Culvert Flow into 2D Flow Areas

In HEC-RAS 6.7, the momentum from culverts into 2D Flow Areas is included. The culvert outlet momentum is only applicable to the Shallow Water Equation solvers SWE-ELM and SWE-EM. Culvert outflows can have the effect of accelerating or deaccelerating the flow depending on the velocity of the outflow and the local flow velocities. Culvert inflows have no effect on the momentum of 2D flow area cells. The momentum contribution from culvert outflows at a computational face can be written as

1)	$\begin{array}{l}\displaystyle \displaystyle \mathcal{F}_{f}^{-} = \mathcal{F}_{e,f}^{-} + \mathcal{F}_{i,f}^{-} u_{N,f}\end{array}$

where

2)

$\begin{array}{l}\displaystyle \mathcal{F}_{e,f}^{-} = \dfrac{1}{\overline{h}_f} \sum_{c \in (L,R)} \dfrac{\alpha^c_f}{A_c} \displaystyle Q_c^{-} \left( \xi_{p,c} \boldsymbol{V}_c \cdot \textbf{n}_f \right) \\ \displaystyle \mathcal{F}_{i,f}^{-} = - \dfrac{1}{\overline{h}_f} \sum_{c \in (L,R)} \displaystyle \dfrac{\alpha^c_f}{A_c} \displaystyle Q^{-}_c }\end{array}$

and

$\begin{array}{l}Q_c^{-}\end{array}$ : culvert outflow at cell $\begin{array}{l}c\end{array}$ [L³/T]
$\begin{array}{l}\boldsymbol{V}_c\end{array}$ : culvert outflow velocity at cell $\begin{array}{l}c\end{array}$ [L/T]
$\begin{array}{l}\xi_{p,c}\end{array}$ : culvert plunging flow factor at cell $\begin{array}{l}c\end{array}$ [-]
$\begin{array}{l}A_c\end{array}$ : cell horizontal area [L²]
$\begin{array}{l}\overline{h}_f = \alpha _f ^L h_L + \alpha _f ^R h_R\end{array}$ [L]
$\begin{array}{l}h_c\end{array}$ : cell hydraulic depth [L]
$\begin{array}{l}\alpha _f ^L = \frac{\Delta x_f^L }{\Delta x_f^L+\Delta x_f^R}\end{array}$ [-]
$\begin{array}{l}\alpha _f ^R = 1 - \alpha _f ^L\end{array}$ [-]
$\begin{array}{l}\textbf{n}_f\end{array}$ : unit vector at face $\begin{array}{l}f\end{array}$ [-]

The calculation of the plunging flow factor is described in the section below.

Plunging Flow Correction

When a culvert outlet is above the local water surface, the culvert flow is considered to be plunging (see figure below).

When plunging flow occurs, only a fraction of the culvert momentum is transferred to the 2D flow model. In HEC-RAS, a simple conceptual model is used to compute the correction factor or plunging flow factor as a function of the impact angle of the culvert flow with the local water surface as

$\begin{array}{l}\displaystyle \xi_p = \cos(\theta_I)\end{array}$

where $\begin{array}{l}\theta_I\end{array}$ is the culvert flow impact angle. The impact angle is computed from projectile theory assuming a horizontal culvert and given the initial horizontal velocity and height of the culvert above the water surface. The figure below shows the culvert plunging factor as a function of the culvert height above the water surface and culvert outlet velocity.

Culvert Plunging Factor as a function of the outlet height and velocity.