Predicting Non-Newtonian Flow Behavior in Ducts of Unusual Cross Section

Miller, C.

doi:10.1021/i160044a015

Cited by 87 publications

(41 citation statements)

References 5 publications

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“…Therefore, this approach necessitates the knowledge of only one parameter (β) as opposed to the two geometric parameters, namely, a and b in the method of Kozicki et al . (1966) and Kozicki and Tiu (1967), albeit a similar suggestion was also made by Miller (1972) and Liu (1983). Finally, for the limiting case of a circular pipe, evidently β=3 thereby leading to a=(1/4) and b=(3/4) and the two definitions of the Reynolds number coincide, as expected.…”

Section: Friction Factors For Turbulent Flow In Smooth Pipessupporting

confidence: 76%

“…Having determined the value of the friction factor f for a specified flow rate and hence Re', the pressure gradient can be calculated in the normal way. (Schechter, 1961 ;Wheeler and Wissler, 1965 ;Miller, 1972 ;Aoyagi, 1969, 1973). On the other hand, semi-empirical attempts have also been made to develop methods for predicting pressure drop for time-independent fluids in ducts of noncircular cross-section.…”

Section: Friction Factors For Turbulent Flow In Smooth Pipesmentioning

confidence: 99%

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Incompressible Non-Newtonian Fluid Flows

Nguyen¹,

Nguyen²

2012

Continuum Mechanics - Progress in Fundamentals and Engineering Applications

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Section: Friction Factors For Turbulent Flow In Smooth Pipessupporting

confidence: 76%

Section: Friction Factors For Turbulent Flow In Smooth Pipesmentioning

confidence: 99%

Incompressible Non-Newtonian Fluid Flows

Nguyen¹,

Nguyen²

2012

Continuum Mechanics - Progress in Fundamentals and Engineering Applications

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“…Although non-circular pipes have been considered extensively in the literature, e.g. Muzychka and Edge (2008), Hanks (1974), Kozick, Chou, and Tiu ( 1966), Liu (1983), Liu, Lin, and Hong (1988), Miller (1972), Mitsuishi, Kitayama, and Aoyagi (1968), most authors assume the pipe is completely full or are concerned with other issues. Since previous results are available for shear-thinning and Newtonian fluids (n ≤ 1), perhaps because shear-thickening fluids are rare, we compare our corresponding results with their results.…”

Section: Determining Optimal Fluid Levelmentioning

confidence: 99%

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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“…Whilst the HS approximation is valid in the slit, the aspect ratio of the distribution channel is such that it cannot be treated directly in this way. Instead, an equivalent HS channel is defined using results for pressure drops in developed flow through prismatic channels of various cross-sections [17] …”

Section: Flow Problemmentioning

confidence: 99%

“…where a is a shape factor appropriate to the manifold cross-section, as given by Miller [17]. A is the cross-sectional area of the manifold, D h its hydraulic diameter and W its width.…”

Section: Flow Problemmentioning

confidence: 99%