Finite Element Numerical Approach Research Articles

Implementing the finite element numerical approach to optimize thermosolutal convection (TSC) energy imparted by discrete heat and solute sources in generalized Newtonian fluid flow in square enclosure

AbstractMesmerizing utilizations of thermosolutal convection (TSC) have been found in metallurgical and petrochemical procedures, crystal growth, thermal exchangers, nuclear waste disposal, and building environment control. In the current study, we considered three heat and solute sources on the left boundary of the cavity, which raises the significance of studying multiple chemical and civil engineering phenomena. Therefore, the prime motivation to commence this work is to attain the optimization of thermosolutal attributes characterized by non-Newtonian (power–law) liquid in the presence of installed sources. For this purpose, the natural convective flow governed by the nonpersistent impact of buoyancy forces is encompassed in the square enclosure. In addition to the source location, the vertical boundaries are considered to be cold, whereas the horizontal boundaries are kept insulated. Owing to the free convective flow, no compositional and thermal gradients are induced by lid movement, and all walls are prescribed with no-slip constraints. To examine the transport mechanism, structuring of problem is attained in the form of dimensional governing expressions by employing conservation laws. Subsequently, constitutive equations in a dimensionless format are accessed through similar variables. The finite element approach is employed to find the solution using COMSOL Multiphysics software. The deviations in the thermal and solutal fields are examined against the involved physical parameters by illustrating graphs and tables. Quantities of interest, such as the mean Nusselt and Sherwood numbers, are also computed against sundry parameters. The assurance of the computed results is validated by constructing a comparison with published studies. A grid sensitivity test is also executed to ensure the credibility of the built-in software (COMSOL). It is observed that the averaged heat and mass flux coefficient diminishes with an elevation in the magnitude of the power-law index (n), irrespective of the change in other involved parameters. The average Sherwood number tends to increase for a positive magnitude of (N) in contrast to negative values of (N). The average heat flux and average mass flux coefficients increase until the Prandtl number (Pr) reaches a value of 5 in shear thinning case at $$Ra\ge {10}^{5},$$ R a ≥ 10 5 , whereas, for n > 1 there is no substantial effect on either the average heat flux coefficient or average mass flux coefficient.

The effect of blanket system and port plugs on the harmonic components of error field and optimizing approach investigation

The fusion plasma is sensitive to the penetration of the toroidal mode numbers harmonic components of the error fields (EFs), and the toroidal mode components of the EFs are closely tied to the toroidal distribution of the magnetic field source. The primary source of EFs within the magnetic field sources is the current source, such as the magnet system, while the magnetic field produced by magnetized ferromagnetic materials may also generate EFs. The ferromagnetic field source, such the reduced-activation ferritic-martensitic steel, represent a smaller portion of the EFs source. However, the use of ferromagnetic materials is expected to increase significantly as tokamak research transitions from experimental devices to demonstration and commercial reactors, particularly for the structural materials of in-vessel components and port plugs. Predictably, the EFs induced by ferromagnetic materials will increase and may even surpass the design specifications. In this study, the EFs introduced by the water-cooling ceramic breeder blanket system and the vacuum vessel port plugs of China Fusion Engineering Test Reactor are comprehensively analyzed by an analytical approach and finite element numerical approach, which is based on the Fourier decomposition. The results reveal a clear linear relationship between the EFs formed by the saturated magnetization module and its rigid displacement deviating from periodic symmetry, as well as the same behavior in EFs and overall magnetization intensity. Compared to the assembly error of the blanket system, the EFs that may be introduced by the equatorial ports and plugs are substantial, including larger toroidal mode harmonic components that can lead to lock mode and disruption. Moreover, using the correlation between harmonic components and symmetrical periods, specific toroidal mode components can be selectively shielded.

