Dimensionless Shape Factor Research Articles

On inherent hyperelastic crease

We present analyses of the inherent hyperelastic crease that entails an unstable degenerative singular perturbation field over a uniformly compressed hyperelastic half-space. The analyses reveal asymptotic far-field characteristics of the singular field that bring out admissible incremental elastic deformation mechanisms of the inherent creasing instability typically observed at a compressive strain of ∼0.354 in neo-Hookean solids. The admissible singular perturbation field has an asymptotic leading-order incremental-stress singularity decaying 1/r2 as the distance from the crease tip r→∞. In general, asymptotic incremental-deformation fields of 1/r2 stress singularity can be introduced by surface flaws. We found that the singular field creates a far-field eigenmode of three energy-release angular sectors separated by two energy-elevating sectors of incremental deformation. The far-field eigenmode braces the near-tip energy-release field of the surface flaw against the transition to an unstable self-similar expansion field of creasing. Two asymptotic far-field parameters can characterize the braced-incremental-deformation (bid) and crease fields. One is the Burgers vector of a projected subsurface dislocation of the asymptotically singular far field. The other is a dimensionless shape factor representing the ratio of the subsurface depth of the dislocation to the Burgers vector. Our analyses show that the shape factor gauges the transition from the stable bid field to the unstable inherent crease field at the crease limit point as the compression increases. Two tangential-manifold conservation integrals are revealed to identify the two parameters. At the crease-limit point, matched asymptotes lead to the ratio between the two separate scaling parameters of the asymptotic solutions of the crease-tip folding field and the leading-order far field. To this end, we introduced a novel finite element method (FEM) for simulating the crease field nearly in a hyperelastic half-space with a finite-size simulation domain. Furthermore, we uncovered with the Gent model (1996) that strain-stiffening in hyperelasticity alters the dependence of the shape factor on the compressive strain, raising crease resistance. The new findings in hyperelastic crease mechanisms will help study ruga mechanics of self-organization and design soft-material structures and skin conditions for high crease resistance.

On the orientation dependence of the pressure and frictional drag experienced by spheroids in creeping flow

The present work deals with the creeping flow past a single oblate or prolate spheroid. On the basis of the investigations by Aoi [J. Phys. Soc. Jpn. 10, 119 (1955)] on the contributions of pressure and frictional drag to the total drag experienced by spheroids when the fluid streams with a speed parallel to the axis of symmetry, we find that the pressure contribution corresponds to half of the dimensionless shape factor γ0 provided by Happel and Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall Inc. Englewood Cliffs, NJ, 1965). Accordingly, we conjecture the validity of this finding when the fluid streams with a speed perpendicular to the axis of symmetry. Therefore, the formulations of dimensionless shape factors α0/2 and β0/2 are confronted with the numerical results at particle Reynolds number of 0.1. Furthermore, the formulations of the pressure and the frictional drag are deduced and extended to any orientation relative to the flow direction. These results give physical insight into the total drag experienced by spheroids in creeping flow and can be helpful for the validation of simulations of the flow past an obstacle.

3-D visual analysis and quantitative characterization on coal matrix based on Micro-CT

Coal matrix, the storage space for adsorbed gas, is highly related to gas recovery and gas outburst disasters. However, existing research predominantly relies on theoretical assumptions, lacking experimental validation. In this study, we employ X-ray computed tomography (CT) to obtain high-resolution (13.45–15.157 μm) internal structure images of various coal samples. The three-dimensional model of coal matrix elements is reconstructed using entropy threshold segmentation and watershed segmentation. A systematic quantification of the size, shape, and spatial arrangement of these matrix elements is then performed. The results reveal that coal matrix element equivalent diameters span 148.45–2800.35 μm, with volume-weighted average equivalent diameters ranging from 1320.82 to 1720.87 μm. Additionally, we explore particle size distribution (PSD) models to characterize size-quantity relationships and identify the Jaky model based on the logarithmic-exponential equation as the optimal PSD model. Observation of the matrix element models shows that large matrix elements typically exhibit flattened morphologies with rough surfaces, while smaller ones tend to be blocky with smooth surfaces. The dimensionless shape factor results suggest that, when scale effects are not considered, the shape of larger matrix elements is more conducive to matrix-fracture gas mass transfer. Based on this, a functional relationship between the matrix shape factor and size, considering changes in matrix morphology, is established. Moreover, we algorithmically determine that the average number of adjacent matrix elements per individual matrix element falls between 13 and 15. For matrix clusters with large volume fractions, the size ratio of the central matrix element to adjacent matrix elements primarily falls within the range of 0.4–0.6, approximately following a Weibull distribution. According to this feature, a method for building a matrix cluster model used for simulations is proposed.

