On the Accuracy of Wall Shear Stress Using DPIV

Abstract

Wall shear stress measurements are important for a variety of fluid mechanics phenomena and engineering applications ranging from estimation of viscous drag to the regulation of endothelial cell function in arterial flows [1–5]. Although DPIV has emerged over the past years as the method of choice for global non-invasive optical flow diagnostics [6–13] the issues associated with the indirect estimation of wall shear stresses from DPIV measured velocities have not been sufficiently addressed. The challenge is even more significant in the presence of deformable and dynamically moving boundaries. In particular such measurements require accurate determination of wall position, near-wall velocity measurements using DPIV algorithms, and the indirect estimation of the velocity derivatives in order to evaluate the shear stress. Dynamically moving boundaries, whether rigid or compliant, require special consideration, as the boundary position must be determined accurately as a function of space and time. It is necessary to quantify the accuracy of each measurement that contributes to the error of the wall shear stress estimation. In this work we decompose the problem into the following three aspects: (a) determination of the exact boundary points (b) DPIV velocity measurement uncertainty in the near wall region. (c) velocity derivative error. Methodologies and improvements addressing each aspect individually are proposed and a systematic parametric study of the related error is performed. To our knowledge, this is the first detailed parametric effort to quantify the errors associated with wall shear stress estimation from DPIV velocities.