A NUMERICAL METHOD FOR 3D TIME-DEPENDENT MAXWELL’S EQUATIONS IN AXISYMMETRIC SINGULAR DOMAINS WITH ARBITRARY DATA

In this article, we propose to solve the three-dimensional time-dependent Maxwell equations in a singular axisymmetric domain with arbitrary data. Due to the axisymmetric assumption, the singular computational domain boils down to a subset of R2. However, the electromagnetic field and other vector quantities still belong to R3. Taking advantage that the domain is transformed into a two-dimensional one, by doing Fourier analysis in the third dimension, one arrives to a sequence of singular problems set in a 2D domain. The mathematical tools of such problems have been exposed in [4,19]. Here, we derive a variational method from which we propose an original finite element numerical approach to solve the problem. Numerical experiments are also shown to illustrate that the method is able to capture the singular part of the solution. This approach can also be viewed as a generalization of the Singular Complement Method to three-dimensional problem.

Improvement of melting performance in a longitudinal finned latent heat thermal energy storage unit

AbstractThis article presents an analysis and enhancement of the charging behavior of a double‐pipe LHTES unit with longitudinal fins for concentrated solar power applications using a finite element numerical analysis approach. The finite element approach is applied to this numerical analysis by using “COMSOL Multiphysics” software. The investigated LHTES system has an operating temperature range of 180°C‐300°C and uses “DelcoTerm Solar E 15” as the heat transfer fluid (HTF) with a eutectic inorganic mixture of sodium nitrite and sodium nitrate as the phase change material (PCM). While also taking into account the impact of the tube material and the number of fins, the primary goal of this study is to evaluate performance improvement by changing the thickness and number of fins in a linked manner without changing the storage unit capacity. The results show a maximal impact on thermal performance which decreased the melting time by 46% and the charging time by 49.6% for the configuration with a fin thickness of 1 mm, 27 longitudinal fins, an inner tube made of aluminum, and a mass flow rate of 60 kg/h.

High power density thermal management of discrete semiconductor packages enabled by additively manufactured hybrid polymer-metal coolers

Discrete-packaged wide bandgap (WBG) semiconductor devices provide a flexible and cost-effective solution for scalable highly dense power electronics. However, their utilization at high power levels is limited due to various challenges, while the effective thermal management if one of them. We develop a liquid cooled thermal management solution for discrete semiconductor packages using polymer-metal hybrid cooling structure design and integration. Coolant flowing through an additively manufactured polymer manifold is guided to finned metal heat sinks having low thermal resistance and overall mass. Here, we study a number of prototypes designed for integration of silicon carbide (SiC) MOSFETs in TO-247 package. The cooling integration is benchmarked with a baseline design having an aluminum heat sink with square inline pin fins. The cooling strategy is tested experimentally with results used to validate a finite element numerical approach. Fin design parameters including fin height, thickness, spacing, and arrangement are studied to assess their impact on heat sink temperature and pressure drop. Zigzag fins showed the most promising performance when compared to straight fins, inline fins, and staggered pin fins. The zigzag design showed lower maximum temperatures at comparable pressure drop with the baseline design. The impact of thermophysical properties of the cooling fluid (water, ethylene glycol, and Novec 7300), heat sink (copper and aluminum), and electrical isolation (gap pad, aluminum nitride) are also reported. The optimal design employing zigzag fins with a copper heat sink and an aluminum nitride heat spreader achieved 32.5 % improvement in thermal performance over the baseline design with a modest 60 % increase in pressure drop and 68 % higher mass. The optimized design enables a maximum heat rejection capability of 225 W per single MOSFET package, an equivalent to 75 W/cm2 heat flux dissipation using single phase cooling.

