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Dam-break waves over movable beds: a "flat bed"
test case
B. SPINEWINE Dept. Civ. and Env. Eng., Université
catholique de Louvain, and Fonds pour la Recherche dans l'Industrie
et l'Agriculture, Belgium
spinewine@gce.ucl.ac.be
Y. ZECH Dept. Civ. and
Env. Engrg., Université catholique de Louvain, Belgium
zech@gce.ucl.ac.be
1 Abstract
2 Introduction
3 Description of the Test Case
4 Description of the measurements
5 Benchmark Description
6 Acknowledgements
7 References
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1. Abstract
We present a set of experiments related to
the propagation of idealised dam-break waves over movable
beds, performed in the framework of the EC-funded IMPACT project.
The objective is to investigate the geomorphic impacts induced
by very rapid and transient floods such as those resulting
from dam-breaks. The aim of this experimental work is also
to serve as a basis for comparison among a range of numerical
models, and to identify the key aspects that are crucial for
modelling this kind of flow. The experiments were performed
in a prismatic channel with a flat bed extending on both sides
of the idealised dam. Additional experimental work will be
performed during the IMPACT project, investigating various
geometries and sediment bed levels. The experimental set-up
and test conditions are described in details, and flow measurements
performed using digital imaging techniques are illustrated,
including velocity fields in the granular phase and interfaces
separating the distinct flow regions. Expected outputs from
the modellers wishing to take part in the benchmark for inter-model
comparison are explained.
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This test case concerns a set of experimental
small-scale laboratory dam-break waves over movable beds.
The objective is to investigate the geomorphic impacts induced
by very rapid and transient floods such as those resulting
from dam-breaks. Since by nature, such geomorphic floods are
not frequent and usually not very well documented, laboratory
experiments offer an interesting complement to the analysis
of real catastrophes. They make it possible to investigate
the mechanisms of sediment entrainment and movement in very
intense and transient conditions, far from the uniform conditions
for which traditional sediment transport theories have been
developed.
The aim of this experimental work is also to serve as a basis
for comparison among a range of numerical models relying on
various hypotheses, and to identify the key aspects that are
crucial for modelling this kind of flow. In the present paper,
the experiments are described in details with the aim of providing
sufficient information to the modellers, so that it can serve
as a benchmark for inter-model comparisons and validation.
The paper is structured as follows: in section 2 a detailed
description of the experimental set-up is presented, including
flume dimensions, initial and boundary conditions, properties
of the sediments, etc. Section 3 focuses on the measurements
performed: it first describes the imaging system used to acquire
sequences of the flow, and then briefly presents home-made
imaging methods used to derive quantitative measurements of
flow elevations and granular velocities as a function of time.
Finally, in section 4, the benchmark is presented: expected
results from the modellers are described, as well as the standard
data format they should adopt in order to facilitate inter-comparison
of model outputs.
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3. Description of
the Test Case
The experiments were performed by the first author at the
Department of Civil and Environmental Engineering, Université
catholique de Louvain, Belgium. A horizontal flume of rectangular
cross-section was used. The test reach had the following dimensions:
length = 2.5 m; width = 10 cm; side-wall height = 35 cm. The
principle of the tests was as follows: following the sudden
raise of a narrow gate retaining an upstream reservoir of
still water, an idealised dam-break wave was released over
an erodible bed.
The initial conditions are sketched in Fig. 1. A sediment
layer of constant thickness of approximately 5 to 6 cm extends
both upstream and downstream of the idealised dam. To simulate
the dam, a thin watertight sluice gate is pulled down to the
flume bottom. The upstream water level is raised progressively
to form a still reservoir with a depth h0
= 10 cm above the top of the sediment bed. Water is also introduced
in the downstream reach up to the level of the bed, in order
to fully saturate the sediment layer. The rapid raise of the
gate is initiated by a falling weight, linked to the gate
by a system of pulleys. The gate was checked to rise entirely
within less than 50 ms.
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| Figure
1. Initial conditions for the erosional dam-break
wave experiments. A horizontal layer of loose water-saturated
sediments extends upstream and downstream of an idealised
dam. A water body of depth h0is retained upstream,
and released at time t = 0 by the sudden collapse of the
dam. |
The bed material is composed of a light sediment
analogue. Given the small scale of the tests, this choice
was made to obtain a larger sediment mobility as compared
to natural material, enhancing the geomorphic processes at
play. The grains are small PVC pellets with a relative density
s = rs/rw = 1.54. Their size is sufficient to enable resolution
of individual grain movements on image sequences captured
with digital cameras, using the imaging algorithms that will
be briefly described in section 3. The grains are cylindrical
in shape, have a diameter of 3.2 mm and a height of 2.8 mm
(hence an equivalent spherical diameter of approximately 3.5
mm). The particles are mostly white in colour, mixed with
a small proportion of black grains used for quick motion inspection.
