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Direct numerical simulations of a statistically stationary streamwise periodic boundary layer via the homogenized Navier-Stokes equations

Joseph Ruan and Guillaume Blanquart

  • California Institute of Technology, Pasadena, California 91125, USA

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Phys. Rev. Fluids 6, 024602 – Published 5 February, 2021

DOI: https://doi.org/10.1103/PhysRevFluids.6.024602

Abstract

We demonstrate a method for direct numerical simulations (DNS) of incompressible, flat-plate, zero pressure gradient, turbulent boundary layers, without the use of auxiliary simulations or fringe regions, in a streamwise periodic domain via the homogenized Navier-Stokes equations. This approach is inspired by Spalart's original (1987) method, but improves upon his drawbacks while simplifying the implementation. Most simulations of flat-plate boundary layers require long streamwise domains owing to the slow boundary layer growth and inflow generation techniques. Instead, we use anticipated self-similarity to solve the equations in a normalized coordinate system to allow for streamwise periodicity, similar to Spalart's original method. The resulting integral values, the skin friction coefficient and shape factor, H12 and Cf, are within ±1% and ±3% of the empirical fits. The mean profiles show good agreement with spatially developing DNS and experimental results for a wide range of Reynolds numbers from Reδ*=1460 to 5650. The method manages to reduce computational costs by an estimated one to two orders of magnitude.

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Phys. Rev. Fluids 6, 024602– Published 5 February, 2021
  • Received 4 February 2020
  • Accepted 6 January 2021
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