Rectangular Aspect Ratio Research Articles

3D seismic bearing capacity of rectangular foundations near rock slopes using upper bound method

The analysis of foundation's bearing capacity is generally conducted under the assumption of plane strain. However, the damage of rectangular foundation usually presents obvious three-dimensional (3D) effect. This article considers this 3D effect, which, for the first time, provides a theoretical framework for assessing the bearing capacity of rectangular foundations placed on rock slopes under seismic condition. In order to apply the kinematic method of limit analysis, a new 3D kinematically admissible collapse mechanism is first constructed. Owing to the point-to-point discretized technique, this 3D mechanism can avoid complex surface integration and effectively reduce spatial coordinate iterative calculations while maintaining high accuracy. The pseudo-static method is adopted to simulate the effects of earthquakes. Generalized multi‑tangential technique is employed to derive the Mohr-Coulomb constants from Hoek-Brown criterion. The comparison between the present results and results of previous literatures proves the validity of the theoretical framework in this paper. Shape factor and reduction factor are introduced in the parametric study, showing that the 3D effect is more obvious when the rectangular foundation aspect ratio is reduced. As the rectangular foundation location moves away from the slope, its bearing capacity gradually converges towards that of the horizontal foundation. The critical collapse mechanism is also explored, demonstrating that the collapse extent expands with increasing internal friction angle of the rock.

Improvement of mixing efficiency in twisted micromixers: The impact of cross-sectional shape and eccentricity ratio

Microfluidic mixers with twisted geometries show promise for high mixing efficiency, especially at elevated flow rates. However, there is a lack of understanding regarding the optimal geometrical parameters to enhance mixing across various Reynolds numbers. This study aimed to explore the influence of pitch number, cross-section geometry, and eccentricity ratio on the performance of the twisted micromixer. The flow field in these micromixers was solved numerically and the mixing index and pressure drop were calculated for Reynolds numbers of 1 to 400. Twisted micromixers with rectangular cross-sections and aspect ratios of 0.5 and 2 outperformed those with square cross-sections by up to 34% in mixing efficiency, exceeding 90% efficiency for Reynolds numbers from 1 to 400. Moreover, the eccentricity ratio (ER) was studied for the first time in twisted micromixers in this study and demonstrated a critical role in improving the mixing performance. For low to intermediate Reynolds numbers, the highest ER of 0.75 showed the best performance, while for high Reynolds numbers, an ER of 0.5 was optimal. These insights offer valuable direction for designing high-performance micromixers for advanced microfluidic systems.

Numerical Investigation of the Impact of the Rectangular Nozzle Aspect Ratio On Liquid Jet in Crossflow

Abstract High fidelity simulation is conducted to investigate liquid jet in crossflow, specifically regarding the rectangular nozzle. The influence of aspect ratio (AR) of nozzles on the atomization characteristics of liquid column in the process of primary breakup is explored by the analysis of the flow structure of crossflow and liquid column. The aspect ratio is ranging from 1 to 8. The results indicate that as the increase of aspect ratio, the disturbance of crossflow to the liquid on the sides is weakened. While the thickness of liquid column also gradually decreases, which enables smaller disturbances to promote droplet shedding. Therefore, surface breakup first weakens and then strengthens. In the column breakup process, the increase of aspect ratio causes crossflow to become the main factor affecting column breakup, and the influence of air pressure gradually weakens. This indicates a shift in the mechanism of surface instability from “Rayleigh-Taylor” (R-T) instability to “Kelvin-Helmholtz” (K-H) instability.

