2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
Dynamic Tidal Power (DTP) – A new approach to exploit tides
Kees Hulsbergen, Director, H2iD
Dollardstraat 5, 8303 LG,
Emmeloord, The Netherlands.
[email protected]
Rob Steijn, Director, Coastal and Marine
Systems, Alkyon (Arcadis) POBox 248,
8300 AE Emmeloord, The Netherlands.
Gijs van Banning, Manager, Coastal and
Marine Systems, Alkyon (Arcadis).
Gert Klopman, Director, Albatros Flow
Research, Kerkstraat 20a, 8011 RV,
Zwolle, The Netherlands.
Astrid Fröhlich, University of Wuppertal,
Civil Engineering Section, Water
Management and Hydraulic Engineering,
Pauluskirchstrasse 7, 42285 Wuppertal
Germany
1. INTRODUCTION
Abstract
The concept of Dynamic Tidal Power (DTP) was
incidentally born in 1996 when during a coffee break we
asked ourselves, staring at a North Sea chart that was on
the table for quite other reasons: “Suppose we build a
straight dam made of floated-in concrete caissons (as was
done at the Delta Protection Project in the nineteen
sixties), say with a length of 30 km (as was done with the
Afsluitdijk, or Separating Dike, in the nineteen twenties)
out to a water depth of say 30 m, attached and
perpendicular to the slightly hollow coastline of central
Holland, in between the sea ports of Amsterdam and
Rotterdam. Then, what will it do to the local tide?” We
imagined that under the influence of the tidal wave,
locally proceeding parallel to the coastline, and due to its
reflection and diffraction around the perpendicular dam
(if the dam was really very long), differences in water
level amplitude and phase would be created between both
sides of the dam, so building up a (time-dependent) head
over that dam. More or less similar to (short) wind waves
acting around a breakwater head, we thought. We were
really interested in the resulting head over the dam, if
any, since such head, together with the length of the dam,
would determine the potential tidal power that might be
exploited.
Until recently there were just two options to exploit
tidal power: (1) Tidal Basin (with artificial and/or
natural boundaries), and (2) Free Turbines mounted
in a natural tidal stream (either in solitary mode, in
park array, or lined up). Both methods have shown
their technical feasibility. They may be seen as
complementary, both having particular preferred
locations as well as various pros and cons under
technical, economic and environmental scrutiny. Both
methods, smartly devised as they are, do exploit tidal
power in a straightforward way.
Both methods focus on a different, ‘one-dimensional’
element isolated from the complex natural tidal wave
phenomenon, thereby using this element perhaps in a
somewhat ‘passive’ way, i.e. just in the form it is
offered on location by nature. The Tidal Basin
method only exploits the naturally existing local water
level range which is turned into an exploitable head,
while the Free Turbines method only exploits the
naturally existing local current velocity, extracting a
part of its available kinetic energy.
As a quite different option nr. 3 we have developed a
more ‘3-D’ and ‘active’ tide exploiting method:
Dynamic Tidal Power (DTP). It is characterized by
(a) actively interfering in specific regional dynamic
tidal systems, (b) using long dams (fitted with
turbines) attached to and perpendicular to the coast,
(c) creating a head over the dam, but avoiding a
closed basin, (d) yielding massive amounts of electric
energy, and (e) thereby providing this power at a
virtually constant rate by applying twin dams
working together in the right tidal phase lag. Due to
its new hydraulic concept (patented), application of
DTP focuses on areas where medium to strong
oscillating tidal currents run more or less parallel to
the coastline, typically encountered in semi-enclosed
seas such as the North Sea, the Irish Sea and the
Yellow Sea between China and Korea.
Someone stated that we could as well forget about such
power exploitation method, simply because the head over
the dam could never be greater than the velocity height
V2/2g represented by the tidal current flowing there
parallel to the coast on its way to the envisaged dam. The
maximum tidal current in front of IJmuiden is around
0.70 m/s, just enough to cause a velocity height of a mere
2 or 3 cm. So far for the long perpendicular dam as a
source of tidal power, that is, based on the tacit (but
erroneous) assumption that permanent flow conditions
are at hand. Tides at first sight may well seem to be a
permanent phenomenon, and sometimes indeed a quasipermanent appreciation of tides is a useful simplification.
Some weeks later our colleague Paul Kolkman at the
then Delft Hydraulics Laboratory (now Deltares) heard
about the issue. Being an expert in non-permanent flow
dynamics (such as in hydraulic gate vibration problems),
Kolkman explained a quite simple and appropriate
approach to our problem. On the back side of a used
envelope he showed us how rewarding it is to first look
at the Keulegan-Carpenter number (KC), before trying to
assess complex hydraulic forces exerted on an object that
DTP is complementary to both methods, and so
appreciably adds to the world-wide potential of
technically extractable tidal power. This paper
discusses recent model results of DTP in coastal
waters off China and Korea, yielding sometimes over
25 GW per DTP structure.
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2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
is submerged in a quasi-permanent or oscillatory flow
(such as a long dam in tidal flow). Under such conditions
the net force is difficult to understand in that both drag
forces (operating in phase with the flow velocity) and
inertia forces (operating in phase with the flow
acceleration, 90 degrees out of phase as compared to the
drag force) play a role. The KC number is a
dimensionless parameter that determines whether the
drag force or the inertia force is by far the dominant
factor, or that both forces have an appreciable effect and
must both be taken along in the analysis.
is the maximum head over the dam (which
Δhmax
occurs near the point of attachment to the coast) [m]
D
is the length of the dam [m]
is the undisturbed maximum harmonic tidal
Vmax
flow velocity at the (envisaged) location of the dam [m/s]
g
is the acceleration due to gravity [9.81 m/s2]
T
is the tidal wave period (about 12.5 hours or
45,000 s for semi-diurnal tides) [s].
