Trapezoidal Cross-section Research Articles

Determination of an allowable value of internal uniform pressure on the underground horisontal working contour with a trapezoidal form of its cross-section

The paper presents the study results of the stress state at the contour points of an underground horizontal working carried out by the methods of the complex variable theory. This study is the basis for solving the problem of determining an allowable value of the uniform pressure transmitted to the contour of the working, with predetermined values of the depth of its laying. The condition proposed by the authors of the paper is used as a criterion of strength (stability), according to which the working’s contour strength is ensured if at any point the amount of the tangential normal stress does not exceed the tensile and compressive strength of the host soil (rock), i.e. σt ≤ σe ≤ σc . As a result of the solution, an assessment of the stress distribution on the contour of an underground horizontal working has been made. The working has a cross-section in the form of a curved trapezoid, which is under the action of uniform all-round stretching of a given intensity with a varying depth and various values of the host mass lateral expansion coefficient. The allowable values of the tensile internal pressure on the contour of an underground horizontal working of a trapezoidal cross-section have been determined at the given values of its depth and a constant coefficient value of the lateral expansion of the host mass μ = 0.25. The materials presented in the paper can be used when choosing the maximum or minimum allowable depth of the working used as a storage facility for liquid or gaseous hydrocarbons.

Geometry and shape optimization of piezoelectric cantilever energy harvester using COMSOL multiphysics software

AbstractIn embedded systems that necessarily require a steady source of power and (or) attaches to a sensor(s), there are opportunities to mix small batteries to supply such power. The aim of this research is to optimize the geometry and shape of piezoelectric cantilevers to harvest more power. Several piezoelectric cantilever geometries with various shapes (rectangular, triangular, circular, and trapezoidal cross section) are tested in COMSOL multiphysics simulator to find the best geometry that provides the highest accomplishable power. The most efficient geometry was found to be conferred by the trapezoidal, cross section cantilever. Next, another improvement method was applied to maximize the harvested power of the cantilever by modifying the shape of the trapezoidal cantilever structure through increasing the number of its faces. The results demonstrated that the highest output power (36 mW) was produced by the four faces, trapezoidal cross section design of cantilever.

Design and Comparative Cost Analysis of Alternative Prefabricated Beef Cattle Barns with Conventional Barn Types

In this study, planning, design and cost analysis of prefabricated beef cattle barns carried out. Steel mesh was used to strengthen the foundation of the structure. Galvanized-sheet material was used as the carrier and cover material, and shaped like a trapezoid cross-section. The barns, which are planned in the form of tunnel cross-section and tie-stalls type, are designed for 10, 20 and 30-cattle to be particularly suitable for family enterprises. Polyurethane (PU) foam and extruded polystyrene sandwich panel (XSP) were used to provide heat and sound insulation. Cost analysis of the galvanized-sheet barns was compared with the barns constructed by the traditional production method. After analyses, we found that as the number of animals increased, barn cost per animal decreased. The cost reduction rates in the PU foam insulated galvanized-sheet barn were 30.1%, 32.7% and 30.6% for the 10, 20 and 30-cattle respectively. These values were 24.9%, 27.8% and 25.5% for the sandwich panel insulated galvanized-sheet barn. The most economical combination was the polyurethane foam insulation of galvanized sheets. Galvanized-sheet barns are technically sufficient, and economically advantageous than the conventional ones, so it can be recommended to both newly established enterprises and enterprises that want to improve their old barns.

Secondary Flows, Mixing, and Chemical Reaction Analysis of Droplet-Based Flow inside Serpentine Microchannels with Different Cross Sections

