•The variable d is only used directly in Equation 9-3. d is everywhere else replaced by

d reg = min max d 0 1

Observe that this includes the way c is calculated, that is

c = 1 – d reg

•An extra diffusion term is added to Equation 9-3 in order to minimize the occurrence of negative values of d . The “barrier” viscosity is calculated as

where the index k indicates that the viscosity and density are taken from the continuous phase if the dispersed phase is a solid and from the dispersed phase otherwise. Observe that b is only nonzero if d is less than zero.

References for the Euler-Euler Model, Laminar Flow Interface

1.M.J.V. Goldschmidt, B.P.B. Hoomans, and J.A.M. Kuipers, “Recent Progress Towards Hydrodynamic Modelling of Dense Gas-Particle Flows,” Recent Research Developments in Chemical Engineering, Transworld Research Network, India, pp. 273-292, 2000.

2.A. Soulaimani, M. Fortin, “Finite Element Solution of Compressible Viscous Flows Using Conservative Variables,” Computer Methods in Applied Mechanics and Engineering, vol. 118, pp. 319–350, 1994.

3.C. Crowe, M. Sommerfeld, and Y Tsuji, Multiphase Flows with Droplets and Particles, CRC Press, Boca Raton, 1998.

4.B.G.M. van Wachem, J.C. Schouten, C.M. van den Bleek, R. Krishna, and J.L. Sinclair, “Comparative Analysis of CFD Models of Dense Gas-Solid Systems,” AIChE Journal, vol. 47, no. 5, pp. 1035–1051, 2001.

5.H. Enwald, E. Peirano and A.-E. Almstedt, “Eulerian Two-Phase Flow Theory Applied to Fluidization,” Int. J. Multiphase Flow, vol. 22, pp. 21–66, 1996.

6.D. Gidaspow, Multiphase Flow and Fluidization, Academic Press, San Diego, 1994.

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7.C.Y. Wen, Y.H. Yu, “Mechanics of Fluidization,” Chemical Engineering Progress Symposium Series, vol. 62, pp. 100–110, 1966.

8.S. Ergun, “Fluid Flow Through Packed Columns,” Chemical Engineering Progress, vol. 48, pp. 89–94, 1952.

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10

P o r o u s M e d i a a n d S u b s u r f a c e F l o w B r a n c h

The fluid flow interfaces are grouped by type under the Fluid Flow main branch. This chapter discusses applications involving the Porous Media and Subsurface Flow branch () in the Model Wizard. The Mechanisms for Modeling Porous Media and Subsurface Flow helps you choose the best one to start with.

In this chapter:

•The Darcy’s Law Interface

•The Brinkman Equations Interface

•The Free and Porous Media Flow Interface

•The Two-Phase Darcy’s Law Interface

•Theory for the Darcy’s Law Interface

•Theory for the Brinkman Equations Interface

•Theory for the Free and Porous Media Flow Interface

•Theory for the Two-Phase Darcy’s Law Interface

307

T h e M e c h a n i s m s f o r M o d e l i n g P o r o u s M e d i a a n d S u b s u r f a c e F l o w

In this section:

•Selecting the Right Interface

•The Porous Media Flow Interface Options

•Coupling to Other Physics Interfaces

Selecting the Right Interface

The Porous Media and Subsurface Flow branch () included with the CFD Module license has a number of subbranches to describe momentum transport. These can be added from the Model Wizard; either singularly or in combination with other interfaces such as mass and energy transfer, and even chemical reactions.

Different types of flow require different equations to describe them. If the flow type to model is known, then select it directly from the Model Wizard. However, when you are not certain of the flow type, or because it is difficult to reach a solution easily, you can start instead with a simplified model and add complexity as you build the model. Then you can test your way forward, comparing models and results. For porous media flow, the Darcy’s Law interface is a good place to start if this is the case.

In other cases, you may know exactly how a fluid behaves and which equations, models, or physics interfaces best describe it, but because the model is so complex it is difficult to reach an immediate solution. Simpler assumptions may need to be made to solve the problem, and other interfaces may be better to fine-tune the solution process for the more complex problem. The next section gives you an overview of each of the interfaces to help you choose.

TABLE 10-1: THE POROUS MEDIA FLOW DEFAULT SETTINGS

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