Given the very short duration of the experiments and the relatively
long test reach, upstream and downstream boundary conditions
need not to be specified very precisely. It may reasonably
be assumed that the upstream reservoir has an infinite length
and a constant width equal to that of the test reach, which
might be implemented numerically either as a solid wall far
upstream or as a supply section where a constant water level
is imposed. On the downstream side, the channel is terminated
by a weir whose crest coincides with the top of the granular
bed. This watertight weir insures full saturation of the sediment
bed before the start of the test, and acts like a free outfall
during the test. In numerical models, the wave may be assumed
to propagate over a sediment bed of infinite length, placing
boundary conditions out of the region of interest, or a far-field
boundary condition may be imposed at the downstream end. Regarding
the evolution of the sediment bed, the erosion never attained
the solid wall at the bottom of the sediment layer, hence
an infinite thickness of this layer may be assumed in numerical
models. As a summary, any set of boundary conditions may be
assumed, as long as they do not influence the development
of the wave for the considered duration of the tests.
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4. Description
of the measurements The flume and measurement apparatus used for
the tests are sketched in Fig. 2, along with a photograph
of the set-up. Visual access to the flume is possible through
the transparent sidewalls. The flows are filmed using two
synchronized fast CCD cameras, operating at frame rates of
200 frames per second. The grey level images have a resolution
of 256 by 256 pixels and a colour depth of 8 bits. To guarantee
a detailed and accurate observation of the individual grain
movements, a minimum of a few pixels per particle is required.
As a consequence of the limited sensor resolution, the maximal
width of view for one camera is about 15 cm, i.e., 30 cm for
the two cameras put aside each other. To be able to capture
the full spatial extent of the waves, tests are repeated a
number of times with the gate displaced upstream or downstream
by multiples of 30 cm. Previous experiments had revealed the
very good reproducibility of the tests, giving confidence
in the results obtained by this method. This was also verified
by filming separate tests in the exact same configuration.
Moving the gate instead of the cameras offers the great advantage
of leaving the imaging system unperturbed: the image sequences
resulting from separate runs can be easily merged together
in coherent mosaic images, avoiding separate camera calibration
procedures and complex post-processing transformations for
image reassembling.
2a |
2b |
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Figure 2a,b.
Flume and experimental apparatus: a) schematic top-view;
b) side view of the laboratory set-up moments after
release of the wave. The components of the device are:
(1) prismatic flume with transparent side-wall and translucent
back-wall; (2) sluice gate; (3) synchronised CCD cameras;
(4) spot heads; (5) back-illumination.
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Lighting is supplied from two frontal spot heads oriented
at an angle of 45 degrees with respect to the camera axis.
To avoid projected shadows and uneven illumination, a translucent
panel placed on the opposite side of the flow provides diffuse
back lighting. The camera axis was located slightly under
the sediment bed level, to avoid ambiguous location of the
bed and water levels on the images. All this yields clear
images on which the white sediment grains stand out saliently
from the surrounding darker fluid, and the flow free surface
contrasts well with the background. Reconstituted image mosaics
of the flow are shown in Fig. 3.
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Click on
the image to see a larger version
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| Figure
3a-e. Reconstituted image mosaics for the erosional
dam-break wave experiments. Selected instants are, from
top to bottom: a t = 0; b t = 0.25 s; c t = 0.50 s; d
t = 0.75 s; e t = 1.00 s |
A quick phenomenological description of the flow can be derived
from the analysis of those mosaic images. The collapse of the
water body initially forms a wave front propagating downstream
and eroding very intensively the underlying sediment bed. Bulking
of sediments into the flow forms a bore at the front of the
wave, made of a mixture of water and densely packed grains.
Sediment entrainment is so intense that, by mixing with the
flow, it forms an active transport layer of finite thickness.
The very presence of the granular phase itself influences in
turn the flow dynamics. Hence, the rheology of the wave propagation
is more connected to that of a two-phase fluid-granular flow,
rather than to that of a pure fluid flow with passive sediment
transport. Following Capart (2000), three different flow regions
can be identified: a pure water layer, a transport layer made
of a mixture of water and grains, and the motionless sediment
bed. Separating those flow regions are three interfaces, whose
positions can be tracked in time on the digital images of the
flow.
