MRI technique for measurement of velocity vectors, acceleration, and autocorrelation functions in turbulent flow

Abstract

In this paper, we show velocity images for liquid flow in a cylindrical pipe at Reynolds numbers of up to 5000. Three orthogonal velocity components are acquired from a single excitation over a timescale of 60 ms thus obtaining an ‘instantaneous’ description of the fluid flow in steady laminar and chaotic turbulent flow. It is also shown how the technique, termed the gradient echo rapid velocity and acceleration imaging sequence (GERVAIS), can be used to acquire acceleration (convective derivative) images by incorporation of double pulsed gradient spin echo (PGSE) pairs into the pulse sequence such that the resulting phase shift is a measure of the change in the velocity over the mixing time between successive PGSE pairs. The technique has also been used to acquire up to 16 successive z-velocity images, providing spatio-temporal information of the velocity fluctuations over a period of 320 ms, which are then used to calculate spatially resolved velocity autocorrelation functions. It is found that over the timescale of the velocity measurements, which is principally determined by the residence time in the coil, the local velocity fluctuations are seen to be small compared to the local velocities, confirming that the data acquisition times achieved are rapid enough to capture ‘instantaneous’ images of the flow field.