Meta-heuristic algorithms in car engine design: a literature survey

Meta-heuristic algorithms are often inspired by natural phenomena, including the evolution of species in Darwinian natural selection theory, ant behaviors in biology, flock behaviors of some birds, and annealing in metallurgy. Due to their great potential in solving difficult optimization problems, meta-heuristic algorithms have found their way into automobile engine design. There are different optimization problems arising in different areas of car engine management including calibration, control system, fault diagnosis, and modeling. In this paper we review the state-of-the-art applications of different meta-heuristic algorithms in engine management systems. The review covers a wide range of research, including the application of meta-heuristic algorithms in engine calibration, optimizing engine control systems, engine fault diagnosis, and optimizing different parts of engines and modeling. The meta-heuristic algorithms reviewed in this paper include evolutionary algorithms, evolution strategy, evolutionary programming, genetic programming, differential evolution, estimation of distribution algorithm, ant colony optimization, particle swarm optimization, memetic algorithms, and artificial immune system

파라미터 추정을 통한 불균일계 촉매 반응의 마이크로키네틱 모델링

학위논문(박사) -- 서울대학교대학원 : 공과대학 화학생물공학부, 2021.8. 이원보.최근에 계속해서 환경 오염 문제가 대두됨에 따라 이산화탄소를 줄이는 것에 대한 관심이 커지고 있다. 이에 따라 다양한 분야의 많은 연구자들과 산업에서도 이산화탄소의 배출을 줄이고자 노력하고 있다. 특히 화학공학자들은 온실 가스를 사용하여 유용한 케미컬을 생산할 수 있는 탄소 활용 반응 공정들을 개발해왔다. 이러한 반응들에 대해 이미 상용 공정들이 개발되어 있지만 이 반응들의 반응 메커니즘에 대해서는 여전히 논쟁이 진행 중이다. 컴퓨터 계산 성능의 발전과 더불어 반응 메커니즘 탐색에 대한 연구는 새로운 국면을 맞아 더욱 활발해지고 있다. 상당한 계산량을 요구하는 계산 화학은 반응 메커니즘 분석에 엄청난 도움이 되고 있다. 더욱이 키네틱 관점에서 메커니즘을 분석할 수 있는 마이크로키네틱 스터디는 계산 화학의 발전과 더불어 시너지 효과를 낼 수 있다. 화학 공학에서 전통적인 키네틱 모델은 주로 공정 개발에 사용되는 반면, 마이크로키네틱 모델은 이러한 장점에 더하여 근본적인 분석이 가능하다. 이러한 이유로 널리 알려진 반응들에 대해서도 마이크로키네틱을 통한 메커니즘 분석은 활발하게 이루어지고 있다. 본 학위 논문에서는 기존의 몇 가지 결점들을 개선할 수 있는 실용적인 마이크로키네틱 모델링 전략을 제안하였다. 메탄올 및 디메틸에테르(DME) 합성 관련 반응들에 대해서 밀도범함수 이론(DFT) 및 이 결과를 이용한 마이크로키네틱 모델링을 수행하고, 이를 통한 반응 메커니즘 분석 및 여러 케이스 스터디를 진행하였다. 파라미터 추정 기법을 이용하여 예측값과 실험값의 차이를 최소화 하는 방향으로 Pre-exponential 인자를 실험 데이터에 피팅하였다. 이러한 마이크로키네틱스에의 실용적인 모델링 접근법은 모델의 계산효율과 신뢰성을 개선할 수 있었다. 논문의 첫 번째 부분으로 Lumped 키네틱 모델과 마이크로키네틱 모델의 차이를 강조하기 위해, Cu/ZnO/Al2O3/ferrierite (CZA/FER) 하이브리드 촉매 하에서 합성가스로부터 디메틸에테르로의 직접 전환 반응에 대해 Lumped 키네틱 모델을 개발하였다. 키네틱 파라미터는 하이브리드 촉매에서의 실험 값에 피팅되도록 추정하였고, 이는 CZA 및 FER 촉매 각각에서 보고된 선행 연구에서의 값과 비교하였다. 하이브리드 촉매에서의 높은 활성화 에너지는 메탄올 합성 단계가 메탄올 탈수 단계보다 전체적인 반응 속도를 조절하는 인자라는 것을 보여주었다. 또한 개발된 키네틱 모델을 통해 200 ~ 220 ℃의 온도에서 운전하는 것이 효율적임을 알 수 있었으며, 최적의 운전 압력 및 공간 속도를 제시하였다. 두 번째 부분에서는 구리 기반 촉매 하에서 합성가스로부터 메탄올을 합성하는 반응에 대해서 마이크로키네틱 모델링을 하기 위한 실용적인 방법에 대해 묘사하였다. 일산화탄소 및 이산화탄소의 수소화 반응, Water-gas shift 반응에 대해 28개의 단일단계반응을 고려하였다. DFT와 반경험적인 방법론인 Unity bond index-quadratic exponential (UBI-QEP) 기법을 조합하여 흡착열 및 활성화 에너지를 도출하였다. DFT 계산을 통해 포름산염(HCOO**)이 이좌배위자(Bidentate) 형태로 흡착되는 것을 확인하였으며, UBI-QEP 계산을 위한 기상과 흡착된 중간 생성물들의 흡착에너지 및 엔탈피를 제공하였다. Pre-exponential 인자의 경우에는 전이상태이론의 Order-of-magnitude에 기반하여 초기 값을 설정하고, 실험 데이터에 피팅하였다. 덕분에 이를 위한 진동 주파수 및 분배 함수를 계산하지 않아 계산 로드를 줄일 수 있었다. 반응기 모델에서는 마이크로키네틱 모델의 경직성을 완화하기 위해 부분평형비를 계산하였다. 상대적으로 빠른 단일단계반응을 기반으로 우세한 반응 경로를 제안하였으며, Degree of rate control 계산을 통해 H3CO*와 H*의 표면 반응이 속도 결정 단계임을 제안하였다. 또한 운전 온도, 압력 및 Feed의 H2 분율이 메탄올 합성 속도에 미치는 영향을 알아보기 위해 개발된 모델을 사용하였다. 