Search results for: non-linear differential equations

Authors: Ugo Galvanetto, Pirto G. Pavan, Mirco Zaccariotto

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The discipline of Computer-integrated surgery (CIS) will provide equipment able to improve the efficiency of healthcare systems and, which is more important, clinical results. Surgeons and machines will cooperate in new ways that will extend surgeons’ ability to train, plan and carry out surgery. Patient specific CIS of the brain requires several steps: 1 - Fast generation of brain models. Based on image recognition of MR images and equipped with artificial intelligence, image recognition techniques should differentiate among all brain tissues and segment them. After that, automatic mesh generation should create the mathematical model of the brain in which the various tissues (white matter, grey matter, cerebrospinal fluid …) are clearly located in the correct positions. 2 – Reliable and fast simulation of the surgical process. Computational mechanics will be the crucial aspect of the entire procedure. New algorithms will be used to simulate the mechanical behaviour of cutting through cerebral tissues. 3 – Real time provision of visual and haptic feedback A sophisticated human-machine interface based on ergonomics and psychology will provide the feedback to the surgeon. The present work will address in particular point 2. Modelling the cutting of soft tissue in a structure as complex as the human brain is an extremely challenging problem in computational mechanics. The finite element method (FEM), that accurately represents complex geometries and accounts for material and geometrical nonlinearities, is the most used computational tool to simulate the mechanical response of soft tissues. However, the main drawback of FEM lies in the mechanics theory on which it is based, classical continuum Mechanics, which assumes matter is a continuum with no discontinuity. FEM must resort to complex tools such as pre-defined cohesive zones, external phase-field variables, and demanding remeshing techniques to include discontinuities. However, all approaches to equip FEM computational methods with the capability to describe material separation, such as interface elements with cohesive zone models, X-FEM, element erosion, phase-field, have some drawbacks that make them unsuitable for surgery simulation. Interface elements require a-priori knowledge of crack paths. The use of XFEM in 3D is cumbersome. Element erosion does not conserve mass. The Phase Field approach adopts a diffusive crack model instead of describing true tissue separation typical of surgical procedures. Modelling discontinuities, so difficult when using computational approaches based on classical continuum Mechanics, is instead easy for novel computational methods based on Peridynamics (PD). PD is a non-local theory of mechanics formulated with no use of spatial derivatives. Its governing equations are valid at points or surfaces of discontinuity, and it is, therefore especially suited to describe crack propagation and fragmentation problems. Moreover, PD does not require any criterium to decide the direction of crack propagation or the conditions for crack branching or coalescence; in the PD-based computational methods, cracks develop spontaneously in the way which is the most convenient from an energy point of view. Therefore, in PD computational methods, crack propagation in 3D is as easy as it is in 2D, with a remarkable advantage with respect to all other computational techniques.

Keywords: computational mechanics, peridynamics, finite element, biomechanics

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Authors: Sofia N. Gonçalves, Duarte M. S. Albuquerque, José C. F. Pereira

