ANSYS FLUENT 12.0 Theory Guide - 16.5.13 Dense Discrete Phase Model

16.5.13 Dense Discrete Phase Model

In the standard formulation of the Largangian multiphase model, described in Chapter 15, the assumption is that the volume fraction of the discrete phase is sufficiently low: it is not taken into account when assembling the continuous phase equations. The general form of the mass and momentum conservation equations in ANSYS FLUENT is given in Equations 16.5-152 and 16.5-153 (and also defined in Section 1.2).

$\frac{\partial \rho}{\partial t} + \nabla \cdot (\rho \vec{v})=S_{DPM}+S_{other}$

(16.5-152)

$\frac{\partial \rho \vec{v}}{\partial t} + \nabla \cdot (\rh... ...la \cdot \tau + \rho \vec{g} + \vec{F}_{DPM} + \vec{F}_{other}$

(16.5-153)

To overcome this limitation of the Lagrangian multiphase model, the volume fraction of the particulate phase is accounted for by extending Equations 16.5-152 and 16.5-153 to the following set of equations (see also Section 16.5.3, written for phase ):

$\frac{\partial}{\partial t}\left(\alpha _p \rho _p\right) +\... ...) =\sum _{q=1}^{nphases}\left(\dot{m}_{qp}-\dot{m}_{pq}\right)$

(16.5-154)

$\frac{\partial}{\partial t}\left(\alpha _p\rho _p \vec{v} _p... ...p\mu _p\left(\nabla \vec{v}_p+\nabla \vec{v}_p^T\right)\right]$

$+\alpha _p \rho _p \vec{g} + F_{vm, lift, user} + \sum _{q=... ...ht) + \dot{m}_{qp}\vec{v}_{qp}-\dot{m}_{qp}\vec{v}_{qp}\right)$

$+K_{DPM}\left(\vec{v}_{DPM}-\vec{v}_p \right)+S_{DPM,explicit}$

(16.5-155)

Here, Equation 16.5-154 is the mass conservation equation for an individual phase and Equation 16.5-155 is the corresponding momentum conservation equation. Currently, the momentum exchange terms (denoted by ) are considered only in the primary phase equations.

In the resulting set of equations (one continuity and one momentum conservation equation per phase), those corresponding to a discrete phase are not solved. The solution, such as volume fraction or velocity field, is taken from the Lagrangian tracking solution.

In the context of the phase coupled SIMPLE algorithm (Section 16.5.12) and the coupled algorithm for pressure-velocity coupling ( this section in the separate User's Guide), a higher degree of implicitness is achieved in the treatment of the drag coupling terms. All drag related terms appear as coefficients on the left hand side of the linear equation system.

Limitations

Since the given approach makes use of the Eulerian multiphase model framework, all its limitations are adopted:

The turbulence models: LES, DES and $k-\omega$ turbulence models are not available.
The combustion models: PDF Transport model, Premixed, Non-premixed and partially premixed combustion models are not available.
The radiation models are not available.
The solidification and melting models are not available.
The Wet Steam model is not available.
The real gas model (pressure-based and density-based) is not available.
The density-based solver and models dependent on it are not available.
Parallel DPM with the shared memory option is disabled.

Granular Temperature

The solids stress acting on particles in a dense flow situation is modeled via an additional acceleration in the particle force balance Equation 15.2-1.

$\frac{du_p}{dt}=F_D\left(u-u_p\right)+\frac{g_x\left(\rho _p - \rho \right)}{\rho _p} + F_x + F_{interaction}$

(16.5-156)

The term $F_{interaction}$ models the additional acceleration acting on a particle, resulting from interparticle interaction. It is computed from the stress tensor given by the Kinetic Theory of Granular Flows as

$F_{interaction}=-\frac{1}{\rho_p}\nabla \cdot \bar{\bar{\tau}}_s$

(16.5-157)

The conservation equation for the granular temperature (kinetic energy of the fluctuating particle motion) is solved with the averaged particle velocity field. Therefore, a sufficient statistical representation of the particle phase is needed to ensure the stable behavior of the granular temperature equation. For details on the Kinetic Theory of Granular Flows, please refer to Section 16.5.3 - Section 16.5.8.

The main advantage over the Eulerian model is that, there is no need to define classes to handle particle size distributions. This is done in a natural way in the Lagrangian formulation [ 279].

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