Fig. 4 The time-frequency variation in the transient velocity of oil when the concentration is 0.65 ppm
Fig. 4 shows the variation in the time-frequency curves of the instantaneous flow velocity and the instantaneous normal velocity when the particle concentration is 0.65 ppm. Fig. 4 (a) presents the change in the instantaneous flow velocity over time. The instantaneous flow velocity fluctuates at approximately 0.2099 under the action of a flow field pulsation base frequency of 0.12 Hz (as shown in Fig. 4 (c)), and the flow velocity appears to have a reflow phenomenon (having a negative velocity) in the first cycle; however, the distribution of the flow velocity tends to be gentle after this cycle. Due to the small particle concentration, the viscous shear force has little effect on the oil, where this force made the pulsation degree increase from -0.4474 to 0.9041, namely, a change of 1.3515. In addition, Fig. 4 (c) shows that the flow velocity pulsation frequency is mainly 0.21 Hz, which is approximately two times the base frequency.
Fig. 4 (b) presents the change in the instantaneous normal velocity with time, and this figure shows that the instantaneous normal velocity at this point fluctuated around 0.0436, indicating that the velocity distribution in the central region is relatively balanced in the normal direction. The change in the amplitude of the normal velocity is relatively flat, from 0.4058 to 0.3965, with a range of 0.8023. Fig. 4 (d) shows that the normal velocity pulsation frequency of the oil mainly includes the base frequencies of 0.12 Hz and 0.21 Hz, which is approximately two times the base frequency.
The time-frequency variations in the instantaneous flow velocity and normal velocity when the particle concentration is 0.97 ppm are shown in Fig. 5. The instantaneous flow velocity changes over time, as shown in Fig. 5 (a), and the instantaneous flow velocity of the point fluctuation is near the value of 0.1683. Under the action of the flow pulsation base frequency of 0.12 Hz (as shown in Fig. 5 (c)), the flow velocity appears to reflow in the first two cycles. Compared with Fig. 4 (a), as the particle concentration increases and the viscous shear force increases, the flow velocity pulsation intensity decreases from -0.3985 to 0.8943; namely, the variation range is 1.2928. In addition, the flow velocity pulsation frequency is 0.18 Hz, which is 1.5 times the base frequency (shown in Fig. 5 (c)).