Pressure and shear stress measurements at the wall in a turbulent boundary layer on a cylinder

Abstract

The fluctuating wall shear stress, wall pressure, and streamwise velocity were measured simultaneously in a cylindrical boundary layer at a momentum thickness Reynolds number of Reθ=2160 and a boundary layer thickness to cylinder radius ratio of δ/a=5 using a hot wire wall shear stress probe mounted just upstream of a hearing aid microphone and a hot wire velocity probe. Variable Interval Time Averaging (VITA) event detection on streamwise velocity indicates that streamwise accelerations are associated with positive wall pressure peaks and sudden increases in wall shear stress. Likewise, positive pressure peak events are associated with streamwise accelerations and sudden increases in wall shear stress. VITA detection on wall shear stress reveals that increasing wall shear stress corresponds to streamwise accelerations and small-amplitude pressure rises, not distinct intense pressure peaks. Detection of strong adverse and favorable instantaneous pressure gradients indicates that a shear layer at y+=13 coincides with a positive peak in the wall pressure, suggesting that a positive wall pressure peak event is the key wall pressure signature associated with the burst cycle. Measurements of the cross-correlation indicate that the pressure–shear stress relationship is about two times weaker than the pressure–velocity relation and about ten times weaker than the shear stress–velocity relation. Thus, a strong relationship exists between wall pressure and streamwise velocity as well as between wall shear stress and streamwise velocity, but the relationship between wall shear stress and wall pressure is quite weak. Because of the similarity of the near-wall structure of all wall-bounded turbulent flows, regardless of transverse curvature, these conclusions should be applicable to planar boundary layers.