# Segregated Methods for Two-Fluid Models

## Abstract

The previous chapter, with its direct simulation of the fluid flow and a modeling approach to the particle phase, may be seen as a transition between the methods for a fully resolved simulation described in the first part of this book and those for a coarse grained description based on the averaging approach described in chapter ??. We now turn to the latter, which in practice are the only methods able to deal with the complex flows encountered in most situations of practical interest such as fluidized beds, pipelines, energy generation, sediment transport, and others. This chapter and the next one are devoted to numerical methods for so-called two-fluid models in which the phases are treated as inter-penetrating continua describing, e.g., a liquid and a gas, or a fluid and a suspended solid phase. These models can be extended to deal with more than two continua and, then, the denomination multi-fluid models might be more appropriate. For example, the commercial code OLGA (Bendiksen et al. 1991), widely used in the oil industry, recognizes three phases, all treated as interpenetrating continua: a continuous liquid, a gas, and a disperse liquid phase present as drops suspended in the gas phase. The moremore »

- Authors:

- Johns Hopkins University
- Princeton University
- ORNL
- Los Alamos National Laboratory (LANL)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- FE USDOE - Office of Fossil Energy (FE)

- OSTI Identifier:
- 930715

- DOE Contract Number:
- DE-AC05-00OR22725

- Resource Type:
- Book

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 97; TWO-PHASE FLOW; FLOW MODELS; MULTIPHASE FLOW; ALGORITHMS

### Citation Formats

```
Prosperetti, Andrea, Sundaresan, Sankaran, Pannala, Sreekanth, and Zhang, Duan Z.
```*Segregated Methods for Two-Fluid Models*. United States: N. p., 2007.
Web.

```
Prosperetti, Andrea, Sundaresan, Sankaran, Pannala, Sreekanth, & Zhang, Duan Z.
```*Segregated Methods for Two-Fluid Models*. United States.

```
Prosperetti, Andrea, Sundaresan, Sankaran, Pannala, Sreekanth, and Zhang, Duan Z. Mon .
"Segregated Methods for Two-Fluid Models". United States.
doi:.
```

```
@article{osti_930715,
```

title = {Segregated Methods for Two-Fluid Models},

author = {Prosperetti, Andrea and Sundaresan, Sankaran and Pannala, Sreekanth and Zhang, Duan Z.},

abstractNote = {The previous chapter, with its direct simulation of the fluid flow and a modeling approach to the particle phase, may be seen as a transition between the methods for a fully resolved simulation described in the first part of this book and those for a coarse grained description based on the averaging approach described in chapter ??. We now turn to the latter, which in practice are the only methods able to deal with the complex flows encountered in most situations of practical interest such as fluidized beds, pipelines, energy generation, sediment transport, and others. This chapter and the next one are devoted to numerical methods for so-called two-fluid models in which the phases are treated as inter-penetrating continua describing, e.g., a liquid and a gas, or a fluid and a suspended solid phase. These models can be extended to deal with more than two continua and, then, the denomination multi-fluid models might be more appropriate. For example, the commercial code OLGA (Bendiksen et al. 1991), widely used in the oil industry, recognizes three phases, all treated as interpenetrating continua: a continuous liquid, a gas, and a disperse liquid phase present as drops suspended in the gas phase. The more recent PeTra (Petroleum Transport, Larsen et al. 1997) also describes three phases, gas, oil, and water. Recent approaches to the description of complex boiling flows recognize four inter-penetrating phases: a liquid phase present both as a continuum and as a dispersion of droplets, and a gas/vapor phase also present as a continuum and a dispersion of bubbles. Methods for these multi-fluid models are based on those developed for the two-fluid model to which we limit ourselves. In principle, one could simply take the model equations, discretize them, and solve them by a method suitable for non-linear problems, e.g. Newton-Raphson iteration. In practice, the computational cost of such a frontal attack is nearly always prohibitive in terms of storage requirement and execution time. It is therefore necessary to devise different, less direct strategies. Two principal classes of algorithms have been developed for this purpose. The first one, described in this chapter, consists of algorithms derived from the pressure based schemes widely used in single-phase flow, such as SIMPLE and its variations (see e.g. Patankar 1980). In this approach, the model equations are solved sequentially and, therefore, these methods are often referred to as segregated algorithms to distinguish them from a second class of methods, object of the next chapter, in which a coupled or semi-coupled time-marching solution strategy is adopted. Broadly speaking, the first class of methods is suitable for relatively slow transients, such as fluidized beds, or phenomena with a long duration, such as flow in pipelines. The methods in the second group have been designed to deal principally with fast transients, such as those hypothesized in nuclear reactor safety. Since in segregated solvers the equations are solved one by one, it is possible to add equations to the mathematical model - to describe e.g. turbulence - at a later stage after the development of the initial code without major modifications of the algorithm.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Mon Jan 01 00:00:00 EST 2007},

month = {Mon Jan 01 00:00:00 EST 2007}

}