Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without effective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional effects, unsteadiness, turbulence, variable material properties, non-newtonian fluids, multi-phase flows, wall slip, and thermal effects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working fluids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse effects due to fouling, and compatibility with power system working fluids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-fitting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses five problems involving our new Reynolds equation. In the first, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the "effective bulk modulus". The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplified formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically three-dimensional flows. A finite difference scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed flows. This Reynolds equation is then solved using perturbation methods for high-speed flows. It is found that the flow structure is comprised of five boundary layer regions in addition to the main ``core'' region. The flow in two of these boundary layer regions is governed by a nonlinear heat equation and the flow in three of these boundary layers is governed by nonlinear relaxation equations. Finite difference schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the flow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical flows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the first detailed discussions of the physics of lubrication in dense and supercritical flows, and the discovery of boundary layer structures in flows associated with thrust bearings. / Doctor of Philosophy / Lubrication theory plays a fundamental role in all mechanical design as well as applications to biomechanics. All machinery are composed of moving parts which must be protected against wear and damage. Without eective lubrication, maintenance cycles will be shortened to impractical levels resulting in increased costs and decreased reliability. The focus of the work presented here is on the lubrication of rotating machinery found in advanced power systems and designs involving micro-turbines. One of the earliest studies of lubrication is due to Osborne Reynolds in 1886 who recorded what is now regarded as the canonical equation governing all lubrication problems; this equation and its extensions have become known as the Reynolds equation. In the past century, Reynolds equation has been extended to include three-dimensional eects, unsteadiness, turbulence, variable material properties, non-newtonian uids, multi-phase ows, wall slip, and thermal eects. The bulk of these studies have focused on highly viscous liquids, e.g., oils. In recent years there has been increasing interest in power systems using new working uids, micro-turbines and non-fossil fuel heat sources. In many cases, the design of these systems employs the use of gases rather than liquids. The advantage of gases over liquids include the reduction of weight, the reduction of adverse eects due to fouling, and compatibility with power system working uids. Most treatments of gas lubrication are based on the ideal, i.e., low pressure, gas theory and straightforward retro-tting of the theory of liquid lubrication. However, the 21st Century has seen interest in gas lubrication at high pressures. At pressures and temperatures corresponding to the dense and supercritical gas regime, there is a strong dependence on gas properties and even singular behavior of fundamental transport properties. Simple extrapolations of the intuition and analyses of the ideal gas or liquid phase theory are no longer possible. The goal of this dissertation is to establish the correct form of the Reynolds equation valid for both low and high pressure gases and to explore the dynamics predicted by this new form of the Reynolds equation. The dissertation addresses ve problems involving our new Reynolds equation. In the rst, we establish the form appropriate for the simple benchmark problem of two-dimensional journal bearings. It is found that the material response is completely determined by a single thermodynamic parameter referred to as the eective bulk modulus. The validity of our new Reynolds equation has been established using solutions to the full Navier-Stokes-Fourier equations. We have also provided analytical estimates for the range of validity of this Reynolds equation and provided a systematic derivation of the energy equation valid whenever the Reynolds equation holds. The next three problems considered here derive local and global results of interest in high speed lubrication studies. The results are based on a perturbation analysis of our Reynolds and energy equation resulting in simplied formulas and the explicit dependence of pressure, temperature, friction losses, load capacity, and heat transfer on the thermodynamic state and material properties. Our last problem examines high pressure gas lubrication in thrust bearings. We again derive the appropriate form of the Reynolds and energy equations for these intrinsically threedimensional ows. A nite dierence scheme is employed to solve the resultant (elliptic) Reynolds equation for both moderate and high-speed ows. This Reynolds equation is then solved using perturbation methods for high-speed ows. It is found that the ow structure is comprised of ve boundary layer regions in addition to the main core region. The ow in two of these boundary layer regions is governed by a nonlinear heat equation and the ow in three of these boundary layers is governed by nonlinear relaxation equations. Finite dierence schemes are employed to obtain detailed solutions in the boundary layers. A composite solution is developed which provides a single solution describing the ow in all six regions to the same accuracy as the individual solutions in their respective regions of validity. Overall, the key contributions are the establishment of the appropriate forms of the Reynolds equation for dense and supercritical ows, analytical solutions for quantities of practical interest, demonstrations of the roles played by various thermodynamic functions, the rst detailed discussions of the physics of lubrication in dense and supercritical ows, and the discovery of boundary layer structures in ows associated with thrust bearings.

