F. Sofos, C. Dritselis, S. Misdanitis, T. Karakasidis, D. Valougeorgis
{"title":"Computation of flow rates in rarefied gas flow through circular tubes via machine learning techniques","authors":"F. Sofos, C. Dritselis, S. Misdanitis, T. Karakasidis, D. Valougeorgis","doi":"10.1007/s10404-023-02689-6","DOIUrl":null,"url":null,"abstract":"<div><p>Kinetic theory and modeling have been proven extremely suitable in computing the flow rates in rarefied gas pipe flows, but they are computationally expensive and more importantly not practical in design and optimization of micro- and vacuum systems. In an effort to reduce the computational cost and improve accessibility when dealing with such systems, two efficient methods are employed by leveraging machine learning (ML). More specifically, random forest regression (RFR) and symbolic regression (SR) have been adopted, suggesting a framework capable of extracting numerical predictions and analytical equations, respectively, exclusively derived from data. The database of the reduced flow rates <i>W</i> used in the current ML framework has been obtained using kinetic modeling and it refers to nonlinear flows through circular tubes (tube length over radius <span>\\(l \\in [0,5]\\)</span> and downstream over upstream pressure <span>\\(p \\in [0,0.9]\\)</span>) in a very wide range of the gas rarefaction parameter <span>\\(\\delta \\in [0,10^3]\\)</span>. The accuracy of both RFR and SR models is assessed using statistical metrics, as well as the relative error between the ML predictions and the kinetic database. The predictions obtained by RFR show very good fit on the simulation data, having a maximum absolute relative error of less than <span>\\(12.5\\%\\)</span>. Various expressions of the form of <span>\\(W=W(p,l,\\delta )\\)</span> with different accuracy and complexity are acquired from SR. The proposed equation, valid in the whole range of the relevant parameters, exhibits a maximum absolute relative error less than <span>\\(17\\%\\)</span>. To further improve the accuracy, the dataset is divided into three subsets in terms of <span>\\(\\delta\\)</span> and one SR-based closed-form expression of each subset is proposed, achieving a maximum absolute relative error smaller than <span>\\(9\\%\\)</span>. Very good performance of all proposed equations is observed, as indicated by the obtained accuracy measures. Overall, the present ML-predicted data may be very useful in gaseous microfluidics and vacuum technology for engineering purposes.</p></div>","PeriodicalId":706,"journal":{"name":"Microfluidics and Nanofluidics","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10404-023-02689-6.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Microfluidics and Nanofluidics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s10404-023-02689-6","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"INSTRUMENTS & INSTRUMENTATION","Score":null,"Total":0}
引用次数: 0
Abstract
Kinetic theory and modeling have been proven extremely suitable in computing the flow rates in rarefied gas pipe flows, but they are computationally expensive and more importantly not practical in design and optimization of micro- and vacuum systems. In an effort to reduce the computational cost and improve accessibility when dealing with such systems, two efficient methods are employed by leveraging machine learning (ML). More specifically, random forest regression (RFR) and symbolic regression (SR) have been adopted, suggesting a framework capable of extracting numerical predictions and analytical equations, respectively, exclusively derived from data. The database of the reduced flow rates W used in the current ML framework has been obtained using kinetic modeling and it refers to nonlinear flows through circular tubes (tube length over radius \(l \in [0,5]\) and downstream over upstream pressure \(p \in [0,0.9]\)) in a very wide range of the gas rarefaction parameter \(\delta \in [0,10^3]\). The accuracy of both RFR and SR models is assessed using statistical metrics, as well as the relative error between the ML predictions and the kinetic database. The predictions obtained by RFR show very good fit on the simulation data, having a maximum absolute relative error of less than \(12.5\%\). Various expressions of the form of \(W=W(p,l,\delta )\) with different accuracy and complexity are acquired from SR. The proposed equation, valid in the whole range of the relevant parameters, exhibits a maximum absolute relative error less than \(17\%\). To further improve the accuracy, the dataset is divided into three subsets in terms of \(\delta\) and one SR-based closed-form expression of each subset is proposed, achieving a maximum absolute relative error smaller than \(9\%\). Very good performance of all proposed equations is observed, as indicated by the obtained accuracy measures. Overall, the present ML-predicted data may be very useful in gaseous microfluidics and vacuum technology for engineering purposes.
期刊介绍:
Microfluidics and Nanofluidics is an international peer-reviewed journal that aims to publish papers in all aspects of microfluidics, nanofluidics and lab-on-a-chip science and technology. The objectives of the journal are to (1) provide an overview of the current state of the research and development in microfluidics, nanofluidics and lab-on-a-chip devices, (2) improve the fundamental understanding of microfluidic and nanofluidic phenomena, and (3) discuss applications of microfluidics, nanofluidics and lab-on-a-chip devices. Topics covered in this journal include:
1.000 Fundamental principles of micro- and nanoscale phenomena like,
flow, mass transport and reactions
3.000 Theoretical models and numerical simulation with experimental and/or analytical proof
4.000 Novel measurement & characterization technologies
5.000 Devices (actuators and sensors)
6.000 New unit-operations for dedicated microfluidic platforms
7.000 Lab-on-a-Chip applications
8.000 Microfabrication technologies and materials
Please note, Microfluidics and Nanofluidics does not publish manuscripts studying pure microscale heat transfer since there are many journals that cover this field of research (Journal of Heat Transfer, Journal of Heat and Mass Transfer, Journal of Heat and Fluid Flow, etc.).