A New Way to Determine the Wall Position and Friction Velocity in Wall-Bounded Turbulent Flows

Abstract

Studies of turbulent boundary layers are often focussed on the near wall region. In experiments an accurate determination of the wall (say within 10 μm) with respect to the measurement probe is not easily achieved through optical or mechanical measurements (see e.g. Ref. [1]). Also the friction velocity (uτ ) is hard to determine with high accuracy. One possibility is to utilize the linear velocity profile (U+ = y+ ) to determine one or both of the mentioned quantities, but is usually impeded by the fact that the hot-wire readings are affected by heat transfer to the wall. The motivation here is to utilize the cumulative distribution function (CDF) of the streamwise velocity in a way so that the influence of the heat transfer can be avoided and thereby obtain accurate estimates of both the wall position and friction velocity.