The Granular Flow Interface
The Granular Flow (gran) interface (), found under the Fluid Flow branch () when adding a physics interface, computes the contact forces in between grains and between grains and geometry walls. The grain motion is usually driven by external fields and is determined by Newton’s second law.
When this physics interface is added, the following default nodes are also added to the Model Builder: Grain Properties, Wall, Contact Between Grains, Contact with Walls, and Gravity. From the Physics toolbar, you can add other nodes that implement, for example, grain release features and additional external forces or torques. You can also right-click the Granular Flow to select physics features from the context menu.
The Label is the physics interface name. The default is Granular Flow.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is gran.
Force
The Granular Flow interface uses contact force models to evaluate the contact forces as a function of displacement and velocity.
Contact Force Model
Select an option from the Contact force model list: Linear elastic, Hertz–MD (the default) or Hertz–MD with adhesion.
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The Linear elastic model is a linear viscoelastic model that includes an elastic force that depends linearly on the overlap, and a viscous force. Spring constants can be specified in the Settings window for Contact Between Grains and Contact with Walls nodes.
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The Hertz–MD model is a nonlinear viscoelastic model that includes a more realistic nonlinear force–displacement relationship.
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The Hertz–MD with adhesion model is an extension of the Hertz–MD model that is used to model adhesive forces during grain–grain and grain–wall interactions. These adhesive forces are tensile forces that arise due to surface adhesion and can cause a prolonged contact after collision.
Compute van der Waals Force
When Hertz–MD or Hertz–MD with adhesion model is selected, the Compute van der Waals force checkbox appears. This checkbox is not selected by default. Selecting this checkbox will add a van der Waals force to the grains, in addition to the forces computed by the Contact force model.
For theory see:
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Contact Force: Linear Elastic Model
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Contact Force: Hertz–MD (Mindlin and Deresiewicz) Model
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Contact Force: Hertz–MD with Adhesion Model
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Contact Force: van der Waals Force
Rotational Resistance
Select an option from the Rotational resistance model list: Constant torque model, Varying torque model (the default), or None. Friction coefficients can be specified using the Settings window for Contact Between Grains and Contact with Walls nodes.
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The Constant torque model applies a constant rotational resistant torque proportional to the normal contact force on colliding grains.
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The Varying torque model applies a continuous rotational resistant torque that depends on the angular velocity of grain and is limited to the maximum of constant resistant torque discussed for the Constant torque model.
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No rotational resistance torque is applied when None is selected.
Rotational Resistance Theory
Additional Variables
Use the settings in this section to add additional variables to the model that can affect the solution and provide additional information about the grains.
Compute Grain Temperature
Select the Compute grain temperature checkbox to compute grain temperatures. This checkbox is not selected by default. When this option is selected, the temperature of the grain is computed by solving an additional ordinary differential equation per grain, which accounts for various heat sources including conduction, convection, and external heat sources. Thermal properties for the grains can be specified in the Settings window for the Grain Properties node. Initial value of grain temperature can be specified using the Settings window for any grain release features used.
Compute Conductive Heat Transfer
When the Compute grain temperature checkbox is selected, the Compute conductive heat transfer checkbox is available when the contact force model is either Hertz–MD or Hertz–MD with adhesion. This checkbox is not selected by default. Selecting this checkbox includes the conductive heat source in the grain–grain and grain–wall heat transfer calculations. Thermal properties for the walls can be specified in the Settings window for the Wall node.
Computing Grain Temperature
Compute Coordination Numbers
The Compute coordination numbers checkbox is not selected by default. When selected, two variables are added to each grain to compute their coordination numbers. The two variables that are added are:
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The number of grains each grain is in contact with (variable name <name>.Ng).
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The number of wall elements each grain is in contact with (variable name <name>.Nw).
Contact is defined as any interaction that can induce a normal force on the grain, and it can therefore include interactions where the grain is not in physical contact with another grain or a wall element.
Out-of-Plane Grain Thickness
The Out-of-plane grain thickness is only available in 2D components. Enter a value for the Out-of-plane grain thickness (SI unit: m). The default is 1 m. In The Granular Flow Interface, 2D components are treated as a planar representation of a 3D component with cylindrical grains and planar walls in the out-of-plane direction. The Out-of-plane grain thickness denotes the extent of the 3D component in that direction.
Depending on the various combinations of the Contact force model, Rotational resistance model, Compute grain temperature, and Compute conductive heat transfer checkboxes that are selected, different settings can appear in the Settings windows of some of the default nodes: Grain Properties, Wall, Contact Between Grains, Contact with Walls, and nodes used for releasing the grains. The available options for the different selections are explained in the respective features.
Advanced Settings
This section is only shown when Advanced Physics Options are enabled (click the Show More Options button () on the Model Builder toolbar, and select Advanced Physics Options in the Show More Options dialog).
Seeds for Random Number Generation
Select an option from the Seeds for random number generation list: Unique (the default), Random, or User defined.
Many release features in the The Granular Flow Interface utilize pseudorandom number generators (PRNGs) to sample the grain positions, release times, distribution of grain properties and initial values of auxiliary dependent variables. The seed for these internal PRNGs are controlled by this setting.
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When Unique is selected, the seeds are set automatically to a unique value.
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When Random is selected, the seeds are set automatically to a random value that depends on machine time. This will ensure that the solution is not reproducible when running a study multiple times.
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When User defined is selected, additional text fields appear in the settings windows for all nodes that use random numbers. This number is used as the seed value. A set of distinct solutions can be obtained by running a Parametric Sweep over several values of this argument.
Note that these PRNGs produce pseudorandom numbers and not truly random numbers derived from a natural entropy source. For simple models, the Unique and User defined options may make the solution reproducible when rerunning the study multiple times. Reproducibility is somewhat easier to achieve when using a manual time step size. However, the results may not be 100% reproducible because even the slightest change in the time step size, down to machine precision, will cause different pseudorandom numbers to be generated. This can have a snowballing effect where the different solution values cause subsequent time steps to take on different sizes, leading to different pseudorandom numbers in all ensuing time steps. The Random option is never expected to make the solution reproducible across multiple runs of the study.
Maximum Number of Cells per Direction
The broad search step in the Contact Search Theory algorithm for detecting grain–grain contact includes the construction of a grid across the modeling domains. The default size of the grid cells is controlled by the contact search radius, which can sometimes lead to large memory requirements, especially when the ratio of grain diameters to the geometry dimensions are very small. This can be mitigated by controlling the maximum number of grid cells in each direction.
Enter the values of the Maximum number of cells per direction to control the size of the grid in each direction (x, y in 2D and x, y, z in 3D) independently. The default values for each direction is 1000.
Dependent Variables
The dependent variables (field variables) are the Grain center position, Grain center position components, Grain velocity, and Grain velocity components.
Theory for the Granular Flow Interface