16.3.9 Open Channel Flow

ANSYS FLUENT can model the effects of open channel flow (e.g., rivers, dams, and surface-piercing structures in unbounded stream) using the VOF formulation and the open channel boundary condition. These flows involve the existence of a free surface between the flowing fluid and fluid above it (generally the atmosphere). In such cases, the wave propagation and free surface behavior becomes important. Flow is generally governed by the forces of gravity and inertia. This feature is mostly applicable to marine applications and the analysis of flows through drainage systems.

Open channel flows are characterized by the dimensionless Froude Number, which is defined as the ratio of inertia force and hydrostatic force.

where $V$ is the velocity magnitude, $g$ is gravity, and $y$ is a length scale, in this case, the distance from the bottom of the channel to the free surface. The denominator in Equation  16.3-19 is the propagation speed of the wave. The wave speed as seen by the fixed observer is defined as

Based on the Froude number, open channel flows can be classified in the following three categories:

• When $Fr < 1$, i.e., $V < \sqrt{gy}$ (thus $V_{\rm w} <$ 0 or $V_{\rm w} >$ 0), the flow is known to be subcritical where disturbances can travel upstream as well as downstream. In this case, downstream conditions might affect the flow upstream.

• When $Fr = 1$ (thus $V_{\rm w}$ = 0), the flow is known to be critical, where upstream propagating waves remain stationary. In this case, the character of the flow changes.

• When $Fr > 1$, i.e., $V > \sqrt{gy}$ (thus $V_{\rm w} >$ 0), the flow is known to be supercritical where disturbances cannot travel upstream. In this case, downstream conditions do not affect the flow upstream.

Upstream Boundary Conditions

There are two options available for the upstream boundary condition for open channel flows:

• pressure inlet

• mass flow rate

Pressure Inlet

The total pressure $p_{\rm0}$ at the inlet can be given as

where $\overrightarrow{b}$ and $\overrightarrow{a}$ are the position vectors of the face centroid and any point on the free surface, respectively, Here, free surface is assumed to be horizontal and normal to the direction of gravity. $\overrightarrow{g}$ is the gravity vector, $\vert\overrightarrow{g}\vert$ is the gravity magnitude, $\hat{g}$ is the unit vector of gravity, $V$ is the velocity magnitude, $\rho$ is the density of the mixture in the cell, and $\rho_{\rm0}$ is the reference density.

From this, the dynamic pressure $q$ is

and the static pressure $p_{\rm s}$ is

which can be further expanded to

where the distance from the free surface to the reference position, $y_{\rm local}$, is

Mass Flow Rate

The mass flow rate for each phase associated with the open channel flow is defined by

Volume Fraction Specification

In open channel flows, ANSYS FLUENT internally calculates the volume fraction based on the input parameters specified in the boundary conditions dialog box, therefore this option has been disabled.

For subcritical inlet flows (Fr $<$ 1), ANSYS FLUENT reconstructs the volume fraction values on the boundary by using the values from the neighboring cells. This can be accomplished using the following procedure:

• Calculate the node values of volume fraction at the boundary using the cell values.

• Calculate the volume fraction at the each face of boundary using the interpolated node values.

For supercritical inlet flows (Fr $>$ 1), the volume fraction value on the boundary can be calculated using the fixed height of the free surface from the bottom.

Downstream Boundary Conditions

Pressure Outlet

Determining the static pressure is dependent on the Pressure Specification Method. Using the Free Surface Level, the static pressure is dictated by Equation  16.3-23 and Equation  16.3-25, otherwise you must specify the static pressure as the Gauge Pressure.

For subcritical outlet flows (Fr $<$ 1), if there are only two phases, then the pressure is taken from the pressure profile specified over the boundary, otherwise the pressure is taken from the neighboring cell. For supercritical flows (Fr $>$1), the pressure is always taken from the neighboring cell.

Outflow Boundary

Outflow boundary conditions can be used at the outlet of open channel flows to model flow exits where the details of the flow velocity and pressure are not known prior to solving the flow problem. If the conditions are unknown at the outflow boundaries, then ANSYS FLUENT will extrapolate the required information from the interior.

It is important, however, to understand the limitations of this boundary type:

• You can only use single outflow boundaries at the outlet, which is achieved by setting the flow rate weighting to 1. In other words, outflow splitting is not permitted in open channel flows with outflow boundaries.

• There should be an initial flow field in the simulation to avoid convergence issues due to flow reversal at the outflow, which will result in an unreliable solution.

• An outflow boundary condition can only be used with mass flow inlets. It is not compatible with pressure inlets and pressure outlets. For example, if you choose the inlet as pressure-inlet, then you can only use pressure-outlet at the outlet. If you choose the inlet as mass-flow-inlet, then you can use either outflow or pressure-outlet boundary conditions at the outlet. Note that this only holds true for open channel flow.

• Note that the outflow boundary condition assumes that flow is fully developed in the direction perpendicular to the outflow boundary surface. Therefore, such surfaces should be placed accordingly.

Backflow Volume Fraction Specification

ANSYS FLUENT internally calculates the volume fraction values on the outlet boundary by using the neighboring cell values, therefore, this option is disabled.