Trapezoidal Surface Research Articles

Shape reconstruction of trapezoidal surfaces from unorganized point clouds

A smooth T-surface can be thought of as a generalization of a surface of revolution in such a way that the axis of rotation is not fixed at one point but rather traces a smooth path on the base plane. Furthermore, the action, by which the aforementioned surface is obtained does not need to be merely rotation but any “suitable” planar equiform transformation applied to the points of a certain smooth profile curve. In analogy to the smooth setting, if the axis footpoints sweep a polyline on the base plane and if the profile curve is discretely chosen then a T-hedra (discrete T-surface) with trapezoidal faces is obtained.The goal of this article is to reconstruct a T-hedron from an already given unorganized point cloud of a T-surface. In doing so, a kinematic approach is taken into account, where the algorithm at first tries to find the aforementioned axis direction associated with the point cloud. Then the algorithm finds a polygonal path through which the axis footpoint moves. Finally, by properly cutting the point cloud with the planes passing through the axis and its footpoints, it reconstructs the surface. The presented method is demonstrated using examples.From an applied point of view, the straightforwardness of the generation of these surfaces predestines them for building and design processes. In fact, one can find many built objects belonging to the sub-classes of T-surfaces such as surfaces of revolution and moulding surfaces. Furthermore, the planarity of the faces of the discrete version paves the way for steel/glass construction in industry. Finally, these surfaces are also suitable for transformable designs as they allow an isometric deformation within their class.

Influence of the anatomy of the proximal articular surface of the trapezium (PAST) and the trapezoidal articular surface of the trapezium (TRAST) in cup placement during trapeziometacarpal arthroplasty

The influence of the anatomy of the proximal articular surface of the trapezium (PAST) and the trapezoidal articular surface of the trapezium (TRAST) on cup placement during trapeziometacarpal arthroplasty was retrospectively evaluated on 56 preoperative anteroposterior radiographs of patients who underwent surgery for trapeziometacarpal osteoarthritis. The percentage coverage of the prosthetic cup by the PAST and the available height of the trapezium were calculated. In 39% of cases, there was a significant difference (up to a mean 4.5 mm, p < 0.001) between the radial height of the trapezium (which is usually considered) and the available height of the trapezium. The anatomy of the PAST and the TRAST has an impact on the placement of the prosthetic cup when trapezium height is low. The results of the present study suggest that these considerations must be known by all operators performing trapeziometacarpal arthroplasty; that lateralization, implant suspension, or surgical alternatives should be considered to prevent several intra- and postoperative surgical complications.Level of evidence: IV.

Effects of surface characteristics on bubble dynamics in nucleation boiling using LBM

In this paper, the hybrid thermal lattice Boltzmann model is adopted to investigate the nucleation boiling. The bubble dynamics behaviors including nucleation, growth, coalescence, and departure, are studied on structured surfaces. Three types of structured surfaces adopting the rectangular, triangular, and trapezoidal structured surfaces are designed with different surface wettability. The numerical results reveal that, firstly, for the single bubble, increasing the opening width of structured surfaces from inside to outside is beneficial for bubble evolution. Then, with the dimensionless separation distance less than 1 between the two nucleation sites for the double bubbles, it presents a more noticeable advantage in the bubble evolution with different surface characteristics. Finally, the dimensionless critical coalescence distance of double bubbles increases significantly with the increment of contact angle on the hydrophobic surface. Besides, the dimensionless bubble critical coalescence distances on the triangular and rectangular structured surfaces are larger than those on the trapezoidal structured surface for the hydrophobic surface.