NB. The term Vmax refers to the peak velocity of the
harmonic tidal flow, but what it actually represents is the
peak acceleration and deceleration of the flow within the
harmonic tidal wave, so reflecting the dominance of the
inertial force, the very basis for the analysis of the head
over the dam resulting in equation (2.1).
Equation (2.1) means that for a given basic tidal period T,
the head that is created over a dam by an oscillating tidal
flow in a semi-diurnal tide is linearly increasing with
increasing dam length and also with the maximum
undisturbed tidal flow velocity. This sums up the
important and clear outcome of Kolkman’s analytical
model. The longer the dam is, and the faster the tidal
current, the higher the head. Note also that the local
vertical tide range is completely absent in eq. (2.1). Table
1 illustrates the implication of equation (2.1).
The KC number is defined as KC = Vmax *T/D, where
Vmax is the maximum flow velocity, T is the (tidal) wave
period, and D is the diameter of the submerged object
(the length of the dam). The term Vmax *T is proportional
to the oscillating water particle excursion. So the KC
number expresses the spatial scale of the water particle
excursion relative to the spatial scale of the object. If KC
is very large, it means that the body is quite small as
compared to the water particle excursion, in which
situation drag forces prevail. But in our dam situation the
KC number appeared to be very small (around unity)
thanks to the extremely large dam length (even if the
wave period itself is also large). Therefore it must be
concluded that the hydraulic forces on the dam are
entirely dominated by the inertia of the tidal movement.
In other words, it is the deceleration and acceleration of
the flow, and not the velocity itself, which is governing
the dynamic situation around the dam.
Table 1. Kolkman’s simple analytical model (2.1).
Maximum head Δhmax over a shoreline-attached
straight watertight dam of length D and undisturbed
harmonic tidal peak flow velocity Vmax.
Vmax [m/s]
Helping us to understand the crucial implications of this
quick analysis for the issue of the head created over the
dam, Kolkman set up an elegant “reversed” analytical
model of the situation with the dam standing in a
longshore tidal wave. Basically, what Kolkman did was
to devise a conceptual model in which only inertial
forces play a role. Thanks to this smart schematization,
an entirely transparent, quantitative expression of the
head over the dam was produced, where the head is a
function of only two parameters: the length of the dam
and the peak velocity of the oscillating tidal current. This
analytical expression then of course had to be tested
against results of a full fledged numerical tidal model of
the North Sea, including dams of various geometrical
characteristics. This work, that has extensively been
reported in a previous paper [Hulsbergen et al., 2005],
will be briefly summarized first in the following chapter,
as a basis for a discussion of more recent work on DTP.
D
[km]
0.50
1.00
1.50
2.00
1
0.014 m
0.028 m
0.042 m
0.057 m
10
0.14 m
0.28 m
0.43 m
0.57 m
20
0.28 m
0.57 m
0.85 m
1.14 m
40
0.57 m
1.14 m
1.71 m
2.28 m
60
0.85 m
1.71 m
2.56 m
3.42 m
The results of Table 1 show that (according to the
analytical model) ordinary dam lengths such as for
harbour moles, hardly cause any head in practice. For
much greater ‘dam’ lengths, such as ‘dams’ in the form
of long and narrow natural headlands reaching far out
into sea, while fast tidal currents run off the cape, one
can expect an appreciable water level difference on both
sides of these capes. There are many situations like this.
They can be used as additional proof of concept for the
analytical model, and thus for the DTP concept as well.
So how realistic is this very simple model? Kolkman’s
analytical model (originally representing inertial forces
exerted by water on an immersed flat plate oscillating in
a direction perpendicular to the plane of the plate, in a
still water tank with no free surface) is assumed here to
be applicable to the target situation of coastal tides near a
long dam, so we must be aware of the differences. First,
the real tide comes with a moving free surface. Second,
actual tidal waves are made up of many constituents and
are not purely harmonic, nor symmetrical. Third, the real
effects of the sloping sea bed (instead of a water tank
side panel), the bed friction, the Coriolis force etc. will
2. PREVIOUS RESULTS
2.1. Dedicated analytical model of Kolkman
A crucially important element in creating Kolkman’s
analytical model where inertia by far dominates drag, is
the quantitative notion of ‘added mass’. Added mass
represents the decelerating mass of water pressing
against the dam thereby raising the water level, while
simultaneously a pull is working on the other side of the
dam. As a result of Kolkman’s elaborate analysis, an
amazingly simple equation finally describes the resulting
maximum head over the dam, as follows:
(2.1)
Δhmax = 4 * π * D *Vmax /(gT)
where
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2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
the length of the dam itself. This is not an unfortunate
by-product, but perfectly reflects the intended functional
intervention of the dam, i.e. the basic concept of DTP.
The head over the dam continuously changes with the
tide, and is not entirely constant over its length. Going
from the coastal attachment point (the location where
Δhmax is quantified in the analytical model) gradually
further out to sea, there is first a slight gradual decrease,
until close to the end of the dam the head sharply drops
to zero. This particular behaviour is perfect in line with
predictions of the analytical model. The numerical model
showed somewhat better ‘filled’ longitudinal head
profiles, especially so near the seaward tip of the dam.
The numerical model fully corroborated eq. (2.1) in that
the head does increase for increasing dam length,
according to a linear function. Also, the head increases
for larger Vmax. A complete quantitative comparison
between the results of the simple analytical approach of
Kolkman (equation 2.1) and the results of the numerical
model was made, and showed that in all cases the
‘numerical’ head was appreciably larger than the
‘analytical’ head. We concluded from the comparison
that an overall average multiplying factor of 1.7 satisfies
to convert the ‘analytical’ into the ‘numerical’ head. This
factor apparently covers the combined effect of all
differences between the analytical and numerical model.
