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23.3.9 Open Channel Flow

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.

 Fr = \frac{V}{\sqrt{gy}} (23.3-19)

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  23.3-19 is the propagation speed of the wave. The wave speed as seen by the fixed observer is defined as

 V_{\rm w} = V \pm \sqrt{gy} (23.3-20)

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

Upstream Boundary Conditions

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

Pressure Inlet

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

 p_{\rm0} = \frac{1}{2}(\rho - \rho_{\rm0} ) V^2 + (\rho - \r... ...vert (\hat{g} \cdot (\overrightarrow{b} - \overrightarrow{a})) (23.3-21)

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

 q = \frac{\rho - \rho_{\rm0}}{2}V^2 (23.3-22)

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

 p_{\rm s} = ( \rho - \rho_{\rm0}) \vert\overrightarrow{g}\vert (\hat{g} \cdot (\overrightarrow{b} - \overrightarrow{a})) (23.3-23)

which can be further expanded to

 p_{\rm s} = ( \rho - \rho_{\rm0}) \vert\overrightarrow{g}\vert ((\hat{g} \cdot \overrightarrow{b}) + y_{\rm local}) (23.3-24)

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

 y_{\rm local} = - (\overrightarrow{a} \cdot \hat{g}) (23.3-25)

Mass Flow Rate

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

 \dot{m}_{\rm phase} = \rho_{\rm phase} (Area_{\rm phase}) (Velocity) (23.3-26)

Volume Fraction Specification

In open channel flows, FLUENT internally calculates the volume fraction based on the input parameters specified in the Boundary Conditions panel, therefore this option has been disabled.

For subcritical inlet flows (Fr $<$ 1), 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:

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  23.3-23 and Equation  23.3-25, 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 FLUENT will extrapolate the required information from the interior.

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

Backflow Volume Fraction Specification

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

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© Fluent Inc. 2006-09-20