962 resultados para Spherical trigonometry.
Resumo:
Blends of conventional fuels such as Jet-A1 (aviation kerosene) and diesel with bio-derived components, referred to as biofttels, are gradually replacing the conventional fuels in aircraft and automobile engines. There is a lack of understanding on the interaction of spray drops of such biofuels with solid surfaces. The present study is an experimental investigation on the impact of biofuel drops onto a smooth stainless steel surface. The biofuel is a mixture of 90% commercially available camelina-derived biofuel and 10% aromatics. Biofuel drops were generated using a syringe-hypodermic needle arrangement. On demand, the needle delivers an almost spherical drop with drop diameter in the range 2.05-2.15 mm. Static wetting experiments show that the biofuel drop completely wets the stainless steel surface and exhibits an equilibrium contact angle of 5.6. High speed video camera was used to capture the impact dynamics of biofuel drops with Weber number ranging from 20 to 570. The spreading dynamics and maximum spreading diameter of impacting biofuel drops on the target surface were analyzed. For the impact of high Weber number biofuel drops, the spreading law suggests beta similar to tau(0.5) where beta is the spread factor and tau, the nondimensionalized time. The experimentally observed trend of maximum spread factor, beta(max) of camelina biofuel drop on the target surface with We compares well with the theoretically predicted trend from Ukiwe-Kwok model. After reaching beta(max), the impacting biofuel drop undergoes a prolonged sluggish spreading due to the high wetting nature of the camelina biofuel-stainless steel system. As a result, the final spread factor is found to be a little more than beta(max). (C) 2014 Elsevier Inc. All rights reserved.
Resumo:
A robust suboptimal reentry guidance scheme is presented for a reusable launch vehicle using the recently developed, computationally efficient model predictive static programming. The formulation uses the nonlinear vehicle dynamics with a spherical and rotating Earth, hard constraints for desired terminal conditions, and an innovative cost function having several components with associated weighting factors that can account for path and control constraints in a soft constraint manner, thereby leading to smooth solutions of the guidance parameters. The proposed guidance essentially shapes the trajectory of the vehicle by computing the necessary angle of attack and bank angle that the vehicle should execute. The path constraints are the structural load constraint, thermal load constraint, bounds on the angle of attack, and bounds on the bank angle. In addition, the terminal constraints include the three-dimensional position and velocity vector components at the end of the reentry. Whereas the angle-of-attack command is generated directly, the bank angle command is generated by first generating the required heading angle history and then using it in a dynamic inversion loop considering the heading angle dynamics. Such a two-loop synthesis of bank angle leads to better management of the vehicle trajectory and avoids mathematical complexity as well. Moreover, all bank angle maneuvers have been confined to the middle of the trajectory and the vehicle ends the reentry segment with near-zero bank angle, which is quite desirable. It has also been demonstrated that the proposed guidance has sufficient robustness for state perturbations as well as parametric uncertainties in the model.
Resumo:
This study is aimed toward obtaining near spherical microstructural features of Rheocast A380 aluminum alloy. Cooling slope (CS) technique has been used to generate semisolid slurry from the superheated alloy melt. Spherodization of primary grains is the heart of semisolid processing which improves mechanical properties significantly in the parts cast from semisolid state compared to the conventional casting processes. Keeping in view of the desired microstructural morphology, i.e., rosette or spherical shape of primary alpha-Al phase, successive slurry samples have been collected during melt flow and oil quenched to investigate the microstructure evolution mechanism. Conventionally cast A380 Al alloy sample shows dendritic grains surrounded by large eutectic phase whereas finer, near spherical grains have been observed within the cooling slope processed slurry and also in the solidified castings which confirms the effectiveness of semisolid processing of the alloy following cooling slope technique. Grain refiner addition into the alloy melt is found to have favorable effect which leads to the generation of finer primary grains within the slurry with higher degree of sphericity.
