Drift flux model

Zhao and Bi (2001b) concluded that the drift-flux model with zero drift velocity and Co = 1.2 - 0.2 Pg/Pl agrees with the measured gas velocities for the three tested miniature channels. 

Ishii (1977) One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase regimes. AML Report ANL-77-47 Ide H, Matsumura H, Tanaka Y, Fukano T (1997) Flow patterns and frictional pressure drop in gas-liquid two-phase flow in vertical capUlary channels with rectangular cross section, Trans JSME Ser B 63 452-160... 

The Chexal-Lellouche model (a flow regime-independent drift flux model)... 

The Ohkawa-Lakey model (a drift flux model with empirically derived coefficients) The Dix model (a drift flux model devised for analyzing boiling water reactors (BWRs) at operating conditions)... 

In reality, the slip velocity may not be neglected (except perhaps in a microgravity environment). A drift flux model has therefore been introduced (Zuber and Findlay, 1965) which is an improvement of the homogeneous model. In the drift flux model for one-dimensional two-phase flow, equations of continuity, momentum, and energy are written for the mixture (in three equations). In addition, another continuity equation for one phase is also written, usually for the gas phase. To allow a slip velocity to take place between the two phases, a drift velocity, uGJ, or a diffusion velocity, uGM (gas velocity relative to the velocity of center of mass), is defined as... 

As mentioned earlier, the drift-flux model is used in slip flows. Equation (3-63) can be written in the form... 

Ishii, M., andT. C. Chawla, 1978, Multichannel Drift-Flux Model and Constitutive Relation for Transverse Drift-Velocity, Rep. ANL/RAS/LWR 78-2, Argonne Natl. Lab., Argonne, IL. (3)... 

To complete the drift-flux model, the phenomenological theory of Lapidus and Elgin (9) is used, wherein it was suggested for dispersed flow systems that the slip velocity depends directly on terminal bubble rise velocity, U, so that... 

For the case of a semibatch bubble column (no liquid flow), the drift flux model takes the form... 

To determine the dispersed phase velocities as occurring in the phasic continuity equations in both formulations, the momentum equation of the dispersed phases are usually approximated by algebraic equations. Depending on the concept used to relate the phase k velocity to the mixture velocity the extended mixture model formulations are referred to as the algebraic slip-, diffusion- or drift flux models. 

This form of the mixture model is called the drift flux model. In particular cases the flow calculations is significantly simplified when the problem is described in terms of drift velocities, as for example when ad is constant or time dependent only. However, in reactor technology this model formulation is restricted to multiphase cold flow studies as the drift-flux model cannot be adopted simulating reactive systems in which the densities are not constants and interfacial mass transfer is required. 

The drift-flux model equations have been assessed in multiphase flow analysis by several authors [112, 85, 145, 231]. 

Understanding of gas-liquid flow in electrochemical systems is very important for system optimization, enhance mass transport and thus gas release efficiency. There are relatively little theoretical studies available in the literature which considers process as a two-phase flow problem. Zeigler and Evans[2] applied the drift - flux model of Ishii[3] to electrochemical cell and obtained velocity field, bubble distribution, mass transfer rate. Instead of treating the bubbles as a second phase, they obtained bubble distribution from concentration equation. Dahikild [4] developed an extensive mathematical model for gas evolving electrochemical cells and performed a boundary layer analysis near a vertical electrode. 

Because of the film between the bubble and the wall, the bubble and liquid velocities are not the same. The bubble velocity, Ub, is given by the drift flux model ... 

This correlation reqnires information on u, which can be estimated using Equation 10.7. This latter equation requires data on as a function of superficial gas velocity to evaluate the terminal rise velocity of the bubble, These data can be obtained throngh simple gas holdup measurements. The drift flux model of Zuber and Findlay (1965) can be used to obtain as per Equation 10.10 ... 

Shamlou et al. [27] developed a model for the liquid circulation rate in internal-loop airlift columns using a combination of a drift-flux model with an energy balance. The superficial liquid circulation rate in the riser is given as... 

Shamlou et al. proposed a model for the prediction of gas holdup and liquid circulation in internal-loop airlift columns [27]. It is based on the drift-flux model of Zuber and Findlay [45] and an energy balance taking into account the physical interactions between the liquid, the bubbles, and the liquid wake associated with the bubbles. The expression for gas holdup obtained from the drift-flux model is written as... 

Separated Flow Model—Drift Flux Model.763... 

Figure 13 The regime transition velocity (a) in a bubble column. Open symbols are obtained by standard deviation of pressure fluctuation and drift flux model closed symbols are calculated by the correlation of Wilkinson et al. (1992). (From Lin et al., 1999.) (b) In a three-phase fluidized bed. (From Luo et al., 1997a.)...

An alternative model suggested by Grevet et al. [50] called drift-flux model which allows partial slip between the phases gives... 

Woo et al. [34] compared the performance of drift-flux, no-slip model and experimentally obtained model for void fraction. One of the representative results is presented in Fig. 9.3, showing the radial variation of the absolute value of mean velocity at z/H = 0.3 and 0.98, respectively, with H being the height of the bath. The predictions from the drift-flux model and the correlation agree satisfactorily... 

Hughes, E.D., Paulsen, M.P., Agee, L.J., 1981. A drift-flux model of two-phase flow for RETRAN. Nuclear Technology 54, 410—421. 

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