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CDA 2009 Annual Conference
Congrès annuel 2009 de l’ACB
CANADIAN DAM ASSOCIATION Whistler, BC, Canada
ASSOCIATION CANADIENNE DES BARRAGES 2009 Oct 3-8
TESTING RIVER2D AND FLOW-3D
FOR SUDDEN DAM-BREAK FLOW SIMULATIONS
Jose A. Vasquez, PhD, Northwest Hydraulic Consultants Ltd., Vancouver, BC, Canada
Jose J. Roncal, National University of Piura, Piura, Peru
ABSTRACT:
The two-dimensional flow model River2D and the three-dimensional Computational Fluid Dynamics (CFD) model Flow-
3D were tested for the first time to simulate instantaneous dam-break flows using high-quality experimental data. The
computer simulations were challenging because the sudden dam-breaks generated highly unsteady and rapidly varied flows
moving over initially dry beds, including large obstacles and non-flat bed topography. The flows were characterized by the
presence of strong hydraulic jumps and waves moving over the computational domain. River2D performed well in cases
when the flood wave moved over a flat bed; however, when there was a rapid rise in bed levels its performance was not
satisfactory. It was found that River2D’s groundwater model, intended for handling wetting and drying in normal (low
slope) river flows, caused an excessive amount of surface water to artificially flow underground in these situations. This
present limitation would prevent River2D from being used to simulate dam-break flows over natural bed topography. Flow-
3D performed well in the three test cases analyzed, without requiring excessive computational times. Flow-3D seems well
suited for practical applications, especially when the flow details near the dam are sought.
RÉSUMÉ:
La modélisation de ruptures subites de barrages a été évaluée pour la première fois en utilisant les modèles d'écoulement
bidimensionnel River2D et tridimensionnel Flow-3D avec un ensemble de données expérimentales. La modélisation fut
complexe car les écoulements résultant d'une rupture sont transitoires et varient rapidement sur des surfaces initialement
sèches, souvent accentuées, et qui comprennent habituellement des obstacles. Les écoulements sont caractérisés par des
ressauts hydrauliques et des ondes qui se déplacent sur le domaine de modélisation. Le modèle River2D représentait bien
les conditions lorsque l’onde de crue se déplaçait sur un terrain plat, mais les résultats étaient moins satisfaisants lorsque les
niveaux du lit étaient accentués. L’étude a aussi démontré que le modèle de nappe phréatiques de River2D, qui prend en
considération les cycles d’humidification et de dessiccation, a été responsable pour une quantité excessive et artificielle
d’eau souterraine. Cette contrainte limite l’utilisation du modèle River2D pour la simulation d’écoulement sur des terrains
naturels suite à la rupture de barrages. Le modèle Flow-3D a donné de bons résultats dans tous les trois cas à l’étude sans
requérir un temps de calculs excessif. Pour les applications pratiques, Flow-3D semble être convenable, surtout lorsqu’il y
a un intérêt pour l’écoulement près du barrage à une échelle plus détaillée.
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
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1. INTRODUCTION
It is well known that the propagation of a flood wave generated by a sudden dam-break event can have
catastrophic effects downstream (Hervouet and Petitjean 1999; Begnudelli and Sanders 2007; Alcrudo and
Mulet 2007). The dynamics of the dam-break wave propagation is quite complex and its behaviour does not
comply with the common assumptions of conventional steady and gradually-varied open channel flows. Dam-
break flows are highly unsteady and rapidly varied, typically with mixed subcritical and supercritical flow
regimes. The flow dynamics can be further complicated if the wave front advances over areas that were initially
dry. An analytical description of these complex flows can only be achieved for very simple cases of limited
practical application.
In the past decades, the ability to predict the dam-break flows has increased with the application of numerical
models. In most practical dam-break applications, one-dimensional (1D) numerical modelling is commonly used
to simulate the flood wave propagation downstream from the dam. However, in certain cases the simplifications
assumed by 1D models may be too restrictive to accurately reproduce the flood wave dynamics; for example
when the flow is not confined to a single channel, the channel has sharp bends or large obstacles are present in
the flooded area (Hervouet and Petitjean 1999). Two-dimensional (2D) models offer the possibility of providing
a better description of the flow, and although their application is not as widespread as 1D models, 2D models
have been successfully applied to simulate real dam-break events (Hervouet and Petitjean 1999; Valiani et al.