Importance of nanochannels shape on blue energy generation in soft nanochannels

Energy production is one of today's most pressing issues. Finding alternative energy sources has become one of the hottest research areas for scholars due to the limited use of fossil resources. Using water sources of different concentrations is one of the newest methods of energy production. Due to the energy of mixing fluids, two fluids of different concentrations on both sides of a nanochannel membrane can produce energy. Given the costs and restrictions of studying complex systems experimentally, simulation is required to investigate their behavior and determine the best states. As a result, using an energy production strategy, this work explores the effect of nanochannel shape on the ion transfer behavior. Asymmetric (bullet, trumpet, cigarette, hourglass, and hill) and symmetric (cylindrical) geometries were utilized. The effects of different geometries, soft layer density, and concentration ratio on energy production considering the effect of ion partitioning in soft surfaces was investigated. A finite element numerical computation approach was employed to solve the Poisson-Nernst-Planck and Navier-Stokes equations at steady-state. The best geometry at various concentration ratios to create the most performance were: cylindrical and cigarette for osmotic current, hourglass and trumpet for transmission number, hourglass and trumpet for diffusion potential, cylindrical for electrical conductivity, cylindrical and trumpet for power capacity, and hourglass and trumpet for energy conversion efficiency, respectively. In the case of considering the ion partitioning at a concentration ratio of CH/CL=1000for trumpet geometry, raising the soft layer's charge density from NPEL/NA=25to100mol/m3 boosted the maximum produced power by about 25 times, from 0.215pW to 5.35pW.

Experimental and numerical evaluation of formability in three-layer metallic sheets with various layer arrangements

Multi-layer metallic sheets are composed of two or more metallic layers connected to each other to achieve desirable features based on the various properties of the constituent layers. This study attempted to predict the forming limits and deformation behavior of three-layer metallic sheets. Additionally, the effects of the layer arrangement on the forming limit diagram (FLD), stress triaxiality, and limiting dome height (LDH) were investigated using a finite element numerical approach. To this end, three-layer metallic sheets made of aluminum (AA3004), stainless steel (SUS304), and copper (Cu1011) bonded by polyurethane as the bonding layer were employed. The numerical results were validated using the experimental results of Nakajima stretch-forming tests. The numerical results were in good agreement with the experimental data. The results indicate that the formability of the three-layer sheet increased by placing the AA3105 layer as the inner layer in contact with the punch, the Cu1011 layer in the middle, and the SUS304 layer as the outer layer. Therefore, the formability of the Al-Cu-SUS sheet was higher than that of the other layer arrangements. Moreover, the results show that the material properties, particularly the tensile strength, play a key role in controlling the FLD of the three-layer sheets.

Lateral Load Capacity and p-Multiplier of Group Piles with Asymmetrical Pile Cap under Seismic Load

Earthquakes are a high-risk natural phenomenon in Indonesia, which is between three tectonic plates: the Eurasian, Pacific, and Indo–Australian plates. This study examines the response of bored piles with asymmetrical pile cap in the Auditorium Building of Brawijaya University to seismic loads, which is still rare to conduct this research. This study assessed based on 3D finite element-numerical approach, where lateral resistance and p-multiplier values compared on the effects of combination lateral loads, pile stiffness, and soil stiffness. The behavior of lateral resistance and deflection group piles with asymmetrical pile cap and single pile with square pile cap gives a good agreement. The side slope of the pile cap can increase the shear zone, increase the lateral resistance, and the most considerable lateral resistance to the lowest occurs in the horizontal direction, opposite the loading direction. In addition, the pile configuration that is not symmetrical gives an increasing p-multiplier value followed by an increasing deflection and the p-multiplier from the 3D finite element method was within the recommended range.

