Rectangular Case Research Articles

Impact of Notch Geometry on the Pressure Bearing Capacity of AISI 316L Austenitic Stainless Steel under Fatigue Loading

In the current research, pressure bearing capacity of AISI 316L austenitic stainless steel is evaluated under fatigue loading through finite element method (ANSYS 18.1) for a specimen with no notch on its surface. Thereafter, the pressure bearing capacity of the same specimen is evaluated with rectangular and V-notches at the center. The notch geometry is changed in terms of its width, depth and the notch central angle (perimeter length) for each of the rectangular and V-notched cases. Fifteen types of rectangular notch and V-notch geometries are undertaken for the research as required by Box-Behnken model of Response Surface Methodology (RSM) analysis. The primary objective of the research is to evaluate the impact of notch geometry on the pressure bearing capacity under fatigue loading conditions. It is observed that fatigue life degraded more with V-notched specimens when compared to rectangular notched ones. Regression equations are developed and surface plots are generated for both rectangular and V-notch cases for the pressure bearing capacity which is dependent on width, depth and notch central angle.

Experimental characterisation of a novel thermal energy storage based on open-cell copper foams immersed in organic phase change material

In this paper, a novel tubes-in-tank thermal energy storage (TIT-TES) based on open-cell copper foams immersed in organic paraffin is presented and experimentally studied. The system consists of a rectangular external case which encloses 16 U-tubes and phase change material (PCM) embedded in copper foams matrix, which guarantee an average power during both heat charge and discharge phases close to 1 kW and high storing/releasing energy efficiency. With the aim of measuring internal temperature, six thermocouples have been installed at two different sections, S1 and S2, located at 1/3 and at 2/3 of the total height, respectively. In order to thermally characterize the system during the heat charge and discharge phases, a series of tests have carried out under different inlet temperatures and flow rate of the heat transfer fluid (HTF). Temperature evolutions have obtained during the tests, and directional temperature derivative profiles, time-durations, average powers and energy efficiencies have derived so to evaluate and characterize the TIT-TES performance. The results have shown how both HTF volumetric flow rate and inlet temperature play a relevant role in heat charge and discharge phases. A larger temperature difference between the HTF and the PCM and a higher HTF input flow rate improve heat transfer and consequently increase the average exchanged power and energy efficiency as well. In particular, during the thermal charge phase, when the HTF temperature increases from 80 °C to 90 °C, the energy efficiencies increase from 73.6% to 91.4% and from 78.7% to 93.8% for the minimum and maximum HTF flow conditions respectively.The analysis of directional temperature derivative profiles have allowed to define some important characteristics of the apparatus, highlighting the preferential directions of the liquefaction/solidification front paths, and also confirming the importance of the HTF inlet temperature and flow rate.

A decoupling control for quadrotor UAV using dynamic surface control and sliding mode disturbance observer

This paper proposes a decoupling tracking controller for quadrotors using dynamic surface control (DSC) and second-order sliding mode disturbance observer (SMDO). The DSC used in this paper is improved with the sliding mode differentiators that replace the original low-pass filter, and the SMDO is utilized to restrain the influence of system uncertainties and external disturbances. In addition, instead of the roll attitude angle ( $$\varphi $$ ) and pitch attitude angle ( $$\theta $$ ), applying $$\sin {\varphi }$$ and $$\sin {\theta }$$ as control variables simplifies the analysis of stability. Moreover, a fuzzy logic-based method is utilized to compensate the influence of battery voltage changing during the procedure of thrust generation. The asymptotic tracking property of the closed-loop system is proven via the Lyapunov-based stability theory. Finally, the real-time experiment results, which contain a hovering case and rectangular path tracking case, are given to validate the practicability of the proposed method.

