Cone Research Articles

Hypersonic shock wave and turbulent boundary layer interaction in a sharp cone/flare model

A direct numerical simulation of hypersonic Shock wave and Turbulent Boundary Layer Interaction(STBLI) at Mach 6.0 on a sharp 7° half-angle circular cone/flare configuration at zero angle of attack is performed. The flare angle is 34° and the momentum thickness Reynolds number based on the incoming turbulent boundary layer on the sharp circular cone is Reθ = 2506. It is found that the mean flow is separated and the separation bubble occurring near the corner exhibits unsteadiness. The Reynolds analogy factor changes dramatically across the interaction, and varies between 1.06 and 1.27 in the downstream region, while the QP85 scaling factor has a nearly constant value of 0.5 across the interaction. The evolution of the reattached boundary layer is characterized in terms of the mean profiles, the Reynolds stress components, the anisotropy tensor and the turbulence kinetic energy. It is argued that the recovery is incomplete and the near-wall asymptotic behavior does not occur for the hypersonic interaction. In addition, mean skin friction decomposition in an axisymmetric turbulent boundary layer is carried out for the first time. Downstream of the interaction, the contributions of transverse curvature and body divergence are negligible, whereas the positive contribution associated with the turbulence kinetic energy production and the negative spatial-growth contribution are dominant. Based on scale decomposition, the positive contribution is further divided into terms with different spanwise length scales. The negative contribution is analyzed by comparing the convective term, the streamwise-heterogeneity term and the pressure gradient term.

Effects of Three-Dimensional Circular Truncated Cone Microstructures on the Performance of Flexible Pressure Sensors.

Three-dimensional microstructures play a key role in the fabrication of flexible electronic products. However, the development of flexible electronics is limited in further applications due to low positioning accuracy, the complex process, and low production efficiency. In this study, a novel method for fabricating three-dimensional circular truncated cone microstructures via low-frequency ultrasonic resonance printing is proposed. Simultaneously, to simplify the manufacturing process of flexible sensors, the microstructure and printed interdigital electrodes were fabricated into an integrated structure, and a flexible pressure sensor with microstructures was fabricated. Additionally, the effects of flexible pressure sensors with and without microstructures on performance were studied. The results show that the overall performance of the designed sensor with microstructures could be effectively improved by 69%. Moreover, the sensitivity of the flexible pressure sensor with microstructures was 0.042 kPa−1 in the working range of pressure from 2.5 to 10 kPa, and the sensitivity was as low as 0.013 kPa−1 within the pressure range of 10 to 30 kPa. Meanwhile, the sensor showed a fast response time, which was 112 ms. The stability remained good after the 100 cycles of testing. The performance was better than that of the flexible sensor fabricated by the traditional inverted mold method. This lays a foundation for the development of flexible electronic technology in the future.

On the geometry of positive cones in finitely generated groups

We study the geometry of positive cones of left-invariant total orders (left-order, for short) in finitely generated groups. We introduce the Hucha property and the Prieto property for left-orderable groups. We say that a group has the Hucha property if in any left-order the corresponding positive cone is not coarsely connected, and the Prieto property if in any left-order the corresponding positive cone is coarsely connected. We show that all left-orderable free products have the Hucha property, and that the Hucha property is stable under certain free products with amalgamatation over Prieto subgroups. As an application we show that non-abelian limit groups in the sense of Z. Sela (e.g., free groups, fundamental group of hyperbolic surfaces, doubles of free groups and others) and non-abelian finitely generated subgroups of free Q $\mathbb {Q}$ -groups in the sense of G. Baumslag have the Hucha property. In particular, this implies that these groups have empty BNS-invariant Σ 1 $\Sigma ^1$ and that they do not have finitely generated positive cones.