세 번째 부분에서는 계산 화학 및 마이크로키네틱 모델링을 통해, H-zeolite 촉매 하에서 메탄올 탈수 반응에 의한 디메틸에테르 합성에 대해서 반응 경로를 분석하였다. 반응 메커니즘으로는 Associative 및 Dissociative 경로에 대해서 9개의 단일단계반응을 포함하였다. 이러한 반응 시스템에서는 분산력의 영향이 있으므로 2차 묄러-플레셋 섭동 이론(MP2)에 기반하여 반응종들의 구조를 최적화하였다. 또한, 반응의 전이 상태를 도출하였으며 이와 최적 분자 구조의 에너지 및 활성화 에너지를 계산하였다. 이 결과에 기반하여 마이크로키네틱 모델을 개발하였고, Pre-exponential 인자는 마찬가지로 실험 데이터에 피팅하였다. 이러한 방법론은 개발된 마이크로키네틱 모델의 신뢰성을 강화하였다. 단일단계반응들의 상대적인 반응 속도를 비교하여 Dissociative 경로가 우세하게 작용함을 알 수 있었으며, 이 경로의 DME 생성 반응(CH3OH-CH3-Z → CH3OCH3-H-Z)을 속도 결정 단계로 제안하였다. 마찬가지로 이 모델을 통해 온도가 촉매 표면의 농도 분포에 미치는 영향을 분석하였다. 마지막으로, Water-gas shift 반응에 대한 마이크로키네틱 모델에 대하여 기계학습 기반의 대체 모델을 제시하였다. 마이크로키네틱 대체 모델은 마이크로키네틱스와 전산유체역학이나 공정 시뮬레이션과 같은 더 높은 차원의 반응 공학 모듈을 이어주는 다리 역할을 할 수 있다. ExtraTrees 알고리즘과 인공신경망을 이용하여 개발된 마이크로키네틱 모델로부터 얻은 데이터셋을 회귀하였다. 보간 기계학습 기법 중에서 인공신경망은 회귀 분석에서 높은 성능을 낼 수 있는 것으로 잘 알려져 있고, ExtraTrees 알고리즘은 특성 중요도를 계산 할 수 있다. 인공신경망 기반의 대체 모델은 평균 오차율 0.01%로 좋은 성능을 보여주었다. ExtraTrees 일고리즘은 특성 중요도를 측정할 수 있어, Water-gas shift 반응에서 중요한 단일단계반응과 중요한 촉매 표면의 중간생성물을 찾아낼 수 있었다.In recent years, as environmental issues continue to emerge, interest in carbon utilization where carbon dioxide is the primary species to be reduced is growing. Accordingly, many researchers and industries in various fields have tried to reduce carbon emissions into the atmosphere. In particular, chemical engineers have developed carbon utilizing reaction processes which produce a variety of useful chemicals by consuming the greenhouse gases. Although the commercial processes related to these reactions have already been developed, controversy over their reaction mechanisms is still ongoing. Along with advances in computational performance, researches on reaction mechanism exploration are becoming more active in a new phase. Computational chemistry, which requires high computational costs, is a great help for reaction mechanism analysis. Moreover, microkinetic study is a study that can analyze mechanisms from a kinetic perspective, creating synergies along with improvements in computational chemistry. While conventional kinetic models in chemical engineering have been mainly used in terms of process design, microkinetic models, in addition to these advantages, allow fundamental analysis. For these reasons, mechanism analysis through microkinetics is actively underway even for common reactions. In this thesis, practical microkinetic modeling strategies that could improve several previous drawbacks were proposed. For reactions related to methanol and dimethyl ether (DME) synthesis, density functional theory (DFT) calculations and microkinetic modeling using the DFT results were conducted, and the reaction mechanism analysis and the several case studies were suggested. By using parameter estimation techniques, pre-exponential factors were fitted to experimental data minimizing the differences between the predicted and the experimental values. This practical modeling approach to the microkinetics improved computational efficiency and reliability of the model. In the first part, a lumped kinetic model for the direct synthesis of dimethyl ether from syngas over Cu/ZnO/Al2O3/ferrierite (CZA/FER) catalyst was presented to highlight the difference from a microkinetic model. Kinetic parameters were estimated by fitting experimental data for the hybrid catalyst, and these were compared with the reported values of conventional catalysts, which