Fig. 12 Distribution diagram of the PSD under different liquid arrangement methods with the liquid spray densities. (a)F s = 1.2 (m/s*(kg/m3)0.5) and (b)F s = 2.0 (m/s*(kg/m3)0.5) in overflow distribution; (c) F s = 1.2 (m/s*(kg/m3)0.5) and (d)F s = 2.4 (m/s*(kg/m3)0.5) in spray distribution.
Fig. 12a, b shows the PSD distributions with different liquid spray densities under an overflow distribution of the liquid. The gas-phase kinetic factors are F s = 1.2 (m/s*(kg/m3)0.5) and 2.0 (m/s*(kg/m3)0.5). For the liquid spray density L W ≤ 78 m3/(m2*h), the two main frequencies move within (2.36 Hz–5.28 Hz). The PSD value changes in the range (0.0044 dB/Hz–0.0104 dB/Hz) and decreases with the increasing liquid spray densities (see Fig. 12a). At this point, the flow pattern corresponds to BFF. The two-phase flow is more stable, and the rotational flow is dominant. The increase in the proportion of the liquid phase will increase the resistance of the gas phase and consume gas-phase energy, resulting in a decrease in the PSD value. For the increasing spray density L W = 104 m3/(m2*h), the flow pattern is CPF. The liquid layer on the unit is thicker, and the liquid phase perforates out from the sieve holes affected by gravity and the driving force of airflow. As shown in Fig. 12b, the gas-phase kinetic factor has increased to 2.0 (m/s*(kg/m3)0.5). The liquid spray density is L W ≤ 52 m3/(m2*h), and the two main frequencies vary within the range of (2.48 Hz–5.64 Hz), compared with BFF. The PSD value is increased and varies in the range of (0.0184 dB/Hz–0.0403 dB/Hz). At this time, the corresponding flow pattern is DMF. The gas-phase ratio and intensity of the perforated flow is increased. The PSD value for the first main frequency increases. When the spray density continues to increase to L W> 52 m3/(m2*h), the two main frequencies remain unchanged, and the PSD value is within (0.0155 dB/Hz–0.0226 dB/Hz), showing a decreasing trend. Then, the flow pattern is transformed into CPF. The liquid layer above the sieve holes is thickened. The gas-phase perforation channel and intensity strength became smaller. The flow is blocked, resulting in a decrease in the PSD values for the main frequencies.
Fig. 12c, d shows the variations of the PSD values under different liquid spray densities, with the kinetic factorsF s = 1.2 (m/s*(kg/m3)0.5) and 2.4 (m/s*(kg/m3)0.5), under a spray distribution of the liquid phase. As shown in Fig. 12c, the two main frequencies change in the range of (2.36 Hz–5.16 Hz), remaining unchanged with the liquid spray densities, and the PSD values show an increasing trend, ranging from (0.0115 dB/Hz–0.0623 dB/Hz). At this operating condition, the corresponding flow pattern at each liquid spray density is FJF, and the liquid phase plays a leading role. The strength of the liquid jet streams hitting the surface of the unit increases with increasing spray density, which intensifies the gas-liquid mixing. In addition, the interaction of the two phases increases, increasing the energy of the main frequencies. For the increasing gas-phase kinetic factor F s = 2.4 (m/s*(kg/m3)0.5), the range of the main frequencies is similar to that of FJF. The PSD value increases, ranging from (0.0189 dB/Hz–0.1925 dB/Hz), (see Fig. 12d). The flow pattern changes to JMF, and the perforation intensity is increased. The velocities of the liquid jet streams increase with the spray densities. The liquid phase flow is more disordered. The liquid jet streams hit the surface of the unit, and then, the interaction between the two phases is more intense. The strength of the two phases is increased. The PSD values of the main frequencies are significantly improved. For the liquid phase spray density L W = 260 m3/(m2*h), the turbulence intensity of the gas-liquid phase flow on the unit surface reaches the maximum. The perforated resistance of the gas-phase flow is also the largest, and the interaction intensity of the gas-liquid phase is the strongest within the experimental operating conditions.

3.3 Operating conditions

Combined with the flow pattern image recognition, time domain, and PSD analysis of the differential pressure pulsation signal, in the range of the experimental operating conditions (0 <F s ≤ 4.0 (m/s*(kg/m3)0.5), 0 <L W ≤ 260 m3/(m2*h)), the distribution of each flow pattern is shown listed in Table 2.
Table. 2 Distribution of the flow patterns within the operation domain