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Simulating Flow Over Stepped Spillways

FLOW-3D is widely used to determine flow parameters on smooth spillways. Often the objective is to find the energy losses over the spillway, which will be used to design downstream stilling basins and other energy dissipaters. There is increasing interest in using FLOW-3D to calculate energy losses on stepped spillways. The process of modeling a stepped spillway can be aided by the following guidelines.

Geometry of a smooth versus a stepped spillway
Figure 1. Typical geometric representation of a smooth and a stepped spillway.

Introduction

Flow on stepped spillways is divided into four general categories: nappe flow, transitional flow, non-aerated skimming flow, and aerated skimming flow. The following tips were developed from a series of models of nappe flow, transitional flow, and non-aerated skimming flow on unventilated stepped spillways up to 45 degrees in slope Additional non-aerated skimming results can be found in Bombardelli et al. (2010, FloSci-Bib33-10) and Meireles et al (2010, FloSci-Bib61-10), while aerated skimming flow model results are available in Sarfaraz and Attari (2011, FloSci-Bib34-11).

 
FLOW-3D captures skimming flow recirculation zones on a stepped spillway, upstream view. On the right is the upstream view and on the left, the downstream view.

Start with Two Dimensions and Select a VOF Method

Run the spillway simulations as a 2-D case first, as long as there are no 3-D inconsistencies in geometry or flow (which is generally true). The results for energy loss won't change much going from 2-D to 3-D. This saves considerably on mesh size and allows much faster simulation runs. For skimming and transitional flows, the default Volume-of-Fluid-Advection (VOF) method seems appropriate (IFVOF=4). For nappe flows, the Split Lagrangian VOF method (IFVOF=6) is recommended to resolve the jet curvature. If the flow regime is not known in advance, use the Split Lagrangian method.

Mesh Resolution

The flow over a stepped spillway exhibits different regimes depending on the upstream velocity and the geometry of the spillway. These different regimes are called skimming, transitional and nappe flows. To correctly predict the flow regime, one needs to make sure that the mesh cells are small enough to capture the flow parameters. For skimming and transitional flows, a relatively low resolution may be acceptable: 4 to 5 cells to resolve the shortest length/height of the step seems sufficient based on a number of tests, although the mesh must be considerably finer when the spillway slope is greater than 45 degrees. Additional resolution was not found to improve the energy loss calculations significantly. Nappe flows, on the other hand, require very fine mesh  to resolve the falling jets.

Comparison of mesh resolution required for skimming and nappe flows
Figure 2. From left to right: fine mesh & skimming flow; coarse mesh & skimming flow; nappe flow & very fine mesh.

 

Boundary Conditions

Upstream, a pressure-type boundary with a defined fluid elevation is more appropriate than a volumetric-flow-type boundary condition. An iterative process may be required to find the correct fluid elevation: reduce the domain (keeping some steps) and measure the critical depth for the known flow rate.

Downstream, it is generally appropriate to use an Outflow-type boundary unless the spillway is submerged. If the modeled flow will be used as an input for a second model (such as for designing a stilling basin), then use the Grid Overlay boundary condition with a restart simulation to provide the upstream flow into the downstream model.

Fluid Initialization

For skimming flow and transitional flow simulations, it is important to initialize the fluid so that it covers the steps and downstream region completely. A number of tests indicated that omitting initialized fluid on the steps causes the flow to skip a few steps at the start, after which it is unable to fill in the gaps due to the fully-ventilated void region approach used when no bubble physics are active (see Figures 3 and 4). Gradually increasing the upstream boundary fluid elevation to emulate a gradual water release still produced skipping over some steps. If it is undesirable to initialize the fluid on the steps, the air entrainment and adiabatic bubble physics models can be activated, which will model suction and bubble breakup and cause the cavities to fill in. The bubble-model approach seems unnecessarily computationally expensive, requires more time to reach steady state, and does not produce much difference in the steady state results for non-aerated skimming and transitional flow, except when the flow rate is high and the spillway steep, in which case skipping can occur even with initialized fluid. For nappe flows, it does not matter if fluid is initialized or not.

Fluid initialized on the steps and the resulting steady-state condition of skimming flow
Figure 3. (a) Fluid initialized on the steps; (b) Steady-state results which show the skimming flow over the stepped spillway.

 

Simulation with no fluid initialized on the steps; steady-state results for skimming flows show that even they tend to skip some steps on the spillway
Figure 4. (a) Simulation with no fluid initialization on steps; (b) Steady-state results even for skimming flows show that they tend to skip some steps over the spillway.

Calculating the Energy Loss

The easy and straightforward way to calculate energy loss over a stepped spillway is to use flux-surface baffles and activate total hydraulic head as additional output. The baffles should be defined at the crest and base of the spillway. The additional output option will write the hydraulic head at the baffles: E­0 and E1 for energy flow at the crest and base of the spillway, respectively. The output is available as Probe > General History data variables Flux-avg hydraulic head @ flux surface (n). Take the relative difference (E0 - E1)/E0 x 100% to find the percent energy dissipation over the spillway.

Output and schematic for measuring energy loss via flux-average hydraulic head
Figure 5. Output and schematic for measuring energy loss via flux-average hydraulic head.

Download the Input Files

The input and geometry files for the example presented in this note are available for download on the FLOW-3D Users Site. After logging onto the users site, go to Example Simulations page, and click on Water & Environmental to find the stepped spillway example.

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