Q & A: Flow Attenuation

Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © RASModel.com. 2012. All rights reserved.

Question: 
When running an unsteady flow model with a single inflow hydrograph, why does my discharge decrease in the downstream direction for a given output profile? 

Answer: 
This is called flow attenuation.  You see this to varying degrees in all unsteady flow models and it is a real phenomenon.  The shallower the reach, or the wider the floodplain, the more pronounced this effect will be.  In very steep streams, you may not notice flow attenuation at all. 
The physical process is as follows:  As the flood level rises, water moving downstream fills in available volume.  This volume is called storage.  Water going into storage is taken away from the flow going downstream and that is why you see a decrease in discharge as you move in the downstream direction.  Wider floodplains and shallower reaches have more available storage volume, which is why flow attenuation is pronounced under these situations.  Once the flood wave passes, and you are on the receding limb of the flood hydrograph, the water that had gone into storage now returns to the active discharge.  In this case you’ll see an increase in flow as you move in the downstream direction.  Notice in the figure below that the discharge at time 0042 (before the peak of the flood wave) decreases in the downstream direction, while the flow at time 0124 (after the peak of the flood wave) increases in the downstream direction.

You can also see this effect when viewing hydrographs in the figure below from two cross sections, one upstream (River Station 2500) and one downstream (River Station 2400).  The attenuation of flow is the difference in peak discharge between these two hydrographs-in this case, about 2.3 cms.  The area between these two curves represents a volume of water.  The area to the left, where the upstream discharge is greater than that downstream discharge, represents water going into storage.  The area to the right, where the upstream discharge is less than the downstream discharge, represents water leaving storage.

Attenuation is included in the conservation of mass equation, which is one of the two equations (the St. Venant equations) used to define the movement of water through a reach in HEC-RAS-the other being conservation of momentum.    From the HEC-RAS Hydraulic Reference Manual (Page 2-22), “Conservation of mass for a control volume states that the net rate of flow into the volume be equal to the rate of change of storage inside the volume.”    In other words, Inflow minus outflow equals the change in storage over time.  The equation is:

where A = flow area, Q equals discharge, t = time, and x = length. 
The discretized form of this is more practical to use and may be more familiar: 

Where I = Inflow to a discrete control volume, O = Outflow, DS = Change in Storage, Dt = time duration (i.e. time step).

How to get a table of Peak Flows and Peak Stages for Unsteady Simulations

Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © RASModel.com. 2012. All rights reserved.
This is a common question.  It’s often desirable to have a table of timing for peak stages and flows for dam breach models.  This allows you to track the arrival of the flood wave at all locations downstream of the dam.  However, the typical output plots in HEC-RAS are not very helpful in providing this information.  You could look at each cross section’s stage and flow hydrograph, and pick off the time for the peaks, but this can be very tedious and time-consuming.  There is a much faster way to get this information using the DSS Viewer in HEC-RAS.

Go to the DSS viewer on the main RAS window.

Once there, filter the records as follows by clicking in the blank cell at the top of each column and selecting what you want to see from the dropdown box:

Part A: Select the Reach you want to look at
Part B: Leave Blank
Part C: Select LOCATION-TIME
Part D: Leave Blank
Part E: Select MAX STAGE or MAX FLOW
Part F: Select the Plan you want to view.


Once you have the record you’re interested in, double click it in the filter table so that it is brought down to the list box at the bottom. Then highlight the record in the list box and click “Plot/Tabulate Selected Pathname(s). You should see a graph that plots out the Simulation Time for Max Flow or Stage for every cross section in the selected reach.

For peak stage…



For peak flow…



Within the DSS Plot window, select the “Table” tab to see tabular output.

Modeling Junctions for Unsteady Flow Analysis

Written by Aaron A. Lee   | WEST Consultants
Copyright © RASModel.com. 2011. All rights reserved.

In the current version of HEC-RAS (v 4.1.0) there are two methods of modeling the hydraulics at a junction for unsteady flow. By default RAS selects the Force Equal WS Elevations (Forced) method, which forces the upstream bounding cross-sections’ water surface equal to the downstream water surface. This method may be adequate for some situations like high depths and shallow bed slopes, but can also cause major instabilities in your model if depths are too low and/or bed slopes are too steep. The alternative is the Energy Balance (Energy) method, which uses the energy equation across the junction to solve for WS elevations. The model presented in this post is part of a dam breach simulation and will demonstrate that there can be significant differences between the two methods. This simulation is a hotstart run which seeks to identify stability issues by starting the downstream stage artificially high, and slowly lowering it to the true solution over the run time. The river system in this model has a normal flow combining junction with a steep transition. Special attention will be paid to the steep transition, especially at low flow conditions. The Figure 1 below shows the 3D view of the model extents, which includes the Middle Reach, Tributary C and Lower Reach.