Chemical bioreactions are an important aspect of many recent microfluidic devices, and their applications in biomedical science have been growing worldwide. Droplet-based microreactors are among the attractive types of unit operations, which utilize droplets for enhancement in both mixing and chemical reactions. In the present study, a finite-volume-method (FVM) numerical investigation is conducted based on the volume-of-fluid (VOF) applying for the droplet-based flows. This multiphase computational modeling is used for the study of the chemical reaction and mixing phenomenon inside a serpentine microchannel and explores the effects of the aspect ratio (i.e., AR = height/width) of rectangular cross-sectional geometries as well as three other cross-sectional geometries including trapezoidal, triangular, and circular, on consumption and production rates of chemical species. It is found that in these droplet bioreactors, the reaction begins from the forward section of the droplet. We investigate the secondary flows and chemical reactions inside the droplets in a serpentine microchannel with different cross-sectional geometries. Different transient Dean vortices and secondary flows in the presence and absence of the droplets are studied and explained based on the position of the droplets. It is found that as the droplets pass through the microchannel turns, the patterns and magnitude of the secondary flows change, depending on the cross-sectional geometry. Eventually, the results demonstrate that the AR = 2 rectangular cross-section is the most helpful geometry, whereas the trapezoidal cross-section takes into account the least efficient one between all geometries.

Fast droplet bouncing induced by asymmetric spreading on concave superhydrophobic surfaces

A droplet can bounce in a short contact time after impacting on superhydrophobic surfaces (SHSs), which is of benefit to the applications like anti-icing, anti-frosting and self-cleaning. In this study, we numerically investigate the fast droplet bouncing induced by asymmetric spreading on the concave SHS with a trapezoidal cross-section and focus on the droplet morphology evolution and contact time variation. A preferential transport at the both sides of the droplet from the inclined part to the flat part will occur because of the concave structure feature. The droplet will exhibit asymmetric spreading behavior. Moreover, the effects of structure parameters and impact velocity on the droplet contact time are explored. Within this concave structure, the droplet contact time is less influenced by the impact velocity and more influenced by the structural parameters. The presence of the tangential momentum can enhance the droplet asymmetric spreading, but it is not always beneficial to the droplet contact time reduction. Therefore, there will be an optimal structure to achieve the minimum droplet contact time. A concave SHS structure with the structure width w= 1–1.2r and the inclination angle of 45° is a more desirable choice, which is expected to reduce the droplet contact time by 40~45%.

Numerical research on a novel flow field design for vanadium redox flow batteries in microgrid

The microgrid (MG) composed of vanadium redox flow battery (VRFB), wind energy, and photovoltaic (PV) renewable energy, it is an effective energy solution. It has attracted much attention because it can effectively solve the problems of randomness, intermittentness, and uncontrollability of renewable energy. The VRFB plays a vital role, and its performance determines the power quality of the MG. This research analyses the development status of renewable energy, the structure of MG, and the problems of VRFB in MG. It is proposed to improve the overall performance of the battery to make up for the defect of low energy density. As the performance of VRFB is strongly affected by the electrolyte's flow rate, designing a novel flow field structure to increase the flow rate and improve the electrolyte uniformity is very important to improve battery performance. The research designed the traditional rectangular cross-section into a trapezoidal cross-section to increase the flow rate of the electrolyte and improve the uniformity of the electrolyte. Numerical simulation results show that the new flow field structure can significantly improve the electrolyte flow, alleviate the concentration polarization of the battery, and improve battery performance and efficiency. Therefore, it is found that a reasonable flow field structure design is helpful for the optimization and application of VRFB's performance. Highlights The development status of renewable energy, the structure and configuration of the microgrid, and the existing problems of VRFB energy storage are analyzed. Establishing a VRFB model for electrochemistry and fluid mechanics. Designing a novel flow field structure to improve the overall performance of the battery.

Heat Transfer in Rotating, Trailing-Edge, Converging Channels With Smooth Walls and Pin-Fins

Abstract The heat transfer and pressure drop characteristics of a rotating cooling channel that has an angled trapezoidal cross section and converges from the hub to the tip in both the streamwise and spanwise directions are experimentally investigated. The channel is oriented 120 deg with respect to the direction of rotation to model the geometry of an internal, trailing-edge cooling passage. Both the leading and trailing sides of the channel are divided into three and six regions in the spanwise and streamwise directions, respectively. The copper plate method is used to obtain regionally averaged heat transfer coefficients. The pressure drop is measured using pressure taps placed at the inlet and outlet of the channel. Experiments were conducted with the inlet Reynolds number ranging from 10,000 to 40,000. The rotational speed varies from 0 rpm to 300 rpm, resulting in the highest rotation number of 0.21. The effects of full pin-fins on the heat transfer and pressure drop characteristics are obtained and compared to the smooth surface converging channel results. The impact of the convergence, which causes variations of flow and geometric parameters through the passage, such as aspect ratio, Reynolds number, and rotation number, on the heat transfer coefficients and pressure drop are addressed. Results show that due to the 120 deg channel orientation, the rotation has a positive impact on the leading and trailing surface heat transfer. Furthermore, the convergence decreases the aspect ratio while increasing the Reynolds number. The convergence significantly enhances heat transfer on both the leading and trailing surfaces along the streamwise and spanwise directions. The convergence also reduces the rotation effect in the streamwise direction for a given mass flow rate.

