Finally, we discuss some open problems closely related to the results obtained in this thesis and give some perspectives. / First, we study global subsonic and subsonic-sonic potential flows through a general infinitely long two dimensional or three dimensional axially symmetric nozzle. It is proved that there exists a critical value for the incoming mass flux so that a global uniformly subsonic flow exists in the nozzle as long as the incoming mass flux is less than the critical value. Furthermore, we establish some uniform estimates for the deflection angles and the minimum speed of the subsonic flows by combining the hodograph transformation and the comparison principle for elliptic equations. With the help of these properties and a compensated compactness framework, we prove the existence of a global subsonic-sonic flow solution in the case of the critical incoming mass flux. / Second, global existence of steady subsonic Euler flows through infinitely long nozzles is established when the variation of Bernoulli's constant in the upstream is sufficiently small and mass flux is in a suitable regime with an upper critical value. One of the main difficulties lies in that the full steady Euler system is a hyperbolic-elliptic coupled system in a subsonic region. A key point is to use stream function formulation for compressible Euler equations. By this formulation, Euler equations are equivalent to a quasilinear second order equation for stream function. We obtain existence of solution to the boundary value problem for stream function with the help of estimate for elliptic equation of two variables. Asymptotic behavior for the stream function is obtained via a blow up argument and energy estimate. This asymptotic behavior, together with some refined estimates on the stream function, yields the consistency of the stream function formulation and the original Euler equations. / Xie, Chunjing. / "August 2007." / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1075. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 139-140). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

本論文會討論有關於二維的耗散準地轉方程，特別是有關於存在性及規律性的問題。有關的討論主要取決於該方程的分數冪。這份論文中將會介紹一些最近有關耗散準地轉方程的結果。 / This paper is discussing about problems in the 2-D Dissipative Quasi-Geostrophic equation, mainly the existence and regularity results, depending on the fractional power. We will introduce the recent results in this topics. / Detailed summary in vernacular field only. / Kwan, Danny. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 65-68). / Abstracts also in Chinese. / Chapter 1 --- Introduction --- p.4 / Chapter 2 --- Main Results in QG --- p.9 / Chapter 2.1 --- Definitions --- p.9 / Chapter 2.2 --- Subcritical Case (γ>[1/2]) --- p.10 / Chapter 2.3 --- Critical Case (γ=[1/2]) --- p.10 / Chapter 2.4 --- Supercritical Case (γ<[1/2]) --- p.11 / Chapter 3 --- The Proofs of Main Results --- p.12 / Chapter 3.1 --- Some Previous Results --- p.12 / Chapter 3.2 --- Subcritical Case (γ>[1/2]) --- p.14 / Chapter 3.2.1 --- Proof of Theorem 1 --- p.14 / Chapter 3.2.2 --- Proof of Theorem 2 --- p.19 / Chapter 3.2.3 --- Proof of Corollary 1 --- p.25 / Chapter 3.2.4 --- Summary for Subcritical Case --- p.27 / Chapter 3.3 --- Critical Case (γ=[1/2]) --- p.28 / Chapter 3.3.1 --- Proof of Theorem 3 --- p.28 / Chapter 3.3.2 --- Proof of Theorem 4 --- p.36 / Chapter 3.3.3 --- Summary for Critical Case --- p.41 / Chapter 3.4 --- Supercritical Case (γ<[1/2]) --- p.41 / Chapter 3.4.1 --- Proof of Theorem 5 --- p.41 / Chapter 3.4.2 --- Proof of Theorem 6 --- p.50 / Chapter 3.4.3 --- Proof of Theorem 7 --- p.54 / Chapter 3.4.4 --- Summary for Supercritical Case --- p.64 / Chapter 4 --- Further Development --- p.65