Transient heat transfer simulation, sensitivity analysis, and design optimization of shallow ground heat exchangers with hollow-finned structures for enhanced performance of ground-coupled heat pumps

Ground-Coupled Heat Pumps (GCHPs) are regarded as an effective technology for building energy development and residential hot water production. The essential challenges to encompass these systems in urbanized areas are the highly drilling and initial costs of GCHPs. To overcome this challenge, researchers and industries are seeking innovative solutions by focusing on optimizing the structure of ground heat exchangers (GHXs), which act as the essential component for efficient geothermal energy extraction in GCHPs. Hence, this paper introduces a comprehensive comparative numerical investigation of an innovative U-tube GHX with a hollow-finned structure for augmenting the performance of the GCHPs. This design remarkably enhances the thermal performances, reduces the thermal resistance, therefore minimizes borehole depth, reduces drilling costs, boosts GCHP's financial viability, and bolsters geothermal energy utilization. Therefore, a series of three-dimensional analyses of transient heat extraction is executed and validated using a practical field experiment performed by the authors' research group to investigate the thermal behavior of the hollow-finned U-tube GHX at different fin configurations and compare its efficacy to typical circular U-tube GHX. More so, a parametric study and sensitivity analysis are also performed to identify the influence of critical operational and design factors on the heat extraction of the proposed hollow-finned U-tube GHX compared to the typical circular GHX. The influences of groundwater flow on the transient heat extraction were also examined. Additionally, a dimensionless shape factor is introduced to assess the implications of the U-tube geometry with hollow-finned on the thermal performance of the GHXs. Furthermore, design optimization was also conducted by examining different branched-shaped hollow-fin's U-tube GHX configurations. The findings indicate that the mean heat transfer rate of hollow-finned U-tube GHX can be increased by 44.58 % compared to the conventional circular U-tube GHX. Correspondingly, the total thermal resistance of hollow-finned U-tubes GHX was reduced by 47.71 %. It also identified that the Y-shaped hollow-finned U-tube GHX was the optimal design among the investigated configurations of branched-shaped hollow-finned U-tube GHXs, demonstrating an increase of 52.64 % compared to the conventional circular U-tube GHX. Moreover, it is revealed that a lower shape factor enhances the heat transfer rate significantly. Furthermore, the optimal mass flow rate and desired number of hollow-finned were estimated as 0.80 kg/s and six fins, respectively. Conclusively, this investigation concludes that the hollow-finned U-tube GHX can greatly enhance the heat extraction rates and reduce borehole thermal resistance, which can increase the efficiency of GCHP systems.

Improved modeling and correlation for heat transfer through a condensate droplet

In dropwise condensation, the heat transfer performance is determined by the heat transfer through a single droplet and the droplet size distribution on the cooled condensing surface. The conduction resistance inside a droplet is an important part of all heat transfer resistances, and it also affects the size distribution of small droplets further, such as in the popular population balance model. The heat transfer of a single droplet can be measured by the Nusselt number (Nu), and internal conduction resistance can be measured by the dimensionless shape factor (f). Previous studies have shown that Nu and f are functions of droplet contact angle (θ) and Biot number (Bi). Based on this, some fitting correlations of Nu or f in a certain range of Bi and θ are established. However, previous results show unreasonable values when Bi is very large or very small, the effective ranges of these fitting correlations are not broad enough, and the fitting accuracy is not gratifying enough. In this paper, the heat transfer characteristics of condensing droplets are investigated by a CFD method which is validated by comparing the simulation results and theoretical solution for hemisphere droplets. By adopting this method, f and Nu are obtained for droplets with 10° ≤θ≤ 170° and 10−3≤Bi≤ 104. Considering the relationship between current numerical results and the model of Kim and Kim (2011), an improved general fitting correlation covering all 374 simulation cases is proposed, and the root mean square (RMS) errors of f and Nu are 3.6% and 2.6%, respectively.

