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Numerical solution of the heat equation with non-linear, time derivative-dependent source term
(2010)
The mathematical modeling of heat conduction with adsorption effects in coated metal structures yields the heat equation with piecewise smooth coefficients and a new kind of source term. This term is special, because it is non-linear and furthermore depends on a time derivative. In our approach we reformulated this as a new problem for the usual heat equation, without source term but with a new non-linear coefficient. We gave an existence and uniqueness proof for the weak solution of the reformulated problem. To obtain a numerical solution, we developed a semi-implicit and a fully implicit finite volume method. We compared these two methods theoretically as well as numerically. Finally, as practical application, we simulated the heat conduction in coated aluminum fibers with adsorption in the zeolite coating. Copyright © 2010 John Wiley & Sons, Ltd.
Lightning safety guidelines
(2010)
Quantifying and minimizing uncertainty is vital for simulating technically and economically successful geothermal reservoirs. To this end, we apply a stochastic modelling sequence, a Monte Carlo study, based on (i) creating an ensemble of possible realizations of a reservoir model, (ii) forward simulation of fluid flow and heat transport, and (iii) constraining post-processing using observed state variables. To generate the ensemble, we use the stochastic algorithm of Sequential Gaussian Simulation and test its potential fitting rock properties, such as thermal conductivity and permeability, of a synthetic reference model and—performing a corresponding forward simulation—state variables such as temperature. The ensemble yields probability distributions of rock properties and state variables at any location inside the reservoir. In addition, we perform a constraining post-processing in order to minimize the uncertainty of the obtained distributions by conditioning the ensemble to observed state variables, in this case temperature. This constraining post-processing works particularly well on systems dominated by fluid flow. The stochastic modelling sequence is applied to a large, steady-state 3-D heat flow model of a reservoir in The Hague, Netherlands. The spatial thermal conductivity distribution is simulated stochastically based on available logging data. Errors of bottom-hole temperatures provide thresholds for the constraining technique performed afterwards. This reduce the temperature uncertainty for the proposed target location significantly from 25 to 12 K (full distribution width) in a depth of 2300 m. Assuming a Gaussian shape of the temperature distribution, the standard deviation is 1.8 K. To allow a more comprehensive approach to quantify uncertainty, we also implement the stochastic simulation of boundary conditions and demonstrate this for the basal specific heat flow in the reservoir of The Hague. As expected, this results in a larger distribution width and hence, a larger, but more realistic uncertainty estimate. However, applying the constraining post-processing the uncertainty is again reduced to the level of the post-processing without stochastic boundary simulation. Thus, constraining post-processing is a suitable tool for reducing uncertainty estimates by observed state variables.
Objective: As high-field cardiac MRI (CMR) becomes more widespread the propensity of ECG to interference from electromagnetic fields (EMF) and to magneto-hydrodynamic (MHD) effects increases and with it the motivation for a CMR triggering alternative. This study explores the suitability of acoustic cardiac triggering (ACT) for left ventricular (LV) function assessment in healthy subjects (n=14). Methods: Quantitative analysis of 2D CINE steady-state free precession (SSFP) images was conducted to compare ACT’s performance with vector ECG (VCG). Endocardial border sharpness (EBS) was examined paralleled by quantitative LV function assessment. Results: Unlike VCG, ACT provided signal traces free of interference from EMF or MHD effects. In the case of correct Rwave recognition, VCG-triggered 2D CINE SSFP was immune to cardiac motion effects—even at 3.0 T. However, VCG-triggered 2D SSFP CINE imaging was prone to cardiac motion and EBS degradation if R-wave misregistration occurred. ACT-triggered acquisitions yielded LV parameters (end-diastolic volume (EDV), endsystolic volume (ESV), stroke volume (SV), ejection fraction (EF) and left ventricular mass (LVM)) comparable with those derived fromVCG-triggered acquisitions (1.5 T: ESVVCG=(56± 17) ml, EDVVCG=(151±32)ml, LVMVCG=(97±27) g, SVVCG=(94± 19)ml, EFVCG=(63±5)% cf. ESVACT= (56±18) ml, EDVACT=(147±36) ml, LVMACT=(102±29) g, SVACT=(91± 22) ml, EFACT=(62±6)%; 3.0 T: ESVVCG=(55±21) ml, EDVVCG=(151±32) ml, LVMVCG=(101±27) g, SVVCG=(96±15) ml, EFVCG=(65±7)% cf. ESVACT=(54±20) ml, EDVACT=(146±35) ml, LVMACT= (101±30) g, SVACT=(92±17) ml, EFACT=(64±6)%). Conclusions: ACT’s intrinsic insensitivity to interference from electromagnetic fields renders
We analyze the influence of dipole-dipole interactions in an electromagnetically induced transparency set up for a density at the onset of cooperative effects. To this end, we include mean-field models for the influence of local-field corrections and radiation trapping into our calculation. We show both analytically and numerically that the polarization contribution to the local field strongly modulates the phase of a weak pulse. We give an intuitive explanation for this local-field-induced phase modulation and demonstrate that it distinctively differs from the nonlinear self-phase-modulation that a strong pulse experiences in a Kerr medium.
