Taşıyıcı yüzey sistemlerinin girdap kafes yöntemi ile analizi ve genetik algoritma ile eniyilemesi

Abstract

Hava araçlarının aerodinamik tasarımı, analizi ve eniyilemesi, akışkanlar dinamiği bilimiyle uğraşan araştırmacıların üzerinde durduğu karmaşık ve esasında çok-disiplinli mühendislik problemleridir. Bu kapsamda, günümüzde uygulanan Hesaplamalı Akışkanlar Dinamiği (CFD) çözümleri tasarım sürecinin ilk aşamalarında birçok sebeple uygun görülmemektedir. Onun yerine daha basit çözümler sunan, akış alanıyla ilgili temel yaklaşımlarda bulunanarak çözümü hızlandıran yöntemlerin kullanımı daha yaygındır.Hesaplamalı aerodinamik uygulamalarında sıkça kullanılan Girdap Kafes Yöntemi (VLM) taşıyıcı yüzeylerin üzerindeki potansiyel akışı çözmektedir. Ludwig Prandtl'ın 1918 yılında tanıttığı taşıyıcı çizgi modeli (PLL) sonlu düz kanatlar için analitik bir çözüm sağlarken, yine Prandtl'ın ortaya koyduğu teoriyi esas alan VLM ile herhangi bir konfigürasyondaki çok elemanlı taşıyıcı yüzey sisteminin incelemesi girdap-kafes modeli ile mümkün olmaktadır. Bu modelde yüzeyler çözümlemenin yapılacağı panellere bölünür ve her panele taşıyıcı özelliğini veren atnalı girdapları yerleştirilir. Potansiyel akım sınır şartı kullanılarak çözülen girdap şiddetleri ile taşıyıcı yüzey üzerine etki eden aerodinamik kuvvetler Kutta-Joukowski Kanunu ile hesaplanır.Konsept ve ön tasarım süreçlerinde ilgili hava aracının taşıyıcı yüzeyleriyle ilgili kanat açıklığı, açıklık oranı, kök ve uç veter uzunlukları gibi birçok parametrenin belirlenmesi gerekmektedir. Ancak, her bir parametrenin belirlenmesi başlı başına bir eniyileme çalışması gerektirmektedir. Bunun sebebi ise taşıyıcı yüzeyler birbirleri arasında aerodinamik etkileşim içindedir. Bir yüzeye ait parametre diğer bir yüzey üzerinde etki yaratmaktadır ve hava aracının genel performansı açısından bu etkinin incelenmesi önem arz etmektedir.Doğanın genetik mekanizmalarını açıklayan Darvinci Evrim Teorisi (DET), yapay sistemlerin eniyilemesinde de etkin bir şekilde kullanılabilmektedir. Evrimsel Algoritmaların (EA) bir alt sınıfı olan Genetik Algoritmalar (GA), doğanın kanunlarını yapay sistemlere uygulayarak, zorluklar karşısında kendi kendini geliştiren sistemler üretmektedir. Bu uygulamanın temellerini John H. Holland 1975 yılında atmıştır. Holland'ın yürüttüğü çalışmalar hem yapay sistemlerin eniyilemesi hem de doğal sistemlerin bilimine büyük katkı sağlamıştır.Bu tez kapsamında çok elemanlı taşıyıcı yüzeylerin nümerik incelemesi için VLM yönteminin bir bilgisayar programını geliştirilmiştir. MATLAB programlama dili kullanılarak geliştirilen yazılımın öncelikle PLL yöntemi ile düz bir kanat analizi için karşılaştırılmış ve elde edilen sonuçlar doğrulanmıştır. Çok elemanlı sistemler içinse ek doğrulama çalışmaları yürütülmüştür. Ters açılı bir çift kanat kullanılarak yer etkisi analizi yapılmış ve kanatlar arası uzaklık artırıldıkça yer etkisinin azaldığı görülmüştür. Bir diğer doğrulama çalışmasında ise bir kanat arkasında yerleştirilen yatay kuyruğun analizi yapılmıştır. Bu analizde aşağı sapmanın etkisiyle kuyruk üzerindeki etkin hücum açısının serbest akımın geliş açısından daha düşük hesaplanması incelenmiştir.Doğrulama çalışmaları neticesinde, taşıyıcı yüzeylerin incelenmesi amacıyla geliştirilen VLM yazılımı evrimsel döngüler sırasında çağırılabilecek bir fonksiyona dönüştürülmüştür. Evrimsel döngülerin değerlendirme aşamasında, her bir birey için bu fonksiyon çağrılmış ve aerodinamik katsayılar hesaplanmıştır. Hesaplanan katsayılar güçlü bireylerin belirlenmesine yarayan uygunluk fonksiyonlarında kullanılmıştır. Çaprazlama ve mutasyon evrelerinden sonra elde edilen çocuk bireylerin sonraki nesle nasıl aktarılacağı konusunda farklı yaklaşımlar denenmiş olup, elde edilen sonuçlar karşılaştırılmıştır. Sonuç olarak geliştirilen taşıyıcı yüzey sistemlerini eniyileme yazılımı uygulamalarda kullanılmış ve elde edilen bulgular paylaşılmıştır.