Experimental investigation of rectangular nozzle aspect ratio effects on high-pressure helium leakage characteristics

High-pressure hydrogen leakage is one of the bottlenecks restricting the development of the hydrogen energy industry. In this study, a high-pressure helium leakage experimental system with stable pressure was built to research the influence of aspect ratio on concentration decay rate and mass flow rate. Similar to the circular nozzle, the centerline helium concentration of the rectangular jet is also inversely proportional to the distance from the nozzle. For the rectangular nozzles with aspect ratio of 1–4, the helium concentration decay rate is consistent with the circular nozzle when the leakage pressure is lower than 6.5 MPa. However, the decay rate is obviously larger for rectangular nozzles with aspect ratio of 10 when the leakage pressure is greater than 5.0 MPa. The aspect ratio has a greater influence on the flow coefficient, which increases with the aspect ratio under the same leakage pressure. To comprehensively consider the effects of nozzle size and shape, a weighted characteristic diameter of equivalent diameter and rectangular width, dc=αde+1−αdw, was proposed in this study. The results indicate that the equivalent diameter has greater impact on the centerline concentration decay rate, while the width of nozzles has substantial influence on the flow coefficient.

Rectangular Cylinder Orientation and Aspect Ratio Impact on the Onset of Vortex Shedding

Rectangular cylinders have the potential to provide valuable insights into the behavior of fluids in a variety of real-world applications. Keeping this in mind, the current study compares the behavior of fluid flow around rectangular cylinders with an aspect ratio (AR) of 1:2 or 2:1 under the effect of the Reynolds number (Re). The incompressible lattice Boltzmann method is used for numerical computations. It is found that the flow characteristics are highly influenced by changes in the aspect ratio compared to the Reynolds number. The flow exhibits three different regimes: Regime I (steady flow), Regime II (initial steady flow that becomes unsteady afterward), and Regime III (completely unsteady flow). In the case of the cylinder with an aspect ratio of 2:1, vortex generation, variation in drag, and the lift coefficient occur much earlier at very low Reynolds numbers compared to the cylinder with an aspect ratio of 1:2. For the cylinder with an aspect ratio of 1:2, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 120, 121 ≤ Re ≤ 144, and 145 ≤ Re ≤ 200, respectively. For the cylinder with an aspect ratio of 2:1, the Reynolds number ranges for Regimes I, II, and III are 1 ≤ Re ≤ 24, 25 ≤ Re ≤ 39, and 40 ≤ Re ≤ 200, respectively. The cylinder with an aspect ratio of 1:2 is found to have the ability to stabilize the incoming flow due to its extended after-body flatness. Generally, it has been found that a cylinder with an AR of 2:1 is subjected to higher pressures, higher drag forces, higher curvatures of cross-flow rotations, and higher amplitudes of flow-induced drag, as well as higher lift coefficients and lower shedding frequencies, compared to cylinders with an AR of 1:2. In Regime III, elliptic and vertically mounted airfoil-like flow structures are also observed in the wake of the cylinders.

Seismic behaviour and modelling of rectangular FRP-concrete-steel tubular columns under axial compression and cyclic lateral loading

Fibre-reinforced polymer (FRP) composites, which have been commonly used to retrofit existing structures, have found increasing applications for new structures. FRP-concrete-steel double-skin tubular columns (DSTCs), which consist of an external layer of FRP, an inner steel tube, and sandwich concrete, are gaining popularity in newly constructed bridges. Previous studies focused on the structural performance of DSTCs in circular and square cross-sections. This paper investigated the cyclic behaviour of rectangular DSTCs under a combined loading condition of axial compression and cyclic lateral loading. The particular focus was placed on the influence of rectangular aspect ratio. In addition, both effects of FRP thicknesses and lateral loading directions (bending around its strong axis or weak axis) were also assessed experimentally. Test results demonstrated that (1) rectangular DSTCs had excellent seismic behaviour (i.e., for the rectangular aspect ratio from 1.0 to 2.0, the ductility index increased monotonically from 3.58 to 5.72), (2) the increase of FRP thickness could improve the peak lateral load of specimens (i.e., the peak lateral load for the specimen with 2.10 mm FRP was 95.3 kN, while that of the corresponding specimen with 1.05 mm FRP was 88.3 kN), and (3) the specimen bending around the strong axis had superior performance compared with the identical specimen bending around the weak axis. The cyclic behaviour of DSTCs was simulated in Open System for Earthquake Engineering Simulation (OpenSees) by the developed models which was capable of providing predictions with reasonable accuracy. In practical engineering, it was recommended that, (1) rectangular DSTCs should be designed with a reasonable aspect ratio to match the specific loading conditions of the two symmetry axes; (2) the FRP thickness along the column height could be optimized in accordance with the bending moment gradient to achieve the efficient use of the FRP strength.

