Generalized theory for wall shear stress measurement using circular-segment electrodiffusion probes
Résumé
The present work establishes a new theoretical framework for wall shear stress measurements with electrodiffusion probes composed of circular segments, a generalization of the theory previously derived for twin semicircular probes. This newly proposed probe design extends the capabilities of near-wall flow measurements and provides deeper insights into boundary layer behavior. By deriving analytical formulas for the mass transfer coefficients, the study quantifies how the probe geometry and fluid flow direction affect mass transfer to each segment of the probe. A numerical solution of the convection–diffusion equation confirms the validity of these analytical formulas. In addition, a practical methodology for evaluating experimental measurements is presented that allows the electrical currents collected by the probe to be converted into a wall shear stress vector. The influence of the insulation gap position on diagnostic performance is also discussed, highlighting how different probe geometries can refine the sensitivity and accuracy of the measurement. Overall, the proposed approach broadens the possibilities of electrodiffusion-based measurements, allowing for a more versatile and detailed characterization of near-wall transport phenomena.