2002; Begnudelli and Sanders 2007). Although 2D depth-averaged flow models neglect the vertical velocity
component and assume a hydrostatic pressure distribution, such simplifications are valid in most cases.
However, on certain localized areas the vertical velocity may be important - for example right at the dam section
where the flow is rushing down or when the flood wave hits a large obstacle (like a building, a bridge or a
powerhouse). Such special cases may require the application of a full three-dimensional (3D) flow model that
solves for the three velocity components under non-hydrostatic conditions. However, the applications of 3D flow
models for dam-break flows seem very limited at present, with only a few examples could be found in the
literature.
DeMaio et al. (2004) applied the commercial model Fluent and a 2D vertical mesh to compute the water surface
profile approximately 1 second after an instantaneous dam-break represented by a sudden gate opening. To
compute the location of the free surface, Fluent used the Volume-of-Fluid (VOF) method. Lohner et al. (2006)
developed a 3D VOF flow model that was applied to simulate the free surface movement after a sudden dam-
break, as well as the interaction of the flood wave with a cylindrical pier, all under laminar flow conditions.
Recently, Crespo et al. (2008) used a 2D vertical Smoothed Particle Hydrodynamics (SPH) model to simulate an
instantaneous dam break caused by a sudden gate opening. More detailed validations of full 3D turbulent flow
models with experimental data of sudden dam-break were not found.
The purpose of the work presented here is to test and verify two popular numerical flow models, River2D and
Flow-3D, by using high quality experimental data of sudden dam-breaks flows. First, a brief description of the
numerical models is presented. Later, three experimental test cases are used to validate the models. The results
showed that River2D only provides good results when the bed is flat; while Flow-3D provided good results in
every case.
2. NUMERICAL MODELS
The 2D depth-averaged flow model River2D and the 3D computational fluid dynamics (CFD) model Flow-3D
were selected for the numerical simulations. A brief description of both models follows.
2.1 River2D
River2D is a freely available (www.River2D.ca) flow model developed by the University of Alberta (Steffler
and Blackburn 2002). The model uses a triangular Finite Element (FE) computational mesh to compute water
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
3
depth (h) and the two depth-averaged velocity components (u,v) in the horizontal plane. The unstructured
triangular mesh provides great flexibility to model complex and irregular plan-form geometries. Some comments
on how River2D compares to other FE flow models are found below.
The first generation of FE flow models, such as the US Army Corp’s RMA2 or the US Federal Highway
Administration’s FESWMS, relied on artificial eddy viscosity for numerical stability, these models were mainly
limited to steady subcritical flow conditions and had difficulties in simulating wetting and drying; therefore, they
could not be used to model sudden dam-breaks. Newer FE flow models, such as River2D and Electricté de
France’s Telemac-2D, use modern shock-capturing techniques to achieve stable solutions, even in cases with
supercritical flow and hydraulic jumps. Telemac-2D has successfully been applied to model real-case dam-break
flows (Hervouet and Petitjean 1999), while River2D has been applied successfully to simulate dam-break flows
in laboratory flumes with flat beds only (Ghanem et al. 1995a, 1995b). One important difference between
Telemac-2D and River2D is the manner in which they handle wetting and drying. River2D uses a physically-
based groundwater model that activates whenever the water depth falls below a minimum value hmin. In this way
a continuous and smooth water surface is computed above and below the ground, avoiding some of the problems
in partially-dry elements exhibited by Telemac-2D (Hervouet and Janin 1994, Ghanem et al. 1995a). River2D
computes the groundwater discharge per unit width in the aquifer qa as
qa = TS (1)
Where T is the aquifer transmissivity (permeability times aquifer thickness) and S is the water surface slope in
the aquifer. For normal river flows, qa is in the order of 1% of the surface flow. Hence, only a small portion of
the total river discharge is expected to flow into the aquifer.
River2D is in fact a suite of three executable programs: a topographic bed interpolation model (Bed.exe), an
automatic mesh generation model (Mesh.exe) and the hydrodynamics model (River2D.exe). Bed.exe is an
optional program intended to help generate the bed file, which contains the topographic and roughness data.
Bed.exe has tools to generate triangular irregular networks (TIN) from scatter topographic data points. Bed
break-lines can also be incorporated to better define linear topographic features, such as banklines or thalweg.
