Zero Thickness Research Articles

Numerical investigation on transpiration cooling with phase change based on multiphysics coupled finite element method

Transpiration cooling with phase change is an efficient active thermal protection method in aerospace. However, conducting numerical simulation of transpiration cooling with phase change is still a challenge, because porous flow, heat transfer and phase change are coupled with each other, which lead to numerical difficulties. In this article, the previous model is modified and the Zero Thickness Area Model (ZTAM) is proposed, which improves the efficiency and convergence significantly. In addition, the local thermal nonequilibrium effect and latent heat can be considered. To verify this ZTAM model, one-dimensional control equations of mass, momentum, and energy transpiration are solved using finite element method. Furthermore, the position of phase change is determined by fixed point iteration numerical algorithm, which shows good convergence. Finally, the influence on cooling effect by heat flux, coolant mass flow rate, porosity and pore diameter is investigated numerically.

Zero Thickness Surface Susceptibilities and Extended GSTCs—Part I: Spatially Dispersive Metasurfaces

A simple method to describe spatially dispersive metasurfaces is proposed where the angle-dependent surface susceptibilities are explicitly used to formulate the zero thickness sheet model of practical metasurface structures. It is shown that if the surface susceptibilities of a given metasurface are expressed as a ratio of two polynomials of tangential spatial frequencies, k|| with complex coefficients, they can be conveniently expressed as spatial derivatives of the difference and average fields around the metasurface in the space domain, leading to extended forms of the standard generalized sheet transition conditions (GSTCs) accounting for the spatial dispersion. Using two simple examples of a short electric dipole and an all-dielectric cylindrical puck unit cells, which exhibit purely tangential surface susceptibilities and reciprocal/symmetric transmission and reflection characteristics, the proposed concept is numerically confirmed in 2D. A Lorentzian representation with angle-dependent parameters is further proposed and found to accurately model the complex temporal-spatial frequency response via their electric and magnetic susceptibilities of two unit cell examples - a metallic dipole and a dielectric puck resonator. For both cases, the appropriate spatial boundary conditions are derived.

Dynamics modeling and vibration transmission visualization of fluid-conveying series pipe system based on FEM-TMM

The fluid-conveying series pipe system (FCSPS) is an important part of the pipe system, and its stress response solution and vibration transmission analysis are of great significance to life prediction and defect analysis. In this paper, the finite element method (FEM) and transfer matrix method (TMM) are combined. The dynamics modeling method named FEM-TMM is proposed to solve the stress response of the FCSPS, and the structural intensity method (SIM) is used to perform vibration transmission visualization. The incompatible solid (Solid-NC) and virtual beam (VBeam) elements are constructed to establish the finite element model of the solid and fluid domains respectively. The zero-thickness (Z-T) and coupling elements are created to simulate the contact of the pipe joint and fluid-solid coupling. TMM is used to solve the responses of fluid velocity and pressure (FVAP) in the frequency domain, then FEM-TMM for the pipe system is obtained and verified by experiments. Furthermore, the stress smoothing method and SIM are introduced to solve the stress response and perform vibration transmission visualization. The results show that the SIM can visualize the vibration transmission of the pipe system, and the pipe joint plays the role of transmission, conversion, and redistribution of vibration energy.

Accelerated IE-GSTC Solver for Large-Scale Metasurface Field Scattering Problems Using Fast Multipole Method (FMM)

