Turbulent stress measurements with phase-contrast magnetic resonance through tilted slices

Abstract

This is crucial in, for example, the pulp and paper industry where not only do fibre suspensions alter turbulent quantities, but the flowfield in many devices used in the paper making process are complex in nature (MacKenzie et al. 2014).Methods such as ultrasonic doppler velocimetry (UDV) and electrical impedance tomography (EIT) have conventionally been used for measuring the flowfield of opaque suspensions, whereas particle image velocimetry (PIV) and laser doppler velocimetry (LDV) are more commonly used for measuring the flowfield of transparent fluids. An advantage of MRV over other experimental techniques is that it can measure the full 3D velocity field in a few minutes for both transparent and opaque fluids (Caprihan and Fukushima 1990). The limitation of MRV is that in many cases computational fluid dynamics (CFD) simulations or PIV data are needed to provide details about the turbulent velocity fluctuations and Reynolds stresses (Elkins et al. 2009;Iaccarino and Elkins 2006). If MRV is to become a reliable method for measuring the flowfield of opaque suspensions at high Reynolds numbers, where conventional methods are unsuitable, it is important to extend the capacity towards measuring turbulent quantities. In doing so, it should be shown that MRV can produce rms values and Reynolds shear stress that agree with direct numerical simulations (DNS) in a well-defined geometry. This paper details our efforts in utilising phase-contrast MRV to measure the variance and covariance components of the Reynolds stress tensor for water in pipe flow. It will be shown that MRV provides reliable and accurate data in a large portion of the pipe. Works on turbulent flow in fibre suspensions will follow.Measurements of diffusion with magnetic resonance has a long history (Stejskal and Tanner 1965) and this ability can be used to quantify turbulence through turbulent Abstract Aiming at turbulent measurements in opaque suspensions, a simplistic methodology for measuring the turbulent stresses with phase-contrast magnetic resonance velocimetry is described. The method relies on flow-compensated and flow-encoding protocols with the flow encoding gradient normal to the slice. The experimental data is compared with direct numerical simulations (DNS), both directly but also, more importantly, after spatial averaging of the DNS data that resembles the measurement and data treatment of the experimental data. The results show that the most important MRI data (streamwise velocity, streamwise variance and Reynolds shear stress) is reliable up to at least r = 0.75 without any correction, paving the way for dearly needed turbulence and stress measurements in opaque suspensions.