Mesh.exe is used to generate the triangular mesh and impose boundary conditions; it has several tools and
options to optimize the mesh geometry. All the programs are written in Visual C++ and have their own
graphical user’s interface with good graphic capabilities. River2D can generate colour plots of several computed
variables, as well as vector velocity plots. It is also possible to extract profile information using user-defined
data points. Although the suite of programs eliminates the need for third-party pre- and post-processing
software, the input and output files are written in a simple ASCII format that make it easy to re-format the files
for transferring to other software, if desired.
Among several consulting companies and research institutions, Northwest Hydraulic Consultant (NHC) has been
using River2D extensively over the last 10 years. NHC has compared River2D with field data collected in
several rivers in Canada and South America, and in every case the model has performed notably well (Vasquez
and Lima 2009). For example, in an unsteady tidal simulation of the Lower Fraser River, River2D matched
observed water levels with 3 cm accuracy, even when the tidal amplitude exceeded 1 m. Vasquez (2005) showed
that River2D was able to reproduce reasonably well the recirculation zone in a channel bifurcation. Vasquez and
Leal (2006) showed that River2D compared well with experimental data of sudden dam-breaks in straight and
curved laboratory channels. Despite these good results for general river flow modelling, River2D has not been
thoroughly tested for sudden dam break flows with obstacles and varying bed elevation.
2.2 Flow-3D
Flow-3D is an advanced 3D CFD model developed by Flow Science Inc. in Santa Fe, New Mexico. Flow-3D
computes the three velocity components (u,v,w) and pressure at the nodes of a orthogonal Finite Difference Grid,
using different turbulence models (k-
ε
, RNG, LES). Among the general-purpose CFD programs commercially
available in the market, Flow-3D stands out for its capabilities intended for hydraulic engineering applications: it
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
4
has excellent capabilities for modelling free surface flow; it can read topographic files in (x,y,z) format;
boundary conditions can be specified as a discharge hydrograph or water level hydrograph; and, local scour at
bridge piers can also be simulated (Vasquez and Walsh 2009). Flow-3D has been used extensively to model
structures such as spillways, stilling basins, water intakes, fish ladders and similar instream structures.
As an interesting fact, Flow Science Inc. was founded by Dr. C.W. Hirt, who pioneered the VOF method, a
unique free surface tracking technique. The VOF is at present the best method available to simulate the
movement of rapidly-varying water surfaces and it is used by all commercial CFD programs when modelling
free surfaces (e.g. Fluent, Star-CCM+, CFX). However, references where Flow-3D has been tested for dam-
break flow simulations could not be found in the literature.
In summary, both River2D and Flow-3D seem in principle capable of simulating sudden dam break flows.
However, probably due to the lack of good quality experimental data, the real capabilities of both models to
simulate dam-break flows has not been properly verified. Recently, as a result of the efforts of a multinational
European research project named IMPACT -Investigation of Extreme Flood Processes and Uncertainty-
(www.impact-project.net), several high quality experimental data sets on dam-break flows have been made
available to the general public (Zech and Soares-Frazao 2007). Some of these data sets have been used as test
cases for verifying the performance of River2D and Flow-3D, as presented in the following sections.
3. STRAIGHT CHANNEL WITH BED STEP
The first case considered in this work involved a relatively simple straight channel configuration with a change
in bed levels at the dam location. Since sediment tends to naturally deposit upstream from a dam, in the event of
a dam-break, it is likely that the bed elevation upstream from the dam will be higher than the bed level
downstream. To study the effect of higher bed elevations upstream from a dam, Leal et al. (2002) performed
dam-break experiments in a rectangular horizontal flume with a 0.12 m high bed step to represent sediment
deposition upstream from a dam. The flume was 19.2 m long, 0.5 m wide and 0.7 m high, and the dam was
simulated by a vertical slide gate installed at the downstream end of the bed step. The bed level downstream
from the dam was set at zd = 0.071 m; while the bed level upstream was zu = 0.190 m. The water level (WL)
upstream from the dam was set to 0.59 m. The water depth downstream from the dam was zero (dry bed) for
Test Ts-25 and 0.075 m (wet bed) for test Ts-28. These tests were actually performed using a movable bed
(sand) and were reproduced by Vasquez and Leal (2006) using River2D-MOR, the movable-bed version of
River2D. However, the duration of the experiment is too short for the movable bed to have a very strong
influence on the water levels, and hence the bed is assumed as fixed for the present simulations.