Non-Boussinesq gravity currents and surface waves generated by lock release in a circular-section channel: theoretical and experimental investigation

We present a combined theoretical and experimental study of lock-release inertial gravity currents (GCs) propagating in a horizontal channel of circular cross-section with open-top surface in the non-Boussinesq regime. A two-layer shallow-water (SW) model is developed for a generic shape of the cross-section with open top, and then implemented in a finite difference numerical code for the solution in a circular-cross-section channel of the type used in the experiments. The model predicts propagation with (almost) constant speed for a fairly long distance, accompanied by a depression of the ambient free open-top surface behind the front of the current. Sixteen experiments were conducted with a density ratio $r=0.587{-}0.939$ in full-depth and part-depth release conditions, measuring the front speed and the free-surface time series at four cross-sections. The channel was a circular tube 409 cm long, with a radius of 9.5 cm; the lengths of the locks were 52 and 103.5 cm. Density contrast was obtained by adding sodium chloride and dipotassium phosphate to fresh water. The theoretical values of the front speed and of the depression overestimate the experimental values, but they predict correctly their trend for varying parameters and provide reliable insights into the underlying mechanisms. In particular, we demonstrate that the circular cross-section increases the speed of propagation as compared to the standard rectangular cross-section case (for the same initial height and density ratio). The discrepancies between the SW predictions and the present experiments are of the same order of magnitude as those of previously published results for simpler systems (Boussinesq, rectangular). In addition to the depression, which is a wave bound to, and following the front of, the GC, the system also displays two kinds of free-surface waves, namely the initial bump (its amplitude is of the same order as the depression) and some short-length and low-amplitude waves in the tail of the bump. These free waves propagate with a celerity well predicted by the ‘fast’ eigenvalues of the mathematical model. Comparison is provided with the celerity of a solitary wave. It is expected that discrepancies between theory and experiments can be partly attributed to the presence of these waves. The reported insights and SW prediction method can be applied to a variety of cross-sections of practical interest (triangles, trapezoids, etc.).

Numerical and experimental investigation on heat transfer of multi-heat sources mounted on an array of printed circuit boards in a rectangular case

Conjugate heat transfer in an electronic module containing an array of printed circuit board assemblies (PCBAs) was experimentally and numerically investigated. Each PCBA was assembled with a matrix of rectangular heat sources (4 × 4 with 0.5 W each). It was inserted in parallel in an aluminum case by leaving two opposite opened ends to allow air to flow through. The experiment and simulation were carried out on three different cases based on module orientations and PCBA arrangement; horizontal orientation with PCBA facing upwards (CASE I) and downwards (CASE II), and vertical orientation (CASE III) under both natural and forced convection at an ambient temperature of 30 °C. The simulation was done by varying the number of PCBAs (N) from 5 to 7 sets, the distance (l) between PCBAs array and module wall from an original design of 10 to 20 mm by an increment step of 5 mm, and air velocity from 1 m/s to 4 m/s. The results showed that under natural convection the global maximum temperature increased slightly (from 64.9 °C to 65.9 °C) as the number of PCBAs increased from 5 to 7 sets for the vertical orientation module (CASE III), while it increased significantly (from 97.9 °C to 127.4 °C) for the horizontal orientation module (CASE I). When the number of boards in the module increased, the board that possessed the global maximum temperature would vary in board position in the module according to the module’s orientation. However, the location of global maximum temperature on that board was still in the same region in the heat source matrix. By increasing the distance (l) between PCBA and the module wall, the heat transfer was enhanced. Under forced convection, it can be observed that the drawback of heat removal from the horizontal orientation module diminished under forced convection when air speed was sufficiently high. The global maximum temperature decreased with an increase in the air speed from 63.5 °C to 48.7 °C and from 64.7 °C to 48.8 °C for the six PCBAs of CASE III and CASE I, respectively. A comparison of the experimental and numerical results shows good agreement for both natural and forced convection.