Automated imaging algorithms are used to characterise the
flow pattern, by tracking grain motions in time and identifying
the position of the interfaces separating the three distinct
flow regions. Designing digital particle tracking velocimetry
(DPTV) algorithms to track individual grain motions in dense,
rapidly sheared particle dispersions, like is the case in
the present experiments, is far from being a trivial task.
Resolving motion ambiguities in such cases is a challenge,
and the originality of the approach used for the present experiments
lies in adopting a robust pattern-based principle to perform
correspondence between sets of particle positions on successive
frames. The principle of the method is illustrated in Fig.
4. Convolution of the digital images with radial filters is
first used to highlight particles and locate their centroid
positions to subpixel accuracy (Fig. 4a). Voronoï diagrams
are then constructed on the sets of particle centres identified
on one frame and on the next (shown respectively in thin and
thick lines in Fig. 4b). While particles themselves are identical,
their Voronoï polygons are not and reflect the local
arrangement of neighbouring grains. This arrangement turns
out to be quite stable over successive frames. By matching
polygons of similar shapes, it is possible to pair positions
corresponding to one and the same physical particle but sampled
at two separate times. Once such a pairing is obtained, the
inter-frame displacement vectors of the individual particles
approximate the velocity field (Fig. 4c). Full details of
the methods are given in Capart et al. (2002) and Spinewine
et al. (2002).
4a
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4b |
4c |
| Figure
4a-c. Steps of the pattern-based Voronoï particle
tracking velocimetry algorithm (Capart et al. 2001): a
image detail with particle centroid positions; b Voronoï
diagrams constructed on the sets of particle centres identified
on one frame (thin lines) and the next (thick lines);
c displacement vectors obtained by matching particles
according to their local Voronoï patterns. |
Obtained using those automated algorithms, particle tracking
results are presented in Fig. 5. The only manual intervention
involved in obtaining the new velocity results is a post-processing
step in which some manifestly incorrect vectors (around 2
% of the total number of vectors) are pruned out.
Besides particle velocities, semi-automated imaging procedures
were developed to locate the three experimental profiles of
interest, separating the three distinct regions of the flow:
Gw , Gs and Gb , separating respectively the successive layers
of air, pure water, moving sediments and immobile granular
substrate. They are extracted from the mosaic images in the
following way. Taking benefit of the good contrast between
the two regions, the flow free surface Gw separating the water
layer or water-granularmixture from the overlying ambient
air is obtained using a succession of custom low-pass and
high-pass filters similar to the ones used to pinpoint particle
positions in Fig. 4a. Interface Gs , dividing the flow into
a sediment-free water sub-layer and a transport layer of water
mixed with densely packed sediments, is acquired manually:
while it is not impossible that an automated procedure similar
to the one used for Gw could be designed, it was found more
straightforward to trace the interface silhouette directly
from the images by manually picking points belonging to the
interface. Finally the location of bed interface Gb distinguishing
the moving transport layer from the underlying motionless
bed is estimated on the basis of the PTV displacement fields.
Roughly, the interface position is chosen as the location
where a linear extrapolation of the upper velocity profile
intercepts zero, leaving a decaying tail of small velocities
below the interface. The three boundaries are overlain onto
the displacement fields shown in Fig. 5. Some degree of judgment
is involved in tracing these various curves, hence they are
not to be interpreted too literally. As the reader can judge
for himself based on the raw images and displacement fields,
however, the interfaces usefully highlight the main aspects
of the flow structure.
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Click on
the image to see a larger version
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| Figure
5a-d. Flow interfaces and velocity fields obtained
from particle displacements tracked over 4 successive
frames (15 ms) for a t = 0.25 s, b t = 0.50 s, c t = 0.75
s, and d t = 1.00 s. Estimated interfaces Gw, Gs and Gb
overlain as thick lines. |
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Following the quick phenomenological description of the flow
presented in the previous section, the wave can be schematised
as a succession of three sub-layers separated by relatively
sharp interfaces. Fraccarollo and Capart (2002) proposed an
analytical description of their related set of flow equations,
describing the flow as a series of shocks and expansion waves
separating regions of constant states, like is illustrated on
the bottom of Fig. 6. If this particular description depends
on its constitutive assumptions and is valid only for a given
mathematical model, it has the merit of highlighting some major
flow features similar to those observed during the experiments.
