• Title/Summary/Keyword: Mathematical Thermal modeling

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Derivation of Simplified Formulas to Predict Deformations of Plate in Steel Forming Process with Induction Heating (유도가열을 이용한 강판성형공정에서 변형량 예측을 위한 계산식 유도)

  • Bae, Kang-Yul;Yang, Young-Soo;Hyun, Chung-Min;Won, Seok-Hee;Cho, Si-Hoon
    • Journal of Welding and Joining
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    • v.25 no.4
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    • pp.58-64
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    • 2007
  • Recently, the electro-magnetic induction process has been utilizing to substitute the flame heating process in shipyard. However, few studies have been performed to exactly analyze the deformation mechanism of the heating process with mathematical model. This is mainly due to the difficulty of modeling the inductor travelling on plate during the process. In this study, heat flux distribution of the process is firstly numerically analysed with the assumption that the process has a quasi-stationary state and also with the consideration that the heat source itself highly depends on the temperature of base plate. With the heat flux, the thermal and deformation analyses are then performed with a commercial program for 34 combinations of heating parameters. The deformations obtained and heating parameters are synthesized with a statistical method to produce simplified formulas, which easily give the relation between the heating parameters and deformations. The formulas are well compared with results of experiment.

Design of Controller for Rapid Thermal Process Using Evolutionary Computation Algorithm and Fuzzy Logic (진화 연산 알고리즘과 퍼지 논리를 이용한 고속 열처리 공정기의 제어기 설계)

  • Hwang, Min-Woong;Do, Hyun-Min;Choi, Jin-Young
    • Journal of the Korean Institute of Intelligent Systems
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    • v.8 no.6
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    • pp.37-47
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    • 1998
  • This paper proposes a controller design method using the evolutionary computation algorithm and the fuzzy logic to control the wafer temperature in rapid thermal processing. First, we design the feedforward static controller to provide the control powers of the lamps for the given steady state temperature. Second, the feedforward dynamic controller is designed for the additional control powers to achieve a given transient response. These feedforward controllers are implemented by using the fuzzy logic to act as a global nonlinear controller over a wide range of operating points. The parameters of these controllers are optimized by using the evolutionary computation algorithm so that it can be used when the mathematical model is not available. In addition, the feedback error controller is introduced to compensate the feedforward controllers when there exist disturbances and modeling errors. The gain of feedback error controller is also obtained by the evolutionary computation algorithm. Through simulations, we verify the proposed control system can give a satisfactory performance.

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Optimal Design of Local Induction Heating Coils Based on the Sampling-Based Sensitivity (샘플링 기반 민감도를 이용한 국부 유도 가열용 코일의 최적 설계)

  • Choi, Nak-Sun;Kim, Dong-Wook;Kim, Dong-Hun
    • Journal of the Korean Magnetics Society
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    • v.23 no.3
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    • pp.110-116
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    • 2013
  • This paper proposes a sampling-based sensitivity method for dealing with electromagnetic coupled design problems effectively. The black-box modeling technique is basically applied to obtain an optimum regardless of how strong the electromagnetic, thermal and structural analyses are coupled with each other. To achieve this, Kriging surrogate models are produced in a hyper-cubic local window with the center of a current design point. Then design sensitivity values are extracted from the differentiation of basis functions which consist of the models. The proposed method falls under a hybrid optimization method which takes advantages of the sampling-based and the sensitivity-based methods. Owing to the aforementioned feature, the method can be applied even to electromagnetic problems of which the material properties are strongly coupled with thermal or structural outputs. To examine the accuracy and validity of the proposed method, a strongly nonlinear mathematical example and a coil design problem for local induction heating are tested.

Dynamic Modeling of Cooling System Thermal Management for Automotive PEMFC Application (자동차용 연료전지 냉각계통 열관리 동적 모사)

  • Han, Jae Young;Lee, Kang Hun;Yu, Sang Seok
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.36 no.12
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    • pp.1185-1192
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    • 2012
  • The typical operating temperature of an automotive fuel cell is lower than that of an internal combustion engine, which necessitates a refined strategy for thermal management. In particular, the performance of the cooling module has to be higher for a fuel cell system because the temperature difference between the fuel cell and the surrounding is lower than in the case of the internal combustion engine. Even though the cooling system of an automotive fuel cell determines the operating temperature and temperature distribution of the fuel cell, it has attracted little research attention. This study presents the mathematical model of a cooling system for an automotive fuel cell system using Matlab/$Simulink^{(R)}$. In particular, a radiator model is developed for design optimization from the development stage to the operating stage for an automotive fuel cell. The cooling system model comprises a fan, pump, and radiator. The pump and fan model have an empirical relation, and the dynamics of the pump and fan are only explained by motor dynamics. The basic design study was conducted, and the geometric setup of the radiator was investigated. When the control logic was applied, the pump senses the coolant inlet temperature and the fan senses the coolant out temperature. Additionally, the cooling module is integrated with the fuel cell system model so that the performance of the cooling module can be investigated under realistic operating conditions.

