Half Angle Research Articles

Study on the Improvement of Theoretical and Electric Field Simulation Methods for the Accurate Prediction of FEEP Thruster Performance

In this study, we investigate and propose an improved theoretical method to more accurately predict the performance of a field-emission electric propulsion (FEEP) thruster with its complex configuration. We identify critical flaws in the previous theoretical methods and derive corrected equations. Additionally, we define and implement the overall half angle of the Taylor cone to account for variations in the Taylor cone’s half angle depending on the applied voltage. Next, we also establish an improved method of the electric filed simulation in a three-dimensional domain to accurately predict a trajectory of extracted ions and a resulting spatial beam distribution of the FEEP thruster by incorporating a configuration of the Taylor cone with the estimated overall half angle from the results of the present theoretical method. Through comparison with the experimental measurements, we found that the present improved methods for theoretical and electric field simulations can yield more accurate predictions than those of the previous methods, especially for higher V and Iem regimes, which correspond to the actual operating conditions of the FEEP thruster. Consequently, we anticipate that the proposed methods can enhance the reliability and efficiency of the design process by accurately predicting performance when developing the new FEEP thruster with its non-symmetric complex configuration to match specific thrust or spatial beam requirements.

Optimization design of hydrogen Laval nozzle based on response surface methodology (RSM)

Abstract To conduct an in-depth study of the injection characteristics of gas fuels, the structural parameters of the nozzle are optimized. Utilizing the Response Surface Method (RSM), this study selects an inlet radius R1 , outlet radius R2 , throat straight radius R0 , expansion half angle θ, and contraction half angle α as design parameters. Based on the validated numerical model, a response surface prediction model for outlet velocity v and mass flow rate Q is established. Using the derived expressions, the contribution and interactive effects of design variables on response variables are analyzed. The findings indicate that the outlet radius and throat radius significantly affect the outlet velocity. The outlet radius positively correlates with the outlet velocity, while the throat radius negatively correlates with it. The mass flow rate is most significantly influenced by the throat radius, increasing with its increase. With outlet velocity and mass flow rate as optimization objectives, the MOGA algorithm is applied for multi-objective optimization. The optimization results indicate that the optimized structural parameters increased the centrifugal nozzle’s atomization cone angle and mass flow rate by 1.86% and 27.4%, respectively.

Propagating an Electrospray Emission Model to Array Scales Using Particle-in-Cell

A multiscale approach to multi-emitter electrospray-ion source modeling has been developed to propagate emission site conditions into spatial domains viable for plume evolution simulations. This framework uses the particle-in-cell method to maintain a feasible computational complexity for consumer-grade hardware. Source models for individual emission sites are informed by an n-body single-emitter model. Molecular effects such as ion-cluster fragmentation are included. This model is used to predict array-level properties such as plume divergence angle, and to demonstrate the computational feasibility of modeling many emitters in parallel. This framework is used to quantify the relationship between array dimensions and space-charge- induced beam divergence. It is shown that including interparticle forces in plume expansion results in an increase in plume half angle by 8.1 deg for 80% and 9.8 deg for 90% of the emitter current for a commercial electrospray thruster. These data indicate that, at the array scale, space charge has a significant effect on plume evolution and must be considered in analysis of these systems.

Prediction of gas-solid nozzle performance based on CFD and response surface methodology

In this work, structural parameters and performance prediction of fan nozzles for powder spraying are investigated. Computational Fluid Dynamics (CFD) was used to simulate the working process of the grooved fan nozzle. A Box-Behnken experimental model was developed to analyze the effects of the structural parameters on the nozzle air flow stability and working performance, taking the nozzle structural parameter contraction angle (α), the ratio of outlet to inlet diameter (d/D), the ratio of outlet diameter to length (L2/d), and the half angle of the “V”– shaped groove (β). The air flow stability and working performance of nozzle were evaluated through coefficient of variation (Cv) and standard deviation (SD). Using multiple regression analysis, the prediction model of Cv and SD on the structural parameters is established. It was obtained that: with the increase of the diameter and length of the nozzle outlet, the spray angle of the nozzle decreases. As the “V”– shaped groove angle increases, the powder spray angle decreases. The effects of structural parameters on Cv are d/D, α, β, and L2/d in ascending order, and on SD are d/D, α, β, and L2/d in ascending order. In addition, the influence of the interaction of each structural parameter on Cv and SD was obtained. This study can provide a reference for the design and structural optimization of fan nozzles for powder spraying.

