Kanallarda blokaj etkisinin belirlenmesi

Abstract

IV ÖZET Sunulan çalışmada, serbest yüzeyli bir kanalın yan duvarları ve dibinin; içinde hareket eden bir cismin direncin de yarattığı etkinin, yani blokaj etkisinin, belirlenmesi için kolay uygulanabilir bir yöntemin elde edilmesi amaçlanmıştır. 1. Bölümde blokaj etkisinin gemi model deneyler indeki önemi açıklanmıştır. Gemi model deneylerinde çeşitli nedenlerle ortaya çıkacak hataları azaltmak amacı ile büyük boyutlu modeller kullanılmak istenir. Bu durumda da blokaj etkisi yeni bir farklılığa neden olur. 2. Bölümde blokaj etkisinin belirlenmesine ilişkin literatürde geçen çalışmaların önemlileri özetlenmiştir. Bu teorik veya deneysel çalışmalar çoğunlukla blokaj etkisi nedeni ile bir (Au) hız artışının bulunmasına yöneliktir. Bir (U) hızında, bir kanaldaki direncin, (U+Au) hızında sınırsız sudaki dirence yaklaşık olarak eşit olduğu düşünülmektedir. 3. Bölümde; (Au) hız artışının kolay ve doğru biçimde bulunması için çeşitli yollar denenmiştir. Maksimum dik kesit alanları, boyları ve hızları eşit olan cisimlerin blokaj açısından eşdeğer oldukları varsayılmaktadır. Böylece, her hangi bir formda bir gemi modeli yerine, ona blokaj açısın dan eşdeğer daha basit dönel bir cisim için hız artışının hesaplanması düşünülmüştür. Bu tür cisimler olarak Rankine Ovoidi ve dönel elipsoid alınmıştır. 3.1. Paragraf ta bir Rankine Ovoidinin sınırsız sıvı için de, serbest su yüzeyi altında ve serbest su yüzeyli kanallar da hareketleri ayrıntılı biçimde incelenmiştir. Bu inceleme için birim kaynağın serbest su yüzeyi altında hareketinde hız potansiyeli (Green fonksiyonu) de çıkarı İmiş t ir. Ayrıca hız potansiyelinin (4>x) türevinin hesaplanmasında ortaya çıkan çift katlı tekil integralin bulunması için bir integras- yon yöntemi verilmiştir. Aynı yöntem biraz daha değiştirilerek (o) hız potansiyelinin ve diğer türevlerinin de hesaplanmalarında uygulanabilir.3. 2. Par agraf ta dönel bir elipsoidin sınırsız sıvı için de ve serbest su yüzeyi altında hareketleri incelenmiştir. Burada elipsoid; odak noktaları arasındaki bir CfeU) kaynak- kuyu dağılımı ile gösterilmiştir. 3. 3. Paragraf ta dönel bir elipsoidin dikdörtgen kesitli bir kanalda hareketinde hız artışı narin cisim yaklaşımına göre formüle edilmiştir. Değişik boyutlu kanallarda, değişik hızlar için bulunan hız artışları kullanılarak, eğri uydurması sonunda; hız artışının blokaj oranı, derinlik Froude sayısı ve hıza bağlı bir ifadesi elde edilmiştir. 4. Bölümde deneysel yolla, değişik boyutlu kanallarda (6) değişik gemi modeli ve bir elipsoidin direnç değişimlerinin bulunması üzerinde bilgi verilmiş ve sonuçlar grafik yolla değerlendirilmiştir. Deneylerde kanal olarak 1. T. Ü. Gemi İnşaatı ve Deniz Bilimleri Fakültesi, Gemi Araştırma ` Merkezi Sirkülasyon Kanalı kullanılmıştır. Sirkülasyon kanalının içine yerleştirilen tahta perdeler arasındaki uzaklık ve su düzeyi ayarlanarak değişik boyutlu (6) kanal elde edilmiştir. Söz konusu sirkülasyon kanalı ilk kez bu çalışmadaki deneylerde kullanılmış olduğundan başlangıçta bazı düzenlemeler gerekmiştir, örneğin; suyun akış hızını ölçme ye yarayan Fitot tüpü ve devresi büyük havuzda kalibre edilmiş, deney bölgesinde oluşan dalgaları önlemek için paralel iki levhadan oluşan bir dalga söndürücüsü yapılmıştır. Ayrıca Pitot tüpünün ve modelin tutulması gereken konumları belirlemek için kanalda baştan sona hız taraması yapılmıştır. Değişik formda (6) gemi modeli sirkülasyon kanalı ve büyük havuzda denenerek direnç eğrileri karşılaştırılmıştır. Narin cisim yaklaşımı sonunda bulunan hız artışları sirkülasyon kanalındaki direnç eğrilerine uygulandığında büyük havuzdakilere çok yakın değerler elde edilmektedir. Bir gemi modeli ve bir elipsoid sirkülasyon kanalından üretilen (6) kanalda denenerek direnç eğrileri büyük havuz sonuçları ile karşılaştırılmıştır. Bu eğrilerin değerlendirilmesi sonunda önerilen (3.88) hız artış formülünün (m = 0.064) blokaj oranından küçük değerler için yeterli bir düzeltme verdiği görülmüştür. Böylece; bu çalışmada verilen blokaj düzeltmesi yönteminin uygulanması ile, model deney tanklarındaki sonuçlardan, sınırsız suda var olması gereken direnç değerleri kolaylıkla elde edilebilir. 5. Bölümde çalışmadan elde edilmiş olan sonuçlar kısaca sıralanmıştır.