Figure 1


For a normal flow-combining junction, the water surface elevations at the upstream bounding cross-sections are based on the computed downstream WS elevation. Longer lengths between the bounding cross-sections will generally make your results less accurate and less stable. By looking closely at the above figure you can see that the bounding cross-sections are spaced far apart, which corresponds to long junction lengths. The results for both methods are shown below in a series of profile plots. Figures 2a and 2b show the junction approximately halfway through the simulation. Figure 2a shows the Energy Balance method and Figure 2b shows the Forced Equal Water Surface method. The water surface is high enough that there are no differences between the two methods. For reference, Tributary C is the steeper of the upstream reaches.


Figure 2a


Figure 2b


Significant differences develop in Figures 3a and 3b as the downstream stage is lowered. At the same time-step, the two profiles are dramatically different. The Forced method produces a large drop at the junction (Figure 3b), while the Energy method produces only a minor instability (Figure 3a). The large drop (shown in Fig. 3b) occurs because RAS must balance the momentum equation from the upstream bounding cross-section at the junction (an unrealistically low water surface) to the cross-section immediately upstream. The only way to provide a balance is to overestimate the upstream WS elevation, which is why the profile for 3b is much higher than 3a. Notice the spike in the energy grade line. The same problem occurs for the Energy method, but at a much smaller degree.


Figure 3a

Figure 3b


Figures 4a and 4b show Tributary C only, just prior to the model crashing for the Forced Equal Water Surface method. There are obvious oscillations in the profile plot, which indicates a very unstable solution. As the stage is lowered downstream, the WS elevation at the junction also becomes lower. At a certain point the WS elevation at the junction approaches the invert for the upstream cross-section; and the model crashes. Figure 4b shows a zoomed in view of the WS elevation relative to the invert of the channel as the channel runs dry.

Figure 4a

Figure 4b


The best solution is to shorten the junction lengths as much as possible, which is done by adding cross-sections closer to the junction. By adding additional cross-sections you are decreasing the length over which RAS makes its calculations, which helps to remove the problems with low water surface elevations over a junction. If surveyed data is unavailable, then start by copying the most downstream cross-sections of the upstream reaches to a location closer to the junction. The positioning of these new cross-sections will be based on the judgment of the modeler, who should know the actual conditions of the river system. Make sure to adjust the downstream reach lengths and junction lengths accordingly.


In this example, cross-sections were placed within 20 ft of the junction. Junction lengths were changed from 573’ and 534’ to 35’ and 28’ for Tributary C and Middle Reach, respectively. In addition, cross-sections were added every 40’ on the steep section of Tributary C by interpolation. Figures 5a and 5b each show the profile plots for both the Energy and Forced method at the junction of Tributary C and Lower Reach.

Figure 5a

Figure 5b


By redefining the geometry around the junction the error is significantly reduced for both methods and the results appear stable. Both profiles are very similar in this case, showing only a slight difference in WS elevations. The dotted line-type represents the profile for the Forced method. It might not always be possible, or realistic, to place new cross-sections close to the junction. The Energy method allows this model to run to completion without the addition of new cross-sections, though the results appear to not be as good. The table below lists the WS elevations at the bounding cross-sections for each of the different plans: the initial Energy method, and the Forced and Energy method after adding additional cross-sections.













The initial plan has the geometry with the long junction lengths, which consistently calculates lower WS elevations than the plans with shorter junction lengths. Although the elevations were underestimated in the initial runs, they are still within 1 ft of the new profiles. For this model, the Energy method provides a stable solution at the junction without having to modify the geometry. However, given the steepness of Tributary C, the addition of cross-sections near the junction improved the accuracy and stability of the model output. Therefore, even though the Energy method can produce stable results for long junctions in steep reaches, adding more cross sections will improve the results.

Mixed Flow Regime Options – LPI Method

Written by Aaron A. Lee | WEST Consultants
Copyright © RASModel.com. 2011. All rights reserved.
By using the Mixed Flow Regime option for Unsteady Flow Analysis, RAS can better handle transitions from subcritical to supercritical flow. This option should be utilized only after determining that a mixed flow situation exists, which requires judgment from the modeler. One application where this could be particularly useful is dam breach modeling, or any other extreme and flashy flood event. Even though a model is stable there may still be small errors in the solution (caused by max. iterations). The Local Partial Inertia (LPI) factor may eliminate or reduce these errors, particularly if they occur when the Froude number is near 1. Figure 1 shows the Unsteady Flow Analysis window with the Mixed Flow Regime option selected. This post will focus on the LPI Filter, which is enabled when Mixed Flow Regime is selected by the modeler.





Figure 1. Unsteady Flow Analysis Window


Once the Mixed Flow Regime option is selected, additional settings can be adjusted to help stabilize the model. Navigate to Options, Mixed Flow Options. This window, shown in Figure 2, allows the user to adjust two inputs for the LPI factor.





