The kinetic theory based Two-Fluid Model (TFM) is a well-established and extensively validated model for simulating gas-particle flows in many industrial applications where it is possible to resolve all microscales present in the flow. In simulations that involve the TFM, gas-particle drag force models (see Interphase Exchange Coefficients) along with kinetic theory based solids stress models (see Solids Pressure and Solids Shear Stresses) can predict macroscale flow features that are usually of interest.

In large-scale applications (such as commercial scale fluidized-beds), gas–particle flows are characterized by heterogeneous structures ranging from microscale to macroscale. Resolving these structures in simulations using the kinetic theory based TFM ([438], [492], [565]) may become expensive due to the requirement for the mesh resolution to be of the order of a few particle diameters everywhere in the domain. For example, Geldart Group A particles, which fluidize well, are often used as a catalyst in many large-scale fluidized beds. The size of these particles typically ranges from 20 μm to 100 μm. Capturing microscale flow features (such as clusters and streamers in circulating fluidized bed or bubbles in bubbling fluidized bed) would require a mesh resolution of a few hundred micrometers. This would make simulations of large-scale fluidized beds prohibitively expensive.

Based on practical considerations such as computational cost, it is often desirable to employ relatively coarse meshes in a simulation. However, coarse-mesh simulations that involve the homogeneous gas-particle drag models (see Interphase Exchange Coefficients) do not account for the effects of microscale structures on the macroscopic flow behavior and typically over-predict fluid-particle drag force and under-predict particle phase stresses. To overcome these challenges, the filtered TFMs have been developed ([438], [565]). The filtered TFMs account for the effects of microscale structures and resolve macroscale structures in simulations with the focus on probing macroscale gas–particle flow features that are of principal interest in large-scale systems.

The conservation equations for filtered TFMs are well documented in literature (see, for example, [438], [565]: The closure relations for the filtered gas-particle drag force and filtered particle phase stress used in Ansys Fluent are further described.

For the filtered drag model of Sarkar et al. [565], the fluid-solid exchange coefficient is computed using Equation 14–290, but with index calculated as:

(14–488)

Here, the non-dimensional slip velocity is defined as:

(14–489)

where and are the velocities of solid and liquid phases, respectively, and is the terminal velocity calculated by:

(14–490)

where is gravity, and are the densities of the liquid and solid phases, respectively, is the viscosity of the liquid phase, and is the diameter of the solid phase particles.

Coefficients , , , and in Equation 14–488 have the following values:

Here,

(14–491)

with the filter length

(14–492)

where is the volume of the mesh cell.

The filtered solid pressure is calculated as:

(14–493)

where is the density of the solid phase, is the scalar filtered rates of strain in the solid phase, is the filtered solid volume fraction, and is defined by Equation 14–491.

The filtered granular viscosity is modeled as:

(14–494)

where is the maximum filtered solid volume fraction.

The radial distribution is not used in the filtered TFM.

Filtered gas-phase stress models can be implemented through user-defined functions.