Trapezoidal Cross-section Research Articles

Optimal construction of an open channel by considering different conditions and uncertainty: application of evolutionary methods

In the present study, different evolutionary methods, namely the bat algorithm (BA), particle swarm optimization (PSO) and their hybrid (HBP), are employed for the design of trapezoidal open-channel cross-sections with minimum construction cost (concrete lining plus excavation costs). For this purpose, considering open channels with uniform and composite roughness, fixed and variable freeboard, and also velocity, Froude number and flooding probability constraints, eight models were defined. The performance of HBP in terms of convergence rate was investigated using 10 random runs, and the resulting coefficient of variation for different models was 0.00001–0.002. Solutions of HBP were also compared to those of other optimization algorithms. The results indicated that using HBP, compared to BA, PSO, LINGO, Lagrange multiplier method and shuffled frog-leaping algorithm, led to a 32% saving in construction cost. Therefore, HBP has high potential for the optimal design of open channels.

Design of channel section for minimum water loss using Lagrange optimization and artificial neural networks

Evaporation and seepage are the most important forms of water loss in an open channel. Evaporation loss depends on the area of free surface while, seepage loss is function of channel geometry. The design that achieves minimum water loss is determined for trapezoidal and rectangular cross sections using Lagrangian method with Manning’s equation as a constraint. The water loss function which comprises evaporation and seepage loss was used. Matlab code is created to solve the equations of optimization by trial and error. An approach to determine the bed width and water depth from known discharge, side slope, longitudinal slope, manning’s coefficient, evaporation rate, and soil type is proposed. Design charts which determine bed width and water depth that ensure minimum water loss are presented. Moreover, artificial neural networks are used to get the best design for any value of evaporation rate. Using the created design charts and neural networks optimum design can be determined easily, accurately and quickly.

New method for assessing lateral distribution of energy gradient in curved channels

The energy gradient is a fundamental physical quantity of flow motion. To date, many studies have concentrated on uniform flow or fully developed curved flow, with the energy gradient approximated as the bed slope. This paper presents a new method to assess the lateral distribution of the apparent energy gradient in curved channels when curved flow is not fully developed. A dimensionless apparent energy gradient (K) is presented. An expression for K is explicitly formulated based on the Reynolds-averaged Navier–Stokes (RANS) equations and the lateral distribution of K is derived from measured velocity data. The method was applied in a 120° curved flume with asymmetric trapezoidal cross-sections. The results showed a bilinear distribution of K; that is, K remained nearly constant in the central region of the channel while, in the inner bank region, K increased linearly as the inner bank was approached. These results were derived for specific cases for curved channels with a side-slope, but the method for deriving K can be applied to other cases, thus providing a new way to study energy loss in curved channels to contribute to river management, such as estimation of discharge capacity and navigation improvement.

Critical Depth of Trapezoidal Open Channel Using Explicit Formula and ANN Approach

Procedures for calculating critical depth in an open channel having a trapezoidal cross section are discussed in this paper. Among the current methods are chart look-up, trial-and-error, iterative, and approximate formula; however, practical application shows that each of these methods has some problems. This paper proposes an explicit solution to critical depth in a trapezoidal channel by introducing data from iteration solution and then applying multiple nonlinear regressions (MNLR) and artificial neural network (ANN) techniques to derive the best estimate. Results show that ANN formulation of the problem of solving for the critical depth is less successful than that by regression. The performance of MNLR in terms of R2 (0.998) and RE (0.025) is excellent and performance of ANN in terms of R2 (0.987) and RE (0.132) is good but its values are slightly perturbed around its numerically obtained values.

The Influence of a Single Charged Interface Trap on the Subthreshold Drain Current in FinFETs with Different Fin Shapes

The influence of the channel shape in a finned (vertical) field-effect transistor (FinFET) on the amplitude of random telegraph noise (RTN) induced by single interface trapped charge has been simulated for the transistors with rectangular and trapezoidal fin cross sections. It is established that, in a subthreshold region of gate voltages, a single charge trapped at the fin top induces RTN of lower amplitude in the case of a trapezoidal cross sections as compared to that in a transistor with rectangular cross sections. However, a single charge built in the middle of the fin side wall induces RTN of significantly higher amplitude in case of the fin with trapezoidal cross section.