Differential formulation and numerical solution for elastic arches with variable curvature and tapered cross-sections

In this paper, an alternative analytical and numerical formulation is presented for the solution of a system of static and kinematic ordinary differential equations for curved beams. The formulation is represented here as being useful in the structural evaluation of arch structures and it is propaedeutic to be used in optimization frameworks. Using a finite-difference method, this approach enables the evaluation of the best solution sets accounting for (1) various arch shapes (i.e. circular, quadratic and quartic polynomial forms); (2) different loading combinations; (3) cross-sections varying along the arch span; and (4) different global radius of arch curvature. The presented original approach based on finite-difference, produces solutions with a good precision in a reasonable computational time. This method is applied to 4 different arch case studies with varying rise, cross-section, loading and boundary conditions. Results show good agreement with those obtained using a numerical finite element approach. The presented approach is useful for the (preliminary) design of arches, a common and efficient structural typology for road and railway bridges and large span roofs. As far as buckling verifications are concerned, the comparisons in terms of maximum acting axial force and critical axial force computed is reported in order to consider the effect of instability phenomena coming to trace for each arch configuration the feasible domain.

Numerical Analysis of Natural Convection in a Concentric Trapezoidal Enclosure Filled with a Porous Medium

Numerical study of natural convection around a heated trapezoidal block of different sizes located centrically in a larger trapezium has been investigated. The annulus between the trapeziums is filled with porous media. The sides of the inner trapezium are heated to a fixed temperature (T_h), and the slanted walls of the outer trapezium are adiabatic while its upper and lower walls are heated to temperatures of 〖T_c+(T_h-T_c)sin〗⁡(πx⁄L) and 〖T_h+(T_h-T_c)sin〗⁡(πx⁄L) respectively. The finite element numerical approach was used to solve the relevant dimensionless equations. Results are gotten for salient parameters including; modified Rayleigh number (10≤Ra_m≤ 1000), Darcy number (10^(-5)≤Da≤ 10^(-2)), and area ratio (1/5≤AR≤ 1/3). The results of this study are shown as isothermal contours, stream functions, and average Nusselt number. The results show that increasing Ra_m improves heat transfer; however, the response of thermal characteristics to AR increment depends on the range of Darcy number considered. Results from this study find application in ingot treatments and microchannel cooling among others.

A Finite Element Analysis Based Approach to Understand the Effects of Targeted Minimum Quantity Cutting Fluid Application on Surface Integrity

Minimum quantity cutting fluid application is targeted upon the rake face and the flank face of the tool to improve the tool life and surface integrity. By strategically targeting/applying the cutting fluid on the tool rake and flank surfaces, the temperatures along the rake face and flank face are altered, thereby affecting surface machining-induced residual stresses. The magnitude of temperature alteration and thereby the machining-induced residual stresses can be affected by the amount of targeted cutting fluid and the composition of the targeted cutting fluid. In this paper, the authors use a numerical finite element approach to understand the effects of the strategically targeted cutting fluid on the flank face improves the sub-surface residual stresses by reducing the tool-tip machining temperatures when machining AISI 1045 annealed steel with an uncoated cemented carbide tool. The machining-induced residual stresses generated from the finite element model have shown that the temperatures near the tool tip reduce by targeting cutting fluid on the flank face. The targeted cutting fluid reduced the machined workpiece temperatures and also assisted in cooling the cutting tool from the flank and rake side.

Topological interface states in translational metamaterials for sub-wavelength in-plane waves

In this work, we numerically investigate topological interface states for subwavelength in-plane waves in elastic metamaterials composed mainly of translational resonators. The relationships among bandgap, effective mass and effective stiffness are analyzed for the mass-spring and continuum models. Besides, the locations of stop-bands and negative effective parameters are manipulated by tuning the parameters of translational resonances. It is observed that the topological phase transition occurs to the single mass-negative region from the single stiffness-negative region while the Zak phase varies following a shift in parameter changing. It also implies that the characteristic behavior of topological interface elastic waves can exist in the sub-wavelength region. Furthermore, the frequency response is analytically and computationally investigated in one heterostructure composed of two lattices with different negative effective properties, which show the existence of the sub-wavelength topological interface mode. Finally, we have further verified the dynamic behavior of the interface state by employing the transient response analysis computed by the finite element numerical approach.

