College of Engineering
Department of Naval Architecture and Marine Engineering
ENGINEERING for the MARINE ENVIRONMENT
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College of Engineering Department of Naval Architecture and Marine Engineering ENGINEERING for the MARINE ENVIRONMENT |
Wave Energy Conversion
ELECTRICITY FROM SEA WAVES
Introduction
During the next 20 years, experts foresee a need for 1500 GW. of additional power supply to meet new demand. This equals to 15000 power plants that are 100 MW each and 59 million barrels of oil consumed in each day. The world Bank estimates that the developing countries alone will need to spend $100 billion each year for the next 30 years installing new power plants most of which will be in the equatorial Zone. These are astronomical figures that could mean enormous quantities of fossil fuel and 2.2 billion tons of CO2 release to the atmosphere per year. Hence, an Urgent needs to switch to alternate energy. Among the alternate energy resources, wave energy is considered as one of the promising alternate energy resources that has high availability factor (day & night) compare with other resources such as Wind energy or Solar energy.
It has been estimated that if less than 0.1% of the renewable energy available
within the oceans could be converted into electricity, it would satisfy the
present world demand for energy more than five times over.
Therefore, it is an equally important and worth wile to conduct experiments
on wave energy harnessing techniques to tap the wave power to generate electricity.
Oscillating Water Column type wave energy harnessing method is considered
as one of the best techniques converting wave energy into electricity.
OWC is economically viable design due to it's simple geometrical construction
and also strong enough to withstand against the waves with different heights
and different wave periods and directions. This design consists of a rectangular
chamber and a pyramidal top which is installed on top of the chamber . .A
conical duct is erected on the pyramidal top to reciprocally move the air
from the chamber and into the chamber during the process of wave approach
and wave leaves the Chamber. A special turbine which is mounted on top of
the duct is subjected to turn at one direction as the airflow moves bi-directional.
A generator is coupled to the turbine that produces electricity by rotating
it's armature shaft which is coupled with the turbine shaft.
Description of the OWC System
This system is considered to be the closest to commercial maturity,
as the principle of operation is simple and the construction uses conventional
technology. The major component of an OWC system is a chamber, which is a
fixed structure with its bottom open to the sea. The wave motion inside the
chamber alternately compresses and decompresses the air that exists above
the water level inside the chamber.
As a result, an alternating stream of high velocity air is generated. This
airflow is driven through a duct to a turbine generator that is used to generate
electricity. The turbine generator used is a special turbine which has the
unique property of turning in the same direction regardless of which way the
air is flowing across the turbine blades. Thus, the turbines continue turning
on both the rise and fall of wave levels within the chamber. The turbine drives
the generator, which converts this power into electricity. The experimental
OWC we used included the chamber and the duct.
Figure 1: Schematic of an Oscillating Water Column
Newly Design Oscillating Water Column Type Chamber at the Department of NA&ME, University of Michigan
Research Site
Macro model of the Chamber was designed and installed on a permanent base
which can be moved back and forth along the towing track of the channel at
Marine Hydro dynamics Lab of the department of Naval Architecture and Marine
Engineering at University of Michigan. The characteristics of wave maker &
water flume are taken as follows: Tank length-109.70m, tank width- 6.70m,
tank depth- (to edge of trough)-3.05m; periods of waves: 0.63 s - 2.2 s.;
Wave heights: up to .33m. Wave maker type: Plunger type capable for generating
regular and irregular waves; computer generated for any irregular wave spectrum.
Exicting wave energy plants in the world
Current and Future Projects
Experiments are in progress to design a demonstrational research sea wave pilot power plant in Sri Lanka which generate 150kw power
Special air turbine to rotate one direction when the air flow is bidirectional
A design of turbine housing
Turbine assembly
Initial locations for various measuring equipment such as pressure transducers, load cells, air flow sensors, ultra sonic equipment for identification the wave heights at the mouth of the chamber are identified with help of VRML modeling.