It must be firmly kept in mind though, that this
conversion factor of 1.7 almost certainly depends on the
specific local conditions at IJmuiden, such as coastal
profile, water depth, bed roughness, value of the Coriolis
force (latitude), and tidal asymmetry.
While keeping this precaution well in mind we have
inserted this multiplication factor 1.7 in equation (2.1) to
express the maximum head in accordance with the
numerical model results:
Δhmax = 6.8 * π * D *Vmax /(gT)
(2.2)
where Δhmax = the maximum head near the point of coast
attachment of a straight, watertight dam with length D,
caused by an undisturbed peak tidal flow velocity Vmax.
Equation (2.2) may now, just for easy use, be turned into
a simple rule of thumb (‘for quick and crude estimations
only’). When we insert the numerical values for g and T,
express D in km instead of in m, and round off within
3%, the result is:
(Δhmax)THUMB RULE = 0.05 * D *Vmax
(2.3)
This simplified equation (2.3) is illustrated in Table 2.
Table 2. Modified analytical approach, using
equation (2.3) based on numerical tidal model results.
Maximum head Δhmax over shoreline-attached
straight watertight dam of length D and undisturbed
peak tidal flow velocity Vmax
all come into action. Fourth, the presence of the dam
does modify the local tidal behaviour. The combined
effects of all of these factors were incorporated in a
sophisticated numerical tidal model, which was used to
study the head over perpendicular dams of varying size
and with different geometries, to check the simple model.
2.2. Numerical tidal model
An existing, well calibrated and reliable numerical tidal
model was specially prepared for this task. This
‘Zunowak’ model of Rijkswaterstaat represents the
Southern North Sea between UK and Holland from the
line Scarborough – Helgoland at 54o in the North down
to Dover – Calais at 51o in the South. The computational
grid of the model was for this goal refined to 1.5 by 1.5
km. Physical and numerical parameters were copied from
the original Zunowak model, but the time step was
reduced to 5 minutes to match the finer computational
grid. The following physical effects are included in the
model: mass conservation, gradients in water levels,
convective acceleration, Coriolis force, exchange of
horizontal momentum through eddy viscosity, and bed
friction. To define the tidal conditions at the boundary
sections, 31 astronomical components were used.
Four dams attached at the coast near IJmuiden were
investigated: D = 20, 30, 40 and 50 km. The dams are in
most cases straight and watertight. Two tidal situations
typical for IJmuiden were represented: spring tide with
Vmax = 0.70 m/s, and neap tide with Vmax = 0.50 m/s.
Vmax [m/s]
D
[km]
Figure 1. Water level differences on both sides of a 30
km long watertight dam at IJmuiden, MHWS
The most important overall model result is, just as
predicted by Kolkman´s analytical model, that a
significant head is produced over the dam. Figure 1
illustrates this, where the 30 km long dam is seen to
cause rather large areas of lower and higher water on
both sides of the dam. In fact, the area that is
significantly affected by the dam is of the order of twice
3
0.50
1.00
1.50
2.00
1
0.025 m
0.050 m
0.075 m
0.100 m
10
0.25 m
0.50 m
0.75 m
1.00 m
20
0.50 m
1.00 m
1.50 m
2.00 m
40
1.00 m
2.00 m
3.00 m
4.00 m
60
1.50 m
3.00 m
4.50 m
6.00 m
2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
in our example case is determined at 0.64 * 3.82 m =
2.44 m.
The central idea of DTP was to let natural tidal dynamics
themselves create a head over a very long dam attached
to the coast. Then water is released to the lower side
through turbines, thereby transforming the pressure
difference over the dam, via the water flow through the
spinning turbines and coupled electrical generators, into
electrical power.
Next to these main results, which all pertain to the
situation of the maximum (near-coast) head over a
straight and watertight dam, a sub-set of varying dam
configurations resulted in additional observations.
First, the simple watertight (closed) straight dam was
changed into a T-form dam, with the ‘bar’ of the T
parallel to the coast and symmetric with respect to the
‘stem’ of the dam. Two T-shaped dam configurations
have been tested in the numerical tidal model, with a
symmetrical T-bar of 10 and 20 km, respectively,
attached to the seaward end of the straight dam with
length D = 30 km. The general result of adding the Tbar, not surprisingly, shows an increase of the head over
the dam, as well as a more constant and better ‘filled’
longitudinal profile of the head. This effect is stronger
for a longer T-bar. Adding a 20 km long T-bar to the
head of a 30 km long straight dam makes the resulting
head increase with some 53%. The assembled result of
adding a T-bar was that for every % of bar-stem ratio,
the head increaese with 0.82% (thereby well keeping in
mind the possibility that this is valid only for the typical
IJmuiden conditions). This would mean that changing a
simple straight dam into a ‘square’ T-dam with a
bar/stem ratio of 100% will increase the head by 82%. It
may be mentioned that for such T-dam, the value of
Δhmax (actually defined at the attachment point where the
head reaches its maximum value), will be present over
virtually the entire length of the dam.
2.3. From head to power and energy
The maximum (peak) electrical power that can
potentially be generated by a head-creating DTP dam can
now be estimated as follows, using basic fluid
mechanics:
(2.4)
PElmax = ρ * g * Δheff * Aturb * Vturb * η
where
is the peak electrical power output [W]
PElmax
ρ
is the density of the fluid [1030 kg/m3]
g
is the acceleration due to gravity [9.81 m/s2]
is the effective head over the dam, which may
Δheff
be determined starting from Δhmax for a straight
watertight dam and then accounting for the presence of a
T-bar and also for the ‘leak’ through the turbines [m]
Aturb
is the net total cross-sectional flow area of all
turbines [m2]
Vturb
is the axial flow velocity through the turbines
[m/s]
(NB Aturb*Vturb equals the total rate of flow through all
turbines in the dam).
