Conical Surface Research Articles

AN ANALYTIC INVERSION FORMULA FOR A RADON TRANSFORM ON A CLASS OF CONES

Since the works of Radon and Cormack on the classical Radon transform on straight lines, several generalizations involving integrations on conical surfaces have been studied. In this article, we introduce a new family of conical surfaces with arbitrary vertices of the space and axes through the origin and study the corresponding Radon transform. We derive its analytical inversion in two and three dimensions. Numerical simulations are carried out for the two-dimensional case.

Elastic property and fracture mechanics of lateral branch-branch junctions in cacti: A case study of Opuntia ficus-indica and Cylindropuntia bigelovii.

Species with various reproductive modes accompanied by different mechanical properties of their (lateral) branch-branch junctions have evolved in the cactus subfamily Opuntioideae. Older branches of Opuntia ficus-indica with fracture-resistant junctions often bear flowers and fruits for sexual reproduction, whereas younger branches break off easily and provide offshoots for vegetative propagation. Cylindropuntia bigelovii plants are known for their vegetative reproduction via easily detachable branches that can establish themselves as offshoots. We characterized the elastic and fracture behaviors of these lateral junctions by tensile testing and analyzed local strains during loading. Additionally, we carried out finite element analyses to quantify the influence of five relevant tissue layers on joint elastic behavior. Our fracture analysis revealed various fracture modes: (i) most young samples of Opuntia ficus-indica failed directly at the junction and had smooth fracture surfaces, and relative fracture strain was on median 4% of the total strain; (ii) most older samples of Opuntia ficus-indica failed at the adjacent branch and exhibited rough fracture surfaces, and relative fracture strain was on median 47%; (iii) most samples of Cylindropuntia bigelovii abscised directly at the junction and exhibited cup and cone surfaces, and relative fracture strain was on median 28%. Various geometric and mechanical properties such as junction area, fracture energy, and tensile strength were analyzed with respect to significant differences between species and age of sample. Interestingly, the abscission of lateral branches naturally triggered by wind, passing animals, or vibration showed the following differences in maximum force: 153 N (older Opuntia ficus-indica), 51 N (young Opuntia ficus-indica), and 14 N (Cylindropuntia bigelovii).

О геометрической интерпретации кватернионов конусами

The geometric interpretation of quaternions is considered. The visualization complexity of quaternions is due to the fact that these objects have four independent parameters. A literature analysis shows that the problem of geometric interpretation of quaternions has not been completely solved to date.
 The first section provides general provisions on quaternions and the necessary notations. The second section describes the classical geometric interpretation of quaternions by arcs on a unit sphere. The third section describes a new geometric interpretation and its application to the problem of a vector finite rotation.
 The geometric interpretation of the quaternion as the surface of a right circular cone is presented. This representation allow demonstrating it as a holistic object in which the scalar and vector parts are interconnected, taking into account their modules and signs.
 For the considered normalized quaternion, it is easy to understanding an important entity, the quaternion versor: in general, it is a cone, which in the limiting case of a pure scalar quaternion transform into a sphere, and in the limiting case of a pure vector quaternion transform into an ordinary vector. This distinctive feature of the proposed geometric interpretation makes it possible, even when projected onto a plane, to clearly distinguish visualization of the quaternions with a nonzero scalar part from pure vector quaternions, which is difficult to do in the other known interpretations. The representation of quaternions by cones clearly demonstrates the need for a double quaternion product, when the vector is rotated around an arbitrary axis.
 Images of quaternions as cones, spheres and vectors can be useful in the study of quaternion algebra, which is currently finding increasing use in engineering.