Evolution of texture distribution in thickness direction of aluminum sheet in metal spinning

We evaluated the texture distribution in the thickness direction of the spun workpieces and clarified the mechanism of the change in the crystal orientation of the texture during metal spinning. Blank aluminum disks with a thickness of 1.44 mm were deformed into circular truncated cone cups by under-, true shear, and over-spinning and into cylindrical cups by 13 passes of conventional spinning. Crystal orientation analysis using electron backscatter diffraction revealed that the calculations of the orientation densities for small Miller indices could lead to a systematic evaluation of high intensity texture. The orientation density of Cu {121}<11¯1> decreased or that of B {110}<11¯2> increased on the roller side of the shear-spun part, of the workpieces formed by shear spinning, and on the roller side of the wall part and on the mandrel side of the open-edge part, of the workpieces formed by conventional spinning. The cosine similarity and Euclidean distance showed that the texture distributions obtained by shear spinning and that of the wall part obtained by conventional spinning were similar. Based on the stress state and preferred crystal orientation in deep drawing, the mechanism of the change in crystal orientation during spinning were described. The density of the texture with {110} (corresponding to B in this study) parallel to a disk plane increased when tensile stress was applied in the circumferential direction, contrarily, when compressive stress was applied in a similar fashion the density of the texture with {112} (corresponding to Cu) parallel to the disk plane increased.

Mass Points, Spaces of Spheres, ”hyperbolae” and Dandelin and Quételet Theorems

The use of mass points eases the definition of a branch of a hyperbola in the Euclidean plane based on a Rational Quadratic Bézier Curve. In the space of spheres, any circular cone, circular cylinder, torus, pencil of spheres or Dupin cyclide is represented by a rational quadratic Bézier curve that is conic arc seen as circle arc. The limit points of the Poncelet pencil or the singular points of the Dupin cyclide can be determined using the asymptotes of this circle. This article shows that the use of mass points simplifies the modelling of these pencils or these Dupin cyclides in the space of spheres. The determination of the Dandelin spheres ends this work as an application.

The Analysis of Cones within the Tianwen-1 Landing Area

On 15 May 2021, the Zhurong rover of China’s first Mars mission, Tianwen-1 (TW-1), successfully landed in southern Utopia Planitia on Mars. Various landforms were present in the landing area, and this area recorded a complex geological history. Cones are one of the typical landforms in the landing area and Utopia Planitia, and they have a great significance to the local geological processes due to the diversity of their origins. Using High-Resolution Imaging Camera (HiRIC) images collected by the TW-1 orbiter, we identified a total of 272 well-preserved circular cones in the landing area. Detailed surveys of their spatial distribution, morphological characteristics, and morphometric parameters were conducted. A preliminary analysis of the surface characteristics of these cones also provides additional information to strengthen our understanding of them. The results of the high-resolution topographic analysis show that the cone heights are in the range of 10.5–90.8 m and their basal diameters range from 178.9–1206.6 m. We compared the morphometric parameters of the cones in the landing area with terrestrial and Martian analogous features and found that our measured cones are consistent with the ranges of mud volcanoes and also a small subset of igneous origin cones. However, the result of spatial analysis is more favorable to mud volcanoes, and the lower thermal inertia of the cones in the landing area compared to their surrounding materials is also a typical characteristic of mud volcanoes. Based on current evidence and analysis, we favor interpreting the cones in the TW-1 landing area as mud volcanoes.

Stress Cone Effect Analysis and Optimum Design of Extra High-Voltage Cable Joint Using Neural Networks

The major problem in high-voltage cable accessories is the electric field stress caused by the high-voltage level at the cable junction. In this paper, a neural network and simulation-based optimal design for extra high-voltage (EHV) cable accessory is proposed to ensure the optimum electrical design. The different kinds of geometries of the EHV underground cable accessory are realized in the Comsol Multiphysics software program, and the electric field analyses are conducted based on the finite element method. The design of high-voltage underground cable accessories is examined both within and without the optimal stress cone geometry. A neural network-based model is developed according to the analysis results obtained in the simulation. Thanks to this model, the geometry of the stress cone is determined. In the simulation-based analysis, the electric field stress caused by the high-voltage level at critical points is controlled with an optimum joint design using neural networks. The proposed model will contribute to EHV cable joint design at different stress levels.

