(c) The time-domain distribution of the normal average velocity (d) The
frequency-domain distribution of the normal average velocity
Fig. 9 The time-frequency curves of the mean velocity of oil
Fig. 9 (a) shows the time-domain distribution of the flow average
velocity under different particle concentrations; it is obvious that the
distribution of the flow average velocity is periodic. In addition, the
base frequency of the flow field is 0.12 Hz, as shown in Fig. 9 (b).
With increasing particle concentration, the change in the flow average
velocity is nonunidirectional, but the overall trend is that the average
velocity of the oil gradually increases. The reason is that due to the
increase in the particle concentration, the particle inertia increases
the average velocity in the near-wall region, so the thickness of the
turbulent viscous bottom layer decreases and the flow velocity gradient
increases[13], which lead to an increase in the flow pulsation peak
value.
The time-domain distribution of the average normal velocity for
different particle concentrations is shown in Fig. 9 (c). As the
particle concentration increases, the change in the average normal
velocity decreases when the particle concentration is below 3.00 ppm,
while this change increases when the particle concentration exceeds 3.00
ppm. This result is because when the particle concentration reaches a
certain level (3.00 ppm) in the horizontal pipeline, the sedimentation
of the particles causes the wall surface to form a rough wall surface,
which enhances the release of the oil sudden turbulence behavior in the
near-wall region and results in increasing normal average velocity. Fig.
9 (d) shows that the main frequency of the normal average velocity is
concentrated in a subharmonic frequency of 0.09 Hz and a base frequency
of 0.12 Hz, which is consistent with the main frequency of the transient
normal velocity.