Resumo:
This work explores the preparation of nanocrystalline Cr3+ (1-5 mol%) doped CaSiO3 phosphors by solution combustion process and study of its photoluminescence (PL) behavior. The nanopowders are well characterized by powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM) and Fourier transform infra-red (FTIR) spectroscopy. PXRD results confirm monoclinic phase upon calcination at 950 degrees C for 3 h. SEM micrographs indicates that the powder is highly porous and agglomerated. The TEM images show the powder to consist of spherical shaped particles of size similar to 30-60 nm. Upon 323 nm excitation, the emission profile of CaSiO3:Cr3+ exhibits a narrow red emission peak at 641 nm due to E-2 -> (4)A(2) transition and broad band at 722 nm due to T-4(2g) -> (4)A(2g). It is observed that PL intensity increases with increase in Cr3+ concentration and highest PL intensity is observed for 3 mol% doped sample. The PL intensity decreases with further increase in Cr3+ doping. This decrease in PL intensity beyond 3 mol% is ascribed to concentration quenching. Racah parameters are calculated to describe the effects of electron-electron repulsion within the crystal lattice. The parameters show 21% reduction in the Racah parameter of free ion and the complex, indicating the moderate nephelauxetic effect in the lattice. (C) 2014 Elsevier B.V. All rights reserved.
Resumo:
The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments. (C) 2014 AIP Publishing LLC.
Resumo:
Dy-doped GdOOH microspherical structures were prepared in minutes without using any structure-directing agents, through the microwave irradiation route. The as-prepared product consists of nearly monodisperse sphere-like entities with each one representing a three-level hierarchy in its formation. Dy:GdOOH powder samples show a bright blue-green luminescence under UV excitation, making these structures potentially important in the field of optical and luminescent devices. Finally, thermal conversion to the corresponding oxide structures occurs at modest temperatures, spherical morphology intact and with enhanced luminescence behaviour. (C) 2014 Elsevier B.V. All rights reserved.
Resumo:
In the present work, the spray structure of diesel from a 200-mu m, single-hole solenoid injector is studied using microscopic imaging at injection pressures of 700, 1000 and 1400 bar for various gas pressures. A long-distance microscope with a high resolution camera is used for spray visualization with a direct imaging technique. This study shows that even at very high injection pressures, the spray structure in an ambient environment of atmospheric pressure reveals presence of entangled ligaments and non-spherical droplets during the injection period. With increase in the injection pressure, the ligaments tend to get smaller and spread radially. The spray structure studies are also conducted at high gas pressures in a specially designed high pressure chamber with optical access. The near nozzle spray structure at the end of the injection shows that the liquid jet breakup is improved with increase in gas density. The droplet size measurement is possible only late in the injection duration when the breakup appears to be complete and mostly spherical droplets are observed. Hence, droplet size measurements are performed after 1.3 ms from start of the injection pulse. Spatial and temporal variation in Sauter Mean `Diameter (SMD) is observed and reported for the case corresponding to an injection pressure of 700 bar. Overall, this study has highlighted the importance of verifying the extentof atomization and droplet shape even in dense sprays before using conventional dropsizing methods such as PDPA.
Resumo:
In the present work, Pt nanoparticles were produced from a reaction mixture containing a trace amount of cobalt carbonyl salt acting as a shape inducer. Nanoparticle shape evolution during reaction mixture reflux was monitored by characterizing particles extracted from the reaction mixture at different times. It was observed that 5 min of reflux produced spherical nanoparticles, 30 min of reflux produced cube shaped nanoparticles, and 60 min of reflux produced truncated octahedron morphology nanoparticles. It is illustrated that during nanoparticle synthesis the reflux process can provide energy needed for shape transformation from a metastable cube morphology to a truncated octahedron morphology which is thermodynamically the most stable geometry for fcc crystals. An optimization of the reaction reflux is thus needed for isolating metastable shapes.
Resumo:
A phase field modelling approach is implemented in the present study towards simulation of microstructure evolution during cooling slope semi solid slurry generation process of A380 Aluminium alloy. First, experiments are performed to evaluate the number of seeds required within the simulation domain to simulate near spherical microstructure formation, occurs during cooling slope processing of the melt. Subsequently, microstructure evolution is studied employing a phase field method. Simulations are performed to understand the effect of cooling rate on the slurry microstructure. Encouraging results are obtained from the simulation studies which are validated by experimental observations. The results obtained from mesoscopic phase field simulations are grain size, grain density, degree of sphericity of the evolving primary Al phase and the amount of solid fraction present within the slurry at different time frames. Effect of grain refinement also has been studied with an aim of improving the slurry microstructure further. Insight into the process has been obtained from the numerical findings, which are found to be useful for process control.
