Poly-dispersed modeling of bubbly flow using the log-normal size distribution. (29th June 2019)

• Record Type: Journal Article
• Authors: Frederix, E.M.A.; Cox, T.L.W.; Kuerten, J.G.M.; Komen, E.M.J.
• Is Part Of: Chemical engineering science. Volume 201(2019)
• Page Start: 237
• Page End: 246
• Publication Date: 2019-06-29
• Subjects: Bubbly flow -- Moment modeling -- Two-fluid model -- Size distribution -- Log-normal -- Population balance; Chemical engineering -- Periodicals; Génie chimique -- Périodiques; Chemical engineering; Periodicals; Electronic journals; 660
• DOI: 10.1016/j.ces.2019.02.013
• Languages: English
• ISSNs: 0009-2509

Abstract

Highlights: A pragmatic and efficient poly-disperse method for bubbly flow simulation is presented. Closure is achieved using the log-normal presumed number density function. Good agreement is found with reference data for bubbly flow in the mono-dispersed limit. Poly-dispersity and poly-celerity are shown to play an important role in bubbly flow. Good agreement is found between our moment method and an accurate sectional approach. Abstract: The bubble size distribution plays an important role in interfacial mass, momentum and energy transfer between bubbles and their carrier liquid in bubbly flow. Accurate modeling of the size distribution is therefore key. A Log-Normal presumed Number Density Function (LNpNDF) approach is proposed, which is embedded into the two-fluid model. Two additional moment transport equations are formulated which are shown to be consistent with the two-fluid model. From the moments, the size distribution can be fully reconstructed using the assumption that its underlying shape is log-normal. This methodology offers closure for the modeling of processes such as bubble coalescence, break-up and bubble poly-celerity. Special attention is paid to the concept of poly-celerity, which is shown to play an important role in the evolution of finite-width size distributions. A new average diameter, which is based on the fifth and third moment of the size distribution, is proposed, and it is shown that this diameter is a more suitable quadrature node for the modeling of bubble–liquid Stokes-like drag. The paper lays the mathematical foundation for a pragmatic, computationally efficient and effective poly-dipsersed method for the modeling of dispersed two-phase flow.