Figure 1:
The research flow chart for using ultrasonic sensor & wavelet transform for measuring sand flow rate.
Figure 2:
Morlet wavelet function.
Figure 3:
Illustration of DWT calculation method.
Figure 4:
Flow loop test facility at Curtin University, (A) Computer system, (B) Collection basket, (C) Piping, and (D) Compressor.
Figure 5:
Block diagram of the flow loop at Curtin University.
Figure 6:
The flow loop facility components (A) Variable speed drive (VSD), (B) Hopper (sand injector device), (C) Ultrasonic sensor and metallic base, and (D) Data acquisition system.
Figure 7:
Spectral analysis of ultrasonic signal at velocity of 7 m/sec and sand rate of 35 g/sec.
Table 1.
Frequency intervals of wavelet transform.
| Interval 1 | 500 kHz–1 MHz | Interval 4 | 62.5–125 kHz | Interval 7 | 7.8125–15.625 kHz |
| Interval 2 | 250–500 kHz | Interval 5 | 31.25–62.5 kHz | Interval 8 | 3.90625–7.8125 kHz |
| Interval 3 | 125–250 kHz | Interval 6 | 15.625–31.25 kHz | Interval 9 | 1.953125–3.90625 kHz |
Figure 8:
Strength of wavelet transform versus sand flow rate at various frequency intervals.
Figure 9:
Sum of wavelet coefficients across two frequency ranges versus the sand flow rate.
Figure 10:
Fitting linear curve to the DWT in frequency range from 15.625–62.5 kHz.
Figure 11:
Energy of DWT in frequency range 15.625–62.5 kHz at various velocities.