Heterogeneous nucleation on the conic surface substrate

Nucleation is an essential step in the crystallization process of materials and determines their properties. In industrial production, nucleating agents are often added to melt or solution systems to control the formation process of the nucleus. In this paper, we investigate the problem of heterogeneous nucleation on conical surface substrates. Within the classical nucleation theory framework, a shape factor is introduced to measure the nucleation ability on a conical surface substrate. We found that the radius of the spherical nucleus is independent of the shape of the conic surface. As the eccentricity of the conic curve increases and the smaller the shape factor for nucleation, the easier it is to nucleate. In particular, there are special cases of the non-spherical nuclei on hyperboloid, paraboloid, and ellipsoidal substrates. We have determined the relationship that the size coefficient, wetting angle, and eccentricity satisfy when spherical nuclei are formed on a conical surface substrate. Therefore, the research results of this paper provide a theoretical model for selecting nucleating agents.

Tuning up catalytical properties of electrochemically prepared nanoconical Co-Ni deposit for HER and OER

Catalysts can be successfully prepared by a simple electrochemical process. Their surface composition distinguishes catalytic activity toward hydrogen and oxygen evolution reactions. In this work, uniform Co-Ni cones were synthesized using the one-step method from an electrolyte containing a crystal modifier. Electrodeposited layers were oxidized and/or reduced in the furnace at 100 °C. Freshly electrodeposited coating was stored in air atmosphere for seven days. This results in an oxide layer forming on the surface of the catalyst. Changes in the surface composition, confirmed by the XPS method, strongly influenced the wettability, catalytic performance, and size of evolved hydrogen bubbles. The conical Co-Ni surface oxidized in a controlled way possesses the best catalytic activity towards hydrogen and oxygen evolution. Conversely, the spontaneously formed oxide layer decreases the catalytic performance in mentioned reactions compared with the fresh sample. The proper storage of synthesized samples is essential due to their desired catalytic applications. Proposed controlled oxidation can be an accessible way to increase nanomaterials catalytic performance.

Heat transfer characteristics of jet impingement onto the concave surface of a cone

ABSTRACT Heat transfer coefficient measurements for jet impingement onto the concave surface of a cone with apex angles equal to 30° and 70° are reported in this study. Static pressure measurements along the cone surface are also reported which aid in explaining the results from the heat transfer measurements. The conical geometry finds application for the heating of aircraft gas turbine engine nose bullet region which could experience ice formation whenever aircraft operates at higher altitudes. The concave surface of the cone is heated by impinging hot air tapped from the compressor. The heat transfer coefficients, which are significantly different compared to flat surface impingement, and are scarcely available, are reported in this study. The influence of the jet axis coincident with the cone axis and impinging into apex region was studied first. The methodology where a thin stainless-steel foil is heated with a known heat flux by passing electric current through it and then measuring the detailed surface temperature using an infrared thermal camera, was used to compute the wall Nusselt distribution. The Nusselt number variation is presented as a function of nondimensional apex to nozzle spacing (L/D) and the nondimensional axis displacement (O/D). Three different diameter (D equal to 10 mm,14 mm and 20 mm) pipes were used for the concentric impingement case and the Nusselt number distribution was observed not depend on the injection diameter. The jet Reynolds number was varied between 25000 and 82000. The peak Nusselt number values are similar to those for flat plate impingement and do not occur at the cone apex, but at a nondimensional distance between 3.2 and 3.9 for 4.25 < L/D < 10.25 for the 30° cone. The peak Nusselt number values increase by almost 30% with decrease in the L/D from 10.2 to 3.0. Wall static pressure measurements indicated that the peak Nusselt number values occur in regions where the interaction between the incoming and outgoing streams is strongest – these regions occur at distances downstream from the stagnation region toward cone exit. The peak heat transfer coefficient location could not be obtained for the 70° cone, but the measured maximum values are higher by 30–50% compared to those for the 30° case. The jet is able to penetrate further toward the apex of the cone for 70° cone compared to 30° cone shifting the peak heat transfer locations closer to the apex for larger apex angle case. There is insignificant influence of jet diameter on Nusselt number variation for the three diameter values investigated in this study. The influence of displacing the jet axis by a distance equal to half the jet diameter in a direction perpendicular to the cone axis was also studied but detailed measurements were possible only for the 30° cone. Two semi-circular regions, one close to the impingement tube and the other away from the tube, displaying similar heat transfer coefficient behavior were observed. A peak in the Nusselt number occurs in each semi-circular region and the magnitude of the peaks are nearly same and they lie on either side of the peak location observed for the concentric impingement case when the flow geometric parameters are similar for the two cases. The measurements for the 70° cone exhibited all features of the 30° cone but the maximum values were higher by nearly 40% for this case.

