Tek serbestlik dereceli dairesel silindirin girdap kaynaklı titreşimleri üzerinde serbest su yüzeyinin etkileri
Free surface effects on vortex-induced vibrations of a single-degree-of-freedom circular cylinder
Yazar: ALKIN ERDAL DEMİRHAN
Danışman: DOÇ. DR. ÖMER KEMAL KINACI
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Gemi ve Deniz Teknoloji Mühendisliği Ana Bilim Dalı / Gemi ve Deniz Teknolojisi Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Deniz Bilimleri = Marine Science ; Enerji = Energy ; Gemi Mühendisliği = Marine Engineering
Dizin: Serbest yüzey = Free surface ; Titreşim = Vibration ; Vorteks = Vortex ; Yenilenebilir enerji = Renewable energy

Özet:
Dünyada son yıllarda artan enerji ihtiyacı ile insanlar yenilenebilir enerji kaynaklarına yönelmiştir. Önceki yüzyıllarda kullanılan geleneksel enerji kaynaklarının sınırlı olması ve çevreye olan zararlı etkileri yenilenebilir enerji kaynaklarına yönelimi hızlandırmıştır. Yenilenebilir enerji kaynağı olarak akla ilk olarak güneş ve rüzgar
gelse de, son dönemlerde suyun gücünden de yararlanma hedefi artmıştır. Deniz ve okyanuslardaki enerji potansiyeli çok daha yüksek olsa da; nehirler, boğazlar veya kanallarda kısacası akan sulardan da hidrokinetik enerji üretmek mümkündür.
Akış kaynaklı hareketler hidrokinetik enerji üretimi yöntemleri arasında son yıllarda önem kazanan bir disiplin olmuştur. Bu kıpırdanmayı başlatan en önemli buluşlardan biri akışkan kaynaklı hareketlerden enerji elde etmeye yarayan VIVACE (Girdap Kaynaklı Titreşimlerden Sucul Yeşil Enerji – İng. Vortex Induced Vibration Aquatic Clean Energy) olarak adlandırılan bir mekanizmadır. Akış kaynaklı hareketlerin (İng. Flow Induced Motions, kısaca FIM) öne çıkan alt
dallarından biri de girdap kaynaklı titreşimlerdir. Girdap kaynakları titreşimler, akış içerisindeki küt bir cismin iz bölgesinde oluşturduğu girdaplardan meydana gelmektedir. Bir akışkan küt bir cisme ulaştığında, cismin etrafında akım ayrılmasına uğramaktadır. Gerçekleşen bu akım ayrılması neticesinde; sürekli, periyodik ve çift yönlü olarak kopan bu girdaplar cisim üzerinde kuvvet oluştur ve cismi hareket ettirir. Söz konusu cismin doğal frekansı, kopan bu girdapların frekanslarına yakın veya eşitse kenetlenme (lock-in) gerçekleşir ve cisim azami düzeyde hareket etmeye başlar. Geçmişte bu durum Tacoma Asma Köprüsü'nde yaşanmış olup, gerçekleşen kontrolsüz hareket neticesinde köprü sulara gömülmüştür.
Bu çalışmada, literatürde de yaygın olduğu üzere, tek serbestlik dereceli (sadece akışa dik olarak düşey yönde hareket edebilen) dairesel bir silindir ele alınmıştır. Silindir, serbest su yüzeyine paralel veya dik olarak yerleştirilebilir. Enerji elde etme bazlı çalışmalarda ise silindir yüzeye paralel olarak yerleştirilmektedir. Ancak serbest su yüzeyinin silindir hareketini engelleyici bir etkisi olduğu bilinmektedir. Bu tez çalışmasında serbest su yüzeyinin girdap kaynaklı titreşimler üzerine etkileri deneysel olarak incelenmiştir. Deneyler, İstanbul Teknik Üniversitesi Gemi İnşaatı ve Deniz Bilimleri Fakültesi'nde Ata Nutku Gemi Model ve Deney Havuzunda bulunan Akış Kaynaklı Hareketler laboratuvarında gerçekleştirilmiştir. Deneyler diğer tüm parametreler sabit tutulmak üzere 6 farklı derinlik ve 3 farklı kütle oranı için yapılmıştır. Söz konusu deneylerdeki Reynolds sayısı 16,000 ile 71,000 arasında değişmektedir. Akışkanlar için çok önemli bir parametre olan Reynolds Sayısı; atalet kuvvetlerinin, viskoz kuvvetlere oranlanmasıyla elde edilmektedir. Yapılan deneyler sonucunda serbest su yüzeyinin girdap kopma frekansını değiştirdiği bulunmuştur. Silindir serbest su yüzeyine yaklaştıkça, senkronizasyon bölgesi daralmakta ve hareket genlikleri azalmaktadır. Senkronizasyon bölgesi, sistemin hareketlerinin gözlendiği aralığa denmektedir. Gerçekleşen en büyük genlik, serbest
yüzeyinden en uzak ve en derin olan silindirde gözlenmiştir. Ayrıca üst bölge (upper branch) ve alt bölge (lower branch) serbet su yüzeyi etkilerinden çok fazla etkilenirken, başlangıç bölgesinin (initial branch) çok fazla etkilenmediği
gözlenmiştir. Elde edilen frekanslar incelendiğindeyse, serbest su yüzeyine en yakın olan silindir frekansının en yüksek olduğu görülmüştür. Ancak bu durumda senkronizasyon aralığı daralmaktadır. Tüm deneylerde frekanslar, hıza göre neredeyse doğrusal olarak artmıştır. Yüksek salınım frekansı elde edilen enerjiyi artırır. Ancak diğer yandan silindirin