Future evolution of risk management for structures : Advancement for the future IEC 62305-2 Ed3
(2011)
The proposed Den Haag Zuidwest district heating system of the city of The Hague consists of a deep doublet in a Jurassic sandstone layer that is designed for a production temperature of 75 °C and a reinjection temperature of 40 °C at a flow rate of 150 m3 h−1. The prediction of reservoir temperature and production behavior is crucial for success of the proposed geothermal doublet. This work presents the results of a study of the important geothermal and geohydrological issues for the doublet design. In the first phase of the study, the influences of the three-dimensional (3D) structures of anticlines and synclines on the temperature field were examined. A comprehensive petrophysical investigation was performed to build a large scale 3D-model of the reservoir. Several bottomhole temperatures (BHTs), as well as petrophysical logs were used to calibrate the model using thermal conductivity measurements on 50 samples from boreholes in different lithological units in the study area. Profiles and cross sections extracted from the calculated temperature field were used to study the temperature in the surrounding areas of the planned doublet. In the second phase of the project, a detailed 3D numerical reservoir model was set up, with the aim of predicting the evolution of the producer and injector temperatures, and the extent of the cooled area around the injector. The temperature model from the first phase provided the boundary conditions for the reservoir model. Hydraulic parameters for the target horizons, such as porosity and permeability, were taken from data available from the nearby exploration wells. The simulation results are encouraging as no significant thermal breakthrough is predicted. For the originally planned location of the producer, the extracted water temperature is predicted to be around 79 °C, with an almost negligible cooling in the first 50 years of production. When the producer is located shallower parts of the reservoir, the yield water temperatures is lower, starting at ≈76 °C and decreasing to ≈74 °C after 50 years of operation. This comparatively larger decrease in temperature with time is caused by the structural feature of the reservoir, namely a higher dip causes the cooler water to easily move downward. In view of the poor reservoir data, the reservoir simulation model is constructed to allow iterative updates using data assimilation during planned drilling, testing, and production phases. Measurements during an 8 h pumping test carried out in late 2010 suggest that a flow rate of 150 m3 h−1 is achievable. Fluid temperatures of 76.5 °C were measured, which is very close to the predicted value.
The msprop program presented in this work is capable of solving the Maxwell–Schrödinger equations for one or several laser fields propagating through a medium of quantum optical few-level systems in one spatial dimension and in time. In particular, it allows to numerically treat systems in which a laser field interacts with the medium with both its electric and magnetic component at the same time. The internal dynamics of the few-level system is modeled by a quantum optical master equation which includes coherent processes due to optical transitions driven by the laser fields as well as incoherent processes due to decay and dephasing. The propagation dynamics of the laser fields is treated in slowly varying envelope approximation resulting in a first order wave equation for each laser field envelope function. The program employs an Adams predictor formula second order in time to integrate the quantum optical master equation and a Lax–Wendroff scheme second order in space and time to evolve the wave equations for the fields. The source function in the Lax–Wendroff scheme is specifically adapted to allow taking into account the simultaneous coupling of a laser field to the polarization and the magnetization of the medium. To reduce execution time, a customized data structure is implemented and explained. In three examples the features of the program are demonstrated and the treatment of a system with a phase-dependent cross coupling of the electric and magnetic field component of a laser field is shown.
