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

The impact of buoyancy on the development of starting flows in the near field was experimentally investigated using the Digital Particle Image Velocimetry and Planar Laser Induced Flourescence techniques. The experiments were conducted by releasing cylindri-cal columns of fluid into a glass water tank. Two diameters (0.95 and 1.9 cm) and four aspect ratios, ranging from 2 to 8, were examined. The fluid was released by bursting the thin latex membrane that held it in the tube. The buoyant fluid had a density difference of 4.7%. The flow was imaged at 60 Hz up to 7 diameters downstream. For the aspect ratio of 2, the flow developed into a single buoyant vortex ring (BVR), and was compared to a purely momentum driven vortex ring (MVR) generated with the same setup. For the aspect ratios of 4, 6, and 8, the flow was similar to a starting plume, with a vortical cap, followed by a columnar tail. The BVR's diameter grew linearly in space, with a full spreading angle of 18 degrees, while the MVR's diameter remained constant. The BVR started out as an axis touching ring, and transitioned to non-axis touching, opposite of the behavior of the MVR. The total circulation for the BVR was more than twice the amount predicted by the slug flow model, and the impulse grew linearly in time. The impulse of the MVR decayed slightly after the intial growth. The flows began to transition to thermal behavior at down-stream distance proportional to the cube root of the initial fluid volume. For all aspect ratios the impulse grew linearly in time. The growth rate was roportional to the initial buoyant force. The circulation generated by the addition of buoyancy was proportional to the square root of the initial buoyant force. Also the addition of buoyancy suppressed the separation of a starting vortex.

<div>The dynamic performance of the momentum and thermal boundary layer linked to the acoustic response dictate the efficiency of heat exchangers and the operational limits of fluid machinery. The specific time required by the boundary layer to establish or adapt to the free stream variations is vital to optimize flow control strategies as well as the thermal management of fluid systems. The proper understanding of the wall fluxes, separated flow regions and free stream response to transient conditions becomes the fulcrum of the further improvement of fluid machinery performance and endurance. Throughout this dissertation the establishment sequence and the main parameters dictating the acoustic response and the boundary layer settlement are quantified together with their implication on the wall fluxes and boundary layer detachment. </div><div><br></div><div>Unsteady Reynolds Average Navier Stokes evaluations, Large Eddy Simulations, Direct Numerical Simulations and wind tunnel experiments are exploited to analyze the transient behavior of attached and detached flow aerodynamics. The core of the research is built upon URANS simulations allowing the realization of multiple detailed parametric analyses. Thanks to its reduced computational cost, hundreds of transient flow evaluations are carried out, enabling the determination of the establishment sequence, the main flow features and relevant non-dimensional numbers. The URANS methodology is verified against experimental and analytic results on the flow conditions of the study. The Large Eddy Simulations and Direct Numerical Simulations allow further characterization of the near wall flow region behavior with much higher resolution while providing an additional source of verification for the coarser numerical tools. An experimental campaign on a novel full visual access linear wind tunnel explores the impact of mean flow sudden accelerations on the boundary layer detachment and reattachment phenomena over an ad-hoc wall mounted hump. The wind tunnel is designed based on the premises of: full visual access, spatial and temporal stability of total and static pressure together with the total temperature and fast flow settlement, minimizing the start-up phase duration of the wind tunnel. A wall mounted hump that mimics the behavior of the aft portion of a low pressure turbine is inserted in the wind tunnel guaranteeing a 2D flow separation phenomena. After steady state test article characterization series of sudden flow discharge experiments reveal the impact of mean flow transients on the boundary layer detachment inception. Finally, taking advantage of the knowledge on transient flow performance, optimum flow control mechanisms to abate boundary layer detachment are proposed. The recommended control approach effectively prevents the boundary layer separation while minimizing the energy requirement.</div>

This Thesis aims to assess the reliability of turbulence models in predicting the flow fields around the horizontal axis wind turbine (HAWT) rotor blades and also to improve our understanding of the aerodynamics of the flow field around the blades. The simulations are validated against data from the NREL/NASA Phase VI wind turbine experiments. The simulations encompass the use of fourteen turbulence models including low-and high-Reynolds-number, linear and non-linear eddy-viscosity models and Reynolds stress models. The numerical procedure is based on the finite-volume discretization of the 3D unsteady Reynolds-Averaged Navier-Stokes equations in an inertial reference frame with the sliding mesh technique to follow the motion of the rotor blades. Comparisons of power coefficient, normalised thrust, local surface pressure coefficients (CP) and the radial variation of the section average of normal force coefficients with published experimental data over a range of tip-speed ratios, lead to the identification of the turbulence models that can reliably reproduce the values of the key performance indicators. The main contributions of this study are in establishing which RANS models can produce quantitatively reliable simulations of wind turbine flows and in presenting the flow evolution over a range of operating conditions. At low (relative to the blade tip speed) wind speeds the flow over the blade surfaces remains attached and all RANS models return the correct values of key performance coefficients. At higher wind speeds there is circumferential flow separation over the downwind surface of the blade, which eventually spreads over the entire surface, Moreover, within the separation bubble the centrifugal force pumps the flow outwards, which at the higher wind speeds suppresses the formation of the classical tip vortices. More refined RANS models which do not rely on the linear effective viscosity approximation generally lead to more reliable predictions over this range of higher wind speeds. In particular the Gibson-Launder version of the Reynolds stress transport model and the high-Re versions of the Lien et al non-linear k-ε produce consistently reliable simulations over the entire range of wind speeds. By contrast some popular linear effective viscosity models, like the SST (k-ω) and the v^2-f, perform the poorest over this complex flow range. Finally all RANS models are also able to predict the dominant (lowest) frequency of the pressure fluctuations and the non-linear effective viscosity models, the Launder and Shima version of RSM and the SST are also able to return some of the higher frequencies measured.

