Membrane wings are used both in nature and small aircraft as lifting surfaces. For these low Reynolds number applications, separated flows are common and are the main sources of unsteadiness. Adaptability of the membrane wing is known to improve the vehicle performance; and membrane compliancy in animal wings such as bats contributes significantly to their astonishing flights. Yet, the aerodynamic characteristics of the membranes are still largely unknown. An experimental study of flexible membranes at low Reynolds numbers was undertaken. Two-dimensional membrane aerofoils were investigated, with particular focus on the unsteady aspects. Membrane deformation, flow fields and fluid-structure interaction were examined over a range of angles of attack and freestream velocities. A comprehensive study of the effect of membrane pre-strain and excess length was carried out. Low aspect ratio membrane wings were investigated for rectangular and nonslender delta wings. The amplitude and mode of membrane vibration are found to be dependent mainly on the location and the unsteadiness level of the shear layer. The results indicate a strong coupling of unsteady flow with the membrane oscillation. With increasing Reynolds number, the separated shear layer becomes more energetic and closer to the surface. The membrane not only has smaller size of the separation region compared to a rigid aerofoil, but also excites the roll-up of large vortices which might lead to delayed stall. The membrane aerofoils with excess length exhibit higher vibration modes, earlier roll-up and smaller separated region, compared to the ones with pre-strain. This smaller separated region delays the onset of membrane vibrations to a larger incidence. For the low aspect ratio membrane wings, the combination of tip vortices and leading-edge vortex shedding results in a mixture of streamwise and spanwise vibrational modes. The flexibility benefits the rectangular wing more than the delta wing by increasing the maximum normal force and the force slope by a larger amount. Similar to the two-dimensional membrane aerofoils, the Strouhal numbers of the oscillations are on the order of unity, and there is a coupling with the wake instabilities in the post-stall region. Stronger tip vortices on membrane wings contribute significantly to total lift enhancement.

Steady, three-dimensional viscous numerical analysis of airflow over a rectangular NACA 0012 base wing (BW) with a rounded tip and with three NACA 0015 tip-sails (WTS) is performed. The flow physics and aerodynamic forces are studied at Reynolds numbers (Re) of 60,000 and 600,000, angles of attack (α) of 0, 5, 7.5, and 10°, and two sets of tip-sail dihedral angles (leading to trailing tip-sail): 50, 45, and 40° and 60, 45, and 30°. The Shear Stress Transport turbulence and intermittency-transition Reynolds number transitional turbulence models were used. For α > 0°, the WTS produced higher lift coefficients (CL) and drag coefficients (CD) than the BW. At Re = 600,000 and α > 0°, the CL/CD was higher for the WTS than the BW. Good agreement was seen with experimental data at Re = 600,000 for the BW results and the WTS CL but not the WTS CD. / October 2015

This thesis investigates bacterial motility from the mechanism permitting individual selfpropulsion to the complex collective flocking motility in Escherichia coli and Bacillus subtilis cells. Understanding bacterial swimming has intrigued scientists for decades and recently there has been a growing interest in collective swimming behaviour. The first part of this thesis reviews the characteristics of E. coli and B. subtilis cells subsequently describing the governing physics and constraints of self-propulsion in the low Reynolds regime. The second part of this thesis presents three self-contained experimental sections, examining individual swimming in non-conventional body shaped cells and subsequently focusing on concentrated bacterial swimming in normal cells. We first investigated motility in mutant spherical E. coli cells KJB24 motivated by simulations, which often model bacteria as self-propelled spheres. Somewhat unexpectedly these spherical cells do not exhibit runs and tumbles but diffuse slower than expected. As an introduction to working with microbiology and to familiarise with microbiology techniques we investigated why these spherical cells do not swim. Secondly we investigated how cellular motility varies as a function of body length by inhibiting cell division in wild-type E. coli with cephalexin; which remained motile despite body elongation. Fluorescent flagella visualization provided evidence of multiple bundle formations along the lateral walls as a mechanism to sustain motility. The average swimming velocity, body and flagella rotation rates, the number of flagella and number of flagella bundles were extracted experimentally as a function of length. The extracted experimental parameters for normal sized cells were consistent with Purcell’s model. We explored simple adaptations and scaling of this model to describe motility for filamentous cells, which agrees with experimental values. The main focus is on collective behaviour of B. subtilis by examining the onset from individual swimming to collective motility using time-lapse microscopy. Results demonstrated a smooth transition where cells self-organize into domains expanding rapidly by recruiting cells. We present advancements in B. subtilis fluorescent flagella staining which revealed unexpected multiple flagella bundle arrangements during runs, contradictory to general conjectures. Novel visualisation of flagella filaments during reversal events is presented in both E. coli and B. subtilis cells, providing experimental evidence for complex flagella ‘flipping’. Cellular reversal is hypothesized as a mechanism for quorum polarity facilitating collective swimming. We present novel flagella imaging in the setting of collective behaviour showing evidence to support quorum polarity. Subsequently we extracted the run length distributions of cells as a function of concentration, yielding a decreasing trend with increasing concentration. Using particle tracking we quantitatively extracted the mean squared displacement of swimming cells versus passive tracers at different concentrations during collective swimming, these novel results are discussed in respect to recent simulations. These presented experiments provide new insights into collective behaviour improving current understanding of this phenomenon.