η
is the total (hydraulic, mechanic, electromagnetic) energy transforming efficiency factor [-].
Before illustrating equation (2.4) by some quantitative
examples, we consider its structure more closely. In
equation (2.4) three factors largely determine the power
PElmax , viz. Δheff, Aturb , and Vturb. The other elements are
more or less fixed. Let us analyse how these three
factors, and thus PElmax, may be expressed in terms of the
original, basic parameters D and Vmax of equation (2.1).
First, the term Δheff increases (just like Δhmax does) in a
linear way with D and with Vmax, according to equation
(2.1).
Second, we look at the term Aturb,, representing the
combined openings for the turbines. The greater we make
Aturb, the greater also the peak power will be according to
equation (2.4). However, there must somewhere be an
optimum point for this effect, due to the simultaneously
increasing head reduction effect caused by the associated
increasing leak through these greater openings. Based on
some exercises, we found that an optimum value for Aturb
is reached if the relative total open area is somewhere
between 5 and 15%, say 10%. This means that we set
Aturb equal to 10% of the total lateral dam surface area,
defined as dam length * water depth. This means that
Aturb will linearly increase with D, (based on an
approximately constant water depth over the dam length).
Third, Vturb is a well known function of Δheff, according
to Torricelli’s law:
(2.5)
Vturb = (2g * Δheff)1/2
So, reminding equation (2.1), Vturb is proportional to D1/2
and to Vmax1/2.
Second, to find out what effect openings in the dam
(needed for turbines) will have on the head over the
dam, the 40 km long straight dam, tested before as a
watertight dam, was opened by leaving out a single
mesh of 1.5 km length, about 10 km from the coast. This
opening accounts for about 3.75% of the entire
submerged lateral dam area (viewed in flow direction
parallel to the coast). As could be expected, the opening
causes a reduction of the head. Based on the (limited
number of) model results off IJmuiden, we concluded
that openings in the dam cause a head reduction of 3.6
% for each % opening of the dam. For example, a 10%
opening (for turbines) would cause a head loss of some
36%, due to ‘leaking’ of the dam. A ‘leak factor’ may
be defined, in this case 0.64, used as a multiplication
factor to be applied to Δhmax in order to arrive at the
reduced actual head over a dam with turbine openings.
Based on the above derived results near IJmuiden, we
may now, in principle, determine the effective head for
any chosen straight dam and T-dam length, in any natural
tidal flow condition defined by its peak flow velocity.
For example, suppose we regard a coast with a maximum
undisturbed tidal current of 1.2 m/s. We plan to build a
‘square’ T-dam of 35 by 35 km, and think about
providing the dam with turbine openings together
covering 10% of the lateral dam area. What will be the
‘effective’ head over the dam with turbines? According
to equation (2.3), a 35 km long straight and watertight
dam with an ambient tidal peak flow of 1.2 m/s creates a
maximum head of 2.10 m. Since our dam is a ‘square’ Tdam, this head is increased by a factor of 1.82 (see
above), resulting in a head of 3.82 m. Finally we make
turbine openings covering 10% of the lateral dam area,
causing a loss of head equal to 10 * 0.036 = 36% (see
also above). Thus finally, the maximum ‘effective’ head
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2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
In conclusion, these considerations about eq. (2.4) lead to
the result that PElmax is proportional to D5/2, and also to
Vmax3/2. This means e.g. that to increase the maximum
power PElmax, D is quite an important and powerful
design factor indeed. Doubling the dam length D, for
example, makes the power grow by a factor of 5.65.
Precisely the dam length D (and an optional T-bar, for
that matter) is the factor we may choose in the initial
design of the DTP installation. The local, undisturbed
tidal characteristic parameter Vmax (or rather the peak
value of the natural tidal flow acceleration!) clearly is
one of the main location selection factors in the process
of DTP development.
To quantitatively evaluate an example of PElmax (equation
2.4), let us look at the ‘square’ T-dam mentioned before
with a length of 35 km, a maximum tidal flow Vmax = 1.2
m/s, and a resulting Δheff = 2.44 m. We set ρ at 1030
kg/m3, g = 9.81 m/s2, and we assume η = 0.85. That
leaves Aturb and Vturb to be determined, as follows.
Above we have mentioned that an approximate optimum
overall relative opening Aturb may be set at 10%. To
express this as an absolute quantity we must know the
average water depth along the dam, which we set at 30 m
for this example. So, remembering that D = 35 km, we
find Aturb = 0.10 * 35,000 m * 30 m = 105,000 m2. For
the effective head of 2.44 m, equation (2.5) gives us Vturb
= 6.92 m/s. (This leads to a total peak rate of flow
through the turbines of about 725,000 m3/s, equivalent to
330 times the Rhine). Finally, equation (2.4) tells us that
the peak power output PElmax = 15,227 MW or 15,2 GW.
To estimate the total energy production over a year, we
must multiply with the average ‘load factor’, which may
be some 30%, leading to an energy production of 15,227
* 0.30 * 8760 MWh/yr = 40 TWh per year. This is 40%
of the present total power station production in The
Netherlands. In general it is more economical to install
not 100% but for example only 70% of the potential
PElmax. That strongly reduces capital investment and
increases the load factor, resulting in reduced cost per
kWh.
If we freeze for a moment the values of the relative
opening (10%), the water depth (30 m) and the overall
efficiency factor (0.85), the peak output power PElmax
may now simply be derived for square T-dams of other
dimensions D, standing in other ambient harmonic peak
flow conditions Vmax. Results are assembled in Table 3.
