Multiphase flows Reynolds number

Kandlikar SG, Joshi S, Tian S (2003) Effect of surface roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Heat Transfer Eng 24 4-16 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 Flow 28 1411-1435 Kennedy JE, Roach GM, Dowling ME, Abdel-Khalik SI, Ghiaasiaan SM, Jeter SM, Quershi ZH (2000) The onset of flow instability in uniformly heated horizontal micro-channels. Trans ASME J Heat Transfer 122 118-125... 

Reducing the bed length while keeping the space velocity the same will reduce the fluid velocity proportionally. This will affect the fluid dynamics and its related aspects such as pressure drop, hold-ups in case of multiphase flow, interphase mass and heat transfer and dispersion. Table II shows the large variation in fluid velocity and Reynolds number in reactors of different size. The dimensionless Reynolds number (Re = u dp p /rj, where u is the superficial fluid velocity, dp the particle diameter, p the fluid density and t] the dynamic viscosity) generally characterizes the hydrodynamic situation. 

In the foregoing discussion, the assumption is that each phase is transported in its own percolating network by a pressure-driven flow mechanism. This is the generally accepted view of multiphase flow in subsurface applications, and is certainly true at low values of the capillary number Ca = vfi/a). However, blob mobilization is a dominant form of transport in many unit operations in chemical engineering, where the capillary number and Reynolds number are higher. In these cases, specialized correlations for multiphase flow should be used. 

Dorgan, a. J. Loth, E. 2007 Efficient calculation of the history force at finite Reynolds numbers. International Journal of Multiphase Flow 33, 833-848. 

S. Kim, Singularity solutions for ellipsoids in low-Reynolds number flows With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids, Ini. J. Multiphase Flow 12, 469-91 (1986). 

Hetsroni G., Haber S., Low Reynolds Number Motion of two Drops submerged in unbounded arbitrary Velocity Field, J. Multiphase Flow, 1978, Vol. 4, p. 1-17. 

In this chapter, we have provided a brief introduction to the LBM for computation of multiphase flows of relevance to atomization and sprays. Since its inception, the LBM has come a long way, especially in overcoming some of the early challenges. In particular, the use of MRT formulation for multiphase flows has been a major step in maintaining numerical stability at lower viscosities or higher Reynolds numbers the use of consistent discretization approaches in the LBM has enabled simulation of high density ratio problems. During the last few years. 

Whereas in a fixed bed reactor with a single fluid phase there exist only two modes of operation, either downflow (which is used in most cases) or upflow, and only two different flow regimes, either laminar or turbulent flow, which can be observed and characterized by a Reynolds number as the single relevant dimensionless group, the fluiddynamics in multiphase catalytic fixed bed reactors are much more complex. 

When the flow is laminar, either single or multiphase, there is only one design class option static or motionless mixers. Other pipeline mixing devices described for turbulent flow are not usable for even the simplest mixing applications in the laminar regime. All rely on turbulence and cannot function at low Reynolds numbers. The only alternative technology is in-line dynamic mixers, which include extruders, rotor-stator mixers, and a variety of rotating screw devices. None of these has the benefits of simplicity and the little or no maintenance characteristic of static mixers. In-line mechanical mixers are discussed briefly later in the chapter. 

Shapira M, Haber S. Low Reynolds-number motion of a droplet in shear flow inclnding wall effeets. Int J Multiphase How 1990 16(2) 305-321. 

Note that the denominator of this equation is positive, which has a stabilizing effect on the solution of the fluid velocity field. This is particularly important for cases where is very large, which is often the case in dense multiphase flows at large particle Reynolds numbers. 

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