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ÖgeA high-order finite-volume solver for supersonic flows(Lisansüstü Eğitim Enstitüsü, 2022) Spinelli, Gregoria Gerardo ; Çelik, Bayram ; 721738 ; Uçak ve Uzay MühendisliğiNowadays, Computational Fluid Dynamics (CFD) is a powerful tool in engineering used in various industries such as automotive, aerospace and nuclear power. More than ever the growing computational power of modern computer systems allows for realistic modelization of physics. Most of the open-source codes, however, offer a second-order approximation of the physical model in both space and time. The goal of this thesis is to extend this order of approximation to what is defined as high-order discretization in both space and time by developing a two-dimensional finite-volume solver. This is especially challenging when modeling supersonic flows, which shall be addressed in this study. To tackle this task, we employed the numerical methods described in the following. Curvilinear meshes are utilized since an accurate representation of the domain and its boundaries, i.e. the object under investigation, are required. High-order approximation in space is guaranteed by a Central Essentially Non-Oscillatory (CENO) scheme, which combines a piece-wise linear reconstruction and a k-exact reconstruction in region with and without discontinuities, respectively. The usage of multi-step methods such as Runge-Kutta methods allow for a high-order approximation in time. The algorithm to evaluate convective fluxes is based on the family of Advection Upstream Splitting (AUSM) schemes, which use an upwind reconstruction. A central stencil is used to evaluate viscous fluxes instead. When using high-order schemes, discontinuities induce numerical problems, such as oscillations in the solution. To avoid the oscillations, the CENO scheme reverts to a piece-wise linear reconstruction in regions with discontinuities. However, this introduces a loss of accuracy. The CENO algorithm is capable of confining this loss of accuracy to the cells closest to the discontinuity. In order to reduce this accuracy loss Adaptive Mesh Refinement (AMR) is used. This algorithm refines the mesh near the discontinuity, confining the loss of accuracy to a smaller portion of the domain. In this study, a combination of the CENO scheme and the AUSM schemes is used to model several problems in different compressibility regimes, with a focus on supersonic flows. The scope of this thesis is to analyze the capabilities and the limitations of the proposed combination. In comparison to traditional implementations, which can be found in literature, our implementation does not impose a limit on the refinement ratio of neighboring cells while utilizing AMR. Due to the high computational expenses of a high-order scheme in conjunction with AMR, our solver benefits from a shared memory parallelization. Another advantage over traditional implementations is that our solver requires one layer of ghost cells less for the transfer of information between adjacent blocks. The validation of the solver is performed in different steps. We assess the order of accuracy of the CENO scheme by interpolating a smooth function, in this case the spherical cosine function. Then we validate the algorithm to compute the inviscid fluxes by modeling a Sod shock tube. Finally, the Boundary Conditions (BCs) for the inviscid solver and its order of accuracy are validated by modeling a convected vortex in a supersonic uniform flow. The curvilinear mesh is validated by modeling the flow around a NACA0012 airfoil. The computation of the viscous fluxes is validated by modeling a viscous boundary layer developing on a flat plate. The BCs for viscous flows and the curvilinear implementation are validated by modeling the flow around a cylinder and a NACA0012 airfoil. The AUSM schemes are tested for shock robustness by modeling an inviscid hypersonic cylinder at a Mach number of 20 and a viscous hypersonic cylinder at a Mach number of 8.03. Then, we validate our AMR implementation by modeling a two-dimensional Riemann problem. All the validation results agree well with either numerical or experimental results available in literature. The performance of the code, in terms of computational time required by the different orders of approximation and the parallel efficiency, is assessed. For the former a supersonic vortex convection served as an example, while the latter used a two-dimensional Riemann problem. We obtained a linear speed-up until 12 cores. The highest speedup value obtained is 20 with 32 cores. Furthermore, the solver is used to model three different supersonic applications: the interaction between a vortex and a normal shock, the double Mach reflection and the diffraction of a shock on a wedge. The first application resembles a strong interaction between a vortex and a steady shock wave for two different vortex strengths. In both cases our results perfectly match the ones obtained by a Weighted Essentially Non-Oscillatory (WENO) scheme documented in literature. Both schemes are approximating the solution with the same order of accuracy in both, time and space. The second application, the double Mach reflection, is a challenging problem for high-order solvers because the shock and its reflections interact strongly. For this application, all AUSM-schemes under investigation fail to obtain