Determination of wall shear stress from mean velocity and Reynolds shear stress profiles

Ralph J. Volino and Michael P. Schultz
Phys. Rev. Fluids 3, 034606 – Published 22 March 2018

Abstract

An analytical method is presented for determining the Reynolds shear stress profile in steady, two-dimensional wall-bounded flows using the mean streamwise velocity. The method is then utilized with experimental data to determine the local wall shear stress. The procedure is applicable to flows on smooth and rough surfaces with arbitrary pressure gradients. It is based on the streamwise component of the boundary layer momentum equation, which is transformed into inner coordinates. The method requires velocity profiles from at least two streamwise locations, but the formulation of the momentum equation reduces the dependence on streamwise gradients. The method is verified through application to laminar flow solutions and turbulent DNS results from both zero and nonzero pressure gradient boundary layers. With strong favorable pressure gradients, the method is shown to be accurate for finding the wall shear stress in cases where the Clauser fit technique loses accuracy. The method is then applied to experimental data from the literature from zero pressure gradient studies on smooth and rough walls, and favorable and adverse pressure gradient cases on smooth walls. Data from very near the wall are not required for determination of the wall shear stress. Wall friction velocities obtained using the present method agree with those determined in the original studies, typically to within 2%.

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  • Received 5 December 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.034606

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Ralph J. Volino1,* and Michael P. Schultz2,†

  • 1Mechanical Engineering Department, United States Naval Academy, Annapolis, Maryland 21402, USA
  • 2Naval Architecture and Ocean Engineering Department, United States Naval Academy, Annapolis, Maryland 21402, USA

  • *volino@usna.edu
  • mschultz@usna.edu

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Issue

Vol. 3, Iss. 3 — March 2018

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