salınım frekansı arttıkça doğal frekanstan uzaklaşılmakta; dolayısıyla hareket genliği düşmektedir. Hareketin genliği ve frekansı üretilen enerji açısından iki önemli parametredir. Cismin serbest su yüzeyine yakın olması frekansı artırmasına karşın genliği düşürdüğünden, elde edilen enerjinin azaldığı fark edilmiştir. Serbest su yüzeyi cismin hareketi için bir bariyer oluşturmaktadır. Bu sınır sebebiyle cisim üzerinden kopan girdap küçülmekte, boyutu küçülen girdap da cisim üzerindeki kuvveti azaltmaktadır. Azalan kuvvet cismin hareket genliğini düşürmektedir. Serbest su yüzeyine yakınlık, frekansı artırsa dahi, toplam üretilen enerji açısından bakıldığında olumsuz olarak değerlendirilmektedir.

Abstract:
In last decades, energy consumption has increased enourmosly around the world. Most of the underground energy resources have been drilled. First, the traditional energy sources were begun to be consumed such as oil, natural gas and coal. Then, the tendency on renewable energy sources has increased especially in the last years because of the environmental damage and the limited reserves of these traditional energy sources. Though the increasement in renewable energy investments started with solar and wind energy in near past, the popularity of energy acquisition from water flow has risen considerably in more recent years. Around 70% of the world is covered with water that has an enormous energy potential. Although the energy potential in oceans is much higher; it is more feasible to convert renewable energy from hydrokinetic energy of flowing waters such as in rivers, straits or canals by adopting vortex-induced vibration (VIV) phenomenon. VIV is one of the prominent sub-branches of flow-induced motions (FIM). Vortexinduced vibrations occur due to vortices which are created by the flow around a bluff body (in the wake region of bluff body). When the flow encounters a bluff body, it is separated into two shear layers, passing through the top and bottom of the body. One
of these shear layers forms a vortex at the aft of the body while the other one attacks and cuts this vortex. As a result of this current separation; these vortices shed continuously, periodically and bidirectionally, which create forces and move the bluff body upward and downward direction according to the route of the eddies. In order to
explain easily VIV sections, some zones are named which are initial branch, upper branch and lower branch. All those zones are included by the syncronization zone. Starting of the motion is in initial branch zone, then frequency of the vortex shedding increases, so amplitude of the system also rises and this zone is called upper branch. The maximum movement is observed in here. Later, frequency of the vortex shedding keeps increasing, but the amplitude of the system drops, that zone is called lower branch zone. After passing through lower branch, desyncronization zone begins. The
movement is unstable here, and it dissappears eventually. In upper branch, there is one point which is the natural frequency and the frequency of the eddies equal each other. If the natural frequency of the object or the structure to which it is attached is equal to the frequencies of vortex shedding, the structure gets resonance. The resonance is
named "Lock-in" in VIV. If there is a lock-in case, maximum motion is achieved. In the past, this case happened on the Tacoma Narrows Bridge. The wind flowed over the bridge and its deck that is bluff body, the wind started to shake the bridge. The frequency of the wind became equal with the vortices which shed from the bridge deck, the bridge got resonance. Finally the bridge collapsed just after 4 months from its opening ceremony. VIV can be observed on different engineering structures such as heat exchangers, lamppost, transmission lines, marine Technologies, offshore structures etc. There are two types of engineering approach on VIV: First, preventing oscillations on structures to prevent failures. Second, galloping VIV to harvest clean hydrokinetic energy of water currents. VIVACE (The Vortex Induced Vibration for Aquatic Clean Energy) can be given as an outstanding example for the second type of studies. In VIV studies, related to energy harvesting, the system is expected to oscillate with higher oscillation amplitudes. In the first type of VIV studies, examining the phenomenon around engineering structures such as submerged offshore platforms, bridges transmissions lines etc. The oscillations are rather aimed to be suppressed. In both type of studies, the examinations should take free surface effects into the calculations to gain more realistic and verifiable results since it plays an important role in the VIV performance of an elastically mounted bluff body in cross flow direction.
