In this work, a finite element simulation of a commercial thermoelectric cell, working as a cooling heat pump, is presented. The specially developed finite element is three-dimensional, non-linear in ...its formulation (using quadratic temperature-dependence on material properties) and fully coupled, including the
Seebeck,
Peltier,
Thomson and
Joule effects. Another special interface finite element is developed to prescribe the electric intensity, taking advantage of repetitions and symmetries. A thorough study of the distributions of voltage, temperature and the corresponding fluxes is presented, and the performance of the cell is compared with that of the manufacturer and with simplified analytical formulations, showing a good agreement. Combining the finite element model with the Monte Carlo technique, a sensitivity analysis is presented to take into account the performance dependence on the material properties, geometrical parameters and prescribed values. This analysis, which can be considered a first step to optimize these devices, concludes that the temperature-dependence of the material properties of electric conductivity and
Seebeck coefficient is very relevant on cell performance.
Thermoelectric materials assembled in Peltier cells are an increasingly widespread option for generating electricity from residual sources and refrigeration, even at the nanoscale. These cells can ...cool below the nominal temperatures with an electric pulse, during short periods and for applications such as laser devices or microchips. The present article uses heuristic algorithms to improve the response of a Peltier cell by concurrently optimizing the pulse and geometry of its thermoelements. The study is based on the Finite Element method, handling full coupling and dynamics of the thermal, electric, and mechanical fields and temperature dependency of the material properties. The optimization algorithm is Simulated Annealing, capable of discarding local minima to reach robust results and permitting set limiting factors such as the maximum stress. The main novelty lies in multilayered geometries and pulse shapes that can reproduce any geometry and pulse virtually. First, a complete parametric analysis under constant pulse is presented to understand the complexities of the temperature, electric flux, and stress distributions in these layered geometries. Second, combined optimizations are discussed. The targets are overcooling temperature, time to reach it, overheating minimization, overcooling duration, and combinations. In the best cases, the first target is doubled, the second is reduced to a few milliseconds, the third is null, and the duration can be 95% of the pulse while reducing the stress up to 40%.
•The proposed methodology develops custom-made solutions for dynamic thermoelectrics.•Multilayered geometries and piecewise pulses can design any Peltier cell.•Maximum overcooling of almost 16 °C and maximum overcooling time of almost 10 s.•Neck positions control overheating and time to reach the minimum temperature.•Optimized geometry and pulse reduce stress, an optimization limiting factor, by 40%.
Understanding seedling performance across resource gradients is crucial for defining the regeneration niche of plant species under current environmental conditions and for predicting potential ...changes under a global change scenario. A 2-year field experiment was conducted to determine how seedling survival and growth of two evergreen and two deciduous Quercus species vary along gradients of light and soil properties in two Mediterranean forests with contrasting soils and climatic conditions. Half the seedlings were subjected to an irrigation treatment during the first year to quantify the effects on performance of an alteration in the summer drought intensity. Linear and non-linear models were parameterized and compared to identify major resources controlling seedling performance. We found both site-specific and general patterns of regeneration. Strong site-specificity was found in the identity of the best predictors of seedling survival: survival decreased linearly with increasing light (i.e. increasing desiccation risk) in the drier site, whereas it decreased logistically with increasing spring soil water content (i.e. increasing waterlogging risk) in the wetter site. We found strong empirical support for multiple resource limitation at the drier site, the response to light being modulated by the availability of soil resources (water and P). Evidence for regeneration niche partitioning among Quercus species was only found at the wetter site. However, at both sites Quercus species shared the same response to summer drought alleviation through water addition: increased first-year survival but not final survival (i.e. after two years). This suggests that extremely dry summers (i.e. the second summer in the experiment) can cancel out the positive effects of previous wetter summers. Therefore, an increase in the intensity and frequency of summer drought with climate change might cause a double negative impact on Quercus regeneration, due to a general reduction in survival probability and the annulment of the positive effects of (infrequent) 'wet' years. Overall, results presented in this study are a major step towards the development of a mechanistic model of Mediterranean forest dynamics that incorporates the idiosyncrasies and generalities of tree regeneration in these systems, and that allow simulation and prediction of the ecological consequences of resource level alterations due to global change.
•High pulse gains cannot be applied: limits in reachable overcooling and stress.•Non-thermoelectric parts are fundamental for thermal dynamics, stress calculations.•Stress distributions are complex, ...tend to concentrate in corners at all instants.•Max stresses occur at end of pulse and predominant component is the vertical.•A pulse threshold variable with TE length exists so that any time can be applied.
