# Detection of Gas-Solid Two-Phase Flow Based on CFD and Capacitance Method
## 4 Experimental Procedure
### Speed Detection Experiments  
To investigate the velocity of the solid phase in the channels simultaneously, the velocity sensor electrode is arranged on the inner wall of the outer pipe. The rig is shown in the left section of Figure 12, in which the inner pipe and the outer pipe can be seen, together with a function generation and an oscilloscope. Electrical sensors are used to measure the speed of the solids. Basically, a sensor is structured like a pair of combs of thin electrodes, with the electrodes interlaced to form a capacitor, shown in Figure 16. During the measurement, one set of electrodes is charged by the signal from the function generator, and the other set of electrodes receive signals. When a lump of solids flow past the electrodes, the set of receiving electrodes will produce a pulse of signal that will be recorded by the oscilloscope.  
Experimental characteristics in speed detection are shown in Table 2. Two sensors \(E\_A\) and \(E\_B\) are mounted on the pipe wall in the inclined section. The upstream sensor is marked as \(E\_A\), and the  
Figure 16: An electrode pair for measurement.  
Figure 15: Reconstructed solids distribution.  
downstream sensor is marked as _E_B_. The two sensors are separated by \(D\) of 30 cm, as indicated in Figure 17. The signals will be collected continuously during an experiment. Thus, two series of curves of signals will be recorded from the two sensors. When a solid lump flows past the two sensors, ideally a peak will appear in each of the recorded curves. The two peaks will be separated by a time interval as the solid lump passes the upstream and the downstream sensors at a different time.  
In the experiment, the sine wave of 100 kHz is used to charge the electrodes, and _Vol_ is 5 V. The waveform is recorded by an oscilloscope, whose _T_u_ is set to 200 ms. After the signals are recorded, the speed of the solids is calculated using cross-correlation method, which indicates the correlation between the two-time series of signals.  
\[R(n)=(1/N)\sum[x(m)y(m+n)] \tag{6}\]  
In the above formula, \(R(n)\) is the cross-correlation coefficient, \(n\) is the shifting number of two series, and m is the number index of the signals ranging from 0 to \(N\)-1. In the experiment, the pipes are inclined at 45 degrees, and a lump of sand is poured into the annular space from one end. Then, the flow velocity is obtained from signal processing using the cross-correlation method in Matlab software.  
Figure 18 shows the signals received from sensor _E_A_, in green colour, and from sensor _E_B_, in red colour. Peak values on each curve can be seen. Also, it can be seen that the range of the peak values on the green curve is slightly broader than on the red curve, indicating that a solid lump spends more time in sensor _E_A_, or that the speed of the solid lump in sensor _E_B_ is faster than in sensor _E_A_. This is reasonable, because of the acceleration the solid lump should flow faster in the downstream lower position, i.e., near sensor _E_B_. According to the data from the oscilloscope, the correlation coefficient of the two waveforms is calculated and shown in Figure 19, which corresponds to _V_e_ of 0.517 m/s.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Experimental Characteristics** & **Description** \\ \hline _E_A_ & The upstream electrode pair \\ _E_B_ & The downstream electrode pair \\ \(D\) & Distance between two sensors \\ _Vol_ & The voltage of the signal \\ _Tu_ & Time Unit \\ _V_e_ & The velocity of lump obtained in the experiment \\ _V_s_ & The velocity of lump obtained in the simulation \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental characteristics in speed detection.  
Figure 17: Schematic of velocity measured with the method of cross-correlation.  
Recalling that the solid speed \(V\_s\) of 0.532 m/s obtained from the simulation using Two-Fluid model, the experimentally measured \(V\_e\) of 0.517 m/s agrees very well with the CFD simulation, with an error of 2.9%. This can be regarded as a good verification of the CFD results.