Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Mechanical Engineering. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / M.S.

Finally, we prove that weak solutions to the compressible Navier-Stokes equations with the Navier boundary condition stabilize to static equilibrium states under a fair condition. / First, we show that the most general class of weak solutions to one-dimensional full compressible Navier-Stokes equations do not exhibit vacuum states in a finite time provided that no vacuum is present initially with the minimum physical assumptions on the data. Moreover, two initially non interacting vacuum regions will never meet each other in the future. / Secondly, we construct the local classical solutions to the compressible Navier-Stokes equations for initial vacuum far fields. In this case, we describe the blow-up phenomena of two-dimensional compact support smooth spherically symmetric solutions. When the far field of the initial state is away from vacuum, we obtain the global classical solutions and show the large time blow-up behavior of the gradient of the density. / This thesis deals with some important problems of compressible Navier-Stokes equations, including the well-posedness of the Cauchy problem, the regularity of the weak solutions constructed by Lions and Feireisl, and the dynamics of vacuum states, etc.. / Luo, Zhen. / Adviser: Zhouping Xin. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 152-161). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The present study aims to explore the dynamical behavior in the uniform flow by numerical method. The theoretical model is based on transient of continuity equation and momentum equation in CFD software: Fluent. With User Define Function¡]UDF¡^, we can simulate the Vortex-induced vibration¡]VIV¡^under the uniform flow by numerical method and plot the contour of amplitude and flow field under different Reynolds number. We will identify the accurate and capable of central difference method in UDF by comparing with the previous study. Also, we focus on whether the amplitude and flow situation will effect by uniform flow in different degrees or not. Furthermore, this study shows how the time step size and mesh effect the conclusion so that we could have the best choice on model.

Circular cylinders in cross-flow or the motion of circular cylinders in a fluid at rest are especially of interest in fields such as offshore and civil engineering or heat exchanger design in particular. A time-independent finite difference scheme, the basic equations are written in the form of the primitive-variable method, is developed to simulate the viscous flow across a streamwise oscillating circular cylinder. The mov-ing boundary of the oscillating cylinder is mapped to a fixed boundary and the boundary condition, therefore, becomes time independent. The finite difference ap-proximation and algorithm were first validated by the reported numerical simulation and flow visualization of the phenomenon £\ and phenomenon £] for a flow across a fixed circular cylinder. Detailed streamline patterns developed in the process are then described and discussed. Surface pressure distribution and position of separation point versus phases of various stationary and oscillating stages are discussed. The flow be-haviors of various amplitudes of exciting velocity and frequency of moving cylinder are simulated and compared. The relation between Keulegan-Carpenter and the drag force on cylinder during cylinder oscillation was also calculated under various Reynolds number.

Thesis (M.S.)--Rutgers University, 2009. / "Graduate Program in Mechanical and Aerospace Engineering." Includes bibliographical references (p. 105-106).

This research deals with several novel aspects of finite element formulations and methodology in parallel adaptive simulation of flow problems. Composite macroelement schemes are developed for problems of thin fluid layers with deforming free surfaces or decomposing material phases; experiments are also run on divergence-free formulations that can be derived from the same element classes. The constrained composite nature and C¹ continuity requirements of these elements raises new issues, especially with respect to adaptive refinement patterns and the treatment of hanging node constraints, which are more complex than encountered with standard element types. This work combines such complex elements with these applications and with parallel adaptive mesh refinement and coarsening (AMR/C) techniques for the first time. The use of adaptive macroelement spaces also requires appropriate programming interfaces and data structures to enable easy and efficient implementation in parallel software. The algorithms developed for this work are implemented using object-oriented designs described herein. One application class of interest concerns heated viscous thin fluid layers that have a deformable free surface. These problems occur in both normal scale laboratory and industrial applications and in micro-fluidics. Modeling this flow via depth averaging gives a nonlinear boundary value problem describing the transient evolution of the film thickness. The model is dominated by surface tension effects which are described by a combination of nonlinear second and fourth-order operators. This research work also includes studies using the divergence-free forms constructed from these elements for certain classes of non-Newtonian fluids such as the Powell-Eyring and Williamson shear-thinning viscosity models. In addition to the target problems we conduct verification studies in support of the simulation development. In the final application investigated, C¹ elements are used in conforming finite element approximations of the Cahn-Hilliard phase field model for moving interface and phase separation problems. The nonlinear Cahn-Hilliard equation combines anti-diffusive configurational free energy based terms with a fourth-order interfacial free energy based term. Numerical studies include both manufactured and physically significant problems, including parametric studies of directed pattern self-assembly in phase decomposition of thin films. The main new contributions include construction of C¹ and div-free macroelement classes suitable for AMR/C with nonconforming hanging node meshes; a posteriori error estimation for fourth-order problems using these and other element classes; use of projection operators to automate the correct treatment of constraints at hanging nodes and through AMR/C steps; design of supporting data structures and algorithms for implementation in a parallel object oriented framework; variational formulations, methodology and numerical experiments with nonlinear fourth-order flow and transport models; and parametric and Monte Carlo studies of directed phase decomposition. / text

Not available / text

published_or_final_version / abstract / toc / Mechanical Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Mechanical Engineering / Master / Master of Philosophy

The two-dimensional, viscous flow around an elliptic cylinder undergoing prescribed unsteady motions is analyzed. The fluid is taken to be incompressible. Departing from the conventional vorticity-stream function approach, the Biot-Savart law of induced velocities is utilized to account for the contribution to the velocity field of the different vorticity fields comprising the flow. These include the internal vorticity due to the rotation of the body, the free vorticity in the fluid surrounding the body, and the bound vorticity distributed along the body contour. In order to apply the method, the body must be assumed to be replaced by fluid of the same density as the undisturbed surroundings. The replacement fluid must have a rigid motion exactly the same as the actual body motion. This can be achieved by placing suitable distributed vorticity fields within and on the surface of the body. The bound vorticity on the body surface is in the form of a vortex sheet, and its distribution is governed by a Fredholm integral equation of the second kind. The equation is derived in detail. It is solved numerically. The motion of the free vorticity in the flow field is governed by the Navier-Stokes equations written in terms of vorticity. The descretized vorticity transport equation is derived for a control volume and is solved numerically using an explicit method with a forward-difference for the time derivative, and a central-difference for the diffusive terms. An upwind method is used for convection terms. The results obtained using the present method are compared with a number of special cases available in the literature. Viscous flows around a circular cylinder rotating in any arbitrary fashion possess an exact solution, as presented in Chapter 2. Two cases of this flow are chosen for comparison. In the first case the circular cylinder is initially given an impulsive twist such that it rotates with a constant velocity about its axis. In the second case, the angular velocity of the circular cylinder increases with time exponentially. For a Reynolds number of 100, based on the cylinder radius and the internal vorticity, the exact solutions are compared with the numerical results. Viscous flow around an elliptic cylinder of .0996 aspect ratio rotating with a constant angular velocity is another special case, available in the literature, which is chosen for comparison. For this case the Reynolds number, based on the cylinder semi-major-axis and internal vorticity is 202. The agreement in all above-mentioned cases is excellent. Finally, viscous flow around an elliptic cylinder of .25 aspect ratio undergoing a combined translation and pitching oscillation is presented. A Reynolds number of 500, based on the semi-major-axis and body translational velocity, is chosen for this case. No similar case has been reported until now. This case, however, is only one of the many cases that can be handled by the present method.