Fluid motion multiphase flow

Whitaker, S. (1969). Advances in Theory of Fluid Motion in Porous Media. I EC., 61,4. Zeininger, G. and Brennen, C. E. (1985). Interstitial Fluid Effects in Hopper Flows of Granular Materials. ASME Cavitation and Multiphase Flow Forum, Albuquerque, N. Mex. 

Turbulence is the most complicated kind of fluid motion. There have been several different attempts to understand turbulence and different approaches taken to develop predictive models for turbulent flows. In this chapter, a brief description of some of the concepts relevant to understand turbulence, and a brief overview of different modeling approaches to simulating turbulent flow processes is given. Turbulence models based on time-averaged Navier-Stokes equations, which are the most relevant for chemical reactor engineers, at least for the foreseeable future, are then discussed in detail. The scope of discussion is restricted to single-phase turbulent flows (of Newtonian fluids) without chemical reactions. Modeling of turbulent multiphase flows and turbulent reactive flows are discussed in Chapters 4 and 5 respectively. 

Lee SL (1987) A unified theory on particle transport in turbulent dilute two-phase suspension flow-11. Int J Multiphase Flow 13(1) 137-144 Lee SL, Borner T (1987) Fluid flow structure in a dilute turbulent two-phase suspension flow in a vertical pipe. Int J Multiphase Flow 13(2) 233-246 Lee SL, Durst F (1982) On the motion of particles in turbulent duct flows. Int J Multiphase Flow 8(2) 125-146... 

Prevost, f., Boree, J., Nuglisch, H.J., Chamay, G. Measurements of fluid/particle correlated motion in the far field of an axisymmetric jet. Int. J. Multiphase Flow, 22, 685-701 (1996)... 

The goal of this chapter is to describe the fluid motion laws in a very general way based on flow systems rather than vahd for special apparatus in narrow ranges of velocities and flttid properties. At first, fundamental laws of one-phase flows are presented because they are the basis for two- and multiphase flow. 

Phase average models apply to well mixed multiphase flows, i.e. when the exact shape of the interfaces is not known, or not relevant e.g. bubbly flows. The principle could be applied under the two-fluid, six-equation model, where separate eonservation equations are required for each phase with appropriate exehange forces, or the homogeneous. Algebraic Slip model. Under sithermal, incompressible flow conditions, the equations of laminar motion for phase A are expressed in the two-fluid formalism as follows ... 

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 averaged Eulerian-Eulerian multi-fluid model denotes the averaged mass and momentum conservation equations as formulated in an Eulerian frame of reference for both the dispersed and continuous phases describing the time-dependent motion. For multiphase isothermal systems involving laminar flow, the averaged conservation equations for mass and momentum are given by ... 

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