There is currently growing interest in the field of Micro Air Vehicles (MAVs). A MAV is characterized by its low Reynolds numbers flight regime which makes lift and thrust creation a significant challenge. One possible solution inspired by nature is flapping flight, but instead of the large-amplitude low-frequency motion suited to the muscular actuators of nature, small-amplitude high-frequency motion may be more suitable for electrical actuators. In this thesis the effect of small-amplitude high-frequency motion is experimentally investigated focusing on three aspects: general performance improvement, deflected jets, and the effect of geometryResults presented herein demonstrate that using small-amplitude high-frequency plunging motion on a NACA 0012 airfoil at a post-stall angle of attack of 15° can lead to significant thrust production accompanying a 305% increase in lift coefficient. At low Strouhal numbers vortices form at the leading-edge during the downward motion and then convect into the wake. This ‘mode 1’ flow field is associated with high lift but low thrust. The maximum lift enhancement was due to resonance with the natural shedding frequency, its harmonics and subharmonics. At higher Strouhal numbers the vortex remains over the leading-edge area for a larger portion of the cycle and therefore loses its coherency through impingement with the upward moving airfoil. This ‘mode 2’ flowfield is associated with low lift and high thrust. At angles of attack below 12.5° very large force bifurcations are observed. These are associated with the formation of upwards or downwards deflected jets with the direction determined by initial conditions. The upwards deflected jet is associated with the counter-clockwise Trailing Edge Vortex (TEV) loitering over the airfoil and thereby pairing with the clockwise TEV to form a dipole that convects upwards. It therefore draws fluid from the upper surface enhancing the upper surface vortex leading to high lift. The downwards deflected jet is associated with the inverse. Deflected jets were not observed at larger angles of attack as the asymmetry in the strength of the TEVs was too great; nor at smaller amplitudes as the TEV strength was insufficient. To understand the effect of geometry comparable experiments were performed for a flat plate geometry. At zero degrees angle of attack deflected jets would form, as for the NACA 0012 airfoil, however their direction would switch sinusoidally with a period on the order of 100 cycles. The lift coefficient therefore also switched. At 15° angle of attack for Strouhal numbers up to unity the performance of the flat plate was comparable to the NACA 0012 airfoil. Above unity, the upper surface and lower surface leading-edge vortices form a dipole which convects away from the upper surface resulting in increased time-averaged separation and reduced lift.

