Drag coefficient and relative velocity in bubbly, droplet or particulate flows
TL;DR: In this article, the relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model, and satisfactory agreements were obtained at wide ranges of the particle concentration and Reynolds number.
Abstract: Drag coefficient and relative motion correlations for dispersed two-phase flows of bubbles, drops, and particles were developed from simple similarity criteria and a mixture viscosity model. The results are compared with a number of experimental data, and satisfactory agreements are obtained at wide ranges of the particle concentration and Reynolds number. Characteristics differences between fluid particle systems and solid particle systems at higher Reynolds numbers or at higher concentration regimes were successfully predicted by the model. Results showed that the drag law in various dispersed two-phase flows could be put on a general and unified base by the present method.
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Dissertation•
01 Jan 2003
TL;DR: In this paper, the authors describe the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows, which employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases.
Abstract: This study describes the development and validation of Computational Fluid Dynamics (CFD) methodology for the simulation of dispersed two-phase flows. A two-fluid (Euler-Euler) methodology previously developed at Imperial College is adapted to high phase fractions. It employs averaged mass and momentum conservation equations to describe the time-dependent motion of both phases and, due to the averaging process, requires additional models for the inter-phase momentum transfer and turbulence for closure. The continuous phase turbulence is represented using a two-equation k − ε−turbulence model which contains additional terms to account for the effects of the dispersed on the continuous phase turbulence. The Reynolds stresses of the dispersed phase are calculated by relating them to those of the continuous phase through a turbulence response function. The inter-phase momentum transfer is determined from the instantaneous forces acting on the dispersed phase, comprising drag, lift and virtual mass. These forces are phase fraction dependent and in this work revised modelling is put forward in order to capture the phase fraction dependency of drag and lift. Furthermore, a correlation for the effect of the phase fraction on the turbulence response function is proposed. The revised modelling is based on an extensive survey of the existing literature. The conservation equations are discretised using the finite-volume method and solved in a solution procedure, which is loosely based on the PISO algorithm, adapted to the solution of the two-fluid model. Special techniques are employed to ensure the stability of the procedure when the phase fraction is high or changing rapidely. Finally, assessment of the methodology is made with reference to experimental data for gas-liquid bubbly flow in a sudden enlargement of a circular pipe and in a plane mixing layer. Additionally, Direct Numerical Simulations (DNS) are performed using an interface-capturing methodology in order to gain insight into the dynamics of free rising bubbles, with a view towards use in the longer term as an aid in the development of inter-phase momentum transfer models for the two-fluid methodology. The direct numerical simulation employs the mass and momentum conservation equations in their unaveraged form and the topology of the interface between the two phases is determined as part of the solution. A novel solution procedure, similar to that used for the two-fluid model, is used for the interface-capturing methodology, which allows calculation of air bubbles in water. Two situations are investigated: bubbles rising in a stagnant liquid and in a shear flow. Again, experimental data are used to verify the computational results.
968 citations
Cites background or methods or result from "Drag coefficient and relative veloc..."
...However, it should be noted that Ishii and Zuber [168] modified the constant given by Harmathy from 0....
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...In this Section, only correlations applicable to particles are given, whereas Ishii and Zuber’s [168] correlations applicable to fluid particles will be presented in Sections 6....
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...1, Ishii and Zuber [168] developed a unified model for particles, droplet and bubbles....
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...They also found that it gives better fits than that proposed by Peebles and Garber [303] and Ishii and Zuber [168]....
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...This mixture viscosity is then used to define the Reynolds number appearing in a suitable drag correlation [15, 168, 208]....
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31 Dec 1996
TL;DR: In this paper, the authors focus on the derivation and closing of the model equations, and the validity of the mixture model is also carefully analyzed, starting from the continuity and momentum equations written for each phase in a multiphase system, the field equations for the mixture are derived.
Abstract: Numerical flow simulation utilising a full multiphase model is impractical for a suspension possessing wide distributions in the particle size or density. Various approximations are usually made to simplify the computational task. In the simplest approach, the suspension is represented by a homogeneous single-phase system and the influence of the particles is taken into account in the values of the physical properties. This study concentrates on the derivation and closing of the model equations. The validity of the mixture model is also carefully analysed. Starting from the continuity and momentum equations written for each phase in a multiphase system, the field equations for the mixture are derived. The mixture equations largely resemble those for a single-phase flow but are represented in terms of the mixture density and velocity. The volume fraction for each dispersed phase is solved from a phase continuity equation. Various approaches applied in closing the mixture model equations are reviewed. An algebraic equation is derived for the velocity of a dispersed phase relative to the continuous phase. Simplifications made in calculating the relative velocity restrict the applicability of the mixture model to cases in which the particles reach the terminal velocity in a short time period compared to the characteristic time scale of the flow of the mixture. (75 refs.)
758 citations
TL;DR: A description of recent spray evaporation and combustion models, taking into account turbulent two-and three-dimensional spray processes found in furnaces, gas turbine combustors, and internal combustion engines, is given in this paper.
747 citations
TL;DR: In this article, a two-fluid formulation for two-phase flow analyses is presented, where a fully threedimensional model is obtained from the time averaging, whereas the one-dimensional model was developed from the area averaging.
738 citations
TL;DR: The fundamentals of microbial kinetics and continuous culture models are presented and the effect of temperature and inhibitors on the intrinsic kinetic rates is discussed, and Stoichiometric and bioenergetic considerations are reviewed.
Abstract: The fundamentals of microbial kinetics and continuous culture models are presented. The kinetics of the anaerobic treatment processes are reviewed recognizing that anaerobic degradation of complex, polymeric organic materials is a combination of series and parallel reactions. Such reactions include hydrolysis, fermentation, anaerobic oxidation of fatty acids, and methanogenesis. The intrinsic rates of each step are reviewed and literature data summarized. Whenever possible, available kinetic information is summarized on the basis of substrate composition (such as carbohydrates, proteins, and lipids). The effect of temperature and inhibitors on the intrinsic kinetic rates is discussed. Stoichiometric and bioenergetic considerations are reviewed. Mass transfer limitations (both external and internal) associated with biofilms and microbial agglomerates, in general, and their effect on the intrinsic kinetic rates are presented. Areas requiring further research are identified.
638 citations