## 23.4.1 Overview and Limitations of the Mixture Model

Overview

The mixture model is a simplified multiphase model that can be used to model multiphase flows where the phases move at different velocities, but assume local equilibrium over short spatial length scales. The coupling between the phases should be strong. It can also be used to model homogeneous multiphase flows with very strong coupling and the phases moving at the same velocity. In addition, the mixture model can be used to calculate non-Newtonian viscosity.

The mixture model can model phases (fluid or particulate) by solving the momentum, continuity, and energy equations for the mixture, the volume fraction equations for the secondary phases, and algebraic expressions for the relative velocities. Typical applications include sedimentation, cyclone separators, particle-laden flows with low loading, and bubbly flows where the gas volume fraction remains low.

The mixture model is a good substitute for the full Eulerian multiphase model in several cases. A full multiphase model may not be feasible when there is a wide distribution of the particulate phase or when the interphase laws are unknown or their reliability can be questioned. A simpler model like the mixture model can perform as well as a full multiphase model while solving a smaller number of variables than the full multiphase model.

The mixture model allows you to select granular phases and calculates all properties of the granular phases. This is applicable for liquid-solid flows.

Limitations

The following limitations apply to the mixture model in FLUENT:

• You must use the pressure-based solver. The mixture model is not available with either of the density-based solvers.

• Only one of the phases can be defined as a compressible ideal gas. There is no limitation on using compressible liquids using user-defined functions.

• Streamwise periodic flow with specified mass flow rate cannot be modeled when the mixture model is used (the user is allowed to specify a pressure drop).

• Solidification and melting cannot be modeled in conjunction with the mixture model.

• The LES turbulence model cannot be used with the mixture model if the cavitation model is enabled.

• The relative velocity formulation cannot be used in combination with the MRF and mixture model (see Section  10.3.1).

• The mixture model cannot be used for inviscid flows.

• The shell conduction model for walls cannot be used with the mixture model.

• When tracking particles in parallel, the DPM model cannot be used with the mixture model if the shared memory option is enabled (Section  22.11.9). (Note that using the message passing option, when running in parallel, enables the compatibility of all multiphase flow models with the DPM model.)

The mixture model, like the VOF model, uses a single-fluid approach. It differs from the VOF model in two respects:

• The mixture model allows the phases to be interpenetrating. The volume fractions and for a control volume can therefore be equal to any value between 0 and 1, depending on the space occupied by phase and phase .

• The mixture model allows the phases to move at different velocities, using the concept of slip velocities. (Note that the phases can also be assumed to move at the same velocity, and the mixture model is then reduced to a homogeneous multiphase model.)

The mixture model solves the continuity equation for the mixture, the momentum equation for the mixture, the energy equation for the mixture, and the volume fraction equation for the secondary phases, as well as algebraic expressions for the relative velocities (if the phases are moving at different velocities).

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