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.

Ratings curves are conventional means to continuously provide estimates of discharges in rivers. Among the most-often adopted assumptions in building these curves are the steady and uniform flow conditions for the open-channel flow that in turn provide a one-to-one relationships between the variables involved in discharge estimation. The steady flow assumption is not applicable during propagation of storm-generated waves hence the question on the validity of the steady rating curves during unsteady flow is of both scientific and practical interest. Scarce experimental evidence and analytical inferences substantiate that during unsteady flows the relationship between some of the variables is not unique leading to looped rating curves (also labeled hysteresis). Neglecting the unsteadiness of the flow when this is large can significantly affect the accuracy of the flow estimation. Currently, the literature does not offer criteria for a comprehensive evaluation of the methods for estimation of the departure of the looped rating curves from the steady ones nor for identifying the most appropriate means to dynamically capturing hysteresis for different possible river flow conditions. Therefore, the overarching goal of this study was to explore the uncertainty of the conventional approaches for constructing stage-discharge rating curves (hQRCs) and to evaluate methodologies for accurate and continuous discharge monitoring in unsteady open channel flows using analytical inference, index velocity rating curves (VQRCs), and continuous slope area method (CSA) with considerations on discharge measurement uncertainty. The study will demonstrate conceptual and experimental evidences to illustrate some of the unsteady flow impacts on rating curves and suggest the development of a uniform end-to-end methodology to enhance the accuracy of the current protocols for continuous stream flow estimation for both steady and unsteady river conditions. Moreover, hysteresis diagnostic method will be presented to provide the way to conveniently evaluate when and where the hysteresis becomes significant as a function of the site and storm event characteristics. The measurement techniques and analysis methodologies proposed herein will allow to dynamically tracking both the flood wave propagation and the associated uncertainty in the conventional RCs.

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.

This study presents an unsteady-state hydraulic model analysis of hurricane storm surge and rainfall-runoff interactions in the Clear Creek Watershed, a basin draining into Galveston Bay and vulnerable to flooding from both intense local rainfalls and storm surge. Storm surge and rainfall-runoff have historically been modeled separately, and thus the linkage and interactions between the two during a hurricane are not completely understood. This study simulates the two processes simultaneously by using storm surge stage hydrographs as boundary conditions in the Hydrologic Engineering Center’s – River Analysis System (HEC-RAS) hydraulic model. Storm surge hydrographs for a severe hurricane were generated in the Advanced Circulation Model for Oceanic, Coastal, and Estuarine Waters (ADCIRC) model to predict the flooding that could be caused by a worst-case scenario. Using this scenario, zones have been identified to represent areas in the Clear Creek Watershed vulnerable to flooding from storm surge, rainfall, or both.

Much research in the area of process integration has focused on steady-state processes. However, there are many process units that are inherently unsteady-state or perform best when operated in an unsteady-state manner. Unsteady-state units are vital to chemical processes but are unable to be included in current process optimization methods. Previous methods to optimize processes containing unsteady-state units place restrictions or constraints on their use. This optimization still does not give the best system design because the solution found will only be the best out of the available options which likely excludes the true optimal design. To remedy this, a methodology was created to incorporate unsteady-state process units into process optimization analysis. This methodology is as general as possible. Unlike many existing unsteadystate optimization methods, it determines all three main components of process design: the network configuration, sizes of units, and operation schedule. This generality ensures that the truly optimal process design will be found. Three problems were solved to illustrate the solution methodology. First, a general mass exchange network was optimized. The optimization formulation resulted in a mixed-integer nonlinear program, and linearization techniques were used to find the global solution. A property interception network was also optimized, the first work done using property integration for systems with unsteady-state behavior. Finally, an industrial semi-batch water purification system was optimized. This problem showed how process integration could be used to optimize a hybrid system and gain insights into the process under many different operating conditions.