Two-Fluid Models

In the two-fluid models, separate continuity and momentum equations are derived for the liquid and gas phases with an appropriate interface mass and momentum transfer relations. The two-fluid method is potentially capable of producing more accurate solutions, since extra relations (specifying Interphase slip, for example) are included in the model. This method has been widely used in nuclear reactor thermal hydraulics following the pioneering work by Harlow and Amsden. Most of these applications have ignored turbulence or simulated it by means of constant effective viscosity. 

The two-phase flow formulation can also be categorized into two groups, namely, the Eulerian-Eulerian models and Eulerian-Lagrangian model. In the Eulerian-Eulerian model, a set of transport equations is solved for the gas phase while in the Eulerian-Lagrangian model, the gas phase is treated as particles, which interact with the continuous phase. 

In the Eulerian-Eulerian models, separate transport equations are solved for each phase. Ilegbusi et al. [7] used such flow model to calculate the flow characteristics 

Within this framework, the governing equations can be expressed as follows. Mass conservation 

The momentum transfer between the phases occurs on the basis of the drag function. negbusi et al. [8] employed the following formulation for momentum exchange between the two phases  

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Eulerian two-fluid model coupled with dispersed itequations was applied to predict gas-liquid two-phase flow in cyclohexane oxidation airlift loop reactor. Simulation results have presented typical hydrodynamic characteristics, distribution of liquid velocity and gas hold-up in the riser and downcomer were presented. The draft-tube geometry not only affects the magnitude of liquid superficial velocity and gas hold-up, but also the detailed liquid velocity and gas hold-up distribution in the reactor, the final construction of the reactor lies on the industrial technical requirement. The investigation indicates that CFD of airlift reactors can be used to model, design and scale up airlift loop reactors efficiently. 

For other discussions of two-phase models and numerical solutions, the reader is referred to the following references thermofluid dynamic theory of two-phase flow (Ishii, 1975) formulation of the one-dimensional, six-equation, two-phase flow models (Le Coq et al., 1978) lumped-parameter modeling of one-dimensional, two-phase flow (Wulff, 1978) two-fluid models for two-phase flow and their numerical solutions (Agee et al., 1978) and numerical methods for solving two-phase flow equations (Latrobe, 1978 Agee, 1978 Patanakar, 1980). 

Granziera, R., and M. S. Kazimi, 1980, A Two-Dimensional Two-Fluid Model for Sodium Boiling in LMFBR Fuel Assemblies, Energy Laboratory Rep. No. MIT-EL-80-011, Massachusetts Institute of Technology, Cambridge, MA. (4)... 

Yadigaroglu, G., and M. Andreani, 1989, Two Fluid Modeling of Thermal-Hydraulic Phenomena for Best Estimate LWR Safety Analysis, Proc. 4th Int. Topical Meeting on Nuclear Reactors Thermal-Hydraulics, Karlsruhe, U. Mueller, K. Rehnee, and K. Rust, Eds., Rep. NURETH-4, pp. 980-996. (3)... 

The above model assumes that both components are dynamically symmetric, that they have same viscosities and densities, and that the deformations of the phase matrix is much slower than the internal rheological time [164], However, for a large class of systems, such as polymer solutions, colloidal suspension, and so on, these assumptions are not valid. To describe the phase separation in dynamically asymmetric mixtures, the model should treat the motion of each component separately ( two-fluid models [98]). Let Vi (r, t) and v2(r, t) be the velocities of components 1 and 2, respectively. Then, the basic equations for a viscoelastic model are [164—166]... 

Andrews, A. T. IV., and Sundaresan, S. Closures for filtered two-fluid model equations of gas-particle flows, Manuscript in preparation (2006). 

In the two-fluid formulation, the motion or velocity field of each of the two continuous phases is described by its own momentum balances or NS equations (see, e.g., Rietema and Van den Akker, 1983 or Van den Akker, 1986). In both momentum balances, a phase interaction force between the two continuous phases occurs predominantly, of course with opposite sign. Two-fluid models therefore belong to the class of two-way coupling approaches. The continuum formulation of the phase interaction force should reflect the same effects as experienced by the individual particles and discussed above in the context of the Lagrangian description of dispersed two-phase flow. 

The number of equations to be solved is, among other things, related to the turbulence model chosen (in comparison with the k-e model, the RSM involves five more differential equations). The number of equations further depends on the character of the simulation whether it is 3-D, 21/2-D, or just 2-D (see below, under The domain and the grid ). In the case of two-phase flow simulations, the use of two-fluid models implies doubling the number of NS equations required for single-phase flow. All this may urge the development of more efficient solution algorithms. Recent developments in computer hardware (faster processors, parallel platforms) make this possible indeed. 

Thus the two-fluid model can be formulated in terms of any two velocities chosen from the set Ug, Us, Umass and Uvoi, which might be useful, for example, to... 

Crowel576] classified the numerical models for dilute sprays as two-fluid model and discrete elementmodel. The Iwo-fluid model treats the dispersed phase as another fluid with appropriate constitutive relationships for effective viscosity and thermal conductivity. The advantage of the two-fluid model is that the same algorithm used for the gas phase can be applied directly to the droplet phase. The drawback is the lack of information on the dispersion coefficient and the effective... 

It is obvious that the role of randomness in the distribution of Mn acceptors and extrinsic defects, which is neglected in the model in question, will grow with approaching the localized regime. According to the two fluid model discussed previously, there is a... 

A. Attou and G. Ferschneider, A two-fluid model for flow regime transition in gas-liquid trickle-bed reactors, Chem. Engng. Science, 54 (1999) 5031-5037. 

A two-dimensional, Two-Fluid model has been developed for modeling the steady-state flow of particulate materials through vertical pneumatic dryer. Two-dimensional flow field interpretations provide information about properties of the continuous and dispersed phases at every point of the flow field. Axial and radial profiles were obtained for the flow variables. 

A. Levy, I. Borde, Two-fluid model for pneumatic drying of particulate materials, Drying Technol. 19 (8) (2001) 1773-1788. 

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