An accelerated integral equations (IE) field solver for determining scattered fields from electrically large electromagnetic metasurfaces using fast multipole method (FMM) is proposed and demonstrated in 2-D. In the proposed method, practical general metasurfaces are expressed using an equivalent zero thickness sheet model described using surface susceptibilities, and where the total fields around it satisfy the generalized sheet transition conditions (GSTCs). While the standard IE-GSTC offers fast field computation compared with other numerical methods, it is still computationally demanding when solving electrically large problems, with a large number of unknowns. Here, we accelerate the IE-GSTC method using the FMM technique by dividing the current elements on the metasurface into near- and far-groups, where either the rigorous or approximated Green’s function is used, respectively, to reduce the computation time without losing solution accuracy. Using numerical examples, the speed improvement of the FMM IE-GSTC method { <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N^{3/2})$ </tex-math></inline-formula> } over the standard IE-GSTC { <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$O(N^{3})$ </tex-math></inline-formula> } method is confirmed. Finally, the usefulness of FMM IE-GSTC is demonstrated by applying it to solve electromagnetic propagation inside an electrically large radio environment with strategically placed metasurfaces to improve signal coverage in blind areas, where a standard IE-GSTC solver would require prohibitively large computational resources and long simulation times.

Modelling of metal – mould interface resistance in the Al-11.5 wt.% Si alloy casting process

AbstractA computational model is developed to include heat transfer, effects of resistance of the metal –mould interface, and pressure in the simulation of the solidification process. The simulation of the interface resistance is based on the Zero Thickness Element, utilizing the Finite Element Method. The solid boundary conditions, including contact resistances, have been modified by a pressure gradient in each of the Zero Thickness Elements. The pressure gradient has been modelled on experimental data. In order to verify the computational results, an Al-11.5 wt.% Si alloy has been poured into a permanent mould and the temperature of the interface measured. Then we modelled the effect of metallostatic pressure on the overall heat transfer coefficient in the metal–mould interface. The comparison between the experimental and the simulation results during the solidification process shows a good consistency that confirms the accuracy of the model for the effect of the interface resistance on solidification time.

Numerical investigation of the flow characteristics and permeability of 2D irregular columnar jointed rock masses

PurposeThe objective of this paper is to provide a better understanding of the effect of irregular columnar jointed structure on the permeability and flow characteristics of rock masses.Design/methodology/approachAn efficient numerical procedure is proposed to investigate the permeability and fluid flow in columnar jointed rock masses (CJRMs), of which the columnar jointed networks are generated by a modified constrained centroid Voronoi algorithm according to the field statistical results. The fractures are represented explicitly by using the lower-dimensional zero thickness elements. And the modeling scheme is validated by a benchmark test for flow in fractured porous media. The effective permeability and representative elementary volume (REV) size of CJRMs are estimated using finite element method (FEM). The influences of joint density and variation coefficient of columnar joint structure on the permeability of the rock mass are discussed.FindingsThe simulation results indicate that the permeability is scale-dependent and tends to be stable with increase of model size. The hydraulic REV size is determined as 3.5 m for CJRMs in the present study. Moreover, the joint density is a dominant factor affecting the permeability of CJRMs. The average permeability of columnar jointed structures increases linearly with the joint density under the same REV size, while the influence from the coefficient of variation can be neglected.Originality/valueThe present paper investigates the REV size of the CJRMs and the effect of joint parameters on the permeability. The proposed method and the results obtained are useful on understanding the hydraulic characteristic of the irregular CJRMs in engineering projects.

Computational evaluation of long-term ravelling susceptibility of Permeable Friction Courses (PFC)

Ravelling is a main distress in Permeable Friction Courses (PFC). This damage process is enhanced by the presence of moisture and ageing, which further reduces the overall durability of the mixtures. This study uses Finite Element (FE) methods to assess long-term ravelling susceptibility of PFC. Different two-dimensional (2D) PFC microstructures were randomly generated through a Microstructure Generator (MG) and Discrete Element (DE) gravimetric methods. These microstructures were located on top of a conventional pavement and subjected to a moving wheel load under different traffic operation conditions. PFC ravelling was assumed to occur at the asphalt mortar located at the stone-on-stone contacts. The linear viscoelastic and fracture properties of the PFC asphalt mortar were experimentally obtained after subjecting the material to long-term ageing conditions and multiple water moisture cycles, which represent several in-service years. Zero thickness Cohesive Zone Elements (CZE) were included within the mortar-mortar contacts of the PFC to better quantify the potential initiation of ravelling. The results show that the ravelling susceptibility of a PFC is drastically affected by the loading conditions (e.g., load magnitude, vehicle breaking over the pavement, vehicle speed) and the environmental and mechanical degradation of the asphalt mortar when subjected to in-service conditions.