Figure 2. Mixed Flow Options Window


For the unsteady flow computation scheme, RAS accounts for a local acceleration and convective acceleration (inertial terms) through the St. Venant equation of Conservation of Momentum. The St. Venant equations, and by extension, HEC-RAS, are designed to work best in gradually varied flow. Transitions from supercritical to subcritical flow (hydraulic jump), and to a lesser extent subcritical flow to supercritical flow, are rapidly varied flow situations. These are not gradual changes, in the hydraulic sense. Near critical depth (Froude number approaching 1) the convective acceleration terms can change very rapidly over a short distance (think of a hydraulic jump) and can lead to oscillations in the solution. These oscillations tend to grow larger until the solution goes completely unstable (HEC, 2010). The LPI factor systematically reduces these inertial terms to dampen the oscillations, helping to stabilize the model. The user can influence the magnitude of reduction by varying the two inputs in Figure 2.


The first input, m, is the exponent for Froude number reduction factor. Its default value is 10 and ranges from 1 to 128. Adjusting m will change the shape of the curve on Figure 2, thus influencing the rate of reduction of the inertial terms. You can see that by making m smaller there is an earlier and more direct reduction in the inertial terms, with respect to the Froude number. Increasing m can make the model more accurate but increases the likelihood of numerical instability.


The second input, F_T, is the Froude number threshold at which the LPI factor is set to zero. In other words, if the calculated Froude number at the current cross-section is larger than F_T the inertial terms will be eliminated from the computations at that cross-section for the current computational time step. The default value is 1. Making F_T smaller will improve the stability of the model, but will also reduce the accuracy. A larger F_T can make the model more accurate, but increases the likelihood of numerical instability as the inertial terms will be more sensitive to fluctuations in Froude number.


A good place to start is to run the simulation with the default values

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and see what the profile looks like. For this flume example, the model ran without reporting any maximum water surface errors. The profile for the default LPI inputs is shown in Figure 3.





Figure 3. Profile Plot, Default Values


Next, a value of 1.6 was chosen for F_T. This simulation yielded small maximum water surface errors, but had maximum iterations at various locations. The value of m was left unchanged. Figure 4 shows the results.





Figure 4. Profile Plot, Increased Froude Number Elimination Threshold


Even though the errors were small, instabilities could be seen in the downstream end. Notice the instabilities around the transitions between the flow regimes. The value of m was reduced from the default of 10 to 7 in order to improve the stability of the model. Figure 5 shows the profile for reduced m and increased F_T. The modeler should choose the largest values of m and F_T that produce a stable model. However, check the results to make sure that the output is reasonable. Notice how the transitions between flow regimes are much better defined in Figure 5 then the default setup shown in Figure 3. That’s because the default LPI parameters (m = 10 and F_T = 1) provide dampening of the results. Though Figure 3 looks very stable (and it is), Figure 5 (m = 7 and F_T = 1.6) is both stable and (by my engineering judgment) more accurate. Also, notice how the slight increase in energy (green dashed line) is less in Figure 5 versus Figure 3. An increase in the energy elevation in the direction of flow is an indication of error in most cases. Further adjustment of the LPI parameters may help to eliminate the error in the energy grade line, while still producing a stable solution.





Figure 5. Profile Plot, Increased Froude Number Elimination Threshold and Decreased Exponent ,m

Contraction and Expansion Losses for Unsteady Flow

Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © RASModel.com. 2010. All rights reserved.
Since unsteady flow was introduced in HEC-RAS years ago, the contraction and expansion loss coefficients were not used, because losses due to contraction and expansion were automatically approximated in the conservation of momentum equation. Since steady flow RAS does not use the momentum equation for backwater computations, we had to approximate the contraction and expansion losses using those loss coefficients that you see for every cross section in the cross section editor. When switching to unsteady flow, you could leave those coefficients in every cross section; RAS just won’t use them.



In the latest version of RAS (version 4.1), the release notes indicate that RAS may not be capturing all of the C&E losses in unsteady flow, particularly at sharp contractions and expansion. And therefore, unsteady contraction and expansion loss coefficients can now be used.

From the 4.1 Release notes:, “In general, contraction and expansion losses are not used in unsteady flow, and therefore the default coefficients are 0.0. Forces due to contractions and expansions are handled in the momentum equation through pressure force differences. However, because HEC-RAS is a one-dimensional unsteady flow model, the one-dimensional momentum equation does not always capture all of the forces action on the flow field at a sharp contraction and/or expansion zone. In order to better approximate the forces acting on the water, and the resulting water surface elevation, at a contraction and/or expansion, the user can enter empirical contraction and expansion coefficients for unsteady flow modeling. These coefficients will be multiplied by a change in velocity head, just like in steady flow modeling, but the resulting energy loss gets converted to an equivalent force for placement into the momentum equation.”

Notice that there is a new table for entering unsteady flow contraction and expansion losses.



So the obvious question is, “what values do we use for unsteady flow contraction and expansion coefficients?” Are they the same as their steady flow counterparts? Also, when do we want to use them?

Any suggestions out there???