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Microwave technology has been gaining importance in contributing to decarbonization processes in high energy demand industries. Despite the several numerical models presented in the literature, a proper Verification and Validation exercise is still lacking. This is important and required to evaluate the physical process model accuracy and adequacy. Another issue addresses impedance matching, which is an important mechanism used in microwave experiments to increase electromagnetic efficiency. Such mechanism is not available in current computational tools, thus requiring an external numerical procedure. A numerical model was implemented to study the continuous processing of limestone with microwave heating. This process requires the material to be heated until a certain temperature that will prompt a highly endothermic reaction. Both a 2D and 3D model were built in COMSOL Multiphysics to solve the two-way coupling between Maxwell and Energy equations, along with the coupling between both heat transfer phenomena and limestone endothermic reaction. The 2D model was used to study and evaluate the required numerical procedure, being also a benchmark test, allowing other authors to implement impedance matching procedures. To achieve this goal, a controller built in MATLAB was used to continuously matching the cavity impedance and predicting the required energy for the system, thus successfully avoiding energy inefficiencies. The 3D model reproduces realistic results and therefore supports the main conclusions of this work. Limestone was modeled as a continuous flow under the transport of concentrated species, whose material and kinetics properties were taken from literature. Verification and Validation of the coupled model was taken separately from the chemical kinetic model. The chemical kinetic model was found to correctly describe the chosen kinetic equation by comparing numerical results with experimental data. A solution verification was made for the electromagnetic interface, where second order and fourth order accurate schemes were found for linear and quadratic elements, respectively, with numerical uncertainty lower than 0.03%. Regarding the coupled model, it was demonstrated that the numerical error would diverge for the heat transfer interface with the mapped mesh. Results showed numerical stability for the triangular mesh, and the numerical uncertainty was less than 0.1%. This study evaluated limestone velocity, heat transfer, and load influence on thermal decomposition and overall process efficiency. The velocity and heat transfer coefficient were studied with the 2D model, while different loads of material were studied with the 3D model. Both models demonstrated to be highly unstable when solving non-linear temperature distributions. High velocity flows exhibited propensity to thermal runways, and the thermal efficiency showed the tendency to stabilize for the higher velocities and higher filling ratio. Microwave efficiency denoted an optimal velocity for each heat transfer coefficient, pointing out that electromagnetic efficiency is a consequence of energy distribution uniformity. The 3D results indicated the inefficient development of the electric field for low filling ratios. Thermal efficiencies higher than 90% were found for the higher loads and microwave efficiencies up to 75% were accomplished. The 80% fill ratio was demonstrated to be the optimal load with an associated global efficiency of 70%.

Keywords: multiphysics modeling, microwave heating, verification and validation, endothermic reactions modeling, impedance matching, limestone continuous processing

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Authors: Sebastian Kehne, Alexander Epple, Werner Herfs

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A new method for optimal selection of components for multi-axes forward-feed drive systems is proposed in which the choice of motors, gear boxes and ball screw drives is optimized. Essential is here the synchronization of electrical and mechanical frequency behavior of all axes because even advanced controls (like H∞-controls) can only control a small part of the mechanical modes – namely only those of observable and controllable states whose value can be derived from the positions of extern linear length measurement systems and/or rotary encoders on the motor or gear box shafts. Further problems are the unknown processing forces like cutting forces in machine tools during normal operation which make the estimation and control via an observer even more difficult. To start with, the open source Modelica Feed Drive Library which was developed at the Laboratory for Machine Tools, and Production Engineering (WZL) is extended from one axis design to the multi axes design. It is capable to simulate the mechanical, electrical and thermal behavior of permanent magnet synchronous machines with inverters, different gear boxes and ball screw drives in a mechanical system. To keep the calculation time down analytical equations are used for field and torque producing equivalent circuit, heat dissipation and mechanical torque at the shaft. As a first step, a small machine tool with a working area of 635 x 315 x 420 mm is taken apart, and the mechanical transfer behavior is measured with an impulse hammer and acceleration sensors. With the frequency transfer functions, a mechanical finite element model is built up which is reduced with substructure coupling to a mass-damper system which models the most important modes of the axes. The model is modelled with Modelica Feed Drive Library and validated by further relative measurements between machine table and spindle holder with a piezo actor and acceleration sensors. In a next step, the choice of possible components in motor catalogues is limited by derived analytical formulas which are based on well-known metrics to gain effective power and torque of the components. The simulation in Modelica is run with different permanent magnet synchronous motors, gear boxes and ball screw drives from different suppliers. To speed up the optimization different black-box optimization methods (Surrogate-based, gradient-based and evolutionary) are tested on the case. The objective that was chosen is to minimize the integral of the deviations if a step is given on the position controls of the different axes. Small values are good measures for a high dynamic axes. In each iteration (evaluation of one set of components) the control variables are adjusted automatically to have an overshoot less than 1%. It is obtained that the order of the components in optimization problem has a deep impact on the speed of the black-box optimization. An approach to do efficient black-box optimization for multi-axes design is presented in the last part. The authors would like to thank the German Research Foundation DFG for financial support of the project “Optimierung des mechatronischen Entwurfs von mehrachsigen Antriebssystemen (HE 5386/14-1 | 6954/4-1)” (English: Optimization of the Mechatronic Design of Multi-Axes Drive Systems).