Research on Noise Reduction of Water Hydraulic Throttle Valve Based on RBF Neural Network and Multi-Island Genetic Algorithm

Excessive pressure drop within the internal flow channel of the water hydraulic throttle valve will generate severe noise. In order to reduce the noise of the throttle valve, in this paper, the model of the throttle valve was established, and the flow characteristics and acoustic characteristics of the valve were simulated. The simulation results showed that the parameters of the throat structure, such as the half angle, throat inlet angle and throat length, have a significant effect on the noise of the valve. Then, the three main structural parameters were used as optimization variables, and radial basis function (RBF) neural networks and multi-island genetic algorithms (MIGA) were used to reduce the noise of the valve. The approximate model of the relationship between the structural parameters of the valve and noise was established by RBF neural networks, and MIGA was used to optimize the approximate model. Finally, the optimal valve model was established based on the obtained optimal parameters, and its noise was analyzed through simulation and experiment. The research results indicated that the optimization method, which combines RBF Neural Network and MIGA, can effectively reduce the noise of hydraulic throttle valves.

Analytical Study on the Buckling of Cylindrical Shells With Circumferential Thickness Variation Under Varying External Pressure

Abstract In this article, the analytical buckling load coefficient formula for a cylinder with circumferential thickness variation subjected to varying external pressure is established for the first time by developing a quadratic perturbation method. Based on the presented formula, some specific examples that consider either circumferential shell thickness variation or varying lateral pressure are studied and compared with those in the published literature. First, classical cosine thickness variation is analyzed. The computed results of buckling load coefficients indicate that most of differences between the proposed formula and finite element (FE) analyses in previous literature are less than 5%. Second, wind-type pressure load is discussed, and the maximum difference of predicted buckling load coefficients between our formula and results in published article is 2.3%. Third, both circumferential thickness variation and linear liquid pressure are analyzed by the proposed analytical formula and validated by the Galerkin method when both thickness and load variations are small. Therefore, accuracy and reliability of the established formula are validated. For the purpose of engineering application, buckling of a circular shell with local circumferential thickness variation due to weld shrinkage under wind-type pressure is analytically investigated. The effects of thickness variation amplitude, load parameter, half angle of thickness variation, and shell dimensions on buckling load coefficients are studied in detail.

Jets from shocked metal surfaces with grooves: Missing experiments

Many studies have investigated the mass outflows generated when a planar shock transits an imperfect (“defected”) metal surface, where the defects are symmetric triangular or sinusoidal grooves. Yet a fundamental question remains unanswered: how does the quantity of outflow mass and its maximum velocity vary as a function of the groove cross-sectional aspect ratio? We identify two sets of missing experiments that must be addressed to answer the question. The aspect ratio (groove depth over width) is equivalently represented by θ, the cross-sectional half angle, or by η0k, the amplitude multiplied by an effective wavenumber. Low θ (high η0k) grooves comprise the first set of missing experiments, which are necessary to determine the validity of theoretical predictions of the nonlinear regime (η0k≥1, θ<57.5°). The second set of missing experiments are those in which the volume of the groove (or equivalently, the axial cross-sectional area) has been held constant as θ or η0k are varied. Such experiments are necessary to independently measure the effects of variations in groove volume and groove aspect ratio on the resulting jets.

The dynamic evolution of powder flow and wall normal stress in different flow pattern silos

Major safety accidents involving silos in industrial processes are closely associated with abnormal wall stresses. The effects of different flow patterns and particle velocity distribution on wall stresses are investigated during silo discharge. The existence of particle velocity retardation layer near the wall boundary in the mass flow was observed by tracer particles and high-speed camera. The silo discharge undergoes a transformation from funnel flow to mass flow at a hopper half angle of 30°. As the outlet diameter increases, the time point of the flow pattern transformation becomes more and more later. The evolution of particle velocity in the central of the funnel flow is related to the outlet velocity wave propagation and the V-shaped surface expansion. The relationship between stress fluctuations and velocity characteristics is established. The flow channel simultaneously expands upwards as the velocity wave propagates and generates a periodic fan-shaped velocity wave at the top. The formation of stress concentration zone at the bin/hopper transition was observed.

Study the Flow Capacity of Cylindrical Pellets in Hopper with Unloading Paddle Using DEM

The hopper is an important piece of basic equipment used for storing and transporting materials in the agricultural, grain, chemical engineering, coal mine and pharmaceutical industries. The discharging performance of hoppers is mainly affected by material properties and hopper structure. In this work, the flow capacity of cylindrical pellets in the hopper with the unloading paddle is studied. A series of numerical simulation analyses with the aid of the discrete element method (DEM) platform are carried out. Then, the discharging process is illustrated, and the flow capacity of pellets in the hopper is analyzed by the mass flow index (MFI), the dynamic discharging angle (DDA) formed in the discharging process and porosity among pellets. Furthermore, the effect of parameters such as hopper half angle, rotation speed of the unloading paddle and outlet diameter of the hopper is investigated. The results show that MFI increases with an increase in hopper half angle or outlet diameter and a decrease in rotation speed. Meanwhile, DDA and porosity decrease with the increase in the hopper half angle or outlet diameter and the decrease in the rotation speed. Finally, the MFI ~0.24 is identified as the criterion to distinguish the mass flow from the funnel flow for the hopper with an unloading paddle, and the optimization results are decided as follows: hopper half angle greater than 60°, outlet diameter greater than 60 mm and rotation speed between 45 rpm and 60 rpm. These results should be useful for providing a theoretical reference for the optimization design of feeding devices for swine feeders.

Investigation of Spindt Cold Cathode Electron Guns for Terahertz Traveling Wave Tubes

In this work, a Spindt cold cathode electron gun with a PPM (periodic permanent magnet) focusing system for a terahertz TWT (traveling wave tube) was designed and simulated based on the Pierce electron gun structure. More specifically, a new 3D (three dimensional) emission model was used, where the cathode radius of the electron gun was 1 mm and the cathode current was 30 mA, with an emitting half angle of about 28°. It was demonstrated that the electron beam was well focused with an electron beam radius of 0.3 mm and a filling ratio of 0.5 when the maximum value of the PPM field along with the axis was 0.122T. According to the simulation results, a planar cold cathode electron gun was developed. Measurements demonstrated that the I/V characteristics of the cold cathode gun were consistent with that of a cold cathode, revealing that the electrons emitted from the cathode are not intercepted when passing through the electron gun.

Exact Expressions for Trigonometric Functions

Summary Solving polynomial equations and trigonometry are typically taught in separate modules or even separate classes. The derivation of a one-third angle formula gives students the opportunity to tie these two topics together. An algorithm for finding the cosine of one-third of a prescribed angle is based on Cardano’s formula. In addition, we show how this algorithm can be combined with half, double, and triple angle formulas to give exact expressions for trigonometric functions written in terms of radicals for an infinite number of angles between 0 and π / 2 .

Numerical study on the influence of nozzle divergence half angle on thrust oscillation characteristic of underwater jet power

Underwater rocket propulsion is increasingly used in advanced marine vehicles that may be subject to supersonic gaseous jets while submerged. This work investigates the influence of supersonic nozzle divergence on the multi-flow field evolution process and the thrust oscillation characteristics by multiple numerical simulations using a VOF multiphase flow model. Four nozzle divergence half angles are taken into consideration. The analysis indicates that the thrust rises sharply at nozzle closure opens, then rapidly decreases and follows another rise. The thrust oscillates at high frequencies. As a result, increase of the nozzle divergence half angle leads to the size decrease of flow bubbles but does not affect the changing trends of the thrust. Increase of the nozzle divergence half angle leads to a reduction of the frequency of the thrust oscillations.

Effect Difference of Centella asiatica Leaves Methanolic Extract on Scratch and Incision of Dimethylbenz [A] Anthracene (DMBA) Induced Dysplasia Incidence

Oral epithelial dysplasia is an abnormal cytology and architectural change that can develop into oral malignancy with a high mortality rate. Centella asiatica leaves possesses the potential to act as a chemopreventive agent and is known for its relative safety and ease of obtainability. Therefore, this study aimed to determine effect of Centella asiatica leaves extract on dysplasia induced by dimethylbenz [a] anthracene (DMBA) with scratch and incision. The in vivo study involved 21 Wistar rats (Rattus novergicus) divided into three groups. The groups received 2% Centella asiatica leaves methanolic extract orally by force-feeding once daily, from day 1 until day 61. At day 29, dysplasia was induced by scratching the buccal mucosa of each rat using a syringe containing 0.5% DMBA. This was conducted with incision 1 cm in length and half angle in depth, 1 cm in length and 1 mm in depth, and 2 cm in length and 1 mm in depth for groups 1, 2, and 3. Furthermore, the rats were sacrificed, and histopathological analysis was performed using hematoxylin-eosin staining. The degree of dysplasia was assessed using the WHO 2017 classification, and the data were analyzed using the Mann-Whitney test. Meanwhile, the statistical test showed significant difference in the degree of dysplasia for all groups. It can be concluded that Centella asiatica methanolic extract leaves possesses the potential to be a chemopreventive agent in reducing dysplasia levels.

Combined Experimental and Numerical Investigation of a Hypersonic Turbulent Boundary Layer by Means of FLDI and Large-Eddy Simulations

This work investigates a hypersonic turbulent boundary layer over a 7° half angle cone at a wall-to-total temperature ratio of 0.1, M∞=7.4 and Re∞m=4.2×106 m−1, in terms of density fluctuations and the convection velocity of density disturbances. Experimental shock tunnel data are collected using a multi-foci Focused Laser Differential Interferometer (FLDI) to probe the boundary layer at several heights. In addition, a high-fidelity, time-resolved Large-Eddy Simulation (LES) of the conical flowfield under the experimentally observed free stream conditions is conducted. The experimentally measured convection velocity of density disturbances is found to follow literature data of pressure disturbances. The spectral distributions evidence the presence of regions with well-defined power laws that are present in pressure spectra. A framework to combine numerical and experimental observations without requiring complex FLDI post-processing strategies is explored using a computational FLDI (cFLDI) on the numerical solution for direct comparisons. Frequency bounds of 160 kHz <f<1 MHz are evaluated in consideration of the constraining conditions of both experimental and numerical data. Within these limits, the direct comparisons yield good agreement. Furthermore, it is verified that in the present case, the cFLDI algorithm may be replaced with a simple line integral on the numerical solution.

Visible Wavelength Flatband in a Gallium Phosphide Metasurface

Engineering the dispersion of light in a metasurface allows for controlling the light–matter interaction strength between light confined in the metasurface and materials placed within its near-field. Specifically, engineering a flatband dispersion increases the photonic density of states, thereby enhancing the light–matter interaction. Here, we experimentally demonstrate a metasurface with a flat dispersion at visible wavelengths. We designed and fabricated a suspended one-dimensional gallium phosphide metasurface and measured the photonic band structure via energy-momentum spectroscopy, observing a photonic band that is flat over 10° of half angle at ∼590 nm. We integrated cadmium selenide nanoplatelets with the metasurface and measured coupled photoluminescence into the flatband. Our demonstration of a photonic flatband enables the possibility of integrating emerging quantum emitters to the metasurface with possible applications in nonlinear image processing and topological photonics.

A novel design of a retarding field electron energy analyzer with a cavity electrode providing extremely high energy resolution

An electron energy analyzer based on the retarding electrostatic field generated by a cavity electrode was prototyped, where the designed energy resolution is smaller than 10 meV at acceleration voltages Vo less than 5 kV and a half angle spread θo less than 20 mrad for the incident electron beams with the scanning voltage range of 3 V. Precise energy resolution, however, has not been recognized experimentally because of the difficulties of equipping such a narrow energy spread electron source. This paper describes the principle of the newly developed energy analyzer and shows the obtained energy spectra from a Schottky emitter ZrO/W(100) with a tip of the curvature radius of 1.5 μm, which could highly reproduce the theoretically expected spectra at various emitter temperatures because of its predominantly thermal emission.

Instability of Rotating-Cone Boundary Layer in Axial Inflow: Effect of Cone Angle

Boundary-layer instability on a rotating cone induces coherent spiral vortices that are linked to the onset of laminar–turbulent transition. This type of transition is relevant to several aerospace systems with rotating components, e.g., aeroengine nose cones. Because a variety of options exist for the nose-cone shapes, it is important to know how their shape affects the boundary-layer transition phenomena. This study investigates the effect of varying cone angle on the boundary-layer instability on rotating cones facing axial inflow. It is found that increasing cone angle has a stabilizing effect on the boundary layer over rotating cones in axial inflow. The parameter space of Reynolds number and local rotational speed ratio is experimentally explored to find the spiral vortex growth on rotating cones of half angle , 45°, and 50°. The previously addressed cases of and 30° are also revisited. Increasing half-cone angle is found to have a stabilizing effect on the boundary layer on the rotating cones with ; i.e., the spiral vortex growth is delayed to higher and . This effect diminishes when the half-cone angle increases from to 50°. The spiral vortex angle decreases with increasing rotational speed ratio for all the investigated cones, irrespective of the half-cone angle. However, the instability on the broader cones is found to induce shorter azimuthal wavelengths.

Investigating energy absorption of thin-walled steel structures with combined mechanisms including inversion, folding and expansion

In this research, thin-walled steel energy absorbers were investigated. The introduced structures absorb energy through the processes of inversion, folding and expansion. Each absorber consists of two end-capped frusta and a cylindrical shell. The intended absorbers were experimentally made and then tested. The mechanical properties of the used materials were extracted by performing tensile tests and then used for simulation. The simulations of this research were carried out using LS-DYNA software. After comparing the experimental and numerical results, a good agreement between the results was observed and then the obtained results were discussed. The intended absorbers were examined in terms of the thickness of the lower frustum, the height of the middle shell and the angle of the upper frustum. The obtained results showed that by increasing the thickness of the lower frustum, energy absorption in the inversion process increased. In addition, the investigations related to the effect of height on the collapse properties showed that increasing the height of the middle shell with a thickness of 2 mm for the lower frustum led to a decrease in energy absorption. Also, in the investigations carried out on the half angle of the frustum, it was found that the contribution of energy absorption in the expansion process was low.

Improving mechanical properties of AZ31 alloy sheets via novel turned-bearing extrusion by introducing shear strain

In this work, novel turned-bearing extrusions (TBE) conducted by using the dies with the single corner and double corner, named SC-TBE and DC-TBE respectively, are developed to introduce additional shear strain during the preparation of AZ31 alloy sheets, which is expected to improve the strengths of sheets. Numerical simulations are conducted to uncover the effect of additional shear deformation on the microstructure during the TBE. The results show that the high strain during the TBE leads to a high nucleation rate for dynamic recrystallization (DRX), resulting in grain refinement of the extruded Mg alloy sheet. However, the high strain also increases the temperature of the material due to the heat generated by plastic deformation, which provides a great driving force for grain growth and consumes dislocations. As these two effects compete with each other when increasing the strain near the die orifice, the SC-TBE sheet has finer grains and a higher residual dislocation density compared to the DC-TBE sheet or the sheet prepared by the conventional extrusion (CE). Fine-grain strengthening and substructure strengthening work together and enhance the tensile yield strength (TYS) of the SC-TBE sheet. The TYSs along extrusion direction (ED), transverse direction (TD) and 45° direction (the half angle between ED and TD) of the SC-TBE sheet are improved by 32 MPa, 65 MPa and 35 MPa respectively compared with the CE sheet. The findings of this research provide some new insights into the development of new preparation methods for Mg alloy sheets with higher strength.

Electron transport in macroscopic borosilicate capillaries with bending angles of 90° and 360°

In this work, we present observations about the transport of 15.2 keV electrons with a beam current of 21 μA through macroscopic dielectric capillaries. These capillaries are made of borosilicate glass with an inner diameter of about 6 mm, and samples with a bending angle of 90° and 360° were investigated. The electron gun was adjusted, and the beam injected into the capillary had a current of 21 μA and a divergence half angle of about 0.75°. A retarding field analyzer (RFA) was installed at the outlet of the capillary to collect the transported current and to investigate the particle energy of exiting electrons (Fig. 1). The transport of electrons to the outlet occurred nearly instantaneous in both capillaries, and the RFA at the outlet detected a current of around 20 μA for both capillary samples resulting in a transmission coefficient of over 95%. Energy measurements showed that the particle energy at the outlet is only at several electron volts, which reveals that electrons lost almost all of their incident energy while traveling through the capillary. A large amount of exiting particles are most likely secondary electrons emitted from the capillary sample. The fact that transmission coefficients for both samples are similarly high, and that the particles can still be transported through the 360° capillary although most of their energy is already lost at 90°, results in many questions that shall be investigated in further studies. The capillaries showed a blueish glow during electron transmission due to cathodoluminescence effects.