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Home energy management strategy to schedule multiple types of loads and energy storage device with consideration of user comfort: a deep reinforcement learning based approach 考虑用户舒适度的多类型负载和储能设备调度家庭能源管理策略:基于深度强化学习的方法
Pub Date : 2024-06-05 DOI: 10.3389/fther.2024.1391602
Tingzhe Pan, Zean Zhu, Hongxuan Luo, Chao Li, Xin Jin, Z. Meng, Xinlei Cai
With the increase in the integration of renewable sources, the home energy management system (HEMS) has become a promising approach to improve grid energy efficiency and relieve network stress. In this context, this paper proposes an optimization dispatching strategy for HEMS to reduce total cost with full consideration of uncertainties, while ensuring the users’ comfort. Firstly, a HEMS dispatching model is constructed to reasonably schedule the start/stop time of the dispatchable appliances and energy storage system to minimize the total cost for home users. Besides, this dispatching strategy also controls the switching time of temperature-controlled load such as air conditioning to reduce the energy consumption while maintaining the indoor temperature in a comfortable level. Then, the optimal dispatching problem of HEMS is modeled as a Markov decision process (MDP) and solved by a deep reinforcement learning algorithm called deep deterministic policy gradient. The example results verify the effectiveness and superiority of the proposed method. The energy cost can be effectively reduced by 21.9% at least compared with other benchmarks and the indoor temperature can be well maintained.
随着可再生能源集成度的提高,家庭能源管理系统(HEMS)已成为提高电网能源效率、缓解电网压力的一种有前途的方法。在此背景下,本文提出了一种针对 HEMS 的优化调度策略,以在充分考虑不确定性的情况下降低总成本,同时确保用户的舒适度。首先,构建 HEMS 调度模型,合理安排可调度电器和储能系统的启停时间,使家庭用户的总成本最小化。此外,该调度策略还能控制空调等温控负载的开关时间,在降低能耗的同时保持室内温度在舒适水平。然后,将 HEMS 的优化调度问题建模为马尔可夫决策过程(MDP),并通过一种称为深度确定性策略梯度的深度强化学习算法来求解。实例结果验证了所提方法的有效性和优越性。与其他基准相比,能源成本至少有效降低了 21.9%,室内温度也得到了很好的保持。
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引用次数: 0
An effect of a snow cover on solar heating and melting of lake or sea ice 雪层对太阳辐射加热和湖泊或海冰融化的影响
Pub Date : 2024-01-15 DOI: 10.3389/fther.2023.1354265
L. Dombrovsky
Solar radiative heating and melting of lake and sea ice is a geophysical problem that has attracted the attention of researchers for many years. This problem is important in connection with the current global change of the climate. Physical and computational models of the process are suggested in the paper. Analytical solutions for the transfer of solar radiation in light-scattering snow cover and ice are combined with numerical calculations of heat transfer in a multilayer system. The thermal boundary conditions take into account convective heat losses to the ambient air and radiative cooling in the mid-infrared window of transparency of the cloudless atmosphere. The study begins with an anomalous spring melting of ice on the large high-mountain lakes of Tibet. It was found that a thick ice layer not covered with snow starts to melt at the ice-water interface due to volumetric solar heating of ice. The results of the calculations are in good agreement with the field observations. The computational analysis showed a dramatic change in the process when the ice is covered with snow. A qualitative change in the physical picture of the process occurs when the snow cover thickness increases to 20–30 cm. In this case, the snow melting precedes ice melting and water ponds are formed on the ice surface. This is typical for the Arctic Sea in polar summer. Known experimental data are used to estimate the melting of sea ice under the melt pond. Positive or negative feedback related to the specific optical and thermal properties of snow, ice, and water are discussed.