The design and optimization of aircraft has been a center of interest for researchers working in the field of fluid dynamics. The science of aircraft design has always been a multidisciplinary subject and therefore, a rather complex field of research. The analysis process of aircraft is nowadays carried out by means of Computational Fluid Dynamics (CFD), which requires a great amount of effort and resources. In consequence, simpler methods based on some basic assumptions about the fluid domain are employed during the concept or preliminary design phase. Methods that solve the inviscid flow are essentially predominant.In the past century, extensive research has been made on methods based on the potential flow. Ludwig Prandtl and his colleagues from Göttingen, Germany introduced Prandtl's Lifting Line (PLL) Theory in 1918. Lifting surfaces are modelled as lines, hence the name of the method. PLL proved to be invaluable for the analysis of finite wings. Nevertheless, the theory can only be used with straight wings (no sweep or dihedral angle) having only one lifting surface. Moreover, numerical derivatives of the method are developed in order to overcome its deficiencies.For instance, the Vortex Lattice Method (VLM) has become increasingly popular in the 1960's and it's still used today for analyzing lifting surfaces. In PLL, a lifting line is an infinite number of nested horseshoe vortices with the bound vortices passing through the quarter chord of the surface and the trailing vortices following the surface until the trailing edge, where they go to infinity parallel to the freestream. The induced velocities by these vortices are calculated at the three-quarters of the surface sections. This quarter-three-quarter method is the fundamental rule of panel methods which arises from the Kutta condition. In VLM, wings are discretesized as a lattice of panels with horseshoe vortices on each individual panel, unlike an infinite number of nested horseshoe vortices in PLL theory. The vortex strengths on these panels are computed using the potential flow boundary condition: the velocity component normal to the surface should be zero. After calculating the vortex strengths, the Kutta-Joukowski Theorem is used in order to calculate the acting aerodynamic forces on the lifting surface. Finally, the lift coefficient and the induced drag coefficient can be calculated.In the concept and preliminary phases of aircraft design, several paramaters such as the span, aspect ratio, root and tip chord lengths have to be determined. These parameters cannot be considered separately since determining each parameter affects the other regarding the overall performance of the aircraft. An optimization has to be made for each parameter, which sometimes requires making a compromise. Hence, this process has to be handled carefully. Current optimization methods offer various solutions while having limitations on the search space concerning continuity, existence of derivatives and other matters.Selecting and applying the right optimization method can be a tedious task. However, one type of optimization is more flexible for varying requirements compared to others: Genetic Algorithms (GA). Genetic algorithms are stochastic searching algorithms known as a subclass of Evolutionary Algorithms (EA).The laws of nature described in the Darwinian Evolution Theory (DET) drive GAs. Features of self-guidance, development and reproduction are the rules of genetics. These rules when applied to artificial systems have the potential to create the fittest product for a given objective. The pioneering experiments on GA introduced by John H. Holland and his colleagues at the University of Michigan in 1975 not only contributed to the science of artificial systems but also biological systems. GA employs the genetic mechanism of the nature through three main principles: heredity, variation and selection. A very robust tool can be created by studying each of these principles and incorporating them in an optimization framework.First, a computer program for the analysis of lifting surface systems is developed using the formulations in the VLM method. The MATLAB programming language is used since it offers many intrinsic functions and tools to generate graphic interfaces. The VLM code is then put to test by analyzing a straight wing and the results are compared with the PLL output. Another analysis is carried out using symmetrically placed lifting surfaces. The ground effect is then