ОПРЕДЕЛЕНИЕ ПАРАМЕТРОВ ШНЕКОЛОПАСТНОГО СМЕСИТЕЛЯ

The purpose of the study is to improve the equipment for mixing dry crumbled feed with regard to the basic opera-tion condition or parameters. As a result of the issue analysis and the existing mixers structure, it was found that many machines used for the preparation of compound feeds are complex in the structure and not reliable in opera-tion, the feed mixture quality does not always meet the zootechnical requirements; the applied standard and exper-imental mixers of compound feeds because of imperfection of technological process and working parts contained, possess high specific power consumption. The construction of a universal low-speed batch mixer with a fixed rec-tangular case and combined two forcibly mixing working parts mounted horizontally is an advanced study direction for feed mixers improving. The study objectives incorporated the development of structural and technological speci-fication of a low-speed auger-blade mixer of batch action; the assessment of the impact of design parameters above mentioned of the mixer on its performance; to identify the rational structural and operating specification of the auger-blade mixer taking into consideration the cycle duration time. The research methodology provided the theo-retical justification of specification of the mixer taking into account the cycle duration period of the blending. Ex-pressions to determine the performance efficiency along the following stages were provided: involving auger con-veyor, the first and the second mixing transporting and throwing blades. Formulas are obtained for estimation the cycle period from the installation angle of the mixing-transporting blades and the rotation frequency of the working parts. Data obtained and given for estimation the cycle time from the installation angle of the mixing-transporting blades and the speed of the working parts allow to operate during the minimum cycle time, that is, to choose the op-timal angle of installation of the blades and the speed of rotation of the working parts.

Laminar-to-transitional evolution of three-dimensional vortical structures in a low-aspect-ratio rectangular synthetic jet

A time-resolved single-camera volumetric particle image velocimetry (SV-PIV) method was used to measure three-dimensional (3D) vortical structures in a transitional rectangular synthetic jet with aspect ratio (AR) of 3 at a Reynolds number of 332. Compared to a laminar circular synthetic jet, the rectangular case displayed more complicated vortical evolution associated with axis switching of the vortex ring and the formation of streamwise vortex (SV-I), arc-like vortex (AV), Λ-like vortex, and their interactions. The differences in the vortical structures between the rectangular synthetic jets and rectangular continuous jets (AR ≥ 2) were discussed in detail. The joint induction of the vortex ring, SV-I, and AV produced an ejection and injection mechanism, suggesting an enhanced mixing property. In addition, the interactions of SV-I and AV with the vortex ring could promote early flow transition, and result in the rapid decay of the enstrophy for the rectangular case. The start of transition could be determined from the power spectrum. Then the velocity triple-decomposition method was applied to reveal different contributions of the large-scale coherent and small-scale turbulent structures to the flow field. The rectangular case displayed an earlier increase in the random turbulence kinetic energy compared to the circular case.

Minimum-width annulus with outliers: Circular, square, and rectangular cases

We study the problem of computing a minimum-width annulus with outliers. Specifically, given a set of n points in the plane and an integer k with 1≤k≤n, the problem asks to find a minimum-width annulus that contains at least n−k input points. The k excluded points are considered as outliers of the input points. In this paper, we are interested in particular in annuli of three different shapes: circular, square, and rectangular annuli. For the three cases, we present first and improved algorithms to the problem.

Rough or wiggly? Membrane topology and morphology for fouling control

During filtration in reverse osmosis membranes (ROM), the system performance is dramatically affected by membrane fouling which causes a significant decrease in permeate flux as well as an increase in the energy input required to operate the system. In this work, we develop a model, able to dynamically capture foulant evolution, that couples the transient Navier–Stokes and the advection–diffusion equations, with an adsorption–desorption equation for the foulant accumulation. The model is validated against unsteady measurements of permeate flux as well as steady-state spatial fouling patterns. For a straight channel, we derive a universal scaling relationship between the Sherwood and Bejan numbers, i.e. the dimensionless permeate flux through the membrane and the pressure drop along the channel, respectively, and generalize this result to membranes subject to morphological and/or topological modifications, i.e. whose shape (wiggliness) or surface roughness is altered from the rectangular and flat reference case. We demonstrate that a universal scaling can be identified through the definition of a modified Reynolds number, $Re^{\star }$, that accounts for the additional length scales introduced by the membrane modifications, and a membrane performance index, $\unicode[STIX]{x1D709}$, an aggregate efficiency measure with respect to both clean permeate flux and energy input required to operate the system. Our numerical simulations demonstrate that ‘wiggly’ membranes outperform ‘rough’ membranes for smaller values of $Re^{\star }$, while the trend is reversed at higher $Re^{\star }$. The proposed approach is able to quantitatively investigate, optimize and guide the design of both morphologically and topologically altered membranes under the same framework, while providing insights into the physical mechanisms controlling the overall system performance.

