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)).