Süpersonik hızlar için roket burnu etrafındaki akışın  hesaplamalı akışkanlar dinamiği analizleri
Computational fluid dynamics analysis of flow around the rocket nose for supersonic speeds
Yazar: AHMET SEMİH ŞİMŞEK
Danışman: PROF. DR. HASAN GÜNEŞ
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Isı-Akışkan Bilim Dalı
Derece: Yüksek Lisans, 2023
Konu: Mühendislik Bilimleri = Engineering Sciences
Dizin: Eliptik = Elliptic ; Hesaplamalı akışkanlar dinamiği (HAD) = Computational fluid dynamics (HAD) ; Sayısal modelleme = Numerical modelling ; Süpersonik = Supersonic

Özet:
Roketlerin kullanılacakları görevlere bağlı olarak farklı özelliklere sahip olması gerekmektedir. Bu özelliklerin başında süpersonik  hızlar olarak adlandırılan Mach 1 üzeri hızlarda aerodinamik ve aerotermal açıdan verimli özelliklere sahip olması gerekliliğidir. Roketlerin sürükleme kuvveti, kaldırma kuvveti özellikleri ve roket etrafında oluşan termal gerilmeler, özellikle akış hızının Mach 3 ve üzeri olduğu durumlarda, hücum açısına bağlı olarak önem kazanmaktadır. Ayrıca bu yüksek hız koşulları altında tasarlanan roketlerin deneysel olarak test edilmesi ve bu testlerin doğrulanması oldukça zor ve maliyetlidir. Bu yüzden test çalışmalarının hesaplamalı akışkanlar dinamiği (HAD) yöntemi kullanılarak gerçekleştirilmesi giderek büyük bir önem kazanmıştır. Deneysel çalışmalar HAD analizlerinden sonra elde edilen sonuçların doğrulanması için sadece temel düzeyde yapılmaya başlanmıştır. Bu çalışmada, literatüre HB-1 test ve doğrulama geometrisi olarak tanıtılan geometri kullanılarak iki farklı HAD çözücü üzerinde modeller hazırlanmış olup farklı hücum açılarında ve Mach sayılarında HAD çözümleri yapılmıştır.
İlk olarak literatürde mevcut standart HB-1 modeli kullanılarak kurulan HAD modeli doğrulanmıştır. Ardından standart HB-1 geometrisi Eliptik, Haack-Serisi, ve Güç-Serisi olarak adlandırılan dört farklı burun profili kullanılarak aerodinamik ve aerotermal özellikleri geliştirmek amacıyla yeniden tasarlanmıştır. Ansys Fluent üzerine kurulan model Yoğunluk Tabanlı çözücü, k-omega SST türbülans modeli, Yüksek Hızlı Sayısal modelleme metodu (HSN) ve kapalı çözücü (implicit) kullanılarak analiz edilmiştir. Açık kaynak kodlu OpenFoam yazılımı kullanılarak HSN dışında benzer koşullar oluşturulmuş ve iki çözücü kendi aralarında karşılaştırılmıştır. Oluşturulan HAD modellerinde, 3 ,4 ,6 ,7 ,8 Mach sayılarında ve 4°, 8°, 12°, 16° hücum açılarında HAD analizleri yapılmıştır.
HAD analizlerinden elde edilen sonuçlar incelenip deneysel veriler ile karşılaştırıldığında Ansys Fluent ve OpenFOAM kullanılarak elde edilen sonuçların deneysel veriler ile aralarındaki farkın %5 ve aşağısında kaldığı gözlenmiştir.
Elde edilen sonuçlar birbirleriyle kıyaslandığı zaman kullanılan farklı modellerden HB-1 olarak adlandırılan modelin en yüksek Cl/Cd oranına sahip olduğu gözlemlenmiştir. Bu oranın yüksek olmasına bağlı olarak yakıt tasarrufu ve manevra kabiliyeti olarak en optimum yapı olduğu gözlemlenmiştir. Ancak HB-1 modelinin yüksek bir Cl/Cd oranına sahip olmasına rağmen sürükleme kuvvetlerinin diğer modellere göre yaklaşık iki kat yüksek olması nedeniyle bir takım dezavantajlara da sahiptir. Bu durumun başında yüzeyde oluşan yüksek sıcaklıklar nedeniyle oluşacak termal gerilmeler gelmektedir. Güç-Serisi modelini yine diğer modellere göre düşük yüzey sıcaklıklarına sahip olması ve bazı Mach sayılarında Güç-Serisine yakın yüzey sıcaklıklarına sahip olması ile Eliptik modeli takip etmektedir.
