Darpa suboff formunun lineer hidrodinamik katsayıları üzerindeki ölçek etkisi
Scale effects on the linear hydrodynamic coefficients of darpa suboff
Yazar: FURKAN KIYÇAK
Danışman: PROF. 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, 2023
Konu: Gemi Mühendisliği = Marine Engineering

Özet:
Gemiler, kullanılış amaçlarına göre dört farklı ana gruba ayrılmaktadır. Bunlar açık deniz araçları, yatlar, ticaret gemileri ve askeri gemilerdir. Askeri gemilerin diğer gemilere göre farklı yapıları ve donanım ilkeleri olsa da, askeri gemiler içerisinde denizaltılar, hem üç ana gruba göre hem de diğer askeri gemilere kıyasla oldukça özgün ve spesifik tasarım özelliklerine sahiptir. Gelişmiş ve gelişmekte olan ülkelerin savunma sanayilerine yaptıkları yatırımlar ise, askeri gemiler ile denizaltılar konusundaki çalışmaları beraberinde getirmektedir. 
Öte yandan, teknolojinin gelişmesi ile harp gemisi tiplerinde de önemli değişiklikler olmuştur. Eski zamanlarda tercih edilen kalın zırhlı ve tonajı büyük savaş gemileri yerine tonajı daha küçük, vurucu gücü yüksek silahlarla donatılmış ve manevra kabiliyeti yüksek olan gemiler tercih edilmeye başlanmıştır. Teknolojik gelişmelerin bir diğer faydası ise bilgisayar kapasitelerinin artması sonucunda hesaplamalı analizlerin hassasiyetinin artmasıdır. Hidrodinamik dizayn, tasarlanan su aracının görevlerini  yerine  getirmesinde etkin bir rol oynamaktadır ve bu sebeple söz konusu hassasiyet artışı gemi hidrodinamiği alanında önemli gelişmelere yol açmıştır. Bilindiği üzere, manevra, gemi hidrodinamiği disiplininde önemli bir yer tutmaktadır ve dolayısıyla gemi manevra kabiliyetinin doğru hesaplanması özellikle askeri projelerde seyrüsefer güvenliğinin sağlanması açısından gereklidir. Manevra hesaplarının yapılabilmesi ve geminin gerekli dizayn kriterlerine sahip olup olmadığının tespiti ise hidrodinamik katsayıların doğru bir şekilde hesaplanmasını gerektirmektedir.
Gemi hidrodinamiği analizlerinde ampirik yöntemler, deneysel yöntemler ve hesaplamalı akışkanlar dinamiği (HAD) kullanılabilir. Askeri projelerde yapılan çalışmalar genelde gizli tutulup toplum ile paylaşılmadığından ampirik yöntemler genellikle kullanışlı değildir. Bu noktada model deneyleri oldukça kullanışlıdır ancak bunun yanında pahalı ve zaman alıcıdır. Hesaplamalı akışkanlar dinamiği yöntemi ise ampirik metodlara göre daha güvenilir, model deneylerine göre ise daha ucuzdur; bu sebeple kullanımı gittikçe yaygınlaşmaktadır. Hesaplamalı akışkanlar dinamiği, araştırmacılara özellikle tasarım  aşamasında önemli  bulgular sağlayıp zamanında önlem alma imkanı sunmaktadır. Böylece dizayn edilecek olan deniz araçları  için bir  ön fikir sahibi olma imkanı tanımaktadır.
Bir gemiye etki eden hidrodinamik kuvvet ve momentler, Froude ve Reynolds sayılarının fonksiyonlarıdırlar. Su altına batık cisimler için, uzak kalan serbest su yüzeyi nedeniyle Froude sayısı önemsizdir; bu nedenle, bu kuvvetler yalnızca Reynolds sayısına bağlıdır. Bu çalışmada, literatürde kapsamlı bir şekilde çalışılan ve deneysel sonuçları açık literatürde yayınlanmış 'DARPA' Suboff formu çıplak gövdesi ele alınmıştır. Bu formda manevra türevleri üzerindeki ölçek etkileri Reynolds sayısına göre incelenmiştir. Bu kapsamda denizaltının çıplak gövde formu üzerinde sayısal çalışmalar yapılmıştır. Sayısal analizler, statik sürüklenme ve döner kol deneylerini kapsamaktadır. Bu tez kapsamında, öncelikle, RANS tabanlı HAD aracılığıyla sonlu hacimler yöntemi kullanılarak 12 farklı Reynolds sayısında ve 6 farklı drift açısında statik sürüklenme deneylerinin simülasyonu yapılmıştır. Daha sonrasında ise 12 farklı Reynolds sayısında ve 5 farklı r'max değerinde döner kol testleri baz alınarak safi savrulma simülasyonları gerçekleştirilmiştir. Literatürde geçen MMG matematik modeli yardımıyla lineer hidrodinamik katsayılar, Reynolds sayısının bir fonksiyonu olarak logaritmik denklemlerle ifade edilmiş ve geminin model ölçeğine bağımlılığı açıkça gösterilmiştir. Elde edilen bulgular, model deneyi sonuçları ile karşılaştırılmış ve hata oranları belirlenmiştir. 
