24.3.1 Modeling Open Channel Flows

Using the VOF formulation, open channel flows can be modeled in ANSYS FLUENT. To start using the open channel flow boundary condition, perform the following:

1.   Enable Gravity and set the gravitational acceleration fields.

General

2.   Enable the volume of fluid model.

(a)   Open the Multiphase Model dialog box.

Models Multiphase Edit...

(b)   Under Model, enable Volume of Fluid.

(c)   Under Scheme, select either Implicit, Explicit.

3.   Under Volume Fraction Parameters, select Open Channel Flow.

In order to set specific parameters for a particular boundary for open channel flows, enable the Open Channel option in the Multiphase tab of the corresponding boundary condition dialog box. Table  24.3.1 summarizes the types of boundaries available to the open channel flow boundary condition, and the additional parameters needed to model open channel flow. For more information on setting boundary condition parameters, see Chapter  7.

Table 24.3.1: Open Channel Boundary Parameters for the VOF Model

Boundary Type	Parameter
pressure inlet	Inlet Group ID; Secondary Phase for Inlet; Flow Specification Method; Free Surface Level, Bottom Level; Velocity Magnitude
pressure outlet	Outlet Group ID; Pressure Specification Method; Free Surface Level; Bottom Level
mass flow inlet	Inlet Group ID; Secondary Phase for Inlet; Free Surface Level; Bottom Level
outflow	Flow Rate Weighting

Defining Inlet Groups

Open channel systems involve the flowing fluid (the secondary phase) and the fluid above it (the primary phase).

If both phases enter through the separate inlets (e.g., inlet-phase2 and inlet-phase1), these two inlets form an inlet group. This inlet group is recognized by the parameter Inlet Group ID, which will be same for both the inlets that make up the inlet group. On the other hand, if both the phases enter through the same inlet (e.g., inlet-combined), then the inlet itself represents the inlet group.

In three-phase flows, only one secondary phase is allowed to pass through one inlet group.

Defining Outlet Groups

Outlet-groups can be defined in the same manner as the inlet groups.

In three-phase flows, the outlet should represent the outlet group, i.e., separate outlets for each phase are not recommended in three-phase flows.

Setting the Inlet Group

For pressure inlets and mass flow inlets, the Inlet Group ID is used to identify the different inlets that are part of the same inlet group. For instance, when both phases enter through the same inlet (single face zone), then those phases are part of one inlet group and you would set the Inlet Group ID to 1 for that inlet (or inlet group).

In the case where the same inlet group has separate inlets (different face zones) for each phase, then the Inlet Group ID will be the same for each inlet of that group.

When specifying the inlet group, use the following guidelines:

• Since the Inlet Group ID is used to identify the inlets of the same inlet group, general information such as Free Surface Level, Bottom Level, or the mass flow rate for each phase should be the same for each inlet of the same inlet group.

• You should specify a different Inlet Group ID for each distinct inlet group.

  For example, consider the case of two inlet groups for a particular problem. The first inlet group consists of water and air entering through the same inlet (a single face zone). In this case, you would specify an inlet group ID of 1 for that inlet (or inlet group). The second inlet group consists of oil and air entering through the same inlet group, but each uses a different inlet ( oil-inlet and air-inlet) for each phase. In this case, you would specify the same Inlet Group ID of 2 for both of the inlets that belong to the inlet group.

Setting the Outlet Group

For pressure outlet boundaries, the Outlet Group ID is used to identify the different outlets that are part of the same outlet group. For instance, when both phases enter through the same outlet (single face zone), then those phases are part of one outlet group and you would set the Outlet Group ID to 1 for that outlet (or outlet group).

In the case where the same outlet group has separate outlets (different face zones) for each phase, then the Outlet Group ID will be the same for each outlet of that group.

When specifying the outlet group, use the following guidelines:

• Since the Outlet Group ID is used to identify the outlets of the same outlet group, general information such as Free Surface Level or Bottom Level should be the same for each outlet of the same outlet group.

• You should specify a different Outlet Group ID for each distinct outlet group.

  For example, consider the case of two outlet groups for a particular problem. The first inlet group consists of water and air exiting from the same outlet (a single face zone). In this case, you would specify an outlet number of 1 for that outlet (or outlet group). The second outlet group consists of oil and air exiting through the same outlet group, but each uses a different outlet ( oil-outlet and air-outlet) for each phase. In this case, you would specify the same Outlet Group ID of 2 for both of the outlets that belong to the outlet group.

For three-phase flows, when all the phases are leaving through the same outlet, the outlet should consist only of a single face zone.

Determining the Free Surface Level

For the appropriate boundary, you need to specify the Free Surface Level value. This parameter is available for all relevant boundaries, including pressure outlet, mass flow inlet, and pressure inlet. The Free Surface Level, is represented by $y_{\rm local}$ in this equation in the separate Theory Guide.

where $\overrightarrow{a}$ is the position vector of any point on the free surface, and $\hat{g}$ is the unit vector in the direction of the force of gravity. Here we assume a horizontal free surface that is normal to the direction of gravity.

