Granular Temperature Model Reference

Table 1. Granular Temperature Model Family Reference
Model Names	Granular Temperature		Models the collision-dominated regime of granular flow.
	Algebraic Granular Temperature		Applies to cases where the local equilibrium assumption holds. These cases include bubbling fluidized beds and applications involving packed beds of particles. This model is less computationally expensive than the Granular Temperature Transport model.
	Granular Temperature Transport		Applies to any granular flow case. This model takes into account convection, production, diffusion, and dissipation of granular energy. It also accounts for dissipation of granular energy due to inter-phase drag. If you select this model, you must select the Granular Energy Transfer model for phase interactions involving the particle dispersed phase.
	User-Defined Granular Temperature		Specify the minimum granular temperature directly.
Theory	See Granular Temperature.
Provided By	[physics continuum] > Models > Optional Models
Example Node Path	[physics continuum] > Models > Granular Temperature
Requires	Physics continuum selections: Material: Multiphase Multiphase Model: Eulerian Multiphase (EMP) (Automatically activates: Multiphase Interaction, Gradients.) Viscous Regime: Laminar Optional Models: Granular Pressure Optional Models: Granular Temperature (selected automatically) Granular Temperature: One of Algebraic Granular Temperature, Granular Temperature Transport or User-Defined Granular Temperature.
Properties	Key properties are: In the physics continuum: Granular Temperature: None. Algebraic Granular Temperature: Granular Temperature Minimum, Particle Kinetic Viscosity See Algebraic Granular Temperature Properties. Granular Temperature Transport: Granular Temperature Minimum, Particle Kinetic Viscosity, Granular Diffusion Coefficient See Granular Temperature Transport Properties. User-Defined Granular Temperature: Granular Temperature Minimum, Particle Kinetic Viscosity See User-Defined Granular Temperature Properties. In each particle phase: Algebraic Granular Temperature: None. Granular Temperature Transport: Granular Temperature Minimum, Particle Kinetic Viscosity, Granular Diffusion Coefficient See Granular Temperature Transport Properties. User-Defined Granular Temperature: Granular Temperature See User-Defined Granular Temperature Properties.
Activates	Physics Models	In each particle phase: Granular Pressure One of Algebraic Granular Temperature, Granular Temperature Transport or User-Defined Granular Temperature (as selected in the physics continuum)
	Initial Conditions	In each particle phase: Granular Temperature See Initial Conditions.
	Boundary Settings	For each particle phase for each wall boundary: Shear Stress Specification For each particle phase for all boundary types except Overset Mesh, Symmetry Plane, and Outlet: Granular Temperature Specification See Boundary Settings.
	Region Settings	For each particle phase in a fluid region: Granular Temperature Source Option See Region Settings.
	Solvers	Granular Temperature See Granular Temperature Solver.
	Field Functions	See Granular Temperature Field Functions.

Algebraic Granular Temperature Properties

This model uses Eqn. (2372) to solve for the granular temperature.

The following properties apply to the physics continuum:

Granular Temperature Minimum

Sets a minimum value for the continuum. Set to 1.0E-10

m^{2} / s^{2}

by default.

Particle Kinetic Viscosity

Specifies the motion behavior of the particles below the maximum packing limit. Use the corresponding Linearized Drag Law with the chosen Kinetic viscosity.

Gidaspow
Use the Gidaspow Kinetic Viscosity model (see Eqn. (2384)). Selected by default.
Syamlal
Use the Syamlal Kinetic Viscosity model (see Eqn. (2385)).

Granular Temperature Transport Properties

When you select this model, Simcenter STAR-CCM+ adds the Granular Temperature solver to the list of solvers.

The following properties apply to the physics continuum:

Granular Temperature Minimum

A minimum value for the continuum. Set to 1.0E-10

m^{2} / s^{2}

by default.

Particle Kinetic Viscosity

The motion behavior of the particles below the maximum packing limit. Use the corresponding Linearized Drag Law with the chosen Kinetic viscosity.

Gidaspow
Use the Gidaspow Kinetic Viscosity model (see Eqn. (2384)). Selected by default.
Syamlal
Use the Syamlal Kinetic Viscosity model (see Eqn. (2385)).

Granular Diffusion Coefficient

The method for calculating the diffusion coefficient in the Granular transport equation.

Gidaspow
Use the Gidaspow method (see Eqn. (2368)). Selected by default.
Syamlal
Use the Syamlal method (see Eqn. (2369)).

The following properties apply to each particle phase:

Secondary Gradients

Neglect or include the boundary secondary gradients for diffusion and/or the interior secondary gradients at mesh faces.

On
Include both secondary gradients.
Off
Exclude both secondary gradients.
Interior Only
Include the interior secondary gradients only.
Boundaries Only
Include the boundary secondary gradients only.

Convection

Sets the convection scheme for flow velocity.

1st-order
Selects the first-order upwind convection scheme.
2nd-order
Selects the second-order upwind convection scheme.

User-Defined Granular Temperature Properties

The following properties apply to the physics continuum:

Granular Temperature Minimum

A minimum value for the continuum. Set to 1.0E-10

m^{2} / s^{2}

by default.

