Granular Pressure Model Reference

The Granular Pressure model estimates the stresses of particle phases in a gas-solid fluidized bed.

Fluidized bed reactors are widely used in combustion, catalytic cracking, and various other chemical and metallurgical processes. Granular pressures are also encountered in many industrial processes.

The closeness of particles to one another, or “packing”, determines the type of particle motion. Where the particles are closely packed, the motion is dominated by contact and a frictional stress model is used. When the particles are below the packing limit, then collisions and kinetic energy determine the motion, handled as part of the Granular Temperature model.

Table 1. Granular Pressure Model Reference
Theory See Granular Stress.
Provided By [physics continuum] > Models > Optional Models
Example Node Path [physics continuum] > Models > Granular Pressure
Requires
Physics continuum selections:
  • Material: Multiphase
  • Multiphase Model: Eulerian Multiphase (EMP) (Automatically activates: Multiphase Interaction, Gradients)
  • Optional Models: Granular Pressure
Properties Key properties are:

In the physics continuum: Radial Distribution Function, Frictional Stress Formulation, Maximum Solid Viscosity

In each particle phase: Maximum Solid Fraction

See Granular Pressure Model Properties.

Activates Physics Models In each particle phase:

  • Granular Pressure

Model Controls

Schaeffer

Specifies the motion behavior of the particles. This behavior is based on the work by Schaeffer ([542]). Available only when the Frictional Stress Formulation property is set to Schaeffer.

See Schaeffer Properties.

Modified Johnson

Specifies the motion behavior of the particles. This behavior is based on the work by Johnson and Jackson [483]. Available only when the Frictional Stress Formulation property is set to Modified Johnson.

See Modified Johnson Properties.

Materials In each particle phase: Particle Diameter

See Material Properties.

Reference Values In each particle phase: Coefficient of Restitution

See Reference Values.

Field Functions See Granular Pressure Field Functions.

Granular Pressure Model Properties

Determines the regimes that are modeled.

The following properties apply to the physics continuum:

Radial Distribution Function
  • Ding-Gidaspow

    The Ding-Gidaspow radial distribution function uses Eqn. (2352) for packing below the packing limit and Eqn. (2353) for packing close to the packing limit.

Frictional Stress Formulation

Specifies the motion behavior of the particles when they approach the maximum packing limit.

  • Schaeffer

    Uses the Schaeffer ([542]) frictional regime equations.

  • Modified Johnson

    Uses the Modified Johnson ([483]) frictional regime equations.

  • Kinetic-Based

    Uses the collisional solid pressure to limit the particle volume fraction near maximum packing. The collisional solid pressure relies on the correction to the particle radial distribution function near maximum packing (Eqn. (2353)).

Maximum Solid Viscosity
Specifies the maximum limit for solid viscosity, which is the summation of kinetic, collisional, and frictional contributions. This property is relevant for modeling contact-dominated granular flows. The default value is 1000 Pa-s.

This value is μp in Eqn. (2382).

The following property applies to each particle phase:

Maximum Solid Fraction
Sets the upper packing limit of the particles. The default value is 0.624, the limit for rigid spherical particles.

Schaeffer Properties

Angle of Internal Friction
Used to determine the effective granular viscosity, which is given by Eqn. (2365). It is set to 25o by default.

Modified Johnson Properties

Critical Volume Fraction
Solid volume fraction at which the frictional stress is activated. Set to 0.5 by default.
Angle of Internal Friction
Used to determine the effective granular viscosity, which is given by Eqn. (2365). Set to 28.5o by default.
Multiplier Fr
Multiplication factor in Eqn. (2361). Set to 0.05 by default.
Exponent r
Numerator exponent in Eqn. (2361). Set to 2.0 by default.
Exponent s
Denominator exponent in Eqn. (2361). Set to 5.0 by default.

Material Properties

The following property applies to each particle phase:

Particle Diameter
The method for defining the mean particle diameter.

  • Constant

  • Field Function

  • Sauter Mean Diameter

    Specifies the Sauter mean diameter profile. (See Eqn. (2177)).

    This method is available only when the S-Gamma particle size distribution model is activated in the particle phase. See S-Gamma Model Reference.

Reference Values

The following reference value applies to each particle phase:

Coefficient of Restitution
Represents the ratio of speeds of the particles before and after an impact. A value of 1 indicates a perfectly elastic collision. The default value is 0.9.

Granular Pressure Field Functions

Diameter of [Particle Phase]

Effective Granular Viscosity of [Particle Phase]

Frictional Solid Pressure of [Particle Phase]

Frictional Viscosity of [Particle Phase]

Maximum Mixture Packing Fraction

Radial Distribution Function of [Particle Phase]

Solid Pressure of [Particle Phase]

Solid Pressure of [Particle Phase] Recon