Holographic measurement of discrete bubbles in cavitating flow and optimization of a multiscale Eulerian-Lagrangian model

Holographic measurement of discrete bubbles in cavitating flow and optimization of a multiscale Eulerian-Lagrangian model | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Holographic measurement of discrete bubbles in cavitating flow and optimization of a multiscale Eulerian-Lagrangian model Yuntian Wang, Beichen Tian, Weiye Zhong, Linmin Li, Biao Huang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9177352/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 5 You are reading this latest preprint version Abstract This study integrates experimental measurements and numerical simulations to systematically investigate multiscale cavitation bubble dynamics in cloud cavitating flow around a NACA66 hydrofoil. Full flow field high-speed imaging technology conducted under an inflow velocity of 8.5 m/s and a cavitation number of 1.4 shows that macroscopic cavity structures display typical periodic evolutionary behavior, including three evolution stages of growth of attached cavity, development of re-entrant jet and cloud cavity shedding. The observed shedding frequency is approximately 45.55 Hz, and the maximum attached cavity length reaches 0.8 times the chord length of hydrofoil. Quantitative measurements of cavitation nuclei in the incoming flow and discrete microbubbles within the cavitation zone are acquired via digital in-line holography (DIH) technology. In the inflow region, the number density and average size of cavitation nuclei exhibit minor temporal fluctuations. In contrast, the spatial number density of microbubbles in the cavity shedding region and the wake flow region shows periodic evolution in response to the development of cloud cavitation. Meanwhile, the bubble size distribution follows a dual-power-law pattern, with smaller bubbles adhering to a − 4/3 power-law scaling and larger ones conforming to a − 10/3 scaling. Additionally, a Eulerian–Lagrangian two-way coupled model is optimized based on the experimental holographic imaging data of microbubble in cloud cavitating flow. Large Eddy Simulation (LES) coupled with the Volume of Fluid (VOF) method is employed for macroscopic cavity dynamics in the Eulerian framework, while the dynamics of nuclei and microbubbles are addressed via a Discrete Bubble Model (DBM) in the Lagrangian framework. The model incorporates physically-based conversion criteria to couple the two frameworks and is validated against experimental observations of microbubble behavior. Validation results demonstrate that the improved model accurately predicts cavitation shedding frequency, cavity morphology, and bubble number density distribution, confirming its reliability and predictive capability for simulating multiscale cavitation dynamics. Digital in-line holography cavitating flow multiscale Eulerian-Lagrangian model Full Text Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Minor revisions 07 Apr, 2026 Reviewers agreed at journal 27 Mar, 2026 Reviewers invited by journal 27 Mar, 2026 Editor assigned by journal 26 Mar, 2026 First submitted to journal 24 Mar, 2026 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9177352","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":613099598,"identity":"849a6206-48fd-4b61-943a-6fe192621cc3","order_by":0,"name":"Yuntian Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA00lEQVRIiWNgGAWjYHACNiC2YGxgBlIfDGzsiNUiAdbCOKMgLZkELUCSmefDITADLzBn7zF78KFCQnZ7O4/hYxuDA8wM7IePbsCnxbLnjLnhjDMSxnMO8xgb5xjc4WPgSUu7gU+LwY3cbdK8bRKJM5jZ0qRzDJ4xM0jwmBHW8vcfWEv6bwuDw4wNRGkBKgNqYT7GzECUljPnv0n2HJMwBmo5LNljkJbMRtAvx9vSJH7U2MjO4D/Y+OHHHxs7fvbDx/BqwQRspCkfBaNgFIyCUYANAACqJEZ1IDkaeAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0009-0001-6479-0203","institution":"Beijing Institute of Technology Zhuhai: Beijing Institute of Technology - Zhuhai Campus","correspondingAuthor":true,"prefix":"","firstName":"Yuntian","middleName":"","lastName":"Wang","suffix":""},{"id":613099599,"identity":"feb71d7c-35e1-459a-ba9f-95b24cd8360d","order_by":1,"name":"Beichen Tian","email":"","orcid":"","institution":"Beijing Institute of Technology Zhuhai: Beijing Institute of Technology - Zhuhai Campus","correspondingAuthor":false,"prefix":"","firstName":"Beichen","middleName":"","lastName":"Tian","suffix":""},{"id":613099600,"identity":"0a5fb3b3-3cd5-4e0b-9b16-12e593507e60","order_by":2,"name":"Weiye Zhong","email":"","orcid":"","institution":"Zhejiang Sci-Tech University","correspondingAuthor":false,"prefix":"","firstName":"Weiye","middleName":"","lastName":"Zhong","suffix":""},{"id":613099601,"identity":"0477068a-588c-48a6-9970-22d223a1ecfd","order_by":3,"name":"Linmin Li","email":"","orcid":"","institution":"Zhejiang Sci-Tech University","correspondingAuthor":false,"prefix":"","firstName":"Linmin","middleName":"","lastName":"Li","suffix":""},{"id":613099602,"identity":"d9e17e61-5165-43f5-a064-52abcb50032b","order_by":4,"name":"Biao Huang","email":"","orcid":"","institution":"Beijing Institute of Technology Zhuhai: Beijing Institute of Technology - Zhuhai Campus","correspondingAuthor":false,"prefix":"","firstName":"Biao","middleName":"","lastName":"Huang","suffix":""}],"badges":[],"createdAt":"2026-03-20 09:36:30","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-9177352/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9177352/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":105731885,"identity":"f63a9300-0c02-4c15-b7d3-1fd8a6d64178","added_by":"auto","created_at":"2026-03-30 11:32:36","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1978610,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript2603242.