were the respective CZA and FER catalysts. High activation energies for the hybrid catalyst showed that the methanol synthesis step may have more control over the rate than the methanol dehydration step. Using the developed kinetic model, a temperature between 200 and 220 °C was determined for thermal energy efficiency, and a further analysis provided the optimal range of the total pressure and space velocity. A practical strategy to develop a microkinetic model for methanol synthesis from syngas over a Cu-based catalyst is described in the second part. The comprehensive model consists of forward and backward reactions of 28 possible elementary-step reactions for CO and CO2 hydrogenation and the water–gas shift reaction. A combination of ab-initio DFT and semi-empirical unity bond index-quadratic exponential (UBI-QEP) methods was used to determine the heat of adsorption and activation energies. DFT calculations confirmed that formate (HCOO**) adsorbs in a bidentate fashion and provided the enthalpies and adsorption energies of gas and surface intermediates for subsequent UBI-QEP calculations. The pre-exponential factors were estimated from the order-of-magnitude of the transition state theory as the initial values and by fitting the experimental data, thus reducing the computational load by not calculating the vibrational frequencies and partition functions for translational, rotational, and vibrational motions. For the reactor model, partial equilibrium ratios were used to reduce the stiffness of the microkinetic model. The most plausible reaction pathways were suggested by considering relatively fast step-reactions, while the surface reaction of H3CO* and H* was found to be the rate-determining step by the degree of rate control. The developed model was also used to evaluate the effects of the temperature, pressure, and H2 fraction in the feed on the methanol synthesis rate to elucidate the suitable operating conditions. In the third part, the reaction pathways of DME synthesis by methanol dehydration over a H-zeolite catalyst were analyzed through both computational chemistry and microkinetic modeling methods. The reaction mechanisms consisted of nine elementary-step reactions for both associative and dissociative pathways. Based on the second-order Møller–Plesset perturbation theory (MP2), to determine the effects of dispersion forces that were important in this reaction system, the structures of all related reaction species were optimized, and the transition states of the associative and dissociative pathways were elucidated. Also, the energies and activation barriers of the optimized structures and transition states were calculated. Then, a microkinetic model was developed using the energies and activation barriers obtained from the MP2 calculations. Meanwhile, the pre-exponential factors of the kinetic parameters were not calculated theoretically but estimated by fitting the experimental data, which enhanced the reliability of the microkinetic model. By comparing the relative elementary-step reaction rates calculated using the developed model, the dissociative pathway was suggested as a dominant pathway of DME synthesis, while the DME formation reaction of the dissociative pathway (CH3OH-CH3-Z → CH3OCH3-H-Z) was found to be the rate-determining step. The developed model was also used to evaluate the effects of temperature