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 τ which are based on the investigation of the passive transport of temperature fluctuations, as obtained from Temperature-Sensitive Paint (TSP) data. The first criterion represents a proof-of-concept about the reliability of the use of the passive transport of temperature fluctuations Tw for the estimation of uτ. 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 expands the former to check the feasibility of the skin friction measurement by means of Tw propagation celerity in a wider range of flow conditions. It is derived by minimizing the deviation from the Taylor hypothesis of the equation of transport of temperature fluctuations, which corresponds to the energy equation for incompressible flows at the investigated conditions. Firstly, a common rule about the relationships between propagation celerity UT of the temperature disturbances at the wall beneath a turbulent boundary layer and friction velocity uτ is assessed from literature. Starting from this theoretical basis, the focus is placed on the flow over the suction side of a NACA 0015 hydrofoil model and in particular on the laminar separation bubble developing on this model surface, investigated experimentally at a chord Reynolds number of Re=1.8×105 and angles of attack AoA=[1°,3°,5°,7°,10°]. The profiles of time- and spanwise-averaged UT(x) and Cf(x) (friction coefficient) are proposed and critically analyzed. Time averaged maps of the same quantities are then reported and commented as well. Paper topics are focused on:•The relationship between the propagation celerity of the velocity disturbances UU and the friction velocity uτ•The relationship between the propagation celerity of the temperature disturbances UT and UU•The algorithms for the extraction of the propagation celerity of temperature perturbations UT based on both the time lag of the correlation peak occurrence and the minimization of the deviation of transport equation for temperature fluctuations from the Taylor’s hypothesis.•The resulting profiles and maps of friction quantities uτ and Cf.