(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.