Contribution of using geogrid under a shallow foundation on sand subjected to static and repeated loads: Laboratory testing and numerical simulations

This paper focuses on the use of a certain punched and drawn geogrid to increase the bearing capacity of a circular shallow foundation subjected to a combination of static and repeated loads. In the experiments, the foundation is first subjected to a prespecified static load, afterwards, a repeated load derived in different proportions of the applied static load is superimposed to that static load. The variables investigated in the tests are the number of geogrid layers, the amplitude of repeated load, and the number of load cycles. The effect of these variables is also investigated by a finite element numerical modeling approach verified with one-dimensional site response analysis, and as a consequence of this effort that refers to the innovation of the study, the consistency between the results obtained from both methods is observed. The test results show that the displacements of the shallow foundation increase rapidly in the first 100 load cycles in all cases. After that, the rate of increase is reduced until about 2000 load cycles and the displacements become negligible. From the experiments, 2 geogrid layers were found to be quite effective in reducing displacements due to both static and dynamic loading cases. In other respects, finite element simulations of the physical experiment have produced numerical results in good agreement with the test results. Plus, the main contribution of the numerical simulation is to indicate the deformed mesh outputs of the model including the geogrids for the foregoing variables.

Optimization procedure for parameter determination of caboche kinematic hardening model

The ratcheting behavior and prediction of 316L stainless steel pipe was developed using numerical finite elementapproach. The Chaboche model parameters to be used in the numerical method were adopted from symmetric post monotonic teston the pipe. The significant property, the elastic limitof the material,was extracted using incremental cyclic uniaxial test. Comparison between two well-known optimization methods, Particle Swarm Optimization and Genetic Algorithm gave the former a slightly better correlation with experimental tests.The Chaboche model in ANSYS was utilized to predict the uniaxial ratcheting behavior of the pipe specimen. Theclose comparison of rate of ratcheting between finite element simulation and experimental test indicates that accurate elastic limit extraction from post monotonic test alone results in improved ratcheting prediction, with PSO method adopted to optimize ratcheting parameters.

Tunable topological interface states in one-dimensional extended granular crystals

This paper theoretically and numerically investigates a topological interface state in a highly tunable granular crystal. This system allows us to tune the contact stiffness in a controllable manner, via altering the precompression between the spheres. The spatial change of particles contact stiffness results in band inversion and topological phase transition in the first kind of sub-lattice, which requires a linear and Hertzian contacts stiffness corresponding to the two interface interactions between particles in one unit cell. The second kind of sub-lattice only composed of particles is developed, of which topological state is not adjusted during the pre-compressed process. Therefore, a one-dimensional extended granular crystal is established by placing adjacently two different sub-lattices. Furthermore, we analytically and computationally consider the frequency response of this periodic structure, and further predict the existence of a tuning-frequency topologically interface mode. Finally, this phenomenon is confirmed through employing the transient response analysis calculated by the state space method and the finite element numerical approach.

Cell dynamics and natural frequencies: scaling and shape matters

Cell dynamics is one of the most investigated areas under the field of biomechanics. Scaling plays a crucial role in determining the dynamic characteristics of biological systems. In the present investigation, cuboidal and cylindrical models of different scales are analysed to depict the dependence of natural frequency on the scaling factors. Three approaches, namely lumped mass system, finite element model (FEM) and numerical approach using Ansys are used to determine the fundamental natural frequencies. Different scaling factors, namely nano, micro (original size), millimeter and meter are considered for the analysis. The results indicate that the natural frequency varies inversely with the size of the cell by the same factor. A simple mathematical relation is derived to support this claim. Results are illustrated with numerical examples and corresponding mode shapes are reported.