Quantum particle in a spherical well confined by a cone

We consider the quantum problem of a particle in either a spherical box or a finite spherical well confined by a circular cone with an apex angle 2θ 0 emanating from the center of the sphere, with 0 < θ 0 < π. This non-central potential can be solved by an extension of techniques used in spherically-symmetric problems. The angular parts of the eigenstates depend on azimuthal angle φ and polar angle θ as where is the associated Legendre function of integer order m and (usually noninteger) degree λ. There is an infinite discrete set of values (i = 0, 1, 3, ...) that depend on m and θ 0. Each has an infinite sequence of eigenenergies , with corresponding radial parts of eigenfunctions. In a spherical box the discrete energy spectrum is determined by the zeros of the spherical Bessel functions. For several θ 0 we demonstrate the validity of Weyl’s continuous estimate for the exact number of states up to energy E, and evaluate the fluctuations of around . We examine the behavior of bound states in a well of finite depth U 0, and find the critical value U c (θ 0) when all bound states disappear. The radial part of the zero energy eigenstate outside the well is 1/r λ+1, which is not square-integrable for λ ≤ 1/2. (0 < λ ≤ 1/2) can appear for θ 0 > θ c ≈ 0.726π and has no parallel in spherically-symmetric potentials. Bound states have spatial extent ξ which diverges as a (possibly λ-dependent) power law as U 0 approaches the value where the eigenenergy of that state vanishes.

The effects of nose bluntness on broadband disturbance receptivity in hypersonic flow

While nose bluntness is known to have a large impact on the stability of hypersonic vehicles, its influence on the freestream receptivity process has not been fully characterized for a wide range of conditions. This paper investigates the effects of nose bluntness on the second mode receptivity coefficients and the development of boundary layer disturbances over two 7° half-angle circular blunt cones at Mach 10 after perturbation with broadband freestream pulses of different types. The cones have nose radii of 9.525 mm (case B) and 5.08 mm (case I). Unsteady direct numerical simulation (DNS) and linear stability theory (LST) results compare well and predict stronger second mode growth for case I in all pulse cases. Unsteady DNS also shows variations in extramodal excitation between the cones depending on freestream disturbance type. Spectral receptivity coefficients are generated by decomposing the unsteady DNS data into discrete frequency Fourier modes, which are then corrected with LST N-factors. Fast acoustic disturbances demonstrate minimal variation in receptivity coefficients, while temperature and vorticity disturbances have much higher coefficients in case I. Planar slow acoustic pulses induce stronger disturbances outside of the second mode in case I, resulting in higher peak receptivity coefficients. Results show significant variation in receptivity response based on nose bluntness, pulse geometry, and the type of incident perturbation.

Applying pytorch toolkit to plan optimization for circular cone based robotic radiotherapy

BackgroundRobotic linac is ideally suited to deliver hypo-fractionated radiotherapy due to its compact head and flexible positioning. The non-coplanar treatment space improves the delivery versatility but the complexity also leads to prolonged optimization and treatment time.MethodsIn this study, we attempted to use the deep learning (pytorch) framework for the plan optimization of circular cone based robotic radiotherapy. The optimization problem was topologized into a simple feedforward neural network, thus the treatment plan optimization was transformed into network training. With this transformation, the pytorch toolkit with high-efficiency automatic differentiation (AD) for gradient calculation was used as the optimization solver. To improve the treatment efficiency, plans with fewer nodes and beams were sought. The least absolute shrinkage and selection operator (lasso) and the group lasso were employed to address the “sparsity” issue.ResultsThe AD-S (AD sparse) approach was validated on 6 brain and 6 liver cancer cases and the results were compared with the commercial MultiPlan (MLP) system. It was found that the AD-S plans achieved rapid dose fall-off and satisfactory sparing of organs at risk (OARs). Treatment efficiency was improved by the reduction in the number of nodes (28%) and beams (18%), and monitor unit (MU, 24%), respectively. The computational time was shortened to 47.3 s on average.ConclusionsIn summary, this first attempt of applying deep learning framework to the robotic radiotherapy plan optimization is promising and has the potential to be used clinically.

