Transcript Scale Effects Related to Small Scale Physical Modelling of Overtopping of Rubble Mound Breakwaters

Scale effects related to small scale physical modelling of
overtopping of rubble mound breakwaters
Coastal Structures 2007, Venice
Burcharth, H. F., Aalborg University, Denmark
Lykke Andersen, T., Aalborg University, Denmark
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Contents
• The problem
• Scale and model effects
• Experimental set-up
• Verification of scaling of model experiments
• Video from experiments
• Results and conclusion
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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The problem
• Admissible overtopping of breakwaters is an important design parameter
as it - roughly speaking - determines the crest level.
• In case of roads, sheds, storage areas etc. just behind the structure we
are dealing with very small limiting overtopping discharges characterized
by average values less than 1 litre/sm.
• The EU-CLASH project
showed that normal
size small scale rubble
mound models under
estimate smaller
overtopping discharges
compared to prototype
measurements.
app. 1 l/sm
Comparison of model and prototype overtopping for antifer cube
armoured breakwater at Zeebrugge (CLASH, 2006)
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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The problem
• Note that small overtopping discharges are caused by very few
waves in a storm.
• Therefore, important to model these few waves kinematically
and statistically correct.
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Scale and model effects
Deviations between model and prototype results are due to scale
and model effects
Scale effects due to incorrect reproduction of ratios between
forces in the model
Inertia forces
Gravity forces
Froude
U
gL
Surface waves
Reynolds
UL

Porous flow
Cauchy
U²

Wave slamming
Viscous forces
Weber
U² L

Air content
Elastic forces
Surface tension
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Scale and model effects
Model effects
• Deviations in wave kinematics (directionality, wave height
distribution, succession of waves, degree of instability)
• Methods in wave recording (pressure gauge, accelerometer
buoy, acoustic, staff)
• Methods of wave analysis
• Geometrical differences (width of overtopping tanks, sea bed
topography, ……)
• Lack of wind and currents
Impossible to separate and quantify scale and model effects for
small overtopping discharges by comparing model and prototype
results.
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Flow regimes
Some scale effects can be studied by comparing small and large scale
models (typical length scale ratios 1:5 – 1:10) because similar incident
waves or flows can be generated due to the controlled environment.
Regimes of scale effects in run-up on rubble slopes:
Wave propagation
1
Wave breaking and impact
(Reynolds, Weber, Cauchy)
2
3
rt of
r pa
e
w
w lo
e flo
c
a
f
Sur nolds)
y
(Re
Surface flow upper part of wedge
(Reynolds, Weber)
4
ge
wed
Porous flow
(Reynolds)
Illustration of surface flow and
porous flow domains during
run-up (Burcharth, 2004)
The run-up height determines the overtopping. The CLASH project showed
bigger overtopping deviations between model and prototype for flatter
slopes. This could be due to increased flow resistance in the upper part of
the run-up wedge. Here the run-up has the characteristics of a flow
between obstacles for which drag coefficients can be very dependent on
the Reynolds number.
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Investigation of scale effects in the upper part
of the run-up wedge by physical models
Reynolds effect
The larger the drag force on the armour the smaller will be the run-up.
The drag coefficients in Morison and Forcheimer equations decreases with
increasing Reynolds number in the actual range of fully turbulent flow.
CD
prototype
model
Schematic illustration
of drag variation with
Reynolds’ number
UL
Re = 
As the reduction in drag coefficients are less for sharp edged objects it
was chosen to use cubes as armour elements in order to demonstrate a
lower limit for the scale impact. Consequently, the scale effect on rock
armour is expected to be larger than seen in the present tests.
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Investigation of scale effects in the upper part
of the run-up wedge by physical models
Surface tension effect
The surface tension is relatively much smaller in large scale
models and prototypes than in the small scale models. This cause
very different air bubble structures with many more smaller air
bubbles in larger scale models and especially in salt water
prototypes (Bullock et al., 2001)
The Reynolds and surface tension scale effects cannot be
separated in the tests.
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Test set-up
A jet-like up-slope flow on a cube armoured impermeable ramp
was generated by instant removal of a hatch to a reservoir.
Cross section
16.7 L
Two geometrically absolute
similar models of length
ratio 1:5 were used:
p
Ram 5
7
1:2.
Hatch
2.5 L
20.8
L
7L
Plane view of ramp
Hatch
18.0 mm small scale
L
90.0 mm large scale
h = 10.9 L
Reservoir
Cube side length L
Porosity = 0.42
Width between cubes = 0.3 L
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Determination of minimum size of model
The flow must imitate as closely as possible wave run-up on an armour
slope.
Critical Reynolds’ number for armour stability:
U L
Re 
 app. 3.5  10 4
U  g Hs



Outflow from reservoir:
U  2gh
with small scale cube side length l = 18 mm and  = 10-6 m2/s
=> head h in reservoir  0.193 m
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Scaling law for initial outflow of reservoir
For the instant flow through the sharp edge hatch opening only gravity
and inertia forces dominates (Froude model) when according to Hager
(1998) the hatch opening time top  1.25(h/g)0.5, which
0.17 s small scale
t op  1.25 h / g 0.5  
0.39 s large scale
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Photos of the two models
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Video – small scale model
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Video – large scale model
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Photos of max run-up
Small scale
Large scale
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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Results and conclusions
The run-up tongue reaches 3 cube length further in the
large model than in the small model.
The vertical run-up height is 1L larger in the large scale
model than in the small scale model.
This shows a significant scale effect solely related to runup in the upper part of the wedge and probably explain
to a large extent why small scale models underpredict
small overtopping discharges.
Equivalent changes in run-up correspond to typical
overtopping discharges is increased by approximately a
factor of 5 to 10 in a large scale model.
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
17 of 18
Difference in mean overtopping discharge
equivalent to run-up height difference L
•
•
•
•
•
•
h=9m
Hs = 5 m
s0p = 0.04
L = 2 m (KD = 4)
Gc = 3L = 6 m
Slope 1:2
Ac = Rc = 6.5 m
Ac = Rc = 4.4 m
=>
=>
Ac,Rc increased by 1 L
Ac = Rc = 8.5 m =>
Ac = Rc = 6.4 m =>
q = 1 l/sm (CLASH NN)
q = 10 l/sm (CLASH NN)
q = 0.15 l/sm (CLASH NN)
q = 1.1 l/sm (CLASH NN)
SCALE EFFECTS RELATED TO SMALL SCALE PHYSICAL MODELLING OF
OVERTOPPING OF RUBBLE MOUND BREAKWATERS
Burcharth & Lykke Andersen
Coastal Structures 2007, Venice, July, 2007
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