The Laminar Flow Interface

The interface (

) is used to compute the velocity and pressure fields for the flow of a single-phase fluid in the laminar flow regime. A flow remains laminar as long as the Reynolds number is below a certain critical value. At higher Reynolds numbers, disturbances have a tendency to grow and cause transition to turbulence. This critical Reynolds number depends on the model, but a classical example is pipe flow, where the critical Reynolds number is known to be approximately 2000.

The physics interface supports incompressible flow, weakly compressible flow (the density depends on temperature but not on pressure), and compressible flow at low Mach numbers (typically less than 0.3). It also supports flow of non-Newtonian fluids.

The equations solved by the Laminar Flow interface are the Navier–Stokes equations for conservation of momentum and the continuity equation for conservation of mass.

The Laminar Flow interface can be used for stationary and time-dependent analyses. Time-dependent studies should be used in the high-Reynolds number regime as these flows tend to become inherently unsteady.

When the Laminar Flow interface is added, the following default nodes are also added in the : , (the default boundary condition is ), and . Other nodes that implement, for example, boundary conditions and volume forces, can be added from the toolbar or from the context menu displayed when right-clicking .

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Physics interface variables can be referred to 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 spf.

The label for a single-phase flow interface (the node name in the Model Builder) is dynamic and is reset according to the turbulence model and the neglect inertial term (Stokes flow) property set at the physics interface level. The availability also depends on the software license.

If the check box is selected, then the Label changes to , which is the same Label that displays when that interface is added from the Model Wizard or Add Physics window.

Depending of the fluid properties and the flow regime, three options are available for the option. In general the computational complexity increases from to to but the underlying hypotheses are increasingly more restrictive in the opposite direction.

When the option (default) is selected, the incompressible form of the Navier–Stokes and continuity equations is applied. In addition, the fluid density is evaluated at the defined in this section. The is set to 293.15 K.

The option models compressible flow when the pressure dependency of the density can be neglected. When selected, the compressible form of the Navier–Stokes and continuity equations is applied. In addition, the fluid density is evaluated at the defined in this section.

When the option is selected, the compressible form of the Navier–Stokes and continuity equations is applied. Ma < 0.3 indicates that the inlet and outlet conditions, as well as the stabilization, may not be suitable for transonic and supersonic flow. For more information, see The Mach Number Limit in the COMSOL Multiphysics Reference Manual.

The velocity component,

, in the azimuthal direction can be included for 2D axisymmetric components by selecting the check box. While

can be nonzero, there can be no gradients in the

direction. Also see General Single-Phase Flow Theory.

For low Reynolds number flows, the inertial terms in the Navier–Stokes equations may be neglected.

With the addition of various modules, the check box is available. Selecting this option, a node, a node, and a subnode are added to the physics interface. These are described for the interface in the respective module’s documentation. The can be applied on all domains or on a subset of the domains.

is available when is activated. It controls how the condition on boundaries and boundaries adjacent to should be treated. The options are (default) and . The latter option provides a unified treatment when the porous matrix is fully resolved as well as when it is under-resolved ensuring a smooth transition between regions with different resolutions; see No Slip under Wall.

When the check box is selected, a global feature is shown in the interface model tree, and the buoyancy force is included in the Navier–Stokes equations.

Also, when the check box is selected, the option changes the pressure formulation from using the total pressure (default) to using the reduced pressure. This option is suitable for configurations where the density changes are very small; otherwise, the default formulation can be used. For more information, see Gravity.

	Natural convection is induced by variations in magnitude of the buoyancy force that is defined from the density. For incompressible flow, the density is constant; hence the buoyancy force is homogeneous and natural convection cannot be modeled. Nevertheless, using the Nonisothermal Flow multiphysics coupling, the buoyancy force is defined using the thermal expansion coefficient and the temperature. Hence, in this case natural convection is accounted for, following the Boussinesq approximation.

Reference values are global quantities used to evaluate the density of the fluid when the or the option is selected.

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 reference density.

The reference temperature is used to define the reference density.

When is selected, the reference position can be defined. It corresponds to the location where the total pressure (that includes the hydrostatic pressure) is equal to the .

The following dependent variables (fields) are defined for this physics interface — the u and its components, and the p.

If required, the names of the field, component, and dependent variable can be edited. Editing the name of a scalar dependent variable changes both its field name and the dependent variable name. If a new field name coincides with the name of another field of the same type, the fields share degrees of freedom and dependent variable names. A new field name must not coincide with the name of a field of another type or with a component name belonging to some other field. Component names must be unique within a model except when two fields share a common field name.

To enable this section, click the button (

) and select in the dialog box.

There are two consistent stabilization methods: and . Usually, both check boxes for these methods are selected by default and should remain selected for optimal performance. Consistent stabilization methods do not perturb the original transport equation. Streamline diffusion must be selected when using equal-order interpolation for pressure and velocity.

Select the check box to approximate the time-scale tensor in time dependent problems from projections of weak expressions. This check box is selected by default. When not selected the actual time-step is used.

To enable this section, click the button (

) and select in the dialog box.

There is usually just one inconsistent stabilization method — . This method is equivalent to adding a term to the diffusion coefficient in order to dampen the effect of oscillations by making the system somewhat less dominated by convection. If possible, minimize the use of the inconsistent stabilization method because by using it you no longer solve the original problem. By default, the check box is not selected because this type of stabilization adds artificial diffusion and affects the accuracy of the original problem. However, this option can be used to get a good initial guess for underresolved problems.

If required, select the check box and enter a δid as a scalar positive value. The default value is 0.25 (a reasonable value to start with is roughly 0.5 divided by the element order). A higher value adds more isotropic diffusion.

To display this section, click the button (

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

The is per default set to . This option can add pseudo time derivatives to the equation when the form is used in order to speed up convergence. Pseudo time stepping is triggered when the Laminar Flow interface is selected in some multiphysics coupling features. Set to to apply pseudo time stepping also for laminar flows. Set it to to disable pseudo time stepping completely.

When is set to or , a should also be defined. For the default option, the local CFL number (from the Courant–Friedrichs–Lewy condition) is determined by a PID regulator.

The check box under is available when the option is set to . When this check box is selected, the default solver for time dependent study steps will use the Block Navier–Stokes preconditioner in iterative solvers for the velocity and pressure. Using this preconditioner may result in shorter solution times for large time dependent problems with high Reynolds numbers.

The default discretization for Laminar Flow is elements — that is, piecewise linear interpolation for velocity and pressure. This is suitable for most flow problems.

Some higher-order interpolations are also available, and they can be cost-effective options to obtain high accuracy for flows with low Reynolds numbers.

The and options, the equal-order interpolation options, are the preferred higher-order options because they have higher numerical accuracy than the mixed-order options and . The equal-order interpolation options do, however, require streamline diffusion to be active.