T h e S i n g l e - P h a s e F l o w , L a m i n a r F l o w a n d C r e e p i n g F l o w I n t e r f a c e s

In this section:

•The Laminar Flow Interface

•The Creeping Flow Interface

•Fluid Properties

•Volume Force

•Initial Values

The Laminar Flow Interface

The Laminar Flow interface (), found under the Single-Phase Flow branch () in the Model Wizard, has the equations, boundary conditions, and volume forces for modeling freely moving fluids using the Navier-Stokes equations, solving for the velocity field and the pressure. The main feature is Fluid Properties, which adds the Navier-Stokes equations and provides an interface for defining the fluid material and its properties.

When this interface is added, these default nodes are also added to the Model Builder— Fluid Properties, Wall (the default boundary condition is No slip), and Initial Values. Right-click the Laminar Flow node to add other features that implement, for example, boundary conditions and volume forces.

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I N T E R F A C E I D E N T I F I E R

The interface identifier is a text string that can be used to reference the respective physics interface if appropriate. Such situations could occur when coupling this interface to another physics interface, or when trying to identify and use variables defined by this physics interface, which is used to reach the fields and variables in expressions, for example. It can be changed to any unique string in the Identifier field.

The default identifier (for the first interface in the model) is spf.

D O M A I N S E L E C T I O N

The default setting is to include All domains in the model to define the fluid pressure and velocity and the Navier-Stokes equations that describe those fields. To choose specific domains, select Manual from the Selection list.

P H Y S I C A L M O D E L

Control the properties of the Laminar Flow interface, which control the overall type of fluid-flow model.

Compressibility

By default the interface uses the Compressible flow (Ma<0.3) formulation of the Navier-Stokes equations. Select Incompressible flow to use the incompressible (constant density) formulation.

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Turbulence Model Type

By definition no turbulence model is needed when studying laminar (or creeping) flows, and no turbulence model is therefore applied in the

interface. The flow state in a fluid-flow model, however, is not always

Note

known beforehand.

Neglect Inertial Term (Stokes Flow)

This interface changes to The Creeping Flow Interface when the Neglect

inertial term (Stokes flow) check box is selected.

Tip

Select the Neglect inertial term (Stokes flow) check box to model flow at very low Reynolds numbers where the inertial term in the Navier-Stokes equations can be neglected. Use the linear Stokes equations instead. This flow type is referred to as creeping flow or Stokes flow and can occur in microfluidics and MEMS devices, where the flow length scales are very small.

Swirl Flow

Use Shallow Channel Approximation

Select the Use shallow channel approximation check box to model shallow

channels in microfluidics applications.

2D

Such channels often have an almost rectangular cross section where the thickness is much less than the channel width, and simple 2D models often fail to give correct results because they exclude the boundaries that have greater effect on the flow. The shallow channel approximation takes the effect of these boundaries into account by

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adding a drag term as a volume force to the fluid-flow equation. The form of this term is

where is the fluid’s dynamic viscosity (SI unit: kg/(m·s)), u is the velocity field (SI unit: m/s), and dz is the channel thickness. This term represents the resistance that the parallel boundaries place on the flow; however, it does not account for any changes in velocity due to variations in the cross-sectional area when the channel thickness differs. Enter a Channel thickness dz (SI unit: m). The default is 1.

D E P E N D E N T V A R I A B L E S

This interface defines these dependent variables (fields). If required, edit the name, but dependent variables must be unique within a model:

•Velocity field u (SI unit: m/s)

•Pressure p (SI unit: Pa)

•Turbulent kinetic energy k (SI unit: m2/s2)

•Turbulent dissipation rate ep (SI unit: m2/s3)

•Specific dissipation rate om (SI unit: 1/s)

•Undamped turbulent kinematic viscosity 0 (SI unit: m2/s)

•Reciprocal wall distance G (SI unit: 1/m)

A D V A N C E D S E T T I N G S

To display this section, click the Show button () and select Advanced Physics Interface Options. Normally these settings do not need to be changed.

Select the Use pseudo time stepping for stationary equation form check box to add pseudo time derivatives to the equation when the Stationary equation form is used. When selected, also choose a CFL number expression—Automatic (the default) or

Manual. Automatic calculates the local CFL number (from the Courant–Friedrichs– Lewy condition) from a built-in expression. If Manual is selected, enter a Local CFL number CFLloc.

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