Hidrofoillerin kavitasyon kovalarının sayısal-parametrik incelenmesi
Numerical investigation cavitation buckets for hydrofoil parametrically
Yazar: MEHMET SALİH KARAALİOĞLU
Danışman: PROF. DR. ŞAKİR BAL
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Gemi İnşaatı ve Gemi Makineleri Mühendisliği Ana Bilim Dalı
Derece: Yüksek Lisans, 2015
Konu: Gemi Mühendisliği = Marine Engineering

Özet:
Kavitasyon lokal basıncın, ortam sıcaklığındaki buhar basıncının altına düşmesi durumunda meydana gelen fiziksel bir olaydır. Sabit sıcaklıktaki bir akışkanın lokal basıncı (p) doymuş buhar basıncının 〖(p〗_v) altına düşmesi durumunda akışkan yapısı parçalanmaya başlar. Bu olaya "kavitasyon" denir. Kavitasyon pervane dümen, stabilize için bulunan finler, pompa ve türbin kesitlerinde meydana gelebilir.
Bu çalışmada sınır elemanları yöntemi ile (Boundary Element Method-BEM) iki boyutlu hidrofoiller üzerindeki basınç dağılımları hesaplanıp kavitasyon kova diyagramları (zarf eğrileri, kavitasyon bukleleri) elde edilmiştir. Her bir durum, kavitasyon başlangıç durumu ve kısmi kavitasyon durumu için ayrı ayrı incelenmiş elde edilen sonuçlar birbirleri ile karşılaştırılmıştır. 
Çalışmada iki boyutlu hidrofoil olarak dört basamaklı NACA foil geometrileri ve bir sualtı türbinine ait S184 geometrisi kullanılmıştır. NACA foil geometrisini temsil eden 4 basamaklı sayı dizisindeki her bir rakam geometrik olarak bir değişkeni temsil etmektedirler. Bu çalışmada mevcut parametreler sistemli olarak değiştirilip farklı geometriler elde edilmiştir. Elde edilen her bir geometri için kavitasyon kova diyagramı hesaplanıp bu parametrelerin bu diyagramlara etkisi analiz edilmiştir. Bu analizler sonucunda hidrofoilin hangi durumda kavitasyon yapıp yapmadığı tayin edilmeye çalışılmıştır. 
Kısmi kavitasyon durumu incelenirken kısmi kavitasyon yapmaya müsaade eden bir panel yöntemi PCPAN kullanılmıştır. PCPAN programında kavitasyon boyu girdi olarak tanımlanır ve kavitasyon sayısı iteratif bir şekilde bulunur. Bu kısımda kavitasyon boyu l/c=0.5 ve l/c=0.7 için incelenmiştir. Kısmi kavitasyon için kavitasyon boyunun kord boyunun 3/4'üne eşit olduğu durum fiziksel olarak özel bir anlam taşır. Kavitasyon sayısı küçüldükçe kavitasyon boyunun arttığı bilinmektedir. Foil için kavitasyon sayısı küçüldükçe kavitasyon boyu artar. Fakat kavitasyon boyunun 3/4'üne yaklaştığında kavitasyon sayısı küçülse dahi kavitasyon boyu artmamaktadır. Bu durum kavitasyon sayısının bir sınırı geçmesine kadar böyle devem eder. Bir değerden sonra yeniden kavitasyon sayısı küçülterek kavitasyon boyu artırılabilir. Fiziksel olarak stabil olmayan bu nokta için kavitasyon kova diyagramı elde edilerek bu özel durum incelenmesi amaçlanmıştır. Fakat PCPAN programı kavitasyon boyu 0.75c tanımlandığında doğru çalışmamaktadır. Bu durumda programın doğru çalıştığı 0.75c noktasına en yakın değer olan 0.7c için hesaplar yapılmıştır.
Son olarak ise bir sualtı türbini kesitine ait olan S184 geometrisi kavitasyon başlangıç durumu için incelenmiştir.