Table 3. Peak power PElmax [MW] for square T-dams
with length D standing in undisturbed peak tidal flow
velocity Vmax; water depth = 30 m, relative opening
for turbines = 10%, efficiency factor = 0.85.
D
[km]
3. YELLOW SEA, CHINA AND KOREA
3.1. Tides in the Yellow Sea
The Yellow Sea is a relatively shallow, marginal sea of
the Pacific Ocean, semi-enclosed by China, North Korea,
and South Korea. The sea is roughly 900 km long and
600 km wide; its opening to the Ocean is 450 km wide.
Water depths are mostly less than 60 m. The Yellow Sea
has a somewhat irregular form caused by a number of
large headlands, extending from China, North Korea and
South Korea, forming large bays, such as the Bohai Sea
not far from Beijing. Powerful tides enter from the
Pacific Ocean and proceed in a general anti-clockwise
mode along the coasts, showing various amphidromic
systems. Tides are sometimes rather irregular. They
exhibit some peculiarities and have a semi-diurnal but
also a mixed character. Especially along the Korean
coasts high tidal ranges occur, up to 10 m, where several
large projects are planned and under construction for
Basin Type tidal power plants. In China many tidal
power plants have been built too, so far of a relatively
small size, but smartly incorporated in the complex lower
river water management systems [Bernshtein, 1965].
Since tidal (and other) conditions in and around the
Yellow Sea seem quite attractive to apply the DTP
concept, we have recently set up a tidal model using
Delft-3D to make initial calculations with various T-dam
configurations. The model grid size for these indicative
calculations is 1.5 km, and we just used a single layer.
The time step is 10 minutes. Figures 2 and 3 give some
snapshots of the tidal water levels and of the tidal flow,
respectively, without dams.
Figure 2. Screenshot of tidal water levels, no dams.
Vmax [m/s]
0.60
0.80
1.00
1.20
1.40
5
42
64
89
117
148
10
235
362
505
664
837
15
647
997
1,393
1,831
2,307
25
2,321
3,574
4,995
6,566
8,274
35
5,384
8,289
11,584
15,227
19,188
45
10,091
15,536
21,712
28,541
35,966
Figure 3. Screenshot of tidal flow, no dams.
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2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
performance in the Yellow Sea. Dam sites were chosen
where a natural promontory already exists. We did not
worry too much about interfering with existing functions
such as fisheries, navigation and other offshore activities,
nor did we care about crossing locally deep natural
channels. Also in this stage we did not try to look for
areas with a high power demand. All of such aspects (and
many more) are obviously quite important, but not at this
stage.
The dam configurations were defined as a T-dam, with
their bar/stem ratio about 75%, since this appears an
effective form. The dams all have a length between 43
and 62 km. The T-bars are between 30 and 49 km long.
Their dimensions are somewhat arbitrarily determined,
sometimes depending on specific bathymetric anomalies.
Also, the model schematization of the dams must be
mentioned, since the dams are implemented in the
numerical model as selected grid meshes that are defined
as closed. As a consequence the dams appear in detail as
zig-zag lines, following the computational grid. The
above given lengths of the dams however are measured
along straight lines. In short, the site selection as well as
the detailed forms of the dams contain an arbitrary and
intuitive component. The group of 4 NK dams has a
somewhat different background, in that we first started
with NK2 and then consecutively changed its location,
orientation, form and size in an attempt to test certain
ideas. Various aspects will be further discussed in some
detail when looking at dam China1.
Dam China1 will be discussed now. China1 is attached to
the most Eastern point of the Province of Shandong,
named Chengshan Jiao. Its form and the local bathymetry
is presented in Figure 5.
With the Yellow Sea tidal model we made runs over a
period of ten days (October 21st – 31st , 2007). From
these results, a narrower time window has been taken, i.e.
October 27th and 28th, to present the provisional dam
analysis. This period is representative for spring tides.
3.2. T-dams in the Yellow Sea
Eight T-dams have separately been tested: 3 in China, 4
in N. Korea and 1 in S. Korea. Figure 4 shows the
locations and Table 4 shows the dimensions. In this stage
of testing all dams were closed: no openings, no turbines.
Figure 4. Location of all eight T-dams tested.
We present some preliminary results in this section as
follows. First, some introductory remarks are made
regarding site selection and chosen dam configurations.
Table 4. Dimensions of the eight T-dams tested. All
dams are closed: no openings, no turbines.
Length
of dam
(‘stem’)
[km]
Length
of Tbar
[km]
Bar/stem
ratio
Mean
depth
[%]
[m]
China1
50.5
37.8
75
40
China2
55.0
42.0
76
20
China3
43.0
30.0
70
40
NK1
58.0
48.0
83
50
NK2
52.0
38.0
73
50
NK3
60.6
46.5
77
40
NK4
58.5
49.0
84
40
SK1
61.5
47.5
77
25
Figure 5. Dam China1. Bathymetry, lay-out and
observation points, including ‘dam 10’ on the North
side of the dam, some 25 km off the present cape.
Close to the coastline, the alignment of dam China1
crosses a deep natural channel and major navigation
lanes. The chosen location, with the T-bar situated in a
deeper area, is not ideal from an economic point of view.
It is stressed again that in this stage of the preliminary
assessment study these aspects were seen as somewhat
less relevant. Fine-tuning of dam sites and configurations
comes later.
To put the effects of dam China1 on the local tides in
perspective, we first show the main undisturbed local
tidal characteristics (i.e. the situation without dam) as a
function of time. Figure 6 shows the water level and
Figure 7 the flow velocity, computed at observation point
dam 10, half way the length of the projected dam.