a stable result. The main form of instability encountered is the Carbuncle phenomenon. Our implementation overcomes this problem by combining the AUSM+M scheme with the formulation of the speed of sound of the AUSM+up scheme. This combination is capable of modeling this problem without instabilities. Our results are in agreement with those obtained with a WENO scheme. Both, the reference solutions and our results, use the same order of accuracy in both, time and space. Finally, the third example is the diffraction of a shock past a delta wedge. In this configuration the shock is diffracted and forms three different main structures: two triple points, a vortex at the trailing edge of the wedge and a reflected shock traveling upwards. Our results agree well with both, numerical and experimental results available in literature. Here, a formation of a vortex-let is observed along the vortex slip-line. This vorticity generation under inviscid flow condition is studied and we conclude that the stretching of vorticity due to compressibility is the reason. The same formation is observed when the angle of attack of the wedge is increased in the range of 0-30. In general, the AUSM+up2 scheme performed best in terms of accuracy for all problems tested here. However, for configurations, in which the Carbuncle phenomenon may appear, the combination of the AUSM+M scheme and the computation of the speed of sound formula of the AUSM+up scheme is preferable for stability reasons. During our computations, we observe a small undershooting right behind shocks on curved boundaries. This is imputable to the curvilinear approximation of the boundaries, which is only second-order accurate. Our experience shows that the smoothness indicator formula in its original version, fails to label uniform flow regions as smooth. We solve the issue by introducing a threshold for the numerator of the formula. When the numerator is lower than the threshold, the cell is labeled as smooth. A value higher than 10^-7 for the threshold might force the solver to apply high-order reconstruction across shocks, and therefore will not apply the piece-wise linear reconstruction which prevents oscillations. We observe that the CENO scheme might cause unphysical states in both inviscid and viscous regime. By reconstructing the conservative variables instead of the primitive ones, we are able to prevent unphysical states for inviscid flows. For the viscous flows, temporarily reverting to first-order reconstruction in the cells where the temperature is computed as negative, prevents unphysical states. This technique is solely required during the first iterations of the solver, when the flow is started impulsively. In this study the CENO, the AUSM and the AMR methods are combined and applied successfully to supersonic problems. When modeling supersonic flow with high-order accuracy in space, one should prefer the combination of the AUSM schemes and the CENO scheme. While the CENO scheme is simpler than the WENO scheme used in comparison, we show that it yields results of comparable accuracy. Although it was beyond the scope of this study, the AUSM can be extended to real gas modeling which constitutes another advantage of this approach.
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ÖgeA modified anfis system for aerial vehicles control(Lisansüstü Eğitim Enstitüsü, 2022) Öztürk, Muhammet ; Özkol, İbrahim ; 713564 ; Uçak ve Uzay MühendisliğiThis thesis presents fuzzy logic systems (FLS) and their control applications in aerial vehicles. In this context, firstly, type-1 fuzzy logic systems and secondly type-2 fuzzy logic systems are examined. Adaptive Neuro-Fuzzy Inference System (ANFIS) training models are examined and new type-1 and type-2 models are developed and tested. The new approaches are used for control problems as quadrotor control. Fuzzy logic system is a humanly structure that does not define any case precisely as 1 or 0. The Fuzzy logic systems define the case with membership functions. In literature, there are very much fuzzy logic applications as data processing, estimation, control, modeling, etc. Different Fuzzy Inference Systems (FIS) are proposed as Sugeno, Mamdani, Tsukamoto, and ¸Sen. The Sugeno and Mamdani FIS are the most widely used fuzzy logic systems. Mamdani antecedent and consequent parameters are composed of membership functions. Because of that, Mamdani FIS needs a defuzzification step to have a crisp output. Sugeno antecedent parameters are membership functions but consequent parameters are linear or constant and so, the Sugeno FIS does not need a defuzzification step. The Sugeno FIS needs less computational load and it is simpler than Mamdani FIS and so, it is more widely used than Mamdani FIS. Training of Mamdani parameters is more complicated and needs more calculation than Sugeno FIS. The Mamdani ANFIS approaches in the literature are examined and a new Mamdani ANFIS model (MANFIS) is proposed. Training performance of the proposed MANFIS model is tested for a nonlinear function and control performance is tested on a DC motor dynamic. Besides, ¸Sen FIS that was used for estimation of sunshine duration in 1998, is examined. This ¸SEN FIS antecedent and consequent parameters are membership functions as Mamdani FIS and needs to defuzzification step. However, because of the structure of the ¸Sen defuzzification structure, the ¸Sen FIS can