太阳辐射加热和湖泊及海冰融化是一个地球物理问题,多年来一直吸引着研究人员的注意力。这一问题与当前全球气候变化密切相关。本文提出了这一过程的物理和计算模型。光散射雪盖和冰中太阳辐射传递的分析解与多层系统中热量传递的数值计算相结合。热边界条件考虑了环境空气的对流热损失和无云大气透明度中红外窗口的辐射冷却。研究从西藏大型高山湖泊春季异常融冰开始。研究发现,由于太阳对冰的体积加热,没有被雪覆盖的厚冰层开始在冰水界面融化。计算结果与实地观测结果十分吻合。计算分析表明,当冰被雪覆盖时,这一过程发生了巨大变化。当积雪厚度增加到 20-30 厘米时,物理过程发生了质的变化。在这种情况下,雪融化先于冰融化,冰面上形成水塘。这是极地夏季北极海的典型现象。已知的实验数据用于估算融化池下海冰的融化情况。讨论了与雪、冰和水的特定光学和热学特性有关的正反馈。
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引用次数: 0
Evaluating the onset conditions of a thermoacoustic Stirling engine loaded with an audio loudspeaker 评估装有音频扬声器的热声斯特林发动机的启动条件
Pub Date : 2023-12-08 DOI: 10.3389/fther.2023.1241411
Shu-Han Hsu, Chuan-Heng Lai
This paper aims to evaluate the onset conditions of a thermoacoustic Stirling engine loaded with a commercially available audio loudspeaker. The thermoacoustic engine converts supplied heat power into mechanical power in the form of sound, without any mechanical moving parts. The simplicity of the acoustical heat engine holds great promise for high reliability and low cost. By utilizing a readily available electromagnetic device, the engine can serve as a durable solution for practical applications. In this study, we assembled a commercially available moving-coil loudspeaker as a low-cost linear alternator for the thermoacoustic Stirling engine, enabling electric generation from supplied heat. We modeled the loudspeaker using linear control equations and experimentally calibrated its acoustic impedances to estimate the acoustic load. For the part of the thermoacoustic engine, we estimated its acoustic characteristics within the framework of the linear thermoacoustic theory. By solving the characteristic equation resulting from the engine loaded with the audio speaker, we estimated the operational point of self-sustained oscillations excited by the coupling of the loudspeaker and the thermoacoustic engine system. To validate the estimations, we tested a prototype of the combined system, comprising the loudspeaker and the thermoacoustic engine. The results highlight the necessity of precise calibration and accounting for complex geometries within the acoustic load for accurate theoretical estimations, especially when incorporating a commercially available loudspeaker into a thermoacoustic engine.
本文旨在评估装有商用音频扬声器的热声斯特林发动机的起动条件。热声发动机将提供的热能以声音的形式转化为机械能,而不需要任何机械运动部件。声热机的简单性为高可靠性和低成本提供了很大的希望。通过利用一个现成的电磁装置,发动机可以作为一个持久的解决方案,为实际应用。在这项研究中,我们组装了一个市售的动圈扬声器,作为热声斯特林发动机的低成本线性交流发电机,使热能发电成为可能。我们使用线性控制方程对扬声器进行建模,并通过实验校准其声阻抗来估计声负载。对于热声发动机部分,我们在线性热声理论的框架内估计了其声学特性。通过求解装有扬声器的发动机的特性方程,估计了由扬声器和热声发动机系统耦合激发的自持续振荡的工作点。为了验证这些估计,我们测试了一个组合系统的原型,包括扬声器和热声发动机。研究结果强调了精确校准和计算声载荷内复杂几何形状的必要性,以便进行准确的理论估计,特别是在将市售扬声器集成到热声发动机中时。
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引用次数: 0
Integration of carbon capture in a pulp mill—effect of strategic development towards better biomass resource utilization 纸浆厂碳捕集一体化战略发展对生物质资源更好利用的影响
Pub Date : 2023-11-01 DOI: 10.3389/fther.2023.1282028
Henrik Skoglund, Chao Fu, Simon Harvey, Elin Svensson
The pulp and paper industry has an important role in the industrial transition towards net zero or negative emissions, given its renewable biomass-based feedstock and energy supply. In particular, pulp and paper mills have large existing sources of biogenic CO 2, with a high potential to contribute to carbon dioxide removal through carbon capture and storage (CCS). To effectively navigate anticipated changes in feedstock and energy markets, there is a need for a better understanding of how different technology pathways for the pulp and paper industry interact with one another, for instance, how enhanced valorization of biomass side streams may affect the potential for carbon capture. This paper aims to investigate the effect of combining carbon capture with lignin extraction in a chemical pulp mill. Pinch analysis is used to study how the targets for heat recovery, fuel usage and electricity generation, are affected by different mill and capture configurations. Based on these results, the effect on carbon flows is evaluated. The results show that when carbon capture technology is implemented and fuel use is minimized at the case-study mill, there is still enough heat available from the recovery boilers to supply the process needs without requiring usage of a utility boiler. However, when carbon capture is combined with lignin extraction, the heat production of the recovery boilers is no longer sufficient to cover the process demands, and additional heat from a utility boiler is required. However, this case implies that some of the carbon leaves the mill embedded in the extracted lignin product, which can be expected to have a higher value than captured carbon dioxide. When back-pressure electricity production was maximized for the different mill configurations, a very high fuel-to-electricity efficiency could be achieved, but since the CO 2 emissions from the utility boiler were not assumed to be captured, this would lead to more carbon being emitted compared to the capture scenarios with minimized fuel use.