Keywords: ball screw drive design, discrete optimization, forward feed drives, gear box design, linear drives, machine tools, motor design, multi-axes design

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Authors: Hilary Modir, Kyle Dutton, Michelle Swab, Shabnam Asghari

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Since its emergence, the cutaneous manifestations of COVID-19 have been documented in the literature. However, the majority are case reports with significant limitations in appraisal quality, thus leaving the role of dermatological manifestations of COVID-19 erroneously underexplored. The primary aim of this review was to systematically examine clinical patterns of dermatological manifestations as reported in the literature. This study was designed as a systematic review of case reports. The inclusion criteria consisted of all published reports and articles regarding COVID-19 in English, from September 1st, 2019, until June 22nd, 2020. The population consisted of confirmed cases of COVID-19 with associated cutaneous signs and symptoms. Exclusion criteria included research in planning stages, protocols, book reviews, news articles, review studies, and policy analyses. With the collaboration of a librarian, a search strategy was created consisting of a mixture of keyword terms and controlled vocabulary. Electronic databases searched were MEDLINE via PubMed, EMBASE, CINAHL, Web of Science, LILACS, PsycINFO, WHO Global Literature on Coronavirus Disease, Cochrane Library, Campbell Collaboration, Prospero, WHO International Clinical Trials Registry Platform, Australian and New Zealand Clinical Trials Registry, U.S. Institutes of Health Ongoing Trials Register, AAD Registry, OSF preprints, SSRN, MedRxiV and BioRxiV. The study selection featured an initial pre-screening of titles and abstracts by one independent reviewer. Results were verified by re-examining a random sample of 1% of excluded articles. Eligible studies progressed for full-text review by two calibrated independent reviewers. Covidence was used to store and extract data, such as citation information and findings pertaining to COVID-19 and cutaneous signs and symptoms. Data analysis and summarization methodology reflect the framework proposed by PRISMA and recommendations set out by Cochrane and Joanna Brigg’s Institute for conducting systematic reviews. The Oxford Centre for Evidence-Based Medicine’s level of evidence was used to appraise the quality of individual studies. The literature search revealed a total of 1221 articles. After the abstract and full-text screening, only 95 studies met the eligibility criteria, proceeding to data extraction. Studies were divided into 58% case reports and 42% series. A total of 833 manifestations were reported in 723 confirmed COVID-19 cases. The most frequent lesions were 23% maculopapular, 15% urticarial and 13% pseudo-chilblains, with 46% of lesions reporting pruritus, 16% erythema, 14% pain, 12% burning sensation, and 4% edema. The most common lesion locations were 20% trunk, 19.5% lower limbs, and 17.7% upper limbs. The time to resolution of lesions was between one and twenty-one days. In conclusion, over half of the reported cutaneous presentations in COVID-19 positive patients were maculopapular, urticarial and pseudo-chilblains, with the majority of lesions distributed to the extremities and trunk. As this review’s sample size only contained COVID-19 confirmed cases with skin presentations, it becomes difficult to deduce the direct relationship between skin findings and COVID-19. However, it can be correlated that acute onset of skin lesions, such as chilblains-like, may be associated with or may warrant consideration of COVID-19 as part of the differential diagnosis.

Keywords: COVID-19, cutaneous manifestations, cutaneous signs, general dermatology, medical dermatology, Sars-Cov-2, skin and infectious disease, skin findings, skin manifestations