Experimental and numerical investigation of pool boiling heat transfer from finned surfaces

An experimental study of the pool boiling process on three test surfaces, namely, Plain surface, Rectangular finned surface, and Trapezoidal finned surface, was carried out using distilled water as the working fluid at atmospheric pressure. A parametric study of finned surfaces was performed to understand the effect of fin spacing and fin height on the pool boiling performance. A high-speed camera was employed to capture the pool boiling process. A numerical investigation was also performed using the Eulerian multiphase model associated with the RPI wall boiling model. A 2-D rectangular boiling chamber filled with distilled water was considered for the numerical study. The numerical results with default models were validated with the experimental results. A correction was proposed for the Bubble Waiting Time coefficient (Cw) of the quenching heat flux to improve the numerical results. Experimental results showed that using rectangular and trapezoidal finned surfaces improved the heat flux values by 52.3% and 101.5%, respectively, compared to the plain surface. The heat transfer coefficient (HTC) depends upon the area availability and type of boiling surface used. Increasing the height of the fins was beneficial, whereas increasing the fin spacing adversely affected the fin performance.

Impact of nanoparticles on speed of discharging considering homogeneous model for thermophysical features

Numerical unsteady approach based on Galerkin method with the inclusion of adaptive mesh was executed in this paper to simulate the freezing of water within a container. The domain has two triangular and trapezoidal cold surfaces and two adiabatic walls. The governing equations show the domination of conduction and transient source term has been involved. Galerkin method for modeling was applied and good accommodation has been reported based on comparison with previous data. Adding nano-powders makes the amount of heat to be released with stronger conduction and freezing time decreases about 26.76% when [Formula: see text]. Augmenting the fraction of powders can make the rate of process increase. For the greatest fraction of powders, an augmenting shape factor can enhance the speed of process about 6.95%.

Improving Temperature-Sensing Performance of Photonic Crystal Fiber via External Metal-Coated Trapezoidal-Shaped Surface

This article describes a photonic crystal fiber (PCF) temperature sensor that utilizes a flat, metal-coated trapezoidal surface. The PCF is made up of two layers of elliptical air holes and a polished trapezoidal surface that allows temperature sensing. An external sensing approach is used to deposit a thin silver layer on the reflective surface, while a thin SiO2 film acts as an oxidation-resistant coating. The top elliptical air hole serves as the interface for energy transformation from the core-guided mode to the surface plasmon-polariton (SPP) mode. Simulations carried out using the finite element method indicate that the proposed SPR-PCF temperature sensor can achieve a maximum temperature sensitivity and resolution of up to 5200 pm/°C and 0.01923 °C, respectively, across a temperature range of 10 to 60 °C. This research has significant potential for sensor design and real-time temperature remote sensing applications.

Evaluating the Use of Surface Plasmon Resonance-Based Sensing for Colorectal Mucosa Cancer Detection

This paper presents an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in silico</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in vitro</i> study concerning the application of a trapezoidal prism-based surface plasmon resonance chip to detect colorectal cancer by analyzing the mucosa tissue. The sensor is a multilayered structure and works in the wavelength interrogation mode. Performance parameters related to the metallic film characteristics, such as thickness and type of metal were determined. For the analyzed noble metals, the silver film of 40 nm has the highest sensitivity of 6,454.12 nm/RIU, and the 60 nm-thick presents the best values for full width at half maximum and χ parameter (20.20 nm and 286.63 RIU <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–1</sup> ). The palladium nanolayer deposition enhanced the sensitivity by 10.81% for copper film and peaks at 6,497.04 nm/RIU for the silver film. The palladium nanolayer also provokes deeper dips in the reflectance spectrum. Tissue phantoms were used to study the sensor response to solid surrounding medium to show the feasibility and the correctness of the proposed methodology.

Die Surface Design Method for Smoothing Shock Line in Sheet Metal Forming

Replacing the material of automobile body panels from steel sheets to aluminum alloy sheets is an approach to reducing the automobile weight. In the press forming of panel parts with aluminum alloy sheets, it is necessary to smooth stepped linear marks of about 5 μm to 50 μm generated during press forming to satisfy the surface quality of the panel parts. These linear marks are called shock lines, which are generated when the blank sheet slides on the die corner radius during press forming. In this research, the protrusion shape of forming dies that enables us to smooth a shock line is investigated using a 1.2-mm-thick 6000 series aluminum alloy sheet. The shock line is smoothed by applying a trapezoidal surface pressure to the blank sheet near the shock line at the bottom dead center. We propose a method of using finite element analysis to calculate the protrusion shape from the amount of elastic displacement of the dies that occurs when the target surface pressure is applied to the dies surface. The protruding shape calculated by the proposed method has been applied to the forming dies for the door inner panel of the 6000 series aluminum alloy sheet. As a result, in our experiments, the shock line has been smoothed by using these forming dies.