High-Throughput Particle Concentration Using Complex Cross-Section Microchannels.

High throughput particle/cell concentration is crucial for a wide variety of biomedical, clinical, and environmental applications. In this work, we have proposed a passive spiral microfluidic concentrator with a complex cross-sectional shape, i.e., a combination of rectangle and trapezoid, for high separation efficiency and a confinement ratio less than 0.07. Particle focusing in our microfluidic system was observed in a single, tight focusing line, in which higher particle concentration is possible, as compared with simple rectangular or trapezoidal cross-sections with similar flow area. The sharper focusing stems from the confinement of Dean vortices in the trapezoidal region of the complex cross-section. To quantify this effect, we introduce a new parameter, complex focusing number or CFN, which is indicative of the enhancement of inertial focusing of particles in these channels. Three spiral microchannels with various widths of 400 µm, 500 µm, and 600 µm, with the corresponding CFNs of 4.3, 4.5, and 6, respectively, were used. The device with the total width of 600 µm was shown to have a separation efficiency of ~98%, and by recirculating, the output concentration of the sample was 500 times higher than the initial input. Finally, the investigation of results showed that the magnitude of CFN relies entirely on the microchannel geometry, and it is independent of the overall width of the channel cross-section. We envision that this concept of particle focusing through complex cross-sections will prove useful in paving the way towards more efficient inertial microfluidic devices.

Flexural performance of composite grid panels with deep ribs

This paper reports on the flexural performance of an innovative composite grid panel composed of glass fiber-reinforced polymer face skins and deep glass fiber-reinforced polymer ribs with a trapezoidal cross-section. Three-point and four-point bending experiments were performed to demonstrate the feasibility of the composite grid panels under concentrated loads. Compared with the composite grid panels without skins, maximum increases in the ultimate load, and initial bending stiffness of the composite grid panels of approximately 68.2% and 306.7%, respectively, were achieved with the existence of both upper and lower skins. Furthermore, an analytical analysis was carried out to predict the initial bending stiffness and mid-span deflection of the composite grid panels. A comparison of the analytical and experimental results showed that the analytical model accurately predicted the flexural performance of the composite grid panels subjected to three-point and four-point bending. Failure mechanism maps were constructed to predict the mechanical response and failure modes of the composite grid panels. Moreover, the validated model was used in a parametric analytical study to further estimate the effects of various parameters on the flexural performance of the composite grid panels. The results demonstrated that the initial bending stiffness can be significantly improved by increasing the trapezoidal section ratio, face skin thickness, and grid height.

Slip Flow Models for Gas Flows in Rectangular, Trapezoidal, and Hexagonal Microchannels

A compact slip flow model is proposed for isothermal, incompressible gas flows in long microchannels of rectangular (square), trapezoidal (triangular), and double-trapezoidal (rhombic) cross sections in the slip flow regime. The model is based on superposition of the dimensionless mean continuum velocity and the dimensionless average slip velocity. The characteristic length used in the Poiseuille and Knudsen numbers is the hydraulic diameter. A novel slip flow parameter is introduced to account for the relationship between the average slip velocity and the average wall shear stress. The novel slip flow parameter lies in the range 0.5–0.6 for equilateral triangular microducts to very narrow rectangular microchannels when the characteristic length is the hydraulic diameter. The agreement between the proposed compact slip flow model and extensive numerical data is within 1% for a wide range of microchannel shapes and aspect ratios.

