{"title":"利用连续片断线性化方法对粘性流体中球形颗粒自由落体的理论研究","authors":"Akuro Big-Alabo , Joseph Chukwuka Ofodu","doi":"10.1016/j.kjs.2024.100211","DOIUrl":null,"url":null,"abstract":"<div><p>This article presents a theoretical investigation of the problem of free fall of a spherical particle in a viscous fluid. The classic Boussinesq-Basset-Oseen (BBO) model for particle motion in laminar flow was modified for generalized flow by using a drag law that is applicable for <span><math><mrow><mn>0</mn><mo><</mo><mi>R</mi><mi>e</mi><mo>≤</mo><mn>2.0</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></math></span>. By assuming that the acceleration in the Basset force integral is constant, the Basset force effect was approximated to form an integrated added mass coefficient. Consequently, the integro-differential equation of the BBO model was transformed to a first-order nonlinear ordinary differential equation that accounts for the Basset force effect and was solved using the continuous piecewise linearization method (CPLM). The CPLM algorithm was developed based on the jerk-velocity relationship and is applicable to zero and non-zero initial conditions, steady motion, increasing or decreasing velocities and the corresponding acceleration and jerk responses. The CPLM algorithm was shown to predict published experimental results accurately and compared very well with numerical solutions and existing analytical solutions. Examination of the fall response under varying parameters showed that the fall distance, fall time and terminal velocity depend strongly on the sphere diameter, sphere density, and the density and viscosity of the fluid medium. Also, an analytical solution for the power dissipated in the fluid medium as the sphere falls to reach its terminal velocity was derived. The power dissipated was found to increase exponentially as the initial velocity deviates positively from the terminal velocity.</p></div>","PeriodicalId":17848,"journal":{"name":"Kuwait Journal of Science","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2307410824000361/pdfft?md5=01f943b7922f54abb010fa86705d9353&pid=1-s2.0-S2307410824000361-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Theoretical investigation of the free fall of a spherical particle in a viscous fluid using continuous piecewise linearization method\",\"authors\":\"Akuro Big-Alabo , Joseph Chukwuka Ofodu\",\"doi\":\"10.1016/j.kjs.2024.100211\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This article presents a theoretical investigation of the problem of free fall of a spherical particle in a viscous fluid. The classic Boussinesq-Basset-Oseen (BBO) model for particle motion in laminar flow was modified for generalized flow by using a drag law that is applicable for <span><math><mrow><mn>0</mn><mo><</mo><mi>R</mi><mi>e</mi><mo>≤</mo><mn>2.0</mn><mo>×</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></math></span>. By assuming that the acceleration in the Basset force integral is constant, the Basset force effect was approximated to form an integrated added mass coefficient. Consequently, the integro-differential equation of the BBO model was transformed to a first-order nonlinear ordinary differential equation that accounts for the Basset force effect and was solved using the continuous piecewise linearization method (CPLM). The CPLM algorithm was developed based on the jerk-velocity relationship and is applicable to zero and non-zero initial conditions, steady motion, increasing or decreasing velocities and the corresponding acceleration and jerk responses. The CPLM algorithm was shown to predict published experimental results accurately and compared very well with numerical solutions and existing analytical solutions. Examination of the fall response under varying parameters showed that the fall distance, fall time and terminal velocity depend strongly on the sphere diameter, sphere density, and the density and viscosity of the fluid medium. Also, an analytical solution for the power dissipated in the fluid medium as the sphere falls to reach its terminal velocity was derived. The power dissipated was found to increase exponentially as the initial velocity deviates positively from the terminal velocity.</p></div>\",\"PeriodicalId\":17848,\"journal\":{\"name\":\"Kuwait Journal of Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-02-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2307410824000361/pdfft?md5=01f943b7922f54abb010fa86705d9353&pid=1-s2.0-S2307410824000361-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kuwait Journal of Science\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2307410824000361\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kuwait Journal of Science","FirstCategoryId":"103","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2307410824000361","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
Theoretical investigation of the free fall of a spherical particle in a viscous fluid using continuous piecewise linearization method
This article presents a theoretical investigation of the problem of free fall of a spherical particle in a viscous fluid. The classic Boussinesq-Basset-Oseen (BBO) model for particle motion in laminar flow was modified for generalized flow by using a drag law that is applicable for . By assuming that the acceleration in the Basset force integral is constant, the Basset force effect was approximated to form an integrated added mass coefficient. Consequently, the integro-differential equation of the BBO model was transformed to a first-order nonlinear ordinary differential equation that accounts for the Basset force effect and was solved using the continuous piecewise linearization method (CPLM). The CPLM algorithm was developed based on the jerk-velocity relationship and is applicable to zero and non-zero initial conditions, steady motion, increasing or decreasing velocities and the corresponding acceleration and jerk responses. The CPLM algorithm was shown to predict published experimental results accurately and compared very well with numerical solutions and existing analytical solutions. Examination of the fall response under varying parameters showed that the fall distance, fall time and terminal velocity depend strongly on the sphere diameter, sphere density, and the density and viscosity of the fluid medium. Also, an analytical solution for the power dissipated in the fluid medium as the sphere falls to reach its terminal velocity was derived. The power dissipated was found to increase exponentially as the initial velocity deviates positively from the terminal velocity.
期刊介绍:
Kuwait Journal of Science (KJS) is indexed and abstracted by major publishing houses such as Chemical Abstract, Science Citation Index, Current contents, Mathematics Abstract, Micribiological Abstracts etc. KJS publishes peer-review articles in various fields of Science including Mathematics, Computer Science, Physics, Statistics, Biology, Chemistry and Earth & Environmental Sciences. In addition, it also aims to bring the results of scientific research carried out under a variety of intellectual traditions and organizations to the attention of specialized scholarly readership. As such, the publisher expects the submission of original manuscripts which contain analysis and solutions about important theoretical, empirical and normative issues.