The computational mesh in River2D was Lx = 20 m long and Ly = 0.5 m wide with roughness height ks =
0.0164 m. Two different meshes with a node spacing of about 0.025 m and 0.050 m were used in a preliminary
analysis. Both meshes led to identical results, indicating that the solution was mesh independent. The results
reported here are for the coarser 0.050 m, whose features are summarized in Table 1. Flow-3D’s rectangular grid
had a cell size of 0.02 m in the horizontal (x,y) direction and 0.01 m in the vertical direction. The number N of
cells in the three spatial directions, as well as the total number of nodes, are detailed in Table 2. Since this is
basically a one-dimensional flow experiment and in order to save computational time, the Flow-3D mesh was
made narrower (Ly = 0.2 m) than the width of the experimental flume. The Flow-3D model used the same
roughness height used by the River2D model (Table 1).
Figure 1 shows the longitudinal profiles of water levels at 1 s and 4 s after dam break for the two experiments,
Ts-25 and Ts-28. Each plot shows the experimental data points, and the profiles computed by both River2D and
Flow-3D. For experiment Ts-25, both models capture very well the movement of a sharp water front over the
initially dry bed downstream from the dam. For experiment Ts-28, both models correctly simulate the formation
of a hydraulic jump and a bore that migrates downstream; although Flow-3D seems to better reproduce the shape
of the hydraulic jump right downstream from the bed step.
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
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In general, the agreement between the experiment and the two numerical models is quite good and it is difficult
to state which model performs better. At time t = 1 s, it appears that Flow-3D produces a better agreement with
experimental data; perhaps because the vertical velocity and non-hydrostatic effects –both ignored by River2D–
are more important at this moment in time when water is quickly rushing down from the reservoir. However, by
t = 4 s, it appears the River2D produces a better agreement with the experimental data.
Table 1: Mesh features and roughness of River-2D models
Dam-break Number of Number of Roughness
Experiment nodes elements height (m)
Channel with bed step 6,076 10,935 0.0164
Triangular sill 5,586 9,880 0.0005
Isolated obstacle 10,933 20,852 0.0002
Table 2: Domain dimensions and number of cells of Flow-3D meshes
Dam-break Dimension (m) Number of cells Total No.
Experiment Lx L
y L
z N
x N
y N
z of cells
Channel with bed step 20.0 0.20 0.60 1000 10 30 300,000
Triangular sill 5.6 0.50 0.16 560 50 32 896,000
Isolated obstacle 17.7 3.64 0.46 501 182 46 4,194,372
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0
Distance (m)
WL (m)
Experiment
Flow-3D
River-2D
Ts-25
t = 1.00 s
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0
Distance (m)
WL (m)
Experiment
Flow-3D
River-2D
Ts-25
t = 4.00 s
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0
Distance (m)
WL (m)
Experiment
Flow-3D
River-2D
Ts-28
t = 1.00 s
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-10.0 -7.5 -5.0 -2.5 0.0 2.5 5.0 7.5 10.0
Distance (m)
WL (m)
Experiment
Flow-3D
River-2D
Ts-28
t = 4.00 s
Figure 1: Longitudinal water surface profiles computed by River2D and Flow-3D at 1.0 s and 4.0 s for the straight channel
with a bed step. The channel downstream was both initial dry (Ts-25, top) and initially wet (Ts-28, bottom).
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
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4. ISOLATED OBSTACLE
The second case evaluated the presence of an isolated obstacle downstream of the dam. After a dam breaks, the
flood wave could hit structures located in its path, such as powerhouses, bridges or buildings, especially if the
dam is located near an urban area. Soares-Frazao and Zech (2007) performed experimental flume studies of the
interaction between a dam-break flood wave and an isolated obstacle. Details of the experimental set-up can be
found in the original publication, and only a brief description is provided here. The channel was 3.6 m wide with
a mildly trapezoidal cross sectional shape. The dam – represented by a vertical lift gate – was only 1 m wide at
the centre of the channel width. The initial water level in the reservoir was 0.4 m, while it was 0.02 m
downstream from the dam. The obstacle was a rectangular block 0.8 m by 0.4 m, skewed 64o relative to the
channel centreline and located about 3.5 m downstream from the dam. Six pressure gauges recorded the dynamic
water levels during the experiment - five gauges (G1 through G5) were located around the obstacle and the sixth
gauge (G6) was located within the reservoir. After the gate was lifted to simulate the sudden dam-break, a very
complex flow pattern developed downstream, with recirculation zones, hydraulic jumps and waves reflecting
from the solid walls. Snapshots of the water surface computed by Flow-3D during the first five seconds of the
experiment –including the initial conditions– are shown in Figure 2. The main features of the River2D and Flow-
3D models are shown in Tables 1 and 2.