Next, we consider that the fluids are isentropic and the domain is also bounded, smooth, simply connected in R2 . We show that the estimates are uniform in all time if the smallness assumption on the initial data is prescribed. It follows that the solutions of compressible Navier-Stokes equations converge to the incompressible ones uniformly in both spatial and temporal variables as the Mach number vanishes. / This thesis deals with the low Mach number limit of the compressible Navier-Stokes equations. It is to verify that the compressible fluids become incompressible as Mach number tends to zero. In another words, the pressure due to compression can be neglected. This is a singular limit. / We will show that, as the Mach number tends to zero, the local smooth solutions of compressible Navier-Stokes equations with zero thermal conductivity coefficient converge strongly to the solutions of incompressible Navier-Stokes equations, provided that the initial data satisfy the "bounded derivative conditions". The key point, which is one of our main contributions, is the uniform high norm estimates in Mach number. We will study two cases. The first case is that, the domain is a finite interval and the boundary condition for the velocity is no-slip. In the second case, the domain is bounded, smooth, and simply connected in R2 . The boundary condition for the velocity is replaced by the slip-type's, thus the vorticity and the divergence of velocity can be estimated separately. / Ou, Yaobin. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3546. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 107-111). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

No description available.

Chu Shun Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 63-65). / Abstracts in English and Chinese. / Acknowledgments --- p.i / Abstract --- p.ii / Introduction --- p.3 / Chapter 1 --- Preliminaries --- p.8 / Chapter 2 --- Singular Integrals --- p.15 / Chapter 2.1 --- Marcinkiewicz Integral --- p.15 / Chapter 2.2 --- Decomposition in cubes of open sets in Rn --- p.17 / Chapter 2.3 --- Interpolation Theorem for Lp --- p.18 / Chapter 2.4 --- Singular Integrals on homogeneous of degree 0 --- p.25 / Chapter 3 --- Solutions to the Euler Equations --- p.36 / Chapter 3.1 --- Existence and Uniqueness of smooth solutions for Euler Equations --- p.36 / Chapter 3.2 --- Rate of Convergence and Decay in Time --- p.43 / Chapter 3.2.1 --- Rate of Convergence --- p.43 / Chapter 3.2.2 --- Lp Decay for Solutions of the Navier-Stokes Equations --- p.46 / Chapter 3.3 --- Weak Solution to the Euler Equations --- p.48 / Chapter 3.3.1 --- Weak Solution to the Velocity Formulation --- p.49 / Chapter 3.3.2 --- Weak Solution to the Vorticity Formulation --- p.52 / Bibliography --- p.63

Not available / text

Bibliography: leaves 77-78 / 78 leaves : ill. (some col.) ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Applied Mathematics, 1986

One approach to examining the stability of a fluid flow is to linearize the evolution equation at an equilibrium and determine (if possible) the stability of the resulting linear evolution equation. In this dissertation, the space of perturbations of the equilibrium flow is split into two classes and growth of the linear evolution operator on each class is analyzed. Our classification of perturbations is most naturally described in V.I. Arnold’s geometric view of fluid dynamics. The first class of perturbations we examine are those that preserve the topology of vortex lines and the second class is the factor space corresponding to the first class. In this dissertation we establish lower bounds for the essential spectral radius of the linear evolution operator restricted to each class of perturbations. / text