Next, the dam China1 is analysed as an example and
elaborated in some detail. Then, the main results of all
individual dams are presented, summarized and briefly
discussed. Section 3.3 finally focuses on a special twindam configuration, consisting of dams NK1 and SK1.
The fact finding character in this stage of the work is
emphasized. Site selection and dam configuration served
our intention to gain some quick impressions of DTP’s
6
2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
creation of this head, i.e. the difference between the
instantaneous water levels on both sides of the dam,
illustrates the core concept of DTP. Figure 8 gives the
impression that the dam affects the ambient tides just like
a natural headland would do (as was discussed before
under Table 1). Especially the fact that an artificial dam
is a very thin structure ‘by nature’ as compared to most
natural headlands, greatly facilitates the exploitation of
tidal power.
For our preliminary analysis we defined, for observation
points half way the dam, the water levels on both sides of
the dam, as well as the resulting head over the dam, both
as a function of time.
Water level without the dam
1
0.8
0.6
water level [m]
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
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12:00 AM
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6:40 AM
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1:20 PM
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8:00 PM
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2:40 AM
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9:20 AM
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4:00 PM
10/28/07
10:40 PM
time
dam10
china1
Figure 6. Water level at projected dam China1,
observation point ‘dam10’ 25 km out. Without dam.
2.5
water level [m]
1.5
velocity without the dam
1
0.9
0.8
0.5
-0.5
-1.5
velocity [m/s]
0.7
0.6
-2.5
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12:00 AM
0.5
0.4
10/27/07
6:40 AM
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1:20 PM
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7:59 PM
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2:39 AM
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9:20 AM
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4:00 PM
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10:39 PM
time
0.3
0.2
dam10
dam28
delta h
0.1
0
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12:00 AM
10/27/07
6:40 AM
10/27/07
1:20 PM
10/27/07
8:00 PM
10/28/07
2:40 AM
10/28/07
9:20 AM
10/28/07
4:00 PM
Figure 9. Dam China1. Water levels on both sides of
the dam and resulting head over the dam, in
observation points half way the dam length.
In Figure 9 it can be seen that some remarkable changes
have happened after inserting China1. First, the tide
range on both sides of China1 is now about 2 m (Figure
9), much greater than in the undisturbed situation (Figure
6), where it was just 1 m. Next, the form of both tide
curves alongside China1 is almost purely harmonic, in
contrast to the original water level curve without dam
(Figure 6), but in line with the original velocity curve.
This should however not come as a complete surprise in
that eq. (2.1) clearly indicated that the head created by
the dam originates from the harmonic velocity range, not
from the original tide range.
It is also interesting to observe in Figure 9 that both new
water level curves are mutually almost completely out of
phase, which is extremely favourable for the resulting
head (the yellow line in Figure 9). The head, exhibiting
twice the frequency of the undisturbed tide, reaches a
maximum value of nearly 2 m at this point along the
dam. Towards the shore the head is somewhat higher,
whereas it decreases a bit towards the T-bar. The time
curve of the head has a nicely ‘filled’ form, which is
favourable for power production and gives a boost to the
‘load factor’ as we will see below.
As a preliminary conclusion, the head over dam China1,
which we would want to be large in view of power
production, depends primarily on the ‘brute force’ of
both new water level amplitudes involved, but very much
on the optimization of their mutual phase difference, too.
A further analysis step was to transfer the head into the
resulting electric power as function of the time, as
potentially delivered by China1, in line with equation
(2.4). In this set of model runs all dams were closed (i.e.
without openings for turbines). To determine the
10/28/07
10:40 PM
time
dam10
Figure 7. Flow velocity at projected dam China1,
observation point ‘dam 10’ . Without dam.
The undisturbed vertical tide range (Figure 6) appears
rather small, reaching about 1.0 m. The undisturbed peak
tidal flow velocity (Figure 7) at the same location reaches
with 0.95 m/s quite a strength. So far for the existing
situation, without a dam.
The 50.5 km long dam China1, once implanted in the
Yellow Sea model, induced an appreciable effect on the
water levels around the dam.
Figure 8. Dam China1. Water levels at the moment of
maximum head over the dam, 27 Oct. 2007, 08:10 AM
Figure 8 shows the jump in water level (the head) over
dam China1 at its maximum value of 1.94 m. The
7
2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
effective head (as if the dam had openings) we reduce the
computed head by a reduction factor of 0.64. So we
allow for the leak through the turbines, thereby assuming
a relative turbine opening equal to 10% of the lateral dam
area, just as we did in section 2. Thereby we assumed the
head at the middle of the dam to be representative for the
whole dam. Figure 10 presents the resulting power at
China1 and the mean power during the 2 day period.
(Bohai Bay side) of dam China2 appears to be very
small. Thus the head is almost exclusively defined by the
behaviour of the water level on the East side of the dam
(at RD21), which shows a range of about 2 m. Therefore
the fact that in this case the mutual phase of both water
level curves is rather unfavourable (as compared to
China1), does not play an important role in defining the
maximum head. So far for dam China2.
china1
china3
10
4
8
3
6
2
water level [m]
water level [m]/ Power [GW]
12
4
2
0
10/27/07 12:00 10/27/07 6:40 10/27/07 1:20 10/27/07 7:59 10/28/07 2:39 10/28/07 9:20 10/28/07 4:00 10/28/07 10:3
AM
AM
PM
PM
AM
AM
PM
PM
Power
-2
-4
10/27/07
12:00 AM
average Power
Figure 10. Dam China1. Head over the dam and
resulting power.
The power, simultaneously with the head, varies in time
along with the tide, but of course with half the tide’s
period. The peak power in this figure reaches about 10.7
GW, while the mean power (thanks to the nicely filled
curve) is about 5.5 GW. So over the regarded 2-day
period the ‘load factor’ (mean power divided by peak
power) is about 0.50. When considered over a longer
period, including neap tides, the load factor will of
course drop, to be evaluated in a next research stage. So
far for a first, crude analysis of dam China1.