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Click on
the image to see a larger version
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| Figure
6a-b. Wave structure of the erosional dam-break flow:
a characteristic paths of the rarefaction fan and shock
wavefront; b schematic flow pattern as depicted by the
three interface profiles Gw, Gs
and Gb. |
Depending on the respective mathematical and numerical models,
flow features may vary substantially. However, any model should
at least capture the front wave propagation speed and the
evolution of water levels and bed levels in time. Therefore,
the proposed simulation results to be compared with the benchmark
data comprise the propagation speeds of the front shock-wave
downstream ( xf (t) ) and of the upstream rarefaction
wave within the reservoir ( xb (t) ), and the
temporal evolution of the interface levels zw, zb
(and zs if relevant) at different locations x
along the channel. Those variables are defined in Fig. 6.
Modellers wishing to take part in the benchmark are invited
to present their models and modelling results in a coherent
way to guarantee easiness and objectiveness of inter-model
comparisons and validation.
Expected results from the modellers include:
- short description of the numerical simulation covering
- the system of equations used for describing flow dynamics
and sediment movements, along with the phenomenological assumptions
leading to this mathematical framework;
- the numerical methodology, or a reference where a description
of the method can be found;
- the type of mesh used, the number of computational cells
or points, the duration of the simulation in terms of CPU
usage;
- comments regarding the simulation and the results, if any.
- Required simulation results, presented in the following
format
- Position of the wave front xf (t)
and of the rarefaction wave xb (t) , presented
as a single text file with the following format:
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File
name : 'Characteristics.txt'
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Col
1
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Col
2
|
col
3
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Time
t [s]
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Wave
front position
xf (t) [m]
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Rarefaction
wave position
xb (t) [m]
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...
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...
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...
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It is proposed to use time increments Dt
= 0.05 s., corresponding to intervals of 10 images.
Note that the origin of the horizontal axis is located
at the gate position, and that the vertical reference
level is taken at the top of the initial sediment bed.
o Evolution of the interface elevation for zw,
zb and zs at 6 specific
cross-sections along the channel: x = -0.50 , -0.25
, 0.00 , 0.25 , 0.50 , and 0.75 m, each presented in a
separate text file with the following format:
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File
name : e.g. 'Interface_-0.50.txt'
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Col
1
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Col
2
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col
3
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Col
4
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Time
t [s]
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Free
surface elevation
zw(t) [m]
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Bed
level elevation
zb(t) [m]
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Transport
layer elevation
zs(t) [m]
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|
...
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...
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...
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Note that the fourth column referring to the elevation
of the top of the transport layer is of relevance only
for numerical models adopting a multi-layer approach.
This column should be left empty if not relevant for a
particular model.
- Additional simulation results could be provided and will
be compared with experimental data: full profiles of the
flow and its various interfaces, velocity maps (only the
velocities in the transport layer will be compared with
experimental data through particle tracking), … Presentation
of those results is left to the spontaneity of the modeller.
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The authors wish to acknowledge the financial support offered
by the European Commission for the IMPACT project under the
fifth framework programme (1998-2002), Environment and Sustainable
Development thematic programme, for which Karen Fabbri was
the EC Project Officer. In addition, the first author wishes
to acknowledge the Fonds pour la Recherche dans l'Industrie
et l'Agriculture, Belgium, for his support through a PhD fellowship.
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7. References
Capart, H. (2000) Dam-break induced
geomorphic flows and the transition from solid- to fluid-like
behaviour across evolving interfaces. PhD thesis, Univ.
catholique de Louvain, Belgium.
Capart, H., Young, D.L., and Zech, Y. (2002) Voronoï
imaging methods for the measurement of granular flows.
Exp. Fluids 32:121-135
Fraccarollo, L., and Capart, H. (2002) Riemann wave
description of erosional dam-break flows. J. Fluid
Mech. 461:183-228
Spinewine, B., Capart, H., Larcher, M., and Zech, Y. (2002)
Three-dimensional Voronoï imaging methods for the
measurement of near-wall particulate flows. Exp. Fluids
(in press)
To view the PDF document for the Dam-break waves over movable
beds: a "flat bed" test case click
here.
(Note: To download the PDF document right-click
on the link and select 'Save Target As'.)
- The deadline for submisison of results is 31 March
2003
- Please email results and questions to Benoit
Spinewine
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