Bu çalışma, bundan sonra DARPA ve benzeri formlar üzerinde yapılacak manevra analizlerinde, elde edilen genelleştirilmiş denklemler yardımıyla doğrudan lineer hidrodinamik katsayıları elde etme olanağı sağlamıştır.

Abstract:
Ships can be classified into four main categories based on their intended use, namely offshore vessels, yachts, commercial ships, and military vessels. While naval vessels differ from other ships in terms of structure and equipment principles, submarines within the naval category have unique design features that set them apart from both the other main groups of ships and other types of naval vessels.
Developed and developing countries invest heavily in defense industries, leading to extensive research on military ships and submarines. Technological advancements have also brought significant changes to warship types. Instead of heavily armored and high-tonnage warships, smaller ships equipped with powerful weapons and high maneuverability are now preferred.
Although underwater vehicles are standardized on a class basis, they are mostly designed for military purposes, so their geometry is kept secret and not shared with the public. To solve this problem, many organizations have tried to build literature by providing generic geometries reflecting the standard geometric properties of underwater vehicles and paving the way for scientific studies on underwater vehicles in the academic world. In this way, generic forms have become frequently used in scientific studies. An example of this is the DARPA Suboff. Although there are different configurations, ITTC recommended researchers use bare hull (AFF-1) and full-appended (AFF-8) configurations. DARPA has pioneered scientific studies on underwater hydrodynamics and provided the opportunity to compare experimental results with the results obtained as a result of studies using empirical and numerical methods.
It is especially important to determine the maneuver characteristics of submarines operating with limited energy, which affect their warfare capabilities and navigational safety, from the preliminary design stage, for the submarines to fulfill their duties and to maintain the trajectory determined during the mission. A submarine has three modes of operation. These are the water surface operation mode, the snorkel depth operation mode, and the deep water operation mode. The submarine spends most of its operational time submerged in deep water, where it performs its main functions. Therefore, it is aimed to have high maneuverability, especially in deep water operations. To examine the maneuvering performance of the submarine, regardless of its operational status, the hydrodynamic forces and moments that occur due to the motion of the solid body in the fluid and which are seen as derivatives or coefficients in the maneuvering motion equations must be accurately calculated at the preliminary design stage.
The calculation of hydrodynamic coefficients is crucial to meet design criteria, and various methods can be employed to analyze hydrodynamics in the shipbuilding industry, including empirical methods, model experiments, and computational fluid dynamics (CFD).
In empirical methods, formulations are usually expressed as a function of parameters such as form properties, velocity, and main dimensions. Empirical methods are predictive methods, they are based on experimental-navigation experience and can be used in the preliminary design phase. Empirical methods are a suitable method to observe the effects of the frequently changing form on the hydrodynamic coefficients during the preliminary design phase.
Although empirical methods seem attractive to users who want to perform hydrodynamic analysis with their advantages such as being fast, low cost, practicality and easy to apply, it should be noted that these methods only provide superficial information at the preliminary design stage and their sensitivity is low. If the method is not used within the limits, there is a high probability of obtaining completely erroneous results. There are also empirical formulas for obtaining the maneuvering coefficients in terms of main dimensions, but the results are generally not satisfactory. It is very difficult to use empirical methods when performing hydrodynamic analysis of an underwater vehicle such as a submarine because the studies and test-navigation experiences related to the submarine are generally kept confidential and not shared with the public.
Although it is a known fact that experimental methods are more reliable than other methods and provide detailed information about flow dynamics, they are not always preferred due to constraints such as their high cost, the need for a long time to get results, and the need for a sufficient experience of the personnel who will perform the experiments. Although it is accepted that the experimental methods give the most realistic results, they may include errors made during the setup phase of the experiments, errors caused by measuring devices, or human errors.
In maneuvering problems, captive test methods are used to obtain hydrodynamic coefficients. These methods involve forcing the form at a certain scale to make predetermined movements depending on a motion mechanism to obtain the hydrodynamic forces and moments on the form. By using the hydrodynamic forces and moments obtained as a result of the experiment, the hydrodynamic coefficients are obtained using the mathematical model. Although there are many types of experiments in maneuvering problems, these two types will be mentioned because static drift test and rotating arm mechanism are both widely used and simulated in this thesis.