The prediction of cross-spectra from first mode instability waves within high-speed flow over sharp and blunt cones with plasma actuation

Leading edge geometries, such as cones, moving at high-speed undergo intense loading due to the growth of instability waves and turbulent transition. These instability waves are highly spatially coherent. Aerodynamic loading related to instability waves and transition cause large-amplitude vibrations within the underlying structure, which may lead to flight-vehicle failure. We examine the effect of plasma actuation on the pressure fluctuations from first mode instability waves on the cone surface via theory with flow-fields predicted by computational fluid dynamics. We present predictions for a seven-degree half-angle cone at free-stream Mach 2.0, 3.5, and 5.0 with varying nose radii. Nose radii range from 0.038 to 38.1 mm and represent both sharp and large leading edge bluntness. For non-actuated flows, we observe that very small radii leading edges do not alter the maximum growth rates. Large radii cones have lower growth rates due to a thicker boundary layer. Spatial coherence of the instability waves decreases with increasing frequency. The growth rates are smaller at higher freestream Mach number. The effect of the simulated plasma actuator adds local heating to the flow-field. Increased nose radii lowers the relative temperature difference between the actuated and base flow-fields. The relative temperature differences are higher at higher freestream Mach number. We find that plasma actuation stabilizes the flow-field and spatial coherence becomes smaller.

Instabilities of the natural convection around a cone in thermally stratified medium.

In this paper, we provide a mathematical description of the onset of instability for buoyancy-driven flow around a cone. The self-similar solutions of the basic flow are derived, where the ambient fluid and the cone have independent temperature gradients. The linear instability properties are investigated by utilizing the Chebyshev collocation method. It is demonstrated that the neutral curves have a two-lobed structure and that changing the Grashof number has only quantitative influence on stability. The critical streamwise location increases when the half-apex angle is increased, and the unstable range of the wave number diminishes. According to the examination of eigenfunction profiles and the progression of the two spatial branches in the (α_{i},α_{r}) planes, the primary instabilities on the surface of cone are identified as type-I mode and type-II mode. The energy analysis is investigated for a typical situation to gain a physical insight, where it is demonstrated that besides the viscous dissipation, the streamline curvature and buoyancy-driven effects are dominant for the type-I mode while inviscid effect plays an essential role in type II. These encouraging results are expected to be conducive to understanding buoyancy-driven systems.

Bubble dynamics near a locally curved region of a plane rigid wall

The dynamics of a bubble near a local axisymmetric convexity or concavity, cosine-like in the axial section, on a plane rigid wall is studied under conditions of formation of a cumulative liquid jet directed to the wall. The study is performed by the boundary element method. Our main attention is focused on the bubble collapse characteristics at the moment tc when the jet impacts on the bubble surface part near the wall, namely, on the jet tip velocity and radius, the internal bubble pressure, the distance between the bubble and the uneven region of the wall, and so on. These characteristics are of interest since they, to a large extent, determine the destructive potential of cavitation. The dependences of these characteristics on the radius of the non-plane region of the wall, the depth of the concave region, the height of the convex region, and the local character of the wall unevenness have been investigated. To estimate the effect of the local character of the wall unevenness, the cases of completely concave and convex walls in the form of blunt conical surfaces are used for comparison. It has been found, in particular, that with changing radius of the convex region of the wall, the bubble shape at the moment tc varies significantly: the shape diversity includes the profiles with a gas microcavity in front of the impacting jet tip, an emerging second oppositely directed jet, and a relatively large area of the jet tip impact at its beginning.