鉴于其可再生生物质原料和能源供应,纸浆和造纸工业在向净零排放或负排放的工业转型中发挥着重要作用。特别是,纸浆和造纸厂有大量现有的生物源二氧化碳,通过碳捕获和储存(CCS)有助于二氧化碳去除的潜力很大。为了有效地应对原料和能源市场的预期变化,需要更好地了解纸浆和造纸工业的不同技术途径如何相互作用,例如,生物质侧流的增强增值如何影响碳捕获的潜力。研究了化学纸浆厂碳捕集与木质素提取相结合的效果。夹点分析用于研究不同的磨机和捕集配置对热回收、燃料使用和发电目标的影响。在此基础上,对碳流的影响进行了评价。结果表明,在案例研究工厂实施碳捕获技术并最大限度地减少燃料使用后,回收锅炉仍有足够的热量来满足工艺需求,而无需使用公用事业锅炉。然而,当碳捕获与木质素提取相结合时,回收锅炉产生的热量不再足以满足工艺需求,并且需要公用事业锅炉提供额外的热量。然而,这种情况意味着一些碳离开磨坊嵌入在提取的木质素产品中,可以预期比捕获的二氧化碳具有更高的价值。当背压发电量在不同的工厂配置中最大化时,可以实现非常高的燃料-电力效率,但是由于公用事业锅炉的二氧化碳排放没有被假定为被捕获,这将导致与最小化燃料使用的捕获方案相比排放更多的碳。
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引用次数: 0
Grand challenges in heat engines 热机的巨大挑战
Pub Date : 2023-10-24 DOI: 10.3389/fther.2023.1301616
Ricardo Novella
SPECIALTY GRAND CHALLENGE article Front. Therm. Eng., 24 October 2023Sec. Heat Engines Volume 3 - 2023 | https://doi.org/10.3389/fther.2023.1301616
专业大挑战文章前沿。小卡。Eng。2023年10月24日热机卷3 - 2023 | https://doi.org/10.3389/fther.2023.1301616
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引用次数: 0
Modeling of diesel particulate filter temperature dynamics during exotherm using neural networks 柴油机微粒过滤器放热过程温度动态的神经网络建模
Pub Date : 2023-10-18 DOI: 10.3389/fther.2023.1265490
Adithya Legala, Venkata LakkiReddy, Phillip Weber, Xianguo Li
Diesel Particulate Filter (DPF) in the diesel engine exhaust stream needs frequent regeneration (exotherm) to remove captured particulate matter (PM, or soot) without damaging to the porous DPF structure by controlling the peak temperatures and temperature gradients across the DPF. In this study, temperature distribution in a DPF is measured at 42 strategic locations in the test DPF under various regeneration conditions of exhaust flow rates, regeneration temperatures and soot loads. Then a data-based model with feed-forward neural network architecture is designed to model the thermal gradients and temperature dynamics of the DPF during the regeneration process. The neural network feature vector selection, network architecture, hyperparameter calibration process, measured data preprocessing, and experimental data acquisition procedure are evaluated. Over 7,400 experimental data points at various regeneration temperatures, flow rates and soot loads are used in training and validating the neural network model. It is found that the neural network model can accurately predict the 42 DPF bed temperatures simultaneously at different locations, and the time series analysis of both model-predicted and experimentally measured temperatures shows a good correlation. This indicates that the currently developed neural network model can provide spatial distribution of temperature in the DPF, and comprehend the nonlinearity of the temperature dynamics due to DPF soot load at exothermic conditions. These results demonstrate that the data-based model has capability in predicting thermal gradients within a DPF, aiding in determining a safer DPF regeneration strategy, onboard diagnostics and DPF development.