Entrance effects on forced convective heat transfer in laminar flow through short hexagonal channels: Experimental and CFD study

Hexagonal channels display promising flow and transfer characteristics, thus they are considered as prospective structured catalyst carriers. While transfer intensity in long channels is rather moderate, it may be greatly enhanced by channel shortening, because developing laminar flow can be reached in the major part of short channels. Heat transfer in honeycomb structures composed of short hexagonal channels was experimentally studied. The structures of three different channel lengths were made from stainless steel using the 3D printing method. Generally, experimental results agreed rather satisfactory with the literature solutions, but some of the observed deviations were difficult to explain. Therefore, CFD modeling was applied. Serious impact of channel wall thickness on the velocity distribution, thus also on the local Nusselt number distribution, was observed. Such behavior differs seriously from the theoretical predictions assuming zero wall thickness. Nevertheless, the average Nusselt number for both zero and non-zero wall thickness were in surprisingly good agreement.

Numerical Modelling of concrete-to-UHPC Bond Strength.

Ultra-High Performance Concrete (UHPC) has been a material of interest for retrofitting reinforced concrete elements because of its pioneer mechanical and material properties. Numerous experimental studies for retrofitting concrete structures have shown an improvement in durability performance and structural behaviour. However, conservative and sometimes erroneous estimates for bond strength are used for numerically calculating the strength of the composite members. In addition, different roughening methods have been used to improve the bond mechanism; however, there is a lack of numerical simulation for the force transfer mechanism between the concrete substrate and UHPC as a repair material. This paper presents an experimental and numerical programme designed to characterize the interfacial properties of concrete substrate and its effect on the bond strength between the two materials. The experimental programme evaluates the bond strength between the concrete substrates and UHPC with two different surface preparations while using bi-surface test and additional material tests, including cylinder and cube tests for compression property, direct tension test, and flexural test to complement UHPC tensile properties. Non-linear finite element analysis was conducted, which uses a numerical zero thickness volume model to define the interface bond instead of a traditional fixed contact model. The numerical results from the zero thickness volume model show good agreement with the experimental results with a reduction in error by 181% and 24% for smooth and rough interface surfaces if compared to the results from the model with a fixed contact.

Polarization and Frequency-Selective Surface for Vehicular Beamforming Communications Requiring Near-Zero Profile

A polarization-selective and reconfigurable Fresnel zone plate consisting of frequency selective surfaces (FSS) loaded with varactor diodes is devised for compact vehicular wireless communication devices. The unit cell constituting the impedance zone exhibits rapid impedance transitions from 0 ohm (electrically-opaque) to 377 ohm (electrically-transparent). An I-shape configuration is employed for the resonant unit cell structure, featuring high compatibility with DC bias voltage network. In addition, double-sided FSS is employed on the top and bottom faces for polarization-selective beamforming. The FSS comprise of a dielectric with near zero thickness ( λ /250 of 2.40 GHz) resulting in intentionally high mutual coupling between the layers. The devised unit cell is designed using an equivalent circuit model analysis and optimized using finite element solver, achieving over 30 dB impedance switching. The proposed unit cell is experimentally confirmed in both vertical and horizontal polarizations. By configuring the DC voltage bias lines, the unit cells of the FSS are transformed into electrically-driven impedance zones formulating alternating and repetitive gratings. The width and the interval of the grating manipulate the constructive and destructive interference resulting in beam scanning range of 30° in both vertical and horizontal polarizations. The proposed approach can provide concise and compact beamforming solutions for future vehicular communications.