be calculated with less computational load, and therefore ¸Sen ANFIS training model has been created. These three approaches are trained on a nonlinear function and used for online control. In this study, the neuro-fuzzy controller is used as online controller. Neuro-fuzzy controllers consist of simultaneous operation of two functions named fuzzy logic and ANFIS. The fuzzy logic function is the one that generates the control signal. It generates a control signal according to the controller inputs. The other function is the ANFIS function that trains the parameters of the fuzzy logic function. Neuro-fuzzy controllers are intelligent controllers, independent of the model, and constantly adapting their parameters. For this reason, these controllers' parameters values are constantly changing according to the changes in the system. There are studies on different neuro-fuzzy control systems in the literature. Each approach is tested on a DC motor model that is a single-input and single-output system, and the neuro-fuzzy controllers' advantages and performances are examined. In this way, the approaches in the literature and the approaches added within the scope of the thesis are compared to each other. Selected neuro-fuzzy controllers are used in quadrotor control. Quadrotors have a two-stage controller structure. In the first stage, position control is performed and the position control results are defined as angles. In the second stage, attitude control is performed over the calculated angle values. In this thesis, the neuro-fuzzy controller is shown to work perfectly well in single layer control structures, i.e., there was not any overshooting, and settling time was very short. But it is seen from quadrotor control results that the neuro-fuzzy controller can not give the desired performance in the two-layered control structure. Therefore, the feedback error learning control system, in which the fuzzy controller works together with conventional controllers, is examined. Fundamentally, there is an inverse dynamic model parallel to a classical controller in the feedback error learning structure. The inverse dynamic model aims to increase the performance by influencing the classical controller signal. In the literature, there are a lot of papers about the structure of feedback error learning control and there are different proposed approaches. In the structure used in this work, fuzzy logic parameters are trained using ANFIS with error input.The fuzzy logic control signal is obtained as a result of training. The fuzzy logic control signal is added to the conventional controller signal. This study has been tested on models such as DC motor and quadrotor. It is seen that the feedback error learning control with the ANFIS increases the control performances. Antecedent and consequent parameters of type-1 fuzzy logic systems consist of certain membership functions. A type-2 FLS is proposed to better define the uncertainties, because of that, type-2 fuzzy inference membership functions are proposed to include uncertainties. The type-2 FLS is operationally difficult because of uncertainties. In order to simplify type-2 FLS operations, interval type-2 FLS is proposed as a special case of generalized type-2 FLS in the literature. Interval type-2 membership functions are designed as a two-dimensional projection of general type-2 membership functions and represent the area between two type-1 membership functions. The area between these two type-1 membership functions is called Footprint of Uncertainty (FOU). This uncertainty also occurs in the weight values obtained from the antecedent membership functions. Consequent membership functions are also type-2 and it is not possible to perform the defuzzification step directly because of uncertainty. Therefore, type reduction methods have been developed to reduce the type-2 FLS to the type-1 FLS. Type reduction methods try to find the highest and lowest values of the fuzzy logic model. Therefore, a switch point should be determined between the weights obtained from the antecedent membership functions. Type reduction methods find these switch points by iterations and this process causes too much computation, so many different methods have been proposed to minimize this computational load. In 2018, an iterative-free method called Direct Approach (DA) was proposed. This method performs the type reduction process faster than other iterative methods. In the literature, studies such as neural networks and genetic algorithms on the training for parameters of the type-2 FLS still continue. These studies are also used in the interval type-2 fuzzy logic control systems. There are proposed interval type-2 ANFIS structures in literature, but they are not effective because of uncertainties of interval type-2 membership functions. FLS parameters for ANFIS training should not contain uncertainties. However, the type-2 FLS should inherently contain uncertainty. For this reason, Karnik-Mendel algorithm is modified, which is one of the type-reduction methods, to apply the ANFIS on interval type-2 FLS. The modified Karnik-Mendel algorithm gives the same results as the Karnik-Mendel algorithm. The modified Karnik-Mendel algorithm also gives exact parameter values for use in ANFIS. One can notice that the ANFIS training of the interval type-2 FLS has been developed successfully and has been used for system control.