柴油发动机排气流中的柴油微粒过滤器(DPF)需要频繁的再生(放热)来去除捕获的颗粒物(PM或烟灰),而不会通过控制DPF的峰值温度和温度梯度来破坏多孔DPF结构。在本研究中,在排气流量、再生温度和烟尘负荷的不同再生条件下,在试验DPF的42个关键位置测量了DPF内的温度分布。然后设计了基于数据的前馈神经网络模型,对再生过程中DPF的温度梯度和温度动态进行了建模。评估了神经网络特征向量选择、网络结构、超参数校准过程、测量数据预处理和实验数据采集过程。在不同的再生温度、流量和烟尘负荷下,使用了7400多个实验数据点来训练和验证神经网络模型。结果表明,该神经网络模型能较准确地同时预测不同地点的42个DPF床层温度,模型预测温度与实验测量温度的时间序列分析均显示出较好的相关性。这表明,目前建立的神经网络模型可以提供DPF内温度的空间分布,并能理解DPF在放热条件下烟灰负荷对温度动态的非线性影响。这些结果表明,基于数据的模型能够预测DPF内部的热梯度,有助于确定更安全的DPF再生策略、机载诊断和DPF开发。
{"title":"Modeling of diesel particulate filter temperature dynamics during exotherm using neural networks","authors":"Adithya Legala, Venkata LakkiReddy, Phillip Weber, Xianguo Li","doi":"10.3389/fther.2023.1265490","DOIUrl":"https://doi.org/10.3389/fther.2023.1265490","url":null,"abstract":"Diesel Particulate Filter (DPF) in the diesel engine exhaust stream needs frequent regeneration (exotherm) to remove captured particulate matter (PM, or soot) without damaging to the porous DPF structure by controlling the peak temperatures and temperature gradients across the DPF. In this study, temperature distribution in a DPF is measured at 42 strategic locations in the test DPF under various regeneration conditions of exhaust flow rates, regeneration temperatures and soot loads. Then a data-based model with feed-forward neural network architecture is designed to model the thermal gradients and temperature dynamics of the DPF during the regeneration process. The neural network feature vector selection, network architecture, hyperparameter calibration process, measured data preprocessing, and experimental data acquisition procedure are evaluated. Over 7,400 experimental data points at various regeneration temperatures, flow rates and soot loads are used in training and validating the neural network model. It is found that the neural network model can accurately predict the 42 DPF bed temperatures simultaneously at different locations, and the time series analysis of both model-predicted and experimentally measured temperatures shows a good correlation. This indicates that the currently developed neural network model can provide spatial distribution of temperature in the DPF, and comprehend the nonlinearity of the temperature dynamics due to DPF soot load at exothermic conditions. These results demonstrate that the data-based model has capability in predicting thermal gradients within a DPF, aiding in determining a safer DPF regeneration strategy, onboard diagnostics and DPF development.","PeriodicalId":73110,"journal":{"name":"Frontiers in thermal engineering","volume":"144 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solvent recovery from solvent-fine coal slurries by filtration and steam stripping 通过过滤和汽提从溶剂细粒煤浆中回收溶剂
Pub Date : 2023-08-22 DOI: 10.3389/fther.2023.1239800
Michael Huylo, Kaiwu Huang, A. Noble, R. Yoon, Rui Qiao
Dewatering of fine coal is a significant industrial challenge with economic and environmental implications. Due to the lack of suitable dewatering technologies, fine coal particles are often discarded to waste impoundments, leading to substantial loss of valuable natural resources while creating environmental problems. The hydrophobic-hydrophilic separation (HHS) process is a unique solution to this problem. In this process, a recyclable solvent is used to simultaneously remove inorganic impurities (ash) and water from a run-of-mine fine coal slurry. A small amount of recyclable oil (or solvent) is added to a fine coal slurry so that the solvent can spontaneously displace the water from the surface of coal particles. The spent solvent is subsequently recovered and recycled in a closed loop. Here, we report the results obtained using two different solvents, i.e., pentane and hexane, to de-ash and dewater ultrafine coal and recover the spent solvent by filtration, followed by steam stripping. Most of the spent solvent can be recovered during the filtration step at 20 psig N₂ and at a 60 s filtration time. The residual solvent left in the cake was then recovered using steam under different conditions. The results showed that the residual solvent concentration could be reduced to <1,400 ppm after 10 s of steam stripping at 150°C and 15 psig.