Figure 3 shows a comparison between the recorded water levels at the five gauges surrounding the obstacle and
the water levels computed by both Flow-3D and River2D. Each plot shows also the location of the pressure
gauge. The experimental results show how complex the flow pattern is, with strong fluctuations in water levels,
with several peaks. The first peak is probably caused by the direct hit of the flood wave, while the following
peaks are probably caused by waves reflected from the walls.
Figure 2: Water surface computed by Flow-3D for the first 5 s of the Isolated Obstacle test case
Initial
t = 0.0 s
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
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G1
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 5 10 15 20 25 30
t (s)
WL (m)
Experiment
FLOW-3D
River2D
G2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 5 10 15 20 25 30
t (s)
WL (m)
Experiment
FLOW-3D
River2D
G3
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 5 10 15 20 25 30
t (s)
WL (m)
Experiment
FLOW-3D
River2D
G4
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 5 10 15 20 25 30
t (s)
WL (m)
Experiment
FLOW-3D
River2D
G5
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 5 10 15 20 25 30
t (s)
WL (m)
Experiment
FLOW-3D
River2D
Figure 3: Water levels computed by River2D and Flow-3D at the five pressure gauges (G1 to G5) for the Isolated Obstacle
test case.
The isolated obstacle experiment is much more complex than the dam-break in a straight flume described
previously and the agreement between the experiment and the numerical models is not as good. By visual
inspection, it appears that Flow-3D produces better results than River2D, which should be expected considering
that the flood wave hitting the obstacle should produce strong vertical velocities. River2D missed the first water
level peaks at gauges G1 and G5, but it did capture the sudden rise at G2. A few sensitivity tests were performed
in Flow-3D changing some parameters in the VOF model and increasing the order of the convection
computation, but none produced any significant improvement to the results presented in Figure 3.
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
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5. TRIANGULAR BOTTOM SILL
The third test case considered the presence of a raised triangular sill in the channel floor downstream of the dam.
Two-dimensional depth-averaged flow models that solve conservation of mass and momentum equations, do not
compute the (u,v) velocity components directly; but instead they solve the equations for the unit discharge
discharge per unit width) in the two horizontal directions qx = uh and qy = vh. Velocity is then computed by
dividing the unit discharge by the water depth: u = qx / h and v = qy / h. An unsolved problem with this approach
is that when q is high and the water depth decrease rapidly (h → 0), the velocity tends to overshoot, making the
numerical model unstable. This can occur for example, when water flows over a shallow submerged obstacle
like a bar or bump and hence the importance of testing dam-break flow models in such cases.
Soares-Frazao (2007) conducted a dam-break experiment in a straight flume which had a triangular bottom sill
(bump), located downstream (Figure 4). The initial water level in the reservoir upstream from the dam (gate) was
0.111 m. The symmetric sill was located 1.61 m downstream from the dam; it had a length of 0.90 m and a
maximum height of 0.065 m, with upstream and downstream slopes of 0.14. Downstream from the sill there was
a pool of water with initial depth of 0.02 m. Three pressure gauges recorded the time evolution of water levels
upstream (G3) and downstream (G1 and G2) from the bottom sill. High speed digital cameras were also used to
capture snapshots of the instantaneous water surface profile around the sill.
The channel was closed at the both ends. After the gate was lifted, a wave front moved quickly over the initially
dry bed upstream from the bottom sill. Around t = 1.5 s the wave reached the sill and started climbing it
(Figure 4). A portion of the water flow made it over the sill’s crest and plunged into the still pool downstream
from the sill generating a strong hydraulic jump that migrated downstream. The remaining of the flow was
reflected by the sill and started to migrate upstream towards the dam. After several wave reflections from both
ends of the flume, the water depth started to asymptotically stabilize around 0.06 m.
Figure 4: Initial conditions and water levels computed by Flow-3D for the triangular bottom sill test case
Figure 5 shows a comparison of water levels measured at the three gauges and the results computed by Flow-3D
and River2D up to 45 s after dam-break; while Figure 6 shows snapshots of the water surface profiles at t = 1.8 s
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CDA 2009 Annual Conference, Whistler, BC, Canada – October 3 to 8, 2009
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and t = 3.0 s, both measured and computed. As before, the details of the meshes for both model are shown in
Tables 1 and 2.
