The electrodiffusional theory for the wall shear stress measurement by two-strip probe

Abstract

This article deals with the derivation of the fundamental theory describing the mass transport on the active surface of a two-strip mass transfer probe for an arbitrary direction of fluid flow. The existence of such a general theory is a critical point for the application of the electrodiffusion method using a two-strip probe. Considering the different possible sizes of the probe segments, the analytical formulas for the average mass transfer coefficients are derived and presented in dimensionless forms for both segments. The correctness of the derived analytical expressions is verified by numerical solution of the convection-diffusion transport equation. A methodology for possible experimental data treatment is also proposed. It is based on the evaluation of two current signals collected from the segments of a two-strip probe. From the derived equations, it is possible to determine the magnitude and direction of the wall shear rate vector for both frontal and reverse flow regimes. From the analysis of the current ratio predictions for different probe geometries, an optimal probe configuration is found with respect to the sensitivity of the flow direction measurement.