细煤脱水是一项具有经济和环境影响的重大工业挑战。由于缺乏合适的脱水技术,细煤颗粒经常被丢弃到废水库,导致宝贵的自然资源大量流失,同时造成环境问题。疏水-亲水分离(HHS)工艺是解决这一问题的独特方法。在这个过程中,使用一种可回收的溶剂同时去除原矿细煤浆中的无机杂质(灰分)和水。在细煤浆中加入少量可回收的油(或溶剂),使溶剂能自发地取代煤颗粒表面的水。废溶剂随后在闭环中回收和循环。本文报道了采用戊烷和己烷两种不同溶剂对超细煤进行脱灰脱水,并对废溶剂进行过滤、汽提回收的结果。在20 psig N₂的过滤步骤中,过滤时间为60 s,大部分废溶剂可以被回收。然后在不同条件下用蒸汽回收饼中残留的溶剂。结果表明,在150℃、15 psig条件下汽提10 s后,残余溶剂浓度可降至< 1400 ppm。
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引用次数: 0
Editorial: Computational modeling of various procedures in thermal therapy of human tumors 社论:人类肿瘤热疗各种程序的计算模型
Pub Date : 2023-08-03 DOI: 10.3389/fther.2023.1253718
Yatao Ren, Sundeep Singh, S. Soni
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引用次数: 0
Impact of colloidal stabilization of MnZn-ferrite nanoparticles by oleic acid on their magnetothermal properties 油酸对纳米MnZn铁氧体磁热性能的影响
Pub Date : 2023-07-07 DOI: 10.3389/fther.2023.1195740
N. N. Liu, Y. Alekhina, A. Pyatakov, M. Zharkov, D. E. Yakobson, N. Pyataev, G. Sukhorukov, N. Perov, A. Tishin
Introduction: The development of magnetic agents for magnetic fluid hyperthermia application is a complex task requiring simultaneous optimization of chemical, biomedical, magnetic, and, in particular, thermal properties of magnetic nanoparticles (MNPs). In the majority of papers, the magnetothermal measurements are carried out on bare MNPs suspended in deionized water with subsequent optimization of the required physiological and medical properties, including toxicity and biocompatibility. However, in real hyperthermia practice, the stable fluids or colloids of magnetic MNPs are used, and the colloidal stabilization can significantly modify their magnetic properties, including magnetothermal ones.Methods: This paper is focused on the study of ZnxMn1-xFe2O4 MNPs stabilized by oleic acid/sodium oleate in this context.Results and Discussion: Our research demonstrates the crucial changes in the magnetic properties and magnetothermal response of ZnMn ferrite MNPs after the colloidal stabilization: while bare MNPs demonstrate significant coercivity, nonzero remanent magnetization, and superquadratic dependence of heat generation on the magnetic field amplitude, the magnetic properties of colloidal ZnMn ferrite MNPs are typical for superparamagnetic ones and their magnetothermal response is described by a conventional quadratic dependence on magnetic field amplitude. Various factors such as size distribution, magnetic anisotropy, and interparticle dipole–dipole interaction are considered as the origins of such an impact on magnetic MNPs’ properties.
