# Pulsed-wire measurements in the near-wall layer in a reattaching separated flow

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## Abstract

Pulsed-wire velocity measurements have been made in the near-wall layer, including the viscous sublayer, beneath a separated flow. A method for correcting the error caused by fluctuations in velocity gradient is given, extending the work of Schober et al. (1998). The measurements show that the r.m.s. of the streamwise velocity fluctuations scale closely in accordance with an inner-layer scaling, where the velocity scale, \({u}\ifmmode{'}\else$'$\fi_{\tau } \), is based on the r.m.s. of the wall shear stress* fluctuations* (measured by means of a pulsed-wire shear stress probe), rather than the mean wall shear stress. The effects of velocity gradient are only significant beneath \({{u}\ifmmode{'}\else$'$\fi_{\tau } y} \mathord{\left/ {\vphantom {{{u}\ifmmode{'}\else$'$\fi_{\tau } y} \nu }} \right. \kern-\nulldelimiterspace} \nu \) of 10 or less.

## Keywords

Wall Shear Stress Velocity Gradient Laminar Boundary Layer Viscous Sublayer Splitter Plate## List of symbols

*C*Calibration constant

*f*Function representing mean velocity

*h*_{f}Height of fence above splitter plate surface

*L*Length scale of outer-layer structures

*s*Distance between pulsed and sensor wires

*u*′r.m.s. of

*U*- \({u}\ifmmode{'}\else$'$\fi_{\tau } \)
Velocity scale based on r.m.s of wall shear stress fluctuation

*U*Instantaneous velocity in

*x*-direction*U*_{m}Instantaneous measured velocity in

*x*-direction*U*_{r}Free-stream reference velocity

*x*Streamwise direction from separation point

*y*Distance from splitter plate surface, in normal direction

*X*_{r}Length of separation bubble

*δ*_{0}Thickness scale in oscillating layer

*η*Blasius laminar boundary layer parameter

*ρ*Density

*τ*Wall shear stress

*τ*′r.m.s. of wall shear stress fluctuation

*ω*Frequency of oscillating layer

*ν*Kinematic viscosity

- \({} \)
Overbar denotes time average

## References

- Aronson D, Johansson AV, Löfdahl L (1997) Shear-free turbulence near a wall. J Fluid Mech 338:363–385CrossRefGoogle Scholar
- Castro IP, Cheun BS (1982) The measurement of Reynolds stresses with a pulsed-wire anemometer. J Fluid Mech 118:41–58Google Scholar
- Castro IP, Dianat M (1990) Pulsed-wire velocity anemometry near walls. Exp Fluids 8:343–352Google Scholar
- Devenport WJ, Sutton EP (1991) Near-wall behaviour of separated and reattaching flows. AIAA J 29(1):25–31Google Scholar
- Hancock PE (2000) Low Reynolds number two-dimensional separated and reattaching turbulent shear flow. J Fluid Mech 410:101–122CrossRefGoogle Scholar
- Hancock PE (2004) Scaling of the near-wall layer beneath reattaching separated flow. In: Proceedings of the IUTAM symposium on Reynolds number scaling in turbulent flow, University of Princeton, New Jersey, September 2002. Kluwer ISBN 1-4020-1775-8Google Scholar
- Hancock PE (2003) Velocity scales in the near-wall layer beneath reattaching turbulent separated and boundary layer flows. Euro J Mech B–Fluid (submitted)Google Scholar
- Hunt JCR, Graham JMR (1978) Free-stream turbulence near plane boundaries. J Fluid Mech 84:209–235Google Scholar
- Le H, Moin P, Kim J (1997) Direct numerical simulation of turbulent flow over a backward-facing step. J Fluid Mech 330:349–374Google Scholar
- Patel VC (1965) Calibration of the Preston tube and limitations on its use in pressure gradients. J Fluid Mech 23:185–208Google Scholar
- Ruderich R, Fernholz HH (1986) An experimental investigation of a turbulent shear flow with separation, reverse flow and reattachment. J Fluid Mech 163:283–322Google Scholar
- Schober M, Hancock PE, Siller H (1998) Pulsed-wire anemometry near walls. Exp Fluids 25:151-159CrossRefGoogle Scholar
- Spalart RP (1988) Direct simulation of a turbulent boundary layer up to
*Re*_{θ}=1410. J Fluid Mech 187:61–98Google Scholar - Thomas NH, Hancock PE (1977) Grid turbulence near a moving wall. J Fluid Mech 82:481–496Google Scholar