Natural Convection Flow over a Vertical Permeable Circular Cone with Uniform Surface Heat Flux in Temperature-Dependent Viscosity with Three-Fold Solutions within the Boundary Layer

The aim of this study is to investigate the effects of temperature-dependent viscosity on the natural convection flow from a vertical permeable circular cone with uniform heat flux. As part of numerical computation, the governing boundary layer equations are transformed into a non-dimensional form. The resulting nonlinear system of partial differential equations is then reduced to local non-similarity equations which are solved computationally by three different solution methodologies, namely, (i) perturbation solution for small transpiration parameter (ξ), (ii) asymptotic solution for large ξ, and (iii) the implicit finite difference method together with a Keller box scheme for all ξ. The numerical results of the velocity and viscosity profiles of the fluid are displayed graphically with heat transfer characteristics. The shearing stress in terms of the local skin-friction coefficient and the rate of heat transfer in terms of the local Nusselt number (Nu) are given in tabular form for the viscosity parameter (ε) and the Prandtl number (Pr). The viscosity is a linear function of temperature which is valid for small Prandtl numbers (Pr). The three-fold solutions were compared as part of the validations with various ranges of Pr numbers. Overall, good agreements were established. The major finding of the research provides a better demonstration of how temperature-dependent viscosity affects the natural convective flow. It was found that increasing Pr, ξ, and ε decrease the local skin-friction coefficient, but ξ has more influence on increasing the rate of heat transfer, as the effect of ε was erratic at small and large ξ. Furthermore, at the variable Pr, a large ξ increased the local maxima of viscosity at large extents, particularly at low Pr, but the effect on temperature distribution was found to be less significant under the same condition. However, at variable ε and fixed Pr, the temperature distribution was observed to be more influenced by ε at small ξ, whereas large ξ dominated this scheme significantly regardless of the variation in ε. The validations through three-fold solutions act as evidence of the accuracy and versatility of the current approach.

Clinical and radiographic assessment of peri-implant tissue changes using two different implant connections with immediate implant placement and loading.

Aim: Radiographic assessment of dimensional changes of peri implant tissues in immediately placed implants with non-functional loading in maxillary esthetic zone with Internal Hex (IH) and Conical Tapered (CT) connections&#x0D; Materials and Methods: 20 immediately placed implant with immediate loading were inserted in the maxillary esthetic zone, patients meeting the inclusion criteria were allocated into one of the two groups: Internal Hex or Conical tapered connection.&#x0D; Results: Pink Esthetic Scores(PES) of the CT connection showed significantly higher values than IH. It was shown that the IH group showed statistically significant higher mean value than the CT connection in the values of crestal bone loss using CBCT.&#x0D; Conclusion: CT connection has proved to result in better clinical, radiographic and volumetric outcomes than IH.

A wrap-film technique for infrared thermography heat-transfer measurements in high-speed wind tunnels

A novel technique for obtaining quantitative infrared-thermography data on metallic (e.g., aluminum or steel) wind-tunnel models is developed. The methodology incorporates a matte-black, thin, wrap-film (3M\ exttrademark Wrap Film Series 1080), which is both commercially available and relatively inexpensive. Compared to painting the model to increase the surface emissivity, using a self-adhesive thin film makes it easier to obtain uniform thickness and roughness and is easier to apply and remove. The relevant surface properties (i.e., thickness, roughness, and directional emissivity) and thermal properties (i.e., thermal conductivity, specific heat capacity, and thermal diffusivity) of the wrap film have been measured and are reported. The high emissivity (0.95) and low thermal conductivity (0.23 W/(m K)) make it an excellent candidate for quantitative infrared-thermography. Using the experimentally measured properties, and the reported data-reduction techniques, stagnation-point heat flux was successfully measured on a blunt 7∘ half-angle circular cone in nominally Mach-6 flow. Fay & Riddell’s theory for calculating heat flux at the stagnation point provided a comparison to verify the effectiveness of the wrap-film technique for quantitative infrared thermography. The heat flux evaluated with the wrap-film technique resulted in excellent agreement with the theoretical solution with a mean error of 4.4%.

