Opinión de los alumnos ante el uso de las TIC

VFR flow is obtained by imposing pipe flow to TVF. As discussed earlier, several authors assumed that the introduction of pipe flow was simply causing the vortices to translate along the length of the reactor6. But the slalom high-velocity regions on the axial direction velocity maps in a VFR (Figure 4.11b) show that the vortices are not simply "pushed" by the addition

of pipe flow. In fact, the velocity field in a VFR appears as a combination between the velocity fields of TVF and pipe flow. These results seem to support the assumption made by Wereley et al.12, that the VFR velocity field could be modelled by an addition of pipe flow and TVF velocity fields. MRI maps offer a simple way of testing this hypothesis, since model VFR maps can be obtained by a pixel-to-pixel addition of pipe flow and TVF velocity maps. Figure 4.14 shows experimental and modelled VFR velocity maps at the same flow and rotation rates.

Figure 4.14. (a) Axial velocity map obtained by linear addition of experimental pipe flow (Q =7.2 cm3 min–1) and TVF (ω =1 Hz) velocity maps. (b) Experimental velocity map of VFR flow at _{ω =1 Hz and Q = 7.2 cm}3 min–1. (c) Axial velocity map obtained by linear addition of experimental pipe flow (Q =13.6 cm3 min–1) and TVF (ω =1 Hz) velocity maps. (d) Experimental velocity maps of VFR flow at ω =1 Hz and Q =13.6 cm3 min–1.

The velocity maps obtained by linear addition show good agreement with the experimental VFR flow ones. The main difference is that the model velocity maps have about 30% higher velocities. Also, by removing the average axial map from the experimental VFR map one

obtains a typical TVF map corresponding to a lower rotation rate12. This could be explained by head loss occurring via the combination of the two flows. The strong TVF flow in azimuthal direction possibly transforms a part of the coherent motion in the z direction into dispersion, not detected by the velocity mapping experiments. Decrease in velocity in the VFR maps is in agreement with experimental results12 showing that the addition of pipe flow increases the critical rotation rate necessary for the formation of the vortices. Also, this phenomenon could explain the possibility of stopping the moving vortices by increasing the rotation rate7.

The properties of the slalom high-velocity region seem closely related to the pipe flow properties. Comparison between VFR velocity maps at Q = 7.2 cm3 min−1 (Figure 4.14b) and Q = 13.6 cm3 min−1

(Figure 4.14d) shows that for higher flow rates, this region is increased. However, the velocity drift, Vd, typically used for analysing the VFR flow properties, was found to be constant for all flow rates at a given rotation rate. These results highlight the limitation of Vd in characterising flow properties in a VFR and in particular the presence and properties of the slalom velocity region. The results presented here, could allow identifying more appropriate parameters for predicting VFR velocity field properties such as the importance of the slalom velocity field. One of these parameters is the pipe flow velocity profile (Figure 4.7a). For a given flow rate, this profile depends mainly on the value of the gap (d), the radii ratio (η), the viscosity (ν) and the material properties of the inner walls. Two reactors with different d would exhibit different profiles and therefore have different VFR flow properties. At equal axial flow rates, a smaller gap VFR device made of high friction coefficient materials will exhibit a steeper pipe flow velocity profile, and hence, tend to have higher velocity deviations from Uax. In that case, the Vd = 1 condition would not be sufficient

to predict plug flow, because of the presence of an important by-pass flow suggested by the z direction velocity maps. A review of the literature reveals that the studies that used the bigger gap VFR reactors and low axial flow rates (flat pipe flow profiles) tend to use the plug-flow approximation6,8,9, whereas studies that used smaller gap reactors (steep pipe flow velocity profiles) tend to study the by-pass flow7,12,24. For plug-flow applications of the VFR, the parameters affecting the shape of the axial velocity profile have to be considered as much as Vd to analyse the quality of the plug-flow.

Diffusion/dispersion maps of the flow could give a measure of the extent of dispersion caused by the superposition of pipe flow and TVF. But diffusion/dispersion imaging typically requires a minimum of 8 q-slices encoding rather than the 2 used for velocity imaging. As discussed earlier, it is difficult to maintain a constant flow rate over the course of an 8 q-slice experiment (2-3 hours). Hence, while diffusion/dispersion mapping within the VFR should also be possible with the pulse sequence timing method, it was not possible to produce VFR diffusion/dispersion maps for this work. An estimation of diffusion/dispersion within the system could be obtained using the 2 q-slice experimental data. These experiments provide with the initial signal and one attenuated signal value, which allow getting information on the signal attenuation for each pixel. Signal attenuation is caused both by incoherent flow (diffusion/dispersion) and velocity shear, generating a spread of phases within the spin packets. The normalisation of the signal attenuation per pixel provides with a diffusion/dispersion variation map but no accurate diffusion/dispersion value can be obtained. Average propagator measurements could provide additional information on molecular displacements.