A Universal Velocity Transformation for Boundary Layers with Pressure Gradients: Article No. A3

Peng Chen, Wen Wu, Kevin Griffin, Yipeng Shi, Xiang Yang

Research output: Contribution to journalArticlepeer-review

Abstract

The logarithmic law of the wall does not capture the mean flow when a boundary layer is subjected to a strong pressure gradient. In such a boundary layer, the mean flow is affected by the spatio-temporal history of the imposed pressure gradient; and accounting for history effects remains a challenge. This work aims to develop a universal mean flow scaling for boundary layers subjected to arbitrary adverse or/and favourable pressure gradients. We derive from the Navier-Stokes equation a velocity transformation that accounts for the history effects and maps the mean flow to the canonical law of the wall. The transformation is tested against channel flows with a suddenly imposed adverse or favourable pressure gradient, boundary layer flows subjected to an adverse pressure gradient, and Couette-Poiseuille flows with a streamwise pressure gradient. It is found that the transformed velocity profiles follow closely the equilibrium law of the wall.
Original languageAmerican English
Number of pages20
JournalJournal of Fluid Mechanics
Volume970
DOIs
StatePublished - 2023

NREL Publication Number

  • NREL/JA-2C00-86571

Keywords

  • Navier-Stokes equations
  • turbulence theory
  • turbulent boundary layers

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