14.10. DDPM Granular Phase Options

When modeling granular phases using the discrete dense phase model (DDPM), Ansys Fluent currently uses only the solids pressure gradient as collision forces. Besides, during the iteration process, the collision forces are calculated using the volume fractions and collision forces from the previous time step.

When beta feature access is enabled, Ansys Fluent offers two modeling options that consider the complete granular stress tensor as well as use the predictor/corrector scheme for calculating the collision forces at each time step. These options help improve robustness, accuracy, and speed of gas/particulate flow simulations when the packing limit exceeds a volume fraction of 63%.

 

14.10.1. Theory

The acceleration of a single particle is expressed by:

(14–4)

where the subscripts and refer to the particle and fluid phases, respectively, is the velocity vector, is the particle relaxation time, is the gravity vector, is the density, and is the pressure.

The first term on the right hand side of Equation 14–4 is the drag, the second is caused by pressure, the third is the buoyancy source term, the fourth term () represents virtual mass effects or any other effects, and the last term () contains any collision effects.

The collision effects depend on the chosen collision model. For example, for the DEM collision model individual contributions to the collision term are computed from other particles that overlap the current particle.

The collision term is currently modeled using kinetic theory of granular flows as:

(14–5)

where

= particle volume fraction
= particle density
= shear stress tensor (which is represented by solids pressure only when beta features are disabled)

The following two modeling options can be used for improving robustness and accuracy of granular flow simulations with the DDPM:

  • Complete granular shear stress tensor

    Without this option, the DDPM solver uses the solids pressure only as the shear stress tensor with various formulations from Lun et al. (397 in Fluent Theory Guide) and Syamlal and O`Brian (638 in Fluent Theory Guide):

    (14–6)

    With this option, the solver considers the full granular shear stress when calculating the collision force acting on the particle:

    (14–7)

    where

    = granular solids pressure
    = unity tensor
    = volume fraction of the granular solid phase
    = velocity
    = granular solid phase viscosity
    = bulk viscosity

  • Predictor/corrector scheme

    Near the close packing limit, particle stresses dominate due to high non-linearity and sensitivity to a change of the solid volume fraction. For accurate modeling of collision forces, the predictor/corrector approach by Verma et al. [1] is used. When collecting the terms and integrating Equation 14–4, the particle velocity at the new time step can be split into two parts:

    (14–8)

    The first part, , is due to fluid forces (such as drag) and is computed in a predictor step. The second part, , arises from collisional forces and is computed as follows. Each intermediate particle location is obtained based on the velocity . Once all particle locations in the domain are determined, the solids pressure and other components of the granular shear stress tensor can be updated. Finally, the velocity is evaluated by:

    (14–9)

    and is used to perform a corrector step for all particles in the domain.

Note that the DDPM granular options are not compatible with the following features:

  • Sliding meshes

  • Periodic boundary conditions

  • Zones with multiple reference frames

  • 2d axisymmetric simulations

Bibliography

[1] V. Verma, J.T. Padding. "A novel approach to MP-PIC: Continuum particle model for dense particle flows in fluidized beds". Chemical Engineering Science. 6. 2020. doi:10.1016/j.cesx.2019.100053.

 

14.10.2. Usage

For DDPM cases with granular phases, you can enable the following options in the Granular Options group box in the Discrete Phase Model dialog box:

  • Granular Stress Tensor

    When this option is enabled, the granular shear stress tensor is used in the collision forces evaluation. While this option increases robustness for smooth meshes, robustness for meshes that are not well crafted may deteriorate.

  • Predictor/Corrector Approach

    This option improves the accuracy of the collision force calculations at each step and, therefore, allows for larger time steps.

See Theory for more information about these options.

These options can also be enabled via the text user interface (TUI).

To enable the predictor/corrector approach to track particles, use the following text command:

/define/models/dpm/numerics/predictor-corrector?
Use predictor/corrector approach to track particles: [no] y

To enable the use of the granular stress tensor in the collision force calculations, use the following text command:

/define/models/dpm/numerics/granular-stress-tensor?
Include granular stress tensor in particle collision force: [no] y

In addition, you can use the following text options that can be helpful when using the DDPM granular phase options described above.

  • define/models/dpm/numerics/limit-granular-forces?
Limit granular forces: [no] yes

    This option enables or disables the limiting of granular forces as described in Equation 14–502 in the Fluent Theory Guide when the predictor/corrector approach is not enabled. This option is not restricted to transient DPM simulations only. Note the following:

    • For transient simulations, if the Predictor/Corrector Approach option is enabled in the Discrete Phase Model dialog box (Numerics tab), the solver will ignore the limit-granular-forces? text option.

    • For steady-state simulations, when the limit-granular-forces? text option is enabled, the solver will ignore the Predictor/Corrector Approach option.

  • define/models/dpm/numerics/packed-region-detection-enabled?
Detect packed region: [no] yes

    When this option is enabled, the solver identifies cells in the packed region of the domain where the packing limit of the granular phase is reached or even exceeded. At the boundary of this packed region, a limiter to the velocity in Equation 14–8 (similar to that described in [1]) is applied in order to avoid unphysical overshoots of the particle velocity. This option is available only when define/models/dpm/numerics/limit-granular-forces? is enabled and/or the predictor/corrector approach is enabled through the GUI or TUI.