0.00
0.02
0.04
0.06
0.08
0.10
0 5 10 15 20 25 30 35 40 45
t (s)
h (m)
Experiment Flow-3D
River2D
G1
0.00
0.02
0.04
0.06
0.08
0.10
0 5 10 15 20 25 30 35 40 45
t (s)
h (m)
Experiment Flow-3D
River2D
G2
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0 5 10 15 20 25 30 35 40 45
t (s)
h (m)
Experiment Flow-3D
River2D
G3
Figure 5: Comparison of water levels computed by River2D and Flow-3D with experimental data at three pressure taps for
the triangular bottom sill test case.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
3.50 4.00 4.50 5.00 5.50
Distance (m)
h (m)
Experiment
Flow-3D
River2D
t = 1.80 s
0.00
0.02
0.04
0.06
0.08
0.10
0.12
3.50 4.00 4.50 5.00 5.50
Distance (m)
h (m)
Experiment
Flow-3D
River2D
t = 3.00 s
Figure 6: Comparison of longitudinal water level profiles computed by River2D and Flow-3D at 1.8 s and 3.0 s around the
triangular bottom sill. Notice migrating hydraulic jump at t = 3.0 s.
Flow-3D produced an excellent agreement with the experimental data. The 3D model was able to accurately
capture the water level fluctuations at the three gauges (Figure 5). The sudden drop of water depth at gauge G2,
caused by the formation of a hydraulic jump is well reproduced. This is also visible in the longitudinal profile at
t = 3.0 s (Figure 6). The discrepancies between Flow-3D and the experiment shown in Figure 5 are in the order
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of the experimental error (see Figures 5 and 10 in Soares-Frazao 2007) and it can be claimed that for this
particular experiment, Flow-3D produced results with the same level of accuracy as the physical model.
However, the results computed by River2D were not as good. Although the model captured some of the
oscillations measured at Gauge G3 (Figure 5), it grossly over-predicted the maximum water levels downstream
from the sill (G1 and G2). River2D missed completely the hydraulic jump formed right downstream from the
sill, as shown in the profile at t = 3.0 s (Figure 6). These results are further discussed in the next section.
6. LIMITATIONS OF RIVER2D FOR DAM-BREAK FLOWS
River2D’s computed water levels for the triangular bottom sill experiment (Figures 5 and 6) were surprising and
rather unexpected. River2D did not exhibit any stability problem or velocity overshoot; however, the agreement
with the experimental data was not satisfactory. The first test in the straight flume with a bed step described in
Section 3 demonstrated that River2D is capable of modelling hydraulic jumps; therefore the surface flow model
cannot be responsible for the failure to model the hydraulic jump in the triangular bottom sill experiment
(Figure 6), the problem lies in the groundwater flow model.
As explained in Section 2.1, River2D assumes that the bottom sill is pervious and part of an aquifer. As the flood
wave tries to climb over the upstream face of the sill, a strong water slope S develops across the sill, as
illustrated in Figure 7 for t = 1.8 s. For that particular time, the slope was S = 0.034, much larger than the typical
values in normal river flows, which are in the order of 10-3 to 10-5. Since the discharge into the aquifer is
proportional to S (equation 1), and in this case the slope is very high, all the incoming flow is forced into the
aquifer (sill) with no water left to move over the sill crest. In other words, the entire flood wave passes through
the sill, instead of over its crest.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
3.50 4.00 4.50 5.00 5.50
Distance (m)
h (m)
River2D
Bottom
t = 1.80 s
Figure 7: Water levels computed by River2D at 1.8 s show groundwater flow (arrows) through the triangular bottom sill.
As water flows through the sill, it feeds the pool downstream rapidly, but gradually, generating a higher than
observed water level at gauges G1 and G2 (Figure 5), but without a hydraulic jump. It is not possible to
eliminate or reduce substantially the groundwater flow; attempts to reduce the value of transmissivity T
(equation 1) led to numerical instabilities. It is likely that some surface flow also went underground into the
inclined trapezoidal faces of the isolated obstacle flume (Figure 2). If that were the case, it would help explain
some of the deviations between River2D and the experimental data (Figure 3).
These rather unexpected results of River2D illustrate the need for testing and validating numerical models,
previous to their application in practical problems. This is especially important when the application is
something for which the model has not been used before or it has only been used under simplified conditions.