Heat Transfer in Rotating, Trailing Edge, Converging Channels With Partial Length Pin-Fins

AbstractIn the current study, the heat transfer and pressure drop characteristics of a rotating, partial pin-finned, cooling channel that has a trapezoidal cross section and converges from the hub to tip in both the streamwise and spanwise directions are experimentally investigated. To model the geometry of an internal trailing edge cooling passage, the channel is oriented with respect to the direction of rotation (β = 120 deg). Isolated copper plates are used to obtain regionally averaged heat transfer coefficients on the leading and trailing surfaces. Pressure drop is measured using pressure taps placed at the inlet and outlet of the channel. Utilizing Dp = 5 mm diameter pins, a staggered array is created. For this array, the streamwise pin-spacing, Sy/Dp = 2.1, was kept constant; however, the spanwise pin-spacing, Sx/Dp, was varied from the hub to tip between 3 and 2.6 due to the channel convergence. Experiments were conducted for two partial pin-fin sets having pin length-to-diameter ratios of Sz/Dp = 0.4 and 0.2. The rotation number was varied from 0 to 0.21 by ranging the inlet Reynolds number from 10,000 to 40,000 and rotation speed from 0 to 300 rpm. A significant decrease in pressure loss and a slight reduction in heat transfer enhancement are observed with the use of partial pin-fins compared with the previously reported full pin-fin converging channel study. This provides better thermal performances of the partial pin-fin arrays compared with the full pin-fin array, in the converging channels.

Featured Collection Introduction: National Water Model III

Featured Collection Introduction: National Water Model III

Long-range spin-wave propagation in transversely magnetized nano-scaled conduits

Magnonics attracts increasing attention in the view of low-energy computation technologies based on spin waves. Recently, spin-wave propagation in longitudinally magnetized nano-scaled spin-wave conduits was demonstrated, proving the fundamental feasibility of magnonics at the sub-100 nm scale. Transversely magnetized nano-conduits, which are of great interest in this regard as they offer a large group velocity and a potentially chirality-based protected transport of energy, have not yet been investigated due to their complex internal magnetic field distribution. Here, we present a study of propagating spin waves in a transversely magnetized nanoscopic yttrium iron garnet conduit of 50 nm width. Space and time-resolved microfocused Brillouin-light-scattering spectroscopy is employed to measure the spin-wave group velocity and decay length. A long-range spin-wave propagation is observed with a decay length of up to (8.0 ± 1.5) μm and a large spin-wave lifetime of up to (44.7 ± 9.1) ns. The results are supported with micromagnetic simulations, revealing a broad single-mode frequency range and the absence of a mode localized to the edges. Furthermore, a frequency nonreciprocity for counter-propagating spin waves is observed in the simulations and the experiment, caused by the trapezoidal cross section of the structure. The revealed long-distance spin-wave propagation on the nano-scale is particularly interesting for an application in spin-wave devices, allowing for long-distance transport of information in magnonic circuits and low-energy device architectures.

