Parabolic Tip Research Articles

Tip Vortex Study of a Rotor with Double-Swept Blade Tips

An experimental aerodynamic study was conducted, analyzing the wake structure of a four-bladed model rotor with a forward-backward swept tip geometry inspired by the ONERA-DLR “Etude d´un Rotor Aéroacoustique Technologiquement Optimisé”-design. Similar tip designs are used on some modern helicopter main rotors. The experiments were conducted at the Rotor Test Facility Göttingen (RTG) in hover-like conditions using a stereoscopic high-speed particle image velocimetry system. The results are compared with those of a reference rotor using a conventional parabolic blade tip. The test parameters include both constant-pitch cases and pitch-oscillating cases with a cyclic swashplate input. The constant-pitch tests show a two-step stall behavior for the double-swept tip, with the first step characterized by a reduced thrust slope and a reduced rotor efficiency. This effect is explained by a repositioning and a structural change of the tip vortex generation. The pitch-oscillating cases show that the double-swept tip results in an earlier tip stall compared to the parabolic geometry while maintaining high thrust levels. The dynamic tip stall yields a break-down of the wake’s tip vortex system, which is replaced by a spanwise band with small-scale turbulent structures and trailed vorticity, but no large-scale vortices.

Fast and accurate determination of the curvature-corrected field emission current

The curvature-corrected field emission current density, obtained by linearizing at or below the Fermi energy, is investigated. Two special cases, corresponding to the peak of normal energy distribution and mean normal energy, are considered. It is found that the current density evaluated using the mean normal energy results in errors in the net emission current below 3% for apex radius of curvature Ra≥5 nm and for apex fields Ea in the range of 3–10 V/nm for an emitter having a work function of ϕ=4.5 eV. An analytical expression for the net field emission current is also obtained for local parabolic tips using the generalized cosine law. The errors are found to be below 6% for Ra≥5 nm over an identical range of apex field strengths. The benchmark current is obtained by numerically integrating the current density over the emitter surface and the current density itself computed by integrating over the energy states using the exact Gamow factor and the Kemble form for the WKB transmission coefficient. The analytical expression results in a remarkable speed-up in the computation of the net emission current and is especially useful for large area field emitters having tens of thousands of emission sites.

Simulation of dendritic grain structures with a Cellular Automaton – Parabolic Thick Needle model

A multiscale numerical model, coupling the Cellular Automaton (CA) method to the Parabolic Thick Needle (PTN) method, is developed to compute dendritic microstructures. It is applied to directional solidification of bi-crystals under a frozen temperature approximation with fixed temperature gradient and fixed cooling rate. A dendritic branch is modeled as a cylinder headed by a parabolic tip. Its kinetics is computed using the PTN method from the composition field in the liquid in the vicinity of the parabola. This dendritic branch takes part in the definition of a grain envelope by its integration in a CA growth algorithm. The so-called Cellular Automaton – Parabolic Thick Needle (CAPTN) model can simulate the growth of dendritic grains while accounting for non-steady diffusion fields. The PTN method is implemented using Finite Element (FE) method on a heterogeneous mesh. An adaptive FE mesh strategy is developed to optimize computational time. The grain boundary orientation angle of a diverging bi-crystal configuration is investigated at steady state and compared to the Phase-Field (PF) method and the classical CA method. It is shown that contrary to the CA method, the CAPTN model is in good agreement with data deduced from PF simulations, demonstrating the interest of this coupling in the modeling of dendritic growth.

Ice drilling system with near-bottom hot water circulation

Ice drilling systems with near-bottom hot water circulation can be used for many challenging scientific tasks in the study of ice sheets, glaciers, and subglacial environments. These systems melt ice using water jets heated directly at the bottom of the hole, thus eliminating the use of long heavy hoses and surface pumps. To investigate the influence of the drill tip shape and nozzle diameter on the drilling process, a simplified laboratory prototype of the drill was designed and tested. The rated power of the downhole electric heater was 5.5 kW. A total of six melting tips in two groups were tested: three tips having a conical shape with different heights/angles and three parabolic tips with different focal parameters. In general, the conical tips provided a more stable drilling process. The experimental results showed that the rate of penetration (ROP) was highest when the specific load on the thermal tip was ~0.5 N cm−2 or 30% of the total drill prototype weight. The highest ROP of 2.5–3.1 m h−1was achieved with a nozzle diameter of 3.0 mm (at a flow rate of 3.0 L min−1). At the same time, the higher the flow rate, the faster the drilling speed was.