Often, detailed simulations of heat conduction in complicated, porous media have large runtimes. Then homogenization is a powerful tool to speed up the calculations by preserving accurate solutions at the same time. Unfortunately real structures are generally non-periodic, which requires unpractical, complicated homogenization techniques. We demonstrate in this paper, that the application of simple, periodic techniques to realistic media, that are just close to periodic, gives accurate, approximative solutions. In order to obtain effective parameters for the homogenized heat equation, we have to solve a so called “cell problem”. In contrast to periodic structures it is not trivial to determine a suitable unit cell, which represents a non-periodic media. To overcome this problem, we give a rule of thumb on how to choose a good cell. Finally we demonstrate the efficiency of our method for virtually generated foams as well as real foams and compare these results to periodic structures.
Modeling contribution to risk assessment of thermal production power for geothermal reservoirs
(2013)
Heat production in the windings of the stators of electric machines under stationary condition
(2014)
In electric machines due to high currents and resistive losses (joule heating) heat is produced. To avoid damages by overheating the design of effective cooling systems is required. Therefore the knowledge of heat sources and heat transfer processes is necessary. The purpose of this paper is to illustrate a good and effective calculation method for the temperature analysis based on homogenization techniques. These methods have been applied for the stator windings in a slot of an electric machine consisting of copper wires and resin. The key quantity here is an effective thermal conductivity, which characterizes the heterogeneous wire resin-arrangement inside the stator slot. To illustrate the applicability of the method, the analysis of a simplified, homogenized model is compared with the detailed analysis of temperature behavior inside a slot of an electric machine according to the heat generation. We considered here only the stationary situation. The achieved numerical results are accurate and show that the applied homogenization technique works in practice. Finally the results of simulations for the two cases, the original model of the slot and the homogenized model chosen for the slot (unit cell), are compared to experimental results.
Following earlier studies, we present forward and inverse simulations of heat and fluid transport of the upper crust using a local 3-D model of the Kola area. We provide best estimates for palaeotemperatures and permeabilities, their errors and their dependencies. Our results allow discriminating between the two mentioned processes to a certain extent, partly resolving the non-uniqueness of the problem. We find clear indications for a significant contribution of advective heat transport, which, in turn, imply only slightly lower ground surface temperatures during the last glacial maximum relative to the present value. These findings are consistent with the general background knowledge of (i) the fracture zones and the corresponding fluid movements in the bedrock and (ii) the glacial history of the Kola area.
Simulating the electromagnetic‐thermal treatment of thin aluminium layers for adhesion improvement
(2015)
A composite layer material used in packaging industry is made from joining layers of different materials using an adhesive. An important processing step in the production of aluminium-containing composites is the surface treatment and consequent coating of adhesive material on the aluminium surface. To increase adhesion strength between aluminium layer and the adhesive material, the foil is heat treated. For efficient heating, induction heating was considered as state-of-the-art treatment process. Due to the complexity of the heating process and the unpredictable nature of the heating source, the control of the process is not yet optimised. In this work, a finite element analysis of the process was established and various process parameters were studied. The process was simplified and modelled in 3D. The numerical model contains an air domain, an aluminium layer and a copper coil fitted with a magnetic field concentrating material. The effect of changing the speed of the aluminium foil (or rolling speed) was studied with the change of the coil current. Statistical analysis was used for generating a general control equation of coil current with changing rolling speed.
