Steady pressure-driven non-Newtonian flow in a partially filled pipe

Davis, A. M. J.; Mai, Tsun-Zee

doi:10.1016/0377-0257(91)87036-w

Cited by 13 publications

(19 citation statements)

References 10 publications

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“…In this paper, we generalize some of the results of Davis and Mai (1991) are partially full with the non-Newtonian power-law fluid obeying Equation (7). Although non-circular pipes have been considered extensively in the literature, e.g.…”

Section: Determining Optimal Fluid Levelmentioning

confidence: 94%

“…Our use of the finite element method departs from the earlier computational work on non-Newtonian flow in partially full circular pipes (Davis and Mai 1991) where a finite difference scheme was used. In order to treat the curved boundary by finite differences, Davis and Mai used two different methods.…”

Section: Methodsmentioning

confidence: 99%

“…The scheme used in Davis and Mai (1991) is essentially a standard Picárd iteration. They begin by computing a linear approximation to the velocity u.…”

Section: Methodsmentioning

confidence: 99%

“…In this case, when the circular pipe is partially full with a single viscous fluid that flows with a horizontal free surface, it can be shown that by considering only a partially full pipe, one can still increase the flux by 27% (Davis and Mai 1991) over the flux for a full pipe. Davis and Mai (1991) have performed a computational study of the limiting case of a single fluid which is further assumed to obey non-Newtonian equations. They show, using the well-known non-Newtonian models of power-law fluids and modified Bingham plastics, that a comparable improvement in flux still holds.…”

Section: Introductionmentioning

confidence: 96%

“…For a pipe with circular cross section (henceforth called a circular pipe) carrying two immiscible Newtonian fluids (i.e. p = 2 in Equation (7)) with a horizontal ripple-free interface, it is known that the volumetric flux of the more viscous fluid can be increased by 37% (Davis and Mai 1991) over the corresponding flux for a pipe completely full with the more viscous fluid. This maximal improvement in flux is achieved by choosing the level of the more viscous fluid such that the angle θ between the horizontal centreline of the pipe and the point where the interface contacts the pipe boundary is π 4 (Mitsuishi, Kitayama, and Aoyagi 1968).…”

Section: Introductionmentioning

confidence: 99%

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Optimal numerical flux of power-law fluids in some partially full pipes

Lefton

Wei

Liu

2014

International Journal of Computational Fluid Dynamics

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Consider the steady state pressure driven flow of a power-law fluid in a partially filled straight pipe. It is known that an increase in flux can be achieved for a fixed pressure by partially filling the pipe and having the remaining volume either void or filled with a less viscous, lubricating fluid. If the pipe has circular cross section, the fluid level which maximizes flux is the level which avoids contact with exactly 25% of the boundary. This result can be proved analytically for Newtonian fluids and has been verified numerically for certain non-Newtonian models. This paper provides a generalization of this work numerically to pipes with non-circular cross sections which are partially full with a power-law fluid. A simple and physically plausible geometric condition is presented which can be used to approximate the fluid level that maximizes flux in a wide range of pipe geometries. Additional increases in flux for a given pressure can be obtained by changing the shape of the pipe but leaving the perimeter fixed. This computational analysis of flux as a function of both fluid level and pipe geometry has not been considered to our knowledge. Fluxes are computed using a special discretization scheme, designed to uncover general properties which are only dependent on fluid level and/or pipe cross-sectional geometry. Computations use finite elements and take advantage of the variational structure inherent in the power-law model. A minimization technique for approximating the critical points of the associated non-linear energy functional is used. In particular, the numerical scheme for the non-linear partial differential equation has been proved to be convergent with known error estimates. The numerical results obtained in this work can be useful for designing pipes and canals for transportation of non-Newtonian fluids, such as those in chemical engineering and food processing engineering.

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Section: Determining Optimal Fluid Levelmentioning

confidence: 94%

Section: Methodsmentioning

confidence: 99%

“…The scheme used in Davis and Mai (1991) is essentially a standard Picárd iteration. They begin by computing a linear approximation to the velocity u.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations