Conical Section Research Articles

A numerical analysis of the porosity of the HTR-10 packed pebble bed

The paper deals with the evaluation of the distribution of the porosity of a model of the HTR-10 packed bed reactor which was generated using a Discrete Element Method (DEM) approach. The porosity of the packed bed was determined using semi-analytical methodologies. To evaluate the validity of the model, selected aspects of the DEM approach were first investigated. It was found that the appropriate packing method is to drop the spheres at a specified rate from the top of the packed bed domain. The preferable model for the contact force between the spheres was found to be the Hertz-Mindlin model. It was also established that the Young’s modulus of the spheres should be larger than 0.1 GPa. A value of less than 0.1 GPa has a marked negative effect on the porosity. The values for the porosity predicted by previously proposed correlations for the radial and axial variations in porosity were determined to be too small. From the analysis of the packed bed model, the overall porosity was found to be 0.382, whilst the average porosities of the pipe, conical and cylindrical sections were found to be 0.439, 0.378 and 0.381 respectively. Correlations are derived to describe the axial variation of the porosity in the pipe, conical and cylindrical regions. A piece-wise constant description of the distribution in the porosity is finally provided by dividing the packed bed into 34 regions and determining the average porosity of each region.

Представяне на понятието конично сечение с компютър

The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented.

Performance Improvement of a Low-Power Wind Turbine Using Conical Sections

This paper examines the performance of conical sections (concentrator and diffuser) to improve the energy-recovery prospects of small-scale wind turbines. Detailed simulation studies of the conical sections with convergence angle viz., concentrator, and divergence angle viz., diffuser were conducted using ANSYS Fluent® software. Using simulation data, a trend analysis was conducted, and the empirical equations were derived for calculating the velocity variation and power variation in terms of the convergence/divergence angles. Working prototype models with optimum angles were fabricated for both the diffuser and concentrator. These models were then augmented with a wind turbine coupled with a 100 W, 24 V DC generator and tested to validate the simulation results. Upon analyzing the simulation data, it was found that a maximum velocity variation of 23.3% was achieved at an angle of 4.5° for the diffuser, whereas a maximum power variation of 65.1% was achieved at an angle of 3.6° for the same diffuser. The aforementioned improvement was achieved by optimizing divergence angle alone. The proposed designs of the diffuser- and concentrator-augmented wind turbine, as well as the empirical equations for calculating the velocity variation and power variation in terms of the divergence and convergence angle, are the major contributions of this article.

Finite element simulation and statistical investigation of an orthodontic mini-implant's stability in a novel screw design.

One of the essential aspects of the mini-implant's successful application is its stability after being installed in the bone. The stability of the mini-implant affected the most by its geometry. In the present research, the effect of the geometry-related parameters of the mini-implant on its lateral displacement is investigated by Finite Element (FE) modeling using ABAQUS software. The parameters studied include length, diameter, pitch, and depth of the screw threads; besides, length and angle of the conical section. The Taguchi method was used to prevent many experiments. The mesh convergence tests and experimental tests confirmed the FE model quantitatively and qualitatively. Mean of means and variance analysis determined the parameters significance and their contribution on the stability. The screw diameter and length have the most contribution to mini-implant' displacement. The effect of screw pitch was less than that for length and diameter. The conical section improved the initial stability by creating compressive stress and additional friction in its surrounding bone. No significant effects on the stability of the mini-implant have been observed for the non-threaded part. By examining the effect of thread depth on its stability by defining the ratio of thread depth to the internal diameter and to maintain the strength of the screw the optimal value for internal to external ratio is set at about 0.7.

Experimental generation of spherical converging shock waves

Spherical converging shock waves with incoming Mach number 1.18 are generated in a conical test chamber fitted to a conventional square-section shock tube. A wave cutter is employed to ensure a proper shock transition from the square to a cylindrical straight pipe installed upstream of the convergent section. The incident planar wave is transformed into a spherical shock by the use of an ellipsoidal membrane acting as a gas lens separating two gases with different densities. The transmitted shock wave propagates within the conical section, and accelerates towards the apex. The trajectory and the shape of the shock wave are both characterized by planar Mie scattering. The spherical shock follows the similarity solution proposed by Guderley (1942), whose trajectory agrees very well with the numerical simulation of the Chester-Chisnell-Whitham (CCW) theory for the geometry considered. The procedure demonstrated here provides a potential method for future investigations of shock focusing and Richtmyer–Meshkov instability in spherical geometry.

Analysis of Gas–Liquid–Solid Three-Phase Flows in Hydrocyclones Through a Coupled Method of Volume of Fluid and Discrete Element Model

Abstract Liquid–gas–solid three-phase flows in hydrocyclones are studied numerically in this paper by employing a coupled method of the volume of fluid (VOF) and discrete element model (DEM) with Reynolds stress model (RSM) turbulence model. The numerical method is validated by comparing the calculated results to those of experiments published in the literature about the separation of particle flows in hydrocyclones. Since VOF-DEM model could capture the gas–liquid interface of particle flows, the three-dimensional formation process of the air-core together with the formation of the spiral trajectory of particles are depicted for the first time. In addition, the effects of the particle concentration ω (less than 12%) on the air-core formation time Tf and diameter Da are studied systematically, which has not been reported in the literature. The increase of ω has both positive and negative actions on the change of Tf and Da, and the compromises of two kinds of actions generate the valley or peak of the curves of Tf versus ω and Da versus ω, respectively. Moreover, the results for three hydrocyclones with different cone angles are also compared to study the effects of the cylindrical and conical section on the air-core formation and the separation performance of the hydrocyclones. By analyzing the flow fields and the pressure changes inside the hydrocyclones, qualitative explanations of the relevant discoveries are given in this paper. The results will be helpful in the investigation of the multiphase flow behaviors in the hydrocyclone and in the selection of the appropriate hydrocyclone.

Discrete Element Modelling of Pit Crater Formation on Mars

Pit craters are now recognised as being an important part of the surface morphology and structure of many planetary bodies, and are particularly remarkable on Mars. They are thought to arise from the drainage or collapse of a relatively weak surficial material into an open (or widening) void in a much stronger material below. These craters have a very distinctive expression, often presenting funnel-, cone-, or bowl-shaped geometries. Analogue models of pit crater formation produce pits that typically have steep, nearly conical cross sections, but only show the surface expression of their initiation and evolution. Numerical modelling studies of pit crater formation are limited and have produced some interesting, but nonetheless puzzling, results. Presented here is a high-resolution, 2D discrete element model of weak cover (regolith) collapse into either a static or a widening underlying void. Frictional and frictional-cohesive discrete elements are used to represent a range of probable cover rheologies. Under Martian gravitational conditions, frictional-cohesive and frictional materials both produce cone- and bowl-shaped pit craters. For a given cover thickness, the specific crater shape depends on the amount of underlying void space created for drainage. When the void space is small relative to the cover thickness, craters have bowl-shaped geometries. In contrast, when the void space is large relative to the cover thickness, craters have cone-shaped geometries with essentially planar (nearing the angle of repose) slope profiles. Frictional-cohesive materials exhibit more distinct rims than simple frictional materials and, thus, may reveal some stratigraphic layering on the pit crater walls. In an extreme case, when drainage from the overlying cover is insufficient to fill an underlying void, skylights into the deeper structure are created. This study demonstrated that pit crater walls can exhibit both angle of repose slopes and stable, gentler, collapse slopes. In addition, the simulations highlighted that pit crater depth only provides a very approximate estimate of regolith thickness. Cone-shaped pit craters gave a reasonable estimate (proxy) of regolith thickness, whereas bowl-shaped pit craters provided only a minimum estimate. Finally, it appears that fresh craters with distinct, sharp rims like those seen on Mars are only formed when the regolith had some cohesive strength. Such a weakly cohesive regolith also produced open fissures, cliffs, and faults, and exposed regolith “stratigraphy” in the uppermost part of the crater walls.

The Effect of Wall Thermal Boundary Condition on Natural Convective Shutdown Cooling in a Gas Turbine

Abstract As a civil gas turbine cools down, asymmetric natural convective heat transfer causes the bottom sector of the rotor to cool faster than the top; this circumferential thermal gradient can potentially cause the shaft to deflect – a phenomenon called thermal or “rotor” bow. Rotor bow is tremendously difficult to predict due to its dependence on a number of engine design parameters, in addition to the complex nature of natural convective flows. A novel experimental facility has been developed to gain further understanding into shutdown cooling of a gas turbine. The scope of this paper is to quantify the effect of basic design features on natural convective cooling in an engine annulus during shut-down; specifically the influence of the thermal boundary wall conditions and the annular diameter ratio. In addition to this, a low-cost, robust thermocouple probe has been developed and validated, which allows for accurate temperature measurements in a natural convective boundary layer. An extensive experimental campaign has been completed. The key finding is that the local radial wall temperature difference was found to be the most influential parameter on the local heat transfer. Non-isothermal walls did not alter the overall distribution of the inner wall equivalent conductivity. This was true for both cylindrical and conical sections. An appropriate characteristic length for use in the Rayleigh number definition for both the concentric cylinder and conical sections have been validated. The conical inner section (5 deg hade angle) did not affect the overall heat transfer in the range of conditions tested. Therefore, the mean surface heat transfer for non-isothermal inner and outer profiles, within the range −0.4<ΔRa/RaLc<0.4, where the thermal gradient is negative in the clockwise from top-dead-center, can be predicted using isothermal correlations for RaLc<5.0×105 and Dr < = 1.5.

Optimization Design of Spray Cooling Fan Based on CFD Simulation and Field Experiment for Horticultural Crops

In recent years, horticultural plants have frequently suffered significant heat damage due to excessive temperatures. In this study, a horticultural spray cooling system was designed, consisting mainly of a jet fan and spraying system. CFD simulation technology and response surface methodology were used to optimize the design of the jet fan, which improved the thrust of the fan. The length of the inlet section was 300 mm, the length of the outlet section was 300 mm, the length of the cone section was 450 mm, and the diameter of the outlet was 950 mm, where the thrust of the jet fan was 225.06 N. By establishing the CFD model of spray cooling in a tea field and designing a L9 (34) orthogonal experiment, the effect of the spray parameters on the maximum temperature drop and effective cooling distance was studied, and the best parameters were selected. The simulation results show that the optimum parameters are a spray flow rate of 4.5 kg/s, a droplet diameter of 15–45 μm, a droplet temperature of 298.15 K, and a nozzle double circle layout. Based on the simulation results of the optimized jet fan and spray parameters selected, a spray cooling test bench was established. Field test results show that when the initial ambient temperature was 310.05 K–310.95 K, the maximum temperature drop of the spray cooling fan was 9.1 K, and the cooling distance was approximately 36.0 m. The temperature drop decreased with increasing distance from the fan. This study is of great significance to protect horticultural plants from extremely high temperatures.

Structural optimization for an axial oil‐water separator with multi‐stage separation

In order to meet the demand of industrial production, an axial separator for oil-water separation is proposed. The separator uses the pattern of multi-stage separation, and it is divided into two chambers by two swirl impellers. The oil phase flows out through three Light Phase Outlet (LPO) at the center of the impeller hub, meanwhile the water phase flows out through Heavy Phase Outlet (HPO). An experimental platform was built to verify the feasibility of multi-stage separation. The Mixture model and Reynolds stress model was used to simulate the separation process, and the numerical results had a well agreement with experimental results. The effects of the diameter of cylindrical section, length of conical section and length of separation chamber on the separation performance were studied. The results show that: changing the diameter of cylindrical section has greatest impact on separation performance. The separation efficiency and pressure drop first increase and then decrease with increase of primary conical section length. With increase of second conical section length, the separation performance has been increasing. If it only looks at the relationship between pressure drop and separation efficiency, then there is a pressure drop to maximize the separation efficiency. Changing the diameter of cylindrical section can adjust the flow split LPOs. Increasing the length of second conical section can increase the split ratio of LPO3, but it has almost no effect on the total split ratio of LPOs. the value of structure is determined and the efficiency of separator exceeds 93 %.

Numerical simulation of two-phase flow and droplet breakage of glycerin-water mixture and kerosene in the cyclone reactor

• The static pressure distribution conformed with the rules of the eddy field. • The vortex motion near the side wall was intense. • The droplet deformed, stretched, and broken. • The small surface tension and large Weber number promoted droplet breakage. A liquid-liquid cyclone reactor (LLCR) was designed to achieve mixing-reaction-separation integration during isobutane alkylation catalyzed by ionic liquids. However, studies of the droplets deformation and breakage in the kind of reactors are lacking. In this work, the research studied the velocity distribution, pressure field, and turbulent field to investigate the flow pattern and the main energy loss location in the LLCR through the computational fluid dynamics (CFD) method. The simulation results were verified by experiemnts to prove the correctness of the model. Then the deformation and breakage process of droplets, and the influencing factors of droplets breakage were studied by remodeling which was based on the tangential velocity distribution result of the three dimensional model. The three dimensional simulation results clearly showed that the pressure of the LLCR was mainly concentrated in the cone section and fluid turbulent motion was the most intense near the lateral wall. The reconstruct the results of the two dimensional model clearly showed that the deformation and breakage location of droplets were mainly occurred in the velocity boundary layer, while it was difficult to break in the mainstream region. In addition, low surface tension and high Weber number had a positive effect on droplet breakage.

Plastic Shaping of Concentrator-Waveguide Tip for Ultrasound Endovascular Ablation

One of the most effective methods of treating intravascular formations at present is the use of stepped ultrasonic waveguide systems of a tubular type (concentrators-waveguides) with a hollow spherical tip, the presence of which makesit possible to supply liquid media to the dislocation zone of an intravascular formation with the aim of additional cavitation effect and as efficiently as possible. destroy intravascular formations due to vibration impact. Based on the results of the analysis on the features of the existing shaping methods for obtaining a hollow spherical tip of the concentrator-waveguide, it is advisable to use methods of plastic deformation – expansion and crimping. The paper presents results of preliminary calculations, numerical modeling and experimental studies of tip shaping processes of the concentrator-waveguide by distribution and crimping. On the basis of the finite element method in the environment of the ABAQUS software package, modeling of the expansion and crimping of a pipe billet was carried out, which has made it possible to: evaluate the stress-strain state of the deformable conical section of the billet, the change in wall thickness during the forming process and calculate the length of the billet for the design of the conical section; to establish the patterns of the influence of geometric parameters on the power modes of the distribution process; to set the parameters of the modes of forming the tip of the concentrator-waveguide by the method of distribution and crimping, which ensure the formation of the required geometry. The obtained results of preliminary calculation, numerical modeling and experimental studies of tip shaping processes of the concentrator-waveguide by distribution and crimping have similar values, which confirms the correctness of using both the method of preliminary calculation and numerical modeling in the development of the technology for manufacturing the concentrator-waveguide.

Parametric Fuzzy Implications Produced via Fuzzy Negations with a Case Study in Environmental Variables

In this paper, we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction. The new Fuzzy Implication Generator takes its final forms after being configured by the fuzzy strong negations and combined with the most well-known fuzzy conjunctions TM, TP, TLK, TD, and TnM. The final implications that emerge, given that they are configured with the appropriate code, select the best value of the parameter and the best combination of the fuzzy conjunctions. This choice is made after comparing them with the Empiristic implication, which was created with the help of real temperature and humidity data from the Hellenic Meteorological Service. The use of the Empiristic implication is based on real data, and it also reduces the volume of the data without canceling them. Finally, the MATLAB code, which was used in the programming part of the paper, uses the new Fuzzy Implication Generator and approaches the Empiristic implication satisfactorily which is our final goal.

Performance evaluation of standard cyclone separators by using CFD–DEM simulation with realistic bio-particulate matter

As an abatement emissions control and energy-consuming device, cyclone separators are the most common device used in bioprocessing to separate fine and coarse particulate matter (PM) from the gas flow. In this investigation, four standard cyclones geometries viz. 1D2D, 2D2D, 1D3D, and 1D3D with 2D2D inlet (1D3D/w2D2D) in addition to a designed one, were simulated to investigate the performance characteristics. The D's refers to the cyclone diameter, and the numbers before each D's relate to the length of the cylindrical and conical sections, respectively. The PM used for testing and modeling was conducted on two types of real heterogeneous bioparticles (jojoba seeds and their leaves). This research is considered the first head start approach to predict the cyclone performance under the true shape modeling of PM. Discrete Element Method (DEM) was employed to simulate the trajectory of each particle, taking into consideration the interactions and collisions. Simultaneously, the Computational Fluid Dynamics (CFD) was used to simulate the highly curved streamlines and the chaotic turbulence of the continuum airflow with the Reynolds stress turbulence model (RSM). The designed cyclone was used to validate the results, which showed a good agreement between simulated data and the experimental work. The result showed that the 1D2D cyclone design has a better performance than that of the other cyclones. The methods used in this work for analyzing the phenomena occurring inside the cyclone separator allow for the conclusion that cyclone performance not only varies significantly with the cyclone type but the operating conditions as well. With these presented characteristics and evaluations, industrialists can utilize the mentioned designs for different processing to get high performance using a coarse and large PM process.

Drag and Heat Flux Reduction using Counterflow Jet and Spike - Analysis of their Equivalence for a Blunt Cone Geometry at Mach 8

This study aims to explore equivalence between active and passive flow control techniques in reducing the wave drag and surface heat flux over a blunt cone model kept in Mach 8 stream. Computational investigations were carried out by using finite volume-based compressible flow solver. Throughout the study, the solution of governing equations is sought by assuming two dimensional-axisymmetric nature of the flowfield. Both counter flow-stagnation point injection and forward facing-physical spike are considered to mitigate the excess drag and heat flux experienced by a blunt body representing the nose cone section of a hypersonic vehicle. Eventually, based on identified drag reductions, the present study proposes equivalence cases between these two methods. It is shown that a pointed spike of L/D=1 provides almost the same drag reduction as the counterflow injection jet with a pressure ratio of 8.25. Similarly, other equivalence cases are identified and the physics behind them is explored. The identified equivalence is expected to help the designers in effectively replacing one technique with another according to the requirement. Equivalence matrix is presented for different spike cases in terms of injection ratios of counterflow injection.

Rotating detonation waves in annular gap with variable stagnation pressure

We consider a three-dimensional unsteady flow with one, two, or four rotating detonation waves arising in an annular gap of an axially symmetric device between two parallel planes perpendicular to its symmetry axis. The corresponding problem is formulated and studied. It is assumed that there is a reservoir with quiescent homogeneous propane–air combustible mixture with given stagnation parameters; the mixture flows from the reservoir into the annular gap through its external cylindrical surface toward the symmetry axis, and the parameters of the mixture are determined by the pressure in the reservoir and the static pressure in the gap. The detonation products flow out from the gap into a space bounded on one side by an impermeable wall that is an extension of a side of the gap. Through a hole on the other side of the gap and through a conical output section with a half-opening angle of $$45^{\circ }$$ , the gas flows out from the engine into the external space. We formulate a model of detonation initiation by energy supply in which the direction of rotation of the detonation wave is defined by the position of the energy-release zone of the initiator with respect to the solid wall situated in a plane passing through the symmetry axis. After a while, this solid wall disappears (burns out). We obtain and analyze unsteady shock-wave structures that arise during the formation of a steady rotating detonation. We measure and compare thrust characteristics for different numbers of detonation waves. It was shown that the thrust weakly depends on the number of waves while the specific impulse increases with increasing number of waves. The study of rotating detonation at various values of the stagnation pressure was conducted. The calculation results show that at a stagnation pressure less than the critical value, the realization of rotating detonation is impossible. It is established that, depending on the stagnation pressure, qualitatively different shock-wave structures can be observed. The analysis is carried out within single-stage combustion kinetics by the numerical method based on the Godunov scheme with the use of an original software system developed for multi-parameter calculations and visualization of flows. The calculations were carried out on the Lomonosov supercomputer at Moscow State University.

The q-difference operator associated with the multivalent function bounded by conical sections

In this paper we obtain some inclusion relations of k - starlike functions, k - uniformly convex functions and quasi-convex functions. Furthermore, we obtain coe¢ cient bounds for some subclasses of fractional q-derivative multivalent functions together with generalized Ruscheweyh derivative.

Exploratory development of a rotary offset crusher

The quest for efficiency in comminution is an ongoing concern as comminution usually constitutes a major cost component in the metal production industry. Such improvements can be made by circuit optimization or development of more efficient equipment. A novel crusher, known as the rotary offset crusher (ROC), promises to deliver in this space. The ROC was invented in 2002 by Michael Hunt, Henry Simonsen, and Ian Sinclair, but failed to garner enough support to progress to production. The original design concept was recently rekindled, and a laboratory version of the crusher has been built and commissioned at the University of the Witwatersrand. The crusher is simple in design, with two cylindrical discs that are parallel to each other, and, as the name implies, there is an offset between the vertical axes of the discs. The top disc has a conical section on its lower face, and this creates a crushing zone between the opposite faces of the two spinning discs. Centrifugal motion transports particles through the crushing zone. Batch experiments have been conducted with quartz at various crusher settings (discs offset, rotational speed, and vertical exit gap) for various feed size distributions. The indications so far suggest that the disc speed is a key factor affecting the performance. Size reduction ratios as high as 11 were recorded from experiments with quartz at a speed of 830 r/min.

Effect of conical section structure on liquid-liquid cyclone reactor for isobutane alkylation catalyzed by ionic liquid

The liquid-liquid cyclone reactor (LLCR) integrating fast mixing and quick separation is a promising device for isobutane alkylation catalyzed by ionic liquids. The conical section of LLCR is an essential part where both mixing and separation occur. To optimize the mixing and separation performance of LLCR, four designs of the conical section (single-cone structure, standard dual-cone structure, parabolic structure and hyperbolic structure) were studied in this work. The cold model experiment and numerical simulation were carried out to investigate the distribution of light phase, mixing performance and separation performance. The formation of the pseudo-steady light phase core was observed from experiments and simulations. The effective mixing zone of LLCR was proposed in this study by obtaining the boundaries of the light phase core and the bottom of the locus of zero axial velocity. The distributions of the turbulent energy dissipation rate and the mean separation efficiency were employed to evaluate the mixing and separation performance, respectively. The result showed that the LLCR with hyperbolic structure were better than the other three structures in terms of mixing performance and separation efficiency.

Quasi-static crushing behavior of stretch formed domes of laser welded tailored blanks

In the present work, similar thickness laser welded blanks (LWBs) and dissimilar thickness laser welded tailored blanks (LWTBs) of extra deep drawing (EDD) steels were fabricated and these were stretch formed by a 50 mm diameter hemispherical punch under lubricated condition. All these stretch-formed domes were manufactured keeping a consistent combined geometry of hemispherical and conical sections. Subsequently, these domes were crushed quasi-statically and the modes of collapse, load-displacement response, mean crushing load and energy absorption were comprehensively investigated both experimentally and numerically to get insight into the effect of weld zone (WZ), thickness ratio, deformation speed, forming histories and material anisotropy. During all the crushing tests, three similar collapse modes were observed and these were identified as flattening of hemispherical section, inward dimpling of hemispherical section and lastly the flattening of conical section. However, an additional collapse mode consisting of two asymmetrical lobes across the WZ with a stationary plastic hinge was identified in case of stretch-formed domes of LWTBs. It was concluded that the mode of collapse was predominantly affected by the presence of thickness ratio. On the other hand, the mean crushing load and energy absorption capacity were enhanced due to the presence of WZ and the selection of thickness combination. The energy absorption effectiveness factor of LWBs and LWTBs were estimated to be 1.33 to 2.75 times higher than that of monolithic EDD steel. It was further suggested through numerical modeling that the incorporation of strain rate, material anisotropy and forming histories such as non-uniform thickness and strain distributions along with WZ properties improved the prediction of modes of collapse, load-displacement response and mean crushing load.