Procedia PDF Downloads 181

Authors: D. Bianco, A. Sollazzo, M. Barbarino, G. Elia, A. Smoraldi, N. Favaloro

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The activities, described in the present paper, have been conducted in the framework of the HYPROB-New Program, carried out by the Italian Aerospace Research Centre (CIRA) promoted and funded by the Italian Ministry of University and Research (MIUR) in order to improve the National background on rocket engine systems for space applications. The Program has the strategic objective to improve National system and technology capabilities in the field of liquid rocket engines (LRE) for future Space Propulsion Systems applications, with specific regard to LOX/LCH4 technology. The main purpose of the HYPROB program is to design and build a Propulsion Test Facility (HIMP) allowing test activities on Liquid Thrusters. The development of skills in liquid rocket propulsion can only pass through extensive test campaign. Following its mission, CIRA has planned the development of new testing facilities and infrastructures for space propulsion characterized by adequate sizes and instrumentation. The IMP test cell is devoted to testing articles representative of small combustion chambers, fed with oxygen and methane, both in liquid and gaseous phase. This article describes the activities that have been carried out for the evaluation of the acoustic impact, and its consequent mitigation. The impact of the simulated acoustic disturbance has been evaluated, first, using an approximated method based on experimental data by Baumann and Coney, included in “Noise and Vibration Control Engineering” edited by Vér and Beranek. This methodology, used to evaluate the free-field radiation of jet in ideal acoustical medium, analyzes in details the jet noise and assumes sources acting at the same time. It considers as principal radiation sources the jet mixing noise, caused by the turbulent mixing of jet gas and the ambient medium. Empirical models, allowing a direct calculation of the Sound Pressure Level, are commonly used for rocket noise simulation. The model named after K. Eldred is probably one of the most exploited in this area. In this paper, an improvement of the Eldred Standard model has been used for a detailed investigation of the acoustical impact of the Hyprob facility. This new formulation contains an explicit expression for the acoustic pressure of each equivalent noise source, in terms of amplitude and phase, allowing the investigation of the sources correlation effects and their propagation through wave equations. In order to enhance the evaluation of the facility acoustic impact, including an assessment of the mitigation strategies to be set in place, a more advanced simulation campaign has been conducted using both an in-house code for noise propagation and scattering, and a commercial code for industrial noise environmental impact, CadnaA. The noise prediction obtained with the revised Eldred-based model has then been used for formulating an empirical/BEM (Boundary Element Method) hybrid approach allowing the evaluation of the barrier mitigation effect, at the design. This approach has been compared with the analogous empirical/ray-acoustics approach, implemented within CadnaA using a customized definition of sources and directivity factor. The resulting impact evaluation study is reported here, along with the design-level barrier optimization for noise mitigation.

Keywords: acoustic impact, industrial noise, mitigation, rocket noise

Procedia PDF Downloads 146

Authors: Patricia Shirley Almeida Prado, Selma Paixão Argollo, Maria De Fátima Teixeira Guimarães, Leticia Matos Sobrinho

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Skeletal differential diagnosis is essential in forensic anthropology in order to differentiate skeletal trauma from normal osseous variation and pathological processes. Thus, part of forensic anthropological field is differentiate skeletal criminal injuries from the normal skeletal variation (bone fusion or nonunion, transitional vertebrae and other non-metric traits), non-traumatic skeletal pathology (myositis ossificans, arthritis, bone metastasis, osteomyelitis) from traumatic skeletal pathology (myositis ossificans traumatic) avoiding misdiagnosis. This case shows the importance of effective pathological diagnosis in order to accelerate the identification process of skeletonized human remains. THE CASE: An unidentified skeletal remains at the medico legal institute Nina Rodrigues-Salvador, of a male young adult (29 to 40 years estimated) showing a massive heterotopic ossification on its right tibia at upper epiphysis and adjacent articular femur surface; an extensive ossification on the right clavicle (at the sternal extremity) also presenting an heterotopic ossification at right scapulae (upper third of scapulae lateral margin and infraglenoid tubercule) and at the head of right humerus at the shoulder joint area. Curiously, this case also shows an unusual porosity in certain vertebrae´s body and in some tarsal and carpal bones. Likewise, his left fifth metacarpal bones (right and left) showed a healed fracture which led both bones distorted. Based on identification, of pathological conditions in human skeletal remains literature and protocols these alterations can be misdiagnosed and this skeleton may present more than one pathological process. The anthropological forensic lab at Medico-legal Institute Nina Rodrigues in Salvador (Brazil) adopts international protocols to ancestry, sex, age and stature estimations, also implemented well-established conventions to identify pathological disease and skeletal alterations. The most compatible diagnosis for this case is hematogenous osteomyelitis due to following findings: 1: the healed fracture pattern at the clavicle showing a cloaca which is a pathognomonic for osteomyelitis; 2: the metacarpals healed fracture does not present cloaca although they developed a periosteal formation. 3: the superior articular surface of the right tibia shows an extensive inflammatory healing process that extends to adjacent femur articular surface showing some cloaca at tibia bone disease. 4: the uncommon porosities may result from hematogenous infectious process. The fractures probably have occurred in a different moments based on the healing process; the tibia injury is more extensive and has not been reorganized, while metacarpals and clavicle fracture is properly healed. We suggest that the clavicle and tibia´s fractures were infected by an existing infectious disease (syphilis, tuberculosis, brucellosis) or an existing syndrome (Gorham’s disease), which led to the development of osteomyelitis. This hypothesis is supported by the fact that different bones are affected in diverse levels. Like the metacarpals that do not show the cloaca, but then a periosteal new bone formation; then the unusual porosities do not show a classical osteoarthritic processes findings as the marginal osteophyte, pitting and new bone formation, they just show an erosive process without bone formation or osteophyte. To confirm and prove our hypothesis we are working on different clinical approaches like DNA, histopathology and other image exams to find the correct diagnostic.

