Nokta soğurucu tipi dalga enerjisi dönüştürücüsü dizilerinin hidrodinamik analizi
Hydrodynamic analysis of point absorber type wave energy converter arrays
Yazar: İLKAY ÖZER ERSELCAN
Danışman: PROF. DR. ABDİ KÜKNER
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Gemi ve Deniz Teknoloji Mühendisliği Ana Bilim Dalı
Derece: Doktora, 2017
Konu: Mühendislik Bilimleri = Engineering Sciences
Dizin: Dalga enerjisi = Wave energy ; Hidrodinamik = Hydrodynamics ; Yenilenebilir enerji = Renewable energy

Özet:
Yenilenebilir enerji kaynaklarından biri olan dalgalar, rüzgar ve yerçekiminin denizlerin ve okyanusların yüzeyine uyguladıkları kuvvetler sonucunda oluşurlar. Dalgalar büyük miktarlarda enerji taşırlar ve bu enerji, dalga enerjisi dönüştürücüsü adı verilen sistemler vasıtasıyla elektrik enerjisine dönüştürülebilmektedir. Bugüne kadar yapılan çalışmalar neticesinde çalışma prensipleri, kuruldukları yerler ve güç dönüşüm sistemleri birbirinden farklı olan çok sayıda dalga enerjisi dönüştürücüsü geliştirilmiştir. Bu çalışmalar kapsamında günümüze kadar alınan patentlerin sayısı binden fazladır. Dalga enerjisi dönüştürücüleri incelendiğinde, bunların bir kısmının henüz kavramsal tasarım aşamasında olduğu, bir kısmının ise kavramsal tasarımının tamamlandığı ve geliştirilmesine devam edilmekte olduğu görülmektedir. Nispeten az sayıda sistem prototip seviyesine ulaşarak açık denizde testlere tabi tutulmuştur. Bu kadar yüksek sayıda dalga enerjisi dönüştürücüsü dizayn edilmiş olmasına rağmen henüz hiç bir sistem, mevcut elektrik üretim yöntemleriyle rekabet edebilecek seviyeye ulaşamadığından, ülkelerin elektrik şebekelerine bu kaynaktan düzenli olarak elektrik sağlayan bir sistem bulunmamaktadır. 
Bu tez çalışmasında bir dalga enerjisi dönüştürücüsünün bir dizinin içinde diğer dalga enerjisi dönüştürücüleriyle yakın mesafede birlikte çalışmasının, performansı üzerine olan etkileri incelenmiştir. Dalga enerjisi dönüştürücüleri ile dalgaların etkileşimleri sonucunda, dalga enerjisi dönüştürücülerine etki eden kuvvetlerin ve bu sistemlerin yapmış olduğu hareketlerin çözümünde potansiyel akım teorisinden faydalanılmıştır. İlk olarak, bu çalışma kapsamında farklı yarıçap/draft oranlarına sahip olan eksenel simetrik yarı elipsoid ve yarı eliptik paraboloid şeklindeki şamandıralar ile yüksek basınçlı hidrolik yağ ile çalışan hidrolik güç dönüşüm sisteminin kullanılmasıyla, birden fazla nokta soğurucu tipi dalga enerjisi dönüştürücüsü dizayn edilmiştir. Daha sonra, şamandıraların hidrodinamik katsayıları ile dalga frekansının ve zamanın bağlısı olarak üzerlerine etki eden dalga kuvvetleri ve salınım hareketlerinin büyüklüğü, tez çalışması boyunca MATLAB ve FORTRAN yazılımları kullanılarak geliştirilmiş olan bir bilgisayar programı vasıtasıyla çözülmüştür. Diğer yandan, güç dönüşüm sistemlerinin ürettiği gücün hesabı parametrik olarak gerçekleştirilmiştir. İlave olarak, bu parametrik denklemler şamandıranın hareket denklemleri ile birleştirilerek güç dönüşüm sistemlerinin şamandıranın hareketleri üzerine olan etkileri problemin çözümüne katılmıştır.
