Taylor hypothesis applied to direct measurement of skin friction using data from Temperature Sensitive Paint

Abstract

We report about the feasibility of two criteria for the direct measurement of the skin friction which ground on the investigation of the passive transport of temperature fluctuations, as obtained from Temperature-Sensitive Paint (TSP) data. To this aim, the relationships between the propagation velocity of the temperature disturbances at the wall beneath a turbulent boundary layer and the friction velocity is firstly assessed from literature as a common rule of these reverse strategies. The first criterion represents a proof-of-concept of the reliability of the use of the passive transport of temperature fluctuations for the estimation of the friction velocity. It relies on the identification of the time lag corresponding to the correlation peak between temperature time histories taken at points separated by fixed streamwise distance from the investigated location. The second criterion is derived by minimizing the deviation from the Taylor hypothesis of the equation of transport of temperature fluctuations (energy equation for incompressible flows at investigated conditions). Starting from these theoretical basis, the focus is placed on the flow around the suction side of a NACA 0015 hydrofoil model and on the Laminar Separation Bubble beneath, investigated experimentally at chord Reynolds number Re = 180000 and angles of attack AoA = [1°; 3°; 5°; 7°; 10°]. The time- and spanwise-averaged propagation velocity of the temperature disturbances and friction coefficient are proposed and criticized. Averaged maps of the same quantities are then reported and commented as well.