An axial compressor for a domestic appliance can be designed to be smaller than an equivalent centrifugal compressor. However, the performance of such a compact axial compression system is limited by increased viscous losses and reduced flow turning at low Reynolds numbers ($Re$). In domestic appliance compressors, $Re$ is typically in the range $10^4$ - $10^5$. Although the aerodynamics of isolated aerofoils operating at these $Re$ have been studied extensively, the flow fields within low $Re$ axial compressors have not been investigated in detail. This dissertation aims to develop an improved understanding of loss variation at low $Re$ and to explore how the losses can be reduced through design changes. Experiments on a 5 times scaled-up single stage axial compressor have been conducted across a range of $Re$ of $10^4$ - $10^5$. The flow field has been characterised using detailed area traverses with a miniaturised five-hole probe at the rotor inlet, rotor exit and stator exit and a miniature hot-wire at the rotor exit. The probe was specifically designed and calibrated for the scale of the experiments and methods to improve the accuracy of the measurements have been applied including a probe geometry correction. The traverse experiments were performed at the design operating condition ($\phi=0.55$ and $Re= 6\times10^4$) and at a condition close to stall for a datum stage design, a stage with an improved stator design and two stators with compound lean. It was found that losses in the rotor were greater than the stator losses across the whole range of $Re$. As expected, the loss decreased with increasing $Re$ for both the stator and rotor. The losses were also increased by three-dimensional flow, with typical loss coefficients at the hub and tip of the blade rows in the range of $20-30\%$. A major contributor to the rotor loss was an unexpected hub separation that increased in size as $Re$ was reduced. At higher $Re$, the major loss sources were the rotor tip leakage, the stator wake and the stator hub separation. The results indicate that an improved stator design that accounts for the actual, measured, rotor exit flow field at low $Re$ could reduce the $Re$ at which blade row losses start to rise dramatically as well as reduce the loss across all $Re$. The improved stator design was better matched to the radial distribution of rotor exit flow angle, which led to a decrease in stator loss across all $Re$. For all stator designs, however, the measured stage stall margin was identical at all $Re$. This, along with the increase in velocity deficit in the rotor tip region at off-design indicates that stall occurred in the rotor and was neither $Re$ nor stator design dependent. The introduction of compound lean to the the stator design had the expected result of decreasing the endwall corner separation loss and increasing midspan losses. The experiments have shown that there was a loss increase in both the midspan and casing region much greater than the corresponding decrease in the stator hub. Also the mass flow redistribution in the experiments was larger that the redistribution predicted by the CFD. Three-dimensional RANS computations at low $Re$ of the same designs as experimentally studied were also conducted in order to investigate the predictive accuracy of industry standard CFD. The simulation results predicted the overall loss distribution but overestimated the end-wall losses and failed to capture the drop in stage performance at low $Re$. The differences with the experiments were caused by the inherent limitations of a fully turbulent solver that cannot reproduce transitional flow-features. Similarly to the experiments, there was no stall margin dependency on $Re$ in the simulations. This thesis has shown that with axial compressors designed specifically for low $Re$, the $Re$ at which the losses start increasing exponentially can be shifted from $10\times10^4$ to $ 4\times10^4$. The loss increase is predominantly caused by the rotor hub corner separation.

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 documents an extensive experimental investigation into low-Reynolds-number turbulent boundary layers flowing over a smooth flat surface in nominally zero pressure gradients. The way in which these layers are affected by variations in R(theta), i.e. the Reynolds number based on the boundary-layer momentum thickness, type of tripping device used and variations in freestream velocity, each considered independently, are investigated.

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.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18770号 / 理博第4028号 / 新制||理||1580(附属図書館) / 31721 / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 山田 道夫, 教授 玉川 安騎男, 准教授 竹広 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

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

Small UAV?s and flight vehicles in other atmospheres such as Mars are characterized by low Reynolds numbers. Low Reynolds number airfoil testing has been difficult to achieve and there are few centers that can accomplish this task. This study is an effort to develop a flight test system that will enable low Reynolds number tests to be performed with a simple glider design. The concept is to develop a high altitude glider that will be transported to altitudes reaching 100,000 feet or more by a helium filled balloon. At altitude, the glider will be released and will perform flight experiments as it descends. This region of Earth?s atmosphere, ?near space? has the conditions desired for low Reynolds number testing as well as similar properties to the surface of Mars. With the knowledge gained from this experiment, a better understanding of accomplishing flight on Mars may be attained.