{"title":"多维粒子种群平衡动力学的三变量矩投影法","authors":"Tongtong Yan , Shaohua Wu , Dezhi Zhou","doi":"10.1016/j.jaerosci.2024.106378","DOIUrl":null,"url":null,"abstract":"<div><p>This study develops a tri-variate moment projection method (TVMPM) for solving particle dynamics problems governed by the population balance equations involving any three internal coordinates of particles, such as volume, surface area, component mass, etc. By leveraging the concept of conditional moments, the multi-dimensional moments are expressed as the product of marginal moments and several conditional moments, facilitating the solution of high-dimensional moments. To obtain abscissas and conditional weights in different dimensions for reconstructing moments, a three-dimensional (3-D) adaptive Blumstein-Wheeler algorithm is proposed and implemented, which can also improve the stability in the third dimension, where ill-conditioning issues are more likely to arise. More importantly, by fixing the smallest particle abscissas, TVMPM can directly track the weight of the smallest particles, thereby closing the shrinkage and fragmentation terms. An analysis of the sources of errors arising from this approach is also presented. To mitigate potential interference from external factors, constant kernels for inception, growth, coagulation, shrinkage and fragmentation are employed to validate the effectiveness of TVMPM. The resulting moments from TVMPM are computed for both individual and combined processes, and subsequently compared with the moments derived from the direct simulation algorithm (DSA). The results demonstrate that TVMPM maintains a high level of accuracy across various numbers of quadrature nodes for particle dynamics with 3-D internal coordinates, while significantly reducing computational efforts compared to DSA. This study reveals that the developed algorithms and framework are promising for further extending MPM to higher dimensions. Moreover, owing to its accuracy and efficiency, TVMPM shows great potential for implementation in computational fluid dynamics (CFD) for particle dynamics in realistic systems.</p></div>","PeriodicalId":14880,"journal":{"name":"Journal of Aerosol Science","volume":null,"pages":null},"PeriodicalIF":3.9000,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A tri-variate moment projection method for multi-dimensional particle population balance dynamics\",\"authors\":\"Tongtong Yan , Shaohua Wu , Dezhi Zhou\",\"doi\":\"10.1016/j.jaerosci.2024.106378\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study develops a tri-variate moment projection method (TVMPM) for solving particle dynamics problems governed by the population balance equations involving any three internal coordinates of particles, such as volume, surface area, component mass, etc. By leveraging the concept of conditional moments, the multi-dimensional moments are expressed as the product of marginal moments and several conditional moments, facilitating the solution of high-dimensional moments. To obtain abscissas and conditional weights in different dimensions for reconstructing moments, a three-dimensional (3-D) adaptive Blumstein-Wheeler algorithm is proposed and implemented, which can also improve the stability in the third dimension, where ill-conditioning issues are more likely to arise. More importantly, by fixing the smallest particle abscissas, TVMPM can directly track the weight of the smallest particles, thereby closing the shrinkage and fragmentation terms. An analysis of the sources of errors arising from this approach is also presented. To mitigate potential interference from external factors, constant kernels for inception, growth, coagulation, shrinkage and fragmentation are employed to validate the effectiveness of TVMPM. The resulting moments from TVMPM are computed for both individual and combined processes, and subsequently compared with the moments derived from the direct simulation algorithm (DSA). The results demonstrate that TVMPM maintains a high level of accuracy across various numbers of quadrature nodes for particle dynamics with 3-D internal coordinates, while significantly reducing computational efforts compared to DSA. This study reveals that the developed algorithms and framework are promising for further extending MPM to higher dimensions. Moreover, owing to its accuracy and efficiency, TVMPM shows great potential for implementation in computational fluid dynamics (CFD) for particle dynamics in realistic systems.</p></div>\",\"PeriodicalId\":14880,\"journal\":{\"name\":\"Journal of Aerosol Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.9000,\"publicationDate\":\"2024-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Aerosol Science\",\"FirstCategoryId\":\"93\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021850224000454\",\"RegionNum\":3,\"RegionCategory\":\"环境科学与生态学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, CHEMICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Aerosol Science","FirstCategoryId":"93","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021850224000454","RegionNum":3,"RegionCategory":"环境科学与生态学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
A tri-variate moment projection method for multi-dimensional particle population balance dynamics
This study develops a tri-variate moment projection method (TVMPM) for solving particle dynamics problems governed by the population balance equations involving any three internal coordinates of particles, such as volume, surface area, component mass, etc. By leveraging the concept of conditional moments, the multi-dimensional moments are expressed as the product of marginal moments and several conditional moments, facilitating the solution of high-dimensional moments. To obtain abscissas and conditional weights in different dimensions for reconstructing moments, a three-dimensional (3-D) adaptive Blumstein-Wheeler algorithm is proposed and implemented, which can also improve the stability in the third dimension, where ill-conditioning issues are more likely to arise. More importantly, by fixing the smallest particle abscissas, TVMPM can directly track the weight of the smallest particles, thereby closing the shrinkage and fragmentation terms. An analysis of the sources of errors arising from this approach is also presented. To mitigate potential interference from external factors, constant kernels for inception, growth, coagulation, shrinkage and fragmentation are employed to validate the effectiveness of TVMPM. The resulting moments from TVMPM are computed for both individual and combined processes, and subsequently compared with the moments derived from the direct simulation algorithm (DSA). The results demonstrate that TVMPM maintains a high level of accuracy across various numbers of quadrature nodes for particle dynamics with 3-D internal coordinates, while significantly reducing computational efforts compared to DSA. This study reveals that the developed algorithms and framework are promising for further extending MPM to higher dimensions. Moreover, owing to its accuracy and efficiency, TVMPM shows great potential for implementation in computational fluid dynamics (CFD) for particle dynamics in realistic systems.
期刊介绍:
Founded in 1970, the Journal of Aerosol Science considers itself the prime vehicle for the publication of original work as well as reviews related to fundamental and applied aerosol research, as well as aerosol instrumentation. Its content is directed at scientists working in engineering disciplines, as well as physics, chemistry, and environmental sciences.
The editors welcome submissions of papers describing recent experimental, numerical, and theoretical research related to the following topics:
1. Fundamental Aerosol Science.
2. Applied Aerosol Science.
3. Instrumentation & Measurement Methods.