The effects of oil/MWCNT nanofluids and geometries on the solid oxide fuel cell cooling systems: a CFD study

In this numerical study, the variations in the surface area of the cooling channels in a solid oxide fuel cell with different cross sections and multi-walled carbon nanotubes oil/MWCNT nanofluid volume fractions are considered. Rectangular, trapezoidal and elliptical cross sections, and nanofluid volume fractions of 0–6% for the fluid are chosen as the studied parameters as well as the mass flow rates. In this research, a 3D model is developed by the finite volume method using the computational fluid dynamics (CFD). Then, the flow field and the heat transfer rate are predicted. The results show that the dissipated heat in the fuel cell is dependent on the mass flow rate of the fluid. That increased heat increases the heat transfer rate. The presence of the solid particles can also reinforce the heat conduction of the coolant fluid and consequently improve the heat transfer performance. The pumping power is maximum for the highest mass flow rate and the highest solid nanoparticle volume fractions. Additionally, the pumping power is dependent on the route in which the sections with lowest momentum changes and lowest pressure drops have the least amount of the pumping power. The ratio of the dissipated heat by the nanofluid over the base fluid is compared to a pressure drop. The movement of flow with the lower mass flow rates will result in penetrations of the thermal boundary layers into different flow regions, which can increase the optimum temperature in the solid part of the fuel cell. By increasing the mass flow rate of the fluid passing through the channels from 0.002 to 0.004 kg s−1, the maximum temperature is decreased by 6.13, 3.34 and 6.35% for rectangular, trapezoidal and elliptical channels, respectively.

Effect of rivet die structure on the quality of riveted aircraft structures using slug rivet

Slug rivet interference-fit riveting is an advanced connection technology. The quality of riveted aircraft structures can be evolved to a higher-level with good sealing performance when using slug rivet. Some research has been conducted to study the effects of riveting process on riveting quality. But, few attentions have been paid on the action mechanism of rivet die structure during riveting process. This paper reveals the internal relation between rivet die structure and riveting quality in the forms of theoretical and numerical analyses as well as experimental verification. Three typical concave rivet die structures and the corresponding combinations have been studied. The result indicates that well-designed rivet die can effectively improve riveting quality. The rivet die with isosceles trapezoid cross-section can generate a larger radial reactive force to prevent the radial flow of rivet metal material to form driven head. More axial material flow can be pushed into rivet hole to increase the interference value. The results considerably improve knowledge about the behavior of rivet die during riveting process. The aim is to find out the appropriate rivet die to improve riveting quality. The study will pave the way for high structural fatigue-resistant design in modern aerospace manufacture.

Current and Modified Flood Discharge Capacity of a Reach of Tigris River between Kut and Amarah Barrages

This study was conducted to examine the discharge capacity of the reach of the Tigris River between Kut and Amarah Barrages of 250km in length. The examination includes simulation the current capacity of the reach by using HEC-RAS model. 247cross sections surveyed in 2012 were used in the simulation. The model was calibrated using observed discharges of 533, 800, 1025 and 3000m3/s discharged at Kut Barrage during 2013, 1995, 1995 and 1988, respectively, and its related water level at three gauge stations located along the reach. The result of calibration process indicated that the lowest Root Mean Square Error of 0.095 can be obtained when using Manning’s n coefficient of 0.026, 0.03 for the Kut- Ali Al Garbi and Ali Al Garbi- Amarah reaches respectively, and 0.03 for the flood plain of the whole reach under study. The reach under study has two lateral inflow streams, UmAljury, which joins Tigris River at station 51km, and Aljabab, which joins Tigris River at station 57km. The discharge of Aljabab varies between 0 and 400m3/s and the discharge of UmAljury varies between 0 and 50m3/s. The results showed that the current capacity of the main channel of the reach of the Tigris River between Kut and Amarah Barrages is 400m3/s. The water levels kept less 1m than both levees in case of discharging 1800m3/s from Kut Barrage, with no lateral inflows, and 1700m3/s with lateral inflow. The reach of Tigris River fails to accommodate the flood discharge of 3300m3/s which is the discharge of the flood of 1988 measured at Kut Barage. It can be concluded that the reach had large amount of sediment for the period from 1988 to 2012 and the reach capacity reduced to about half its capacity of 1988 during this period. The results of removing 12 islands and 2 sidebars by reshaping the current condition into trapezoidal cross-section will decrease the surface water levels by 20cm and flow of 1900m3/s can be discharged safely at Kut Barrage without any lateral inflow and 1800m3/s with lateral inflow from the tributaries. While, expand 58 narrow cross-sections that choking the flow, the water levels along the reach are lowered by an average of 20cm in addition to that 20cm when modifying the cross-sections at the islands and sidebars. In this case, flow of 2100m3/s can safely be discharged from Kut Barrage without any lateral inflow and 1900m3/s with lateral inflow. The result when modifying additional 111 cross-sections showed that the reach can safely accommodate a flood wave of 3300m3/s from Kut Barrage without any lateral inflow and 3000m3/s with lateral inflow.