Effects of the Aspect Ratio and Cross-Sectional Area of Rectangular Tubes on Packing Characteristics of Mono-Sized Pebble Beds

The packing characteristics of a pebble bed are essential to understand the heat- and mass-transfer processes occurring within a granular system. Therefore, the packing characteristics of rectangular prismatic pebble beds randomly packed with mono-sized pebbles are analyzed. In terms of the average and local packing fraction distribution, coordination number, and radial distribution function, the effects of the rectangular tube aspect ratio and cross-sectional area on the packing properties of pebble beds are explored in depth. The findings indicate that the packing structures of the rectangular pebble bed exhibit noticeable fixed-wall effects. The average packing fraction and coordination number gradually decline as the rectangular tube aspect ratio rises. Close to the fixed wall, a noticeable wall effect can be seen in the distribution of axial and local packing fractions and the pebble center distribution. The wall effect has an increasing effect on the axial and local packing fraction distributions in rectangular tubes with increasing aspect ratios. Additionally, the average packing fraction and the average coordination number also increase as the cross-sectional area increases, indicating a gradual weakening of the wall effect as the cross-sectional area increases. Furthermore, the cross-sectional area and aspect ratio of the rectangular tubes affect the RDF values of the rectangular pebble beds but have no impact on the RDF features. The findings reported in this paper will be helpful for designing and optimizing pebble beds in the breeding blanket of fusion reactors.

The Effect of Rectangular Confinement Aspect Ratio on the Flame Transfer Function of a Turbulent Swirling Flame

Abstract The flame transfer function (FTF) has been experimentally investigated for a premixed, turbulent and highly swirled flame in rectangular enclosures with varying aspect ratio. A range of equivalence ratios and inlet bulk velocities are considered to vary the length of the flame. Increasing confinement is also shown to increase flame length. More confined flames become increasingly asymmetric, with significant changes to the mean flame shape. Characteristic peaks and dips are observed in the FTF gain for several configurations, caused by constructive and destructive interference between different sources of flow perturbations. Changes in the geometrical confinement distinctly affects these interactions, with FTFs in the most confined chamber containing more pronounced peaks and dips. Analysis of the phase-averaged dynamics has been conducted for two limiting operational conditions in the least and most confined enclosures: a short flame at a low bulk velocity and high equivalence ratio condition; and a long flame at a high velocity and low equivalence ratio condition. The analysis of the short flames shows similar behavior in both enclosures, both in terms of the global response and the local structure of the heat release rate oscillations. Small differences in local response symmetry in the flame due to the close confinement do not affect the global flame response. By comparison, close confinement significantly affects the symmetry of the flame dynamics in the long flame. However, the changes in symmetry do not significantly modify the response, and more important is the change in flame length, which significantly alters the cutoff frequency, reducing the gain at high frequencies.

Efficient calculation of the free energy for protein partitioning using restraining potentials

An approach for the efficient simulation of phase-separated lipid bilayers, for use in the calculation of equilibrium free energies of partitioning between lipid domains, is proposed. The methodology exploits restraint potentials and rectangular aspect ratios that enforce lipid phase separation, allowing for the simulation of smaller systems that approximately reproduce bulk behavior. The utility of this approach is demonstrated through the calculation of potentials of mean force for the translation of a transmembrane protein between lipid domains. The impact of the imposed restraints on lipid tail ordering and lipid packing are explored, providing insight into how restraints can best be employed to compute accurate free-energy surfaces. This approach should be useful in the accurate calculation of equilibrium partition coefficients for transmembrane protein partitioning in heterogeneous membranes, providing insight into the thermodynamic driving forces that control this fundamental biophysical phenomenon.