This dissertation includes two fluid dynamics studies that involve fluid flows on vastly different scales, and therefore vastly different physics. The first study is of bacterial swimming using a flagellum for propulsive motion. Because bacteria are only about 10 [micrometers] in length, they swim in a very low Reynolds number (10⁻⁴) world, which is described by the linear set of governing equations known as the Stokes equations, that are a simplified version of the Navier-Stokes equations. The second study is of harmonic generation from nonlinear effects in internal, ocean-like wave beams that reflect from boundaries in a density stratified fluid. Internal wave reflection is an important oceanic process and may help sustain ocean circulation and affect global weather patterns. Such ocean processes have typical Reynold's numbers of 10¹⁰ or more and are only described by the full, nonlinear Navier-Stokes equations. In the low Reynolds number study, I examine theories by Gray et al.(1956) and Lighthill (1975) that describe swimming microorganisms using a helical flagellum for propulsive motion. I determine the resistance matrix, which can fully describe the dynamics of a flagellum, for flagella with different geometries, defined by: filament radius a, helical radius R, helical pitch [lambda], and axial length L. I use laboratory experiments and numerical simulations conducted in collaboration with Dr. Hepeng Zhang. The experiments, conducted with assistance from a fellow graduate student Chih-Hung Chen, use macroscopic scale models of bacterial flagella in a bath of highly viscous silicone oil. Numerical simulations use the Regularized Stokeslet method, which approximates the Stokeslet representation of an immersed body in a low Reynolds number flow. My study covers a biologically relevant parameter regime: 1/10R < a < 1/25R, R < [lambda] < 20R, and 2R< L <40R. I determine the three elements of the resistance matrix by measuring propulsive force and torque generated by a rotating, non-translating flagellum, and the drag force on a translating, non-rotating flagellum. I investigate the dependences of the resistance matrix elements on both the flagellum's axial length and its wavelength. The experimental and numerical results are in excellent agreement, but they compare poorly with the predictions of resistive force theory. The theory's neglect of hydrodynamic interactions is the source of the discrepancies in both the length dependence and wavelength dependence studies. I show that the experimental and simulation data scale as L/ln(L/r), a scaling analytically derived from slender body theory by my other collaborator Dr. Bin Liu. This logarithmic scaling is new and missing from the widely used resistive force theory. Dr. Zhang's work also includes a new parameterized version of resistive force theory. The second part of the dissertation is a study of harmonic generation by internal waves reflected from boundaries. I conduct laboratory experiments and two-dimensional numerical simulations of the Navier-Stokes equations to determine the value of the topographic slope that gives the most intense generation of second harmonic waves in the reflection process. The results from my experiments and simulations agree well but differ markedly from theoretical predictions by Thorpe (1987) and by Tabaei et al. (2005), except for nearly inviscid, weakly nonlinear flow. However, even for weakly nonlinear flow (where the dimensionless Dauxois-Young amplitude parameter value is only 0.01), I find that the ratio of the reflected wavenumber to the incoming wavenumber is very different from the prediction of weakly nonlinear theory. Further, I observe that for incident beams with a wide range of angles, frequencies, and intensities, the second harmonic beam produced in reflection has a maximum intensity when its width is the same as the width of the incident beam. This observation yields a prediction for the angle corresponding to the maximum in second harmonic intensity that is in excellent accord with my results from experiments and numerical simulations. / text

The purpose of the current study was to answer several questions related to hypersonic, low Reynolds number, turbulent boundary layers, of which available data related to turbulence quantities is scarce. To that end, a unique research facility was created, instrumentation was developed to acquire data in the challenging low Reynolds number (low density) domain, and meaningful data was collected and analyzed. The low Reynolds number nature of the boundary layer (Re_theta = 3700) allows for tangible DNS computations/validations using the current geometry and conditions. The boundary layer examined in this experiment resembled other, higher Reynolds number boundary layers, but also exhibited its own unique characteristics. The Van Driest equivalent velocity scaling method was found to perform well, and the log layer of the law of the wall plot matched expected theory. Noticeably absent from the data was an overlap region between the two layers, which suggests a different profile for the velocity profiles at these low Reynolds number, hypersonic conditions. The low density effects near the wall may be having an effect on the turbulence that modifies this region in a manner not currently anticipated. The Crocco-Busemann relation was found to provide satisfactory results under its general assumptions. When compared to available data, the Morkovin scaled velocity fluctuations fell almost an order of magnitude short. Currently, it is not known if this deficit is due to inadequacies with the Strong Reynolds Analogy, or the Morkovin scaling parameters. The trips seem to promote uniformity across the span of the model, and the data seems to generally be in agreement across the spanwise stations. However, additional information is needed to determine if two-dimensional simulations are sufficient for these boundary layers. When the turbulent boundary layer power spectra is analyzed, the result is found to follow the traditional power law. This result verifies that even at low Reynolds numbers, the length scales still follow the behavior described by Kolmogorov. Moving downstream of the trips, the peak RMS disturbance value grows in amplitude until it reaches a critical value. After this point, the peak begins to decrease in amplitude, but the affected region spreads throughout the boundary layer. Once the influenced region covers a significant portion of the boundary layer, transition occurs.