10/27/07
6:40 AM
10/27/07
1:20 PM
10/27/07
7:59 PM
10/28/07
2:39 AM
10/28/07
9:20 AM
10/28/07
4:00 PM
10/28/07
10:39 PM
time
l7
r7
delta h
Figure 12. Dam China3. Water levels on both sides of
the dam and resulting head over the dam, in
observation points half way the dam length.
Dam China3 is situated right across China2, also in the
entrance to Bohai Bay, but now extending from the
northern headland near the city of Dalian, Liaoning
Province. Although China3 is shorter than China2, the
water level range on its East side, some 4 m, is much
larger than at China2. But since the water level on the
other side of dam China3 has a rather unfavourable
phase, the resulting head is only slightly higher than at
China2. So far for dam China3.
The other 7 dams were analysed in a similar way, with
more or less similar results. For each dam we just present
the resulting curves of the water levels at both sides and
its associated head, just as in Figure 9. See Figures 11
through 17. The resulting peak head and peak power for
all dams are then summarized in Table 5.
Next, the cluster of 4 NK dams is discussed, see Figures
13, 14, 15 and 16. Along North Korea’s coasts the
naturally existing tides are in general much stronger than
in China. This is reflected in the performance of the
dams. The dams NK1 through NK4 show some variation
in created water level ranges and resulting head, as a
result of the various locations, orientations, and
dimensions of the dams (see Figure 4 and Table 4).
china2
4
3
2
1
north_korea1
0
-1
4
-2
3
-3
2
-4
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12:00 AM
10/27/07
6:40 AM
10/27/07
1:20 PM
10/27/07
7:59 PM
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2:39 AM
10/28/07
9:20 AM
10/28/07
4:00 PM
water level [m]
water level [m]
0
-1
-3
time
delta h
1
10/28/07
10:39 PM
time
LD24
RD21
delta h
1
0
-1
-2
-3
Figure 11. Dam China2. Water levels both sides of the
dam and resulting head over the dam, in observation
points half way the dam length.
Dam China2 was earlier discussed with China’s NDRC,
since it would form an interesting combination with
existing plans to build a large bridge over Bohai Bay
entrance, to better connect China’s Northern provinces.
At dam China2, water levels on both sides behave in a
rather different way as compared to China1. The water
level range in observation point LD24 on the West side
-4
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6:40 AM
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1:20 PM
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7:59 PM
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2:39 AM
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9:20 AM
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4:00 PM
10/28/07
10:39 PM
time
l7
r6
delta h
Figure 13. Dam North Korea1 (NK1). Water levels on
both sides of the dam and resulting head over the
dam, in observation points half way the dam length.
Observation point r6 at the South side of NK1 shows a
water level range of about 5 m. On the North side of
NK1, at observation point l7, a range of the same order
8
2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
of magnitude is seen. However, their mutual phase is not
optimal. With a more favourable mutual phase relation
(which could be arranged by changing the site,
orientation, size and configuration of the dam), the
resulting head, now about 3.5 m, could be enhanced,
probably to around 5 m.
south_korea1
4
3
water level [m]
2
north_korea2
4
-2
-4
10/27/07
12:00 AM
2
water level [m]
0
-1
-3
3
1
10/27/07
1:20 PM
10/27/07
7:59 PM
10/28/07
2:39 AM
10/28/07
9:20 AM
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4:00 PM
10/28/07
10:39 PM
time
0
l6
-2
-4
10/27/07
12:00 AM
10/27/07
6:40 AM
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1:20 PM
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7:59 PM
10/28/07
2:39 AM
10/28/07
9:20 AM
10/28/07
4:00 PM
kor24
10/28/07
10:39 PM
delta h
Figure 14. Dam North Korea2 (NK2). Water levels on
both sides of the dam and resulting head over the
dam, in observation points half way the dam length.
At NK2, point kor24 is at the South side of the dam.
north_korea3
4
3
2
1
0
-1
-2
-3
-4
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12:00 AM
10/27/07
6:40 AM
10/27/07
1:20 PM
10/27/07
7:59 PM
10/28/07
2:39 AM
10/28/07
9:20 AM
10/28/07
4:00 PM
10/28/07
10:39 PM
time
l10
r10
delta h
Figure 15. Dam North Korea3 (NK3). Water levels on
both sides of the dam and resulting head over the
dam, in observation points half way the dam length.
At NK3, point r10 is at the South side of the dam.
north_korea4
Max.
head
3
2
1
0
[m]
-1
-2
-3
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6:40 AM
10/27/07
1:20 PM
10/27/07
7:59 PM
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2:39 AM
10/28/07
9:20 AM
10/28/07
4:00 PM
10/28/07
10:39 PM
time
l5
r5
delta h
Table 5. Power potential for all eight T-dams tested.
4
-4
10/27/07
12:00 AM
r6
Figure 17. Dam South Korea1 (SK1). Water levels on
both sides of the dam and resulting head over the
dam, in observation points half way the dam length.
Dam SK1 is located in a relatively small water depth of
25 m, much smaller than at the NK dams (see Table 4).
At dam SK1, observation point r6 is on the South side of
the dam. The water level ranges created on both sides are
larger than for all 7 other dams, reaching about 6 to 7 m.
The resulting head however is regarded as relatively
modest at 3 m. The head at SK1 could be much larger if
the mutual phase difference could be enhanced, as can be
inferred from Figure 17. In an optimum situation the
head could in principle grow to about 6 or 7 m. So far for
SK1, the last one discussed in the list of 8 dams.