Analysis of the Antiplane Problem with an Embedded Zero Thickness Layer Described by the Gurtin-Murdoch Model

The antiplane problem of an infinite isotropic elastic medium subjected to a far-field load and containing a zero thickness layer of arbitrary shape described by the Gurtin-Murdoch model is considered. It is shown that, under the antiplane assumptions, the governing equations of the complete Gurtin-Murdoch model are inconsistent for non-zero surface tension. For the case of vanishing surface tension, the analytical integral representations for the elastic fields and the dimensionless parameter that governs the problem are introduced. The solution of the problem is reduced to the solution of the hypersingular integral equation written in terms of elastic stress of the layer. For the case of a layer along a straight segment, theoretical analysis of the hypersingular equation is performed and asymptotic behavior of the elastic fields near the tips is studied. The appropriate numerical solution techniques are discussed and several numerical results are presented. Additionally, it is demonstrated that the problem under study is closely related to the specific case of the well-known problem of a thin and stiff elastic inhomogeneity embedded into a homogeneous elastic medium.

Hydromechanical modeling of unrestricted crack propagation in fractured formations using intrinsic cohesive zone model

Production from unconventional reservoirs has revolutionized the oil and gas industry strongly through the development of innovative applications, such as horizontal drilling and shale stimulation by hydraulic fracturing. However, the presence of geological discontinuities such as natural fractures (NFs) complicates the hydraulic fracturing treatment and affects the general geometry of the hydraulic fracture (HF). For that reason, it is essential to develop and implement robust numerical methods capable of simulating the phenomena present during hydraulic fracturing in a naturally fractured formation. This paper presents a novel mesh fragmentation technique to simulate unrestricted hydraulic fracture propagation in fractured media. This method is based on the hydromechanical zero thickness interface element combined with the cohesive zone model (CZM). An algorithm for inserting the especial triple-noded interface elements into conventional 2D finite element meshes is described. We introduce a simple but effective topological data structure that considers each finite element independent of others. The proposed topological structure ensures the generation of new nodes and faces which are necessary for the insertion of interface elements. The implementation is validated by simulating some cases of fracturing experiments in laboratory. The numerical procedure provides very good agreement with the laboratory tests and shows the robustness of the proposed computational approach. Some advantages and limitations of the proposed methodology are discussed.

A cohesive model for concrete mesostructure considering friction effect between cracks

Compressive ability is one of the most important mechanical properties of concrete material .The compressive failure process of concrete is pretty complex with internal tension, shear damage and friction between cracks. To simulate the complex fracture process of concrete at meso level, methodology for meso-structural analysis of concrete specimens is developed; the zero thickness cohesive elements are pre-inserted to simulate the crack initiation and propagation; the constitutive applied in cohesive element is established to describe the mechanism of crack separation, closure and friction behavior between the fracture surfaces. Aseries of simulations were carried out based on the model proposed in this paper. The results reproduced the main fracture and mechanical feature of concrete under compression condition. The effect of key material parameters, structure size, and aggregate content on the concrete fracture pattern and loading carrying capacities was investigated. It is found that the inner friction coefficient has a significant influence on the compression character of concrete, the compression strength raises linearly with the increase of the inner friction coefficient, and the fracture pattern is sensitive to the mesostructure of concrete.

Investigation of shear slip in hot fractured rock

This paper presents the results of a shear slip experiment in hot rock and its simulation and analysis using 3D coupled thermo-poromechanical model with the aim of assessing the role of pore pressure and temperature change on shear slip in granitic rock. The test is carried out in a triaxial system at representative reservoir pressure and temperature using right circular cylindrical specimens of Westerly granite with a 30° precut and ground surface. After the pore pressure and temperature were stabilized, the differential stress and absolute pore pressure were systematically varied to produce different effective stress states to evaluate the shearing response of the saw-cut fracture. The key objective of the experiment is to test the cooling effect on the fracture slip. The experimental results were then analyzed using a newly developed 3D thermo-poromechanical finite element model which uses traditional 4 node tetrahedron elements for intact rock deformation and transport processes. Zero thickness contact interface element is employed to capture the closure and slip on the fracture surface. The stick/slip state of fracture is determined by the Mohr-Coulomb criterion. Simulation results show that the convective cooling effects on rock/fracture surface promote deformation and slip of the fracture. The cold fluid cools the surrounding rock material and results in normal stress reduction that causes portions of the fracture surface to undergo stick/slip state changes, and induces irreversible slip. The experimental work along with modeling provides a physics-based understanding of the role of coupled processes on shear stimulation phenomenon.