A methodology for the design of small autonomous underwater vehicle propulsion systems has been developed and applied to the Virginia Tech 690 AUV. The methodology is novel in that it incorporates fast design level codes capable of predicting the viscous effects of low Reynolds number flow that is experienced by small, slow turning propellers. The methodology consists of determining the minimum induced loss lift distribution for the propeller via lifting line theory, efficient airfoil sections for the propeller via a coupled viscous-inviscid flow solver and optimization, brushless DC motor identification via ideal motor theory and total system efficiency estimates. The coupled viscous-inviscid flow solver showed low Reynolds number flow effects to be of critical importance in the propeller design. The original Virginia Tech 690 AUV propulsion system was analyzed yielding an experimental efficiency of 26.5%. A new propeller was designed based on low Reynolds number airfoil section data yielding an experimental efficiency of 42.7%. Finally, an entirely new propulsion system was designed using the methodology developed herein yielding a predicted efficiency of 57-60%. / Master of Science

No description available.

An adaptive wing, a zero mass ux ow control device for low speed airfoil separation control, is investigated both experimentally and computationally at low speeds. The adaptive mechanism in the wings provides variable camber that can be actuated across a range of frequencies and amplitudes. Piezoelectric actuators are housed in a NACA 4415 airfoil with a chord length of :203 m. The entire adaptive wing assembly is then wrapped under a layer of latex membrane to provide a exible and smooth upper surface pro le. Experimental diagnostics include ow visualization, particle image velocimetry, as well as lift and drag measurements. The numerical simulation uses a 2D incompressible CFD code based on a nite-volume structured formulation with a chimera overset grid for the purpose of parallel computing. In the current study, the dimensionless speed range examined is 2:5 104 Re 1:5 105, where particular focus is given to Re 7:5 104, where Re = U` . All experiments and simulations are conducted in the range of attack angles from 0 24 and between reduced frequency values from 0 f+ 1:09, where f+ = f` U1 . Both experimental and computational results show that the region of separation is reduced when the actuation is turned on, thus enhancing aerodynamic e ciency. The maximum coe cient of lift increases by 26% when the reduced frequency, f+, is approximately :2, where the ow control mechanism appears to be most e ective. Phase-locked PIV and CFD vorticity plots reveal that the downward motion of the surface actuation decelerates the boundary ow and increases surface pressure, resulting in the formation of a series of cross-stream vortices that provides uid entrainment towards the suction surface, hence reducing separation.

No description available.

<div>A strongly implicit, nonlinear Crank-Nicolson-based finite-difference scheme was constructed for the numerical study of the self-similar behavior of viscous gravity currents. Viscous gravity currents are low Reynolds number flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. Under the lubrication approximation, the mathematical description of the spreading of these fluids is reduced to solving a nonlinear parabolic partial differential equation for the shape of the fluid interface. This thesis focuses on the finite-speed propagation of a power-law non-Newtonian current in a variable width channel-like geometry (a "Hele-Shaw cell'') subject to a given mass conservation/balance constraint. The proposed numerical scheme was implemented on a uniform but staggered grid. It is shown to be strongly stable, while possessing formal truncation error that is of second-order in space and it time. The accuracy of the scheme was verified by benchmarking it against established analytical solutions, which were obtained via a first-kind self-similarity transformation. A series of numerical simulations confirmed that the proposed scheme accurately respects the mass conservation/balance constraint. Next, the numerical scheme was used to study the second-kind self-similar behaviour of Newtonian viscous gravity currents flowing towards the end of a converging channel. Second-kind self-similar transformations are not fully specified without further information from simulation or experiment. Thus, using the proposed numerical scheme, the self-similar spreading and leveling leveling of the current was definitively addressed. The numerical results showed favorable comparison with experimental data.</div>