Abstract:
Cavitation is defined as the process of formation of the vapor phase of a liquid when it is subjected to reduced pressures at constant ambient temperature.
Cavitation occurs not only at propellers but everywhere where locally high velocities appear, e.g. at rudders, shaft brackets, struts, sonar domes, hydrofoils, stabilizing fins, pump, turbine. Cavitation is a result of the pressure reduction. So cavitation can be prevented or the severity reduced with pressure control. Cavitation occurs in areas where pressure values vary sharply. It is an undesirable phenomenon in many engineering application due to the detrimental effects of cavitation such as erosion (in the case of developed cavitation if the velocity difference between the liquid and the solid wall is high enough), noise, alteration of the performance of the system (reduction in thrust of propeller, increase in drag of foil, etc.) and vibration caused by the growth and collapse of vapour bubbles. Vibration and noise arising from cavitation are serious problem especially types of ships where sonar device. 
Cavitation may be classified by location (tip cavitation, root cavitation, leading edge or trailing edge cavitation, suction side (back) cavitation, face cavitation etc.), cavitation form (sheet cavitation, cloud cavitation, bubble cavitation, vortex cavitation), dynamic properties of cavitation (stationary, instationary, migrating). 
In the present thesis, cavitation was analyzed using bucket diagram. Bucket diagram represent the cavitation behavior of a blade section in a two dimensional sense. This diagram is plotted as a function of section angle of attack (α) versus section cavitation number (σ). The width of the bucket (α) is a measure of the tolerance of the section to cavitation free operations. Whilst useful for design purposes the bucket diagram is based on 2D flow characteristics and can be therefore give misleading results in areas of strong 3D flow; for example near the blade tip and root. Four regions that make up the bucket diagram, can be identified; 1. Cavitation free area inside the bucket. 2. Back sheet outside the upper part of bucket 3. Face cavitation outside the lower part of bucket 4. Bubble cavitation outside the side of bucket.
In the present thesis, pressure distribution is calculated on two dimensional geometry of hydrofoil through BEM (Boundary element method) and cavitation bucket diagram is plotted. Each case is analyzed for cavitation inception case and partial cavitation case and obtained results were compared with each other. Constant source-dipole panel method is used to calculate pressure distribution at cavitation inception case. 
PCPAN programme is used to calculate pressure distribution at partial cavitation case. PCPAN, is the code prepared by the FORTRAN programming language that sheet cavitation on the hydrofoil solves potential based panel method code. Sheet cavitation is solved by low-order potential based boundary element method in non-linear theory. PCPAN solves the 2D fixed-length partial cavitation problem. In PCPAN, cavity length, angle of attack (α) hydrofoil geometry, maximum iteration number are defined as programme input. The cavity shape, the foil lift and drag and cavitation number are all output. The exact nonlinear solution is found by the iterative method. Some simplifications have been made to create the numerical model. Numerical model of PCPAN results from the following simplifications:
	Flow is steady an incompressible.
	All types of cavitation is neglected except sheet cavity.
	No mass flux between cavity and flow.
	Cavity height is zero at cavity leading and trailing edges.
	Cavity length is fixed.
	Pressure is constant on the cavity surface
Inside of cavitation bucket is cavitation free area. Partial cavitation condition has been investigated for two different cavitation length ( l = 0.5c  and  l = 0.7c ). In all cases examined; l =0.7c  cavitation bucket curve wider than  l =0.5c  cavitation bucket curve. In the section of partial cavitation, the inner part of curve is safe area for specified length of cavitation. For example; cavity whose length is equal to 0.5 times chord length inside area of l=0.5c  curve. It is not clear whether occurring shorter cavity inside l=0.5c cavitation bucket.

In this study the four-digit NACA foil geometry and a two-dimensional hydrofoil S184 of marine current turbine geometry is used.
In the early 1930s, the National Advisory Committee for Aeronautics constructed airfoil series rationally and systematically.  The geometry of the NACA airfoil is defined by means of logical numbering system.  Each digits described parameter of geometry. Maximum camber as percentage of the chord is described first digit.  The distance of maximum camber from the airfoil leading edge in tens of percents of the chord. (For NACA2412 maximum camber 0,02c; location of maximum camber along the chord from the leading edge 0,4c; maximum thickness 0.12c.) Different geometries are obtained by changing this three parameters in a systematic way.  The effect of three parameters are analyzed by comparing cavitation bucket diagrams for each geometry. As a result of analysis, geometry which whether to occur cavitation or not, is determined.
Underwater currents that have potential for power generation. The marine current turbines (MCTs) exploit underwater currents for energy generation. Cavitation is usually seen in each of the turbine blades. It is certainly a case to be considered in the MCT's performance analysis. In this study S184's bucket diagram was plotted and analyzed. 
The analysis obtained as a result can be listed as follows. 
	Effect of maximum thickness ratio varies depending on the range of    〖-C〗_P. This result is the same for partial cavitation condition and cavitation inception condition.
	For cavitation inception condition, risk of cavitation reduced as increasing chamber ratio in positive angle of attack. Conclusion is not reached about chamber ratio for partial cavitation condition.
	Partial cavitation condition has been investigated for two different cavitation length (l/c=0.5 and    l/c=0.7). The results are the same features for both cases.
	When S184's geometry is observed, maximum chamber is close to trailing edge. Minimum cavitation risk for marine current turbines is provided by being close to trailing edge.