Aerodynamic inverse design using multifidelity models and manifold mapping

Aerodynamic inverse design is proposed using multifidelity models and the manifold mapping (MM) technique. Aerodynamic inverse design aims at achieving a target performance characteristic, such as a pressure coefficient distribution of an airfoil or local lift distribution of a wing. Due to the high computational cost of accurate aerodynamic models and the large number of design variables, the overall cost of inverse design can be prohibitive. The MM-based optimization algorithm leverages the speed of the low-fidelity model to accelerate the optimization process, but refers back to the high-fidelity model to ensure an accurate solution. In this work, the MM technique is applied to the characteristic distribution under consideration in each application. In particular, the pressure coefficient distribution is modeled with the MM technique in the case of airfoil inverse design, and the sectional lift distribution in the case of wing design. The proposed method is tested and evaluated on six airfoil inverse design cases and one rectangular wing inverse design case. In the two-dimensional cases, parameterized with eight design variables, direct aerodynamic inverse design using pattern search required 700 to 1200 high-fidelity model evaluations, which took 300 to 700 hours in total. The MM-based design algorithm required less than 20 high-fidelity simulations and 1000 to 2000 low-fidelity evaluations, which took 30 to 90 hours. In the three-dimensional case, parameterized with three design variables, direct aerodynamic inverse design took around 50 hours, whereas the MM-based design needed around six hours.

Optimized composites with the largest material usage efficiency

This paper is aimed to seek for the optimized composite microstructure for highest material usage efficiency. An energy-measured material usage efficiency is proposed as the criterion for structural optimization design, and we believe it is the best choice among all single parameters to evaluate the performance. The staggered bio-composites consisting of rectangular platelets and soft matrix have been widely studied, and proved to possess good mechanical properties. It is found that this staggered structure can be further optimized to achieve higher material usage efficiency. Based on the shear-lag analysis, the optimization shows that the optimal platelet shape is rhombic, which leads to more uniform stresses in both the platelet and the matrix compared with the widely used platelet shape, i.e. rectangle. The rhombic platelet case also possesses higher stiffness and strength than that of the rectangular platelet case.

Three-dimensional interaction of a shock with a thin non-circular channel of low-density gas

Numerical simulation of three-dimensional interaction of a shock with thin circular or non-circular – elliptic or rectangular – low-density gas channel is presented. Euler’s equations for inviscid gas are solved using 5th-order finite-difference WENO scheme. Large-scaled shock wave precursor structure is described in detail. It is shown that in three-dimensional flow internal shear layer instabilities develop faster than in axisymmetric case. High-pressure jet cumulation effect is found to amplify moderately for elliptic and rectangular cases. An influence of channel cross-section shape on the precursor growth rate is studied. It is found that the duration of linear precursor growth phase is greatly increased for stretched channel cross-section shapes.

Spatial Effects of Interaction of a Shock with a Lateral Low-Density Gas Channel

Three-dimensional interaction of a shock with lateral low-density gas channel of round, elliptic or rectangular cross-section is numerically studied using Euler’s equations. The structure of formed shock wave precursor is described in detail. Internal shear layer instabilities in three-dimensional flow are shown to develop faster than in axisymmetric case. Moderate amplification of high-pressure jet cumulation effect is noted for elliptic and rectangular channel cases. Dependence of precursor growth rate on cross-section shape is studied. It is found that stretching of cross-section shape significantly increases the duration of linear precursor growth phase.

Design of a Plasmonic Photocatalyst Structure Consisting of Metallic Nanogratings for Light-Trapping Enhancement

In this paper, a novel SPP-based photocatalytic system with high photocatalytic performance consisting metallic nanograting elements is proposed and simulated numerically with finite-differential time-domain (FDTD) method. Various nanograting metallic shapes, rectangular and trapezoidal, are studied. Results shows that the absorption significantly increases for the trapezoidal grating-based structure compared to its flat and rectangular grating elements. In addition, the effect of the incident angle of the sun light is considered to achieve an optimum design. It is found that in all angles of the incidence, trapezoidal grating (TG) has larger visible photocatalytic activities than the flat and rectangular cases. The best configuration was realized for the trapezoidal grating-based structure at 60° of inclination when the height of the grating elements is 43 nm. The photocatalytic activity of the metallic grating structure was attributed to scattering of the incident light and return to the host TiO2 medium and the surface plasmon excitation of the metallic elements.