Current research in experimental and computational fluid dynamics is focused in the area of flow control. Flow control devices are usually classified as either passive or active. Plasma actuators are active flow control devices that require input from an external power source. Current efforts have modeled the effects of plasma actuators as a body force near the electrode. The research presented herein focuses on modeling the fluid-plasma interaction seen in dielectric barrier discharge plasma actuators as a body force vector in the region above the embedded electrode using computational fluid dynamics (CFD). This body force is modeled as the product of the gradient of the potential due to the electric field and the net charge density. In a passive flow control study, two-dimensional simulations using CFD are done with a smooth and bumpy Eppler 398 airfoil with laminar, transition, and turbulent models in an effort to improve the understanding of the flow over bumpy airfoils and to quantify the advantages or disadvantages of the bumps.

Both the need for mixing highly viscous liquids more effectively and the advance of micro-scale applications urge the development of technologies for liquid mixing at low Reynolds numbers. However, currently engineering designs which offer effective jet mixing without structural and operational complexity are still lacking. In this project, the method of enhancing liquid mixing using active pulsation in the laminar flow regime is explored experimentally. This work started by improving the inline pulsation mechanism in an existing confined jet configuration whereby the fluid from a primary planar jet and two surrounding secondary planar jets are pulsated by active fluid injection control via solenoid valves in the out-of-phase mode. The influence of Reynolds number, pulsation modes, frequency, duty cycle on mixing is then investigated using PLIF and PIV experimental techniques. A combination of different mixing mechanisms is found to be at play, including sequential segmentation, shearing and stretching, vortex entrainment and breakup. At a given net flow Reynolds number, an optimal frequency exists which scales approximately with a Strouhal number (Str=fh/Uj) about 1. This optimal frequency reflects the compromise of the vorticity strength and segmentation length. Furthermore, a lower duty cycle is found to produce a better mixing due to a resultant higher instantaneous Reynolds number in the jet flow. Overall, the improvement of the rig has resulted in an excellent mixing being achieved at a net flow Reynolds number of 166 which is at least order of magnitude lower than in the original rig. In order to achieve fast laminar mixing at even lower Reynolds numbers, the active pulsation mechanism using lateral synthetic jet pairs is designed and tested at a net flow Reynolds number ranging from 2 to 166 at which a good mixing is achieved. The influence of actuation frequency and amplitude, and different jet configuration is evaluated using PLIF and PIV experimental techniques. At the mediate to high Reynolds numbers tested in this study, the interaction and subsequent breakup of vortices play a dominant role in provoking mixing. In contrast, at the lower end of Reynolds numbers the strength of vortex rollup is weakened significantly and as a result folding and shearing of sequential segments provide the main mechanism for mixing. Therefore it is essential to use multiple lateral synthetic jet pairs to achieve good mixing in both mixing channel and synthetic jet cavity at this Reynolds number. It is found that an increase in both the actuation magnitude and frequency improves mixing, thereby the velocity ratio represents the relative strength of the pulsation velocity to the mean flow velocity is crucial for mixing enhancement. In order to identify actuation conditions for good mixing, a regression fit is conducted for the correlation between the dimensionless parameters, net flow Reynolds number Ren, stroke length L and Strouhal number Str. Over the tested range of the net flow Reynolds number from 2 to 83, the relationship of parameters is found and the velocity ratio at least above 2.0. Suggested by the comparatively small exponent, net flow Reynolds number is less influential than stroke length and Strouhal number. The success in obtaining excellent mixing using lateral synthetic jet pairs at low Reynolds numbers in the present work has opened up a promising prospect of their applications in various scenarios, including mixing of highly viscous liquids at macro-scale and micro-mixing.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24279号 / 理博第4877号 / 新制||理||1698(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)講師 市川 正敏, 教授 佐々 真一, 教授 山本 潤 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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.