Effect of Anisotropically-etched Silicon Electrode on Electrolytic Products Flow in Micro ECM

Stray corrosion and electrolytic products deposition in the machining gap are major influence factors seriously restricting the application of micro electrochemical machining (ECM). Currently, one technical bottleneck is preparing thin and durable insulating films on electrode sidewall to restrain the stray corrosion. In previous work, we proposed an anisotropically-etched silicon electrode for micro ECM, on which silicon dioxide and silicon nitride are deposited as insulating films. The heavily doped silicon electrode body has good electrical conductivity, and the silicon-based films have excellent insulating property. The anisotropically-etched silicon electrode on (1 0 0) crystal plane has an isosceles trapezoid cross section. To get better machining performance compared with cylindrical electrode, the silicon electrode is rapidly rotated on a spindle in micro ECM process. The periodically varying lateral gap has a special effect on the electrolyte flow characteristics. A simulation model of electrolyte flow and discrete phase distribution is established by Fluent software. Simulation results indicate that the normal flow rate of electrolyte with silicon electrode is 50 times higher than that with cylindrical electrode, which is benefit for removing solid electrolytic products smoothly. The maximum concentration and residual ratio of solid electrolytic products are decreased with the rotating speed increasing. When the rotating speed is higher than 1200 rpm, the residual ratio is reduced to 13%. ECM experimental results indicate that electrolytic products on the workpiece machined by a silicon electrode are much fewer than that by cylindrical electrode. Silicon electrodes with trapezoidal cross section have a distinct advantage for reducing electrolytic products deposition.

Comparative study between turbulence models in curved channels

ABSTRACT This paper presents a comparative study between results obtained in two-dimensional computational simulations performed with three different turbulence models: constant viscosity; Elder Model and k˗Ꜫ Model. The simulations were performed using the software Telemac 2D. These results were compared to data obtained from a study in experimental channel with trapezoidal cross-section and composed of straight stretches and curves. The main objective of this comparison is to explore how turbulence models affect the general behavior of the simulated flow. To support these comparisons, statistical analysis were adopted to quantify the differences between the velocity fields obtained in the simulations and that observed in the experimental channel. The results showed that, despite the theoretical limitations, the use of the simpler turbulence closure model, that is the constant turbulent viscosity, can lead to results as good as or better than those obtained with more sophisticated models.

Raising of Hydraulic Efficiency and Operational Reliability of Large Canals

The article considers the flow efficiency and operational reliability of large canals. In order to raise efficiency and reliability of exploitation of canals hydraulic control model to change the flow depth was created. It was determined by the law of water transmission in optional time. Patterns based on determination of hydraulic relations under changing values of hydraulic parameters of water flow in the trapezoid cross-section irrigation canal were examined.

Numerical Study of Enhanced Heat Transfer of MicroChannel Heat Sink with Nanofluids

The electronic devices on the circuit board of the navigation device have the defects of high power and difficulty in heat dissipation, thereby restricting their performance. In view of the above defects, this paper proposes a miniature water-cooled radiator with a trapezoidal cross-section spoiler arranged at equal intervals. The numerical simulation of the three-dimensional laminar flow and heat transfer is carried out to study the performance of the micro water-cooled heat sink. The effects of Reynolds numbers and the types of nanofluids on the heat transfer performance of microchannel heat sink are also investigated. The results show that when the Reynolds number ranges from 100 to 500, the existence of the spoiler column makes the heat dissipation effect of the microchannel heat sink significantly improved, and the friction coefficient decreases with the increment of the Reynolds number. With the increasing of the volume fraction in the nano-particles, the heat transfer performance of microchannel heat sink is also improved. The heat transfer performance of SiC nanofluids is better than that of TiO2 nanofluids under the same flow rate.

