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Initial Conditions - They're Important

Initializing flow in the domain is an essential part of setting up a simulation in FLOW-3D. Benefits from initializing flow are:

It is important that the initialized flow matches the modeled physical condition in the real world. This Hints & Tips article discusses a case where the choice of initial conditions affects the results, using a Morning Glory spillway as an example (see Figure 1).

Morning Glory Spillways

Cut-away view of a morning glory spillway
Figure 1. 3-D Cut-away view of a morning glory spillway.

Morning Glory spillways are comprised of three-dimensional curved inlets that lead to a discharge conduit below the surface of a pond, lake, or reservoir. They are typically designed and constructed so that the curvature of the spillway surface matches the empirically-determined curvature of the nappe that forms over a hydraulically-similar circular sharp-edged weir. Designers have the option of broadening the weir curve to minimize sub-atmospheric pressures (USACE 1987, USBR 1987). Frequently encountered problems with morning glory spillways include vortexing, surging in the conduit, and related flow instability and reduced flow capacity (USBR 1938, Beichley 1954, McBirney 1960, Posey & Hsu 1965). Deflectors are often added to the approach region to reduce vortexing (Peterka 1956, McBirney 1960). Several FLOW-3D users have modeled morning-glory spillways, for example Ho & Riddette (2010).

An Incorrect Initialization

It seems reasonable to initialize fluid in the domain up to the level at which the Morning Glory spillway will operate. In this case, it is designed to operate at 10 ft of head above the crest, which is located at z = 100 ft. Figures 2 and 3 show the effect of setting upstream pressure-type boundaries with free surface elevation (FSE) at 110 ft, and a matching global initialized fluid elevation of 110 ft.

 
Globally-initialized fluid depth floods the spillway and conduitFigure 2. Globally-initialized fluid depth floods the spillway and the conduit (2D view)
Global initial condition
Figure 3. Global initial condition sets free surface elevation to design head at 110 ft.

The Problem

Unfortunately, this initialization gives poor results. The problem is that the discharge conduit starts out completely full, and remains so throughout the simulation. As water in the full conduit flows downstream, it draws additional water in behind it due to pressure. This is physically correct for cases where the pipe is completely full, but it does not represent typical operation for this spillway. The net result is that the flow rate is much higher than expected: on the order of 2600 cubic feet per second (cfs), whereas the expected flow is about 2000 cfs. The disagreement between numeric and empiric flow rate is 30%. In fact, the pipe is expected to flow about half-full when the crest is under 10 feet of head.

The Solution

More realistic flow rate and surface profile results can be obtained by not filling the pipe entirely in the first place. The expected operation of the spillway will occur when the reservoir fills slowly or rapidly and overtops the spillway. This is modeled in FLOW-3D by setting time-dependent upstream boundary conditions: the free-surface elevation is increased from the reservoir floor to the design head, while the global fluid initialization is set to match the downstream water level, as shown in Figure 4.

Boundary condition raises upstream water level to overtop spillway
Figure 4. Boundary condition raises upstream water level to overtop spillway, global initial condition `Set Free Surface to Downstream Elevation`.

In this case, the flow rate is much more reasonable: 1980 cfs, representing a 1% disagreement between empirical and numerical models. The conduit flows about half full, as expected (see Figure 5).


Time-dependent boundary conditions create the correct flow profile (2-D view).

A Tip, and a Hint

3D cut-away view of correctly initialized operation
Figure 5. 3D cut-away view of correctly initialized operation.

This hints and tips article illustrates the importance of paying close attention to not just the geometry, mesh, fluid properties, and boundary conditions, but also to the way fluid is initialized in the domain. Initialized fluid must match the physical situation in the real world. In this example, setting the global initial fluid depth to the maximum expected depth is not applicable. In cases like this example, a simulation may need to be run on a coarse grid to create the desired initial conditions. That simulation can be used to launch future simulations with finer meshes and/or more detailed physics options.


References

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