As a water resources engineer, many of the hydraulic models you prepare will be steady flow. This is because steady flow models are simpler and require less time to prepare. In many instances, this is appropriate. However, there are times when a more computationally sophisticated model is required to represent the physical processes that occur in a river or channel. The following blog post describes when it is appropriate to prepare an unsteady model and when it is appropriate to prepare a steady model.
Classifying Flow – Steady and Unsteady Flow
Flow is classified as steady or unsteady based on how it changes with respect to time. If flow depth and velocity do NOT vary with time, the flow is considered to be steady. If flow depth and velocity DO vary with time, the flow is considered to be unsteady. The energy equation is used in steady flow modeling. The energy equation can be analytically solved. In other words, it has an exact solution. The Saint Venant equations are used to perform the calculations associated with unsteady flow modeling.
In reality, flow is always unsteady. However, changes in depth and velocity often occur very slowly, even during a flood event (not a dam break). In such cases, it is appropriate to assume steady flow.
Steady Flow Modeling
As previously mentioned, steady flow modeling is an approximation of the real world. These models are typically simpler, easier to prepare, and more stable. This is because the user enters the modeled flow rate and the HEC-RAS program solves for one unknown (water surface elevation) at each cross section using the energy equation. Steady flow models are appropriate for situations where channel geometry and flow conditions do not vary greatly. FEMA floodplains are typically generated using steady flow models.
It is important to note that steady flow models typically generate conservative water surface elevations because it is assumed that flow (often peak flow) is constant within a reach. This means that steady flow results are showing what the water surface elevation at a particular location would be if the modeled flow rate was held constant long enough to fill all available storage.
Advantages of Steady Flow Modeling
- Simpler
- Appropriate approximation for many situations
- Less data is required
Disadvantages of Steady Flow Modeling
- Not appropriate for situations where there are significant flow restrictions or attenuation
- Can be overly conservative
- Can only model one flow rate at a time
Unsteady Flow Modeling
As previously mentioned, unsteady flow modeling is based on the Saint Venant equations. Unlike the energy equation, the Saint Venant equations (a combination of the continuity equation and the momentum equation) calculate stage/water surface elevation and flow. These equations do not have an exact solution and must be reduced to a discrete form (finite difference approximation). This is because exact analytical solution methods cannot be applied to nonlinear equations. There is a small amount of error associated with applying a finite difference approximation. By default, HEC-RAS uses the Skyline/Gaussian finite difference matrix solver for 1D unsteady flow models. However, in version 6.0, HEC also added the option to apply the 1D Finite Volume solution algorithm for solving the 1D Shallow Water equations. This could be a good option if you are modeling low flows.
Unsteady flow models (rather than steady flow) should be used in the following situations:
- Attenuation
- Bidirectional flow (e.g., stream junction, tidal river),
- Flow restrictions (e.g., undersized culvert),
- Dam breaks,
- Systems with pumps or gates, and
- Systems with complex flow patterns (e.g., flow splits, reverse flow).
Attenuation
I have heard the term “attenuation” thrown around throughout my career. However, it took me a long time to actually understand what the term means. It’s actually a fairly simple concept – attenuation of flow refers to any means by which peak flow is reduced. Therefore, the attenuation of flow is the difference between the peak of the inflow hydrograph and the outflow hydrograph. There are man-made structures, such as dams and basins, that store water and reduce peak flow. In other words, these structures attenuate flow. Attenuation also occurs naturally in streams/rivers that contain wide floodplains or lakes. When a channel has a wide floodplain, it can take a significant amount of time to fill the floodplain with water. While the floodplain is filling, less flow is being conveyed downstream. Unlike a steady flow model, an unsteady flow model can adjust the hydrograph based on whether the volume in the flood wave is less than or greater than the amount of storage available in the channel.
In a steady flow model, attenuation is not accounted for (unless the modeler modifies flow rates based on hydrologic modeling results) because the program applies the flow specified at the reach’s upstream boundary to every cross section within the reach.
Flow Restrictions
Upstream of a significant flow restriction, such as an undersized culvert, the flow will back up behind the restriction. Steady flow models calculate the energy grade necessary to convey the specified flow through the culvert/restriction without accounting for the storage effects of the backed-up water. However, depending on the amount of upstream storage capacity, the actual flow (and associated energy grade) through the restriction could be less than what is estimated in a steady flow model.
Flow Splits
For situations where flow diverges/splits, it is important to understand how much flow enters each branch. In some cases, the amount of flow that enters a particular stream branch may depend on the tailwater elevation. Flow in a branched system is estimated through addition and subtraction in steady flow modeling. In some cases, simple addition and subtraction is an over-simplification. This is because steady flow modeling does not account for the fact that a flow split is partly a function of the downstream water surface elevation, which is a function of the flow split.
Advantages of Unsteady Flow Modeling
- More accurate (as long as they are prepared correctly)
- Allows the user to model more complex systems
Disadvantages of Unsteady Flow Modeling
- More complex
- Requires more data than a steady flow model
- Can be unstable
Hydrologic Routing Analyses
Hydrologic routing is sometimes referred to as quasi-unsteady analyses. These simplified unsteady flow analyses can be performed using a hydrology program such as HEC-1 or HEC-HMS. These programs can be used to determine the peak discharge from a watershed. This data can then be used as an input for HEC-RAS.