1988
DOI: 10.1115/1.3265610
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Encyclopedia of Fluid Mechanics (Gas-Liquid Flows, Vol. 3)

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Cited by 11 publications
(14 citation statements)
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“…The corresponding slopes and R 2 -factors are given in Table 1. For µm-sized particles, the equation is known for the concentration dependence of density in the two-phase mixtures [6]. Pak and Cho [7] implemented the same equation for nano-sized particles, which is expressed as ρ nf l = φρ p + (1 − φ) ρ f l , where ρ nf l , ρ p , ρ f l are densities of the two-phase mixture, particles, and pure fluid, respectively, and φ is the particle volume fraction.…”
Section: Resultsmentioning
confidence: 99%
“…The corresponding slopes and R 2 -factors are given in Table 1. For µm-sized particles, the equation is known for the concentration dependence of density in the two-phase mixtures [6]. Pak and Cho [7] implemented the same equation for nano-sized particles, which is expressed as ρ nf l = φρ p + (1 − φ) ρ f l , where ρ nf l , ρ p , ρ f l are densities of the two-phase mixture, particles, and pure fluid, respectively, and φ is the particle volume fraction.…”
Section: Resultsmentioning
confidence: 99%
“…An increased gradient indicates an increase in the frictional factor and can be explained by the fact that when gas is introduced and the flow becomes two-phase we have an increase in the turbulence level (1) . Forces such as the friction between the flow and the pipe surface, interaction between bubbles and liquid gravitational and acceleration forces must be considered.…”
Section: Pressure Distributionmentioning
confidence: 99%
“…Many studies concerning phase change and the flow regime characteristics of twophase flow through straight pipes have been conducted and a great deal of knowledge has been gathered (1) - (4) . However, few studies have focused on two-phase flow characteristics in a vertical upward sudden contraction pipe and a few are mentioned in the bibliography (2), (8), (9) .…”
Section: Introductionmentioning
confidence: 99%
“…It also requires an equivalent pipe length Le that depends on the elbow radius to the pipe diameter ratio (r/D), as well as the angle of the elbow bend [23]. The increment of Le as a function of r/D is mainly due to friction, centrifugal force, and the secondary flow that is present in the elbows.…”
Section: Chisholm Modelmentioning
confidence: 99%