Determination of Principal Reynolds Stresses in Pulsatile Flows After Elliptical Filtering of Discrete Velocity Measurements

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Abstract
The purpose of this study was to develop a method to accurately determine mean velocities and Reynolds stresses in pulsatile flows. The pulsatile flow used to develop this method was produced within a transparent model of a left ventricular assist device (LVAD). Velocity measurements were taken at locations within the LVAD using a two-component laser Doppler anemometry (LDA) system. At each measurement location, as many as 4096 realizations of two coincident orthogonal velocity components were collected during preselected time windows over the pump cycle. The number of realizations was varied to determine how the number of data points collected affects the accuracy of the results. The duration of the time windows was varied to determine the maximum window size consistent with an assumption of pseudostationary flow. Erroneous velocity realizations were discarded from individual data sets by implementing successive elliptical filters on the velocity components. The mean velocities and principal Reynolds stresses were determined for each of the filtered data sets. The filtering technique, while eliminating less than 5 percent of the original data points, significantly reduced the computed Reynolds stresses. The results indicate that, with proper filtering, reasonable accuracy can be achieved using a velocity data set of 250 points, provided the time window is small enough to ensure pseudostationary flow (typically 20 to 40 ms). The results also reveal that the time window which is required to assume pseudostationary flow varies with location and cycle time and can range from 100 ms to less than 20 ms. Rotation of the coordinate system to the principal stress axes can lead to large variations in the computed Reynolds stresses, up to 2440 dynes/cm2 for the normal stress and 7620 dynes/cm2 for the shear stress.

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