Haidong Yu,Xiaobo Quan,Haipeng Wei,Matevž Dular, Song Fu
{"title":"新型非线性动态气蚀模型的开发及其数值验证","authors":"Haidong Yu,Xiaobo Quan,Haipeng Wei,Matevž Dular, Song Fu","doi":"10.4208/aamm.oa-2023-0041","DOIUrl":null,"url":null,"abstract":"Aiming at modeling the cavitation bubble cluster, we propose a novel nonlinear dynamic cavitation model (NDCM) considering the second derivative term in\nRayleigh-Plesset equation through strict mathematical derivation. There are two improvements of the new model: i) the empirical coefficients are eliminated by introduction of the nonuniform potential functions of $\\psi_v$ and $\\psi_c$ for growth and collapse processes respectively, and ii) only two model parameters are required, which both base\non physical quantities–the Blake critical radius $R_b$ and the average maximum growth\nradius $R_m.$ The corresponding cavitation solver was developed by using OpenFOAM\nin which we implemented the modified momentum interpolation (MMI) method to\nensure that the calculated results are independent of time step size. Three validation\ncases, namely numerical bubble cluster collapse, ultrasonic horn experiment, and hydrodynamic cavitation around slender body are employed. The results indicate that $\\psi_v$ and $\\psi_c$ can reveal the nonlinear characteristics for cavity accurately, and $R_b$ and $R_m$ can reflect the relevance between cavitation model and actual physical quantities.\nMoreover, it is discussed the potentiality of NDCM that is generally applied on the\ncavitating flow possessing with dispersed bubbly cloud.","PeriodicalId":54384,"journal":{"name":"Advances in Applied Mathematics and Mechanics","volume":"30 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Development of a Novel Nonlinear Dynamic Cavitation Model and Its Numerical Validations\",\"authors\":\"Haidong Yu,Xiaobo Quan,Haipeng Wei,Matevž Dular, Song Fu\",\"doi\":\"10.4208/aamm.oa-2023-0041\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Aiming at modeling the cavitation bubble cluster, we propose a novel nonlinear dynamic cavitation model (NDCM) considering the second derivative term in\\nRayleigh-Plesset equation through strict mathematical derivation. There are two improvements of the new model: i) the empirical coefficients are eliminated by introduction of the nonuniform potential functions of $\\\\psi_v$ and $\\\\psi_c$ for growth and collapse processes respectively, and ii) only two model parameters are required, which both base\\non physical quantities–the Blake critical radius $R_b$ and the average maximum growth\\nradius $R_m.$ The corresponding cavitation solver was developed by using OpenFOAM\\nin which we implemented the modified momentum interpolation (MMI) method to\\nensure that the calculated results are independent of time step size. Three validation\\ncases, namely numerical bubble cluster collapse, ultrasonic horn experiment, and hydrodynamic cavitation around slender body are employed. The results indicate that $\\\\psi_v$ and $\\\\psi_c$ can reveal the nonlinear characteristics for cavity accurately, and $R_b$ and $R_m$ can reflect the relevance between cavitation model and actual physical quantities.\\nMoreover, it is discussed the potentiality of NDCM that is generally applied on the\\ncavitating flow possessing with dispersed bubbly cloud.\",\"PeriodicalId\":54384,\"journal\":{\"name\":\"Advances in Applied Mathematics and Mechanics\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2024-02-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Applied Mathematics and Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.4208/aamm.oa-2023-0041\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Mathematics and Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.4208/aamm.oa-2023-0041","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Development of a Novel Nonlinear Dynamic Cavitation Model and Its Numerical Validations
Aiming at modeling the cavitation bubble cluster, we propose a novel nonlinear dynamic cavitation model (NDCM) considering the second derivative term in
Rayleigh-Plesset equation through strict mathematical derivation. There are two improvements of the new model: i) the empirical coefficients are eliminated by introduction of the nonuniform potential functions of $\psi_v$ and $\psi_c$ for growth and collapse processes respectively, and ii) only two model parameters are required, which both base
on physical quantities–the Blake critical radius $R_b$ and the average maximum growth
radius $R_m.$ The corresponding cavitation solver was developed by using OpenFOAM
in which we implemented the modified momentum interpolation (MMI) method to
ensure that the calculated results are independent of time step size. Three validation
cases, namely numerical bubble cluster collapse, ultrasonic horn experiment, and hydrodynamic cavitation around slender body are employed. The results indicate that $\psi_v$ and $\psi_c$ can reveal the nonlinear characteristics for cavity accurately, and $R_b$ and $R_m$ can reflect the relevance between cavitation model and actual physical quantities.
Moreover, it is discussed the potentiality of NDCM that is generally applied on the
cavitating flow possessing with dispersed bubbly cloud.
期刊介绍:
Advances in Applied Mathematics and Mechanics (AAMM) provides a fast communication platform among researchers using mathematics as a tool for solving problems in mechanics and engineering, with particular emphasis in the integration of theory and applications. To cover as wide audiences as possible, abstract or axiomatic mathematics is not encouraged. Innovative numerical analysis, numerical methods, and interdisciplinary applications are particularly welcome.