Gemilerin parametrik yalpa rezonansının 2.nesil stabilite kurallarına göre değerlendirilmesi
Evaluation of parametric roll resonance of the ships according to second generation stability rules
Yazar: BUĞRA UĞUR YAZICI
Danışman: PROF. DR. METİN TAYLAN
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Gemi İnşaatı ve Gemi Makineleri Mühendisliği Ana Bilim Dalı / Gemi Makineleri Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2018
Konu: Gemi Mühendisliği = Marine Engineering

Özet:
Gemilerin güvenli bir biçimde seyredebilmesi ve taşıdığı personel ile yükün güvenli bir şekilde istenilen yere sevkedebilmesi gereksinimi, gemi inşaatı mühendislerinin gemilerin tasarım aşamasından üretim aşamasına kadar uyması gereken kuralların ortaya çıkmasını sağlamıştır. Böylelikle uluslararası kuruluşlar tarafından gemilerin uyması gereken stabilite kuralları ortaya konulmuştur. Bu kurallar 1969 tarihinden itibaren IMO (International Maritime Organization) A.167 önergesiyle yürürlüğe konulmuştur. Gemi üzerine dışarıdan etkiyen kuvvetlerin de stabilite hesabına katılması amacıyla 1985 yılında A.562 önergesiyle hava kriteri yürürlüğe konulmuştur. 1993 yılında A.749 önergesiyle ilk kez bir araya getirilen bu kurallar, daha sonra MSC (Maritime Safety Committee) tarafından 2008 yılında IS Code (Intact Stability Code) - hasarsız stabilite kuralları olarak 24 metre ve üzeri gemilere uygulanacak şekilde kabul edilmiş ve 1 Temmuz 2010 tarihinden itibaren yürürlüğe konulmuştur. Ancak devam eden süreçte yaşanan kazalar, bu kuralların gemi stabilitesini değerlendirmek için yeterli olmadığı sonucuna varılmasını sağlamış ve ikinci nesil stabilite kurallarının oluşturulması gerektiği fark edilmiştir. 
Bu çalışmada IMO tarafından taslak çalışmaları yapılan ikinci nesil yeni nesil stabilite konularından bir tanesi olan parametrik yalpa rezonansı çalışmalarının, mevcut gemiler üzerindeki etkisinin görülebilmesi için bir tasarım ve analiz ortamı oluşturulmuştur. İleride bu parametrik yalpa rezonansı değerlendirmesi yapmak isteyen araştırmacı ve mühendislere yol gösteren bir rehber olabilmesi amacıyla, karşılaşılabilecek zorluklar ve soru işaretlerinin ortadan kaldırabilmesi amaçlanmıştır. Bu kapsamda, güncel taslak kurallar ışığında, parametrik yalpa rezonansı zafiyet kriteri seviyeleri 1 ve 2 detaylı bir şekilde incelenerek adım adım yapılması gerekenler anlatılmıştır.
Bu çalışmanın ilk olarak, ikinci nesil stabilite kuralları ile getirilmesi planlanan parametrik yalpa rezonansı kriteri ve stabilite kurallarının tarihi gelişimi incelenmiştir. Sonrasında, parametrik yalpa rezonansının fiziksel olarak nasıl geliştiği ele alınmıştır. Üçüncü ve dördüncü bölümde parametrik yalpa rezonansı kriterleri ve bu kriterlerin sayısal olarak nasıl çözülebileceği üzerinde durulmuş ve son bölümde parametrik yalpa zafiyet seviyeler içerisinde bulunan kriterlerin çözümleri için uygulama yapılmıştır.

Abstract:
The need to safe navigation of ships and secure transportation of its load and its personnel to the targeted destination necessitated the development of rules that shipbuilding engineers have to comply with including at the design stage and production stage. Thus, the stability rules that the vessels must comply with are set forth by international organizations. These rules have been enacted by A.167 resolution of IMO (International Maritime Organization) starting from 1969. The weather criterion was put into force in 1985 with A562 in order to include the external forces acting on the ship in the stability calculation. All these rules were combined under A.749 resolution in 1993 and were later accepted by the MSC (Maritime Safety Committee) in 2008 as IS Code (Intact Stability Code) applicable to ships over 24 meters. A.749 resolution has been put into effect on July 1, 2010. However, the ongoing accidents have led to the conclusion that these rules are not sufficient to assess ship stability and it has been recognized that the second generation stability rules must be established.
The purpose of this study is to establish a design and analysis environment for the parametric roll resonance, one of the second generation next generation stability issues, to be undertaken by IMO as a draft study, to determine the effect on existing ships. It is aimed to remove the difficulties and questions that may be encountered in the future in order to be a guide to researchers and engineers who want to evaluate the parametric roll resonance. In this context, the parametric roll resonance failure criterion levels 1 and 2 are examined in detail in the light of the current draft rules.