Keywords: bone disease, forensic anthropology, hematogenous osteomyelitis, human identification, human remains

Procedia PDF Downloads 325

Authors: Piotr K. Szewczyk, Arkadiusz Gradys, Sungkyun Kim, Luana Persano, Mateusz M. Marzec, Oleksander Kryshtal, Andrzej Bernasik, Sohini Kar-Narayan, Pawel Sajkiewicz, Urszula Stachewicz

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Piezoelectric polymers have received great attention in smart textiles, wearables, and flexible electronics. Their potential applications range from devices that could operate without traditional power sources, through self-powering sensors, up to implantable biosensors. Semi-crystalline PVDF is often proposed as the main candidate for industrial-scale applications as it exhibits exceptional energy harvesting efficiency compared to other polymers combined with high mechanical strength and thermal stability. Plenty of approaches have been proposed for obtaining PVDF rich in the desired β-phase with electric polling, thermal annealing, and mechanical stretching being the most prevalent. Electrospinning is a highly tunable technique that provides a one-step process of obtaining highly piezoelectric PVDF fibers without the need for post-treatment. In this study, voltage polarity and relative humidity influence on electrospun PVDF, fibers were investigated with the main focus on piezoelectric β-phase contents and piezoelectric performance. Morphology and internal structure of fibers were investigated using scanning (SEM) and transmission electron microscopy techniques (TEM). Fourier Transform Infrared Spectroscopy (FITR), wide-angle X-ray scattering (WAXS) and differential scanning calorimetry (DSC) were used to characterize the phase composition of electrospun PVDF. Additionally, surface chemistry was verified with X-ray photoelectron spectroscopy (XPS). Piezoelectric performance of individual electrospun PVDF fibers was measured using piezoresponse force microscopy (PFM), and the power output from meshes was analyzed via custom-built equipment. To prepare the solution for electrospinning, PVDF pellets were dissolved in dimethylacetamide and acetone solution in a 1:1 ratio to achieve a 24% solution. Fibers were electrospun with a constant voltage of +/-15kV applied to the stainless steel nozzle with the inner diameter of 0.8mm. The flow rate was kept constant at 6mlh⁻¹. The electrospinning of PVDF was performed at T = 25°C and relative humidity of 30 and 60% for PVDF30+/- and PVDF60+/- samples respectively in the environmental chamber. The SEM and TEM analysis of fibers produced at a lower relative humidity of 30% (PVDF30+/-) showed a smooth surface in opposition to fibers obtained at 60% relative humidity (PVDF60+/-), which had wrinkled surface and additionally internal voids. XPS results confirmed lower fluorine content at the surface of PVDF- fibers obtained by electrospinning with negative voltage polarity comparing to the PVDF+ obtained with positive voltage polarity. Changes in surface composition measured with XPS were found to influence the piezoelectric performance of obtained fibers what was further confirmed by PFM as well as by custom-built fiber-based piezoelectric generator. For PVDF60+/- samples humidity led to an increase of β-phase contents in PVDF fibers as confirmed by FTIR, WAXS, and DSC measurements, which showed almost two times higher concentrations of β-phase. A combination of negative voltage polarity with high relative humidity led to fibers with the highest β-phase contents and the best piezoelectric performance of all investigated samples. This study outlines the possibility to produce electrospun PVDF fibers with tunable piezoelectric performance in a one-step electrospinning process by controlling relative humidity and voltage polarity conditions. Acknowledgment: This research was conducted within the funding from m the Sonata Bis 5 project granted by National Science Centre, No 2015/18/E/ST5/00230, and supported by the infrastructure at International Centre of Electron Microscopy for Materials Science (IC-EM) at AGH University of Science and Technology. The PFM measurements were supported by an STSM Grant from COST Action CA17107.

