerically. The governing partial differential equations have been solved over the ranges of the dimensionless parameters, namely, Rayleigh number, 10 2 to 10 6 ; Prandtl number, 10 to 100 and Bingham number, 0.01 to 100 for seven locations of inner cylinders as, 0.25, 0.2, 0.1 and 0. These values correspond to the range of Grashof number varying from 10 to 10 5 . The detailed flow and temperature fields are visualized in terms of the streamlines and isotherm contours. Further insights are developed by examining the iso-shear rate contours and the yield surfaces delineating the fluid-like and solid-like regions. The corresponding heat transfer results are analyzed in terms of the distribution of local Nusselt number along the cylinder surface together with its surface averaged value as functions of the Rayleigh number, Prandtl number, Bingham number and positions of the cylinders. It is found that the average Nusselt number increases with the increasing values of the Rayleigh number and decreases with the increasing Bingham number. For sufficiently large values of the Bingham number, the average Nusselt number reaches its asymptotic value wherein heat transfer takes place solely by conduction. Based on the present numerical results, simple correlations for the prediction of the average Nusselt number and the limiting Bingham number have been developed. Also, a dimensionless criterion denoting the cessation of convection regime is outlined for this configuration.

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Section: Streamlines and Isotherm Contoursmentioning

confidence: 93%

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Baranwal

Chhabra

2016

Heat Transfer Engineering

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“…In fact, the determination of the constant B in a shear rate dependent viscous or viscoelastic non-Newtonian fluid, without a yield stress, is also a difficult problem. Using the viscometric fluidity function, 1 an iterative procedure has been proposed in [4], with a summary appearing in [5]. Thus, it is not surprising that a complete analysis of the helical flow in a viscoplastic fluid is yet to be found.…”

Section: Helical Flowmentioning

confidence: 99%

Analytic Solutions: Steady Flows

Huilgol

2015

Fluid Mechanics of Viscoplasticity

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In this chapter, a collection of analytic solutions to the steady flows of Bingham fluids is presented. First of all, the steady velocity fields in a simple shearing flow, the flow down an inclined plane, that in a pipe of circular cross-section, in a concentric annulus, and in a Couette flow are derived. In each case, the role of the yield stress is emphasised. Next, the helical flow of a Bingham fluid is analysed and a general method to find a complete solution of this problem is presented. Attention is also drawn to the steady flows of non-Bingham fluids. Later on, a simple problem involving heat transfer in a shearing flow between parallel walls is included to illustrate the role played by the Nusselt number. Subsequently, attention is drawn to results pertaining to entry flows and those far downstream in a circular tube and between parallel walls in the presence of heat transfer.In each shearing flow, except in the simple shearing flow, one is faced with the following difficulty which arises from the constitutive equation for the Bingham fluid. From (4.2.11), we see that

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“…Two possible approaches have been explored in the literature to address this issue. First is to reformulate the problem as a variational inequality [28][29][30] and to use either operator splitting methods [31][32][33][34] or an augmented Lagrangian approach 35,36 to solve the problem. Second is the introduction of a regularized constitutive relation.…”

Section: Governing Equationsmentioning

confidence: 99%

“…Note that both nonzero matrix blocks on the left hand side of Equation 30 have the structure of a mass matrix. In practice, they are approximated by a diagonal mass matrix, which allows us to obtain the projections through the solution of a diagonal linear system.…”

Section: Matrix Formulationmentioning

confidence: 99%

Simulation of two‐ and three‐dimensional viscoplastic flows using adaptive mesh refinement

Cotela-Dalmau

Rossi

Larese

2017

Numerical Meth Engineering

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This paper presents a finite element solver for the simulation of steady non-Newtonian flow problems, using a regularized Bingham model, with adaptive mesh refinement capabilities.The solver is based on a stabilized formulation derived from the variational multiscale (VMS) framework. This choice allows the introduction of an a posteriori error indicator based on the small scale part of the solution, which is used to drive a mesh refinement procedure based on element subdivision.This approach applied to the solution of a series of benchmark examples, which allow us to validate the formulation and assess its capabilities to model 2D and 3D non-Newtonian flows.

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Fluid Mechanics of Viscoplasticity

Cited by 49 publications

References 0 publications

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Effect of Fluid Yield Stress on Natural Convection From Horizontal Cylinders in a Square Enclosure

Analytic Solutions: Steady Flows

Simulation of two‐ and three‐dimensional viscoplastic flows using adaptive mesh refinement

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