Defining Field Functions for the Restitution Coefficients

Create field functions to represent the restitution coefficients.

Restitution coefficients are used to predict the angle with which a particle rebounds off a solid wall. In this tutorial, the relations that were developed by Forder et al. ([967]) are used:

ϵT=10.78αp+0.84αp20.21αp3+0.028αp40.022αp5

ϵN=0.9880.78αp+0.19αp20.024αp3+0.027αp4

Represent these equations in Simcenter STAR-CCM+ using user field functions. The quantities referred to in user field functions must come from the predefined system field functions or other user field functions. In this simulation you require a predefined system field function for the particle incidence angle.

To define field functions for the restitution coefficients:

  1. Open the Automation > Field Functions node.


  2. Scroll down the list until the Particle Incidence Angle function is visible.


  3. Select Particle Incidence Angle and note the value of the Function Name property.


Having noted the required name of ParticleIncidenceAngle, it is now possible to create the function for the Normal Restitution Coefficient.

  1. Right-click the Automation > Field Functions node and select New > Scalar from the pop-up menu.

    A new User Field Function 1 node appears in the object tree.

  2. Rename User Field Function 1 to ENormal.
  3. Select ENormal and set the following properties:
    Property Setting
    Function Name NormalRestitutionCoefficient
    Dimensions Dimensionless
    Definition 0.988 - 0.78*$ParticleIncidenceAngle + 0.19*(pow($ParticleIncidenceAngle, 2)) - 0.024*(pow($ParticleIncidenceAngle, 3)) + 0.027*(pow($ParticleIncidenceAngle, 4))

The same steps are now repeated for the tangential restitution coefficient.

  1. Right-click the Automation > Field Functions node and select New > Scalar from the pop-up menu.

    A new User Field Function 1 node appears in the object tree.

  2. Rename User Field Function 1 to ETan.
  3. Select ETan and set the following properties:
    Property Setting
    Function Name TangentialRestitutionCoefficient
    Dimensions Dimensionless
    Definition 1 - 0.78*$ParticleIncidenceAngle + 0.84*(pow($ParticleIncidenceAngle, 2)) - 0.21*(pow($ParticleIncidenceAngle, 3)) + 0.028*(pow($ParticleIncidenceAngle, 4)) - 0.022*(pow($ParticleIncidenceAngle, 5))