a brief Synopsis
DAED ALUS Informatics
Athens, Greece 01/10/1994* double click on empty space anywhere on page, to access pagetop
4. SEKE - the Wave Energy Conversion Device4.2. C.M.W. - The Critical Momentum Wedge as a potential Energy Carrier:An introduction to Concept and underlying Theory
Principal definition The critical depth H cmw bellow the SWL, computed for any continuous sea area, define an integral momentum carrying surface-locus we will hereafter call the "centers of critical moments". This surface is a horizontal plane at a fixed and defined depth for seas of large depth, mostly depending on wavelength L. Hence, the characteristic ratio Hcmw /(L/4) increases for decreasing depth. This means that the Center of Critical Moment depth at a given sea location (it is the point at depth Hcmw below the water surface) approaches the seabed as the depth of the sea decreases, or as we approach the seashore, as depicted in sketch (1). Moreover, the elliptical orbital motion of particles in the Hcmw area, is rapidly increasing its x-axis component whilst decreasing the y-axis one, as to eventually break into linear motion (2). As is described below, by taking advantage of these properties, we can collect a large part of the kinetic and potential energy (the latter due to the height of the water above the Sea Water Line) in a properly designed converter -in this case the SEKE device. If the sea bed in front of the above vertical wall is given a suitable gradual -i.e. exponential- modification, then the motion of the running wave during its ascending phase follows the sea bed surface, carrying with it most of its total energy (1). This energy, at the end of the phase of ascent becomes partly potential, i.e. "water level". The height to which the wave rises before its surface line "breaks", depends on the energy that its water mass includes, which in turn is proportional to the square of the wave height.
As is expected, once the kinetic energy of the wave turns into potential (water level), its velocity becomes zero and the phase of descent begins. Meanwhile, the motion of the Centers of Critical Momentums has followed the path of the running waves, whilst the paths of the sea particles contained inside the volume V(Hcmw), formed a group motion, which we will hereafter call the "Critical Momentum Wedge - CMW ". As shown in (1), the formation of CMW comes gradually closer to the sea bed, whereas its direction between point A (initial) and point E changes by 90 o (i.e. the vertical wave velocity becomes progressively higher than the horizontal one). The curves A through E are the loci of the centers of the circular -or elliptical- motions of the sea particles at various positions during the motion of the running wave. As a theoretical assumption according to the CMW principle, at some point of this orbital progression and after the upper wave motion has ceized, the resultant action of three composite forces, that is, the one due to the horizontal wave velocity (celerity) Fwv , the hydrostatic pressure Fwh and the reaction normal to and upward from the sea bed F sb, as depicted in (2), will cause the current orbit to collapse and therefore provide a rapid kinetic energy burst acting as a linear hydraulic ram. After the completion of this phase, the phenomenon repeats itself with a period equal to the period corresponding to the specific wavelength.It transpires from the hitherto presentation that it is possible, through a properly shaped sea floor or through an artificial immersed surface, to direct the Critical Momentum Wedge inside a special device that will receive the energy of the sea particles participating in the motion. Such a suitable device -called SEKE- along with the preliminary kinematic analysis for its operation, will be described within following chapters of this report. A primary mathematical approach to the CMW behavior is provided in document (3). A schematic simulation of the CMW dynamics is rendered in (4)
Experimental Results
As this point we should recapitulate on the governing principles of the C.M.W. theory. Hence, the water particle orbits (motion orbits) in the presence of progressive waves are either circles or ellipses, the horizontal diameters of which decrease exponentially with depth. According to the theory, there is a region of momentum between the water surface and the depth at which the particle orbits become zero, which represents the resultant of all other momentums upwards and downwards of that region. In other words, if we average the momentums of all the particle motion -except for those very close to the surface- we would obtain a result equal to the momentum of C.M.W.
A significant experimental indication of the C.M.W. existence, is provided by the experimental works of Prof.W.Dursthoff (Hanover Univ.). According to the published proceedings (NEL publication "1993 EUROPIAN WAVE ENERGY SYMPOSIUM") Prof. Dursthoff tests were performed on large-scale, quasi-prototype model sites (Hanover Large Wave Flume), and actual digital recordings were obtained on the incident impact forces normal to a breakwater, as induced by four representative cases of variable wavelength waves. A graphical representation of the respective results is provided by DIAGRAMS "LOADING CASE 1 to 4", in section (5).
As demonstrated, longer wavelengths apply as developing from "LOADING CASE 1 to CASE 4" and different "wave-breaking" effects are subsequently obtained. A significantly longer wave length is apparent in CASE 4 by -comparison to the previous cases-and the respective Horizontal Velocity vector VH is significantly greater than in the previous cases. As expected, the opposite holds for the Vertical Velocity vector Vv, which is now significantly lesser than in the previous cases. Clearly demonstrated in case 4, is the occurrence of two well-defined humps. This indicates the existence of two momentum carriers in the time domain separated by a magnitude of fragments of a second, and a distance in the order of a few meters.
Back to diagram -- "LOADING CASE 4', the first hump appeared due to the momentum carried by the wave front. The second hump is apparently due to the C.M.W. momentum. A reasonable question appears now, as to the reasons that clearly defined second humps do not appear on the other "loading diagrams". A simplified conclusion is that the longer the wavelength is, the better the C.M.W. effect becomes apparent. Dursthoff's tests were performed in a wedge-shaped formatted sea-bed. When a progressive wave is confronted with a formatted sea-bed, a gradual deformation of the particle orbits will also commence. Consequently for longer wave lengths the C.M.W. would delay accordingly, with respect to the wave front. Therefore in short wave front from the action of C.M.W. may well be incomplete and less powerful. On the contrary, in long wavelengths this distinction becomes clear. Hence, the diagrams corresponding to "Loading cases 1-3" do not clearly depict the secondary loading effects due to the C.M.W., since it is so close to the surface that its loading action occurs almost simultaneously to the wave front action.An appropriately formatted sea-bed, will not only accomodate a wide number of wavelenghts, but will also allow a distinct and amplified C.M.W. effect, as is presented in schematic (6)
(1) CMW envelope development over a modified sea bed
- Schematic presentation -(2) Water particles orbit deflection on modified sea bed
- Schematic presentation -(3) CMW kinematics intoduction
- Basic theoretical model -(4) CMW kinematics simulation
- Schematic presentation -1 2
3(5) CMW dynamics behavior
- Experimental tests -(6) CMW fully developed dynamics behavior
- Schematic presentation -
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