on the site fractions over the catalyst. Finally, machine learning-based surrogate models of the microkinetic model for the water-gas shift reaction were developed. The surrogate model can play a role in a bridge between the microkinetics and the higher-scale reaction engineering modules such as computational fluid dynamics or process simulations. The ExtraTrees algorithm and the artificial neural network (ANN) were used for regressing the datasets acquired from the developed microkinetic model. Among interpolative machine learning techniques, an ANN is well known for its high performance in regression, and the feature importance can be calculated with the ExtraTrees algorithm. As a result, the ANN showed the great performance with an average error of 0.01 %. ExtraTrees could measure the feature importance, so that the important elementary reactions and surface intermediates to the overall reaction of the water-gas shift reaction were figured out.Chapter 1 Introduction 16 1.1 Research Motivation 16 1.2 Outline of the Thesis 18 1.3 Associated Publications 18 Chapter 2 Background Theory 19 2.1 Microkinetics 19 2.2 Kinetic Parameter 22 2.2.1 Computational Chemistry 24 2.2.2 Transition State Theory 25 2.2.3 UBI-QEP 28 Chapter 3 Lumped kinetic modeling for direct synthesis of DME from syngas 30 3.1 Background 30 3.2 Methods 34 3.2.1 Experimentals 34 3.2.2 Kinetic Model 37 3.3 Application Results and Discussion 42 Chapter 4 Microkietic modeling of methanol synthesis from syngas 53 4.1 Background 53 4.2 Reaction Mechanism 59 4.3 Methods 63 4.3.1 Activation Energy 63 4.3.2 Microkinetic Model 67 4.4 Application Results and Discussion 74 4.4.1 DFT Calculations 74 4.4.2 Microkinetic Model 78 4.4.3 Rate-Determining Step 88 4.4.4 Effects of Operating Conditions 89 Chapter 5 Microkinetic modeling of DME synthesis from methanol over H-zeolite catalyst 92 5.1 Background 92 5.2 Reaction mechanism 97 5.3 Methods 102 5.3.1 Computational Chemistry 102 5.3.2 Microkinetic Model 106 5.4 Application results and discussion 109 5.4.1 MP2 Calculations 109 5.4.2 Microkinetic Model 126 Chapter 6 Machine Learning-based Surrogate Model of Microkinetics for the Water-Gas Shift Reaction 136 6.1 Background 136 6.2 Reaction Mechanism 138 6.3 Methods 140 6.3.1 Microkinetic Model 140 6.3.2 Surrogate Model 143 6.4 Application Results and Discussion 148 6.4.1 Microkinetic Model 148 6.4.2 Surrogate Model 151 Chapter 7 Concluding Remarks 157 7.1 Summary of Contributions 157 7.2 Future Work 160 Appendix 162 Supporting Information 162 Bibliography 165 Abstract in Korean (국문초록) 177박

A Surrogate Model Assisted Evolutionary Algorithm for Computationally Expensive Design Optimization Problems with Discrete Variables

Real-world computationally expensive design optimization problems with discrete variables pose challenges to surrogate-based optimization methods in terms of both efficiency and search ability. In this paper, a new method is introduced, called surrogate model-aware differential evolution with neighbourhood exploration, which has two phases. The first phase adopts a surrogate-based optimization method based on efficient surrogate model-aware search framework, the goal of which is to reach at least the neighbourhood of the global optimum. In the second phase, a neighbourhood exploration method for discrete variables is developed and collaborates with the first phase