Stress concentration of perforated cement sheath and the effect of cement sheath elastic parameters on its integrity failure during shale gas fracturing

Due to the extremely low porosity and permeability of shale, fracturing is often used to develop shale gas reservoirs. During shale fracturing, extremely high fracturing pressure may invalidate the integrity of the cement sheath and bring hidden dangers to the safe development of shale gas. This paper compares the stress state of the three-dimensional unperforated and perforated finite element models of casing-cement sheath-formation to obtain the influence of perforation on the stress concentration and failure area of the cement sheath. The stress state comparison incorporates three sets of perforation models with different hole densities and diameter verifies the stress concentration law of perforation on the cement sheath. By studying the effects of the elastic modulus and Poisson’s ratio of the cement sheath on the maximum tensile and compressive stresses of the cement sheath under fracturing pressure, the integrity failure form of the cement sheath and the measures for integrity failure are obtained. The results show that the peak stress concentration of the perforated cement sheath is about twice the normal value of the stress. The failure area is the two ends of the perforation, the shape is similar to the bottom surface of the elliptical cone, and the thickness is up to half of the wall thickness of the cement sheath. The line length of the largest failure area is 4.5 times the diameter of the hole. Under fracturing conditions, the cement sheath generally undergoes tensile failure. The lower the elastic modulus and Poisson’s ratio of the cement sheath, the smaller the tensile stress of the cement sheath, and the less likely it is to cause tensile failure.

On Time-Dependent Rheology of Sutterby Nanofluid Transport across a Rotating Cone with Anisotropic Slip Constraints and Bioconvection.

The purpose and novelty of our study include the scrutinization of the unsteady flow and heat characteristics of the unsteady Sutterby nano-fluid flow across an elongated cone using slip boundary conditions. The bioconvection of gyrotactic micro-organisms, Cattaneo–Christov, and thermal radiative fluxes with magnetic fields are significant physical aspects of the study. Anisotropic constraints on the cone surface are taken into account. The leading formulation is transmuted into ordinary differential formate via similarity functions. Five coupled equations with nonlinear terms are resolved numerically through the utilization of a MATLAB code for the Runge–Kutta procedure. The parameters of buoyancy ratio, the porosity of medium, and bioconvection Rayleigh number decrease x-direction velocity. The slip parameter retard y-direction velocity. The temperature for Sutterby fluids is at a hotter level, but its velocity is vividly slower compared to those of nanofluids. The temperature profile improves directly with thermophoresis, v-velocity slip, and random motion of nanoentities.

Ultrastructural features on the oral cavity floor (tongue, sublingual caruncle) of the Egyptian water buffalo (Bubalus bubalis): gross, histology and scanning electron microscope.

The present work was focused on the evaluation of morphological characteristics of the lingual caruncles and tongue with its papillae of Egyptian water buffalo (Bubalus bubalis) using gross examination, light and scanning electron microscopy. The ventral surface of the sublingual caruncle carried a small opening of the duct of both monostomatic and mandibular salivary gland. The lingual mucosa of dorsal, lateral border and, to some extent, of ventral surface of apex had lingual papillae (filiform, fungiform), while the lingual mucosa of the lingual body especially at torus linguae had conical papillae, but circumvallate papillae observed at the caudal part of body and root. The dorsal surface of the apex and body carried numerous long, thread-like, with blunt apex, caudally directed filiform papillae that covered with keratinised scales without secondary papillae. The degree of keratinisation classified filiform papillae into rostral part of high keratinisation and caudal of less keratinisation. Conical papillary surface carried exfoliated epithelium with longitudinal groove on its rostral surface and carried secondary papillae. Fungiform papillae were scattered among filiform papillae on the dorsal and ventral surface of the apex and its convex surface had exfoliated keratinised epithelium. Circumvallate papillae were surrounded by circular deep groove bordered by vallum that carried small secondary papillae that ended into the primary groove. Taste buds of circumvallate papillae opened in the lateral lining epithelium facing the groove. Von Ebner's glands were observed in computed tomography under papillae especially toward the groove and their ducts open into the base of the groove.