Verilen farklı değerlerin tek bir pencereden incelenip nihai optimum modele karar verebilmek amacıyla ortak bir sonuca varacak olursak Güç-Serisi düşük hücum açılarında Cl/Cd oranı ve yüzey sıcaklıkları konusunda optimum model olarak karşımıza çıkmaktadır. Ancak Mach 3 ve Mach 4 hızlarında hücum açıları yükseldiğinde ise Güç-Serisi modeli bu durumu Eliptik modele bırakmaktadır. Mach 6 ve yukarısı durumlar incelendiğinde Güç-Serisi modeli CL/CD oranı ve termal gerilmelerin beraber gözönüne alındığında en optimum model olarak karşımıza çıkmıştır.
İrtifa kıyaslaması için yapılan analizler incelendiğinde ise 0 km irtifa yani atmosfer şartları, 10 km yükseklik ve 30 km irtifa olarak 3 farklı analiz HB-1 modeli ve bu modele ait literatür verilerinden faydalanılarak gerçekleştirilmiştir. 0 km irtifadan 10 km'ye geçildiğinde değerlerin değişimleri incelendiğinde farklar yaklaşık olarak %3 cıvarlarında olduğu gözlemlenmiştir. Aynı kıyaslama 10 km ve 30 km irtifalarda elde edilen değerler için yapıldığında ise bu oranın %5 mertebelerine çıktığı gözlemlenmiştir.

Abstract:
Rockets are vehicles that can be used in different tasks such as attack, tracking, carrying, lifting. Depending on the tasks to be used, rockets must have different properties. If we list these features, it should have the longest range with the least possible energy requirement at high speeds and in different environmental conditions. Similarly, with high speeds, the thermal stresses that will occur on the structure should be in a way that will cause the least damage to the structural integrity of the rocket and the components inside. These properties gain great importance in flow regimes above Mach 1, which are called supersonic velocities. In rockets, these features appear as a function of drag and lift forces. 
Lifting force is one of the biggest factors in the fuel and energy consumed by rockets and even other aircraft when starting their first motion. A high level of this force will reduce the energy need to be obtained by using external fuel to start the movement, and the fuel savings provided by this situation will provide working time gain in long range missions. Since the drag forces will create a resistance in the opposite direction to the movement of the rocket, as low as possible these forces will reduce the negative effects that will be encountered for the start and continuation of the movement, and thus will ensure that the movement continues with less fuel use.
The adverse effects of these two force parameters with respect to each other should be taken into account while designing the rocket. The primary design requirement for reducing drag forces is to reduce the projected area of the rocket where it directly encounters the counter air as it moves. In order to achieve this situation, thinning the nose structure of the rocket and thus the overall diameter may be a suitable option. However, the thin nose structure will cause the thermal stresses on the surface to be transmitted more into the rocket, and this will adversely affect the structural integrity of the rocket as well as the operation of the electronic components inside the rocket.
It is necessary to check whether these requirements are met with the necessary tests before the designs are completed and the production processes are started. Because it is necessary to determine which needs the design made before production can meet and therefore for which tasks it will be produced.
Experimental testing and validation of rockets designed under these high velocity conditions is very difficult and costly. Therefore, it has become increasingly important to perform test studies using the computational fluid dynamics (CFD) method. 
Computational fluid dynamics method is a method of calculating fluid motion, heat and mass transfer, chemical reactions and related events by mathematical methods. The solutions are realized by solving the conservation equations of mass and energy. When the solutions are completed, pressure, velocity and temperature distributions, drag and buoyancy forces and similar information can be obtained.
CFD analyzes are carried out in order to determine the most suitable conditions for experimental studies before the start of experimental studies. Since these preliminary analyzes are carried out in order to start experimental studies, the accuracy rates of the results are in the background, as they are done to quickly reach the result and get an idea. With the results obtained from CFD analysis, the most suitable conditions are provided for the experimental studies to be carried out and experimental studies are carried out.