Investigation of NO Formation Characteristics in Multi Staged Air Combustor (공기 다단 연소기 화염의 NO 발생특성에 관한 연구)

  • Kim, Han-Seok;An, Guk-Yeong;Baek, Seung-Uk;Yu, Myeong-Jong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.25 no.11
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    • pp.1594-1605
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    • 2001
  • In this study, a numerical simulation was developed which was capable of predicting the characteristics of NO formation in pilot scale combustor adopting the air-staged burner flame. The numerical calculation was constructed by means of establishing the mathematical models fur turbulence, turbulent combustion, radiation and turbulent nitric oxide chemistry. Turbulence was solved with standard k-$\xi$ model and the turbulent combustion model was incorporated using a two step reaction scheme together with an eddy dissipation model. The radiative transfer equation was calculated by means of the discrete ordinates method with the weighted sum of gray gases model for CO$_2$and H$_2$O. In the NO chemistry model, the chemical reaction rates for thermal and prompt NO were statistically averaged using the $\beta$ probability density function. The results were validated by comparison with measurements. For the experiment, a 0.2 MW pilot multi-air staged burner has been designed and fabricated. Only when the radiation was taken into account, the predicted gas temperature was in good agreement with the experimental one, which meant that the inclusion of radiation was indispensable for modeling multi-air staged gas flame. This was also true of the prediction of the NO formation, since it heavily depended on temperature. Subsequently, it was found that the multi-air staged combustion technique might be used as a practical tool in reducing the NO formation by controlling the peak flame temperature.

A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation

  • Tounsi, Abdelouahed;Al-Dulaijan, S.U.;Al-Osta, Mohammed A.;Chikh, Abdelbaki;Al-Zahrani, M.M.;Sharif, Alfarabi;Tounsi, Abdeldjebbar
    • Steel and Composite Structures
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    • v.34 no.4
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    • pp.511-524
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    • 2020
  • In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

Size Distributions of Particulate Matter Emitted during 3D Printing and Estimates of Inhalation Exposure (3D 프린팅 가동 조건 별 발생 입자크기 분포와 흡입 노출량 추정)

  • Park, Jihoon;Jeon, Haejoon;Park, Kyungho;Yoon, Chungsik
    • Journal of Environmental Health Sciences
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    • v.44 no.6
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    • pp.524-538
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    • 2018
  • Objective: This study aimed to identify the size distributions of particulate matter emitted during 3D printing according to operational conditions and estimate particle inhalation exposure doses at each respiratory region. Methods: Four types of printing filaments were selected: acrylonitrile-butadiene-styrene (ABS), polylactic acid (PLA), Laywood, and nylon. A fused deposition modeling (FDM) 3D printer was used for printing. Airborne particles between 10 nm and $10{\mu}m$ were measured before, during, and after printing using real-time monitors under extruder temperatures from 215 to $290^{\circ}C$. Inhalation exposures, including inhaled and deposited doses at the respiratory regions, were estimated using a mathematical model. Results: Nanoparticles dominated among the particles emitted during printing, and more particles were emitted with higher temperatures for all materials. Under all temperature conditions, the Laywood emitted the highest particle concentration, followed by ABS, PLA, and nylon. The particle concentration peaked for the initial 10 to 20 minutes after starting operations and gradually decreased with elapsed time. Nanoparticles accounted for a large proportion of the total inhaled particles in terms of number, and about a half of the inhaled nanoparticles were estimated to be deposited in the alveolar region. In the case of the mass of inhaled and deposited dose, particles between 0.1 and $1.0{\mu}m$ made up a large proportion. Conclusion: The number of consumers using 3D printers is expected to expand, but hazardous emissions such as thermal byproducts from 3D printing are still unclear. Further studies should be conducted and appropriate control strategies considered in order to minimize human exposure.

Heat-Transfer Performance Analysis of a Multi-Channel Volumetric Air Receiver for Solar Power Tower (타워형 태양열 발전용 공기흡수기의 열전달 성능해석)

  • Jung, Eui-Guk
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.36 no.3
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    • pp.277-284
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    • 2012
  • In this study, a heat-transfer performance analysis is carried out for a multi-channel volumetric air receiver for a solar power tower. On the basis of a series of reviews regarding the relevant literature, a calculation process is proposed for the prediction of the wall- and air- temperature distributions of a single channel at given geometric and input conditions. Furthermore, a unique mathematical model of the receiver effectiveness is presented through analysis of the temperature profile. The receiver is made of silicon carbide. A total of 225 square straight channels per module are molded to induce the air flow, and each channel has the dimensions of $2mm(W){\times}2mm(H){\times}0.2mm(t){\times}320mm(L)$. The heat-transfer rate, temperature distribution and effectiveness are presented according to the variation of the channel and module number under uniform irradiation and mass flow rate. The available air outlet temperature applied to the solar power tower should be over $700^{\circ}C$. This numerical model was actually used in the design of a 200 kW-level commercial solar air receiver, and the required number of modules satisfying the thermal performance could be obtained for the specified geometric and input conditions.

Nonlinear Modeling and Application of PI Control on Pre-cooling Session of a Carbon Dioxide Storage Tank at Normal Temperature and Pressure (상온 상압의 이산화탄소 저장용 탱크를 위한 예냉과정의 비선형 모델링 및 비례-적분 제어 적용)

  • Lim, Yu Kyung;Lee, Seok Goo;Dan, Seungkyu;Ko, Min Su;Lee, Jong Min
    • Korean Chemical Engineering Research
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    • v.52 no.5
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    • pp.574-580
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    • 2014
  • Storage tanks of Carbon dioxide ($CO_2$) carriers utilized for the purpose of carbon capture and storage (CCS) into subsea strata have to undergo a pre-cooling session before beginning to load cryogenic liquid cargos in order to prevent physical and thermal deterioration of tanks which may result from cryogenic $CO_2$ contacting tank walls directly. In this study we propose dynamic model to calculate the tank inflow of $CO_2$ gas injected for precooling process and its dynamic simulation results under proportional-integral control algorithm. We selected two cases in which each of them had one controlled variable (CV) as either the tank pressure or the tank temperature and discussed the results of that decision-making on the pre-cooling process. As a result we demonstrated that the controlling instability arising from nonlinearity and singularity of the mathematical model could be avoided by choosing tank pressure as CV instead of tank temperature.