Magnetic Resonance Velocimetry Measurement of Viscous Flows through Porous Media: Comparison with Simulation and Voxel Size Study

Studies that use magnetic resonance velocimetry (MRV) to assess flows through porous media require a sufficiently small voxel size to determine the velocity field at a sub-pore scale. The smaller the voxel size, the less information is lost through the discretization. However, the measurement uncertainty and the measurement time are increased. Knowing the relationship between voxel size and measurement accuracy would help researchers select a voxel size that is not too small in order to avoid unnecessary measurement effort. This study presents a systematic parameter study with a low-Reynolds-number flow of a glycerol–water mixture sent through a regularly periodic porous matrix with a pore size of 5 mm. The matrix was a 3-dimensional polymer print, and velocity-encoded MRV measurements were made at 15 different voxel sizes between 0.42 mm and 4.48 mm. The baseline accuracy of the MRV velocity data was examined through a comparison with a computational fluid dynamics (CFD) simulation. The experiment and simulation show very good agreement, indicating a low measurement error. Starting from the smallest examined voxel size, the influence of the voxel size on the accuracy of the velocity data was then examined. This experiment enables us to conclude that a voxel size of 0.96 mm, which corresponds to 20% of the pore size, is sufficient. The volume-averaged results do not change below a voxel size of 20% of the pore size, whereas systematic deviations occur with larger voxels. The same trend is observed with the local velocity data. The streamlines calculated from the MRV velocity data are not influenced by the voxel size for voxels of up to 20% of the pore size, and even slightly larger voxels still show good agreement. In summary, this study shows that even with a relatively low measurement resolution, quantitative 3-dimensional velocity fields can be obtained through porous flow systems with short measurement times and low measurement uncertainty.

Inverse Problems in Magnetic Resonance Velocimetry: Shape, Forcing and Boundary Condition Inference

We derive and implement an algorithm that takes noisy magnetic resonance velocimetry (MRV) images of Stokes flow and infers the velocity field, the most likely position of the boundary, the inlet and outlet boundary conditions, and any body forces. We do this by minimizing a discrepancy norm of the velocity fields between the MRV experiment and the Stokes problem, and at the same time we obtain a filtered (denoised) version of the original MRV image. We describe two possible approaches to regularize the inverse problem, using either a variational technique, or Gaussian random fields. We test the algorithm for flows governed by a Poisson or a Stokes problem, using both real and synthetic MRV measurements. We find that the algorithm is capable of reconstructing the shape of the domain from artificial images with a low signal-to-noise ratio.

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

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

An Experimental and Numerical Investigation of the Three-Dimensional Flow Field and Heat Transfer of a Row of Impinging Jets

Impingement cooling is a well-established technique to reduce the thermal load of hot gas components in gas turbines. Although the technique is widely used, correlations are nonetheless the standard design method, as the flow field and heat transfer are notoriously difficult to predict with state-of-the-art commercially viable CFD calculations. The primary challenges to CFD are phenomena such as shear layers and crossflow interactions. Therefore, a demand for spatially highly resolved measurements exists. An experimental investigation of a confined row of round jets impinging on a flat surface representative of gas turbine geometries with and without an initial crossflow has been conducted. The effect of the distance between the impingement plate and the target surface as well as the effect of the crossflow flow rate on the interaction of the jets with each other and with the crossflow are assessed. The three-dimensional impingement flow field and the heat transfer characteristics on the target surface are measured. The former has been visualised by Magnetic Resonance Velocimetry (MRV). This measurement technique is relatively novel for engineering applications, but very well suited for low-Mach number flows in complex geometries. It yields millions of measurement points and is thus ideal for a comparison with CFD. The local Nusselt number distribution is obtained using steady-state Thermochromic Liquid Crystals (TLC) on the same test set-up. Secondary losses and errors associated with this method are evaluated by means of an energy balance. The experiments are accompanied by a CFD simulation using an approach typically used for designing impingement configurations in industry as well as a more advanced method.

Experimental Study of Flow Inside a Centrifugal Fan Using Magnetic Resonance Velocimetry

Three-dimensional (3D), three-component time-averaged velocity fields have been measured within a low-speed centrifugal fan with forward curved (FC) blades. The model investigated is representative of fans commonly used in automotive applications. The flow was analyzed at two Reynolds numbers for the same ratio of blade rotational speed to outlet flow velocity. The flow patterns inside the volute were found to have weak sensitivity to Reynolds number. A pair of counter-rotating vortices evolves circumferentially within the volute with positive and negative helicity in the upper and lower regions, respectively. Measurements have been further extended to capture phase-resolved flow features by synchronizing the data acquisition with the blade passing frequency. The mean flow field through each blade passage is presented including the jet-wake structure extending from the blade and the separation zone on the suction side of the blade leading edge.