On the monodimensional approach to the estimation of the highest Reynolds shear stress in a turbulent flow

The measurement of the Reynolds stress tensor, or at least of some of its components, is a necessary step to assess if the turbulence associated with the flow near prosthetic devices can damage blood constituents. Because of the intrinsic three dimensionality of turbulence, in general, a three-component anemometer should be used to measure directly the components of the Reynolds stress tensor. However, this can be practically unfeasible, especially in vivo; therefore, it is interesting to investigate the possibility of characterizing the turbulent flows that may occur in the circulatory system with the monodimensional data that a less complete equipment (e.g., a pulsed ultrasound Doppler) can yield. From the general expression of the Reynolds stress tensor, the highest shear stress can be deduced, as well as the Reynolds normal stress in the main how direction. The relation between these two quantities, which is an issue already addressed in previous works, can thus be rigorously formulated in terms of some characteristic parameters of the Reynolds stress tensor, the principal normal stresses and the angles that the directions that define them form with the main flow direction. An experimental verification of the ratio of the two above-mentioned quantities for the flow across bileaflet valves, investigated by means of two-dimensional laser Doppler anemometry, will illustrate the limitations of the monodimensional approach estimating the maximum load on blood constituents. (C) 2000 Published by Elsevier Science Ltd. All rights reserved.