Comparison of several models for multi-size bubbly flows on an adiabatic experiment

Vertical upward two-phase flow CFD using interfacial area transport equation

“…It is worth mentioning that the interfacial area concentration data taken by Serizawa et al (1975a;1975b) are not correct due to the use of an incorrect equation for converting interfacial velocity into interfacial area concentration (Lin and Hibiki, 2014). Morel et al (2010) tested four different approaches to predict bubble sizes. They were (1) single-size approach for bubbly flows (Wu et al, 1998), (2) first moment density approach using a bubble diameter distribution function represented by a log-normal law (Kamp et al, 2001), (3) second moment density approach using a bubble diameter distribution function represented by a quadratic law (Ruyer, 2008;Ruyer et al, 2007;Seiler and Ruyer, 2008) and (4) multi-field approach.…”

“…These approaches were benchmarked with an experimental data taken in vertical round tube . Morel et al (2010) selected the interfacial area transport model developed by Wu et al (1998) for the single-size approach and found that the single-size approach could reproduced the axial development of cross-sectional averaged interfacial area concentration and bubble Sauter mean diameter in the first half of the test section and the radial profile of void fraction with core peaking well. Morel et al pointed out that other interfacial area transport models such as Hibiki and Ishii (2000a) and Yao and Morel (2004) could not predict the interfacial area transport well.…”

“…The multi-field approach could reproduce the axial development of the interfacial area concentration fairly well although the computed coalescence term was excessive. Morel et al (2010) stated that the multi-field approach was promising although further studies were indispensable to address the effect of the bubble diameter range and on its discretization. Wang and Sun (2010) optimized the coefficients in one-group interfacial area transport model with the data taken in a vertical round pipe (Fu, 2001) for three-dimensional CFD use.…”

A Combined Multifluid-Population Balance Model for Vertical Gas−Liquid Bubble-Driven Flows Considering Bubble Column Operating Conditions

“…In the absence of phase change, the bubble mass is conserved along its trajectory. As a consequence, the bubble growth velocity and the gas density variation in space and time are related through: 12 The fluid particle mass can be defined as:…”

“…In the absence of phase change, the bubble mass is conserved along its trajectory. As a consequence, the bubble growth velocity and the gas density variation in space and time are related through: v ξ ( r , ξ , t ) = − ξ 3 ρ d ( r , t ) true( ∂ normalρ normald false( boldr , t false) ∂ t + v normalr false( boldr , normalξ , t false) · ∇ normalr normalρ normald false( boldr , t false) true) The fluid particle mass can be defined as: m ( r , ξ , t ) = V ( ξ ) ρ d ( r , t ) = 1 6 π ξ 3 ρ d ( r , t ) The volume fraction α d is defined by the third moment of ξ: …”