The performance and biomass yield of the perennial energy plant Sida hermaphrodita (hereafter referred to as Sida) as a feedstock for biogas and solid fuel was evaluated throughout one entire growing period at agricultural field conditions. A Sida plant development code was established to allow comparison of the plant growth stages and biomass composition. Four scenarios were evaluated to determine the use of Sida biomass with regard to plant development and harvest time: (i) one harvest for solid fuel only; (ii) one harvest for biogas production only; (iii) one harvest for biogas production, followed by a harvest of the regrown biomass for solid fuel; and (iv) two consecutive harvests for biogas production. To determine Sida's value as a feedstock for combustion, we assessed the caloric value, the ash quality, and melting point with regard to DIN EN ISO norms. The results showed highest total dry biomass yields of max. 25 t ha⁻¹, whereas the highest dry matter of 70% to 80% was obtained at the end of the growing period. Scenario (i) clearly indicated the highest energy recovery, accounting for 439 288 MJ ha⁻¹; the energy recovery of the four scenarios from highest to lowest followed this order: (i) ≫ (iii) ≫ (iv) > (ii). Analysis of the Sida ashes showed a high melting point of >1500 °C, associated with a net calorific value of 16.5–17.2 MJ kg⁻¹. All prerequisites for DIN EN ISO norms were achieved, indicating Sida's advantage as a solid energy carrier without any post-treatment after harvesting. Cell wall analysis of the stems showed a constant lignin content after sampling week 16 (July), whereas cellulose had already reached a plateau in sampling week 4 (April). The results highlight Sida as a promising woody, perennial plant, providing biomass for flexible and multipurpose energy applications.
A refined substructure technique in the frequency domain is developed, which permits consideration of the interaction effects among adjacent containers through the supporting deformable soil medium. The tank-liquid systems are represented by means of mechanical models, whereas discrete springs and dashpots stand for the soil beneath the foundations. The proposed model is employed to assess the responses of adjacent circular, cylindrical tanks for harmonic and seismic excitations over wide range of tank proportions and soil conditions. The influence of the number, spatial arrangement of the containers and their distance on the overall system's behavior is addressed. The results indicate that the cross-interaction effects can substantially alter the impulsive components of response of each individual element in a tank farm. The degree of this impact is primarily controlled by the tank proportions and the proximity of the predominant natural frequencies of the shell-liquid-soil systems and the input seismic motion. The group effects should be not a priori disregarded, unless the tanks are founded on shallow soil deposit overlying very stiff material or bedrock.
The behaviour of infilled reinforced concrete frames under horizontal load has been widely investigated, both experimentally and numerically. Since experimental tests represent large investments, numerical simulations offer an efficient approach for a more comprehensive analysis. When RC frames with masonry infill walls are subjected to horizontal loading, their behaviour is highly non-linear after a certain limit, which makes their analysis quite difficult. The non-linear behaviour results from the complex inelastic material properties of the concrete, infill wall and conditions at the wall-frame interface. In order to investigate this non-linear behaviour in detail, a finite element model using a micro modelling approach is developed, which is able to predict the complex non-linear behaviour resulting from the different materials and their interaction. Concrete and bricks are represented by a non-linear material model, while each reinforcement bar is represented as an individual part installed in the concrete part and behaving elasto-plastically. Each brick is modelled individually and connected taking into account the non-linearity of a brick mortar interface. The same approach is followed using two finite element software packages and the results are compared with the experimental results. The numerical models show a good agreement with the experiments in predicting the overall behaviour, but also very good matching for strength capacity and drift. The results emphasize the quality and the valuable contribution of the numerical models for use in parametric studies, which are needed for the derivation of design recommendations for infilled frame structures.
This paper proposes a quick and simplified method to describe masonry vaults in global seismic analyses of buildings. An equivalent macro-element constituted by a set of six trusses, two for each transverse, longitudinal and diagonal direction, is introduced. The equivalent trusses, whose stiffness is calculated by fully modeled vaults of different geometry, mechanical properties and boundary conditions, simulate the vault in both global analysis and local analysis, such as kinematic or rocking approaches. A parametric study was carried out to investigate the influence of geometrical characteristics and mechanical features on the equivalent stiffness values. The method was numerically validated by performing modal and transient analysis on a three naves-church in the elastic range. Vibration modes and displacement time-histories were compared showing satisfying agreement between the complete and the simplified models. This procedure is particularly useful in engineering practice because it allows to assess, in a simplified way, the effectiveness of strengthening interventions for reducing horizontal relative displacements between vault supports.