Keywords: crystallinity, electrospinning, PVDF, voltage polarity

Procedia PDF Downloads 134

Authors: David A. Olasehinde, Peter I. Olasehinde, Segun M. A. Adelana, Dapo O. Olasehinde

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An investigation was carried out on underground water system dynamics within Ilorin metropolis to monitor the subsurface flow and its corresponding pollution. Africa population growth rate is the highest among the regions of the world, especially in urban areas. A corresponding increase in waste generation and a change in waste composition from predominantly organic to non-organic waste has also been observed. Percolation of leachate from non-engineered landfills, the chief means of waste disposal in many of its cities, constitutes a threat to the underground water bodies. Ilorin city, a transboundary town in southwestern Nigeria, is a ready microcosm of Africa’s unique challenge. In spite of the fact that groundwater is naturally protected from common contaminants such as bacteria as the subsurface provides natural attenuation process, groundwater samples have been noted to however possesses relatively higher dissolved chemical contaminants such as bicarbonate, sodium, and chloride which poses a great threat to environmental receptors and human consumption. The Geographic Information System (GIS) was used as a tool to illustrate, subsurface dynamics and the corresponding pollutant indicators. Forty-four sampling points were selected around known groundwater pollutant, major old dumpsites without landfill liners. The results of the groundwater flow directions and the corresponding contaminant transport were presented using expert geospatial software. The experimental results were subjected to four descriptive statistical analyses, namely: principal component analysis, Pearson correlation analysis, scree plot analysis, and Ward cluster analysis. Regression model was also developed aimed at finding functional relationships that can adequately relate or describe the behaviour of water qualities and the hypothetical factors landfill characteristics that may influence them namely; distance of source of water body from dumpsites, static water level of groundwater, subsurface permeability (inferred from hydraulic gradient), and soil infiltration. The regression equations developed were validated using the graphical approach. Underground water seems to flow from the northern portion of Ilorin metropolis down southwards transporting contaminants. Pollution pattern in the study area generally assumed a bimodal pattern with the major concentration of the chemical pollutants in the underground watershed and the recharge. The correlation between contaminant concentrations and the spread of pollution indicates that areas of lower subsurface permeability display a higher concentration of dissolved chemical content. The principal component analysis showed that conductivity, suspended solids, calcium hardness, total dissolved solids, total coliforms, and coliforms were the chief contaminant indicators in the underground water system in the study area. Pearson correlation revealed a high correlation of electrical conductivity for many parameters analyzed. In the same vein, the regression models suggest that the heavier the molecular weight of a chemical contaminant of a pollutant from a point source, the greater the pollution of the underground water system at a short distance. The study concludes that the associative properties of landfill have a significant effect on groundwater quality in the study area.

Keywords: dumpsite, leachate, groundwater pollution, linear regression, principal component

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Authors: Artur Tyliszczak, Ewa Szymanek, Maciej Marek