A novel combined dual-conical indentation model for determining plastic properties of metallic materials

Based on the equivalent energy principle (EEP), an explicit theoretical model between conical indentation response and uniaxial mechanical parameters is derived. In order to avoid the defect that sharp indentation technique always requires at least two indenters to penetrate different positions successively and the compatibility between the indentation points, an energy-based combined dual-conical indentation (CDI) model is created by using a novel combined indenter with dual conical surfaces. A typical piecewise load-depth curve is observed during the combined dual-conical indentation and two characteristic loading curvatures are respectively acquired from the single penetration response. Numerical verifications for the novel method are conducted by finite element analysis (FEA) within a large range of elastic–plastic materials. For six kinds of metallic materials, based on the stable load-depth curves obtained by the combined indentation tests, the uniaxial stress–strain curves as well as the yield stress, strain hardening exponent and tensile strength are predicted by CDI model. The results show that the predictions of CDI method are consistent with those from uniaxial tension. The novel method is expected to be more convenient for mechanical testing and evaluation of materials or structures.

Modeling and Analysis of Micro-Grinding Processes with the Use of Grinding Wheels with a Conical and Hyperboloid Active Surface.

In this article, a method of grinding small ceramic elements using hyperboloid and conical grinding wheels was presented. The method allowed for machining with a lower material removal speed and extending the grinding zone without reducing the efficiency of the process. In order to assess the process output parameters, numerical simulations were carried out for single-pass machining. This strategy allows for automation of the process. Grinding with a low material removal speed is recommended for the machining of small and thin elements, since this can avoid fracturing the elements. The methodology for selecting process parameters as well as the results of the abrasive grains activity analyses were presented. The analyses also concerned the roughness of machined surfaces and the variability of their textures. This grinding method was applied in the production of small ceramic elements that are used in the construction of electronic systems, and in the processing of small piezoceramic parts. This grinding technique could also be used in other grinding processes, where the removal of small machining allowances with high efficiency is required.

Geometry-induced wave-function collapse

When a quantum particle moves in a curved space, a geometric potential can arise. In spite of a long history of extensive theoretical studies, to experimentally observe the geometric potential remains a challenge. What are the physically observable consequences of such a geometric potential? Solving the Schr\"odinger equation on a truncated conic surface, we uncover a class of quantum scattering states that bear a strong resemblance to the quasiresonant states associated with atomic collapse about a Coulomb impurity, a remarkable quantum phenomenon in which an infinite number of quasiresonant states emerge. A characteristic defining feature of such collapse states is the infinite oscillations of the local density of states (LDOS) about the zero energy point separating the scattering from the bound states. The emergence of such states in the curved (Riemannian) space requires neither a relativistic quantum mechanism nor any Coulomb impurity: they have zero angular momentum and their origin is purely geometrical, hence the term ``geometry-induced wave-function collapse.'' We establish the collapsing nature of these states through a detailed comparative analysis of the behavior of the LDOS for both the zero and finite angular momentum states as well as the corresponding classical picture. Potential experimental schemes to realize the geometry-induced collapse states are articulated. Not only does our paper uncover an intrinsic connection between the geometric potential and atomic collapse, it also provides a method to experimentally observe and characterize geometric potentials arising from different subfields of physics. For example, in nanoscience and nanotechnology, curved geometry has become increasingly common. Our finding suggests that wave-function collapse should be an important factor of consideration in designing and developing nanodevices.

Motion Trajectory Planning and Design of Material Spraying Service Robot

The application of robots reduces repetitive and dangerous tasks for humans, especially the spraying robot, because many spraying materials are corrosive, toxic, and harmful. This paper designs the motion trajectory planning of the material spraying service robot. With the increasing demand for technology, there are strict requirements for the uniformity and thickness of spraying. In view of this, this paper proposes an algorithm for modeling kinematics using a joint screw and optimizes the modeling algorithm using particle swarm optimization. This makes the industrial spraying robot more intelligent and more capable of completing high-standard tasks. The experimental results in this paper show that when the spraying radii on the large-curvature cone surface are 44.5 and 49.5 mm, respectively, the coating distribution in the intersection area of the curved surfaces can be well controlled, and the optimized algorithm can better plan the path of the spraying robot.