to further improve the obtained solutions. Empirical studies on various benchmark problems and a real-world network-on-chip design optimization problem show the combined advantages in terms of efficiency and search ability: when only a very limited number of exact evaluations are allowed, the proposed method is not slower than one of the most efficient methods for the targeted problem; when more evaluations are allowed, the proposed method can obtain results with comparable quality compared to standard differential evolution, but it requires only 1% to 30% of exact function evaluations

A Surrogate Model Assisted Evolutionary Algorithm for Computationally Expensive Design Optimization Problems with Discrete Variables

Real-world computationally expensive design optimization problems with discrete variables pose challenges to surrogate-based optimization methods in terms of both efficiency and search ability. In this paper, a new method is introduced, called surrogate model-aware differential evolution with neighbourhood exploration, which has two phases. The first phase adopts a surrogate-based optimization method based on efficient surrogate model-aware search framework, the goal of which is to reach at least the neighbourhood of the global optimum. In the second phase, a neighbourhood exploration method for discrete variables is developed and collaborates with the first phase to further improve the obtained solutions. Empirical studies on various benchmark problems and a real-world network-on-chip design optimization problem show the combined advantages in terms of efficiency and search ability: when only a very limited number of exact evaluations are allowed, the proposed method is not slower than one of the most efficient methods for the targeted problem; when more evaluations are allowed, the proposed method can obtain results with comparable quality compared to standard differential evolution, but it requires only 1% to 30% of exact function evaluations

복잡한 동특성을 갖는 다상 반응기의 설계를 위한 계산 효율적인 모사 및 최적화 전략

학위논문(박사)--서울대학교 대학원 :공과대학 화학생물공학부,2020. 2. 이종민.본 박사학위논문에서는 멀티 스케일 모델링, 실험 결과를 이용한 모델 보정법, 최적화 순으로 진행되는 산업용 화학 반응기의 설계 전략을 제시한다. 반응기는 화학 공정에서 제일 중요한 단위이지만, 그 설계에 있어서는 최신 수치적 기법들보다는 여전히 간단한 모델이나 실험 및 경험 규칙에 의존하고 있는 현실이다. 산업 규모의 반응기는 물리, 화학적으로 몹시 복잡하고, 관련 변수 간의 스케일이 크게 차이나는 경우가 많아 수학적 모델링 및 수치적 해법을 구하기가 어렵다. 모델을 만들더라도 부정확하거나 시뮬레이션 시간이 너무 긴 문제가 있어 최적화 알고리즘에 적용하기가 힘들다. 반응기 내 현상의 복잡성과 스케일 차이 문제는 멀티 스케일 모델링을 통해 접근할 수 있다. 전산유체역학 기반 구획 모델(CFD-based compartmental model)을 이용하면, 불균일한 혼합 패턴을 보이는 대형 반응기에서도 긴 시간 동안의 동적 모사가 가능하다. 이 모델은 큰 반응기를 완벽하게 균일한 작은 구획들의 네트워크로 간주하고, 각 구획을 반응 속도식들과 CFD 결과로부터 가져온 유동 정보가 포함된 질량 및 에너지 균형 방정식으로 표현한다. 기체, 액체, 고체 3상이 상호작용하며 복잡한 유동을 보이는 수성 광물 탄산화 반응기를 이 방법을 사용해 모델링하였다. 이 때 모델은 미분 대수 방정식(DAE)의 형태를 띠며, 메커니즘 상 모든 반응들(기-액 간 물질 전달 반응, 고체 용해 반응, 이온 간 반응, 앙금 침전 반응)과 유체 역학, 반응열, 열역학적 변화 및 운전 상의 이벤트 발생을 모두 고려할 수 있다. 모델을 이용해 이산화탄소 제거 효율, pH 및 온도 변화를 예측하여 실제 운전 데이터와 비교한 결과, 파라미터를 통한 보정이 전혀 없이도 7 % 이내의 오차를 보여주었다. 모델의 부정확성 문제는 모델링 후 실험 결과를 이용한 모델 보정으로 극복 할 수 있다. 본 논문에서는 광물 탄산화 반응기 모델을 베이지안 보정(Bayesian calibration)을 통해 강화하는 방법을 제시한다. 먼저 모델 중 불확실한 부분에 8개의 파라미터를 도입한 후, 베이지안 파라미터 추정법(Bayesian parameter estimation) 및 실험실 규모에서의 실험 결과들을 이용하여 파라미터들의 사후 확률 분포를 추정하였다. 얻어진 파라미터의 확률 분포들은 모델 및 실험의 불완전성으로 인해 나타나는 파라미터의 불확실성 및 다중 봉우리 특성을 반영하고 있다. 