As a preliminary general conclusion for the hydraulic
effects of all dams discussed, the possibility of increasing
the head (and thus the potential power) depends on a
further fine tuning by changing the location, orientation,
size and form (lay-out) of the dam, each in their own
particular tidal domain. This is clearly a subject of further
research.
The resulting maximum head and the associated potential
peak power of all dams during the 2-day spring tide
period, as was discussed for dam China1 in Figure 10, is
presented in Table 5. For reference, also the main
dimensions and mean water depth is included. The given
assessment of the potential power, just as for some other
parameters and issues, is regarded as only tentative,
awaiting further research and analysis.
time
kor5
water level [m]
10/27/07
6:40 AM
-1
-3
water level [m]
1
delta h
Figure 16. Dam North Korea4 (NK4). Water levels on
both sides of the dam and resulting head over the
dam, in observation points half way the dam length.
Observation point r5 is on the South side of the dam. The
various resulting heads at the four NK dams reflect the
importance of choosing the detailed dam configuration in
such a way as to reach not only large tide ranges, but
especially to get their mutual phase tuned right.
9
Potenti
al peak
power
[GW]
Length
of dam
Mean
depth
[km]
Length
of Tbar
[km]
[m]
Ch1
1.94
10.7
50.5
37.8
40
Ch2
2.07
6.8
55.0
42.0
20
Ch3
2.28
11.7
43.0
30.0
40
NK1
3.93
44.6
58.0
48.0
50
NK2
3.27
30.3
52.0
38.0
50
NK3
3.28
28.4
60.6
46.5
40
NK4
2.78
21.4
58.5
49.0
40
SK1
3.19
17.3
61.5
47.5
25
2nd International Conference on Ocean Energy (ICOE 2008), 15th – 17th October 2008, Brest, France
The fact that the heads of SK1 and NK1 are almost
perfectly out of phase (Figure 19) is in principle a quite
favourable circumstance, thinking of the sum of their
individual power production, which would show a rather
constant curve if feeding into a common grid. However,
for the sum of the power to be about constant, both
power amplitudes must be equal, which is not the case
here (see Table 5). Peak power for SK1 and NK1 is 17.3
MW and 44.6, respectively. The combined power of SK1
and NK1 in twin mode is shown in Figure 20.
3.3. Twin T-dams SK1and NK1
As an addition to the analysis of the 8 individual dams,
and just as another provisional test, dams SK1 and NK1
have been simultaneously inserted in the tidal model,
without changing anything in the dams themselves. This
was especially done to see what the result is of their
simultaneously produced power. First, the twin dam
situation for SK1 and NK1 is presented in Figure 18.
Head and Power of the combined dams
40
water level [m]/ Power[GW]
35
30
25
20
15
10
5
0
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12:00 AM
10/27/07
6:40 AM
10/27/07
1:20 PM
10/27/07
7:59 PM
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2:39 AM
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9:20 AM
10/28/07
4:00 PM
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10:39 PM
time
delta h (north_korea1)
Figure 18. Location of twin dams SK1 and NK1.
The distance between SK1 and NK1 is about 200 km.
The fact that they are now both present in the same
region, each with their own influence on the tides around
them, will cause a certain amount of mutual influence.
Since the ambient tides will change for both of the dams,
the expectation is that their head in the new twin mode
will also change somewhat as compared to the previous
situation when they were in stand-alone mode.
As a next development step, DTP design is planned in a
more integrated framework, in the Yellow Sea and in
West-European coastal seas, to assess the power that can
be produced in a combined configuration, consisting of
an array of cooperating and coupled DTP-dams. Massive
tidal power production as discussed in this paper requires
very large structures, in a technical, financial and
organizational sense. Special construction methods are
needed, some of which already exist while others should
be designed according to specifications yet to be
determined.
Head of the combined dams
5
water level [m]
4
3
2
1
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PM
PM
AM
AM
PM
REFERENCES
[1] Hulsbergen, K., Steijn. R., Hassan R., Klopman G.,
10/28/07
10:39 PM
time
delta h (north_korea1)
Power
3.4. Final remarks
Figure 19 shows the resulting heads of SK1 and of NK1,
now operating as twin dams.
0
10/27/07
12:00 AM
delta h (south_korea1)
Figure 20. SK1 and NK1 operating as twins.
Individual heads, and combined power.
Figure 20 shows that the summed power of SK1 and
NK1 operating as twins is still far from constant. A more
constant combined power output would of course be
preferred. Yet, the combined power curve of Figure 20 is
much improved as compared to the output of a stand
alone dam, the fluctuations of the power being much
reduced. In the case at hand, a logical improvement for
the twin dam set up would be to shorten dam NK1 and/or
to extend SK1, or some combination of both measures.
Then the fluctuations in the combined power curve will
diminish, a favourable oucome in economic terms.
delta h (south_korea1)
Figure 19. Heads at SK1 and NK1, operating as twins.
When SK1 and NK1 operate simultaneously, as twins, as
given in Figure 18 and 19, their heads appear to be
approximately out of phase. This is an interesting result,
to be analysed in somedetail. When each head is
compared to its individual ‘stand alone’ head, differences
can be seen. The head of SK1 in twin mode (Figure 19),
for instance, is about 15% larger than it was as a single
dam (compare Figure 17). In the same time however, the
head of NK1 appears to diminish (compare Figure 13).
[2]
10
Hurdle D., (2005). Dynamic Tidal Power (DTP), 6th
European Wave and Tidal Energy Conference,
Glasgow, UK, August 29th – September 2nd 2005.
Bernshtein, L. B., (1965). Tidal energy for electric
power plants. Translated from Russian. Israel
Program for Scientific Translations, Jerusalem,
1965.