Parabolic Diamond Scanning Probes for Single-Spin Magnetic Field Imaging

Enhancing the measurement signal from solid state quantum sensors such as the nitrogen-vacancy (NV) center in diamond is an important problem for sensing and imaging of condensed matter systems. Here we engineer diamond scanning probes with a truncated parabolic profile that optimizes the photonic signal from single embedded NV centers, forming a high-sensitivity probe for nanoscale magnetic field imaging. We develop a scalable fabrication procedure based on dry etching with a flowable oxide mask to reliably produce a controlled tip curvature. The resulting parabolic tip shape yields a median saturation count rate of 2.1 $\pm$ 0.2 MHz, the highest reported for single NVs in scanning probes to date. Furthermore, the structures operate across the full NV photoluminescence spectrum, emitting into a numerical aperture of 0.46 and the end-facet of the truncated tip, located near the focus of the parabola, allows for small NV-sample spacings and nanoscale imaging. We demonstrate the excellent properties of these diamond scanning probes by imaging ferromagnetic stripes with a spatial resolution better than 50 nm. Our results mark a 5-fold improvement in measurement signal over the state-of-the art in scanning-probe based NV sensors.

Reference Electrode Positioning in PEM Fuel Cell at a Parabolic Anode Tip

AbstractTwo‐dimensional (2D) distribution of proton exchange membrane (PEM) fuel cell cathode overpotential η in the vicinity of parabolic anode tip is described by nonlinear Poisson–Boltzmann equation. The 2d shape of η is calculated numerically for the anode tip curvature varying by two orders of magnitude. It is shown that the reference electrode for measuring cathode overpotential can be located at a distance on the order of two characteristic lengths from the anode tip. For typical PEM fuel cell parameters, this distance is about 5.5 cm. A compact design for the reference electrode positioning is suggested.

Analysis and formulation of spur gear stresses with different tip modifications

Spur gears are widely used in the power transmission mechanism of several machines. Due to the transmitted torque, spur gears experience high stresses which could cause gear tooth failure by surface pitting or root fracture. Tip relief and other gear profile modification have been considered for reducing the induced stresses in the gear tooth. In this work, the influence of tip relief on stresses on a pair of identical spur gear was analyzed using commercial FEA software ANSYS, and formulae for estimating contact and bending stresses were derived. Three cases of gear sets were analyzed; a non-modified pair and another two sets with linear and parabolic tip relief profiles. The non-modified gear set frictionless contact stress was validated against the calculated AGMA pitting resistance, Hertzian contact stress and a reported contact stress value in the literature. The four methods agreed well with each other. Similarly, bending stress was also compared with the AGMA bending strength and Lewis bending stress for validation. Then, friction coefficient was varied from 0.0 to 0.3 with increment of 0.1. The gear contact stress increased up to 11% relative to the frictionless case, whereas bending stress decreased by 6%. Linear tip relief modification was carried out for increasing normalised tip relief values of 0.25 to 1.0 with increment of 0.25. The gear frictionless contact and bending stresses decreased by a maximum of 4% and 2%, respectively. Frictional contact stress increased by up to 7.1% and the bending stress is almost identical with the frictionless case. Parabolic tip relief was also carried out with similar normalised tip relief values. Frictionless contact stress decreased by 5% while frictional contact stress increased by up to 11.5% and the bending stress is also almost identical with the frictionless case. Finally, four formulae were introduced for estimating the contact and bending stresses for a tip modified spur gear.

Role of defects on the surface properties of HfC

HfC has shown promise as a material for field emission due to the low work function of the (100) surface and a high melting point. Recently, HfC tips have exhibited unexpected failure after field emission at 2200 K. Characterization of the HfC tips identified faceting of the parabolic tip dominated by coexisting (100) and (111) surfaces. To investigate this phenomenon, we used density functional theory (DFT) simulations to identify the role of defects and impurities (Ta, N, O) on HfC surface properties. Carbon vacancies increased the surface energy of the (100) surface from 2.35 J/m2 to 4.75 J/m2 and decreased the surface energy of the carbon terminated (111) surface from 8.75 J/m2 to 3.48 J/m2. Once 60% of the carbon on the (100) surface have been removed the hafnium terminated (111) surface becomes the lowest energy surface, suggesting that carbon depletion may cause these surfaces to coexist. The addition of Ta and N impurities to the surface are energetically favorable and decrease the work function, making them candidate impurities for improving field emission at high temperatures. Overall, DFT simulations have demonstrated the importance of understanding the role of defects on the surface structure and properties of HfC.