Free convection nanofluid flow past a vertical isothermal cone surface in the presence of viscous dissipation and MHD with heat flux

Free convection nanofluid flow past a vertical isothermal cone surface in the presence of viscous dissipation and MHD with heat flux

A numerical study of a suspended compound droplet solidifying under forced convection

In this study, we numerically investigate the solidification process of a suspended compound droplet in a cold environment under forced convection by a front-tracking method. The compound droplet consisting of an inner gas core (i.e., inner bubble) surrounded by a phase-change liquid shell (i.e., outer droplet) starts solidifying from a nucleus at its bottom. The phase-change interface evolves upward to form the solid shell with an upper conical outer surface due to volume expansion. We monitor main parameters such as the Reynolds number (Re) in the range of 25–200, the Stefan number (St) in the range of 0.05–1.6, the inner-to-outer radius ratio (Rio) in the range of 0.2–0.7, the solid-to-liquid density ratio (ρs1) in the range of 0.8–1.2, the nucleus size (r0/R) in the range of 0.05–0.3, the initial eccentricity (ε0) in the range of -0.15–0.3 and the growth angle (ϕgr) in the range of 0°–15°. It is found that an increase in St, ρsl or a decrease in ϕgr leads to a decrease in the height of the solidified droplet. In contrast, an increase in Re, r0/R, ε0 or Rio has a minor effect on the drop height after complete solidification. In contrast to ρsl, which has less influence on the solidification time, the change in the value of these parameters considerably modifies the solidification time. The inner and outer aspect ratios of the solidified droplet are also revealed.

Space-streamline-based method of characteristics for inverse design of three-dimensional super/hypersonic flows

The inverse design of super/hypersonic flows is widely utilized in aerospace, especially in waveriders, inlets, and nozzles. However, most of the existing methods are intended for the two-dimensional (2D) problem. The inverse method for generalized three-dimensional (3D) supersonic flows is still immature and is the main purpose of the space-streamline-based method of characteristics (SMOC) presented in this paper. The key of SMOC is to integrate an additional Euler predictor–corrector algorithm for pressure gradients in the unit calculation process. In this way, the temporary orientation of the osculating plane (OP) of the space streamline is determined, and the conventional 2D axisymmetric method of characteristics can be adopted in the OP. Three common unit processes of SMOC and the posedness are introduced, and the astringency is demonstrated by corresponding algebraic calculations. With this method, inviscid super/hypersonic flows can be solved on the basis of specified flow features, such as a 3D shock surface or a 3D wall pressure distribution. The accuracy and efficiency of SMOC are verified by using an inverse design example, that is, the flow produced by an elliptic conical surface at a freestream Mach number of 6. The numerical simulation of the inverse design result indicates that the 3D shock wave geometry and the 3D wall pressure distribution match the targets completely. The relative root-mean-squared error of the surface geometry is 10−3 magnitude, and the computation time cost of the inverse design is less than that of the general direct Euler solver.

Experimental Investigation of Laminated Metal Matrix Composite Used in Drone Frame

Abstract: In this project design, fabrication, and analysis of sheet laminated Metal Matrix Composites will be carried out. It will be very useful for Aircraft Nose Cone, drone frames, and other surface materials of aircraft. The model of laminated metal matrix composite is designed using Catia V5 and also material to be applied to the body. Imported Geometry from Catia V5 to ANSYS will be analyzed by applying material properties and loads under different conditions. Based on ANSYS results the laminated metal matrix composite will experiment with. In that I take there are three types of Combinations of Laminated Metal Matrix Composites 1) Top and Bottom Aluminum Plate between Carbon fiber (aluminum top 1mm bottom 1mm +carbon 0.5 mm= 2.5mm thickness), 2) Top, Bottom, and Middle Aluminum in between Carbon fiber (aluminum (1+1+1)3mm + carbon 1mm= 4mm thickness), and 3) Top and Bottom Carbon and Middle Aluminum (Carbon (0.5+0.5) 1mm +aluminum 1mm =2mm thickness) which means 25%, 33%, and 50 % of carbon reinforced into aluminum metal.