VI SUMMARY The aim of this study is to investigate the effect of the side walls and the bottom of a channel on the resistance of a moving body. The effect of the side walls and the bottom of a channel on the resistance of a moving body is briefly called `The Blockage Effect`. The resistance in unrestricted water can be easily determined from the variation of the resistance in a channel by the method presented in this study. By using this method, the variation of the resistance in another channel can be determined from the resistance in unrestricted water or in a channel. In the First Section, the importance öf the blockage effect on the ship model experiments, has been explained. To reduce the errors that could arise from various effects, the models are required to have the largest possible dimensions. But, in that case, the blockage effect. ??.:..--.. causes an error of a quite different nature. In this research; the correlation methods of the results of ship model experiments in a channel have been studied from the blockage effect point of view. In the Second Section, the relevant literature in the ; field have been reviewed. These experimental or theoretical studies are mostly directed to determine the velocity - increase or the velocity increase ratio arising from blockage effect. Around a body that moves in channel with the velocity (U), a flow occures similar to the flow around the same body moving in unrestricted water with the velocityVII (U.+Au).. If this increase öf velocity (Au) could be determined, the resistance in a. channel at a velocity (U) can be taken approximately equal to the resistance in unrestricted water at the velocity (U+Au). The studies at the literature have mostly determined the ratio (Au/U); from the experimental data or assuming a mean flow around the model. In the Third Section, the various methods aiming at the simple and correct determination of the velocity increase have been tested. At the conclusion, a method giving rather close results to the experiments has been obtained by the application of the slender body approximation to an ellipsoid of revolution. The bodies which have the same maximum cross-sectional area, length and velocity are assumed to be equivalent to each other, from the blackage point of view. Thus, an equivalent body of revolution has been. taken into account in the actual computations instead of a corresponding ship model. The body of revolution has been selected either as a Rankine*s ovoid or as an ellipsoid of revolution. In the Paragraph 3.1 the motions of Rankine's Ovoid have been studied in detail, for the following three cases: 1) The motion in unrestricted water (without a free surface), 2) The motion in unrestricted water below the free surface, 3) The motion in a rectangular channel with a free surface. In this paragraph, the velocity potential (Green's- function) for a unit source moving below the free surface has been given and used. Also, a method for the integration has been given to evaluate the singular double integral which appears in the computation of the velocity potential and its derivatives. This method evaluates the integral by choosing an appropriate integration contour and using the necessity of real-valuedness. Wave heights obtainedVIII have been compared with the literature and a very good aggreement: has been observed. Later in the paragraph the component tu-<J>x) of the velocity field developing around the body and at the free surface when Rankine's ovoid moves in a channel» hâs been calculated by the application of the method of images. The calculated velocity increases have been seen to be very close to the increases obtained by the application of slender body approximation. la the Paragraph 3.2 the motions of an ellipsoid of revolution in unrestricted water without a free surface and in unrestricted water below the free surface have been studied. The numerical results show that the wave heights for similar Rankine*s ovoid and ellipsoid of revolution are in the same order of magnitude. Here the ellipsoid of revolution has been represented by a source- sink distribution ($xU) between foci. For the execution of numerical computations, the distance between foci of ellipsoid has been divided into even number of equal parts. The precision of the results depends on the number of divisions. If the method of images is used to determine the motion of an ellipsoid in a channel the required computation time increases exceedingly. For this reason, the velocity increase for the ellipsoid in the channel has been computed by the slender body approximation. In the Paragraph 3.3, the velocity increase for a -moving ellipsoid of revolution in a rectangular channel. has been formulated by means of the slender body approximation. By some arrangements, a formula has been obtained. By using this formula the velocity increases in various channels at various velocities have been computed numerically. By employing the obtained numerical results and applying the curve fitting by least squares method, a velocity increase formula has been obtained as; tl.m £u=- =- { £2.356-18. 