This paper presents a numerical study on the influence of pulsed electric signals applied to the overcooling of thermoelectric devices. To this end, an experimental setup taken from the literature and a commercial cell are simulated using a complete, specially developed research finite element code. The electro-thermal coupling is extended to include the elastic field, demonstrating that the increment of cooling can produce mechanical failure. Numerical results are developed and the variation of overcooling versus pulse gain and versus duration is validated towards a new analytical expression and the experimental data. The issue of optimal intensity at steady-state is also newly developed. Thermal and mechanical trends are presented using constant and variable (with temperature) material properties for a single thermoelement. While some of the first trends are similar to those of published works, others are different or directly new, all closer to those of the experiments. The mechanical results have not been thoroughly studied until recently. The three-dimensional finite element mesh includes non-thermoelectric materials that are fundamental for the current study. Distribution of stresses during steady and transient states are shown inside the thermoelement, for five components and for the combined Tresca stress. Concentrations at corners of the lower side appear close to the cold face. Due to these concentrations, 27-node isoparametric, quadratic brick elements are used. It is shown that the mechanical field is an important factor in the design of pulsed thermoelectrics, since for practical applications the stress levels are close or slightly above the admissible limits.
•To find optimal electric intensity pulse for overcooling with thermoelements.•Heuristic optimization simulated annealing. Non-linear coupled dynamic finite element.•Multi-objective-parametric: ...overcooling, uptime, time max. overcooling, overheating.•Parametric study and coupling with mechanical field to limit maximum stresses.
The objective of this work is to determine the optimal shape, gains and duration of an electric pulse applied to a Peltier cell, together with the length of the thermoelectric to maximize cooling while minimizing electric consumption. For this purpose, a fully coupled, multiphysics, dynamic finite-element model, which solves for the thermal, electric and mechanical fields is used. Because of the demanding computing requirements of the optimization process, a special mesh is designed and a convergence analysis is carried out before using the multiphysics model. The highly non-linear optimization is done by simulated annealing, a heuristic algorithm in the Markov chain Monte-Carlo family. A preliminary parametric investigation is presented, analyzing the impact of some of the parameters. The results of this preliminary analysis help to understand the effect of the different shapes in the evolution of the cold face temperature. Some of these results are expected and have already been discussed elsewhere, but others can only be explained after further analysis and a full system modeling. Pulse optimization is multiobjective and multiparametric, i.e., it can consider several targets such as maximizing the cooling temperature, the cooling duration or others. The trade-offs between the different targets are studied. In all cases, stresses inside the thermoelement are examined at all points, and the pulses must meet the restriction that an equivalent stress is not above the allowable value.
Masonry structures are constructions made of discontinuous blocks that require unique numerical methods incorporating contact, friction, and cohesion models for their analysis. Given the large number ...of aging structures of this type still in use, there is a demand to combine these numerical methods with optimization algorithms to help in structural health monitoring. This paper combines discrete and finite methods with genetic algorithms for parametrizing two masonry structures. The first is a bridge with a large number of blocks, the material properties of which are estimated with a small error. Since the loads are low, the mortar’s properties are irrelevant. The second is a buried ogival vault; starting from only four pieces of experimental data from the literature and related with the failure loads, the material and contact properties are calculated. From them, many other failure loads are again iteratively calculated and favorably compared with the rest of the data. To further validate the inverse problem, the computed properties are used for several runs of the same vault but under different loads, obtaining again an almost perfect agreement with the experiments.
•Wall experimental crack simulated with FemDem getting same trend and 17% max. error.•Masonry bridge discretized with 212 blocks, 529 finite elements, 78 control nodes.•Young’s moduli, Poisson coef and density identified with only 2.3%, 4%, 2.2% errors.•Contact and material parameters optimized from global experimental results.•Ogival vault global experiment results fitted well with four conditions’ data.
In the present work, a three-dimensional, dynamic and non-linear finite element to simulate thermoelectric behavior under a hyperbolic heat conduction model is presented. The transport equations, ...which couple electric and thermal energies by the Seebeck, Peltier and Thomson effects, are analytically obtained through extended non-equilibrium thermodynamics, since the local equilibrium hypothesis is not valid under the hyperbolic model. In addition, unidimensional analytical solutions are obtained to validate the finite element formulation. Numerically, isoparametric eight-node elements with two degrees of freedom (voltage and temperature) per node are used. Non-linearities due to the temperature-dependence on the transport properties and the Joule effects are addressed with the Newton–Raphson algorithm. For the dynamic problem, HHT and Newmark-β algorithms are compared to obtain accurate results, since numerical oscillations (Gibbs phenomena) are present when the initial boundary conditions are discontinuous. The last algorithm, which is regularized by relating time steps and element sizes, provides the best results. Finally, the finite element implementation is validated, comparing the analytical and the numerical solutions, and a three-dimensional example is presented.