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Flow through granular materials is important to a vast array of industries, for instance in construction industry where granular layers are used for bulkheads and isolators, in chemical engineering and catalytic reactors where large surfaces of packed granular beds intensify chemical reactions, or in energy production systems, where granulates are promising materials for heat storage and heat transfer media. Despite the common usage of granulates and extensive research performed in this field, phenomena occurring between granular solid elements or between solids and fluid are still not fully understood. In the present work we analyze the heat exchange process between the flowing medium (gas, liquid) and solid material inside the granular layers. We consider them as a composite of isolated solid elements and inter-granular spaces in which a gas or liquid can flow. The structure of the layer is controlled by shapes of particular granular elements (e.g., spheres, cylinders, cubes, Raschig rings), its spatial distribution or effective characteristic dimension (total volume or surface area). We will analyze to what extent alteration of these parameters influences on flow characteristics (turbulent intensity, mixing efficiency, heat transfer) inside the layer and behind it. Analysis of flow inside granular layers is very complicated because the use of classical experimental techniques (LDA, PIV, fibber probes) inside the layers is practically impossible, whereas the use of probes (e.g. thermocouples, Pitot tubes) requires drilling of holes inside the solid material. Hence, measurements of the flow inside granular layers are usually performed using for instance advanced X-ray tomography. In this respect, theoretical or numerical analyses of flow inside granulates seem crucial. Application of discrete element methods in combination with the classical finite volume/finite difference approaches is problematic as a mesh generation process for complex granular material can be very arduous. A good alternative for simulation of flow in complex domains is an immersed boundary-volume penalization (IB-VP) in which the computational meshes have simple Cartesian structure and impact of solid objects on the fluid is mimicked by source terms added to the Navier-Stokes and energy equations. The present paper focuses on application of the IB-VP method combined with large eddy simulation (LES). The flow solver used in this work is a high-order code (SAILOR), which was used previously in various studies, including laminar/turbulent transition in free flows and also for flows in wavy channels, wavy pipes and over various shape obstacles. In these cases a formal order of approximation turned out to be in between 1 and 2, depending on the test case. The current research concentrates on analyses of the flows in dense granular layers with elements distributed in a deterministic regular manner and validation of the results obtained using LES-IB method and body-fitted approach. The comparisons are very promising and show very good agreement. It is found that the size, number of elements and their distribution have huge impact on the obtained results. Ordering of the granular elements (or lack of it) affects both the pressure drop and efficiency of the heat transfer as it significantly changes mixing process.

Keywords: granular layers, heat transfer, immersed boundary method, numerical simulations

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Authors: Sumeyra Karatas, Veysel Karatas, Reyhan Safak, Gamze Bulut-Ozturk, Ozgul Kartal

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Productive struggle entails a student's cognitive exertion to comprehend mathematical concepts and uncover solutions not immediately apparent. The significance of productive struggle in learning mathematics is accentuated by influential educational theorists, emphasizing its necessity for learning mathematics with understanding. Consequently, supporting productive struggle in learning mathematics is recognized as a high-leverage and effective mathematics teaching practice. In this study, the investigation into the role of productive struggle in learning mathematics led to the development of a comprehensive rubric for productive struggle pedagogy through an exhaustive literature review. The rubric consists of eight primary criteria and 37 sub-criteria, providing a detailed description of teacher actions and pedagogical choices that foster students' productive struggles. These criteria encompass various pedagogical aspects, including task design, tool implementation, allowing time for struggle, posing questions, scaffolding, handling mistakes, acknowledging efforts, and facilitating discussion/feedback. Utilizing this rubric, a team of researchers and teachers designed eight 90-minute lesson plans, employing a productive struggle pedagogy, for a two-week unit on solving systems of linear equations. Simultaneously, another set of eight lesson plans on the same topic, featuring identical content and problems but employing a traditional lecture-and-practice model, was designed by the same team. The objective was to assess the impact of supporting productive struggle on students' mathematics learning, defined by the strands of mathematical proficiency. This quasi-experimental study compares the control group, which received traditional lecture- and practice instruction, with the treatment group, which experienced a productive struggle in pedagogy. Sixty-six 10th and 11th-grade students from two algebra classes, taught by the same teacher at a high school, underwent either the productive struggle pedagogy or lecture-and-practice approach over two-week eight 90-minute class sessions. To measure students' learning, an assessment was created and validated by a team of researchers and teachers. It comprised seven open-response problems assessing the strands of mathematical proficiency: procedural and conceptual understanding, strategic competence, and adaptive reasoning on the topic. The test was administered at the beginning and end of the two weeks as pre-and post-test. Students' solutions underwent scoring using an established rubric, subjected to expert validation and an inter-rater reliability process involving multiple criteria for each problem based on their steps and procedures. An analysis of covariance (ANCOVA) was conducted to examine the differences between the control group, which received traditional pedagogy, and the treatment group, exposed to the productive struggle pedagogy, on the post-test scores while controlling for the pre-test. The results indicated a significant effect of treatment on post-test scores for procedural understanding (F(2, 63) = 10.47, p < .001), strategic competence (F(2, 63) = 9.92, p < .001), adaptive reasoning (F(2, 63) = 10.69, p < .001), and conceptual understanding (F(2, 63) = 10.06, p < .001), controlling for pre-test scores. This demonstrates the positive impact of supporting productive struggle in learning mathematics. In conclusion, the results revealed the significance of the role of productive struggle in learning mathematics. The study further explored the practical application of productive struggle through the development of a comprehensive rubric describing the pedagogy of supporting productive struggle.