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ÖgeDynamic and aeroelastic analysis of advanced aircraft wings carrying external stores(Lisansüstü Eğitim Enstitüsü, 2021) Aksongur Kaçar, Alev ; Kaya, Metin Orhan ; 709160 ; Uçak ve Uzay MühendisliğiBu çalışma gelişmiş uçak kanatlarında harici yük ve takip edici kuvvet altında kanadın dinamik ve aeroleastik davranışlarını incelemektedir. Harici yüklerin ağırlığı, pozisyonu, birbirine göre yerleşimi, kompozit katmanların yönelimi ile itki kuvveti etkileri incelenmiş ve hepsinin kanadın doğal frekansı ve kritik çırpınma hızına olan etkileri tespit edilmiştir.
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ÖgeInvestigations on the effects of conical bluff body geometry on nonpremixed methane flames(Graduate Institute, 2021) Ata, Alper ; Özdemir, İlyas Bedii ; 675677 ; Department of Aeronautics and Astronautics EngineeringThis thesis is composed of three experimental studies, of which the first two are already published, and the third is under peer review. The first study investigates the effects of a stabilizer and the annular co-flow air speed on turbulent nonpremixed methane flames stabilized downstream of a conical bluff body. Four bluff body variants were designed by changing the outer diameter of a conically shaped object. The co-flow velocity was varied from zero to 7.4 m/s, while the fuel velocity was kept constant at 15 m/s. Radial distributions of temperature and velocity were measured in detail in the recirculation zone at vertical locations of 0.5D, 1D, and 1.5D. Measurements also included the CO2, CO, NOx, and O2 emissions at points downstream of the recirculation region. Flames were visualized under 20 different conditions, revealing various modes of combustion. The results evidenced that not only the co-flow velocity but also the bluff body diameter play important roles in the structure of the recirculation zone and, hence, the flame behavior. The second study analyzes the flow, thermal, and emission characteristics of turbulent nonpremixed CH4 flames for three burner heads of different cone heights. The fuel velocity was kept constant at 15 m/s, while the coflow air speed was varied between 0 – 7.4 m/s. Detailed radial profiles of the velocity and temperature were obtained in the bluff body wake at three vertical locations of 0.5D, 1D, and 1.5D. Emissions of CO2, CO, NOx, and O2 were also measured at the tail end of every flame. Flames were digitally photographed to support the point measurements with the visual observations. Fifteen different stability points were examined, which were the results of three bluff body variants and five coflow velocities. The results show that a blue-colored ring flame is formed, especially at high coflow velocities. The results also illustrate that, depending on the mixing at the bluff-body wake, the flames exhibit two modes of combustion regimes, namely fuel jet- and coflow-dominated flames. In the jet-dominated regime, the flames become longer compared to the flames of the coflow-dominated regime. In the latter regime, emissions were largely reduced due to the dilution by the excess air, which also surpasses their production. The final study examines the thermal characteristics of turbulent nonpremixed methane flames stabilized by four burner heads with the same exit diameter but different heights. The fuel flow rate was kept constant with an exit velocity of 15 m/s, while the co-flow air speed was increased from 0 to 7.6 m/s. The radial profiles of the temperature and flame visualizations were obtained to investigate the stability limits. The results evidenced that the air co-flow and the cone angle have essential roles in the stabilization of the flame: Increase in the cone angle and/or the co-flow speed deteriorated the stability of the flame, which eventually tended to blow-off. As the cone angle was reduced, the flame was attached to the bluff body. However, when the cone angle is very small, it has no effect on stability. The mixing and entrainment processes were described by the statistical moments of the temperature fluctuations. It appears that the rise in temperature coincides with the intensified mixing, and it becomes constant in the entrainment region.