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<p>In the Reynolds-Averaged Navier–Stokes (RANS) approach in computational fluid dynamics, the paradigms that drive the procedure of the mesh sensitivity test are: the successive mesh refinement leads to more accurate results, and the choice of the turbulence model and wall function dictates the level of mesh refinement. However, as far as the simulated physics moves away from benchmark cases, even just adding perturbations in a straight pipe under turbulent fully developed flows, both paradigms seem to be compromised. We exhaustively challenge RANS models and their variations in obtaining disturbed velocity profiles in pipe flows over 500 simulation setups by combining different mesh refinements, wall functions, and pipe fittings. Our simulated velocity profiles are compared to experimental results from the literature using the mean absolute percentage error (MAPE). The proposed methodology recovers the expected behavior for the straight pipe flow—more refined meshes should lead to more accurate results. Conversely, when applied to inhomogeneous flow, the MAPE behaves non-monotonically or divergently with increasing mesh refinement level—physical modeling errors outbalance discretization errors. Finally, approximately 90% of the simulated velocity profiles of inhomogeneous pipe flows using an average <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40430_2024_5365_Article_IEq1.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">\(y^+\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>y</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation> between 15 and 45 present a MAPE smaller than 10%.</p>

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Statistical considerations on RANS simulations of inhomogeneous pipe flows

  • 期刊论文

  • 发表日期：

    2025年1月8日

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  • Guilherme Siqueira de Aquino,
  • Ramon Silva Martins,
  • Marcio Ferreira Martins,
  • Rogério Ramos

摘要

In the Reynolds-Averaged Navier–Stokes (RANS) approach in computational fluid dynamics, the paradigms that drive the procedure of the mesh sensitivity test are: the successive mesh refinement leads to more accurate results, and the choice of the turbulence model and wall function dictates the level of mesh refinement. However, as far as the simulated physics moves away from benchmark cases, even just adding perturbations in a straight pipe under turbulent fully developed flows, both paradigms seem to be compromised. We exhaustively challenge RANS models and their variations in obtaining disturbed velocity profiles in pipe flows over 500 simulation setups by combining different mesh refinements, wall functions, and pipe fittings. Our simulated velocity profiles are compared to experimental results from the literature using the mean absolute percentage error (MAPE). The proposed methodology recovers the expected behavior for the straight pipe flow—more refined meshes should lead to more accurate results. Conversely, when applied to inhomogeneous flow, the MAPE behaves non-monotonically or divergently with increasing mesh refinement level—physical modeling errors outbalance discretization errors. Finally, approximately 90% of the simulated velocity profiles of inhomogeneous pipe flows using an average \(y^+\) y + between 15 and 45 present a MAPE smaller than 10%.