Some submerged or semi-submerged bluff bodies like offshore structures, wavepower generation devices, ships, underwater vehicles and submarines work near the free surface that could be affected by the free surface effects. When a bluff body is exposed to VIV around the free surface, the vortices in the wake may not have enough space in the water. Thus, some unexpected results may be examined in the VIV response. Moreover, these submerged bluff bodies or equipments may not work effectively, face some vibration problems, damaging parts of the system, the unwanted motions like heave, etc. can be seen. Therefore, free surface effects must be considered in the calculations. The effect of free surface on vortex-induced vibration (VIV) of an elastically mounted rigid circular cylinder in cross-flow investigated experimentally in this thesis over a wide range of Reynolds numbers (1.6x104 < Re < 7.1x104) in order to reveal the role of this effect on three main branches of VIV response; initial branch, upper branch and lower branch. In the experimental study, the edges of the cylinder are extended to the walls of the water channel to avoid from possible tip effects. The tests are carried out at Flow Induced Motion Laboratory of Istanbul Technical University (ITU FIM Lab). The cylinder is submerged into 6 different depths for this purpose and 3 different mass ratios are employed in the tests to observe the correlation between mass ratios and free surface effect, while keeping all other parameters constant. There are some nondimensional
numbers which affect the VIV issue. For example, one dimensionless number is Reynolds number. Normally, Froude number can be ignored while the experiments are performed enough space between the cylinder and the free surface. However, in this thesis, Froude Number plays an important role about affecting to the VIV system and it must be consired. Before carrying out the experiments, the system is set-up by adjusting each component to allow the observation of three main branches of VIV within the desired Reynolds numbers. First, the outer frame is mounted and moored on the sides of recirculation channel of ITU FIM Lab. The cylinder has 8 cm diameter and smooth surface which is screwed on the side struts. A balancing bar is connected between these struts. These components are treated as solid during the experiments. The moving components are attached into the rails by means of U groove guiding pulleys. The springs are connected to between the struts and main frames. A sensor system is put into the middle of the frame in order to gauge distance between the cylinder and itself which is called amplitude. The experiments are performed in 10 days in total at similar air and water temperatures. The flow velocity range for the experiments is 0 – 0.884 m/s. The tests started from still water and the velocity of the water is increased by 0.05m/s. For each speed, the amplitude and frequency data of the cylinder are measured by means of a sensor. During this process, the 60-second oscillation data of the cylinder are collected. The first test is carried out at a distance of 6 cm from the free water surface to the center of the cylinder. The second experiment is done with a distance of 9 cm between the free water surface and the center of the cylinder. In the following experiments, the cylinder is relegated one by one with a diameter distance (8 cm) and
a total of 18 experiments are conducted, 3 for 6 depths and 3 at different mass ratios. The results of the experiments show that the vortex shedding frequency is changed by the free water surface effects. As the cylinder approaches to the free water surface, the synchronization zone narrows down and the amplitudes decrease obviously. When all the experiments are examined at the same velocity; the greatest amplitude is observed in the experiment whose cylinder is the deepest and furthest from its free surface. It is also observed that while the upper branch and lower branch are dramatically affected by the free water surface effects, the initial branch is slightly affected. For a selected
flow velocity, the frequency value is higher if the cylinder is closer to free surface. However, the synchronization range of a cylinder closer to the free water surface is narrower that ends with a slighter upper branch. Therefore; the frequency value for a deeper cylinder case at a greater flow velocity exceeds the frequency of the experiment which is closer to the free surface. It is also figured out that the frequency of all experiments increases almost linearly.
Frequency and energy are directly proportional quantities in energy harvesting studies of VIV. If the oscillation frequency of the cylinder rises and exceeds VIV system's natural frequency in water, the response loses its harmony and desynchronize. Here, even though more energy is provided into the system from incoming water flow, the system responds with less amplitude. Eventually, the captured energy from the phenomenon is decreased. This proves that both frequency and amplitude are two important parameters for harvesting energy. As a result; it is determined that the closer
the system is to the free water surface, the less energy is harvested. The reason why the free water surface affects the motion or frequency of the body; because of presence to the free surface, when a stream line reaches the cylinder, it
cannot shed into the bidirectional and periodic eddies as usual, compared to the cylinder which is far from the free water surface. The cylinder goes to upwards with the force created by the vortex shedding. However, there is no water volume above the cylinder to be shed vortex usually. Thus, the cylinder cannot go back to the downward in a healthy way. Nonetheless, it is thought that how the free surface affects the system, in order to be proven of the case, the streamlines must be observed.