Effect of Time Dependent Variables on Different Types of PSC Box Girder Bridges.

Time dependent variables such as temperature gradient, effective temperature, creep, and shrinkage lead to long term deflection in prestressed concrete girders. This in turn effects the serviceability and sustainability of the bridge in the long run. Therefore, research and analysis is of paramount importance before deciding the type of girder to be used. A parametric study was carried out in order to determine the most desirable and efficient type of box girder to be used for a prestressed concrete bridge having a continuous span. Three prestressed concrete box girder bridge models of single, multi-cell rectangular and multi-cell trapezoidal cross section, having similar span, width and depth were taken into consideration. The finite element models were analysed using MIDAS Civil. The behaviour of the box girder cell types under various time dependent properties such as temperature, creep and shrinkage are presented in this paper. The results show that the prestressed concrete box girder bridge of multi-cell rectangular cross section exhibits greater forces and moments due to time dependent variables in comparison to the other two box girder cell types.

Computer Optimization of Schematic Model for Sawing a Log into Rectangular and Trapezoidal Cross-section Boards for Panel Products

Computer Optimization of Schematic Model for Sawing a Log into Rectangular and Trapezoidal Cross-section Boards for Panel Products

The Influence of Fin Shape on the Amplitude of Random Telegraph Noise in the Subthreshold Regime of a Junctionless FinFET

The dependence of random telegraph noise (RTN) amplitude on the gate overdrive in a junctionless field-effect transistor (FinFET) with rectangular and trapezoidal channel (fin) cross sections manufactured using silicon-on-insulator technology has been numerically simulated. It is established that the RTN amplitude in the subthreshold region of gate voltages for a FinFET with a trapezoidal cross section of channel is significantly lower than that for the transistor with rectangular cross section of a channel. In addition, under the same conditions, the RTN amplitude at the threshold gate voltage in a junctionless FinFET is significantly lower than that in planar fully depleted and in usual FinFET.

Treatment technology of liquid phase at industrial waste landfill

The authors suggest the complex technology of their treatment on the example of the specific industrial waste landfill. The technology involves industrial liquid waste treatment by stages. The solution of petroleum oil wastes being pumped from the pond at the landfill is supplied to the primary purification in the conventional oil separator which is combined with the settling pond. Additional treatment of water from oil products and suspended solids is carried out by a flotation unit. After the flotation unit for post-treatment of water from heavy metals, it is fed through a channel of trapezoidal cross-section to a filter dam being made of sorbent. The channel has been constructed in the earth water course. The subsoil is heavy loam and clay. The channel has a filter barrier, the design of which is constructed in the form of 2 metal frames being covered with wire nettings. There is a waterproofing layer made of polyvinyl chloride film at the bottom of the channel under the frames. A packing of fibrous sorbent is placed between the wire nettings to finally purify liquid wastes from petroleum residue, which allows treating discharge in accordance with the requirements of maximum permissible concentrations for fish-husbandry water utilization.

Modeling depth-averaged streamwise velocity in straight trapezoidal compound channels with ice cover

This study considers the flow of water in ice-covered compound channels with straight trapezoidal cross-sections. For describing the lateral distribution of depth-averaged streamwise velocity in aforementioned channels, a modified analytical model, which incorporates the influences of channel bed friction, ice cover resistance, lateral shear turbulence and secondary currents, is derived by the Shiono and Knight method and a two-layer hypothesis. Then the analytical model is applied to straight compound channels with full ice cover and symmetrical shore ice. The modeled results of the two cases, which employ appropriate boundary conditions, indicate good predictions for the transverse distribution of depth-averaged streamwise velocity when compared with captured experimental results. Subsequently, the intensities and rotational directions of secondary flows and the dimensionless comprehensive eddy viscosity effect are exhaustively discussed, finding that the intensities of secondary flows in the main channel domain for the two cases present opposite changing laws as flow depth increases, and the signs of secondary flow coefficients are verified to be consistent with experimental observations. The theoretical approach used herein can supply some guidance for investigating the flow characteristics of ice-covered channels.