Innovative pre-stressing and cambering of timber-to-timber composite beams

The paper focuses on an innovative method to pre-stress and camber composite beams. The method relies on the compression force that can be generated by distributed screw fasteners inserted at an angle to the axes of the elements forming the composite structure (no external props or tendons are needed to pre-stress the structure). The method principles, which are applicable to different structural materials, are explained and then validated by referring to timber-to-timber composite (TTC) solutions. An analytical formulation to predict the final camber and the internal forces generated by the method is also provided. Additionally, a finite element numerical approach was developed and used to investigate the influence of the relevant parameters. To validate both the analytical formulation and the modelling approach, two full-scale TTC floor specimens, with a 6.4 m span were assembled by adopting the method presented herein and then tested to failure. A remarkable agreement was observed between the predictions from the analytical, numerical models and the experimental evidence. From the research outcome, the proposed assembly method appears capable of producing significant levels of camber and pre-stress that can be accurately predicted and designed.

Surface Induction Hardening of Steels: Process Modelling and Numerical Simulation

Heat treatments are widely used in industry to improve the surface behavior of components exposed to external mechanical actions and, therefore, undergoing wear phenomena. If compared to the conventional thermal treatments, induction hardening is an interesting candidate solution when the effect should be limited to the surface without affecting the microstructure and properties at the material core. Furthermore, this solution is appealing considering energy saving and cost reduction. In this process, an intense electric alternating current flows through a conductive coil enveloping the component to be treated. Such current generates a magnetic field and, as a consequence, eddy currents arise in the conductive work-piece providing a heat generation by the Joule effect. Due to this mechanism, the induction heating is characterized by faster heating rates with respect to the heating in a hot furnace. On the other hand, the induction hardening process requires a more challenging control of the operative parameters, namely the current density and frequency and the coil advancing speed. Numerical modeling and simulation are recognized as a very useful tool to predicting the effects induced by a treatment, avoiding undesired insufficient- or over-heating. The present work deals with a finite element numerical approach to the simulation of an induction hardening treatment of a steel component. The model is based on the subsequent solution of two numerical submodels. Firstly, the electro-magnetic field generated by the current flowing through a coil surrounding the processing part is inferred solving the Maxwell governing equations. Then, the magnetic field is used as input load for the subsequent heat transfer transient finite element model. The influence of the current density and frequency as well as other processing parameters on the magnetic and thermal fields is discussed.

Implication of end restraint in triaxial tests on the derivation of stress–dilatancy rule for soils having high compressibility

Constitutive models for soils are developed and validated against laboratory tests assuming these give representative information on the true material behaviour. However, data from standard laboratory tests reflect the sample response rather than the true material behaviour, due to nonuniformities in stresses and strains generated over the experimental test. The work examines the implications of end restraint on the definition of the stress–dilatancy rule of highly compressible soils with a finite element numerical approach. The numerical model replicates a reconstituted peat, typically characterized by a combination of high compressibility and high friction angle, which increases the severity of end restraint effects. Simulated results show that the global measurements from standard triaxial tests with rough end platens would not give the proper stress–dilatancy rule, if they were interpreted as the response of a single soil element at the constitutive level. Both overestimation and underestimation of the true dilatancy compared to the material response can be observed, depending on the deformation mode. To support the validity of the numerical results, experimental findings from drained triaxial tests on reconstituted peat are presented. Practical indications are given on how the standard interpretation of drained triaxial tests data on peats can be improved.

Fatigue crack initiation prediction using phantom nodes-based extended finite element method for S355 and S690 steel grades

The assessment of fatigue crack initiation behavior of steel structures is essential and important especially to improve the application of high strength steel in construction. For a complete understanding of fatigue endurance, it is necessary to combine the phenomenological damage model with finite element numerical approach. In this paper, phantom nodes-based extended finite element method is used to predict the fatigue crack initiation of steel material, considering a prediction by XFEM of coupon tests made of steel grades S355 and S690. A user-defined fatigue damage initiation subroutine based on Smith, Watson, and Topper (SWT) damage model combined with non-linear isotropic/kinematic cyclic hardening model is implemented to predict fatigue crack initiation. The proposed method is successfully validated based on fatigue coupon test results of both steel grades, S355 and S690.