A Diode‐like Scalable Asymmetric Solar Evaporator with Ultra‐high Salt Resistance

AbstractPassive solar‐driven interfacial evaporation is an environmental‐friendly approach for seawater desalination. However, non‐volatile salts usually precipitate on the evaporator surface during evaporation, significantly reducing the evaporation rate and blocking the evaporator. Although several strategies have been proposed for this issue, they are usually only effective under low salinity conditions and natural solar irradiation. In this study, a scalable solar evaporator is proposed, which is expediently fabricated by carbonizing the commercially available coconut fiber cloth, through designing and optimizing an asymmetric bi‐layer structure with a trapezoidal evaporation surface and a wide leg‐strengthened water supply pathway. Both experimental and simulation results indicate that the evaporator presents ultra‐high salt tolerance, which keeps running steadily for consecutive 14 days under the high salinity of 14 wt% NaCl and high irradiation of 4 suns. This excellent salt resistance arises from a diode‐like ion migration introduced by its asymmetric structure. Meanwhile, a remarkable evaporation rate of 7.28 kg m−2 h−1 is also achieved under the harsh condition, resulting from the high solar absorbance and the reduced evaporation enthalpy of the evaporator. Such an evaporator is confirmed as a simple, low‐cost, scalable, efficient, and long‐term stable device for producing freshwater under harsh desalination conditions.

Numerical analysis of liquid desiccant dehumidification system with novel trapezoidal baffled surface

Environmental concerns as well as a rapid decrease in fossil fuel reserves, raise the need for a substitute to the conventional vapor compression system (VCS). Low-grade energy run liquid desiccant absorption system is emerging to be a viable substitute to the VCS. One of the major barriers to the development of a liquid desiccant absorber (LDA) is its low effectiveness. Current study proposes a modification of the flat surface profile of a falling film type liquid desiccant absorber with a trapezoidal baffled profile. The numerical model involves a 2-D transient, multiphase-multicomponent system with conjugate heat-mass interaction. The complex governing equations are solved using ANSYS FLUENT 19.2. The computational model under consideration is validated using the experimental results. The maximum deviation is observed to be 10.31% and 0.38 K in terms of humidity and temperature, respectively. It is observed that the performance is maximized with an trapezoidal baffled configuration of p:e = 10:1.5. The incorporation of trapezoidal baffled surface (p:e = 10:1.5) augmented the dehumidification and enthalpy effectiveness of the system by 26.1% and 24.2%, respectively. The desiccant solution concentration of 35% and temperature of 293 K are optimum inlet conditions for better designing of the absorber. Also, it is observed that minimum the air velocity, maximum is the effectiveness. The proposed modification is found to have 12.1% improved dehumidification effectiveness compared to the earlier configuration of the triangular corrugated solution wall. The same is observed to yield lesser dehumidification effectiveness of 4.85% compared to sinusoidal geometry, proposed earlier.

Comparative performance analysis of flat plate solar collector having circular &trapezoidal corrugated absorber plate designs

Flat plate Solar collectors are in use for a long time and have well-established technologies for low-temperature thermal applications. Use of newglazing materials, absorber plate designs, selective coatings, and advanced working fluids, thermal conversion efficiencies of these devices can be further improved. Design modification always comes under top priority because it brings auxiliary changes that further modify the system's overall efficiency. Increasing energy demand puts extra attention on the researchers to develop solar thermal energy-based systems. The presented experimental analysis is based on the design modification of the collector absorber plate to modify the contact area between the absorber plate and collector tubes. We performed a comparative performance of the circular absorber surface and the trapezoidal surface of contact with absorber tubes. The following results indicate that the trapezoidal absorber surface serves better over circular and plate absorber surfaces.Thermal efficiency increases by 8.74% and 12.85% for absorber plate's circular and trapezoidal corrugated surfaces. Exergy efficiency is improved by 16.88, 23.31%, and the overall heat loss coefficient decreases by 7.49 and 8.72% for circular and trapezoidal corrugated surfaces, respectively. The collector's heat removal factor is also significantly higher for trapezoidal corrugated absorber plate than the normal collector absorber surface.