Experimental study and new-proposed mathematical correlation of flame height of rectangular pool fire with aspect ratio and mass burning rate

An experimental study is carried out on the combustion characteristics of rectangular heptane pool fire with a fixed area of 400 cm2 but different aspect ratios of (length-width ratio, n) n = 1, 2, 4, 6, 8, 10, 12 and 16. The results show that the mass burning rate decreases initially and increases afterwards with an increase in aspect ratio. Based on heat transfer theory, the mass burning rate of rectangular pool fires versus aspect ratio is divided into two regimes, namely heat convection and flame radiation coupled regime and heat conduction-dominated regime with a threshold value of aspect ratio n = 6. The flame height has a positive relationship with mass burning rate but a negative relationship with aspect ratio. Based on air entrainment theory, a new correlation of flame height against coupling of mass burning rate and aspect ratio is proposed and validated by experimental observations. The hydraulic diameter is introduced into the classical formula of pulsation frequency, and the experimental and modelling results show that the pulsation frequency of flame height increases linearly with the hydrodynamic diameter incorporating aspect ratio of rectangular pool in the correlation of f∝(n+1n)12.

Wake transitions and steady -instability of an Ahmed body in varying flow conditions

The paper investigates experimentally the flow past a flat-back, taller than wide Ahmed body having rectangular base aspect ratio $H/W=1.11$ in the context of ground vehicle aerodynamics. Parametric studies at Reynolds number $2.1\times 10^5$ explore the sensitivity of the aerodynamic force and body pressure distribution with respect to varying flow conditions defined from variable ground clearance $C$ (taken at mid-distance from the front and rear axles of the body), pitch angle $\alpha$ , and yaw angle $\beta$ (equivalent to a crosswind). Two-dimensional parametric maps in the parametric spaces $(\beta,C)$ and $(\beta,\alpha )$ are obtained for parameter ranges covering real road vehicle driving conditions. The study of the base pressure gradient reveals non-trivial and sharp transitions identified as significant changes of near wake orientation in both parametric spaces. All unsteady transitions correspond to fluctuation crises of the vertical gradient component only. These transitions are summarized in phase diagram representations. Both phase diagrams in $(\beta,C)$ and $(\beta,\alpha )$ parametric spaces can be unified at large yaw in the $(\beta,C_r)$ space, where the rear clearance $C_r$ separating the lower edge of the base from the ground is a simple function of the pitch $\alpha$ and the clearance $C$ . The impacts of the wake transitions are clearly identified in the base drag, drag, lift and side force coefficients. The contribution of the steady near wake $z$ -instability (Grandemange et al., Phys. Fluids, vol. 25, 2013a, pp. 95–103) is assessed by repeating the sensitivity analysis with a rear cavity. As reported previously, the rear cavity suppresses the steady instability by symmetrizing the wake. A domain for the existence of the instability is finally proposed in the attitudes map $(\beta,\alpha )$ defined from regions where the mean lateral force coefficients are significantly decreased by the presence of the rear cavity. In addition, it is found that the steady instability forces the wake to be less unsteady for all attitudes that do not correspond to unsteady transitions.

Parameters of liquid cooling thermal management system effect on the Li-ion battery temperature distribution

In order to investigated the influence on the liquid cooling system cooling effect by changing the structural parameters, single Li-ion battery heat generation model is conducted, and used in following simulation. Subsequently, sixteen models are designed by orthogonal array, and the results are obtained by extremum difference analysis, which can quantify the influence degree, identify major and minor factors, and find the relatively optimum combination. Finally, different channel entrance lay-out is adopted to investigated. With a series of work, the effective of single battery heat generation model is proved by the discharge experiment. The coolant velocity has most evident influence on the Li-ion battery temperature rise, rectangular channel aspect ratio is second one, and the heat conducting plate thickness has the smallest influence. Similarly, for Li-ion battery temperature difference, the effect of heat conducting plate thickness and rectangular channel aspect ratio as the same, both are secondary factor, and coolant velocity is main factor. With different channel entrance lay-out, both the maximum temperatures denote a same upward trend, and better balance temperature distribution is obtained by adopt Case C system which with alternating arrange channel entrance lay-out.