Using Facial Tissue Expanders in Repositioning of Linear and Irregular Cheek Scars for the Quest of Superior Aesthetic Results

Background: The motive of this study was that the resultsof some cheek scars revisions may appear to be disappointingowing to their sites or direction even with much efforts. Byusing tissue expanders, the scars repositioning and reorientationin relation to the cheek unit borders and Resting Skin TensionLines (RSTLs) may provide the basis of superior results inscar revision and management. So, we aim to demonstratethe effect of cheek skin expansion by tissue expanders on scarrepositioning and reorientation to achieve a superior aestheticoutcome.Methods: This prospective study was conducted on 13patients with obvious linear (8 cases) or irregular (5 cases)cheek scars who were willing to move these scars to lessconspicuous sites. We used rectangular tissue expanders inall cases with (40 to 200ml.) capacity. They were selectedsuitable to be inserted under the donor tissue and generatethe proposed expansion required for scar repositioning.Results: The concept of complete moving the scar outsidethe cheek unit (optimal revision) has been applicable to 5 in13 patients (38.5%). However, suboptimal revision has beenapplicable in the form of scar reorientation typically in RSTLssucceeded in 5 of 13 patients (38.5%) or repositioning thescar outside the malar region in one case (7.7%). Partialrevision in the form of incomplete scar resection occurred in1 case (7.7 %). Only in one case (7.7%), the expansion wasaborted due to early wound dehiscence (failure). In 10 out of13 tissue expansion cases (77%) were achieved withoutcomplications. At the same time, one minor complication hasoccurred in one patient i.e. hematoma (7.7%). Major complicationshave occurred in 2 cases i.e. expanders were exposed(15.4%).Conclusion: Facial tissue expander usage in repositioningand revision of linear and irregular cheek scar is a

Characteristics and mechanism of mixing enhancement for noncircular synthetic jets at low Reynolds number

In this paper, the evolution of the flow structures and the mixing characteristics in low-aspect-ratio (AR) noncircular incompressible synthetic jets are investigated. Two elongated configurations, elliptic and rectangular orifices with AR = 3 and 5 are used to produce synthetic jets at a Reynolds number of 166. The velocity fields in different spatial planes are measured by time-resolved two-dimensional particle image velocimetry (2D-PIV), and stereoscopic particle image velocimetry (S-PIV), respectively. The results show that the evolution of the vortical structures and the flow physics are influenced by the orifice configuration and AR. The first axis-switching location of the elliptic cases is closer to the jet orifice than that of the rectangular cases, while the AR = 3 cases undergo more upstream location and more times of axis switching than the AR = 5 cases. In addition to axis switching, noncircular synthetic jets are observed to develop streamwise vortices. The rectangular cases develop stronger streamwise vortices than the elliptic cases. The extended angle of streamwise vortices increases with the increasing AR, and is larger for the rectangular cases than the elliptic cases. In particular, the AR = 3 rectangular case has larger values of centerline streamwise velocity fluctuation, Reynolds stresses, mass flow rate and momentum flux than the other cases in the second axis-switching region, suggesting significantly enhanced mixing and momentum transportation characteristics. The mechanism could be attributed to its more evident vortex deformation and stronger streamwise vortices.

The development of microprocessor measuring system for the inclination angles of an object relative to the horizon plane