Particle Kinetic Viscosity

The motion behavior of the particles below the maximum packing limit. Use the corresponding Linearized Drag Law with the chosen Kinetic viscosity.

Gidaspow
Use the Gidaspow Kinetic Viscosity model (see Eqn. (2384)). Selected by default.
Syamlal
Use the Syamlal Kinetic Viscosity model (see Eqn. (2385)).

The following property applies to each particle phase:

Granular Temperature: Specifies the granular temperature of the phase. The default is a constant value of 1.0E-6 m^2/s^2.

Initial Conditions

The following initial condition applies to each particle phase:

Granular Temperature: Specifies the granular temperature of the phase. The default is a constant value of 1.0E-6 m^2/s^2.

Boundary Settings

The following boundary condition applies to each particle phase for each wall boundary:

Shear Stress Specification

Sets the wall shear stress specification method.

The Slip method is recommended at wall boundaries. However, if an estimate of the Specularity Coefficient is available, use the Partial-Slip method.

Method	Corresponding Physics Value Nodes
No-Slip The tangential velocity is set to 0.	None.
Partial-Slip This method is available only when the Granular Temperature Transport model is activated.	Specularity Coefficient A value of 0 corresponds to Slip, while a value of 1 corresponds to No-Slip. This value is $ϕ$ in Eqn. (2387).
Slip No shear stress at the boundary.	None.

The following boundary condition applies to each particle phase for all boundary types except Overset Mesh, Symmetry Plane, and Outlet. In addition, User granular temperature specification method is not available on wall boundaries, and Specified Flux and Johnson-Jackson temperature specification methods are only available on wall boundaries.

Granular Temperature Specification

The granular temperature value that you specify is used to calculate the solid pressure at the boundaries, which has a significant influence on the simulation results.

Method	Corresponding Physics Value Nodes
Zero Gradient The gradient for the granular temperature at the boundary is set to 0.	None.
User Specify your own boundary value. This method is not available on wall boundaries.	Granular Temperature The granular temperature of the phase at the boundary. The default is a constant value of 1.0E-6 m²/s².
Specified Flux Use this option to specify a granular temperature flux at the wall. This method is only available on wall boundaries.	Granular Temperature Flux The granular temperature flux of the phase at the wall boundary. The default is a constant value of 1.0E-6 J/m²s.
Johnson-Jackson Use the Johnson-Jackson model to model wall shear stress for particle phases in granular flows. This model is a more physically sound method of estimating granular temperature near the walls. This method is only available on wall boundaries.	Wall Coefficient of restitution The coefficient of restitution for collisions between particles and the wall. This value represents the ratio of speeds of the particles before and after an impact. This value is set to 0.9 by default. A value of 1 indicates a perfectly elastic collision. This value is $e_{w}$ in Eqn. (2387).

Region Settings

Applies to fluid regions.

Each particle phase has the following Phase Condition:

Granular Temperature Source Option

Sets the Granular Temperature Source Term.

Setting	Corresponding Physics Value Nodes
Activated	Granular Temperature Source Granular Temperature Source Derivative
Deactivated	None.

Granular Temperature Solver

This solver is available only when Granular Temperature Transport is activated in the physics continuum.

The properties in the Expert category are for a temporary debug situation, at the expense of simulation accuracy and higher memory usage. Do not change any of these properties unless you are thoroughly familiar with the discretization techniques used in Simcenter STAR-CCM+.

Under-Relaxation Factor: At each iteration, this property governs the extent to which the newly computed solution supplants the old solution. The default value is 0.8.
Reconstruction Frozen: When On, Simcenter STAR-CCM+ does not update reconstruction gradients with each iteration, but rather uses gradients from the last iteration in which they were updated. Activate Temporary Storage Retained in conjunction with this property. This property is Off by default.
Reconstruction Zeroed: When On, the solver sets reconstruction gradients to zero at the next iteration. This action means that face values used for upwinding (Eqn. (905)) and for computing cell gradients (Eqn. (917) and Eqn. (918)) become first-order estimates. This property is Off by default. If you turn this property Off after having it On, the solver recomputes the gradients on the next iteration.
Solver Frozen: When On, the solver does not update any quantity during an iteration. It is Off by default. This is a debugging option that can result in non-recoverable errors and wrong solutions due to missing storage. See Finite Volume Solvers Reference for details.
Temporary Storage Retained: When On, Simcenter STAR-CCM+ retains additional field data that the solver generates during an iteration. The particular data retained depends on the solver, and becomes available as field functions during subsequent iterations. Off by default.

Granular Temperature Field Functions

The following field functions are available when the Granular Temperature Transport model is activated.

Bulk Viscosity of Particle

Collisional Solid Pressure of Particle

Collisional Viscosity of Particle

Granular Energy Dissipation of Particle

Granular Energy Production of Particle

Granular Temperature Diffusion Coefficient of Particle

Granular Temperature of Particle

Kinetic Solid Pressure of Particle

Kinetic Viscosity of Particle