Volume of fluid model

SOLA — VOF SOLution Algorithm for the Volume Of Fluid model... 

FLUENT provides the volume of fluid model (VOF) for the description of separated multiphase flows. The VOF model is based on the resolution of the phase interface in a fixed Eulerian mesh. The conservation equations here are not solved separately for the individual phases but rather for the entire calculation domain with material properties averaged across the phases. For this purpose, an additional conservation equation is introduced for the volume fraction f in the continuous phase. A cell contains either the dispersed phase only f = 0), the continuous phase only f = 1), or the phase interface (0 < / < 1). In order to avoid blurring... 

Volume of Fluid Model. In stirred tank applications, the volume of fluid (VOF) free surface model is useful for tracking the shape of the liquid surface during operation. This includes the transition to a parabolic shape during startup, which can lead to the (undesired) drawdown of air. The velocity data model can be used in 2D or 3D for simulations of this type. The VOF model can have a steady or time-dependent implementation, and both are fiilly compatible with this steady-state treatment of the impellers. 

It Is important to know how much each well produces or injects in order to identify productivity or injectivity changes in the wells, the cause of which may then be investigated. Also, for reservoir management purposes (Section 14.0) it is necessary to understand the distribution of volumes of fluids produced from and injected into the field. This data is input to the reservoir simulation model, and is used to check whether the actual performance agrees with the prediction, and to update the historical data in the model. Where actual and predicted results do not agree, an explanation is sought, and may lead to an adjustment of the model (e.g. re-defining pressure boundaries, or volumes of fluid in place). 

The general class of free boundary flow problems can, however, be modelled using the volume of fluid (VOF) approach (Nichols et ai, 1980). The main concept in this technique is to solve, simultaneously with the governing flow equations, an additional equation that represents the unknown boundary. Three different versions of this method are described in the following sections. 

Simulations of multiphase flow are, in general, very poor, with a few exceptions. Basically, there are three different kinds of multiphase models Euler-Lagrange, Euler-Euler, and volume of fluid (VOF) or level-set methods. The Euler-Lagrange and Euler-Euler models require that the particles (solid or fluid) are smaller than the computational grid and a finer resolution below that limit will not give a... 

The subject of liquid jet and sheet atomization has attracted considerable attention in theoretical studies and numerical modeling due to its practical importance.[527] The models and methods developed range from linear stability models to detailed nonlinear numerical models based on boundary-element methods 528 5291 and Volume-Of-Fluid (VOF) method. 530 ... 

The PDF of an inert scalar is unchanged by the first two steps, but approaches the well mixed condition during step (3).108 The overall rate of mixing will be determined by the slowest step in the process. In general, this will be step (1). Note also that, except in the linear-eddy model (Kerstein 1988), interactions between Lagrangian fluid particles are not accounted for in step (1). This limits the applicability of most mechanistic models to cases where a small volume of fluid is mixed into a much larger volume (i.e., where interactions between fluid particles will be minimal). 

Euler-Euler models assume interpenetrating continua to derive averaged continuum equations for both phases. The probability that a phase exists at a certain position at a certain time is given by a phase indicator function, which, for steady-state processes, is equivalent to the volume of fraction of the correspondent phase (volume-of-fluid technique). The phase-averaging process introduces further unknowns into the basic conservation equations their description requires empirical and problem-dependent input (94). In principal, Euler-Euler models are applicable to all multiphase flows. Advantages and disadvantages of both methods are compared, e.g., in Refs. 95 and 96. 

In this section, we present the two-mode models for loop and recycle reactors. In a loop reactor (Fig. 10) of loop length L, a flow rate of qm with an average velocity of u-m) enters and leaves the reactor at points a = 0 and x — l, respectively (where a is the length coordinate along the loop), and the total flow rate in the loop is Q + qin between points a = 0 and x — l, and is Q between points x — l and x — L, due to a recycle rate of Q. The recycle ratio A is the ratio of the volume of fluid returned to the reactor entrance per unit time to the volume of fluid leaving the system per unit time, and is given by A = Q/q-m. 

The model has demonstrated its versatility, allowing a detailed description of the various phenomena involved, but failed in predicting nearly segregated configurations for which numerical difficulties occurred. As the gas fraction approaches 1, the electrolyte conductivity tends towards 0. Moreover, from a fluid mechanics standpoint, the validity of the Euler-Euler model is questionable and a Volume of Fluid approach should be preferred. 

FIGURE 4.1 Modeling approaches for multiphase flows, (a) Volume of fluid approach, (b) Eulerian-Lagrangian approach, (c) Eulerian-Eulerian approach. 

Rigby et al. (1997) also applied a CFD-based model to understand bubble break-up from ventilated cavities in gas-liquid reactors. Ranade etal. (2001d) used a volume of fluid (VOF) approach to understand cavity formation behind blades. Observations and insight gained through such studies may be used to develop appropriate sub-models, which can then be incorporated in a detailed reactor-engineering model. 

In general, it may be concluded that it is possible to develop appropriate Eulerian-Eulerian models to simulate complex gas-liquid (solid) flows, with some support from the experimental data. Some of the possible applications of such models are discussed in the next section. Before discussing these applications, recent simulations carried out with Eulerian-Lagrangian and volume of fluid (VOF) approaches are briefly reviewed here. 

As part of the specification of the physical models and boundary conditions, the user has to specify the body forces on the fluid. Body forces are those forces that act on the entire volume of fluid throughout the domain. These forces include gravity, electromagnetic forces (if relevant), and the Coriolis force for rotating domains. 

The purpose of this section is to give an overview of the pertinent high resolution methods often referred in the literature on multiphase reactor modeling. These are The Maker and Cell (MAC) method [96], the Simplified MAC method [6], the volume of fluid (VOF) method[108], the level set (LS) front capturing method [214, 20, 186], and finally the front tracking method [227, 221[. 

In this sub-section the basis elements of the volume of fluid method are described. In general the VOF model is composed of a set of continuity and momentum equations, as well as a transport equation for the evolution of a... 

Zaleski S (1999) Multiphase-Flow CFD with Volume of Fluid (VOF) Methods. In Modelling and Computation of Multiphase Flows, Short Course, Zurich, Switzerland, March 8-12, 15B/17B l-43. 

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