The OWC system used is shown with its dimensions
The first thing we need to know is the available wave energy. The total wave energy would be the sum of the kinetic and the potential energy. The potential energy can be calculated through the formula:
(J)
where: m = wρy (kg): wave mass
ρ: water density (kg/m3)
w: wave width (m) (assumed equal to the width of the chamber)
y = y(x, t) = asin(kx-ωt) (m): the wave equation (assuming sinusoidal waves)
a = h/2 (m): wave amplitude
h: wave height
: wave number
λ: wave length (m)
(rad/sec): wave
frequency
T: wave period
The potential energy can be written as:
We want to calculate the wave potential energy over one period. We assume that the waves are only a function of x and are independent of time, thus: y (x, t) = y (x). So, we have:
Considering that 
and 
, we get:
The total kinetic energy over one period is equal to the total potential energy:
Eventually, the total energy over one period will be:
EW = P.E.
+ K.E. = 
(J)
Through the energy definition, we can also calculate other useful quantities, such as the energy density, the available wave power and its respective density.
Energy Density: 
Power: PW
= 
(W)
Power Density: PWD
= 
Now, we may consider the case of deep water, where the dispersion relation becomes:
By applying the formula: 
in the relations for the energy and the power, we get:
(J)
(W)
Finally, if we use the wave height instead of the wave amplitude, we get:
(J)
(J/m2)
(W)
(W/m2)
In the experiment we conducted, we used T and h as parameters. Although these wave properties are set as input (nominal values) to the wave maker, we considered that it would be better if we measured them in order to get more accurate results. The water density, ρ, and the gravity constant, g, are known, and without loss of accuracy can take the values 1025 kg/m3 and 9.81 m/sec2, respectively. The wave width, w, can be considered to be equal to the chamber width. Eventually, EW, EWD, PW, PWD can be easily calculated using the above formulas.
In order to check the efficiency of the OWC system, we calculated the power at the upper end of the duct. This point is actually the last point before the turbine. It is very important to know the efficiency coefficient between the chamber and the duct. If we want to design an OWC system, we have to optimize first the chamber-duct part. The main criterion for this optimization will be the maximization of the efficiency coefficient. In order to calculate the power, we used the experimental values for the pressure and flow speed at that point. The Bernoulli equation gives the total pressure. First we have the static term, which is the differential pressure at that point. We considered this pressure to be the difference between the mean and the minimum of the measured pressure. The second term is the dynamic pressure, which is a function of the square of the airflow speed and the air density. The sum of these terms gives the total pressure at that point. The respective power will be the product of the pressure times the airflow speed times the cross sectional area at that point. The above procedure is defined by the following formula:
(W)
where: PU: power at the upper end of the duct (W)
pE: air pressure at the upper end of the duct (Pa)
ρa : air density (kg/m3)
va: airflow speed at the upper end of the duct
A: cross sectional area at the
upper end of the duct (for a circular-shaped duct 
)
During the experiment, we measured pE, ρa, va and D. By using the measured values we calculated PU. The efficiency coefficient, η, will then be:
The output of the measuring devices was initially analyzed using a statistical analysis software package, provided by the Marine Hydrodynamics Laboratory. The results of this analysis are shown on Table 1.
Table 1: MHL Stats v1.0 statistical analysis
In the first column, we recorded the test number and in the second, the submerged height of the OWC. In the next two columns we recorded the nominal wave height and frequency, as they were input to the wave maker. The rest of the data are obtained from the software package. As we already mentioned in a previous section, we measured the pressure at the chamber (‘bottom pressure’), the measure at the upper end of the duct (‘top pressure’) and the wave height. All these data were sent to the computer and analyzed by the analysis software tool. In order to do that we used three input channels. Columns 5 ~ 7 include the statistical analysis of the wave height measurements. That is the wave height peak frequency, the mean and the standard deviation of the wave height. As we observe, the values measured are close enough to the nominal values. In columns 8 ~ 10 and 11 ~ 13, we recorded the analysis for the bottom pressure and the top pressure respectively. Finally, in column 14, we recorded the measure outflow air velocity in the upper end of the duct, as recorded by the handheld electronic wind indicator.
In Table 2 we present the analysis of the output using Microsoft Excel. This time, we didn’t do a peak frequency calculation. The procedure we followed was to obtain the time series of the measurements and use Excel functions in order to get the mean, the minimum, the maximum and the standard deviation of each measured quantity (wave height, bottom and top pressure). As we observe the mean values coincide with the values obtained from the statistical analysis software package we used initially. There is a small deviation in the standard deviation calculation but that is probably due to decimal digits round offs. What is really important is that the results we got from the statistical analysis tool are verified by the Excel analysis.