Dissociation of GaN2+ and AlN2+ in APT: Electronic structure and stability in strong DC field.

We investigate from a theoretical point of view the stability of AlN2+ and GaN2+ dications produced under high static electric fields like those reached in Atom Probe Tomography (APT) experiments. By means of quantum chemical calculations of the electronic structure of these molecules, we show that their stability is governed by two independent processes. On the one hand, the spin-orbit coupling allows some molecular excited states to dissociate by inter-system crossing. On the other hand, the action of the electric field lowers the potential energy barrier, which ensures the dication stability in standard conditions. We present a detailed example of field emission dynamics in the specific case of the 11Δ states for a parabolic tip, which captures the essentials of the process by means of a simplified model. We show that the dissociation dynamics of AlN2+ and GaN2+ is completely different despite the strong resemblance of their electronic structure.

Phase-Field Study of Electromigration-Induced Shape Evolution of a Transgranular Finger-Like Slit

Electromigration damage due to void propagation in thin films has garnered much attention due to its implications for efficient design of interconnects. Voids can drift along the line, preserving its shape, or evolve into various time-dependent configurations, which are governed by the interplay between the capillarity and electron wind force. We have employed the phase-field method to elucidate the transition of a circular void to a finger-like slit. Following an initial transient regime, the void attains an equilibrium shape with a narrow parallel slit-like body, which contains a circular rear end, and a parabolic tip. The subsequent drift of the void is characterized by shape invariance along with a steady-state slit width and velocity, which scale with the applied electric field as $$E^{-1/2}$$ and $$E^{3/2}$$ , respectively. The results obtained from phase-field simulations are critically compared with the sharp-interface solution. Repercussions of the study, in terms of prediction of void migration in flip-chip Sn-Ag-Cu solder bumps and fabrication of channels with desired micro/nanodimensions, are discussed.

Field-emission from parabolic tips: Current distributions, the net current, and effective emission area

Field emission from nano-structured emitters primarily takes place from the tips. Using recent results on the variation of the enhancement factor around the apex [Biswas et al., Ultramicroscopy 185, 1–4 (2018)], analytical expressions for the surface distribution of net emitted electrons, as well as the total and normal energy distributions are derived in terms of the apex radius Ra and the local electric field at the apex Ea. Formulae for the net emitted current and effective emission area in terms of these quantities are also obtained.

Solar air heater with hyperbolic ribs: 3D simulation with experimental validation

In this paper, 3D CFD simulations have been performed on the hyperbolic rib with parabolic tip using ANSYS FLUENT 15.0. The present work is undertaken on the optimized hyperbolic rib geometry obtained from the 2D CFD analysis recently performed by our group. The results of 3D simulation have been validated with our own experimental results and with existing well established correlations. The model predictions are in good agreement with the Blasius, Dittus Boelter correlations and the experimental results. The range of percentage deviation is less than 5%, which is reasonably good. With an aim to further improve the performance of hyperbolic ribs, the present numerical study is extended to evaluate thermo-hydraulic performance of different rib configurations such as inclined rib, V-shaped and W-shaped. For each arrangement, the rib inclination angle is varied from 30° to 90°.The inclination of rib results in an additional heat transfer enhancement due to flow separation and generation of secondary flow along the ribs. Thermohydraulic performance for V-shaped arrangement with 60° rib inclination is found to be the best at Re = 6000.