Effect of liquid cooling system structure on lithium-ion battery pack temperature fields

In this article, we studied liquid cooling systems with different channels, carried out simulations of lithium-ion battery pack thermal dissipation, and obtained the thermal distribution. According to the results shown in the study, the number of channels is inversely proportional to the highest temperature and the temperature dispersion. A liquid cooling system with a square channel can achieve a lower highest temperature than that of a liquid cooling section with a circular channel. Simultaneously, the highest temperature is also negatively correlated with the rectangular channel aspect ratio. In addition, as the aspect ratio increases, the temperature dispersion of the battery pack initially decreases and then increases. Furthermore, from the entrance, along the direction of coolant flow, the temperature dispersion of a single lithium-ion battery will initially increase and then gradually decrease, which indicates that the No. 5 lithium-ion battery is the most balanced module in the battery pack.

Investigation on the engineering effects of the geometrical configuration of the jacking rectangular pipe

For rectangular pipe-jacking construction, the primary priorities of smooth construction include minimizing the ground response and designating the appropriate jacking force to achieve the best results in environmental protection and energy conservation. The geometric cross-section design of the jacking rectangular pipe and its engineering performances such as the ground surface displacement, the jacking force consumption, and the stress-bearing state are easy to be ignored in the field construction. In this paper, the ground response characteristics under four kinds of rectangular pipe aspect ratio (H/W) with the same utilization cross-section area were investigated by using the calibrated finite element method (FEM) based on a case study conducted in Japan. The theoretical jacking force of each pipe section design was calculated and compared to provide a reference for long-distance or large-section jacking conditions. The stress-bearing state of each pipe was considered under different buried depths. The results show that the ground surface response decreases while the jacking force increases with increasing the aspect ratios. Thus, a reasonable design of the rectangular pipe section should comprehensively consider the influence of geometric effects on the ground and its stress-bearing state during the jacking construction. The findings of this study provide a practical reference for the safe and economic design of the jacking rectangular pipe and engineering management.

The discrepancy of random rectangular matrices

AbstractA recent approach to the Beck–Fiala conjecture, a fundamental problem in combinatorics, has been to understand when random integer matrices have constant discrepancy. We give a complete answer to this question for two natural models: matrices with Bernoulli or Poisson entries. For Poisson matrices, we further characterize the discrepancy for any rectangular aspect ratio. These results give sharp answers to questions of Hoberg and Rothvoß (SODA 2019) and Franks and Saks (Random Structures Algorithms2020). Our main tool is a conditional second moment method combined with Stein's method of exchangeable pairs. While previous approaches are limited to dense matrices, our techniques allow us to work with matrices of all densities. This may be of independent interest for other sparse random constraint satisfaction problems.

Fully turbulent flows of viscoplastic fluids in a rectangular duct

Turbulent flows of viscoplastic fluids at high Reynolds numbers have been investigated recently with direct numerical simulations (DNS) but experimental results have been limited. For this reason, we carry out an experimental study of fully turbulent flows of a yield stress fluid in a rectangular aspect ratio channel with a high-resolution laser doppler velocimetry (LDA) setup. We employ aqueous Carbopol solutions, often considered to be a simple yield stress fluid. We formulate different concentrations to address the effect of the rheology of the fluid on the turbulence statistics at an approximately constant Reynolds number. Additionally, we also perform experiments with a single Carbopol formulation at different Reynolds numbers to study its effect. The flow analysis is performed via rheology measurements, turbulence statistics and power spectral densities of velocity fluctuations. The addition of Carbopol to the flow increases turbulence anisotropy, with an enhancement of streamwise velocity fluctuations and a decrease in wall normal velocity fluctuations in comparison to water at the same mean velocity. This change is reflected on the power spectral densities of streamwise velocity fluctuations, where we observe a large increase in energy of large scale turbulent structures. Conversely, the energy of smaller scales is decreased in comparison to water, where the energy drops with a steeper scale than the Newtonian power law of $k_x^{-5/3}$. As we increase the Reynolds number with a Carbopol solution, the streamwise Reynolds stresses approach Newtonian values in the core, which suggests diminishing effects of shear-thinning. The power spectral densities reveal that the energy content at larger scales decreases slightly with the Reynolds number. However, the shear thinning effects do not disappear even as the Reynolds number approaches 50000.