Abnormal Shapes Identification of Gedong Mango Using Dimensionless Shape Factors in Image Processing

In addition to size, export quality requirements for gedong mango among others are clean surface, free of damaged mechanically or biologically, free from pests and diseases, and normal fruit shape. The abnormal fruit shape in mangoes is known as sitting mango, which is not easy to roll over when pushed because the fruit surface is flat on certain sides. Several dimensionless shape factors can be used to identify the shape of an object through image processing. Some shape factors that are often used to identify shapes of object in image processing include roundness, roundness ratio, sphericity, axial ratio, inequality degree of projected area and spherical disproportion. This study aims to identify the shape of the fruit using several dimensionless shape factors and determine the shape factors that can be used to distinguish normal and abnormal fruit shapes for gedong mangoes. The results showed that abnormal and normal mango gedong fruit shapes could be distinguished by image processing using the roundness, sphericity, and spherical disproportion form factors in certain deviant shapes but not for all samples.

Hyperelastic hold-down solution for CLT shear walls

The use of cross-laminated timber (CLT) shear walls in tall buildings poses large demands on hold-downs (HD). While commonly used HDs behave as dissipative connections, the current Canadian Standard for Engineering Design in Wood recommends designing HDs as a non-dissipative connection. To satisfy this requirement, a hyperelastic elastomeric (rubber) HD was developed. Material level tests showed that the compressive behaviour of rubber layers relied on a dimensionless geometrical shape factor (SF). Component level tests on a total of 16 different HD configurations varying the width and thickness of the rubber pads were conducted under quasi-static monotonic and cyclic loading, the latter with two different loading protocols. Under monotonic loading, the rubber HDs behaved hyperelastic without any residual inelastic deformation and no damage was observed in the CLT panels or the steel parts. The HD load-displacement behaviour was mostly influenced by SF, with smaller SF leading to lower stiffness. A power function was developed to describe the load-displacement behaviour of the HD. Under cyclic loading, no strength or stiffness degradation was observed, even after multiple loading cycles. When designing CLT shear walls with the proposed hyperelastic HD, both the CLT panel as well as the steel parts must be capacity protected to prevent the brittle failure of the CLT or premature yielding of the steel.

Heat conduction in rectangular solids with internal heat generation

A representative steady-state heat conduction problem in rectangular solids with uniformly distributed heat generation has been investigated analytically. An analytical solution is provided by solving a non-homogeneous PDE. A simple and accurate model is proposed to predict the dimensionless shape factor parameter for the first time. The dimensionless shape factor is obtained in the light of the solution of Poisson equation with constant wall temperature boundary conditions. The area-mean temperature is found by integration on the rectangular cross-section. The model is very concise and nice for quick real world approximations, and it provides acceptable accuracy for engineering practice.

Thermal performance of the vertical ground heat exchanger with a novel elliptical single U-tube

Ground-Coupled Heat Pumps (GCHPs) are known as a promising technology for building climatization and domestic hot water production. The main concern to employ these systems in urban areas is their high drilling and initial cost. This cost could be rebated by lowering the borehole thermal resistance and by shortening the borehole depth. In the present paper, a novel and simple design of the Ground Heat Exchanger (GHE), namely the vertical GHE with an elliptical U-tube, is proposed to improve thermal performance of GCHP systems. To prove that; a series of 3D finite element simulations are performed to study the thermal comportment of elliptical U-tubes and to compare their performance with typical single U-tubes. A dimensionless shape factor γ is introduced to evaluate effect of the elliptical U-tube geometry on thermal performance of the GHE. Furthermore, influential parameters on thermal performance of elliptical U-tubes are investigated and the decrement percentage of the borehole thermal resistance, with reference to the typical U-tube, are compared for each parameter. The results show that elliptical U-tubes could enhance heat transfer to significant extent and could decrease the borehole thermal resistance by more than 17 %, compared with typical single U-tubes. It is shown that the higher value of the shape factor γ leads to the better heat transfer enhancement. It is concluded that elliptical U-tubes are able to decrease the borehole thermal resistance and to boost the coefficient of performance (COP) of GCHP systems.