If a test scenario in which CFD analyzes would not be used was being studied, 80 times would have to be experimentally studied for different Mach numbers, angles of attack and geometry combinations for the study examined within the scope of this study. However, according to this methodology, experimental studies of a few base cases selected from among these 80 different cases are made and the results are obtained. Afterwards, the appropriate model for CFD analysis is established and firstly, base cases with experimental results are analyzed. The obtained results are compared with the experimental results and the established CFD model is verified. Then, solutions are made for Mach number, angle of attack and geometry combinations belonging to other cases and results are obtained.
In this study, models were prepared on two different CFD solvers using the geometry introduced in the literature as HB-1 test and verification geometry, and CFD solutions were made using two different solvers at different attack angles and Mach numbers. Thus, a methodology that can be solved at high supersonic speeds for two different CFD software has been studied, and these data have been brought to the literature by examining the aerodynamic and aerothermal properties for four different designs.
First, the CFD model was constructed by using the standard HB-1 model, the results of the experimental studies available in the literature. Then, drawings were made for the standard HB-1 geometry using the existing design in the literature and the digital mesh structure was started to be created. Before deciding on the final digital network structure, solutions were tried on 3 different digital network structures and the point where the results became independent from the digital network was determined and the final digital network structure to be used was decided. Afterwards, CFD analyzes were performed and validated using the results available in the literature. It has been redesigned to improve aerodynamics and aerothermal properties using three different nose profiles, Elliptical, Haack-Series, and Güç-Series.
While making rocket designs, a reference size is selected and this size is used as a coefficient in each design parameter, and related designs are realized. In addition, each of the parameters used in these designs also represents an important detail of the rocket structure. Examples of these parameters are total length, wetted area, bluntness ratio and fineness ratio parameters.
CFD solutions were performed separately using Ansys Fluent commercial HAD software and OpenFOAM open source HAD software. The results obtained using these two software are compared with each other in terms of accuracy and solver performance. The reason for choosing and using these two separate software for the solution is to examine the performances of the two programs, which are heavily preferred for similar problems, for similar problems, as well as to examine the existing advantages and disadvantages relative to each other.
The model built on Ansys Fluent was analyzed using Density Based solver, k-omega SST turbulence model, High Speed Numerical modeling method (HSN) and closed solver (implicit). Using the open source software OpenFoam, similar conditions were created outside of HSN and the two solvers were compared among themselves. In the CFD models created, CFD analyzes were performed for four different models with Mach numbers of 3, 4, 6, 7, 8 and 4°, 8°, 12°, and 16° attack angles. 
The results obtained from CFD analyzes were examined and compared with the experimental data. When the results obtained using Ansys Fluent and OpenFOAM are compared with the experimental data, it has been observed that the accuracy rates vary depending on the capacities of the programs according to different Mach numbers and angles of attack. It has been observed that Ansys Fluent results show higher accuracy than OpenFOAM results, especially in cases where the mach number is 6 and below, thanks to the HSN method used in the software.
When the obtained results were compared with each other, it was observed that the model called HB-1 among the different models used had the highest Cl/Cd ratio. Due to the high rate of this ratio, it has been observed that it is the most optimum structure in terms of fuel economy and maneuverability. However, although the HB-1 model has a high Cl/Cd ratio, it also has some disadvantages as its drag forces are approximately twice as high as other models. At the beginning of this situation is the thermal stresses that will occur due to the high temperatures on the surface. The Power-Series model is followed by the Elliptical model, with lower surface temperatures compared to other models and surface temperatures close to the Power-Series at some Mach numbers.
If we come to a common conclusion in order to examine the different values given from a single window and decide on the final optimum model, the Power-Series emerges as the optimum model for Cl/Cd ratio and surface temperatures at low angles of attack. However, when the angles of attack increase at Mach 3 and Mach 4, the Power-Series model leaves this situation to the Elliptical model. When Mach 6 and above situations are examined, the Power-Series model has emerged as the most optimal model when the Cl/Cd ratio and thermal stresses are considered together.
In later studies, more efficient designs can be obtained in terms of aerodynamics and aerotherms by using different nose profiles. Using OpenFOAM open source HAD software, solvers with different properties can be developed at supersonic speeds. In this study, CFD models can be created for different supersonic flow problem solutions to be realized later by using the current analysis results.