Experiment shows that the steady axisymmetric flow past a sphere becomes unstable in the range 120 < Re < 300. The resulting time-dependent nonaxisymmetric flow gives rise to nonaxisymmetric vortex shedding at higher Reynolds numbers. The present work reports a computational investigation of the linear stability of the axisymmetric base flow. When the sphere is towed, fixed, or otherwise constrained, stability is determined solely by the Reynolds number. On the other hand, when the sphere falls due to gravity, the present work shows that a additional parameter, the ratio of fluid density to sphere density (β = ρ(f)/ρ(s)) is involved. We use a spectral technique to compute the steady axisymmetric flow, which is in closer agreement with experiment than previous calculations. We then perform a linear stability analysis of the base flow with respect to axisymmetric and nonaxisymmetric disturbances. A spectral technique similar to that employed in the base flow calculation is used to solve the linear disturbance equations in streamfunction form for axisymmetric disturbances, and in a modified primitive variable form for nonaxisymmetric disturbances. For the density ratio β = 0, which corresponds to a fixed sphere, the analysis shows that the axisymmetric base flow undergoes a Hopf bifurcation at Re = 175.1, with the critical disturbance having azimuthal wavenumber m = 1. The results are favorably compared to previous experimental work.

A dissertation submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Master of Science in Engineering Johannesburg, May 2017 / Flow around flat plates that were uniformly accelerated from rest with acceleration of 13g is analysed with overset mesh from Star CCM+ commercial CFD software. The particular interest is more on the vortices shed from the plate edges. Three 8mm thick plates of the same cross-sectional areas (108mm length equilateral triangular, 71mm length square and 80mm diameter circular) were simulated. The validation of the numerical method was achieved by using laser vapor sheet method to visualize the flow profiles of accelerating circular plate and comparing the CFD and experimental results. The CFD and experimental results were consistent with each other. It was found that when a plate accelerated in air, it displaced air particles out of its way. The shear layers of air separated from the front edges of the plate and rolled around a vortex core forming a primary vortex ring in the plate wake. The size of the primary vortex increased with Reynolds number (Re) that was increasing with time. This was because as Re increased, more fluid particles were displaced from the front face of the plate at a time. More displacement of the fluid particles led to shear layers separating from the plate edges with stronger momentum resulting in larger vortex ring. The shape of the primary vortex depended on the shape of the accelerating plate. For the circular plate, all the points on the front edge being equidistant from the plate centroid, fluid particles were evenly displaced from that separation edge. The result was an axis-symmetric ring of primary vortex around a circular vortex core. The asymmetric plates (triangular and square) did not evenly displace air particles from their edges of separation. The result was an asymmetric vortex ring. More air particles separated from the plate at separation points closest to the plate centroid and led to the largest vortical structure there. That is; the primary vortex ring was largest at the midpoints of the plate edges because they were the closest points of separation from the plate centroid. The size of the primary vortex continuously reduced from the mid-points of the plate edges to the corners. The corners had the smallest primary vortical structure due to being furthest points of separation from the plate centroid. The parts of the vortex ring from the two edges of the plate interacted at the corner connecting those edges. / MT 2017

Atualmente, os avanços tecnológicos, especialmente dos recursos computacionais, possibilitam a realização de cálculos cada vez mais complexos. Em função destes avanços, transitórios hidráulicos antes desprezados ou estimados de forma rudimentar já podem ser calculados, especialmente nos casos em que o comportamento dos transitórios é crítico. Assim, torna-se necessário o desenvolvimento de métodos de cálculo que permitam prever quantitativamente tais transitórios uma vez que não há solução analítica para este problema. Neste trabalho são estudadas as condições de contorno para a utilização do modelo rígido de coluna líquida e sua respectiva solução numérica para o cálculo de transitórios durante o enchimento de uma tabulação com ramificação. Os modelos matemáticos foram testados em laboratório sob diversas condições, comprovando a viabilidade da utilização das ferramentas teóricas e numéricas desenvolvidas. / Nowadays there have been many technological advances, especially related to computational resources, that make possible more complex and huge calculations. Due to these advances, the evaluation of hydraulics transients, which have been disregarded or roughly estimated, is allowed to be more precisely performed especially when transient phenomena have significant importance. Then, the development of calculating methods that evaluates these transients effects becomes necessary once the analitic solution to these problems does not exist. This work presents the study of the boundary conditions of the rigid model applied to the fluid column and its numeral solution in order to calculate the transient behavior during filling of pipeline with ramifications. The results of mathematical models were compared with those from laboratory experiments under several conditions proving the feasibility of theoretical and numeral models.