101 mt 90.975 m2] A-yI h + 0-0.466-6.179 m -88. 280 m2J Fh 4- [1.0484 7.273 m+ 66.246 m2] F2 }.. hIX m A body channel ü F. h 'gh In this foramla; the velocity increase has been written as a function of the blockage ratio and the depth Froude number. In the Fourth Section; the resistance variations of a number of models in different channels have been obtained experimentally and these results have been compared with each other. In the experiments, the circulating water channel of Shipbuilding Research Center (The Faculty of Naval Architecture and Ocean Engineering, Technical University of Istanbul) has been used. The wooden bulkheads have been placed parallel to the flow in the circulating water channel. By changing the gap between them and choosing the appropriate water level to keep height to breadth ratio always equal to (1/2), six different channel sections have been obtained. In the circulating water channel, the model is kept stationary connected to the measuring dynamometer while water runs around it. Thus, the relative motion of the model is as if it moves in a channel of infinite length. The circulating water channel has a lot of advantages like; long experimenting time, better vision and stationary measuring devices. But, on the other hand, it has the following incoveniences : 1) Improbability of an exactly uniform flow, 2) Small dimensions, 3) Impossibility of obtaining high velocities. The above-mentioned circulating water channel has been used for the first time in the experiments of this study. Thus, some preparations had to be performed. For example;X 1> The Pitot Tube which is used to measure the flow velocity has been calibrated at the Towing Tank» 2} For damping the waves occuring at the test region» a device that consists from two parallel plates, has been developed,. 3) Because of the non-uniform velocity distribution, the region where the Pitot tube and model has to be maintained» must be determined at the outset of the experiments. For this purpose, the velocity distribution of the channel has been found out by the direct measurements at different points. Following this, by using the measurements performed, the velocity isolines of various channel cross-sections have been drawn. Further, the velocity profiles alongside the straight lines both perpendicular and parallel to the free surface have been graphically displayed. By careful examination of data and above-mentioned diagrams the most appropriate place for Pitot tube has been selected. Pi tot tube must be placed at a distance of (25-50 cm) from the model's bow submerged at the mid-depth. Six ship models with different forms have been tested both in the circulating water channel and in the towing tank, and resistance curves have been obtained. The dimensions of the towing tank are very large compared to the dimensions of models used; so it can be taken as unrestricted water. By applying the above-explained blockage correction method and velocity increase formula to the experimental resistance results in channel, the modified resistance curves have been obtained which display a very good correlation with the resistance curves of the towing tank. Also, one of these ship models and an ellipsoid of revolution have been tested in the six different sections obtained by placing bulkheads in the circulating water channel, and the resistance values have been compared with the results of the towing tank. As an outcome of these comparisons, the velocity increase formula and blockage correction methods given above have been seen to be sufficiently correct for the blockage ratios up to m = 0.0636.XL In the Fifth Section, the results obtained in this research have been outlined. These can be summarised as follows : 1) Wave heights of the Rankine's ovoid can be calculated by using the integration method given in the Paragraph 3.1.3. A similar method, can be used for the evaluation of the velocity potential as well as its derivatives. 2) The method of images can be applied to determine the motion of the bodies in channels. But, in this case, the computation time may increase exceedingly. 3) Taking a source-sink distribution (3xU) between foci, as kinematical equivalent of an ellipsoid of revolution, is a good approximation. 4) If the above-mentioned blockage correction method and velocity increase formula are applied to blockage ratios up to ( - 0.064), the resistance variations in the unrestricted water can be obtained with an excellent approximation. 5) The arrangements made at the circulating water channel have been proven to be suitable. The modified test results obtained by applying the blockage correction to the experimental values measured in the circulating water channel can be reliably used. 6) At very large blockage ratios (m > 0,064) the given blockage correction method becomes insufficient.