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Determination of rough-surface skin friction coefficients from wake profile measurements

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Abstract

A technique for determining the skin friction coefficients from wake profile measurements is described, and is applied to symmetric turbine airfoils with rough surfaces, which operate in a compressible, high-speed flow environment. The procedure involves the measurement of profiles of streamwise momentum in the wakes which form downstream of different airfoils with different levels of surface roughness. Different physical phenomena which affect such wake profiles are discussed and related to different effects, such as surface roughness, form drag, flow separation zones, and laminar-to-turbulent transition. With the same inlet experimental condition for each case, overall skin friction coefficients for the rough airfoils are determined. Resulting values increase considerably as the magnitude of equivalent sandgrain roughness size increases.

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Abbreviations

A :

test airfoil surface area

A i :

test section inlet area

A e :

test section exit area

c :

chord length of airfoil

C f/2 :

skin friction coefficient

(C f/2)smooth :

skin friction coefficient for smooth airfoil

(C f/2)rough :

skin friction coefficient for rough airfoil

F s :

force from surface shear stress

F p :

force from form drag due to airfoil blockage and separated flow

F w :

force imposed by the top and bottom test section walls

F s,smooth :

force from surface shear stress for smooth airfoil

F s,rough :

force from surface shear stress for rough airfoil

h :

height of test section

k :

roughness height

k s :

equivalent sand grain roughness

L :

total length of airfoil surface from leading edge to trailing edge

p :

airfoil passage effective pitch

P o :

stagnation pressure

P oe :

exit local stagnation pressure

P oe,∞ :

exit freestream stagnation pressure

P oi :

inlet stagnation pressure

P s :

static pressure

P se :

exit static pressure

s :

distance along airfoil surface from leading edge

u :

local streamwise velocity

u i :

local streamwise velocity at test section inlet

u e :

local streamwise velocity at test section exit

u ∞ :

local freestream streamwise velocity at test section exit

w :

width of test section

x :

linear distance along airfoil centerline from airfoil leading edge

y :

normal coordinate measured from airfoil centerline

γ :

ratio of specific heats

Λ s :

roughness parameter

ρ i :

local static air density at test section inlet

ρ e :

local static air density at test section exit

ρ ∞ :

local static air density in freestream at test section exit

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Acknowledgments

The research reported in this paper was sponsored by the National Science Foundation (NSF Grant Number CTS-0086011). Dr. Stefan Thynell and Dr. Richard Smith were the NSF program monitors. The authors also acknowledge Dr. Mike Blair of Pratt & Whitney Corp., Dr. Hee-Koo Moon of Solar Turbines Inc., Dr. Ed North and Dr. Ihor Diakunchak of Siemens-Westinghouse Corp. and Dr. Ricardo Trindade of Pratt & Whitney-Canada Corp. for guidance and suggestions on this research effort, and for providing roughened turbine blade hardware from engines for analysis and comparison.

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Authors and Affiliations

  1. Convective Heat Transfer Laboratory, MEB 2110, 50 S. Central Campus Drive, Department of Mechanical Engineering , University of Utah, Salt Lake City, UT, 84112-9208, USA

    Q. Zhang & P. M. Ligrani

  2. School of Mechanical Engineering, Kumoh National University of Technology, , 730-701, Gumi, Gyongbook, Korea

    S. W. Lee

Authors
  1. Q. Zhang
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  2. P. M. Ligrani
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  3. S. W. Lee
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Correspondence to P. M. Ligrani.

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Zhang, Q., Ligrani, P.M. & Lee, S.W. Determination of rough-surface skin friction coefficients from wake profile measurements. Exp Fluids 35, 627–635 (2003). https://doi.org/10.1007/s00348-003-0712-z

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  • DOI: https://doi.org/10.1007/s00348-003-0712-z

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