Threshold of motion of bivalve and gastropod shells under oscillatory flow in flume experiments

AbstractThe threshold of motion of non‐fragmented mollusc shells was studied for the first time under oscillatory flow. In this regard, flume experiments were used to investigate the threshold of motion of three bivalve and three gastropod species, two typical mollusc classes of coastal coquina deposits. The sieve diameters ranged from 2·0 to 15·9 mm. These experiments were performed on a flat‐bottom setup under regular non‐breaking waves (swell) produced by a flap‐type wave generator. The critical Shields values for each species of mollusc were plotted against the sieve and nominal diameter. Moreover, the dimensionless Corey shape factor of the shells was evaluated in order to investigate the effect of mollusc shell shapes on the threshold of motion. According to their critical Shields parameter, the mollusc threshold data under oscillatory flow present smaller values than the siliciclastic sediments when considering their sieve diameter. In addition, the mollusc datasets are below the empirical curves built from siliciclastic grain data under current and waves. When considering the nominal diameter, the critical Shields parameter increases and the mollusc data are closer to siliciclastic sediments. Bivalves, which have a flat‐concave shape (form factor: 0·27 to 0·37), have a higher critical Shields parameter for smaller particles and more uniform datasets than the gastropod scattered data, which have a rounded shape (form factor: 0·58 to 0·62) and have varied morphologies (ellipsoidal, conical and cubic). The comparison between previous current‐driven threshold data of bioclastic sediment motion and the data of mollusc whole shells under oscillatory flow shows a fair correlation on the Shields diagram, in which all datasets are below the mean empirical curves for siliciclastic sediments. These findings indicate that the shape effect on the transport initiation is predominant for smaller shells. The use of the nominal diameter is satisfactory to improve the bioclastic and siliciclastic data correlation.

Wind tunnel tests and analysis of snow load distribution on three different large size stadium roofs

The article contains comparison and analysis of snow load tunnel tests for three different roofs of sport facilities. Tests were performed in a wind tunnel with boundary layer modelling. Snow precipitation and redistribution tests were performed using powdered polystyrene foam as artificial snow. The results of snow load distributions were presented as dimensionless roof shape factor of snow load for both the precipitation and redistribution simulations.

Experimental study of the effectiveness of air curtains of variable width and injection angle to block fire-induced smoke in a tunnel configuration

Small-scale experiments have been conducted to study the sealing effect of an air curtain for fire-induced smoke confinement in a tunnel configuration. The processed data confirmed the results obtained earlier from blind Computational Fluid Dynamics (CFD) simulations [1] using the Fire Dynamics Simulator (FDS) 6.5.3 [2,3]. Furthermore, the CFD simulations provided complementary information on the detailed flow and temperature fields which are difficult to obtain in experiments with the available techniques. A parametric study is performed, covering a range of air curtain velocities, slot widths, injection angles and total fire heat release rates (HRRs). The momentum ratio R, defined as the ratio of the vertically downward air curtain momentum to the horizontal smoke layer momentum at the position of the air curtain, is confirmed to be a key parameter for the air curtain performance. A ratio R ≈ 10 is recommended for the optimum sealing effect in terms of smoke confinement. In addition, two other important parameters that determine the performance of air curtains for smoke confinement are presented. The first parameter is the dimensionless shape factor AR (AR = Width/Length) that characterizes the dilution effect of the air curtain jet. The second parameter is the injection angle θ that characterizes the horizontal force of the air curtain. The air curtain sealing effectiveness increases with both the increase of slot width (shape factor AR) and injection angle (θ). The air curtain width has a limited influence on the performance of the air curtain whilst the injection angle has a more significant influence on the sealing effectiveness of the air curtain for the scenarios considered in this study. An optimal injection angle of 30° inclined to the fire source is recommended in the engineering design of the air curtain for smoke confinement for situations where the fire location can be pre-determined to be only at one side of an air curtain.