Table 2: Microsoft Excel statistical analysis
In Table
3 we present the calculations for the energy and the
power. In the first column we recorded the experiment number. In columns 2 and
3, we recorded the nominal wave height and the calculated one through the Excel
analysis (from Table 2, we subtract the minimum from the maximum value),
respectively. As we observe, in some cases the deviation is more than one
hundred per cent. This is due to the fact that we used the maximum and minimum
measurements we got for the wave height, which weren’t necessarily in the same
period. The nominal wave period and the experimental wave period (calculated
from the peak frequency in Table
1) are presented in columns 4 and 5. In this case, the
nominal values seem to coincide with the experimental ones. We decided to use
the measured data in our calculations instead of the nominal one because we
considered them to be more realistic and accurate. In columns 6 and 7 we
calculated the maximum wave power density and the maximum wave power,
respectively. The maximum available wave power was calculated using the
formula: 
. In columns 8 ~ 10 we just copied the statistical analysis
of the pressure time series as we did it in Microsoft Excel (Table 2), however we converted the values from (psi) to (Pa).
In the next column (11) we copied the outflow air velocity in the upper end of
the duct, as recorded by the handheld electronic wind indicator (Table 1). The reason we did that, was that we wanted to
compare the measured values with the theoretical ones and obtain an efficiency
coefficient for the outflow (column 14). In column 12, we calculated the
theoretical outflow air velocity using the Bernoulli equation. We took as a
differential pressure the difference between the minimum and the mean top
pressure (columns 8 and 9 respectively). In column 13 we used the Bernoulli equation
for the calculation of the theoretical inflow air velocity. In that case, we
considered as a differential pressure the difference between the mean and the
maximum top pressure (columns 9 and 10 respectively). In column 15 we
calculated the outflow power as the product of the total pressure (obtained by
Bernoulli) times the outflow air velocity times the cross sectional area. Finally, in column 16 we obtained the
efficiency coefficient of the OWC system by dividing the outflow power (column
15) by the maximum available wave power (column 7).
Table 3: Bernoulli equation and power calculations
The following pages contain surface plots with the processed data presented in the previous Tables. Data selected for plotting was: Air Speed (m/s), Top and Bottom Pressure Standard Deviation (Pa), Maximum Power (W) and Power Efficiency (%).
The Air Speed came directly from the measurements made with the wind speed indicator, that is, it is related to the maximum outflow air speed. The pressure measurements are in the form of standard deviations in order to show their relative variation, without running into maximum or minimum peak values. These results are not used for further analysis in the report. The Maximum Power is related to the Maximum Power column in Table 3, as well as the Power Efficiency. Also, the regression equations are in parallel with the data presented in the legend of each regression graph.
Figure 1: Maximum Outflow Air Speed vs. Submerged Height and Wave Height
Figure 2: Maximum Outflow Air Speed vs. Submerged Depth and Wave Period
Figure 3: Maximum Outflow Air Speed vs. Wave Period and Wave Height
Figure 4: Bottom Pressure Standard Deviation vs. Submerged Depth and Wave Height
Figure 5: Bottom Pressure Standard Deviation vs. Submerged Depth and Wave Period
Figure 6: Bottom Pressure Standard Deviation vs. Wave Height and Wave Period
Figure 7: Maximum Power vs. Submerged depth and Wave Height
Figure 8: Maximum Power vs. Submerged Depth and Wave Period
Figure 9: Maximum Power vs. Wave Height and Wave Period
Figure 10: Power Efficiency vs. Submerged Depth and Wave Height
Figure 11: Power Efficiency vs. Submerged Depth and Wave Period
Figure 12: Power Efficiency vs. Wave Height and Wave Period
Figure 13: Top Pressure Standard Deviation vs. Submerged Depth and Wave Height
Figure 14: Top Pressure Standard Deviation vs. Submerged Depth and Wave Period
Figure 15: Top Pressure Standard Deviation vs. Wave Height and Wave Period