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9177352/v1_covered_45944b72-bc31-44bc-a4f4-5d9b7a85bb42.pdf"}],"financialInterests":"","formattedTitle":"Holographic measurement of discrete bubbles in cavitating flow and optimization of a multiscale Eulerian-Lagrangian model","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-hydrodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ijhd","sideBox":"Learn more about [Journal of Hydrodynamics](http://link.springer.com/journal/42241)","snPcode":"42241","submissionUrl":"https://www.editorialmanager.com/ijhd/default2.aspx","title":"Journal of Hydrodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Digital in-line holography, cavitating flow, multiscale, Eulerian-Lagrangian model","lastPublishedDoi":"10.21203/rs.3.rs-9177352/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9177352/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study integrates experimental measurements and numerical simulations to systematically investigate multiscale cavitation bubble dynamics in cloud cavitating flow around a NACA66 hydrofoil. Full flow field high-speed imaging technology conducted under an inflow velocity of 8.5 m/s and a cavitation number of 1.4 shows that macroscopic cavity structures display typical periodic evolutionary behavior, including three evolution stages of growth of attached cavity, development of re-entrant jet and cloud cavity shedding. The observed shedding frequency is approximately 45.55 Hz, and the maximum attached cavity length reaches 0.8 times the chord length of hydrofoil. Quantitative measurements of cavitation nuclei in the incoming flow and discrete microbubbles within the cavitation zone are acquired via digital in-line holography (DIH) technology. In the inflow region, the number density and average size of cavitation nuclei exhibit minor temporal fluctuations. In contrast, the spatial number density of microbubbles in the cavity shedding region and the wake flow region shows periodic evolution in response to the development of cloud cavitation. Meanwhile, the bubble size distribution follows a dual-power-law pattern, with smaller bubbles adhering to a\u0026thinsp;\u0026minus;\u0026thinsp;4/3 power-law scaling and larger ones conforming to a\u0026thinsp;\u0026minus;\u0026thinsp;10/3 scaling. Additionally, a Eulerian\u0026ndash;Lagrangian two-way coupled model is optimized based on the experimental holographic imaging data of microbubble in cloud cavitating flow. Large Eddy Simulation (LES) coupled with the Volume of Fluid (VOF) method is employed for macroscopic cavity dynamics in the Eulerian framework, while the dynamics of nuclei and microbubbles are addressed via a Discrete Bubble Model (DBM) in the Lagrangian framework. The model incorporates physically-based conversion criteria to couple the two frameworks and is validated against experimental observations of microbubble behavior. Validation results demonstrate that the improved model accurately predicts cavitation shedding frequency, cavity morphology, and bubble number density distribution, confirming its reliability and predictive capability for simulating multiscale cavitation dynamics.\u003c/p\u003e","manuscriptTitle":"Holographic measurement of discrete bubbles in cavitating flow and optimization of a multiscale Eulerian-Lagrangian model","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-30 11:15:08","doi":"10.21203/rs.3.rs-9177352/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Minor revisions","date":"2026-04-07T04:51:51+00:00","index":"","fulltext":""},{"type":"reviewerAgreed","content":"","date":"2026-03-27T07:50:11+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2026-03-27T07:20:06+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-26T11:54:42+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Hydrodynamics","date":"2026-03-24T06:28:53+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-hydrodynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"ijhd","sideBox":"Learn more about [Journal of Hydrodynamics](http://link.springer.com/journal/42241)","snPcode":"42241","submissionUrl":"https://www.editorialmanager.com/ijhd/default2.aspx","title":"Journal of Hydrodynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c564fa49-78f3-4369-a8cc-db54879464d2","owner":[],"postedDate":"March 30th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-04-23T06:25:51+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-30 11:15:08","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9177352","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9177352","identity":"rs-9177352","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}