4.4.3. Bulk Nodes

For some engineering problems the variation of a field variable over the problem domain can be roughly represented by some average behavior. In these cases it may be more appropriate to understand the averaged behavior rather than to resolve the behavior in fine detail. When numerically modeling these types of problems, it is convenient to devise lumped parameter models that simulate this averaged behavior. One such modeling strategy, a bulk node model, is employed to capture bulk fluid behavior without regard to spatial resolution. Herein the bulk node model is described within the context of a Galerkin finite element model where the terms bulk fluid element and bulk node are often used interchangeably.

Following standard finite element method procedures, balance equations are written for a physical region surrounding the bulk node where the equations possibly include contributions from unknowns associated with the bulk node. A general conservation equation containing mass and source terms for the bulk node degrees of freedom is included in the fully finite element model system of equations. Coupling between the volumetric and bulk node degrees of freedom is accomplished via boundary conditions on the surface surrounding the bulk node to model, for example, convective or radiative heat transfer between the fluid in the bulk volume and the surface. Some care is needed when selecting the heat transfer coefficient for a bulk node convection boundary condition. For example if modeling the fluid between two parallel plates via a bulk node, using a convection coefficient appropriate for the convective heat transfer between two plates would under-predict the heat transfer because that convection coefficient already accounts for the effect of the intervening fluid.

Example usage of the bulk node capability is outlined below, and a full command reference is available here

Begin Sierra myJob
  .
  Begin Aria Material a_bulk_volume
    # properties for bulk volume
  End
  .
  Begin Procedure My_Aria_Procedure
    .
    Begin Solution Control Description
      # transient solution control commands
    End
    .
    Begin Aria Region My_Region
      .
      Begin bulk fluid element bulk_volume_name
        material = a_bulk_volume
        bulk EQ Energy for temperature with P0 using mass
        .
      End
      .
    End
    .
  End
  .
End Sierra myJob

4.4.3.1. Boundary Conditions

At present there are two supported methods for applying boundary conditions that couple equations on a bulk fluid element to volumetric equations. For heat transfer problems where the energy equation is being solved for temperature on both the volume and the bulk volume element then either a convective or a radiative boundary condition block can be coupled to the bulk fluid element. For either type of boundary condition the “USE BULK ELEMENT” line command should be added to the input block.

Begin Sierra myJob
  .
  Begin Procedure My_Aria_Procedure
    .
    Begin Aria Region My_Region
      .
      Begin bulk fluid element my_bulk_node
        .
      End
      .
      Begin Convective Flux Boundary Condition
        Use Bulk Element my_bulk_node
        .
      End
      .
    End
    .
  End
  .
End Sierra myJob

For all equations boundary conditions may be applied by using a line command of the form:

BC BULKNODE_FLUX FOR energy ON surface_name = generalized_nat_conv BULK_NODE=my_bulk_node

In some cases it is desirable to couple equations being solved for different degrees of freedom on the volume and the bulk fluid element. For example coupling a porous media equation for the gas phase temperature on a volume block to an overall temperature on the bulk fluid element, or an equation solved for enthalpy to an equation solved for temperature. If the same degree of freedom is not present on the bulk node and the volume then the following mappings are checked for:

• Same degree of freedom (e.g. temperature, pressure, mass fraction) but without a material phase specification on the bulk node when one is present on the volume block.

• Temperature degrees of freedom on the volume will check for enthalpy in either the same material phase or no material phase on the bulk node (and vice versa for an enthalpy degree of freedom on the volume). Additional mappings can be supported where they make sense, please email sierra-help@sandia.gov if you have such a use case.

If either no valid mapping or multiple valid mappings are found the simulation will terminate during initialization.

In addition to boundary conditions coupling a bulk fluid element to the surface of a volumetric block it is possible to directly couple bulk fluid elements to one another via the bulk node coupling block. One common use case for this is coupling between pressurization zones.

4.4.3.2. Restarting With Bulk Fluid Element

The bulk fluid element capability is supported for restarted simulations. It is worth noting that while bulk fluid element is generally not part of the original mesh discretization the element is being created internal to the code and is also being added to the results file as well as the restart file if defined. In some cases one may wish to initialize a simulation from a previous restart file that does not contain the bulk fluid element. In this case provision must be made to ignore the fact that the initialization does not include the bulk fluid element so that the bulk fluid element can be created anew.

Input for restart jobs subsequent to the bulk fluid element being added to a model should not contain the BULK NODES IGNORE RESTART command line.