Spanwise Differences in Static and Dynamic Stall on a Pitching Rotor Blade Tip Model

An experimental investigation of static and dynamic stall on a rotor blade tip model with a parabolic tip geometry and aspect ratio 6.2 at a chord Reynolds number of 900,000 and a Mach number of 0.16 is presented. The resulting flow is analyzed based on unsteady surface pressure measurements and quantitative flow visualizations by high-speed particle image velocimetry. The flow separation is found to be delayed near the parabolic blade tip for static angles of attack as well as for sinusoidal angle of attack motions. The maximum effective angle of attack prior to stall is shifted to approximately two-thirds of the span outboard from the root because of a positive twist of the model with an increasing geometric angle of attack towards the tip. The stall onset is observed near the section with the maximum effective angle of attack, with a subsequent spanwise spreading of the flow separation. Different stages of flow separation for static angles of attack are identified one of them with the occurrence of two stall cells. During dynamic stall, the leading edge vortex formation starts near the maximum effective angle of attack and the pitching moment peak resulting from the passage of the dynamic stall vortex is higher at this section. Further inboard the maximum aerodynamic loads are of comparable magnitude whereas the outboard section shows reduced peaks due to the influence of the wing tip vortex.

Three-dimensional dendritic needle network model for alloy solidification

We present a three-dimensional (3D) formulation of the multiscale Dendritic Needle Network (DNN) model for dendritic microstructure growth. This approach is aimed at simulating quantitatively the solidification dynamics of complex hierarchical networks in spatially extended dendritic arrays, hence bridging the scale gap between phase-field simulations at the scale of a few dendrites and coarse-grained simulations on the larger scale of entire polycrystalline structures. In the DNN model, the dendritic network is represented by a network of branches that interact through the solutal diffusion field. The tip velocity V(t) and tip radius ρ(t) of each needle is determined by combining a standard solvability condition that fixes the product ρ2V and a solute flux conservation condition that fixes the product ρV2 in 2D and ρV in 3D as a function of a solutal flux intensity factor F(t). The latter measures the intensity of the solute flux in the dendrite tip region and can be calculated by contour (2D) or surface (3D) integration around the tip of each needle. We first present an extended formulation of the 2D DNN model where needles have a finite thickness and parabolic tips. This formulation remains valid for a larger range of tip Péclet number than the original thin needle formulation and is readily extended to 3D needles with paraboloidal tips. The 3D DNN model based on this thick-needle formulation is developed for both isothermal and directional solidification. Model predictions are validated by comparisons with known analytical solutions that describe the early transient and steady-state growth regimes. We exploit the power of the DNN model to characterize the competitive growth of well-developed secondary branches in 3D on the scale of the diffusion length. The results show that the length of active secondary branches increases as a power law of distance behind the tip with an exponent in good quantitative agreement with experimental measurements. Finally, we apply the model to simulate the three-dimensional directional solidification of an Al-7wt% Si alloy, which we directly compare to observed microstructures from microgravity experiments onboard the International Space Station. The predictions of selected microstructural features, such as dendrite arm spacings, show a good agreement with experiments. The computationally-efficient DNN model opens new avenues for investigating the dynamics of large dendritic arrays at length and time scales relevant to solidification experiments and processes.

Efficiency and Durability Predictions of High Performance Racing Transmissions

Efficiency and durability are key areas of research and development in modern racing drivetrains. Stringent regulations necessitate the need for components capable of operating under highly loaded conditions whilst being efficient and reliable. Downsizing, increasing the power- to-weight ratio and modification of gear teeth geometry to reduce friction are some of the actions undertaken to achieve these objectives. These approaches can however result in reduced structural integrity and component durability. Achieving a balance between system reliability and optimal efficiency requires detailed integrated multi-disciplinary analyses, with the consideration of system dynamics, contact mechanics/tribology and stress analysis/structural integrity. This paper presents an analytical model to predict quasi-static contact power losses in lubricated spur gear sets operating under the Elastohydrodynamic regime of lubrication. Tooth Contact Analysis (TCA) is used to predict variations in contact loads, local surface curvature and rolling and sliding velocities. This is combined with an extrapolated oil film thickness formula available in literature, to predict instantaneous lubricant film thickness and sub-surface stresses. Subsequently, viscous and boundary friction are estimated, enabling calculation of power losses. The presented methodology has been used to investigate the effects of parabolic tip relief on power loss and induced sub-surface stresses. The results of this investigation are also presented.

Polymer Optical Fiber Compound Parabolic Concentrator fiber tip based glucose sensor: in-Vitro Testing

We present in vitro sensing of glucose using a newly developed efficient optical fiber glucose sensor based on a compound parabolic concentrator (CPC)-tipped polymer optical fiber (POF). A batch of nine CPC-tipped POF sensors with a 35-mm fiber length is shown to have an enhanced fluorescence pickup efficiency with an average increment factor of 1.7 as compared with standard POF sensors with a plane cut fiber tip. in vitro measurements for two glucose concentrations (40 and 400 mg/dL) confirm that the CPC-tipped sensors can efficiently detect both glucose concentrations.