引言:开发用于磁流体热疗应用的磁性试剂是一项复杂的任务,需要同时优化磁性纳米颗粒(MNP)的化学、生物医学、磁性,特别是热性能。在大多数论文中,磁热测量是在悬浮在去离子水中的裸MNP上进行的,随后优化了所需的生理和医学特性,包括毒性和生物相容性。然而,在实际的热疗实践中,使用磁性MNP的稳定流体或胶体,并且胶体稳定可以显著改变其磁性性质,包括磁热性质。方法:本文对油酸/油酸钠稳定的ZnxMn1-xFe2O4-MNPs进行了研究。结果和讨论:我们的研究证明了胶体稳定后ZnMn铁氧体MNP的磁性能和磁热响应的关键变化:而裸露的MNP表现出显著的矫顽力、非零剩余磁化强度以及发热对磁场振幅的超二次依赖性,胶体ZnMn铁氧体MNP的磁性是超顺磁性MNP的典型磁性,并且它们的磁热响应通过对磁场振幅的传统二次依赖性来描述。尺寸分布、磁各向异性和粒子间偶极-偶极相互作用等各种因素被认为是对磁性MNP性能产生这种影响的原因。
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引用次数: 0
Editorial: Editor’s challenge in heat transfer mechanisms and applications: 2022 社论:编者在传热机制和应用方面的挑战:2022
Pub Date : 2023-05-09 DOI: 10.3389/fther.2023.1203906
L. Dombrovsky
In the study of many heat transfer processes, it is necessary to consider the interaction of heat conduction, natural or forced convection, and heat transfer by thermal radiation. The greatest difficulties in the computational modeling of combined heat transfer are related to time-consuming calculations of radiative transfer in absorbing and scattering media. Such media are, for example, gases or liquids with suspended particles, as well as dispersed materials and solids with microcracks or bubbles. Natural objects of study include the Earth’s atmosphere and ocean, snow and ice, powders or dust, ordinary sand, and even biological tissues with optically heterogeneous living cells. In thermal engineering, these are combustion products containing soot and fly ash particles, porous ceramics and heatshielding materials, particles in thermochemical reactors, and melt droplets from a possible severe nuclear reactor accident. Thermal radiation has a wide spectral range in which the optical properties of substances and materials are usually substantially dependent on the radiation wavelength. Therefore, in order to calculate the contribution of thermal radiation to heat transfer, radiative transfer calculations must be carried out for a large set of different wavelengths. In the numerical solution of transient heat transfer problems, such calculations, carried out at each time step, are the main factor influencing the computation time. It is also important that the numerical solution of the integrodifferential radiative transfer equation (RTE) regarding the radiation intensity, which is dependent not only on the coordinates but also on the direction, is a very complex procedure (Coelho, 2014). This means that the use of simple but sufficiently accurate models of radiative transfer in scattering media is absolutely essential for solving many problems of combined heat transfer. Fortunately, heat transfer problems (unlike optical diagnostics problems) have a number of physical features that allow simpler mathematical models. Note that we are usually dealing with multiple scattering of radiation in a medium when the angular distribution of the radiation in a single scattering is irrelevant. In this case, the so-called transport approximation can be used (Dombrovsky, 2012); the integral term in RTE is missing and the scattering anisotropy is taken into account by a transport scattering coefficient. The high accuracy of the transport approximation has been confirmed for diverse problems (Dombrovsky, 2010; Dombrovsky, 2019). OPEN ACCESS
在许多传热过程的研究中,需要考虑热传导、自然对流或强制对流以及热辐射传热的相互作用。复合传热计算建模的最大困难是吸收介质和散射介质中辐射传递的耗时计算。例如,这种介质是带有悬浮颗粒的气体或液体,以及带有微裂纹或气泡的分散材料和固体。研究的自然对象包括地球的大气和海洋、雪和冰、粉末或灰尘、普通的沙子,甚至是具有光学异质活细胞的生物组织。在热能工程中,这些是含有烟尘和飞灰颗粒的燃烧产物,多孔陶瓷和隔热材料,热化学反应堆中的颗粒,以及可能发生严重核反应堆事故的熔融液滴。热辐射具有很宽的光谱范围,其中物质和材料的光学特性通常在很大程度上取决于辐射波长。因此,为了计算热辐射对传热的贡献,必须对一组大的不同波长进行辐射传递计算。在瞬态传热问题的数值解中,这种在每个时间步进行的计算是影响计算时间的主要因素。同样重要的是,关于辐射强度的积分微分辐射传递方程(RTE)的数值解是一个非常复杂的过程,它不仅取决于坐标,而且取决于方向(Coelho, 2014)。这意味着在散射介质中使用简单但足够精确的辐射传递模型对于解决许多联合传热问题是绝对必要的。幸运的是,传热问题(与光学诊断问题不同)具有许多物理特征,可以使用更简单的数学模型。注意,当单次散射中辐射的角分布无关紧要时,我们通常处理的是介质中辐射的多次散射。在这种情况下,可以使用所谓的输运近似(Dombrovsky, 2012);RTE中缺少积分项,散射各向异性由输运散射系数来考虑。输运近似的高精度已被证实适用于各种问题(Dombrovsky, 2010;Dombrovsky, 2019)。开放获取
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引用次数: 0
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Frontiers in thermal engineering
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