Drift flux

Rhodes, and Scott Can. j. Chem. Eng., 47,445 53 [1969]) and Aka-gawa, Sakaguchi, and Ueda Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles Can. ]. Chem. Eng., 52, 25-35 [1974]) and Barnea, Shoham, and Taitel Chem. Eng. Sci, 37, 741-744 [1982]). Use of drift flux theoiy for void fraction modeling in downflow is presented by Clark anci Flemmer Chem. Eng. Set., 39, 170-173 [1984]). Downward inclined two-phase flow data and modeling are given by Barnea, Shoham, and Taitel Chem. Eng. Set., 37, 735-740 [1982]). Data for downflow in helically coiled tubes are presented by Casper Chem. Ins. Tech., 42, 349-354 [1970]). 

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 Liao, Parlos, and Griffith model (a flow regime-based drift flux formulation including bubbly, churn-turbulent, and annular flows)... 

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)... 

Optical probes were used to measure the bubble size, frequency and velocity within the dense bed. The bubble velocity for an actively bubbling bed was found to closely agree with the drift flux form proposed by Davidson and Harrison (1963). In contrast, the volumetric flow rate of the bubbles was found to be far less than that predicted by the two-phase hypothesis (Fig. 40). 

While one might question some of the assumptions of their model, such as D0 = D+ and f = constant, it is not unlikely that the model gives roughly correct results over at least a good part of the range of experimental conditions. This would be the case, for example, if the diffusion flux of H° is usually small compared with the drift flux of H+ and would still be so if D0 were equal to D+, and if the most important transport occurs in a reverse bias depletion region where n+/n0 has a nonequilibrium universal... 

The interpretation of these results has not been completely clarified. A plausible starting point might be to assume that in the steady state, all concentrations and fluxes in the crystal are functions of the single variable C — x — vetf, where x is position relative to the original (t = 0) crystal surface, t is the time since the start of etching, and vet is the etch velocity. At any f, the diffusion-drift flux J of hydrogen must obey... 

Equilibrium state, 24 642. See also Equilibrium progress toward, 24 649 Equilibrium value, 14 611 Equilibrium volume parameters, from density measurements, 13 435-436 Equimolar counterdiffiision, 1 39-40 drift flux correction, 1 55-58 Equipment. See also Failure mode and effects analysis (FMEA)... 

The quantity uG>L is called the characteristic velocity or drift flux and has an important physical significance, which can be seen by making the following manipulations ... 

Calculation methods are given here for cases (a) to (c). In section A3.4 below, references are given to a calculation method for case (d). The level swell calculation methods presented here use the drift flux correlations developed by DIERS[11. The DIERS correlations apply to a vertical cylindrical vessel, which is most often the case for chemical reactors. Modifications for horizontal cylindrical vessels are given by Sheppard[2,3]. 

SuperChems Expert 161 is a code developed by Arthur D Little Inc. for risk assessment consequence analysis, which also has a relief system sizing option. The code has a physical properties package that can handle highly non-ideal properties. It can also consider the effect of chemical reaction in the relief system piping. The code uses the DIERS drift flux methods for level swell and has the option of a rigorous two-phase slip model for the. relief system capacity. 

In concluding, let us comment on the time needed to attain the steady state after establishing the surface activities. Two transient processes having different relaxation times occur I) the steady state vacancy concentration profile builds up and 2) the component demixing profile builds up until eventually the system becomes truly stationary. Even if the vacancies have attained a (quasi-) steady state, their drift flux is not stationary until the demixing profile has also reached its steady state. This time dependence of the vacancy drift is responsible for the difficulties that arise when the transient transport problem must be solved explicitly, see, for example, [G. Petot-Er-vas, et al. (1992)]. 

Figure 11-6 defines the transport problem in a quasi-binary ionic system (A,B)X with a miscibility gap, if both chemical (V/i,) and electrical (Vp) driving forces act simultaneously (case 3)). If the chemical force is negligible, we are dealing with case 2) and the electrical drift flux of the cations shifts the boundary b in the direction of the flux. We can conclude that, in agreement with Figure 11-5 a, the boundary morphology is unstable if... 

Akagawa, Sakaguchi, and Ueda (Bull JSME, 14, 564-571 [1971]). Correlations for flow patterns in downflow in vertical pipe are given by Oshinowo and Charles (Can. J. Chem. Eng., 52,25-35 [1974]) and Barnea, Shoham, and Taitel (Chem. Eng. Sci., 37, 741—744 [1982]). Use of drift flux theory for void fraction modeling in downflow is... 

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