As an initial research, historical evolution of the stability rules and the parametric roll resonance phenomenon which are planned to be originated from second generation intact stability rules are analysed. As a further analysis, physical evolution of the parametric rolling resonance phenomenon is examined. In the third and the fourth sections, parametric rolling resonance phenomenon criteria and their numerical resolution are elaborated and in the last section, a case study is given for the solutions of the criteria in parametric rolling vulnerability levels. As a result of the investigations, it could be seen that the rules of 2nd Generation Stability Code are based on operational/performance data whereas intact stability rules are based on experimental and statistical data. In consequence of APL China, MV Aratere and Chicago Express accidents, it was concluded that the parametric roll resonance can damage the cargo, cargo and personnel. In this context, the SLO group was established by the IMO in 2002 and the development of the second-generation stability rules started. The first important studies carried out have been in the SLF 48th session held in 2005. When evaluating the 2nd stability criteria, three types of stability faults have been addressed as restoring arm variation problems, stability under dead ship condition and maneuvering related problems. Parametric roll resonance is considered within the problem of restoring arm variation among these error types.
As a further analysis, physical evolution of the parametric rolling resonance phenomenon is examined. In the third chapter, definition and development of parametric rolling resonance are discussed. The period of wave encounter with varying speeds of a ship navigating in longitidunal waves is changing. Where the wave encounter period is equal to two times the natural frequency of the ship, a parametric roll resonance can occur.
When the ship is making a roll motion, the amount of restoring moment applied to the ship will be greater because the area under the GZ curve is higher when the roll movement reaches the maximum amplitude towards the starboard / port side if the ship is in the wave trough. When the ship even reaches the keel position, the wave crest is positioned in the midship section and the area under the GZ curve is reduced because the roll period equals twice the wave encounter period. For this reason, the resistance to the restoring moment, which is relatively higher than that encountered in the wave crest, is reduced. The ship starts to roll in the opposite direction to complete the roll movement. At the point where the rolling amplitude is maximum, more restoring moment is applied since the ship will be in the wave trough again. Since this movement is carried out periodically, after each roll movement, the rolling amplitudes start to increase. Therefore the ship is exposed to the parametric roll resonance.
In the fourth chapter, parametric rolling resonance phenomenon criteria and their numerical resolution are elaborated. The solution methods for the vulnerability levels 1 and 2 proposed by IMO for the parametric roll resonance are explained. When calculations for vulnerability criterion 1 are made, the ship's calm water GZ value is first calculated. Later, for the sinusoidal wave form, the wave length value is taken equal to the vessel length and the wave height is taken equal to 0.0167 times the vessel length. After that wave crest is located 10 different position equally and longitudinally placed on the ship. The arithmetic mean is the difference between the maximum and minimum GM values within these 10 values. If the ratio between the GM difference value and the calm water GM value is calculated above the critical value, vulnerability to the parametric roll resonance is considered to exist.
When the level 2 criterion 1 is calculated, GM variability calculations and critical speed calculations are handled. If any one of these two calculations is provided, vulnerability to the parametric roll resonance is considered to exist. The GM variation calculation is the same as the method given by level 1 criterion 1, but the difference is that the wavelength and wave heights vary. There are 16 different wavelengths and wave heights in the proposed method.
Critical speed calculations are based on the comparison of the given critical speed formula with the service speed of the ship.
The level 2 criterion 2 is different from the conventional ship stability calculations. Here, the differential equation, expressed as the Mathieu equation, needs to be solved. For this purpose, assuming that external forces are at negligible level at longitudinal regular waves; acceleration, velocity and moment of inertia must be calculated.
In order to be able to calculate accelerations from these terms, it is necessary to calculate the moment of inertia of the ship and additional water mass moment terms. For this purpose, these terms are calculated using the empirical formulas defined in the IS Code, if the terms of inertia and additional water mass calculated using numerical methods are not available.
Two different methods have been proposed for roll damping corresponding to the speed term. The first is that the coefficients corresponding to the linear and cubic coefficients of the roll amplitude are calculated before the solution of the differential equation. Another solution is to solve the differential equation by recalculating the equivalent damping coefficient at each solution step.
By using Ikeda's simplified method to calculate the roll damping terms; wave damping, lift damping, friction damping, eddy making damping and bilge keel damping. The values found are normalized and used in the differential equation.
The quasi-static method is used to calculate the restoring arm moment term. With the position of the wave crest shifting along the ship, GZ calculations are made for the condition corresponding to each wave crest position. The calculations are carried out by means of the values read out over the surface created by the cubic interpolation of the values obtained by the rolling angle of 5 degrees between 90 and 90 degrees. In this case, the restoring arm moment is obtained at each of the solution steps of the differential equation as a result of the use of the varying wave crest position as a parameter depending on the roll amplitude value and the wave encounter period in the previous iteration step.
In the seventh chapter, the proposed method for numerical solution of the differential equation is explained. In order to be able to perform calculations using the Runge-Kutta 45 method, it is necessary to reduce the degree of the Mathieu equation, which is in the form of the second ordinary differential equation. How to do this is given in detail.
In the eighth chapter, a description of the solution environment created by the computer softwares used in this study has been made. Geometric hull form and its general characteristics were defined and information was given on how to make panel meshes for stability calculations, which analysis method was used for hydrostatic calculations, and the necessary procedures for solution.
In the last section, a case study is given for the criteria of parametric rolling vulnerability levels. As a result of the work done, the solutions created within the scope of this study are compared with the benchmark results made by IMO and the validation of the code with relatively low differences is ensured.