Computation of flow rates in rarefied gas flow through circular tubes via machine learning techniques

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.