Development and validation of an MRI-based method for 3D particle concentration measurement

Highlights: • A new method for measuring particle concentration in turbulent flows is presented. • Quantitative, 3D data are obtained without optical access using a standard MRI. • Measurements in a homogeneous, turbulent channel flow agree well with theory. • Transport of a particle streak in a ribbed square channel flow is studied. - Abstract: A novel method, denoted MRP (short for Magnetic Resonance Particle concentration), was developed to obtain 3D volume fraction measurements for a dispersed particulate phase in turbulent water flows using Magnetic Resonance Imaging (MRI). MRI images taken near a single stainless steel particle suspended in agarose gel showed good agreement with the analytical solution for the disturbance to a uniform magnetic field induced by an immersed sphere. For a random distribution of particles, a linear relationship between the MRI signal decay rate ($R_2^{*}$) and particle volume fraction (${\varphi }_{\text{v}}$) has previously been predicted in the MRI literature. This relationship was investigated for various types of particles suspended in agarose gel vials. Good agreement with theory was observed for particles with a high magnetic susceptibility difference from water. $R_2^{*}$ was also measured in a square channel flow containing a uniform distribution of titanium particles at two fully turbulent Reynolds numbers. Experimental results again agreed well with theory in the majority of the channel for both Reynolds numbers studied. Data from this flow were used to examine the expected SNR and dynamic range for MRP in future experiments. Some discrepancy was observed near the entry region of the channel, with possible explanations including inflowing fluid and large-scale flow structure effects behind the channel's mixing pin array. Finally, the new method was used to measure the 3D concentration distribution for a streak of titanium particles injected into a turbulent square channel flow with angled ribs. The transport of the streak was analyzed quantitatively, and a minor asymmetry in the channel geometry was shown to have important implications for the mean transport of the particle streak.