Polymer optical fiber compound parabolic concentrator tip for enhanced coupling efficiency for fluorescence based glucose sensors.

We demonstrate that the light excitation and capturing efficiency of fluorescence based fiber-optical sensors can be significantly increased by using a CPC (Compound Parabolic Concentrator) tip instead of the standard plane-cut tip. We use Zemax modelling to find the optimum CPC tip profile and fiber length of a polymer optical fiber diabetes sensor for continuous monitoring of glucose levels. We experimentally verify the improved performance of the CPC tipped sensor and the predicted production tolerances. Due to physical size requirements when the sensor has to be inserted into the body a non-optimal fiber length of 35 mm is chosen. For this length an average improvement in efficiency of a factor of 1.7 is experimentally demonstrated and critically compared to the predicted ideal factor of 3 in terms of parameters that should be improved through production optimization.

Coupled FEM and experimental analysis to characterize initial crack growth regime in AISI 316L(N) stainless steel

Purpose – The purpose of this paper is to present a methodology to predict initial crack growth behavior of crack or notch like stress raisers in AISI 316L(N) stainless steel material subjected to monotonic loading condition. Design/methodology/approach – The methodology for critical crack blunting corresponding to crack initiation in crack or notch like stress raisers is based on critical plastic strain (Epc) at a characteristic distance (lc), where uniform strain (Eu) is considered as Epc and two grain diameter is considered as lc. Further crack growth is based on parabolic crack tip opening displacement (CTOD) scheme established based on coupled experimental and FEM analysis of compact tension (CT) specimen subjected to mode-I loading condition. The FEM predicted load-displacement plots is compared with experimental result of CT specimens with different a/W ratios. It has shown that the proposed methodology could account initial crack blunting appropriately and predict the fracture load and load-displacement plots for initial crack growth regime. Findings – The results show that for crack growth with near straight crack front, experimental data from a CT specimen of particular a/W ratio coupled with plane strain 2D FEM analysis could predict load vs displacement plots for different a/W ratios when initial crack blunting is accounted appropriately with a local damage model. Originality/value – The present study is a part of developing methods to analyse fracture behavior of AISI 316L(N) SS material components used for fast breeder reactor-based power plant being built at Kalpakkam, India.

Measurement of the roughness of nano-scale surfaces, both unannealed and with limited anneal, by atomic force microscopy

The roughness and bias measured for surfaces scanned by a parabolic atomic-force microscope tip are analyzed computationally for surfaces exhibiting a random, Gaussian population of heights, uncorrelated from pixel to pixel. The fraction of the surface with which the probe is in contact is then analyzed in detail to show the area fraction of the surface that is, in practice, contacted within a defined tolerance. This shows that it is very difficult to measure much of these surfaces for any significant roughness even though the roughness value may sometimes be approximately correct. The surface is then allowed a limited anneal, and the improvement in the validity of the measurement is determined. Annealing removes the very short-range structure and permits more meaningful roughnesses to be determined with a greater fraction of the surface contacted by the probe. This limited anneal may simulate the behaviour of hot atoms that are incident or impacted by energetic ions and that rapidly cool at the surface. Asymmetric, non-Gaussian height distributions are also analyzed, and these generate a significantly different measurement bias that can be more sensitive to the tip radius. The height distribution shapes alter with the tip radius, so accurate estimation of the originating height distribution is not possible. Simple equations are provided to describe the effects.

Selection of stable growth conditions for the parabolic dendrite tip in crystallization of multicomponent melts

Free growth of a dendrite crystal in a stationary multicomponent melt is investigated. A mathematical model of the process is developed and its analytic solution is constructed. A stability criterion is obtained for a 2D parabolic dendrite and the refined relation is derived for the growth rate of the dendrite tip taking into account the anisotropy of surface tension at the solid phase-melt interface. It is shown that the accumulation of impurity in the front of a dendrite makes it tip thinner and reduces its velocity. The theory contains limiting transitions to the familiar dendrite growth criteria for one-component and binary systems.