Dikey dairesel silindirik açık su havuzlarında hidrodinamik kuvvetler

Abstract

ÖZET Burada sunulan tezin amacı, lineer teori koşulları içerisinde serbest su yüzeyi ihtiva eden sıkış tırılamaz viskositesiz, irrotasyonel ve sonlu derinlikte akışkan ortamında çok küçük genlikli zorlanmış titreşim hareketi yapan dairesel halka kesitli düşey eksenli silindirik bir açık su havuzuna gelen hidrodinamik kuvvetlerin bulunma sıdır. Akışkan ortamının irrotasyonel alınmasından dola yı hız bir potansiyelden türetilebilir. Bilinmeyen hız potansiyelleri ise karmaşık sınır değer problemini sağla yacak şekilde çözülmüştür. Sonlu kalınlıklı silindirin içinde tabandan serbest su yüzeyine uzanan iç bölge (I) silindir tabanı ile su tabanı arasında kalan alt bölge (II) ve silindirin dışında sonsuza uzanan bölge (III) ol mak üzere üç bölgeye ayrılmıştır. Her bir bölgede hız potansiyelleri özfonks iyonlar cinsinden seriler yardımıyla yazılmıştır. Bölgeler ara sındaki sınırda fiktif yüzeyler üzerinde basıncın ve nor mal hızların sürekliliğini sağlayacak şekilde hız poten siyelinin bilinmeyen kortpleks. katsayıları tayin edilmiştir, Basınç, Bernouilli denkleminin lineer kısmıyla ifa de edilerek bulunmuştur. Boyutsuz Hidrodinamik büyüklük ler (eksu kütlesi ve sönüm katsayısı) dış çap, iç çap ve derinlik parametrelerine bağlı olarak değişik oranlar i çin verilmiştir. Teoriden bulunan sonuçlara ilave olarak sonlu derin likli suda, değişik peryodlarla salınım yapan bu matema tik modelin deneyi yapılarak oluşturduğu su yüzeyi for masyonu yazıcı osilograf yardımıyla belirlenmiştir. Ba sınç değerlerini bulabilmek için yüzeye yerleştirilen transduserler analog-digital bilgisayara bağlanarak orta lama basınç değerleri doğrudan elde edilmiştir. - iv -

