The Euler-Euler Model, Laminar Flow Interface

The interface (

), found under the branch (

) when adding a physics interface, can be used to simulate the flow of two continuous and fully interpenetrating incompressible phases (see Ref. 1 under the Theory for the Euler-Euler Model Interfaces). The physics interface can model flow at low and moderate Reynolds numbers. Typical applications are fluidized beds (solid particles in gas), sedimentation (solid particles in liquid), or transport of liquid droplets or bubbles in a liquid.

The physics interface solves two sets of Navier-Stokes equations, one for each phase, in order to calculate the velocity field for each phase. The phases interchange momentum as described by a drag model. The pressure is calculated from a mixture-averaged continuity equation and the volume fraction of the dispersed phase is tracked with a transport equation.

When this physics interface is added, the following default physics nodes are also added in the —, , and . Then, from the toolbar, add other nodes that implement, for example, boundary conditions and volume forces. You can also right-click to select physics features from the context menu.

The is the default physics interface name.

The 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 field. The first character must be a letter.

The default (for the first physics interface in the model) is ee.

Select a — or .

When is selected, the Solid Pressure section is available in the Phase Properties node. Also see Dispersed Phase in the theory section.

Select a — or .

When is selected, the Solid Pressure section is available in the Phase Properties node. Also see Dispersed Phase in the theory section.

Reference values are global quantities used to evaluate the density of the fluid and define the absolute pressure.

There are generally two ways to include the pressure in fluid flow computations: either to use the absolute pressure pA = p + pref, or the gauge pressure p. When pref is nonzero, the physics interface solves for the gauge pressure whereas material properties are evaluated using the absolute pressure. The reference pressure level is also used to define the density of incompressible fluids.

The reference temperature is used to define the reference density.

Turbulent flow can be simulated by changing the to ε(Reynolds-Averaged Navier–Stokes, k-ε).

The dependent variables (field variables) are:

The names can be changed but the names of fields and dependent variables must be unique within a component.

To display this section, click the button (

) and select in the dialog box.

To display this section, click the button (

) and select in the dialog box.

Inconsistent stabilization can be activated independently for the momentum equation for the continuous phase, the momentum equation for the dispersed phase, and for the dispersed phase transport equation respectively by selecting the corresponding check box. Each inconsistent stabilization contribution has a tuning parameter.

To display this section, click the button (

) and select in the dialog box. Normally these settings do not need to be changed.

The ,

c,res, and ,

d,res, set the smallest values used to avoid division by zero when evaluating terms that involve 1/

c and 1/

d. Observe that this value does not prevent

c or

d from becoming smaller than

c,res and

d,res, respectively.

Select the check box to add pseudo time derivatives to the equation when the form is used. When selected, also choose a — (the default) or . sets the local CFL number (from the Courant–Friedrichs–Lewy condition) to the built-in variable CFLCMP which in turn triggers a PID regulator for the CFL number. For enter a CFLloc (dimensionless).

The Euler-Euler Model, Laminar Flow interface supports three options for the basis functions: (the default option), , and . They all represent Lagrangian basis functions of different orders:

•

– Linear basis functions for all degrees of freedom. Linear basis functions are computationally less expensive than the higher-order options and are also more robust. This option requires that is activated for both of the momentum equations.

•

– Quadratic basis functions for all degrees of freedom except the pressure which is described by linear basis functions. Higher order elements, as compared to linear elements, are a computationally effective way to obtain high accuracy but only if the flow is well resolved. This requirement is most likely fulfilled for flows with very low velocities and/or small length scales.

•

– Cubic basis functions for all degrees of freedom except the pressure which is described by quadratic basis functions. This option is computationally very expensive and the least robust one but it is also the option with the highest formal accuracy.

To see all settings available in this section, click the button (

) and select .