Effects of travel speed on mechanical properties of AA7075-T6 ultra-thin sheet joints fabricated by high rotational speed micro pinless friction stir welding

0.5 mm thick AA7075-T6 ultra-thin sheets were joined successfully by high rotational speed friction stir welding using a pinless tool. Friction stir welding was performed under a high rotational speed of 6000 rpm, and the travel speed ranged from 300 mm/min to 1200 mm/min. Zero thickness reduction and delamination phenomenon were observed in the nugget zone when the travel speed was 1200 mm/min. In this condition, the dynamic recrystallization occurred in the lower part of the nugget zone is incomplete. The mechanical properties gradually improved with the increasing in the travel speed. All the tensile specimens fractured along the boundary between the thermo-mechanically affected zone and the nugget zone, and the morphology showed a shear fracture mode. The maximum tensile strength of 482 MPa (equivalent to ∼90% of base metal) was obtained at the travel speed of 1200 mm/min, which presented a ductile fracture mode and a large amount of η phase (MgZn2) precipitates and thick tear ridges were detected on the fracture surfaces.

Zero-Depth Interfacial Nanopore Capillaries.

High-fidelity analysis of translocating biomolecules through nanopores demands shortening the nanocapillary length to a minimal value. Existing nanopores and capillaries, however, inherit a finite length from the parent membranes. Here, nanocapillaries of zero depth are formed by dissolving two superimposed and crossing metallic nanorods, molded in polymeric slabs. In an electrolyte, the interface shared by the crossing fluidic channels is mathematically of zero thickness and defines the narrowest constriction in the stream of ions through the nanopore device. This novel architecture provides the possibility to design nanopore fluidic channels, particularly with a robust 3D architecture maintaining the ultimate zero thickness geometry independently of the thickness of the fluidic channels. With orders of magnitude reduced biomolecule translocation speed, and lowered electronic and ionic noise compared to nanopores in 2D materials, the findings establish interfacial nanopores as a scalable platform for realizing nanofluidic systems, capable of single-molecule detection.

Finite-Difference Time-Domain Modeling of Space–Time-Modulated Metasurfaces

A finite-difference time-domain modeling of finite-size zero thickness space–time-modulated Huygens’ metasurfaces based on generalized sheet transition conditions is proposed and numerically demonstrated. A typical all-dielectric Huygens’ unit cell is taken as an example and its material permittivity is modulated in both space and time, to emulate a traveling-type spatio-temporal perturbation on the metasurface. By mapping the permittivity variation onto the parameters of the equivalent Lorentzian electric and magnetic susceptibility densities, $\chi _{\text {ee}}$ and $\chi _{\text {mm}}$ , the problem is formulated into a set of second-order differential equations in time with nonconstant coefficients. The resulting field solutions are then conveniently solved using an explicit finite-difference technique and integrated with a Yee-cell-based propagation region to visualize the scattered fields taking into account the various diffractive effects from the metasurface of finite size. Several examples are shown for both linear and space–time varying metasurfaces which are excited with normally incident plane and Gaussian beams, showing detailed scattering field solutions. While the time-modulated metasurface leads to the generation of new collinearly propagating temporal harmonics, these harmonics are angularly separated in space, when an additional space modulation is introduced in the metasurface.