The environmental and monetary cost of energy has renewed interest in horizontal-axis wind turbines (HAWT). One problem with HAWT design is turbulent winds, which cause cyclic loading and reduced life. Controlling short-term aerodynamic fluctuations with blade pitching or mechanical flaps is limited by the speed of actuation. The objective was to investigate using jet-flap-like fluidic actuators on the 'suction surface' of an aerofoil for rapid aerodynamic control. A NACA 0025 aerofoil was constructed for wind-tunnel experiments. The low Reynolds number (Re) flow was measured non-intrusively with particle image velocimetry (PIV). The jet showed limited effect compared to published work. The sharp trailing edge and distance to the jet were determined to be critical factors. At Re≈100000 the 'suction surface' jet sheet is less useful for control than the conventional 'pressure surface' sheet. The experiment suggests usage near the blade root on truncated aerofoils.

The environmental and monetary cost of energy has renewed interest in horizontal-axis wind turbines (HAWT). One problem with HAWT design is turbulent winds, which cause cyclic loading and reduced life. Controlling short-term aerodynamic fluctuations with blade pitching or mechanical flaps is limited by the speed of actuation. The objective was to investigate using jet-flap-like fluidic actuators on the 'suction surface' of an aerofoil for rapid aerodynamic control. A NACA 0025 aerofoil was constructed for wind-tunnel experiments. The low Reynolds number (Re) flow was measured non-intrusively with particle image velocimetry (PIV). The jet showed limited effect compared to published work. The sharp trailing edge and distance to the jet were determined to be critical factors. At Re≈100000 the 'suction surface' jet sheet is less useful for control than the conventional 'pressure surface' sheet. The experiment suggests usage near the blade root on truncated aerofoils.

The aerodynamics of two-dimensional and three-dimensional flapping motion in hover is analyzed in incompressible, laminar flow at low Reynolds number regime. The aim of this study is to understand the physics and the underlying mechanisms of the flapping motion using both numerical tools (Direct Numerical Simulation) and experimental tools (Particle Image Velocimetry PIV technique). Numerical analyses cover both two-dimensional and three-dimensional configurations for different parameters using two different flow solvers. The obtained results are then analyzed in terms of aerodynamic force coefficients and vortex dynamics. Both symmetric and cambered airfoil sections are investigated at different starting angle of attacks. Both numerical and experimental simulations are carried out at Reynolds number 1000. The experimental analysis is carried out using Particle Image Velocimetry (PIV) technique in parallel with the numerical tools. Experimental measurements are taken for both two-dimensional and three-dimensional wing configurations using stereoscopic PIV technique.

This work is focused on the aerodynamics for a proprietary laminar flow airfoil for Unmanned Aerial Vehicle (UAV) applications. The two main focuses are (1) aerodynamic performance at Reynolds number on the order of 10,000, (2) the effect of a conventional hot-wire probe on laminar separation bubbles. For aerodynamic performance, pressure and wake velocity distributions were measured at Re = 40,000 and 60,000 for a range of angles of attack. The airfoil performed poorly for these Reynolds numbers due to laminar boundary layer separation. 2-D boundary layer trips significantly improved the lift-to-drag ratio. For probe effects, three Reynolds numbers were investigated (Re = 100,000, 150,000, and 200,000), with three angles of attack for each. Pressure and surface shear distributions were measured. Flow upstream of the probe tip was not affected. Transition was promoted downstream due to the additional disturbances in the separated shear layer.