Leidenfrost Temperature on Trapezoidal Grooved Surface

In this study, we reported experimental results of a water droplet falling on trapezoidal grooved surfaces of heated silicon wafers with the groove width varied from 20 μm to 640 μm and the depth from 20 μm to 40 μm. Based on the observation of droplet dynamics captured by high-speed camera, we found that on the denser grooved surface, the maximum spreading diameter of the droplet perpendicular to the groove direction was smaller than that on the sparser grooved surface with the same groove depth. The residence time of the droplet on the denser grooved surface was shorter than that on the sparser grooved surface. The Leidenfrost point increased 50 °C with the groove width varied from 20 μm to 640 μm and decreased 10 °C when the depth was changed from 20 μm to 40 μm, which were higher than that on the smooth surface. Due to the deformation of the droplet during the droplet dynamics, it was difficult to calculate the heat transfer by measuring the droplet volume reduction rate. Based on the convective heat transfer from the grooved surface to the droplet, a Leidenfrost point model was developed. The results calculated by the model are in agreement with the experimental data.

Role of surface microstructure and shape on light extraction efficiency enhancement of GaN micro-LEDs: A numerical simulation study

One of the bottlenecks for today’s micro-light-emitting-diodes (micro-LEDs) is the low light extraction efficiency. How to effectively boost this efficiency is especially important for micro-LEDs because their surface-to-volume ratio is much larger than normal LEDs. The trapezoidal chip structure, surface grating, and surface coarsening are simulated in this paper, with the aim to obtain their contributions to enhance the light extraction efficiency. Through the simulation, we have found that all of the three methods can increase the light extraction, but with different extents. When the trapezoidal angle of the mesa is 12°, the extraction efficiency reaches its maximum (by this method) of 64.5%. If the surface grating on n-GaN (the light output surface) has a period of 300 nm, a height of 147 nm and width of 243 nm, the light extraction efficiency can be as high as 72%, which is much higher than that of the micro-LED without any grating. For the random roughening of n-GaN, a maximum value of 56% can be obtained if the roughness extent is optimized. Our results are of reference value for scientists and engineers working in micro-LEDs and can serve as guidelines for GaN based high efficiency micro-LED design for future displays.

Static Compression and Dynamic Sliding Conditions of 2D Trapezoid Square and Circle Contact Surface Shapes

In addition to force-body interaction problems, deformable bodies problems are quite common in engineering applications and their investigations are more complex. The friction force and contact pressure formed between the surfaces are dominant and mostly studies are investigated considering the static and quasi-static conditions. However, considering the elastic/elasto-plastic deformation and dynamic conditions, the geometric surface shape is important. In this study, using the finite element analysis method, the pressure distribution of the surfaces containing square, trapezoidal and circular surface shapes on a flat surface and the dynamic deceleration condition during the surface interaction of an object with initial velocity are investigated. The material used is steel whose ground geometry does not show linear behaviour and nylon material is used for surface geometry. In order to ensure that the surface effect is dominant in the dynamic examination, a linear increasing pressure is applied on the examined part. In the results, it was determined that there is an irregularity in the stress and velocity deceleration curve. The effect of compression pressure and friction coefficient has been examined in detail and the results are discussed.

