Slugging configuration, of 0.83 0.14 and 1 0.20 m/s respectively. Within the speedy Troriluzole Biological Activity fluidization case, a phase inversion happens, as well as the velocity measured by the cross-correlation is then relative to clusters of particles [20].Energies 2021, 14,upward velocity in the slug of 0.42 0.04 m/s. Figures 15c,d correspond to tests at 1.7 and two.five sm3/h aeration flow rates respectively, i.e., top to a turbulent and a quick fluidization regimes. Since there’s no noise on the connected power spectra, the cross correlation functions exhibit smoothed shapes. The upward velocities of the perturbations are higher than within the slugging configuration, of 0.83 0.14 and 1 0.20 m/s respectively. 18 of 25 Within the speedy fluidization case, a phase inversion occurs, along with the velocity measured by the crosscorrelation is then relative to clusters of particles [20].(a) (b)(c) (d)Figure 15. Several crosscorrelation functions corresponding to distinct fluidization regimes in the tube, at various heights Figure 15. Various cross-correlation functions corresponding to distinctive fluidization regimes inside the tube, at many heights and aeration flow prices: (a) single bubbling, (b) wallslugging, (c) turbulent, and (d) rapidly fluidization. and aeration flow prices: (a) single bubbling, (b) wall-slugging, (c) turbulent, and (d) rapidly fluidization.The previous outcomes indicate that varying the aeration flow rate induces variations with the upward velocity of voids and clusters detected by the cross-correlation process. Combining each of the tests, it appears that the improve on the particles mass flux leads also to an increase of the measured upward velocity. This tendency is represented in Figure 16. Because the cross-correlation can not detect bubbles and their velocities, the 1.68 m height has been fixed to compare the velocities measured in slugging, turbulent and rapid fluidization regimes together with the theory. In the Figure, values are plotted versus the sum from the excess air velocity along with the upward particles velocity, U p = G p / p i , for the many G p values. The dashed line inside the Figure represents the upward slugs velocities calculated using the two-phase theory of fluidization for the case of axisymmetric slugs, exactly where Us,th = Uair – Um f U p k gDt (inside a fluidization column) [33,39]. In this equation, a coefficient k of 0.35 or 0.7 applies for the axisymmetric or the wall slugging regime respectively. The theoretical velocities for wall slugs are usually not presented within the Figure for the sake of clarity, since the two theoretical curves are extremely equivalent. For the tests leading to a slugging regime, i.e., for low aeration flow prices, the measured velocities are in superior agreement together with the two-phase theory. However, for the turbulent and fast fluidization regimes, the measured velocities are greater than 1 m/s i.e., larger than the value estimated using the theory for the slugging regime which confirms the regime transition. Nevertheless, uncertainties are powerful (around 20 and more of relative error). Consequently, this approach has a limited accuracy for higher perturbation velocities, resulting from the low acquisition frequency imposed (20 Hz). In conclusion, the use of the cross-correlation function gives upward void velocities in superior agreement using the two-phase theory for the slugging regimes, at low air velocities. At greater air velocities, the strategy just isn’t accurate but allows the identification of high upward velocities of voids and particles (clusters) for the turbulent and fast fluidization.
