{"title":"最大李雅普诺夫指数和香农熵:分析流化床混合的两个指数","authors":"","doi":"10.1016/j.cherd.2024.08.026","DOIUrl":null,"url":null,"abstract":"<div><p>The quality of mixing in fluidized beds greatly influences performance in many applications. Assessing quality of mixing involves measuring the mixing rate and evaluating the bed mixedness. Quantifying the bed mixedness is typically done using mixing indices. However, the application of existing mixing indices to fluidized beds can be problematic due to aeration and complications from the particle phase in the Two-Fluid Model (TFM).</p><p>The objectives of this study are twofold. First, the largest Lyapunov exponent is proposed to quantify mixing in fluidized beds. Its effectiveness is shown on a mono-disperse bed with varying gas velocities. The increase in mixing rate with higher gas velocity is accurately represented by the largest Lyapunov exponent. Second, the Shannon entropy mixing index is adopted to quantify the bed mixedness for TFM results. This index is tested on a bi-disperse bed to predict segregation and evaluate the effect of bed composition and superficial gas velocity on this process. The effect on segregation is reflected in the entropy components: distributional entropy showed minimal variation, whereas conditional entropy was significantly affected. Evaluating bed mixedness at different length scales showed that increasing bin spatial resolution slightly reduced conditional entropy. The results are validated against experimental data.</p></div>","PeriodicalId":10019,"journal":{"name":"Chemical Engineering Research & Design","volume":null,"pages":null},"PeriodicalIF":3.7000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0263876224005045/pdfft?md5=f00977a778425751a911febc65d2ceed&pid=1-s2.0-S0263876224005045-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Largest Lyapunov exponent and Shannon entropy: Two indices to analyze mixing in fluidized beds\",\"authors\":\"\",\"doi\":\"10.1016/j.cherd.2024.08.026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The quality of mixing in fluidized beds greatly influences performance in many applications. Assessing quality of mixing involves measuring the mixing rate and evaluating the bed mixedness. Quantifying the bed mixedness is typically done using mixing indices. However, the application of existing mixing indices to fluidized beds can be problematic due to aeration and complications from the particle phase in the Two-Fluid Model (TFM).</p><p>The objectives of this study are twofold. First, the largest Lyapunov exponent is proposed to quantify mixing in fluidized beds. Its effectiveness is shown on a mono-disperse bed with varying gas velocities. The increase in mixing rate with higher gas velocity is accurately represented by the largest Lyapunov exponent. Second, the Shannon entropy mixing index is adopted to quantify the bed mixedness for TFM results. This index is tested on a bi-disperse bed to predict segregation and evaluate the effect of bed composition and superficial gas velocity on this process. The effect on segregation is reflected in the entropy components: distributional entropy showed minimal variation, whereas conditional entropy was significantly affected. Evaluating bed mixedness at different length scales showed that increasing bin spatial resolution slightly reduced conditional entropy. The results are validated against experimental data.</p></div>\",\"PeriodicalId\":10019,\"journal\":{\"name\":\"Chemical Engineering Research & Design\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.7000,\"publicationDate\":\"2024-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0263876224005045/pdfft?md5=f00977a778425751a911febc65d2ceed&pid=1-s2.0-S0263876224005045-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chemical Engineering Research & Design\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0263876224005045\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, CHEMICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chemical Engineering Research & Design","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0263876224005045","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
Largest Lyapunov exponent and Shannon entropy: Two indices to analyze mixing in fluidized beds
The quality of mixing in fluidized beds greatly influences performance in many applications. Assessing quality of mixing involves measuring the mixing rate and evaluating the bed mixedness. Quantifying the bed mixedness is typically done using mixing indices. However, the application of existing mixing indices to fluidized beds can be problematic due to aeration and complications from the particle phase in the Two-Fluid Model (TFM).
The objectives of this study are twofold. First, the largest Lyapunov exponent is proposed to quantify mixing in fluidized beds. Its effectiveness is shown on a mono-disperse bed with varying gas velocities. The increase in mixing rate with higher gas velocity is accurately represented by the largest Lyapunov exponent. Second, the Shannon entropy mixing index is adopted to quantify the bed mixedness for TFM results. This index is tested on a bi-disperse bed to predict segregation and evaluate the effect of bed composition and superficial gas velocity on this process. The effect on segregation is reflected in the entropy components: distributional entropy showed minimal variation, whereas conditional entropy was significantly affected. Evaluating bed mixedness at different length scales showed that increasing bin spatial resolution slightly reduced conditional entropy. The results are validated against experimental data.
期刊介绍:
ChERD aims to be the principal international journal for publication of high quality, original papers in chemical engineering.
Papers showing how research results can be used in chemical engineering design, and accounts of experimental or theoretical research work bringing new perspectives to established principles, highlighting unsolved problems or indicating directions for future research, are particularly welcome. Contributions that deal with new developments in plant or processes and that can be given quantitative expression are encouraged. The journal is especially interested in papers that extend the boundaries of traditional chemical engineering.