Fluid mechanics multiphase

Advances in engineering fluid mechanics multiphase reactor and polymerization system hydrodynamics / Nicholas P. Cheremisinoff, editor in collaboration with M. Abid. . . [et al.J. p. cm. 

Benjamin TB (1968) Gravity currents and related phenomena. J. Fluid Mechanics 31(2) 209-248 Butterworth D (1975) A comparison of some void-fraction relationships for co-current gas-liquid flow. Int J Multiphase Flow 1 845-850... 

Kawahara A, Chung PM, Kawaji M (2002) Investigation of two-phase flow pattern, void fraction and pressure drop in a micro-channel. Int J Multiphase Plow 28 1411-1435 Kawaji M (1999) Fluid mechanics aspects of two-phase flow Flow in other geometries. In Kand-likar SG, Shoji M, Dhir VK (eds) Handbook of phase change boiling and condensation. Taylor and Francis, Washington, DC, pp 205-259... 

Krishna, R. (1993). Analogies in Multiphase Reactor Hydrodynamics. In Encyclopedia of Fluid Mechanics. Supplement 2. Advances in Multiphase Flow. Ed. N. P. Cheremisinoff. Houston Gulf Publishing. 

Additional information on hydrodynamics of bubble columns and slurry bubble columns can be obtained from Deckwer (Bubble Column Reactors, Wiley, 1992), Nigam and Schumpe (Three-Phase Sparged Reactors, Gordon and Breach, 1996), Ramachandran and Chaudhari (Three-Phase Catalytic Reactors, Gordon and Breach, 1983), and Gianetto and Silveston (Multiphase Chemical Reactors, Hemisphere, 1986). Computational fluid mechanics approaches have also been recently used to estimate mixing and mass-transfer parameters [e.g., see Gupta et al., Chem. Eng. Sci. 56(3) 1117-1125 (2001)]. 

Clearly, the capability of relatively rapid and inexpensive numerical solutions of a proposed set of governing equations or boundary conditions that can be used in an interactive way with experimental observation represents a profound new opportunity that should greatly facilitate the development of a theoretical basis for fluid mechanics and transport phenomena for complex or multiphase fluids that are the particular concern of chemical engineers. 

Fraser Russell I d like to say a bit about multiphase fluid mechanics. If one is concerned with design and, as Gary said, focusing on the macroscale (Fig. 1), one needs a lot more information about the creation and/or movement... 

In the previous section, stability criteria were obtained for gas-hquid bubble columns, gas-solid fluidized beds, liquid-sohd fluidized beds, and three-phase fluidized beds. Before we begin the review of previous work, let us summarize the parameters that are important for the fluid mechanical description of multiphase systems. The first and foremost is the dispersion coefficient. During the derivation of equations of continuity and motion for multiphase turbulent dispersions, correlation terms such as esv appeared [Eqs. (3) and (10)]. These terms were modeled according to the Boussinesq hypothesis [Eq. (4)], and thus the dispersion coefficients for the sohd phase and hquid phase appear in the final forms of equation of continuity and motion [Eqs. (5), (6), (14), and (15)]. However, for the creeping flow regime, the dispersion term is obviously not important. 

The drag force depends upon the particle Reynolds number. Different Co-Re relationships have been used in the past. Further, several investigators have attempted fluid-mechanical description of multiphase systems. It was thought desirable to analyze all these attempts in view of the discussion given earlier. Such an analysis is summarized in Table II. Some additional points are given next. 

Spalding D.B. (1980) Numerical computation of multiphase flow and heat transfer. In Recent Advances in Numerical Methods in Fluid Mechanics (Ed. by C. Taylor K. Morgan), Pineridge, Swansea, pp. 139-168... 

The steady-state fluid mechanics problem is solved using the Fluent Euler-Euler multiphase model in the fluid domains. Mass, momentum and energy balances, the general forms of which are given by eqn. (4), (5), and (6), are solved for both the liquid and the gas phases. In solid zones the energy equation reduces to the simple heat conduction problem with heat source. By convention, / =1 designates the H2S04 continuous liquid phase whereas H2 bubbles constitute the dispersed phase 0 =2). 

Kolditz, O. Computational Methods in Environmental Fluid Mechanics Springer Berlin, 2002. Parker, J.C. Multiphase flow and transport in porous media. Rev. Geophys. 1989, 27 (3), 311-328. 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

In this chapter several numerical methods frequently employed in reactor engineering are introduced. To simulate the important phenomena determining single- and multiphase reactive flows, mathematical equations with different characteristics have to be solved. The relevant equations considered are the governing equations of single phase fluid mechanics, the multi-fluid model equations for multiphase flows, and the population balance equation. 

Balachandar, S. Eaton, J. K. 2010 Turbulent dispersed multiphase flow. Annual Review of Fluid Mechanics 42, 111-133. 

Fox, R. 0.2012 Large-eddy-simulation tools for multiphase flows. Annual Review of Fluid Mechanics 44,47-76. 

Thorenz, C. 2001. Model Adaptive Simulation of Multiphase and Density Driven Flow in Fractured and Porous Media. Ph.D. thesis. Institute of Fluid Mechanics and Computer Applications in Civil Engineering, University of Hannover, Report 62/2001, Hannover. 

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