Theoretical explanation for thermoelectric hysteresis in photovoltaic materials. Energy dissipation introduced by dissipative fluxes related to relaxation times. Explanation verified using finite ...element code developed in previous publications. Inverse problem for characterization of general properties from one experiment. Numerical simulations for future laboratory experiments to validate explanation.
The main objective of the present work is to develop and prove a theoretical explanation based on the Extended Non-Equilibrium Thermodynamics (ENETs) for the hysteretical thermoelectric behavior observed in certain thin-film photovoltaic materials. The ENET introduces dissipative fluxes in the entropy balance that could explain this behavior. To verify this explanation from a numerical point of view, results are generated using a Finite Element (FE) formulation based on the ENET and already developed in previous publications by the authors. In addition, an identification Inverse Problem (IP) is formulated; a cost function is defined as the quadratic difference between experimental and numerical results and the IP is solved minimizing the cost function using genetic algorithms. The conclusion is that the loop-like distributions are due to energy dissipation introduced by dissipative fluxes that are closely related with relaxation times. Also, the FE-IP combination permits to find an approximated characterization of properties for several materials from single experimental curves. Finally, several numerical simulations are proposed for laboratory experiments to further validate the theoretical interpretation and to confirm the relation between relaxation times and hysteresis.
► Behavior of masonry arches studied using Discontinuous Deformation Analysis DDA. ► Equilibrium reached by contact forces in blocks calculated with contact algorithm. ► Masonry blocks simulated by ...macroblocks composed by pseudo-rigid blocks glued by contact. ► Linkage allows simulation collapse by instability or stress failure accurately. ► Results compared with experiments with very good agreement.
The behavior of buried masonry arches is studied in this article using the Discontinuous Deformation Analysis (DDA), a numerical method that allows for the physical simulation of the intrinsic structure discontinuities since it is based on contact and friction among pseudo-rigid blocks. Two types of arches (or vaults) are studied with a specially developed computer program, one of semicircular and another of ovoidal shape. The loads are self-weight, lateral filling, embankment thrusts and concentrated (through a short distribution) forces close to the peak. These loads are transformed into point forces applied to the center of gravity of each block with simple formulae from classical mechanics. Equilibrium is reached in the whole structure through contact forces calculated with a standard contact algorithm: penalty plus Coulomb friction.
DDA-macroblocks composed of linked (through penalty contact springs) pseudo-rigid blocks are formulated. This linkage allows for the simulation of collapse by instability or by stress compressive failure more accurately than traditional DDA analyses, for instance funicular polygons.
The numerical results are compared with those of the experiments taken from the literature with, for most cases, very good agreement given the uncertainties on geometry and material properties and given the intrinsic quality dispersion of masonry structures. Collapse loads as function of number of joints, safety factors and limit point forces from the numerical and experimental results are compared. The hinges that appear prior to collapse are also compared, obtaining again for most cases very good agreement.
The present paper provides a dynamic, non-linear and fully coupled Finite Element (FE) formulation based on the Timoshenko beam theory to study elasto-thermoelectric responses in thermoelectric ...devices. The two main motivations of this work are: i) to study mechanical responses in thermoelectric devices, which must be taken into account in the design of Peltier cells due to the fragility and relative low strength of the semiconductors, and ii) to provide a numerical tool that decreases the CPU time to allow the introduction of designs based on optimization processes and on sensitivity analyses that could require many evaluations. In order to undertake the objectives of this work, the general three-dimensional governing equations are reduced to one-dimensional ones by means of several assumptions. Then, a set of five multi-coupled partial differential equations is obtained. The resultant expressions are thermodynamically consistent and form a multi-coupled monolithic FE formulation, differently to stagger formulations that require two separated steps to reach the final result. Numerically, this set of multi-coupled equations is discretized using the FE method and implemented into FEAP Taylor, 2010 1. For a proper validation of the code, four benchmarks are performed using one-dimensional dynamic analytical solutions developed by the authors. Finally, this formulation is compared with a three-dimensional FE formulation also developed by the authors in Pe´rez-Aparicio et al., 2015 2 to model a commercial Peltier cell. This comparison reveals that: i) relative errors are lower than 13% and ii) CPU times decrease significantly, more than one order of magnitude. In conclusion, the beam thermoelectric formulation is an accurate model that reduces CPU time and could be used in future design of thermoelectric devices.
•Elasto-thermoelectric beam formulation based on the Timoshenko beam model.•Monolithic and thermodynamically consistent finite element formulation.•Analytical solutions to study elasto-thermoelectric behavior in thermoelements.•Study of mechanical behavior of commercial Peltier cells.•Comparison between three-dimensional and one-dimensional finite element formulations.
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