Static drift tests help calculate the necessary coefficients to estimate the maneuverability of the ship. The most basic experimental method in maneuver analysis is static drift tests and is a time-independent method. As a result of this test, the sway force and yaw moment depending on the linear velocities formed on the form pulled at constant speed at certain drift angles are calculated and thus static maneuvering derivatives are obtained. Static drift tests are carried out in the towing tank. One of the experimental methods used is the rotary arm mechanism, which is a time-independent method that enables the calculation of rotational coefficients. In this experiment, the model is attached to the model using a rotating arm placed from the center of a circle towards the arc of the circle, and rotational motion is made around the circle. As a result of this test, the sway force and yaw moment on the form which is rotated at constant angular velocity and certain rotational diameters are calculated and thus rotational maneuver derivatives are obtained.
The fact that hydrodynamic analyzes based only on empirical methods generally do not seem sufficient and reliable, and experimental methods are expensive and require long setup times, encourage researchers to use numerical methods. Parallel to this, the capabilities of the software used within the scope of CFD are also increasing, and with the advancement of modern CFD techniques, it is believed that the method gives very accurate estimates. These software have also given the academic world the advantage of testing the accuracy of the findings by comparing them with the findings obtained by conducting experiments. Thanks to CFD, researchers can obtain important information, especially during the preliminary design phase, and with the help of this information, an idea about the vehicles planned to be designed can be obtained.
In the scope of CFD, while determining the hydrodynamic coefficients in the maneuvering problems of water vehicles, it includes the simulation of the experimental methods with restricted motion in a computer environment. In addition to being more reliable than empirical formulas and cheaper than model experiments, it is also possible to analyze full-scale Reynolds numbers with CFD. Another advantage of CFD over model experiments is that it can perform the necessary predictions without the support braces required for fixed model experiments.
Obtaining the hydrodynamic coefficients starts with obtaining the hydrodynamic forces and moments on the form in which the experiment is applied using the mechanism in experimental methods, and the hydrodynamic forces and moments on the form in which the simulation is applied in CFD. Then, the hydrodynamic coefficients are calculated with the help of a mathematical model accepted as suitable for experiments or simulation. In the literature, two different methods are generally suggested for the mathematical model to be used for maneuvering problems. These are defined as the Abkowitz model, which is a hydrodynamic coefficient-based model, and the Maneuver Modeling Group model, which is a modular-based model.
The Abkowitz model is based on the third-order Taylor series expansion of hydrodynamic forces and moments. In this model, the water vehicle is considered as a whole, and a non-linear approach is used in the calculation of hydrodynamic forces and moments. The MMG model divides the hydrodynamic forces and moments into three components: the bare hull, rudder, and propeller, and considers the interaction between these three components. In the thesis study, the MMG mathematical model was taken as a basis.
As well known, forces and moments acting on a ship are functions of Froude and Reynolds numbers. As a ship gets larger in size, these two numbers grow, which leads to different flow regimes around the hull. Recently, internal and external factors affecting the hydrodynamic coefficients, which are the expressions of these forces and moments in terms of coefficients, have been the subject of research, and especially the scale effect has become the focus of attention of researchers. In maneuver calculations, the hydrodynamic coefficients are considered constant for model and full ship scales. However, although it is undesirable for the scaled form to affect the results, there is no method developed to get rid of the scale effect. 
For submerged bodies, the Froude number is insignificant due to the distant free water surface; therefore, these forces only depend on the Reynolds number. In this study, we consider the benchmark 'DARPA' Suboff form, which is extensively studied in the literature, and investigated the scale effects on the hydrodynamic coefficients with respect to the Reynolds number. Numerical studies are carried out on the bare hull form of the submarine. Captive motions of static drift and pure yaw motions are conducted utilizing the static drift and rotating arm tests via RANS-based CFD. Linear hydrodynamic coefficients are expressed with logarithmic equations as functions of the Reynolds number, explicitly showing the dependency on the ship's model scale.
As a result of the study, although the results in the Yv', Nv', and Yr' maneuver derivatives are very close to the experimental results, there is a difference between the EFD and HAD and the test result for the Nr' coefficient. Nr is known to be very sensitive to the boat's center of gravity; any small change in this value can be reflected as a large difference in this hydrodynamic coefficient. It is also possible for the deviations to be caused by a geometric problem such as the moment of inertia. However, this study reveals the dependence of the hydrodynamic coefficients on the Reynolds number. Therefore, care should be taken when estimating the exact scale from scale model maneuver tests. Speed variation tests in some mathematical models attempt to compensate for this lack of state-of-the-art technology, but it is believed that using hydrodynamic coefficients as a function of the Reynolds number will improve the accuracy of the maneuver simulations.