Experimental investigation on flame morphology and improved flame radiation model of rectangular heptane pool fire

AbstractThe safety process and effectiveness of in situ burning (ISB) method dealing with spilling liquids depend on flame morphology, mass burning rate and flame radiation. In this work, eight rectangular pools with a fixed area of 400 cm2 but different aspect ratios (length–width ratio, n = 1, 2, 4, 6, 8, 10, 12, and 16, respectively) are used. As the aspect ratio increases from n = 1 to n = 16, the flame height decreases from 105.6 to 72.9 cm, whereas the incident heat flux increases from 0.283 to 0.562 kW/m2. The mass burning rate decreases initially at n ≤ 6 and increases afterwards at n &gt; 6. The traditional flame radiation model overestimates experimental measurement because the radiation model assumes that the flame surface is rectangular, but the actual flame shape shows a trapezoidal surface due to air entrainment. The mathematical linear interpolation method is proposed to make an improvement of rectangular radiation model. The new‐proposed flame radiation model is validated by experimental measurements with the relative error &lt; 5%. The current work provides a good method to evaluate the magnitude of loss prevention of oil leakage.

A 2-D analytical model for the wetting behavior of various microtextured surfaces

In this work, a physical model for various microtextured surfaces was proposed to investigate their wettability, and in particular, superhydrophobicity. Using such an analytical model, the thermodynamic states, and specifically, free energy and free energy barriers of the concerned surfaces such as trapezoidal, vertical and inverse-trapezoidal surfaces, which were correlated the contact angle and contact angle hysteresis, can be exactly calculated. It was demonstrated based on the theoretical results that the contact angle, which was restricted by sidewall angle of micropillars of these microstructures, was not an independent parameter to affect the wetting behavior, and the re-entrant structures played an important role in the transition from hydrophilicity to superhydrophobicity. Furthermore, the transition criterion was generalized that the sidewall angle should be less than the intrinsic contact angle, and the pillar width and height should be as small as possible, in particular, for the T-shape microstructure. Moreover, it was found that for these transitions, a positive energy barrier could support liquid/vapor interfaces and separate the Wenzel and Cassie state on the hydrophilic substrates. Finally, it was expected that using the present simple and robust model and the corresponding theoretical results, the guidelines for the optimal design of practical superhydrophobic microtextured surfaces could be achieved.

Understanding superhydrophobic behaviors on hydrophilic materials: a thermodynamic approach

Some experiments have proved that superhydrophobic behaviors can be achieved on inherently hydrophilic substrates without low surface energy modification at micro-scale. However, the thermodynamic mechanisms about these results have not been well-understood. In this work, a 2D analytical model was reported to analyze this unexpected experimental observations and wetting behaviors on trapezoidal, vertical and inverse-trapezoidal microstructure surfaces. Theoretical results showed that intrinsic contact angle, which was restricted by sidewall angle of micropillars, was not an independent parameter to affect superhydrophobicity. And re-entrant structures were critical in the realization of microstructures alone inducing transition from hydrophilicity to superhydrophobicity. The wetting transition criterion was that sidewall angle should be less than intrinsic contact angle. On this occasion, a positive energy barrier could support liquid/vapor interfaces and separate Wenzel and Cassie state on hydrophilic substrates. And the physical explanations can be found that the positive energy barrier mainly came from the growth of the high-energetic solid/vapor interfaces to be wetted by the drop with liquid/vapor interfaces moving down inverse-trapezoidal pillars. As for the optimal design of microstructures, considering the limitation of pillar width and the ‘sag’ transition caused by pillar height, T-shape microstructures could be a good choice.

How to Achieve a Monostable Cassie State on a Micropillar-Arrayed Superhydrophobic Surface.