simulated on the surfaces by changing the distance between them. Lastly, the downwash effect on the horizontal tail behind a wing is analyzed and the decreasing effective angle of attack on the tail surface is observed.After the validation process, the VLM code is transformed into a function and implemented into another code which carries out evolutionary loops in order to optimize the lifting surface by means of GA.First of all, a random population is generated and analyzed using the VLM function. The code then uses fitness functions with the aerodynamic coefficients as inputs in order to determine the strongest specimen. If the variation is no longer satistifed, the evolutionary loop is broken. This is handled by checking the mean fitness curve of the population at each generation. If the curve's slope reaches zero, it means that the variation principle is compromised.A mating pool is created in which the strong specimen having a better chance of reproducing. Parent genes are used in a process called `crossover` and by consequence, an offspring is produced. The offspring must have traits coming from both their parents. Additionaly, the offspring are sometimes subjected to mutation which can completely alter their genes. At the end of each generation, the offspring are added to the population while weak specimen are removed. This process forces the population to produce better specimen by removing defective genes and developing better ones.The way the offspring are added to the next generation is another matter. In this work, three different ways of handling this process are analyzed: inheritance, controlled inheritance and survival. In the first method, the offspring takes the place of its parents. In the controlled inheritance method, the offspring is only added to the population if its fitness is greater then its parents. In the last method, the offspring takes the place of the weakest specimen in the population and if its fitness is even lesser, the offspring is discarded. The first method results in an everchanging mean fitness curve while other converge towards a fitness value.The GA code is used in two applications in order to fully demonstrate its capabilities. An arbitrary wing design is defined in the code with a goal lift coefficient. A fitness function is written with alues closer to the goal lift coefficient returning a higher value. After entering its limitations, the wing is added to a randomly generated wing population with the same goal. After several generations, a better wing is obtained with a greater fitness value.In the following application, a horizontal tail is placed behind the optimized wing and the longitudinal stability requirement is added to the fitness function. The genes of both lifting surfaces are subjected to evolutionary process and the resulting fittest specimen is analyzed. The addition of the tail to the system and the longitudinal stability requirement with it, forced the previously optimized wing to change and adapt.In conclusion, the use of GAs in optimization of lifting surface systems offers a robust multi-objective design framework. This thesis only conducts aerodynamic analysis and checks for simple aerodynamics and stability requirements. However, any type of requirement and related analysis procedure can be added to the process without making major changes to the optimization framework. This is essentially why GAs are widely used in the field of design and optimization, they are flexible and compatible with any change or addition to evaluation process of the design parameters.The use of GAs are mostly encouraged for the optimization procedure of very complex systems where a great amount of variables is present. Considering all these variables are to be handled in a population of specimen, calculating the fitness of each specimen at each generation is significantly time consuming for problems of higher order. Therefore, the computers of today are only capable of optimizing relatively simple problems in the matter of preliminary design of artificial systems. However, the future of computer science can overcome this issue of time and resource consumption since the quantum computers hold a great potential.