Hypogene speleogenesis and paragenesis in the Dolomites

The Dolomites of northern Italy feature some of the most intensively studied carbonate rocks worldwide. Yet, little is known about the long karst history of this mountain range dating back to the Miocene. This study scrutinizes three caves (F10, Milchloch and Cioccherloch) in the Fanes-Sennes-Prags Nature Park (Province of South Tyrol) and the adjacent Fosses area in the Natural Park of Ampezzo Dolomites (Province of Belluno, Veneto). Paleo-phreatic passages of these limestone caves mostly follow a NW-SE orientation, similar to the nearby Val Salata fault. A multi-method approach including cave morphological and isotopic analyses of wall-rock cores was applied to reconstruct the multi-stage speleogenetic history of these cavities. Clastic sediments partly cemented to the cave walls and paragenetic features such as ceiling channels and solutional ramps are present in all studied caves. F10 cave shows widespread laughöhle geometries, including inverted cone chambers and horizontal passages with trapezoid cross sections, characteristic of slow water convection in a hypogene regime. Drill cores in F10 cave exhibit a systematic depletion in both oxygen and carbon isotopes close to the cave wall. The thickness of this isotopically altered zone ranges from a few mm to 4 cm and alteration can sometimes also be macroscopically identified. The amplitude of the isotopic shift ranges from 2.0 to 5.0‰ for δ13C and from 1.9 to 4.9‰ for δ18O. One of the wall rock cores from Cioccherloch also shows a thin isotopic halo, while no evidence of isotopic alteration was found in Milchloch. Our results provide strong geochemical evidence of wall rock alteration driven by hypogene water-rock interaction in at least two of the caves. We propose an early hypogene speleogenetic phase, followed by uplift and denudation resulting in the opening of these cavities to the surface that allowed clastic sediment influx. The sediment infill in combination with the abundant paragenetic features records a second phase in the karst evolution. This paragenetic phase did not involve hypogene waters, as indicated by the lack of isotopic alteration in the wall rock of paragenetic features. The latest phase of speleogenesis is represented by vadose morphologies and vadose speleothems locally dating back to at least 650 ka. This study demonstrates that the combination of morphological analyses and geochemical fingerprinting represents a powerful approach to decipher the commonly complex speleogenetic history of limestone caves.

Experimental study of uni- and bi-directional exchange flows in a large-scale rotating trapezoidal channel

A large-scale experimental study has been conducted at the Coriolis Rotating Platform to investigate the dynamics of uni- and bi-directional exchange flows along a channel with a trapezoidal cross section under the influence of background rotation. High-resolution two-dimensional particle image velocimetry and micro-conductivity probes were used to obtain detailed velocity fields and density profiles of the exchange flow generated across the channel under different parametric conditions. Experimental measurements give new insight into the stratified-flow dynamics dependence on the magnitude of Burger number, defined as the ratio of the Rossby radius to the channel width, such that values lower than 0.5 characterize unsteady exchange flows. The measurements highlight the role that both ambient rotation and net-barotropic forcing have on the geostrophic adjustment of the dense outflowing layer and on the corresponding counter-flowing water layer fluxes. The coupled effect of these two parametric conditions largely affects the transverse velocity distribution and, for the largest net-barotropic flow in the upper fresh water layer, leads to the partial blockage of the lower saline outflow. Moreover, an increase in the mixing layer thickness, associated with larger rotation rates, and due the interface dynamics, is observed, with shear-driven interfacial instabilities analyzed to highlight the influence of both ambient rotation and net-barotropic forcing.

Analytical Models for Optimal Design of a Trapezoidal Composite Channel Cross-Section

Abstract In this paper, several analytical models are presented for the optimal design of a trapezoidal composite channel cross-section. The objective function is the cost function per unit length of the channel, which includes the excavation and lining costs. To define the system, design variables including channel depth, channel width, side slopes, freeboard, and roughness coefficients were used. The constraints include Manning’s equation, flow velocity, Froude number, and water surface width. The Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm was used to solve the optimization problem. The results are presented in three parts; in the first part, the optimal values of the design variables and the objective function are presented in different discharges. In the second part, the relationship between cost and design variables in different discharges is presented in the form of conceptual and analytical models and mathematical functions. Finally, in the third part, the changes in the design variables and cost function are presented as a graph based on the discharge variations. Results indicate that the cost increases with increasing water depth, left side slope, equivalent roughness coefficient, and freeboard.

Hydraulic Characteristics of Microbend River with Vegetation on the Slope

The flow pattern of the water with vegetation is complex. For the micro-bend channel which has compound cross-sections and has vegetation on the slope, the situation is more complex. This paper measures and analyses the hydraulic characteristics of the micro-bend channel with trapezoidal cross-sections and with vegetation on the slope,by using the ACM2-RS electromagnetic flow meter. The influence of vegetation structure changes on the hydraulic characteristics are further analysed, which includes flow velocity distribution, turbulence intensity and channel roughness. Studies have shown that, with the decrease of the rigidity of vegetation density, the sinuosity of the hydrodynamic axis increases, the longitudinal velocity of each section in the main channel has an obvious trend of decrease. Besides, the longitudinal and lateral turbulence intensity keeps constant in the main channel, have obvious decreasing trends on the slopes. In addition, river manning roughness coefficient increases with the increase of rigid vegetation density.