Crack arrest testing at the micro-scale

Crack arrest testing of micro-sized cantilever beams (≈8 × 4 × 6 μm, length, width and height, respectively) was conducted in order to evaluate the suitability of a new method to quantify local crack arrest properties. Chevron notched cantilevers were milled to match the (1 0 0)[0 1¯ 1] crack system in α-iron, where earlier attempts to obtain brittle or rapidly propagating fracture proved difficult. Brittle crack initiation and propagation was achieved by means of the deposition of a layer of SiOX on the surface, acting as a brittle starter. All tests were performed at −75 °C, using an in-house designed cooling system. The cracks arrested after propagation into the iron cantilever. A finite element model was developed to determine the appropriate dimensionless shape factor and provide a rigorous computer analysis of these complexly shaped cantilevers. KQC and KQa, at initiation and arrest respectively, were determined and evaluated. The cantilevers were later displaced further at 40 K to allow evaluation of crack jump lengths and to obtain a more complete analysis of the fracture surfaces. The average fracture toughness was determined to be 3.89 ± 1.00 MPam, and the average arrest toughness to be 2.6 ± 0.86 MPam. The finite element model highlights the effect of small variations in geometry which was larger than anticipated and strongly affects the shape factor, up to a 25% difference in f(a/W). As small variations in geometry are inevitable when milling with FIB, the need for individual models tailored to every cantilever is discussed.

A two-dimensional porous electrode model for designing pore structure in a quinone-based flow cell

Abstract A two-dimensional porous electrode model for designing a pore structure in a quinone-based flow battery was developed and validated by using experimental data from a metal-free quinone-based flow battery. The effects of porosity and pore size distribution on electrode performance and concentration fields were analyzed, the appropriate porosity and pore size distribution were obtained. In addition, the comprehensive effect of pore volume, specific surface area and pore size were considered, the dimensionless number shape factor SF was introduced to characterize the morphology, and the effect of morphology on the electrode performance was also investigated. This model was expected to understand the effect of morphology on the electrode performance and guide the preparation of the electrode. Extensions to the model in actual tests and future work were suggested.

Geometrical Effect on Thermal Conductivity of Unidirectional Fiber-Reinforced Polymer Composite along Different In-plane Orientations

This paper focuses on the anisotropic characteristics of the in-plane thermal conductivity of fiber-reinforced polymer composite based on experiment and simulation. Thermal conductivity along different in-plane orientations was measured by laser flash analysis (LFA) and steady-state heat flow method. Their heat transfer processes were simulated to reveal the geometrical effect on thermal conduction. The results show that the in-plane thermal conduction of unidirectional carbon-fiber-reinforced polymer composite is greatly influenced by the sample geometry at an in-plane orientation angle between 0° to 90°. By defining radius-to-thickness as a dimensionless shape factor for the LFA sample, the apparent thermal conductivity shows a dramatic change when the shape factor is close to the tangent of the orientation angle (tanθ). Based on finite element analysis, this phenomenon was revealed to correlate with the change of the heat transfer process. When the shape factor is larger than tanθ, the apparent thermal conductivity is consistent with the estimated value according to the theoretical model. For a sample with a shape factor smaller than tanθ, the apparent thermal conductivity shows a slow growth around a low value, which seriously deviates from the theory estimation. This phenomenon was revealed to correlate with the change of the heat transfer process from a continuous path to a zigzag path. These results will be helpful in optimizing the ply scheme of composite laminates for thermal management applications.

Cavity shape transformation during peeling on elastic microchannel-patterned substrates filled with a viscous liquid.

Inspired by the detachment mechanics of natural adhesive pads, we studied the change in cavity shape during peel tests on a 10% cross-linked polydimethylsiloxane (PDMS) elastic microchannel filled with 1% cross-linked viscous PDMS liquid (patterned bilayer). During peeling, we explored cavity shape as a function of microchannel dimensions and correlated the dimensionless cavity shape factor (CSF) and characteristic stress decay length, K-1. The peel test on the liquid-filled elastic microchannel shows three distinct cavity-shape regimes, elliptical, circular, and binary, based on the values of CSF and K-1. Such cavity formation and shape regimes could be important for improving the design of pressure-sensitive adhesives.

