Reynolds stress tensor measurements using magnetic resonance velocimetry: expansion of the dynamic measurement range and analysis of systematic measurement errors

Abstract

This study presents magnetic resonance velocimetry (MRV) Reynolds Stress measurements in a periodic hill channel with a hill Reynolds number of Re = 29,500. The velocity encoding scheme is based on the ICOSA6 method with six icosahedral encoding directions and multiple encoding values are measured to increase the dynamic range. The full Reynolds stress tensor is obtained from a voxel-wise three-dimensional Gaussian fit using the magnitude data of all acquisitions. The MRV results are compared to a wall-resolved large eddy simulation and laser Doppler velocimetry measurements conducted in the same channel. It is shown that the MRV Reynolds stress data have excellent precision and agree qualitatively with the reference data. However, there are apparent systematic deviations. One of the most prominent error contributions is the signal attenuation caused by higher orders of motion, which leads to an overestimation of the turbulence level. Another fundamental error is identified in the assumption that the turbulence is Gaussian distributed. With the presented reconstruction technique, the MRV data are fitted to a statistical model, and depending on the examined flow setup, the Gaussian model can lead to considerable errors. Possible ways of how to reduce all identified errors are presented. In summary, this technique enables Reynolds stress tensor measurements in complex internal flows with high dynamic range and excellent precision. However, several issues need to be resolved to make the turbulence quantification more accurate. Graphic abstract

Characterization of unsteady flow in a 3D‐printed Schwarz Diamond monolith using magnetic resonance velocimetry

“…A previous MRI study demonstrated that significant error in the velocity variance is introduced by incorrectly assuming the form of the velocity distribution function. 33 Because the flow characteristics of the Schwarz Diamond geometry are unclear, we assume that the velocity fluctuations are normally distributed with a variance of u 2 for simplicity. Therefore, integrating with respect to u and normalizing by the signal at p = 0, which is defined by S 0 , gives the signal in terms of the velocity distribution parameters:…”

“…A previous MRI study demonstrated that significant error in the velocity variance is introduced by incorrectly assuming the form of the velocity distribution function 33 . Because the flow characteristics of the Schwarz Diamond geometry are unclear, we assume that the velocity fluctuations are normally distributed with a variance of for simplicity.…”