The impact of target positioning error and tumor size on radiobiological parameters in robotic stereotactic radiosurgery for metastatic brain tumors.

This study aimed to evaluate the effect of target positioning error (TPE) on radiobiological parameters, such as tumor control probability (TCP) and normal tissue complication probability (NTCP), in stereotactic radiosurgery (SRS) for metastatic brain tumors of different sizes using CyberKnife. The reference SRS plans were created using the circular cone of the CyberKnife for each spherical gross tumor volume (GTV) with diameters (φ) of 5, 7.5, 10, 15, and 20mm, contoured on computed tomography images of the head phantom. Subsequently, plans involving TPE were created by shifting the beam center by 0.1-2.0mm in three dimensions relative to the reference plans using the same beam arrangements. Conformity index (CI), generalized equivalent uniform dose (gEUD)-based TCP, and NTCP of estimated brain necrosis were evaluated for each plan. When the gEUD parameter "a" was set to - 10, the CI and TCP for the reference plan at the φ5-mm GTV were 0.90 and 80.8%, respectively. The corresponding values for plans involving TPE of 0.5-mm, 1.0-mm, and 2.0-mm were 0.62 and 77.4%, 0.40 and 62.9%, and 0.12 and 7.2%, respectively. In contrast, the NTCP for all GTVs were the same. The TCP for the plans involving a TPE of 2-mm was 7.2% and 68.8% at the φ5-mm and φ20-mm GTV, respectively. The TPEs corresponding to a TCP reduction rate of 3% at the φ5-mm and φ20-mm GTV were 0.41 and 0.99mm, respectively. TPE had a significant effect on TCP in SRS for metastatic brain tumors using CyberKnife, particularly for small GTVs.

On blockage coefficients: flow past a body in a pipe

Blockage coefficients characterize the presence of an object on uniform flow along a rigid pipe. The main purpose of the paper is to develop analytical methods for the calculation of these coefficients. For potential flow, blockage coefficients are related to the added mass of an object moving along a pipe. They also arise when matched asymptotic expansions are used to solve acoustic problems, in which Laplace’s equation is appropriate for related inner problems. Steady diffusion problems can also lead to similar harmonic problems. The paper includes some general results (such as a version of Webster’s horn equation for slender rigid objects) and some specific results for objects of various simple axisymmetric shapes (spheroids, spindles, finite circular cylinders, double cones and thin discs). Applications to various physical situations are expected in future work.

Comparison of the Bond Strength of Circular and Oval-Shaped Fiber-Reinforced Composite Posts in Oval Shaped Canals

Background: Fiber reinforced composite resin (FRC) posts are used to restore endodontically treated teeth. Many factors affect the bond strength of posts; however, there is a concern regarding the mismatch between the posts and oval root canals and its effect on posts retention. Aim: To compare the bond strength of circular and oval-shaped fiber-reinforced composite posts in oval shaped canals. Materials and Methods: Forty Five extracted single rooted human premolars with single oval-shaped root canals were decorated, endodontically treated and prepared to receive quartz reinforced composite resin posts, then they were randomly assigned to three groups, the posts in the first group (control) (n=15) were parallel with circular cross section (Match post, RTD, France), the posts in the second group (n=15) were taper with circular cross section (DtLight Illusion post, RTD, France), The posts in the third group were oval shaped (Macro lock oval post, RTD, France). The posts in the three groups were cemented with dual cure resin cement (Permflo DC Composite Luting, Ultra dent, USA). All samples were then stored in 100% relative humidityat at room temperature for 24 hours then pull-out test was performed and data were analyzed using one-way analysis of variance (ANOVA) followed by Bonferonni's post hoc test (a = 0.05). Results: Oval shaped posts showed higher bond strength values than circular posts, whether the circular posts were conical(taper)or parallel (control) (p&lt;0.05).Conclusions: The bond strength of fiber reinforced composite resin posts in oval root canals increased when the posts were oval-shaped.

