Sponding to the turbulent tran four.two.four. Stress Fluctuations Amplitude sition is of your order on the velocity determined previously. Ultimately, the final technique consists of a direct study with the relative stress fluctuations For a provided regime, the amplitudes of your stress fluctuations are increasing with inside the tube. This quantity is defined as the ratio in between the typical deviation of a the tube height. On the other hand, the increase price may well vary depending on the regime. This phe differential temporal stress signal and its imply worth, (Pi)/Pi . Figure 17 illustrates nomenon is mostly because of void coalescence. In reality, the evolutions on the pressure fluctu representative final results of all the tests carried out. The plots proof 3 main trends. ations are strongly correlated together with the evolutions of your perturbation size presented in 1st, the transitions of Carbazochrome References regimes appear more clearly within the non-particle circulation mode Section 4.2.two. This confirms the Parseval’s identity, where the energy of a signal is kept than inside the particle circulation mode. Second, stress fluctuations are a lot more intense within the | | [40]. Additionally, it means that the energy regardless the representation: | |former mode than in the latter mode. Third, the stress fluctuations improve using the spectra obtained by the coherence evaluation are constant. 4′-Methoxyflavonol custom synthesis height within the tube for a given fluidization regime.(a)Figure 17. Cont.(b)Energies 2021, 14, 7392 Energies 2021, 14, x FOR PEER REVIEW20 of 25 21 of(c) (d)Figure 17. Evolutions from the pressure fluctuations with superficial excess air velocity (calculated at the amount of the aera Figure 17. Evolutions with the stress fluctuations with superficial excess air velocity (calculated in the level of the aeration), tion), for 3 particle mass flux configurations, at fixed heights: (a) 0.18 m, (b) 0.93 m, (c) 1.68 m and (d) 2.18 m. for three particle mass flux configurations, at fixed heights: (a) 0.18 m, (b) 0.93 m, (c) 1.68 m and (d) 2.18 m.4.three. Synthesis The regime transitions can be connected with amplitude levels in the pressure fluctuations. According to [19], the slugging regime occurs in a fluidization column when the A combination of analysis approaches of pressure signal is necessary to recognize and relative stress fluctuations reach ten . In actual fact, in Figure 17, the relative pressure fluctuacharacterize the many fluidization regimes encountered in the particleintube notion. tions linked with low air velocities i.e., points in slugging regime are roughly The incoherent analysis (in the frequency domain), the crosscorrelation (in the temporal 105 , with an increase in height because of the slug coalescence. Then, by grouping domain), plus the amplitude of differential pressure fluctuations are applied as complemen the outcomes with the sub-figures, one particular notes that the turbulent regime corresponds to relative tary approaches, following the same methodology as for the risers [348]. Two primary gas fluctuations of about 150 , along with the speedy fluidization corresponds to relative fluctuations solid flow behaviours are identified as a function of tube height and air velocity, (1) coex higher than 20 , also with a rise together with the height in the tube. istence of two fluidization regimes inside the tube and (two) single fluidization regime. In the stress fluctuations slightly lower when the particles are circulating. This the former state, two instances occur: bubbling and slugging regimes, and bubbling and is because of the reduce o.