Heat transfer performance enhancement of liquid cold plate based on mini V-shaped rib for battery thermal management

Liquid cooling is an effective method for thermal management of high-power battery packs. A number of studies have shown that the general methods to enhance heat transfer performance by increasing flow rate will significantly increase pump power consumption. Here, in order to reduce the pump power consumption while enhancing heat transfer, the mini V-shaped ribs is used to optimize the structure of the liquid cold plate. The flow and heat transfer characteristics of square, triangular, semicircular and trapezoidal cross-section V-shaped ribs are investigated. The main results show that the Nusselt Number and Friction Factor of channel with V-shaped ribs are higher than those of smooth channel and the channel with straight rib. Additionally, compared with other rib structures, the V-shaped rib with triangular cross-section can reach the same heat transfer performance under smaller flow rate and pump power consumption. It is also found that the near wall hot fluid is stripped by the V-shaped ribs, so that the cold fluid in the mainstream can directly exchange heat with the wall, in addition, the twisted tape vortex caused by V-shaped rib can inhibit the development of the sidewall boundary layer.

On the unidirectional free-surface flow behavior in trapezoidal cross-sectional open-channels

In this paper, consideration was given to the numerical prediction of free-surface wave behavior in trapezoidal open-channels. The Mac-Cormack scheme was implemented for the numerical discretization of the 1-D Extended St.-Venant equations, based on the Prandtl power law as a momentum correction coefficient. To verify the validity of the used numerical technique, the computed results were compared with experimental data and alternative numerical solutions quoted in the literature. These comparisons demonstrated that the results issued from the discretization of the 1-D Extended St.-Venant equations led to a more realistic description of the wave behavior than the ones obtained from the discretization of the 1-D Conventional St.-Venant equations. Furthermore, the results obtained by the developed numerical solver agreed well with those obtained by the Finite Element Method. However, the former solver was more advantageous than the latter with regard to computational time saving. The test cases addressed the trapezoidal particular shape of the open-channel cross-section. The findings highlighted that the adequate selection of the geometric characteristics of the open-channel cross-section could improve significantly the efficiency of these structures. Particularly, results demonstrated that the selection of an optimum side slope of the trapezoidal cross-section led to a maximum flow-rate while preserving a low value of the wetted cross-section area.

Numerical study for the improvement of bead spreading architecture with modified nozzle geometries in additive manufacturing of polymers

Purpose This paper aims to develop a numerical model of bead spreading architecture of a viscous polymer in fused filament fabrication (FFF) process with different nozzle geometry. This paper also focuses on the manufacturing feasibility of the nozzles and 3D printing of the molten beads using the developed nozzles. Design/methodology/approach The flow of a highly viscous polymer from a nozzle, the melt expansion in free space and the deposition of the melt on a moving platform are captured using the FLUENT volume of fluid (VOF) method based computational fluid dynamics code. The free surface motion of the material is captured in VOF, which is governed by the hydrodynamics of the two-phase flow. The phases involved in the numerical model are liquid polymer and air. A laminar, non-Newtonian and non-isothermal flow is assumed. Under such assumptions, the spreading characteristic of the polymer is simulated with different nozzle-exit geometries. The governing equations are solved on a regular stationary grid following a transient algorithm, where the boundary between the polymer and the air is tracked by piecewise linear interface construction (PLIC) to reconstruct the free surface. The prototype nozzles were also manufactured, and the deposition of the molten beads on a flatbed was performed using a commercial 3D printer. The deposited bead cross-sections were examined through optical microscopic examination, and the cross-sectional profiles were compared with those obtained in the numerical simulations. Findings The numerical model successfully predicted the spreading characteristics and the cross-sectional shape of the extruded bead. The cross-sectional shape of the bead varied from elliptical (with circular nozzle) to trapezoidal (with square and star nozzles) where the top and bottom surfaces are significantly flattened (which is desirable to reduce the void spaces in the cross-section). The numerical model yielded a good approximation of the bead cross-section, capturing most of the geometric features of the bead with a reasonable qualitative agreement compared to the experiment. The quantitative comparison of the cross-sectional profiles against experimental observation also indicated a favorable agreement. The significant improvement observed in the bead cross-section with the square and star nozzles is the flattening of the surfaces. Originality/value The developed numerical algorithm attempts to address the fundamental challenge of voids and bonding in the FFF process. It presents a new approach to increase the inter-bead bonding and reduce the inter-bead voids in 3D printing of polymers by modifying the bead cross-sectional shape through the modification of nozzle exit-geometry. The change in bead cross-sectional shape from elliptical (circular) to trapezoidal (square and star) cross-section is supposed to increase the contact surface area and inter-bead bonding while in contact with adjacent beads.