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7. POTENTIAL APPLICATION OF FLOW-3D FOR REAL DAM-BREAK FLOWS
Compared with a 2D model, the main limitation of any 3D model for practical applications is the significant
increase in the mesh size caused by including the vertical dimension (compare Tables 1 and 2), which translates
in longer computational times. For the isolated obstacle test case, which required the largest of the Flow-3D
mesh tested (Table 2), Flow-3D version 9.3 required 9.5 hours to run in an 8-core computer (with Xeon E5430
processors running at 2.66 GHz under Windows XP). Although computational times for the three laboratory
experiments simulated were manageable, their geometries were rather simple and not as complex as expected in
a real dam break case. For that reason, a qualitative simulation was performed using real topographic data to test
how Flow-3D would perform under a more realistic scenario.
The computational domain was Lx = 540 m long, Ly = 420 m wide and Lz = 70 m high and included a narrow
valley were a concrete dam was assumed to be initially in place. A powerhouse building, immediately
downstream from the dam, was also included in the model (Figure 8). The computational grid was made of
5’439,000 cells. Assuming that the dam vanished instantaneously at t = 0 s, Flow-3D was applied to simulate the
flow conditions during the first 100 s after that event. The water surface computed at t = 10 s is shown in Figure
8. The total computational time was about 7 hours.
Figure 8: Qualitative simulations of a hypothetical instantaneous dam-break using Flow-3D.
Although this was just a qualitative simulation, it has proved for the first time that Flow-3D could be used to
model dam break flows under realistic conditions within reasonable computational effort. These encouraging
results pave the way for future practical engineering applications, where the details of the dam-break flow in the
vicinity of the dam are sought. However, it seems unlikely that Flow-3D could be used to route the flood wave a
long distance away from the dam, because that would demand a very large computational time in a present-day
computer; a 2D model is probably more suitable for such a task.
8. SUMMARY AND CONCLUSIONS
The 2D depth-averaged flow model River2D always assumes that water moves over an alluvial pervious bed
with a defined groundwater transmissivity T. This assumption allows some surface water to flow into an
assumed underlying aquifer when the water depth drops below a minimum low value, in such a way that wetting
and drying processes under normal river flow conditions can be efficiently modelled. The amount of aquifer
flow is governed by the product of T and the water surface slope S in the aquifer. If a dam-break flood wave
moves over an initially dry bed which is flat, S will also remain flat (S = 0) and the aquifer flow will be
negligible. However, a flood wave moving over a non-flat bed will generate high values of S, forcing a large
amount of surface flow into the aquifer. In cases when the bed slope intersects the flood wave, (e.g. up-sloping
t = 0 s t = 10 s
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bed in the downstream direction), up to a 100% of the incoming flood wave can disappear into the groundwater
aquifer. Since it is not possible to set T = 0, or even T ≈ 0, without making River2D unstable, this model should
not be applied to simulate sudden dam-break flows over natural bed topography until this problem is fixed. This
however, does not mean that River2D should not be used for normal river flows; experience using River2D for
those types of applications has shown that the model is quite accurate and very reliable. Sudden dam-breaks are
a special case River2D was not intended for.
Flow-3D was able to achieve a very good agreement with the experimental data in the three experimental test
cases analyzed. One important factor in the success of Flow-3D was its robust VOF solver used for tracking the
location of the free surface. The computational effort for all the test cases analyzed (three experiments plus
hypothetical dam) was reasonable, adding to that Flow-3D’s ability to accommodate the complex geometries
typically found at dam sites (Figure 8), suggest that Flow-3D can be a valuable tool for real dam-break flow
modelling. Flow-3D seems perfectly suitable for analyzing the details of the dam break flows near the dam; for
example to investigate different failure scenarios, for calculating the discharge hydrograph caused by the dam
failure and especially for studying the interaction between the flood wave and nearby structures (e.g.
powerhouse, bridge). However, flood routing far away from the dam would be too computationally demanding
and probably not practical at the moment.
9. ACKNOWLEDGEMENTS
The numerical simulations and graphic post-processing were performed using the software and computer
facilities available at Northwest Hydraulic Consultants (NHC) in its North Vancouver office (BC). Mr. Brian
Hughes provided useful comments that enhanced the manuscript; Ms. Vanessa O’Connor translated the abstract
to French, their help is greatly appreciated.
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