이를 이용하여 실험 결과를 잘 따라가는 확률론적 모델 예측치(stochastic model response)를 얻을 수 있었다. 16개의 실험 데이터셋 및 테스트셋의 피팅 에러(fitting error)는 결정론적인 최적화 알고리즘(deterministic optimization)을 사용할 때보다 비슷하거나 낮은 것으로 측정되었다. 수학적 최적화에 쓰이기에 너무 긴 시뮬레이션 시간 문제는 베이지안 최적화 알고리즘을 적용하여 해결할 수 있다. 화학 반응기 설계 최적화를 위해 본 논문에서는 다중 목적 베이지안 최적화(Multi-objective Bayesian Optimization, MBO)를 사용해 시뮬레이션 횟수를 최소화 하는 CFD 기반 최적 설계 방법을 제안하였다. 여섯 가지 설계 변수를 가지는 기-액 교반 탱크 반응기에서 전력 소비를 최소화하고 가스 분율(gas holdup)를 극대화하기 위해 이 방법을 이용한 결과, 단 100 회의 시뮬레이션 만으로 최적 파레토 커브(Pareto curve)를 얻을 수 있었다. 제안된 최적 설계안들은 문헌에 보고된 기존 반응기들과 비교해 뛰어난 성능을 보여주었다. . 본 논문을 통해 제안된 CFD 기반 구획 모델링법, 베이지안 모델 보정법 및 베이지안 최적화 방법은 복잡한 물리적 및 화학적 특징을 갖는 산업 규모의 화학 반응기에 적용될 수 있을 것으로 기대된다.This thesis presents a design strategy for industrial-scale chemical reactors which consists of multi-scale modeling, post-modeling calibration, and optimization. Although the reactor design problem is a primary step in the development of most chemical processes, it has been relied on simple models, experiments and rules of thumbs rather than taking advantage of recent numerical techniques. It is because industrial-size reactors show high complexity and scale differences both physically and chemically, which makes it difficult to be mathematically modeled. Even after the model is constructed, it suffers from inaccuracies and heavy simulation time to be applied in optimization algorithms. The complexity and scale difference problem in modeling can be solved by introducing multi-scale modeling approaches. Computational fluid dynamics (CFD)-based compartmental model makes it possible to simulate hours of dynamics in large size reactors which show inhomogeneous mixing patterns. It regards the big reactor as a network of small zones in which perfect mixing can be assumed and solves mass and energy balance equations with kinetics and flow information adopted from CFD hydrodynamics model at each zone. An aqueous mineral carbonation reactor with complex gas–liquid–solid interacting flow patterns was modeled using this method. The model considers the gas-liquid mass transfer, solid dissolution, ionic reactions, precipitations, hydrodynamics, heat generation and thermodynamic changes by the reaction and discrete operational events in the form of differential algebraic equations (DAEs). The total CO2 removal efficiency, pH, and temperature changes were predicted and compared to real operation data. The errors were within 7 % without any post-adjustment. The inaccuracy problem of model can be overcome by post-modeling approach, such as the calibration with experiments. The model for aqueous mineral carbonation reactor was intensified via Bayesian calibration. Eight parameters were intrduced in the uncertain parts of the rigorous reactor model. Then the calibration was performed by estimating the parameter posterior distribution using Bayesian parameter estimation framework and lab-scale experiments. The developed Bayesian parameter estimation framework involves surrogate models, Markov chain Monte Carlo (MCMC) with tempering, global optimization, and various analysis tools. The obtained parameter distributions reflected the uncertain or multimodal natures of the parameters due to the incompleteness of the model and the experiments. They were used to earn stochastic model responses which show good fits with the experimental results. The fitting errors of all the 16 datasets and the unseen test set were measured to be comparable or lower than when deterministic