Silos generally work as storage structures between supply and demand for various goods, and their structural safety has long been of interest to the civil engineering profession. This is especially true for dynamically loaded silos, e.g., in case of seismic excitation. Particularly thin-walled cylindrical silos are highly vulnerable to seismic induced pressures, which can cause critical buckling phenomena of the silo shell. The analysis of silos can be carried out in two different ways. In the first, the seismic loading is modeled through statically equivalent loads acting on the shell. Alternatively, a time history analysis might be carried out, in which nonlinear phenomena due to the filling as well as the interaction between the shell and the granular material are taken into account. The paper presents a comparison of these approaches. The model used for the nonlinear time history analysis considers the granular material by means of the intergranular strain approach for hypoplasticity theory. The interaction effects between the granular material and the shell is represented by contact elements. Additionally, soil–structure interaction effects are taken into account.
Contemporary research appreciates a diverse workforce as a potential source of innovation. Researchers explore the fine details of why diversity management is central for generating innovations in heterogeneous research groups and how it could be effectively implemented into organizations. Complex research associations that discuss topics with a high impact on society increasingly address the necessity of establishing a diverse workforce to confront the challenges of tomorrow. Characterized by complex management structures as well as hierarchies, research associations have not been a subject of investigation until now. For this reason, the presented research project aims to develop a diversity and innovation management strategy with the ultimate goal of inducing change in the corporate culture. The proposed approach consisted of six phases; the first two phases investigated the status quo of diversity in the existing organizational structures of member institutes and the variety of particular working cultures within the research association. The third and the fourth phases utilized qualitative and quantitative studies. The third phase focused on the connection of management level to diversity and innovation, and the need for diversity and innovation management, and tailor-made methods of implementing them. The first three phases have been accomplished successfully; preliminary results are already available. The fourth phase will mainly focus on exploring the mind-set of the employees. The fifth phase will consolidate the findings in the first four phases into an implementable strategy. The final phase will address the implementation of this strategy into the organization. Phases 4 to 6 have not yet been undertaken
In this paper, a coupled multiphase model considering both non-linearities of water retention curves and solid state modeling is proposed. The solid displacements and the pressures of both water and air phases are unknowns of the proposed model. The finite element method is used to solve the governing differential equations. The proposed method is demonstrated through simulation of seepage test and partially consolidation problem. Then, implementation of the model is done by using hypoplasticity for the solid phase and analyzing the fully saturated triaxial experiments. In integration of the constitutive law error controlling is improved and comparisons done accordingly. In this work, the advantages and limitations of the numerical model are discussed.
Due to the Renewable Energy Act, in Germany it is planned to increase the amount of renewable energy carriers up to 60%. One of the main problems is the fluctuating supply of wind and solar energy. Here biogas plants provide a solution, because a demand-driven supply is possible. Before running such a plant, it is necessary to simulate and optimize the process. This paper provides a new model of a biogas plant, which is as accurate as the standard ADM1 model. The advantage compared to ADM1 is that it is based on only four parameters compared to 28. Applying this model, an optimization was installed, which allows a demand-driven supply by biogas plants. Finally the results are confirmed by several experiments and measurements with a real test plant.
In recent years, many onshore wind turbines are erected in seismic active regions and on soils with poor load bearing capacity, where pile grids are inevitable to transfer the loads into the ground. In this contribution, a realistic multi pile grid is designed to analyze the dynamics of a wind turbine tower including frequency dependent soil-structure-interaction. It turns out that different foundations on varying soil configurations heavily influence the vibration response. While the vibration amplitude is mostly attenuated, certain unfavorable combinations of structure and soil parameters lead to amplification in the range of the system's natural frequencies. This testifies the need for overall dynamic analysis in the assessment of the dynamic stability and the holistic frequency tuning of the turbines.
The article presents the investigation of the seismic behaviour of a modern URM building located in the municipality of Finale Emilia in province of Modena, Northern Italy. The building is situated in the centre of the series of the 2012 Northern Italy earthquakes and has not suffered any damage during the earthquake series in 2012. The observed earthquake resistance of the building is compared with predicted resistances based on linear and nonlinear design approaches according to Eurocode. Furthermore, probabilistic analyses based on nonlinear calculation models taking into account scattering of the most relevant input parameters are carried out to identify their influence to the results and to derive fragility curves.