Closures for the Bubble Size Distribution and Interfacial Area Concentration

2015 ◽  
pp. 205-249
Author(s):  
Christophe Morel
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Interfacial Area ◽  
Bubble Size Distribution ◽  
Interfacial Area Concentration

scholarly journals Numerical investigation on the performance of coalescence and break-up kernels in subcooled boiling flows in vertical channels

2016 ◽  
Vol 9 (2) ◽  
pp. 71-85 ◽  
Author(s):  
Sara Vahaji ◽  
Sherman CP Cheung ◽  
Lilunnahar Deju ◽  
Guan Yeoh ◽  
Jiyuan Tu
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubble Dynamics ◽  
Interfacial Area ◽  
Bubble Size Distribution ◽  
Heated Wall ◽  
Bubble Coalescence ◽  
Two Phase ◽  
Interfacial Area Concentration ◽  
Break Up

In order to accurately predict the thermal hydraulic of two-phase gas–liquid flows with heat and mass transfer, special numerical considerations are required to capture the underlying physics: characteristics of the heat transfer and bubble dynamics taking place near the heated wall and the evolution of the bubble size distribution caused by the coalescence, break-up, and condensation processes in the bulk subcooled liquid. The evolution of the bubble size distribution is largely driven by the bubble coalescence and break-up mechanisms. In this paper, a numerical assessment on the performance of six different bubble coalescence and break-up kernels is carried out to investigate the bubble size distribution and its impact on local hydrodynamics. The resultant bubble size distributions are compared to achieve a better insight of the prediction mechanisms. Also, the void fraction, bubble Sauter mean diameter, and interfacial area concentration profiles are compared against the experimental data to ensure the validity of the models applied.

Bubble size distribution and gas–liquid interfacial area in a modified downflow bubble column

2006 ◽  
Vol 122 (1-2) ◽  
pp. 1-10 ◽  
Author(s):  
Subrata Kumar Majumder ◽  
Gautam Kundu ◽  
Dibyendu Mukherjee
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubble Column ◽  
Interfacial Area ◽  
Bubble Size Distribution

scholarly journals Measurement of Bubble Size, Gas holdup and Interfacial Area in Bubble Columns using Image Processing Techniques

2019 ◽  
Vol 9 (1) ◽  
pp. 4475-4479
Keyword(s):  
Image Processing ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubble Column ◽  
Rectangular Cross Section ◽  
Bubble Diameter ◽  
Water System ◽  
Interfacial Area ◽  
Gas Holdup ◽  
Bubble Size Distribution

Bubble sizes in bubble column affect transfer processes. Therefore, it’s important to calculate bubble size and interfacial area. Bubble size distribution (BSD) in a bubble column of rectangular cross section with dimensions 0.2m x 0.02m was measured using photographic method (400 fps) for air-water system. Gas holdup, Sauter-mean bubble diameter, aspect ratio and specific interfacial area were estimated from BSD. Effect of superficial gas velocity and static bed height on these parameters was investigated. The bubble size distribution exhibited mono-modal distribution showing the presence of non-uniform homogeneous bubbling regime. The frames of video were analysed using image processing steps to obtain major and minor axis of elliptical bubbles. Values of d32, , and ai were estimated from the data. The value of d32 increased with increasing Ug but is independent of Hs. The values of d32 were somewhat higher than the values reported by other investigators. The value of ai increases with increasing Ug and with decreasing Hs. Present values of compared well with the data reported in literature.

Closure Laws for the Transport Equation of Interfacial Area in Dispersed Flow

2002 ◽  
Author(s):  
X. Rioua ◽  
J. Fabrea ◽  
C. Colin
Keyword(s):  
Transport Equation ◽  
Size Distribution ◽  
Bubble Size ◽  
Interfacial Area ◽  
Bubble Size Distribution ◽  
Bubble Coalescence ◽  
Size Distributions ◽  
Mean Diameter ◽  
The Mean ◽  
Two Fluid

Derivation of a transport equation for the interfacial area concentration. In two-phase flows, the interfacial area is a key parameter since it mainly controls the momentum heat and mass transfers between the phases. An equation of transport of interfacial area may be very useful, especially for the two-fluid models. Such an equation should be able to predict the transition between the flow regimes. With this aim in view, we shall focus our attention on pipe flow. Besides in a first step, our study will be limited to dispersed flows. Different models are used to predict the evolution of bubble sizes. Some models use a population balance that provides a detailed description of the bubble size distributions, but they require as many equations as diameter ranges (Coulaloglou & Tavlarides1). Some others use only one equation for the transport of the mean interfacial area (Hibiki & Ishii2). In that case the bubble size distribution is treated as it would be monodispersed, its mean diameter being equal to the Sauter diameter. An intermediate approach was proposed by Kamp et al.3, in which polydispersed size distributions can be taken into account. It is the starting point of the present study in which: • The choice of an interfacial velocity is discussed. • The sink and source terms due to bubble coalescence, break-up or phase change are established. The model of Kamp et al. consists of transport equations of the various moments of the density probability function P(d) of the bubble diameter. In many experimental situations, P(d) is well predicted by a log-normal law (with two characteristic parameters d00 the central diameter of the distribution and a width parameter): The different moments of order ? of P(d) may be calculated: Sγ=n∫P(d)dγd(d)(1) where n is the bubble number density, S1/n, the mean diameter and S2/?, the interfacial area. A transport equation can be written for each moment: ∂Sγ∂t+∇·(uGSγ)=φγ(2) The lhs of (2) is an advection term by the gas velocity uG and the rhs is a source or sink term due to bubble coalescence, break-up or mass transfer. Since the bubble size distribution is characterised by the two parameters d00 and σˆ, only two transport equations (for S1 and S2) have to be solved to calculate the space-time evolution of the bubble size distribution. These two equations are still too cumbersome for a two-fluid model. Under some hypotheses (σˆ ∼ constant), they are lead to a single equation for the interfacial area. In its dimensionless form the interfacial area ai+ (ai+ = π S2 D, where D is the pipe diameter) reads: d/dt+(ai+)=f(RG,Re,We,ai+)(3) where RG is the gas fraction, Re is the Reynolds number of the mixture, We the Weber number of the mixture and t+ a dimensionless time.

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