The need to measure the angles of inclination is essential for many branches of technology and industry. At the current Ukrainian market of devices there are no domestic accelerometer devices for measuring roll and pitch angles (DMRPA),which would meet the following requirements: the mean square error less than one angular minute in the range of angles ± 10 °, the operating temperature range -40 ... + 70 ° С, output information in a digital code with a discreteness of 1 angular second. Such DMRPAs are needed to control the position of radars and antennas, horizontals of platforms and vehicles.The developed microprocessor system for measuring the inclination angles of an object relative to the horizon plane (MSMIA) provides measurements of the roll and pitch angles in accordance with the above requirements. Issuance of output digital data for consumer is carried out on the interface RS-422.The MSMIA's metal rectangular case consists of a bottom base plate having three legs for attachment to the object base surface and a casing. On the base plate two accelerometer sensors (AS) – primary accelerators transducer, with mutually perpendicular measuring axes, are installed. Digital temperature transducers are installed near them. The analogue parts of the device electronic circuit board contain the electronics for the transformation of the pendulum sensitive elements displacement into the voltage, and electronics of the feedback regulators, the current from which goes to the coil of the reverse compensating converter. This current is proportional to the projection of gravity accelerating on the sensitivity axis of the AS, and is converted into a voltage across the precision resistor. The microcontroller located on the board includes two high precision analogue-digital converters, converting signals from these resistors into digital codes, proportional to measured acceleration. The microcontroller software performs algorithmic compensation for the measurement errors of the acceleration and the calculation of the roll and pitch angles. During the experimental tests, it has been confirmed that for various combinations of temperatures with range - 40 ... + 70 ° С and angles of inclination in the range of ± 10 °, the mean square error is not more than one angular minute, which is unique for the devices presented on the modern domestic market.Consequently, this development will allow Ukraine to establish the production of high-precision MSMIAs to meet the needs of domestic new technical manufacturers. Further research can be directed to the study of long-term instability of the MSMIA's parameters, the reduction of the mean-square error due to the installation of additional temperature sensors and the improvement of temperature errors compensation.

Factorization of differential expansion for non-rectangular representations

Factorization of the differential expansion (DE) coefficients for colored HOMFLY-PT polynomials of antiparallel double braids, originally discovered for rectangular representations [Formula: see text], in the case of rectangular representations [Formula: see text], is extended to the first non-rectangular representations [Formula: see text] and [Formula: see text]. This increases chances that such factorization will take place for generic [Formula: see text], thus fixing the shape of the DE. We illustrate the power of the method by conjecturing the DE-induced expression for double-braid polynomials for all [Formula: see text]. In variance with the rectangular case, the knowledge for double braids is not fully sufficient to deduce the exclusive Racah matrix [Formula: see text] — the entries in the sectors with nontrivial multiplicities sum up and remain unseparated. Still, a considerable piece of the matrix is extracted directly and its other elements can be found by solving the unitarity constraints.

RGSE-Based SPICE Model of Ferrite Core Losses

A SPICE model for estimating and simulating core losses of a ferrite magnetic device is presented. The approach is based on a proposed revised generalized Steinmetz equation (RGSE) and requires only the use of the Steinmetz coefficients and core geometry data. The letter presents a RGSE-based SPICE simulation strategy that can both estimate and simulate the effect of the core losses on the circuit. Primary advantages of RGSE approach are that it does not require switching frequency data and is applicable to arbitrary excitation and not just sinusoidal excitation as the Steinmetz equation approximation does. RGSE model is also insensitive to dc bias, this is an improvement over the earlier model. Comparison of previously reported measured and calculated core loss values with the simulation results of the presented SPICE RGSE model shows excellent agreement in the sinusoidal case and good agreement in the rectangular pulse case.

Heat transfer on topographically structured surfaces for power law fluids

The three-dimensional power law fluid flow through rough microchannels has been studied numerically to determine the effects of the topographic structures on the thermal and hydrodynamic characteristics of the system. Rectangular, triangular and sinusoidal element shapes have been considered in order to investigate the effects of roughness height, width, pitch and channel separation on the pressure drop and heat transfer. Uniform wall heat flux boundary condition has been applied for all the peripheral walls.The results indicate that the global heat transfer performance can be improved or reduced by the roughness elements at the expense of pressure head when compared with the smooth channels. The maximum heat transfer performance has been obtained for triangular roughness shapes with the relative roughness height of 0.333. In most cases heat performance is smaller than unity. It is also revealed that for the sinusoidal and triangular cases by decreasing the relative roughness width, heat transfer performance is improved. Furthermore, the effects of the roughness features and the channel separation are intensified in power-law fluids. For dilatant fluids with a power-law index equal to n = 1.25, channel separation ratio reduction causes a steep rise in normalized friction factor up to 140.8 in the rectangular case. By increasing the relative roughness pitch of the cases with rectangular elements and the power-law index of n = 0.75, a reasonable heat transfer performance enhancement has been observed.