A thesis submitted to the Faculty of Engineering and the Built Environment, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2016 / The blind headings created in room and pillar mining are known to be the high risk areas of the coal mine, since this is where the coal production is actually taking place and hence the liberation of maximum quantity of methane. The ventilation of this region called the localized ventilation is carried out using auxiliary ventilation devices. This ventilation may be planned and be the subject of mine standards, but it is not very well understood and implementation on a day to day basis is usually left to the first level of supervisory staff. Majority of the methane explosions have been found to occur in these working areas and blind headings. The correct use of auxiliary ventilation devices can only be carried out once the effect of the system variables associated with each device is very well understood and can be calculated mathematically. Presently, no mathematical models or empirical formulas exist to estimate the effect of the associated system variables on the flow rates close to the face of the heading. The extent of ventilation of a heading ventilated without the use of any auxiliary device is not clear. Furthermore, to design additional engineering solutions, the flow patterns inside these heading ventilated with the auxiliary ventilation devices needs to be understood. The study of the face ventilation systems and the effect of the system variables associated system with each auxiliary ventilation device can be carried out experimentally, but doing a large number of experiments underground is very difficult as it disturbs the mine production cycles. Furthermore, studying the flow patterns experimentally is even more cumbersome, and can only be done to some extent using smoke or tracer gas. Therefore, Computational Fluid Dynamic‟s (CFD) advanced numerical code ANSYS Fluent was used to study the effect of a number of system variables associated with the face ventilation systems used in blind headings. As part of the procedure, the CFD model used was validated using four validation studies, in which the numerical results were compared with the actual experimental results. The numerical results differed to a maximum of 10% for all the experimental results. The system variables associated with ventilation of a heading, without the use of any auxiliary device, with the use of Line Brattice (LB) and fan with duct were selected. A range of values was chosen for each variable, and scenarios were created using every possible combination of these variables. All the scenarios were simulated in Ansys Fluent, the air flow rates, air velocities, velocity vectors, and velocity contours were calculated and drawn at different locations inside the heading. The effect of each system variable was found using a comparative analysis. The results were represented in simple user-friendly form and can be used to estimate the air flows at the exit of the LB and face of the heading for various settings of the LB and fan and duct face ventilation systems. The analysis of the ventilation of a heading without the use of LB shows that a maximum penetration depth is found with the Last Through Road (LTR) velocity of 1.35m/s. The flow rates and the maximum axial velocities increase with the increase in the LTR velocity up to a depth of 10m (maximum air flowing into a heading of 1.26m3/s and 1.58m3/s is found for the 3m and 4m high heading using 2m/s LTR velocity). For the LB ventilation system the LTR velocities, heading height, length of the LB in the LTR and heading, angle of the LB in LTR, and distance of the LB to the wall of the heading (side wall) were varied to identify clearly the effect of these control variables, on the flow rate at the exit of the LB, and close to the face of the heading. The flow rate at the exit of the LB is found to be proportional to the product of the distance of the LB to the wall in the LTR and heading. The flow rate at the exit of the LB, face of the heading, and inside the heading is found proportional to the LTR velocity and height of the heading. It is found that a minimum length of LB is associated with each distance of the LB to the wall in the heading, to maximize the delivery of air close to the face of the heading. This length is found to be equal to 15m for 1m LB to wall distance, and 10m for 0.5m LB to wall distance. Mathematical models were developed to estimate the effect of each studied system variables on the flow rates at the exit of the LB and close to face of the heading. For the fan and duct systems the length, diameter, and the fan design flow rates were varied. It is found that for a force fan duct system only a maximum of 50% of the total air that reaches the face is fresh and the remaining 50% is recirculated air. The flow rate with the exhaust fan system is found to be much lower than the force fan duct system. It increases with the reduction in duct mouth to heading face distance, and increase in duct diameter. Mathematical models are developed to calculate the flow rates at the face of the heading using the effect of each studied system variable. The research reveals that the ANSYS numerical code is an appropriate tool to evaluate the face ventilation of a heading in a three dimensional environment using full scale models. The South African coal mining industry can benefit from the outcomes of this study, specially the mathematical models, in a number of ways. Ventilation engineers can now estimate the flow rates close to the face of the heading for different practical mining scenarios and ensure sufficient ventilation by using the appropriate auxiliary ventilation settings. The results can easily be developed into training aids using easy to use excel spread sheets to ensure that mineworkers at the coal face have a better understanding of the working of the auxiliary ventilation devices. It can also serve Academia as part of the curriculum to teach the future mining engineers how the different variables associated with the auxiliary ventilation system affect the ventilation in a heading. The research therefore, has the potential to provide a significant step toward, understanding airflow rates delivered by the auxiliary devices close to the face of the heading and the air flow patterns inside the heading as a basis for improving the working environment for underground mineworkers. / MT2017