Influence of Jaw Setting in the Determination of Stereotactic Small-Field Output Factors with Different Detectors.

Background:The experimental determination of relative output factors presents the greatest challenge, especially for small fields with different detectors. The aim of this study is to evaluate the influence of jaw positions on small-field output factors for the fields defined by micro-multileaf collimator and circular cones with different detectors.Materials and Methods:The stereotactic output factors were measured on Primus linear accelerator with BrainLab micro-multileaf collimator (mMLC) and circular cones as add-on tertiary collimators. Square field sizes ranging from 0.6 cm × 0.6 cm to 9.8 cm × 9.8 cm and circular fields of diameter ranging from 1.0 cm to 4.0 cm were defined by mMLC and circular cones, respectively. The influence of jaw position on output factor was assessed for different geometric configurations with three different detectors.Results:The values obtained with PinPoint ion chamber were consistent with microDiamond detector for fields greater than 24 mm × 24 mm, but an underestimation of 23.9% was noticed in 6 mm x 6 mm field size. For the mMLC defined field size of 6 mm × 6 mm, when the X-Y jaw was moved from 8 mm × 8 mm to 80 mm × 80 mm, an increase in the output by a factor of 1.7 was observed with both microDiamond and stereotactic radiosurgery diode, whereas an increase in output by a factor of 1.9 was noticed with PinPoint ion chamber.Conclusion:Output factors obtained with different detectors show high differences in the smallest field size for all collimating systems. This study confirms that the position of X and Y jaw above the tertiary collimator significantly influences the small-field output factor.

Bolt Coupling Structure of Contact Stress and the Influence Factors of Joint Stiffness Based on Finite Element Method

Considering the nonlinear factors, such as the contact and friction between plates as well as bolt and plates, bolt preload, etc.Three-dimensional finite element model of a bolted structure was constructed. Based on the elastic strain theory and finite element simulation technology, the contact stress and joint surface stiffness of bolt connection structure are studied. Assuming that the compressive stress of the connected parts is distributed in a cone, the cubic expression of the contact stress distribution is established; Through a large number of simulation experiments, the empirical formulas for calculating the stiffness of the connected parts are given, and compared with several main theoretical analysis methods, the validity and feasibility of the formulas are verified.Three mathematical expressions of contact stress was deduced, which was based on the assumption that stress distribution in a circular cone. Compared with the finite element analysis, the corresponding error is within 5.8%; The influence to contact stress between connected components was analyzed with different thickness of the connected component, the diameter of nut. the experience formula of the connection stiffness was got, compared with the finite element analysis, the error of obtained member stiffness less than 14.3%.

Acute Triangulations of the Surface of Circular Cone

Acute Triangulations of the Surface of Circular Cone

Exploring the mechanics of fish escape attempts through mesh

Predictive selectivity modelling is used to study fishing gear selectivity. These models rely on fish morphology parameters and fall-through experiments. Here, we developed a model of the mechanical interaction between a fish and a netting mesh during an escape attempt. In this model, the fish is described with three parameters: the first parameter measures its mechanical ability to penetrate a mesh and the others are body stiffness coefficients accounting for fish body deformation under mesh twine pressure. These parameters were identified from the results of a bench test simulating a fall-through experiment through a single 60-mm Polyethylene (PE) mesh. A rigid circular cone, a rigid elliptical cone and a small number of horse mackerel and haddock, offering a limited length range, were tested. Results were generalised and compared with those obtained on a piece of netting. Within the model's assumptions, it is possible to predict the success of an escape attempt if one knows the three fish parameters and the mesh load in normal and transverse directions. The study showed that escape potential is greater through an actual deformable mesh than through a non-deformable mesh. The potential size of this difference depends on the mesh load and orientation.