Öncelikle, güç dönüşüm sistemlerinin parametrik olarak analizi yapılarak bir yıl içinde Karadeniz'de karşılaşılacak deniz durumlarında en fazla enerjinin üretilmesini sağlayacak eşleşme tespit edilmeye çalışılmıştır. Güç dönüşüm sistemlerinin analizinde dikkate alınan dizayn parametreleri çift etkili hidrolik piston silindirin etkin kesit alanı, akışkanın debisi, hidrolik akümülatörün en yüksek gaz basıncı ve akışın süresidir. Yapılan analizler sonucunda en fazla enerjinin elde edildiği parametreler ve şamandıra geometrisi kullanılarak nokta soğurucu tipi bir dalga enerjisi dönüştürücüsü tasarlanmıştır. Son olarak, tasarlanan bu dalga enerjisi dönüştürücüsü kullanılarak farklı sayılarda sisteme sahip bir adet doğrusal ve iki adet kare şeklinde, toplam üç ayrı dizi meydana getirilmiş ve yine Karadeniz'de karşılaşılan deniz durumlarında dalga enerjisi dönüştürücülerinin dizi halinde iken ürettikleri güç değerleri, farklı ara mesafeler ve dalga ilerleme yönleri için hesaplanarak, dizi halinde bulunmanın enerji üretimine olan etkileri araştırılmıştır. Yapılan hesaplamalar göstermektedir ki, dizileri oluşturan dalga enerjisi dönüştürücüleri arasındaki hidrodinamik etkileşimler, ara mesafeye, dalgaların ilerleme yönüne ve dizinin şekline bağlı olarak farklı karakterlerde olmakta, dizi büyüdükçe etkileşimler karmaşık bir hale gelmektedir. Dizilerin ürettiği yıllık enerji miktarları ara mesafenin ve dalga ilerleme yönünün değişimiyle rastgele bir değişim göstermektedir. Bazı ara mesafe ve dalga ilerleme yönü eşleşmelerinde etkileşimlerin olumlu olduğu ve üretilen enerjinin arttığı, bazılarında ise olumsuz yönde olduğu ve üretilen enerjinin azaldığı görülmektedir. Bu durumun sebebi dizi içindeki dalga enerjisi dönüştürücülerine etki eden dalga kuvvetlerine ait bileşenlerin birbirleriyle benzer fazlarda veya ters fazlarda olup toplam dalga kuvvetini büyütmeleri veya küçültmeleridir. Bunun yanısıra, dalga enerjisi dönüştürücülerinin çalışma parametreleri izole bir sistemin çalışma şartlarına göre değil, dizilerin çalışma şartlarına göre belirlenmeli ve ara mesafe ile dizinin kurulum yönü yönü de, sistemin çalışma parametreleri ile belli bir bölgedeki dalgaların karakteristiklerine göre tayin edilmelidir.

Abstract:
The Energy Crisis of 1970's affected both daily and industrial activities deeply and showed that it might result in serious problems when the supply of the primary source of energy, fossil fuels, is interrupted. Besides meeting the energy needs mainly from fossil fuels possess risks in terms of supply, the harmful effects of consuming fossil fuels in an increasing rate on the environment also started to become noticeable. The emission rates of greenhouse gases in the world show that carbon dioxide is the primary greenhouse gas which is mostly produced due to the consumption of fossil fuels and industrial activities. Additionally, a similar rate of carbon dioxide emission is applicable for Turkey, of which the energy production is the main reason. Moreover, the amount of electricity consumed increases regularly among all types of energy. Consequently, new energy sources must be found in order to meet the energy requirements and to prevent environmental pollution due to the wide consumption of fossil fuels. Renewable or alternative energy sources are examples of sustainable and environment friendly sources of energy, of which the wind, waves, ocean currents, tides, solar energy, geothermal energy and biomass are several examples. 
Waves, which are one of the renewable energy sources, are generated by the forces acting on the surfaces of seas and oceans by the wind and the gravity. Waves possess great amounts of energy and it can be converted into electricity by devices called wave energy converters. Many wave energy converters have been developed so far, of which their principles of extracting the energy, the places they are installed and their power take-off systems are different from each other. Wave energy converters which benefit from the oscillations of their floats due to the wave forces acting on them convert heave, surge or pitch motions into electricity. These devices which are generally known as oscillating body type wave energy converters can be either floating on the surface of the sea or submerged completely. Another type of wave energy converter uses the vertical motion of waves to compress the air inside a chamber, which then drives an air turbine coupled to an electric generator. This type of wave energy converters are called oscillating water column wave energy converters and are built either as a floating structure or as a shoreline structure. Furthermore, one type of wave energy converter directs the waves towards a ramp by reflectors or by a narrowing and elevating channel. As a result, the waves break over the ramp and the water is collected in a reservoir, which then flows through an opening and drives a hydro-turbine coupled to a generator. This type of wave energy converters are called overtopping wave energy converters and can be built either on the shoreline or as floating. The wave energy converters generate electricity via their power take-off systems. Currently, there are four different types of power take-off systems utilized in these systems, which are high pressure hydraulic power take-off system, water turbines, air turbines and linear generators. Although there are many different types of wave energy converters and more than one thousand patents were issued so far, it is hard to say that these devices reached their pinacles of development. It can be seen that the wave energy converters are in different stages of development. A portion of these devices are in the conceptual design stage, while there are others of which the conceptual design have been completed and are in a stage of further development. The prototypes of a very small number of wave energy converters were built and tested in real sea conditions until today. Despite such a high number of wave energy converters have been developed, currently there is not any system, which supplies great amount of electricity into the grids regularly since none of these systems are able to compete with the conventional methods of generating electricity. 
