LEE- Uçak ve Uzay Mühendisliği Lisansüstü Programı

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http://hdl.handle.net/11527/19473

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Yazar "Çelik, Bayram" ile LEE- Uçak ve Uzay Mühendisliği Lisansüstü Programı'a göz atma
  • Öge
    A high-order finite-volume solver for supersonic flows
    (Lisansüstü Eğitim Enstitüsü, 2022) Spinelli, Gregoria Gerardo ; Çelik, Bayram ; 721738 ; Uçak ve Uzay Mühendisliği
    Nowadays, 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.
  • Öge
    Aeroacoustic investigations for a refrigerator air duct and flow systems
    (Graduate School, 2022-02-16) Demir, Hazal Berfin ; Çelik, Bayram ; 511181186 ; Aeronautics and Astronautics Engineering
    Noise has become an important public health problem with industrialization, and has become a crucial design problem for engineering. For this reason, noise reduction studies have became the focus, especially in the white goods, automotive and aviation sectors, which requires interaction with human. Among the vehicles and products in the aforementioned sectors, the refrigerators, unlike the others, are located in the center of the living area and work throughout the day. Therefore, possible sound problems are observed more quickly by the users and are found to be disturbing. At this point, the investigation and reduction of the acoustic propagation of existing products by various numerical and experimental methods is a valuable contribution to both industry and literature. Within the scope of this thesis, the freezer compartment of a refrigerator with a No frost cooling system was investigated from an aeroacoustic perspective. The freezer compartment consists of three drawers where food will be placed, an axial fan that provides air flow, an evaporator cover that separates the evaporator pipes and the interior volume, and plastic walls surrounding them. The main source of air flow noise in the system is the axial fan. For this reason, in the first step of the study, solo aeroacoustic examination of the axial fan was made. Afterwards, the entire freezer volume was examined and the study was completed with three different model proposals in which acoustic emission was reduced. The flow field analysis of the axial fan with an operational speed of 1200 rpm was carried out with commercial software ANSYS Fluent. In this numerical model, Shear Stress Transport 𝑘 – 𝜔 turbulence model was used. Governing equations was solved under three-dimensional, transient, viscous, incompressible flow assumptions. The rotation of the fan was defined by the sliding mesh method. The numerical flow solution was validated with experimental volumetric flow rate data. According to the numerical and experimental results, the flow rate of the axial fan under the specified conditions was determined as 19 L/s. A hybrid aeroacoustic model is created by giving the pressure outputs of the flow solution as input to the acoustic model. For the acoustic solution, Ffowcs Williams & Hawkings (FW-H) model defined in ANSYS Fluent was used and the result of the solution was compared with the sound pressure data collected in the full anechoic acoustic room. Although there is some difference between the numerical and experimental sound pressure curves, it was observed that the hybrid model established to understand the general trend and to catch the blade passing frequency was successful. It was predicted that the difference between experimental and numerical measurements occurred for two reasons. The first is absence of the fan motor in the numerical analysis. Another reason is that the acoustic propagation resulting from the excitation of the air flow to the system structures cannot be predicted with this model. In the second step of the study, the model validated with axial fan solutions was applied to the freezer compartment. The aim here is to reveal the air flow distribution in the freezer volume and to identify the regions where turbulence effects increase. In the numerical model, the axial fan was rotated at an operational speed of 1200 rpm and this rotation was achieved by the sliding mesh method. As a result of the analysis, it was seen that the turbulence formation started at the wing tips as observed in the solo fan analyses, and the vortices coming out of the trailing edge tips were especially concentrated in the region between the upper wall of the freezer volume and the upper two drawers. In addition, a turbulent area was detected at the bottom of the evaporator cover (which is the fan suction area). As a result of the hybrid aeroacoustic model solution, the sound pressure data collected from 1 meter away from the front, rear and side surfaces of the freezer and the sound pressure data collected from the same locations in the full anechoic acoustic room were compared. When the total sound pressure in the range of 10-10000 Hz is compared, it is seen that there is a difference of 3-7 dBA between the numerical model and the experimental results. As a result of the investigations of the axial fan in the solo and freezer volume, three different freezer models have been proposed to improve air flow, reduce turbulence and reduce the resulting noise caused by air flow. In the fist suggested model, the bottom part of the evaporator cover has changed and the acostic propagation has decreased 0.24 dBA at 1200 rpm rotational speed. The position of the axial fan and its distance from the structures in the suction and discharge directions are the parameters affecting the acoustic propagation. In the second model, it is aimed to provide acoustic gain by changing the fan position. In this context, the fan was moved on the shaft by 5 mm and brought closer to the blowing region. With this modification, total sound power level was decreased 2.18 dBA. The final model is the superposition of the first two models. Here, it was aimed to see the combined effect of two mentioned model. At 1200 rpm rotational speed, 3.27 dBA gain was achived by the third model.