Superhydrophobic surfaces with a monostable Cassie state possess numerous interesting applications in many fields, such as microfluidics, oil-water separation, drag reduction, self-cleaning, heat dissipation, and so on. How to guarantee a monostable Cassie state of a superhydrophobic surface is still an interesting problem. In this paper, considering the influence of external interferences that may induce the possible wettability transition, the whole wetting process of a droplet on a trapezoidal micropillar-arrayed superhydrophobic surface is divided into six possible stages. Both the Gibbs-free energy in each stage and the energy barrier between adjacent stages are obtained and analyzed theoretically. It is interesting to find that the finally stable wettability of a trapezoidal micropillar-arrayed superhydrophobic surface significantly depends on the apparent contact angle of the lateral surface of a single micropillar, which can be divided into three regions from 0 to 180°, corresponding to the Wenzel state, metastable Cassie state, and monostable Cassie state. Furthermore, the size of each region is explicitly related to and can be well-tuned by the geometry of microstructures. Such a wettability classification is well verified by a number of existing experimental results and our numerical simulations. As a relatively general case, such a trapezoidal micropillar-arrayed superhydrophobic surface can also be conveniently degenerated to the triangular or rectangular micropillar-arrayed surface. All the results should be useful for the precise design of functional surfaces of different wettabilities.

Guidelines and procedure for tailoring high-performance, steady-state traveling waves for propulsion and solid-state motion

Structure-Borne Traveling Waves (SBTWs) have significant promise as a means of underwater propulsion, solid-state motion, and drag reduction. However, there is limited understanding over how to tailor SBTWs for these applications. This study establishes guidelines and a procedure for tailoring SBTWs on thin-walled two-dimensional (2D) surfaces. These guidelines were specifically crafted to yield SBTWs favorable for propulsion and solid-state motion: propagation along a uniform direction and with consistent amplitude. SBTWs are steady-state traveling waves generated by taking advantage of a surface’s modal properties (i.e. mode shapes). This novel mechanism provides significant benefits including a minimal actuation footprint, a wide frequency bandwidth, and active variability (propagation direction, wavelength, etc). However, this mechanism also introduces a dependence on the mode shapes and actuator location. Thus, to tailor SBTWs favorable for propulsion the relationship between SBTWs, the mode shapes, and actuator locations must be understood. Eight Guidelines governing this relationship are established. These Guidelines are demonstrated using SBTWs generated on a previously validated model of a 2D plate. Among others, it is shown that the frequency bandwidth can be broken into distinct frequency regions, and each region can be classified as yielding favorable or unfavorable SBTWs. A multi-step procedure is then introduced that enables SBTWs to be tailored on any thin-walled surface. Numerically or experimentally applicable, the actuator configuration can be defined to tailor SBTWs with a specific propagation direction; all that is required is knowledge of the mode shapes. Finally, a case study is presented in which the guidelines and procedure are implemented to tailor SBTWs on a trapezoidal surface. Two different sets of SBTWs are tailored, each propagating in different directions and with various wavelengths. Thus, the established guidelines and procedure enable SBTWs to be tailored for specific applications, such as propulsion and solid-state motion.

Delineator for Separated Bicycle Lanes at Sidewalk Level

The City and County of San Francisco sponsored research to identify a delineator for separated bicycle lanes at sidewalk level that is at least as detectable as truncated-dome detectable warning surface (DWS) by pedestrians with visual impairments, and that is not a barrier to pedestrians with mobility impairments. Tested as potential delineators were a 12-in. wide continuous raised trapezoid (0.75 in. high), and 12- and 24-in. wide installations of relatively wide flat-top bars (FTBs) and of a “corduroy” surface of narrower bars spaced more closely together (both 0.2 in. high). Thirty-one visually-impaired participants detected all five surfaces in addition to DWS, a total of six times each, from 90° and 25° approaches, with mean detection accuracies better than 90% for all surfaces (no significant differences). The long white cane intruded into the cycle track significantly less frequently with 24-in. wide surfaces. In a counterbalanced manner, participants also briefly stepped onto each surface eight times, each time identifying it as “domes,”“bars,” or “trapezoid.” They identified the trapezoid significantly better (mean rate of correct identification = 98.8%) than all other surfaces. A majority of participants with vision disabilities preferred the trapezoid. Thirty participants with a variety of mobility impairments, using a variety of aids, crossed each surface four times with little significant difference from the DWS in effort, instability, and discomfort or pain. No surface was found to be a barrier to crossing. The trapezoidal surface was recommended as the delineator, although the 24-in. FTBs also performed very well.