A computational software system to design order picking warehouses

Even though order picking is the most costly operation in a warehouse, current design practices have used the same principles (straight rows with parallel pick aisles and perpendicular cross aisles) to reduce travel distances between pick locations for more than sixty years. We present an open-source computational software system for facilitating the design of warehouse layouts to near-optimality considering average walking distance of the picker as the objective function. This software is particularly novel because a wide variety of traditional and innovative designs are automatically generated and evaluated. For the warehouse design parameters we consider the rectangular aspect ratio of the floor plan, the number and location of cross aisles, the number and location of pick aisles, and the location of a single input/output location. The main components of the design system are importing pick list profile data, creating the warehouse layout design as a network, product allocation (slotting) of SKUs through the warehouse, routing of pickers on a sample of orders using an exact routing algorithm, and design optimization using a meta-heuristic. We provide both mathematical and computational descriptions of the algorithms used by the software system, describe the types of problems that can be solved, and summarize our computational experience. This software is open source available on a GitHub website under an MIT license.

Surface, size and topological effects for some nematic equilibria on rectangular domains

We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, , which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the 0 limit relevant for macroscopic domains and the limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the limit, whereas we observe fractional point defects in the 0 limit. The analytical studies are complemented by some bifurcation diagrams for these reduced equilibria as a function of and the rectangular aspect ratio. We also introduce the concept of ‘non-trivial’ topologies and study the relaxation of non-trivial topologies to trivial topologies mediated via point and line defects, with potential consequences for non-equilibrium phenomena and switching dynamics.

Ionic liquid-water flow in T-shaped microchannels with different aspect ratios

In this article we investigate the influence of a rectangular microchannel aspect ratio on the liquid–liquid flow. An ionic liquid was chosen as one of the working fluids due to a vast scope of applications. Immiscible ionic liquid-water flow in T-shaped microchannels with 160μm hydraulic diameter and aspect ratios equal to 2 and 4 was studied experimentally. Flow pattern maps were drawn and compared for two channels in terms of We*Oh dimensionless number. Parallel flow was shown to prevail for the channel with higher aspect ratio. The influence of channel aspect ratio on plug flow peculiarities was studied in detail. Plug length and velocity were measured at different bulk flow rates. Velocity fields in aqueous plugs were measured using the micro-PTV technique. Velocity circulations were calculated for different flow rates. Total circulation value inside plugs was found to be higher in the channel with the lower aspect ratio.

Nonlinear Reduced Order Model for Aeroelastic Static Deformations of Cantilevered Rectangular High Aspect Ratio Wing Model

The paper is motivated by the increasing interest in the use of high aspect ratio (HAR) wings to utilize its aerodynamic properties to gain better endurance. Nevertheless, the drawback of the issue is that with increment in the aspect ratio of the wing, the geometric nonlinearity gains more significance hence the linear solution is no longer acceptable. Even though, a number of nonlinear solution package are available in the market, but the solution is a very time consuming process. Hence, to help reduce the complexity of the nonlinear aeroelastic analysis, a Combined Model/Finite Element (CMFE) technique is employed to develop a Nonlinear Reduced Order Model (NROM) which describe the nonlinearity of the HAR wing from a solution of nonlinear static analysis for a range of prescribed loading cases. Three loading types were considered for the production of the NROM of which the force subjected to the wing model was normalized to follow the normal mode of the wing model. The three loading types are of the first bending mode, the first torsional mode and a combination of the first bending and torsional modes. The NROM equations are then developed utilizing the backward regression method. In order to verify the NROM equation accuracy with respect to the results obtained from the finite element analysis (FEA) software, the comparisons are made in terms of mean error and standard deviation of the error. The results indicate the NROM developed using a combination of the first bending mode and first torsional mode of the wing model has better accuracy than the NROM developed with the modes individually. The NROM also portrays greater accuracy when developed using the data due to the load from the first bending and the first torsional mode.