Resumo:
A method to estimate the Hall-Petch coefficient k for yield strength and flow stress of steels through nanoindentation experiments is proposed. While determination of k(f) for flow stress is on the basis of grain boundary strengthening evaluated by sharp indentation, k(y) for yield strength was computed with pop-in data from spherical indentations. Good agreement between estimated and literature data, obtained from the tensile tests, validates the proposed methodology. (C) 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
Resumo:
We propose an analytic perturbative scheme in the spirit of Lord Rayleigh's work for determining the eigenvalues of the Helmholtz equation in three dimensions inside an arbitrary boundary where the eigenfunction satisfies either the Dirichlet boundary condition or the Neumann boundary condition. Although numerous works are available in the literature for arbitrary boundaries in two dimensions, to the best of our knowledge the formulation in three dimensions is proposed for the first time. In this novel prescription, we have expanded the arbitrary boundary in terms of spherical harmonics about an equivalent sphere and obtained perturbative closed-form solutions at each order for the problem in terms of corrections to the equivalent spherical boundary for both the boundary conditions. This formulation is in parallel with the standard time-independent Rayleigh-Schrodinger perturbation theory. The efficacy of the method is tested by comparing the perturbative values against the numerically calculated eigenvalues for spheroidal, superegg and superquadric shaped boundaries. It is shown that this perturbation works quite well even for wide departure from spherical shape and for higher excited states too. We believe this formulation would find applications in the field of quantum dots and acoustical cavities.
Resumo:
The stuffed fullerene-like nano clusters based on the approximately spherical B-84, (B-12@B-12@B-60, fragment of the beta-rhombohedral boron), are proposed using Wade's Rules and the criterion of overlap matching. Thus the fifty additional electrons required to make the B-84 skeleton electron sufficient, are provided by replacing 26 boron atoms by carbon atoms and 12 boron atoms by nitrogen atoms giving rise to C26B46N12. This particular combination has the added advantage of the fullerene surface made from C2B3N five-membered rings having less strain arising from the pyramidalization of the sp(2) hybridised trigonal planar carbon or nitrogen; the natural angle needed to have an optimum overlap is not far from the 31.7 degrees required for icosahedral symmetry. The advantage from overlap-matching can be further increased by capping the two pentagonal faces of the cluster by a Li atom each, keeping the electron count the same by replacing 12 carbon atoms with 12 boron atoms. DFT based computational results support these formulations.
Resumo:
The self-organized motion of vast numbers of creatures in a single direction is a spectacular example of emergent order. Here, we recreate this phenomenon using actuated nonliving components. We report here that millimetre-sized tapered rods, rendered motile by contact with an underlying vibrated surface and interacting through a medium of spherical beads, undergo a phase transition to a state of spontaneous alignment of velocities and orientations above a threshold bead area fraction. Guided by a detailed simulation model, we construct an analytical theory of this flocking transition, with two ingredients: a moving rod drags beads; neighbouring rods reorient in the resulting flow like a weathercock in the wind. Theory and experiment agree on the structure of our phase diagram in the plane of rod and bead concentrations and power-law spatial correlations near the phase boundary. Our discovery suggests possible new mechanisms for the collective transport of particulate or cellular matter.
Resumo:
One of the greatest challenges in contemporary condensed matter physics is to ascertain whether the formation of glasses from liquids is fundamentally thermodynamic or dynamic in origin. Although the thermodynamic paradigm has dominated theoretical research for decades, the purely kinetic perspective of the dynamical facilitation (DF) theory has attained prominence in recent times. In particular, recent experiments and simulations have highlighted the importance of facilitation using simple model systems composed of spherical particles. However, an overwhelming majority of liquids possess anisotropy in particle shape and interactions, and it is therefore imperative to examine facilitation in complex glass formers. Here, we apply the DF theory to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Furthermore, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical heterogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids.
Resumo:
In present work, a systematic study has been carried out to understand the influence of source concentration on structural and optical properties of the SnO2 nanoparticles. SnO2 nanoparticles have been prepared by using chemical precipitation method at room temperature with aqueous ammonia as a stabilizing agent. X-ray diffraction analysis reveals that SnO2 nanoparticles exhibit tetragonal structure and the particle size is in range of 4.9-7.6 nm. High resolution transmission electron microscopic image shows that all the particles are nearly spherical in nature and particle size lies in range of 4.6-7 nm. Compositional analysis indicates the presence of Sn and O in samples. Blue shift has been observed in optical absorption spectra due to quantum confinement and the bandgap is in range of 4-4.16 eV. The origin of photoluminescence in SnO2 is found to be due to recombination of electrons in singly occupied oxygen vacancies with photo-excited holes in valance band.