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<p>We present a data-driven approach to Reynolds-averaged Navier-Stokes (RANS) turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_668_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(k\)</EquationSource> </InlineEquation>-<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10494_2025_668_Article_IEq2.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\omega\)</EquationSource> </InlineEquation> SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.</p>

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Data-Driven Turbulence Modelling for Magnetohydrodynamic Flows in Annular Pipes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月24日

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  • Alejandro Montoya Santamaría,
  • Tyler Buchanan,
  • Francesco Fico,
  • Ivan Langella,
  • Richard P. Dwight,
  • Nguyen Anh Khoa Doan

摘要

We present a data-driven approach to Reynolds-averaged Navier-Stokes (RANS) turbulence closure modelling in magnetohydrodynamic (MHD) flows. In these flows the magnetic field interacting with the conductive fluid induces unconventional turbulence states such as quasi two-dimensional (2D) turbulence, and turbulence suppression, which are poorly represented by standard Boussinesq models. Our data-driven approach uses time-averaged Large Eddy Simulation (LES) data of annular pipe flows, at different Hartmann numbers, to derive corrections for the \(k\) - \(\omega\) SST model. Correction fields are obtained by injecting time averaged LES fields into the MHD RANS equations, and examining the remaining residuals. The correction to the Reynolds-stress anisotropy is approximated with a modified Tensor Basis Neural Network (TBNN). We extend the generalised eddy hypothesis with a traceless antisymmetric tensor representation of the Lorentz force to obtain MHD flow features, thus keeping Galilean and frame invariance while including MHD effects in the turbulence model. The resulting data-driven models are shown to reduce errors in the mean flow, and to generalise to annular flow cases with different Hartmann numbers from those of the training cases.