optimization methods are used. The heavy simulation time problem for mathematical optimization can be resolved by applying Bayesian optimizaion algorithm. CFD based optimal design tool for chemical reactors, in which multi-objective Bayesian optimization (MBO) is utilized to reduce the number of required CFD runs, is proposed. The developed optimizer was applied to minimize the power consumption and maximize the gas holdup in a gas-sparged stirred tank reactor, which has six design variables. The saturated Pareto front was obtained after only 100 iterations. The resulting Pareto front consists of many near-optimal designs with significantly enhanced performances compared to conventional reactors reported in the literature. It is anticipated that the suggested CFD-based compartmental modeling, post-modeling Bayesian calibration, and Bayesian optimization methods can be applied in general industrial-scale chemical reactors with complex physical and chemical features.1. Introduction 1 1.1. Industrial-scale chemical reactor design 1 1.2. Role of mathematical models in reactor design 2 1.3. Intensification of reactor models through calibration 5 1.3.1. Bayesian parameter estimation 6 1.4. Optimization of the reactor models 7 1.4.1. Bayesian optimization 9 1.5. Aqueous mineral carbonation process : case study subject 10 1.6. Outline of the thesis 12 2. Multi-scale modeling of industrial-scale aqueous mineral carbonation reactor for long-time dynamic simulation 14 2.1. Objective 14 2.2. Experimental setup 15 2.3. Mathematical models 19 2.3.1. Reactor model 19 2.3.2. CFD model 28 2.3.3. Numerical setting 30 2.4. Results and discussions 32 2.4.1. CFD-based compartmental model for industrial-scale reactor. 32 2.4.2. Design and simulation of higher-scale reactors 42 2.5. Conclusions 47 3. Model intensification of aqueous mineral carbonation kinetics via Bayesian calibration 50 3.1. Objective 50 3.2. Experimental methods 51 3.2.1. Solution and gas preparation 51 3.2.2. Laboratory-scale mineral carbonation process 53 3.3. Mathematical models 56 3.3.1. Kinetics of aqueous mineral carbonation process 56 3.3.2. Differential algebraic equation (DAE) model for the reactor 65 3.3.3. Discrete events for simulation procedure 71 3.3.4. Numerical setting 72 3.4. Bayesian parameter estimation 72 3.4.1. Problem formulation 73 3.4.2. Bayesian posterior inference 76 3.4.3. Sampling 81 3.5. Results and discussions 82 3.5.1. Stochastic output response 82 3.5.2. Quality of parameter estimtates 86 3.5.3. Assessment of parameter uncertainties 91 3.5.4. Kinetics study with the proposed model parameters 99 3.6. Conclusions 103 4. Multi-objective optimization of chemical reactor design using computational fluid dynamics 106 4.1. Objective 106 4.2. Problem Formulation 107 4.3. Optimization scheme 113 4.3.1. Multi-objective optimization algorithm 113 4.3.2. CFD-MBO optimizer 120 4.4. CFD modeling 125 4.4.1. Tank specifications 125 4.4.2. Governing equations 125 4.4.3. Simulation methods 127 4.5. Results and discussion 128 4.5.1. CFD model validation 128 4.5.2. Optimization results 130 4.5.3. Analysis of optimal designs 139 4.6. Conclusions 144 5. Concluding Remarks 146 Bibliography 149 Abstract in Korean (국문초록) 163Docto

Numerical simulation of a single floating point absorber wave energy converter using OpenFOAM

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