AlSi9Mg aluminum alloy semi-solid slurry preparation by intermediate frequency electromagnetic oscillation process

A novel method is developed herein to simplify the process of semi-solid forming. The process working principle is similar to that of intermediate frequency heating. In this preparation process, the melting process and stirring process are combined. Nucleation and dendrite growth of the metallic material are affected by the intermediate frequency electromagnetic stirring and forced convection. The AlSi9Mg aluminum alloy is investigated in intermediate frequency electromagnetic oscillation process (IFEOP). Experiments and simulations are carried out to study the effect of process parameters. After about 10 periods of time, the average size of the semi-solid slurry grains was 28μm, the dimensionless shape factor was 0.87 and the porosity was 0.15%. Grains turn to spherical crystal when the semi-solid material was reheated to 565°C for 25min or to 575°C for 10min. The number of periods, holding time and holding temperature were observed to have significant influences on properties of semi-solid material.

The Effects of Surface Shape of Microchannels on Methane/Moist Air Catalytic Combustion

This paper studied the methane/moist air combustion characteristics in smooth microtube and microtubes with five different shape grooves and proposed the microtube groove dimensionless shape factor F=4πS/L2. The results show that the appearance of five grooves make combustion components and velocity occur jumping change and the vortex flow appears. The highest methane conversion rate is for the microtube with triangle grooves, which also indicates that the smaller shape factor is more in favor of methane conversion.

Relating vesicle shapes in pyroclasts to eruption styles

Vesicles in pyroclasts provide a direct record of conduit conditions during explosive volcanic eruptions. Although their numbers and sizes are used routinely to infer aspects of eruption dynamics, vesicle shape remains an underutilized parameter. We have quantified vesicle shapes in pyroclasts from fall deposits of seven explosive eruptions of different styles, using the dimensionless shape factor $\Omega $ , a measure of the degree of complexity of the bounding surface of an object. For each of the seven eruptions, we have also estimated the capillary number, Ca, from the magma expansion velocity through coupled diffusive bubble growth and conduit flow modeling. We find that $\Omega $ is smaller for eruptions with ${\rm{Ca}} \ll 1$ than for eruptions with Ca $\gg 1$ . Consistent with previous studies, we interpret these results as an expression of the relative importance of structural changes during magma decompression and bubble growth, such as coalescence and shape relaxation of bubbles by capillary stresses. Among the samples analyzed, Strombolian and Hawaiian fire-fountain eruptions have ${\rm{Ca}} \ll 1$ , in contrast to Vulcanian, Plinian, and ultraplinian eruptions. Interestingly, the basaltic Plinian eruptions of Tarawera volcano, New Zealand in 1886 and Mt. Etna, Italy in 122 BC, for which the cause of intense explosive activity has been controversial, are also characterized by ${\rm{Ca}} \gg 1$ and larger values of $\Omega $ than Strombolian and Hawaiian style (fire fountain) eruptions. We interpret this to be the consequence of syn-eruptive magma crystallization, resulting in high magma viscosity and reduced rates of bubble growth. Our model results indicate that during these basaltic Plinian eruptions, buildup of bubble overpressure resulted in brittle magma fragmentation.

Advective–diffusive mass transfer in fractured porous media with variable rock matrix block size

Traditional dual porosity models do not take into account the effect of matrix block size distribution on the mass transfer between matrix and fracture. In this study, we introduce the matrix block size distributions into an advective–diffusive solute transport model of a divergent radial system to evaluate the mass transfer shape factor, which is considered as a first-order exchange coefficient between the fracture and matrix. The results obtained lead to a better understanding of the advective–diffusive mass transport in fractured porous media by identifying two early and late time periods of mass transfer. Results show that fractured rock matrix block size distribution has a great impact on mass transfer during early time period. In addition, two dimensionless shape factors are obtained for the late time, which depend on the injection flow rate and the distance of the rock matrix from the injection point.