Modeling a Bioretention Basin and Vegetated Swale with a Trapezoidal Cross Section using SWMM LID Controls

The Low Impact Development (LID) Control module is utilized in the United States Environmental Protection Agency’s Stormwater Management Model (USEPA SWMM) to predict the hydraulic performance of a variety of sustainable stormwater technologies. Data collected in 2019 from the monitoring of a pilot project in Montreal was used to verify the ability of the Bioretention LID Control (which assumes a rectangular cross-section) to accurately simulate outflow from a structure with a trapezoidal cross-section. Two types of LID facility were modeled: one releases captured inflow through a perforated underdrain below the soil layer (bioretention basin; BB); and the other is drained at the surface of the soil layer (vegetated swale; VS). Initially, the modeled LID structures were sized identically to the field surface areas. However, it was necessary to change their model representation to account for the non-rectangular shape of the soil layer. In addition, a sensitivity analysis was completed, and the most influential parameters were identified as the conductivity slope and seepage rate. Both the alteration of the LID structure representation and the parametric calibration greatly improved the simulated outflows from the vegetated swale resulting in an increase of the Nash–Sutcliffe efficiency (NSE) coefficient from −0.6 to 0.64 (NSE >0.5 is acceptable for hydrologic models according to the literature). The bioretention basin calibration did not prove as successful. The evaluated LID Control module presented better predictive capabilities for the basin with a simpler overall design (VS).

Effect of FSW process parameters and tool profile on mechanical properties of AA 5082 and AA 6061 welds

In the present paper, similar and dissimilar combinations of AA 5052 and AA 6061 Aluminum grades were joined using FSW to obtain desirable mechanical properties. Modified HSS tool containing 10% cobalt with taper pins of circular and trapezoidal cross sections are developed to obtain FSW sheet joints. Process parameters are selected same for both the pin profiles for obtaining weld joints of similar and dissimilar combinations. Welds were obtained at tool rpm of 1600 and 2600 with feed of 15 mm/min. and 20 mm/min. Tensile and hardness properties of AA 5082 and AA 6061 weld joints were analyzed by tensile test and hardness test respectively. It was observed that the taper pin with square tip has produced better mechanical properties in similar and dissimilar weld joints.

Hydraulic Analysis of a Sloped Trapezoidal Non-cavity Drain Improved by a Pipe Drainage

Non-cavity drains usually have rectangular or trapezoidal profile in cross-section, hydraulic analysis of which is developed. Trapezoidal cross-sections in non-cavity drains facilitates their higher water absorption capacity at approximately the same level of water drainage capacity in comparison to pipe draining system. The water drainage capacity of a non-cavity drain can be improved by installing a pipe drain inside a non-cavity one. However, no hydraulic analysis of such combined drain has been developed. It is assumed that motion of water in both non-cavity part of a drain and pipe one changes gradually. In non-cavity part of the drain, transient flow takes place and it is turbulent in pipe one. Laminar flow is observed in non-cavity and pipe parts of the drain only near the source and has almost no influence on pressure losses lengthwise along the drain. There are obtained calculation dependencies to determine specific afflux to every part of the drain as well as the depth (head in the pipe part of the drain) at the source of drainage and at the section of maximum depth. This was achieved by solving a system of two equations describing the flow of water in non-cavity and pipe parts of the drain.