Real-time GIS-based snow cover approximation and rendering for large terrains

Various terrain visualization techniques based on geographic information system (GIS) data already exist. One major drawback of existing visualizations is that they do not capture seasonal variations well. Besides vegetation variations, in colder areas this particularly also applies to snow cover. In this paper, we propose a real-time multi-scale snow cover approximation and visualization for large terrains. The computation runs on a large grid, calculates the snow/water equivalent based on precipitation data from a GIS and snowmelt based on a physically-based solar radiation calculation combined with a degree-day snowmelt approach using level of detail (LOD). The snow visualization is divided into two parts: Zero thickness snow cover textures are generated for distant views. For close up views the terrain’s height field is modified using displacement maps and tessellation to produce thick snow covers. The GPU-based data-parallel computation and the visualization run on the GPU in real-time on a modern desktop computer. The implementation is tested using a real area in the Swiss Alps, with a size of 14.16 by 12.88 km, a grid resolution of 222 × 206, and a time step of 1 h. We compare the rendered results spanning several months with a time series of photographs from webcams for visual accuracy.

Non-Linear Modeling of Masonry Arches Strengthened with FRCM

Recent seismic events, such as the Central Italy (2016), the Emilia (2012) and L’Aquila (2009) earthquake, have demonstrated the high vulnerability of cultural heritage represented by historical and monumental buildings. These structures are often characterized by the presence of elements with a curved geometry such as arches and vaults, which interact with the vertical elements (walls or columns) during the earthquake motion, producing a significant effect on the seismic response of the entire structure. Aiming at the reduction of the seismic vulnerability of curved masonry elements, several techniques of reinforcing based on composite fiber materials, have been recently developed and widely investigated by means of experimental tests and numerical simulations. The using of fiber reinforced systems, applied through cementitious mortar (FRCM), is becoming a very common technique of retrofitting for historical and monumental masonry buildings. This technique, if compared to the using of fiber polymeric materials (FRP), is more compatible with the mechanical properties of the masonry and more appropriate with the preservation needs of cultural heritage, associated to the historical constructions. A discrete macro-modeling approach, already available in the literature for modeling masonry structures with plane and curved geometry, is here employed to predict the non-linear behaviour of masonry arches strengthened with FRCM. In that approach the reinforcement is explicitly modeled by using a rigid plate, while the interaction between the reinforcement and the masonry support is governed by a discrete zero thickness interface. In this paper the interfacial behavior is updated with a more sophisticated bond-slip constitutive law specifically conceived for FRCM reinforcement within the framework of fracture mechanics; in particular the proposed calibration takes into account both the pure opening mode (mode I) and the in plane shear mode (mode II). The obtained numerical results are compared with an analytical closed form solution of the problem and validated by mean of experimental tests on prototypes, available in the literature.

Cohesive element approach for dynamic crack propagation: Artificial compliance and mesh dependency

Zero thickness cohesive element approach for arbitrary crack propagation has a deficiency of introducing artificial compliance to the model, especially when cohesive elements are inserted into every element interfaces. For dynamic problems, the artificial compliance decreases the stress wave speed and makes the result less accurate. In this paper, the reason of the artificial compliance is examined, and the bilinear and exponential cohesive law are compared. The work shows that by choosing the right cohesive stiffness, element size and using bilinear cohesive law rather than exponential cohesive law, the artificial compliance issue can be limited to a negligible level without greatly increasing the computational time. Three numerical simulations are used to support the argument. The bilinear cohesive law also shows more robust behavior in terms of cyclic loading than exponential law, and a new cyclic loading formulation is proposed to help fix the discontinuity observed in exponential law. According to our finding, in order to limit the artificial compliance and computational time, large element size is recommended, however, in fracture problems, small element size around crack tip is essential to capture the cohesive zone behavior. To escape the dilemma, we modify the cohesive zone enlargement approach presented in the literature (Dugdale, 1960) and adopt it for arbitrary crack propagation. The modified methodology enlarges cohesive zone size by reducing the cohesive strength only around crack tips to allow more cohesive elements inside the cohesive zone. Two benchmark numerical simulations are carried out to verify the modified methodology.