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 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 re-set 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.

For example, a Laminar Flow interface is added to the Model Tree. If the ε turbulence model is selected, the interface changes to ε, which is the same Label that displays when the corresponding interface is added from the Model Wizard or Add Physics window.

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 and at the defined in . The fluid dynamic viscosity is evaluated at the .

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 .

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.

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

The velocity component, uϕ, in the azimuthal direction can be included for 2D axisymmetric components by selecting the check box. While uϕ can be nonzero, there can be no gradients in the ϕ 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.

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.

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 which is defined from the density. For incompressible flow the density is constant, hence the buoyancy force is homogeneous and natural convection can not 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 Boussinesq approximation.

For 2D components, selecting the check box enables modeling of fluid flow in shallow channels in microfluidics applications. Such channels often have an almost rectangular cross section where the dz is much smaller than the channel width. Simple 2D components often fail to give correct results for this type of problems because they exclude the boundaries that have the greatest effect on the flow. The shallow channel approximation takes the effect of these boundaries into account by adding a drag term as a volume force to the momentum equation. The form of this term is

where μ is the fluid’s dynamic viscosity, u is the velocity field, and dz is the channel thickness. This term represents the resistance that the parallel boundaries impose on the flow; however, it does not account for any changes in velocity due to variations in the cross-sectional area of the channel.

Reference values are global quantities used to evaluate the density and viscosity of the fluid when the or the option is selected and to define the gravity force.

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.

The Projection Method for the Navier-Stokes Equations requires additional dependent variables. These are the uc and the pc.

If required, the names of the field, component, and dependent variable may 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 display this section, click the button (

) and select . Normally these settings do not need to be changed.

The option adds pseudo time derivatives to the equation when the form is used in order to speed up convergence. When selected, 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 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 these can 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 since they have higher numerical accuracy than the mixed order options, and . The equal order interpolation options do however require streamline diffusion to be active.