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Simple model for mean stress in turbulent boundary layers

Praveen Kumar and Krishnan Mahesh*

  • Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota 55455, USA

  • *kmahesh@umn.edu
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Phys. Rev. Fluids 6, 024603 – Published 10 February, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.024603

Abstract

The mean stress is one of the most important quantities of interest in turbulent boundary layers. The governing equations for the mean flow are used to derive a relation between the mean total stress and the mean velocity in a zero pressure gradient turbulent boundary layer, allowing the mean shear stress to be written as a function of wall-normal distance. The relation contains an unknown term, which is modeled using a linear function of the wall-normal distance, inspired by existing data sets. The model for the mean total stress requires the wall-normal mean velocity profile, which requires modeling if not available. The existing data sets and scaling arguments are used to obtain a simple and compact fit for the mean wall-normal velocity, which is subsequently used to obtain a simple model for the mean total stress. The model shows good agreement with the available simulation and experimental data for a large range of Reynolds number.

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Outline

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Phys. Rev. Fluids 6, 024603– Published 10 February, 2021
  • Received 4 November 2020
  • Accepted 28 January 2021
Article part of CHORUS
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