In this work, a two-dimensional model representing the vortices that animals produce, when they are flying/swimming, was constructed. A D{shaped cylinder and an oscillating airfoil were used to mimic these body{shed and wing{generated vortices, respectively. The parameters chosen are based on the Reynolds numbers similar to that which is observed in nature (104). In order to imitate the motion of ying/swimming, the entire system was suspended into a water channel from frictionless air{bearings. The position of the apparatus in the channel was regulated with a linear, closed loop PI controller. Thrust/drag forces were measured with strain gauges and particle image velocimetry (PIV) was used to examine the wake structure that develops. The Strouhal number of the oscillating airfoil was compared to the values observed in nature as the system transitions between the accelerated and steady states... As suggested by previous work, this self-regulation is a result of a limit cycle process that stems from nonlinear periodic oscillations. The limit cycles were used to examine the synchronous conditions due to the coupling of the foil and wake vortices. Noise is a factor that can mask details of the synchronization. In order to control its effect, we study the locking conditions using an analytic technique that only considers the phases.. The results suggest that Strouhal number selection in steady forward natural swimming and flying is the result of a limit cycle process and not actively controlled by an organism. An implication of this is that only relatively simple sensory and control hardware may be necessary to control the steady forward motion of man-made biomimetically propelled vehicles. / by Cyndee L. Finkel. / Thesis (Ph.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

本論文討論了具有非平凡旋度的穩態亞音速流體的適定性問題。 / 首先，我們研究了通過無限長週期管道的二維亞音速流禮。當管道某一週期位置伯努利函數擾動很小，且質量數介於與適當的範圍時，有且僅有唯一的亞音速流禮。特別地，對於伯努利函數為常值的情形，我們還通過結構緊性的方法證明了亞音速-音速流體的存在性。此時，質量數可以達到一臨界值。謝春景和辛周平在處理二維司壓歐拉方程時曾引入了一個重要的處理方法一一流函數表達式。然而，對於週期流體的問題，伯努利函數和流函數的相互關係是無法事先確定的。為此，我們建立了一個關於流函數的非線性映射。該映射的不動點給出了相應歐拉方程的解。 / 其次，對於二維亞音速流體通過對稱障礙物的問題，當來流的伯努利函數關於y方向對稱，且擾動很小時，我們給出了流体的存在性和唯一性的証明。这里，我們利用歐拉方程的流函數方法，得到了對應于流函數的二階方程的解。能量方法以及動量場與來流動量場之差的L2可積性給出了流函數的漸進行為。這一漸進行為結合障礙物外無駐點的事實說明了流函數表示與原先歐拉方程是相容的。 / 最后，我們研究了當給定管道壁上法向动量時，三維穩態流體通過方體管道的問題。如果入口處伯努利函數的擾動和旋度的法向分量為零，則當邊界的法向動量不超過一臨界值時，無旋的亞音速流體存在。對於一般情形，若伯努利函數的擾動和旋度的法向分量很小時，我們利用將速度均分解均無旋部分和旋度部分的方法給出了流體存在性的證明。這裡，我們通過求解一加權的散旋系統得到了旋度部份的解:而無旋部份則由一擬線性橢圓方程的解給出。 / In this thesis, the wellposedness theory of steady subsonic flows with nontrivial vorticities is studied in various aspects. / First, we study 2-D subsonic flows through infinitely long periodic nozzles. It is showed that when mass flux lies in a suitable regime and the variation of Bernoulli's function at some given section is sufficiently small, there exists a unique global subsonic flow in the periodic nozzle. In particular, if Bernoulli's function is a constant, the existence of subsonic flow is also obtained when mass flux takes the critical number by a compensated compactness framework. One of the main tools to handle 2-D compressible Euler equations is the stream function formulation first established by Xie and Xin. The main difficulty in adapting this formulation in periodic nozzles is that the relation between Bernoulli's function and stream function cannot be fixed. We resolve this difficulty via setting up a nonlinear map from stream function at the given section to itself. The fixed point of this map induces a solution of corresponding Euler equations. / Second, the existence and uniqueness of 2-D subsonic flows past a symmetric body are established under the assumption that Bernoulli's function is given symmetrically in the upstream with small variation. By the stream function formulation for 2-D compressible Euler equations, one obtains the solution of the Euler equations via solving a quasilinear second order equation for stream function. This is achieved with the help of the theory of elliptic equations of two variables. Asymptotic behavior for the stream function is obtained via energy method and L²-integral of the difference between the momentum and its asymptotic behavior in the upstream. The asymptotic behavior, together with the property that stagnation points are absent outside the body, yields that the stream function formulation is consistent with the original Euler system. / Finally, we study the existence of 3-D steady subsonic flows in rectangular nozzles when prescribing the normal component of the momentum on the boundary. If, in addition, the normal component of the voriticity and the variation of Bernoulli's function at the exit vanish, then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number. In general, if the normal component of the vorticity and the variation of Bernoulli's function are both sufficiently small, we prove the existence of Euler flows by decomposing the velocity into the vortical part and the potential part. A div-curl system with given weighted function is used to obtain the vortical part and the potential part is induced by the solution to a quasilinear elliptic equation. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Chao. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 111-120). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Preliminaries --- p.12 / Chapter 3 --- 2-D subsonic flows through in finitely long periodic nozzles --- p.23 / Chapter 3.1 --- Introduction and main result --- p.23 / Chapter 3.2 --- Stream function formulation of potential flows --- p.27 / Chapter 3.2.1 --- Bernoulli's law and stream function formulation --- p.27 / Chapter 3.2.2 --- Potential flows and proof of Theorem 3.1.1 --- p.30 / Chapter 3.3 --- Analysis of the well-posedness of Euler flows --- p.32 / Chapter 3.3.1 --- Existence, uniqueness, and periodicity of truncated flows --- p.34 / Chapter 3.3.2 --- Existence and uniqueness of Euler flflows --- p.41 / Chapter 4 --- 2-D subsonic flows past a symmetric body --- p.47 / Chapter 4.1 --- Motivation and mathematical formulation --- p.47 / Chapter 4.2 --- Truncated problem --- p.53 / Chapter 4.3 --- Asymptotic behavior at upstream and downstream --- p.59 / Chapter 4.4 --- Existence and uniqueness of Euler flflows --- p.61 / Chapter 5 --- 3-D subsonic Euler flows through nitely long nozzles --- p.67 / Chapter 5.1 --- Mathematical formulation and main results --- p.67 / Chapter 5.2 --- Some preliminaries --- p.71 / Chapter 5.3 --- 3-D potential flows --- p.76 / Chapter 5.3.1 --- Apriori estimates for truncated potential flows --- p.77 / Chapter 5.3.2 --- Existence and uniqueness of potential flows --- p.91 / Chapter 5.4 --- General 3-D steady Euler systems --- p.94 / Chapter 6 --- Further discussions and future work --- p.109 / Bibliography --- p.111