HYDRODYNAMIC FORCES FOR VERTICAL AXIS CIRCULAR CYLINDER CONTAINING A CONCENTRIC CYLINDRICAL HOLE IN FINITE DEPTH SUMMARY * There is considerable interest at present in de vising method for extracting energy from ocean resources and ocean waves. Also, the rapidly increasing demand to exploit known offshore oil fields throughout the world, and the costly conventional method of piping the oil to the shore have given support to the concept of offshore storage terminals located in the immediate vicinity of the field. The Khazzan Dubai oil storage tanks at Fateh field and the new offshore reinforced-concrete storage tank at the Ekofisk field in the North Sea, show the new attitude which the offshore oil production industry has developed toward this system. There are many engineering aspects in the design of such a structure which is to be operated continuously in the open sea. The concept of using- a rigid barrier extending from above the water surface to some distance below the surface to create a sheltered area goes back to World War II. An enclosed type of bottomless barrier would create off-shore port facilities or sheltered lagoons to overcome the poor dynamic behaviour of the drilling vessels or other problems of off-shore construction. With this problem in mind several methods of launching and retrieving subsea units, especially manned and un manned submersibles and diving bells, have been deve - loped and some have been put to practical use with vary ing degrees of success. One of these systems which has shown considerable merits and consequently won reason able popularity is the moonpool system. Moonpools are vertical wells of various cross sectional shapes usually situated at the centre of a floating body with its lower end open to the sea. Moon- pools are frequently found in drilling ships. At pre - v -sent only relatively small and compact units, such as diving bells, remote control vehicles and one man at mospheric diving suits, are launched and recovered through the moonpool. The relative advantages of using moonpool system for these purposes are threefolds : (i) by positioning the moonpool at the centre of floatation of the ship at the normal work ing draught, the adverse effects of the ship's angular motions can be minimised ; (ii) the water oscillation inside the moonpool is such that the higher frequency components of the wave are 'filtered out'. (iii) it provides good protection from the horizon tal force elements. The behaviour of a moonpool is of very complicated nature. Fukuda (19 77) investigated the effects of water column oscillation in a moonpool on ship motions with particular emphasis on the Increase of ship's forward motion resistance. It was shown that, when a model with a moonpool was towed in calm water, the resistance in creased by up to % 7 compared to a model without one. However, there is no direct application to the present problem, except the fact that an empirical formula for the water column added mass was derived through a series of transient tests. Knoot ve Flower (1980) performed experimental studies on the water oscillation in half immersed vertical tubes fixed in space. Their main in terest was to study the eddy motion near the lower exit of the tube due to the water oscillation. Newman (19 74) solved the problem of a closely spaced double barrier with infinitesimal thickness in waves. The flow field was divided into inner and outer regions are examined separately. The inner region covers the flow field near the lower exit of the slit formed between the two barriers and the channel-like flow near the free-surface inside the slit. The flow in this region is solved by using Schwarz-Christoffel transfor mation. In the outer region, which covers the flow field far removed from the slit, the two barriers are assumed to be collapsed into one. The flow into and out of the lower entrance is represented by a source singularity of an undetermined strength. The velocity potential in this region is obtained by summing incident wave potential, diffraction potential and the potential due to the source. The solution of the two regions are then matched to each other in the overlap domain to give the expressions for two unknown constants. This completes the solution for the singular perturbation problem and the water column oscillation in the slit - vx -can be estimated from linearised free-surface condition. Numerical studies based on this solution have shown that the characteristic features of the water column oscilla tion are very similar to those of the heave motion res ponse of a free floating thin solid column in waves. Another important conclusion of this work is that the most influential parameter governing the behaviour of water oscillation is the ratio of barrier separation distance to the depth of immersion. Evans (1961) applied this theory to compute the energy extraction efficiency for a wave energy device based on a surface-piercing tube. In the absence of pro per evaluation of damping terms the result is removed from the reality, but it is meaningful in a sense that this approach gives the maximum rate of energy extrac tion of this particular device, and this was shown to be 0.5. Miloh (1983) solved the problem of wave loads on a floating solar. pond. The pond is floating on a free- sürface in an open sea. of finite depth and is exposed to wave action. Also computed is the pressure distribution and the water run-up on the periphery of the pond. The transmitted wave motion inside the pond is discussed and the resonance conditions for heave and pitch motions are investigated. The basic geometrical assumptions of these authors are that the wall thickness is infinitesimal. Lee (1982) formulated the ship-moonpool system as a coupled mechanical oscillator with the help of in sight gained during the theoretical study. The numerical values of hydrodynamic coefficients including coupling terms are obtained by experimental methods of both free- and forced-oscillation tests. The theoretical analysis described in this study deals with very narrow ducts. It is, therefore, necessary to tackle the problem from the other extremity, i.e. a wide duct problem. Although heave motion of the ship is believed to be the most important mode influencing the vertical water os cillation in the moonpool, the effect of other modes of motion is neglected. In this research work is concerned with linearized radiation problem of a single semi-submerged bottomless cylindrical body with vertical symmetry and finite wall thickness in finite depth. In recent years, hydrodynamic characteristics of vertical circular cylinders and elliptical cylinders oscillating in free surface have been studied by many - vii -authors. In computing hydrodynamical forces, numerical techniques must be resorted to. These include the tra ditional wave source distribution method by Garrison (1975), finite element variational formulations by Chen and Mei (19 74). Scattering and radiation problems for various obstacles including the vertical circular cy linder were also treated by the Schwinger variational technique by Black et.al. (1971). The axisymmetry simply by the use of eigen functions alone (Garrett, 19 70) de veloped the expressions of the interior and exterior problems in terms of the potential at the common boundary and match the normal derivatives together. The theory is based upon the usual assumptions of classical hydrodynamics, i.e. that the fluid is inviscid and uniform density and that the motion starts from rest, and remains irrational. It is also assumed that the mo tion is three-dimensional and the body possesses both a vertical axis of symmetry and a horizontal plane of sym metry. Non-linear terms in the equation of motions are neglected. Also damping coefficients expressed as a linear function of the oscillation amplitude. The velocity potential satisfies the Laplace equa tion, the dynamic and kinematic boundary conditions at the free surface, the kinematic boundary conditions on the rigid body for heave and surge motion, the bottom boundary condition, and the radiation condition at in finity which assures the uniqueness of the solution. Thus a linear boundary value problem is obtained as out lined Chapter 2. The linearized radiation problem of the bottomless cylindrical body with finite wall thickness has been solved by matching technique by satisfying conditions of continuity for pressure and mass flux between adja cent regions. The velocity potentials for the different regions was solved by seperation of variables and expresse in terms of e igenf unctions and the resulted simultaneous linear equations solved for the unknown complex velo - city potentials. The section of the boundary value problem for the surge motion was solved in Chapter 3. The horizontal force may be obtained by integrating the pressure (3.65) over the vertical surface of the cylinder. The added mass and damping coefficient are given by the equation (3.66). Also heave motion was solved in chapter 4 and non-dimensional added mass, damping coefficients are given by the equation (4.42). viii -The experimental study were performed in Hydraulic Laboratory öf the Civil Engineering Faculty of Î.T.Ü. The smooth -walled cylindrical made of transparent acrylic material were used as model. The model basin is 9.30 m. wide by 9.30 m. long. The water depth h in this study is 0.50 m. The forced oscillation test were analysed in Chapter 6. The model was allowed to pure heave and the result ing motion was measured. For such a system it is essential to know the peak response frequency either to detune it from the opera - tional environment as in the case of the moonpool, or to tune into it as in the case of a certain type of wave energy device. Therefore, it is highly desirable to pre dict the behaviour of the water column oscillation in a moonpool at the design stage. Although heave motion of the model is believed to be the most important mode in- luencing the vertical water oscillation in the moonpool. The model however was allowed to pure heave and the re sulting motion was measured. Wave elevation and the re sultant water column oscillation in the moonpool were detected by wave gauges and recorded on a pen recorder. Although, it may be noticed the severe distortion of the waves near the walls caused by the heaving motion of a relatively large model in a small tank, thus intro ducing appreciable experimental error. The response at the resonance is extremely sensi tive to the magnitude of damping. A small inaccuracy in damping which has small values itself, can change the response at the resonance substantially. The weak point of this study is damping of the vertical water oscillation in a moonpool is considered as linear damping and should be expressed as a quadratic function of a oscillation amplitude. Some vortex forma tions may also exist around the periphery of the cylin der. However, according due to linearaziton of this study, eddy losses is neglected. - xx -