Keywords: effective mathematics teaching practice, high school algebra, learning mathematics, productive struggle

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Authors: Mina Naeini, Thomas A. Adams II

Abstract:

Solid Oxide Fuel Cells (SOFCs) feature high electrical efficiency and generate substantial amounts of waste heat that make them suitable for integrated community energy systems (ICEs). By harvesting and distributing the waste heat through hot water pipelines, SOFCs can meet thermal demand of the communities. Therefore, they can replace traditional gas boilers and reduce greenhouse gas (GHG) emissions. Despite these advantages of SOFCs over competing power generation units, this technology has not been successfully commercialized in large-scale to replace traditional generators in ICEs. One reason is that SOFC performance deteriorates over long-term operation, which makes it difficult to find the proper sizing of the cells for a particular ICE system. In order to find the optimal sizing and operating conditions of SOFCs in a community, a proper knowledge of degradation mechanisms and effects of operating conditions on SOFCs long-time performance is required. The simplified SOFC models that exist in the current literature usually do not provide realistic results since they usually underestimate rate of performance drop by making too many assumptions or generalizations. In addition, some of these models have been obtained from experimental data by curve-fitting methods. Although these models are valid for the range of operating conditions in which experiments were conducted, they cannot be generalized to other conditions and so have limited use for most ICEs. In the present study, a general, detailed degradation-based model is proposed that predicts the performance of conventional SOFCs over a long period of time at different operating conditions. Conventional SOFCs are composed of Yttria Stabilized Zirconia (YSZ) as electrolyte, Ni-cermet anodes, and LaSr₁₋ₓMnₓO₃ (LSM) cathodes. The following degradation processes are considered in this model: oxidation and coarsening of nickel particles in the Ni-cermet anodes, changes in the pore radius in anode, electrolyte, and anode electrical conductivity degradation, and sulfur poisoning of the anode compartment. This model helps decision makers discover the optimal sizing and operation of the cells for a stable, efficient performance with the fewest assumptions. It is suitable for a wide variety of applications. Sulfur contamination of the anode compartment is an important cause of performance drop in cells supplied with hydrocarbon-based fuel sources. H₂S, which is often added to hydrocarbon fuels as an odorant, can diminish catalytic behavior of Ni-based anodes by lowering their electrochemical activity and hydrocarbon conversion properties. Therefore, the existing models in the literature for H₂-supplied SOFCs cannot be applied to hydrocarbon-fueled SOFCs as they only account for the electrochemical activity reduction. A regression model is developed in the current work for sulfur contamination of the SOFCs fed with hydrocarbon fuel sources. The model is developed as a function of current density and H₂S concentration in the fuel. To the best of authors' knowledge, it is the first model that accounts for impact of current density on sulfur poisoning of cells supplied with hydrocarbon-based fuels. Proposed model has wide validity over a range of parameters and is consistent across multiple studies by different independent groups. Simulations using the degradation-based model illustrated that SOFCs voltage drops significantly in the first 1500 hours of operation. After that, cells exhibit a slower degradation rate. The present analysis allowed us to discover the reason for various degradation rate values reported in literature for conventional SOFCs. In fact, the reason why literature reports very different degradation rates, is that literature is inconsistent in definition of how degradation rate is calculated. In the literature, the degradation rate has been calculated as the slope of voltage versus time plot with the unit of voltage drop percentage per 1000 hours operation. Due to the nonlinear profile of voltage over time, degradation rate magnitude depends on the magnitude of time steps selected to calculate the curve's slope. To avoid this issue, instantaneous rate of performance drop is used in the present work. According to a sensitivity analysis, the current density has the highest impact on degradation rate compared to other operating factors, while temperature and hydrogen partial pressure affect SOFCs performance less. The findings demonstrated that a cell running at lower current density performs better in long-term in terms of total average energy delivered per year, even though initially it generates less power than if it had a higher current density. This is because of the dominant and devastating impact of large current densities on the long-term performance of SOFCs, as explained by the model.

Keywords: degradation rate, long-term performance, optimal operation, solid oxide fuel cells, SOFCs

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