We can simply calculate the free surface level in two steps:

1.   Determine the absolute value of height from the free surface to the origin in the direction of gravity.

2.   Apply the correct sign based on whether the free surface level is above or below the origin.

If the liquid's free surface level lies above the origin, then the Free Surface Level is positive (see Figure  24.3.1). Likewise, if the liquid's free surface level lies below the origin, then the Free Surface Level is negative.

Determining the Bottom Level

For the appropriate boundary, you need to specify the Bottom Level value. This parameter is available for all relevant boundaries, including pressure outlet, mass flow inlet, and pressure inlet. The Bottom Level, is represented by a relation similar to this equation in the separate Theory Guide.

where $\overrightarrow{b}$ is the position vector of any point on the bottom of the channel, and $\hat{g}$ is the unit vector of gravity. Here we assume a horizontal free surface that is normal to the direction of gravity.

We can simply calculate the bottom level in two steps:

1.   Determine the absolute value of depth from the bottom level to the origin in the direction of gravity.

2.   Apply the correct sign based on whether the bottom level is above or below the origin.

If the channel's bottom lies above the origin, then the Bottom Level is positive (see Figure  24.3.1). Likewise, if the channel's bottom lies below the origin, then the Bottom Level is negative.

Figure 24.3.1: Determining the Free Surface Level and the Bottom Level

Specifying the Total Height

The total height, along with the velocity, is used as an option for describing the flow. The total height is given as

where $V$ is the velocity magnitude and $g$ is the gravity magnitude.

Determining the Velocity Magnitude

Pressure inlet boundaries require the Velocity Magnitude for calculating the dynamic pressure at the boundary. This is to be specified as the magnitude of the upstream inlet velocity in the flow.

Determining the Secondary Phase for the Inlet

For pressure inlets and mass flow inlets, the Secondary Phase for Inlet field is significant in cases of three-phase flows.

Note that only one secondary phase is allowed to pass through one inlet group.

Consider a problem involving a three-phase flow consisting of air as the primary phase, and oil and water as the secondary phases. Consider also that there are two inlet groups:

• water and air

• oil and air

For the former inlet group, you would choose water as the secondary phase. For the latter inlet group, you would choose oil as the secondary phase.

Choosing the Pressure Specification Method

For a pressure outlet boundary, the outlet pressure can be specified in one of two ways:

• by prescribing the local height (i.e., a hydrostatic pressure profile)

• by specifying the constant pressure

This option is not available in the case of three-phase flows since the pressure on the boundary is taken from the neighboring cell.

Limitations

The following list summarizes some issues and limitations associated with the open channel boundary condition.

• The conservation of the Bernoulli integral does not provide the conservation of mass flow rate for the pressure boundary. In the case of a coarser mesh, there can be a significant difference in mass flow rate from the actual mass flow rate. For finer meshes, the mass flow rate comes closer to the actual value. So, for problems having constant mass flow rate, the mass flow rate boundary condition is a better option. The pressure boundary should be selected when steady and nonoscillating drag is the main objective.

• Specifying the top boundary as the pressure outlet can sometimes lead to a divergent solution. This may be due to the corner singularity at the pressure boundary in the air region or due to the inability to specify local flow direction correctly if the air enters through the top locally.

• Only the heavier phase should be selected as the secondary phase.

• In the case of three-phase flows, only one secondary phase is allowed to enter through one inlet group (i.e., the mixed inflow of different secondary phases is not allowed).

Recommendations for Setting Up an Open Channel Flow Problem

The following list represents a list of recommendations for solving problems using the open channel flow boundary condition:

• In the cases where the inlet group has a different inlet for each phase of fluid, then the parameter values (such as Free Surface Level, Bottom Level, and Mass Flow Rate) for each inlet should correspond to all other inlets that belong to the inlet group.

• The solution begins with an estimated pressure profile at the outlet boundary.

  In general, you can start the solution by assuming that the level of liquid at the outlet corresponds to the level of liquid at the inlet. The convergence and solution time is very dependent on the initial conditions. When the flow is completely subcritical (upstream and downstream), in marine applications for instance, the above approach is recommended.

  If the final conditions of the flow can be predicted by other means, the solution time can be significantly reduced by using the proper boundary condition.

• The initialization procedure is very critical in the open channel analysis.

  If you are interested in the final steady state solution, then perform the following initialization procedure:

  1.   Initialize the domain by setting the volume fraction of the secondary phase to 0, and providing the inlet velocity.

  2.   Patch the domain using a volume fraction value of the secondary phase to 1, up to the Free Surface Level specified at the inlet.

  3.   Patch the inlet velocity again in the full domain.

  If the Free Surface Level values are different at the inlet and outlet, then patching some regions with inlet Free Surface Level values and some regions with outlet Free Surface Level values could be useful for some problems.

  The same steps for initialization are also recommended for transient flows, but now the initial conditions are dependent on the user.

• For the initial stability of the solution, a smaller time step is recommended. You can increase the time step once the solution becomes more stable.