The performances of wave energy converters, which are both isolated and laid out as an array and work close to each other, are studied in this thesis. Potential flow theory is utilized in the solution of wave-body interactions and in the calculation of wave forces acting on the wave energy converters and in the resulting oscillations. The solution of the problem associated with the oscillations of bodies in the free surface of a deep fluid is established and a computer program was developed by utilizing MATLAB and FORTRAN programming languages in order to evaluate the necessary calculations. First, the surfaces of the floats are modeled by discrete triangular panels. Then, three dimensional pulsating sources are distributed over the panels and a body boundary problem is solved in order to calculate radiation forces acting on a body due to its oscillations in the free surface of a deep fluid. The solution of the radiation problem results in the added masses and damping coefficients of a body. Furthermore, the results obtained by the panel method was validated by comparing the added mass and damping coefficients of a semi sphere to the ones obtained by an analytical method. The results calculated by both analytical and numerical methods are in very good agreement. Finally, the incident wave forces and diffraction wave forces are calculated by integrating pressure field induced by the plane progressive waves and the diffracted waves over the surface of the body.  
The design of a wave energy converter requires both determining the most suitable float geometry and the power take-off system. As a result, eight different float geometries and two different power take-off systems are considered for evaluation and for determining the most suitable match. A high pressure hydraulic power take-off system and a Pelton turbine are considered as the power take-off systems of the wave energy converters and the methods for evaluating both systems are established. The high pressure hydraulic system was chosen as the power take-off of the wave energy converter after evaluating both systems. Moreover, the hydraulic power take-off system was designed in detail and four system parameters are determined and different numbers of working values are assigned for each parameter. In addition to determining the float geometries and the power take-off system, another study was also carried out in order to model the sea states observed in the Black Sea. The sea states observed in both Sinop and Hopa are modeled by using JONSWAP Spectrum and the mean spectral parameters which were determined by the analysis of wave data collected during NATO TU-Waves Project. Consequently, a great number of wave energy converters are designed by combining different float geometries and power take-off system parameters, which are the effective area of the double acting hydraulic piston, the flow rate of the hydraulic fluid, the maximum pressure of the gas accumulators and the duration of the discharge of the hydraulic fluid from the high pressure accumulator. Each wave energy converter is evaluated by solving the equation of motion of a mass-spring-dashpot system coupled with the equations modeling the dynamic response of the power take-off system in all sea states observed in Sinop and Hopa and by calculating annual energy production of each wave energy converter. Consequently, a float geometry and a set of power take-off system parameters are determined for Sinop and Hopa. 
The wave energy converter which is capable of generating the highest amount of energy in one year from the waves in Sinop was chosen in order to configure arrays of wave energy converters. Three different array layouts are considered for evaluating the interactions between wave energy converters in an array and their effects on the energy production. The arrays considered in this study are a linear array which is established from two wave energy converters, a square array which has four wave energy converters and another square array which has nine wave energy converters. The annual energy production of each array is evaluated for fourteen different gap distances and seven incident wave angles.  The performances of the arrays are evaluated by calculating a parameter, which is called q factor. q factor is the ratio of the total energy generated by an array to the total energy generated by the same number of isolated wave energy converters that the array has. The results show that the total energy generated by each array changes with gap distance and incident wave angle. The interactions among the wave energy converters may be either positive which increases the total energy output or negative which decreases the total energy generated. It is observed that the amount of annual energy generated increases due to the positive interactions in some pairs of gap distance and incident wave angle, while it decreases due to negative interactions in another pairs of gap distance and incident wave angle. When the waves diffracted and radiated from all of the wave energy converters interact with the incident waves acting on a wave energy converter at similar phase, the total wave forces acting on the wave energy converters increase, thus the energy generated by that array increases. On the other hand, if the radiated and diffracted waves interact with the incident waves at an opposite phase, the total wave forces acting on the wave energy converters decreases, thus the energy generated by the array decreases. Consequently, it can be said that the amount of energy generated by an array of wave energy converters depends on how the waves interact with each other. Moreover, the results show that the hydrodynamic interactions among the wave energy converters in an array have different characteristics according to the gap distance, incident wave angle and the layout of an array and become more complex with the growing size of the array. The annual energy production of the arrays changes irregularly with gap distance and incident wave angle. Furthermore, the annual energy productions of the rows of the arrays are also evaluated. The calculations show that the first rows of the arrays which meet with the incident waves first, generate more energy than each other row generates. This result is a consequence of that the first rows always benefit from the wave generated by the wave energy converters in the back rows, a similar result also reported by other researchers. 
The performances of arrays indicate that the parameters of the power take-off system must be determined according to the characteristics of arrays but not to those of an isolated WEC and the gap distance and the orientation of the array must also be determined according to the characteristics of both the system and the waves in a designated area. Moreover, the calculations carried out in order to determine the performances of arrays should be carried out by assigning different calculation periods and the convergence of the results should be evaluated. Furthermore, the amount of energy generated annually by the arrays should also be calculated by modeling each sea state with assigning different sets of random phase angles and the results must be checked for convergence. Finally, floats with different displacement tonnages should also be considered while designing the wave energy converters, along with different array layouts such as rhombus or rectangular.