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND AERO. / Includes bibliographical references. / by Peter Frederick Lorber. / M.S.

The proper orthogonal decomposition (POD) has been widely used in fluid dynamic applications for extracting dominant flow features. The “gappy” POD is an extension to this method that allows the consideration of incomplete data sets. In this paper, the gappy POD is extended to handle unsteady flow reconstruction problems, such as those encountered when limited flow measurement data is available. In addition, a systematic approach for effective sensor placement is formulated within the gappy framework. Two applications are considered. The first aims to reconstruct the unsteady flow field using a small number of surface pressure measurements for a subsonic airfoil undergoing plunging motion. The second considers estimation of POD modal content of a cylinder wake flow for active control purposes. In both cases, using the dominant POD basis vectors and a small number of sensor signals, the gappy approach is found to yield accurate flow reconstruction results. / Singapore-MIT Alliance (SMA)

High turbine inlet temperature becomes necessary for increasing thermal efficiency of modern gas turbines. To prevent failure of turbine components, advance cooling technologies have been applied to different portions of turbine blades. The detailed film cooling effectiveness distributions along a rotor blade has been studied under combined effects of upstream trailing edge unsteady wake with coolant ejection by the pressure sensitive paint (PSP). The experiment is conducted in a low speed wind tunnel with a five blade linear cascade and exit Reynolds number is 370,000. The density ratios for both blade and trailing edge coolant ejection range from 1.5 to 2.0. Blade blowing ratios are 0.5 and 1.0 on suction surface and 1.0 and 2.0 on pressure surface. Trailing edge jet blowing ratio and Strouhal number are 1.0 and 0.12, respectively. Results show the unsteady wake reduces overall effectiveness. However, the unsteady wake with trailing edge coolant ejection enhances overall effectiveness. Results also show that the overall effectiveness increases by using heavier coolant for ejection and blade film cooling. Leading edge film cooling has been investigated using PSP. There are two test models: seven and three-row of film holes for simulating vane and blade, respectively. Four film holes’ configurations are used for both models: radial angle cylindrical holes, compound angle cylindrical holes, radial angle shaped holes, and compound angle shaped holes. Density ratios are 1.0 to 2.0 while blowing ratios are 0.5 to 1.5. Experiments were conducted in a low speed wind tunnel with Reynolds number 100,900. The turbulence intensity near test model is about 7%. The results show the shaped holes have overall higher effectiveness than cylindrical holes for both designs. As increasing density ratio, density effect on shaped holes becomes evident. Radial angle holes perform better than compound angle holes as increasing blowing and density ratios. Increasing density ratio generally increases overall effectiveness for all configurations and blowing ratios. One exception occurs for compound angle and radial angle shaped hole of three-row design at lower blowing ratio. Effectiveness along stagnation row reduces as increasing density ratio due to coolant jet with insufficient momentum caused by heavier density coolant, shaped hole, and stagnation row.

Thesis (M.S.)--Mississippi State University. Department of Aerospace Engineering. / Title from title screen. Includes bibliographical references.

Thesis (Ph. D.)--Brigham Young University. Dept. of Mechanical Engineering, 2003. / Includes bibliographical references (p. 133-136).