Universal correlation for the rise velocity of long gas bubbles in round pipes

• Published in: Journal of fluid mechanics 2003-11, Vol.494, p.379-398, Article S0022112003006165
• Main Authors: VIANA, FLAVIA, PARDO, RAIMUNDO, YÁNEZ, RODOLFO, TRALLERO, JOSÉ L., JOSEPH, DANIEL D.
• Format: Article
• Language: English
• Subjects: Bubbles; Buoyancy; Drops and bubbles; Exact sciences and technology; Flows in ducts, channels, nozzles, and conduits; Fluid dynamics; Fundamental areas of phenomenology (including applications); Nonhomogeneous flows; Physics; Reynolds number; Surface tension
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/S0022112003006165

We collected all of the published data we could find on the rise velocity of long gas bubbles in stagnant fluids contained in circular tubes. Data from 255 experiments from the literature and seven new experiments at PDVSA Intevep for fluids with viscosities ranging from 1 mPa s up to 3900 mPa s were assembled on spread sheets and processed in log–log plots of the normalized rise velocity, $\hbox{\it Fr} \,{=}\,U/(gD)^{1/2}$ Froude velocity vs. buoyancy Reynolds number, $R\,{=}\,(D^{3}g (\rho_{l}-\rho_{g}) \rho_{l})^{1/2}/\mu $ for fixed ranges of the Eötvös number, $\hbox{\it Eo}\,{=}\,g\rho_{l}D^{2}/\sigma $ where $D$ is the pipe diameter, $\rho_{l}$, $\rho_{g}$ and $\sigma$ are densities and surface tension. The plots give rise to power laws in $Eo$; the composition of these separate power laws emerge as bi-power laws for two separate flow regions for large and small buoyancy Reynolds. For large $R$ ($>200$) we find \[\hbox{\it Fr} = {0.34}/(1+3805/\hbox{\it Eo}^{3.06})^{0.58}.\] For small $R$ ($