# Reverse Circulation Drilling Method Based on a Supersonic Nozzle for Dust Control
## 3 Experimental  
### Orthogonal Experimental Design and Experimental Setup  
As shown in Figure 2, the experimental reverse-circulation apparatus consists of three parts, a supporting pedestal, a simulated reverse-circulation bit, and an upper discharge passage, respectively. For easier facility parameter adjustment, a modular design method was applied to the design of the simulated bit in the laboratory. The simulated reverse-circulation bit is divided into two modules; namely, the center passage with supersonic nozzles and flushing nozzle modules. The center passage is connected to the upper discharge passage so that the flow rate of the mixing air can be measured by mass flow meter. There exists a certain gap between the supporting pedestal and bit to simulate the annular space in borehole where the outside air can be inhaled into the bit through the air vent on the supporting pedestal. An air compressor is used as the air source, and a surge tank is utilized to provide a steady pressure in experimental system. As the analysis using conventional experimental methods is inefficient and expensive, the orthogonal design is applied in this paper. By application of this method, less experimental work is required to study multiple levels of all input parameters and some effects due to statistical variations can be filtered out. The quantity of the supersonic nozzle (\(N_{\mathrm{s}}\)), the flushing nozzle diameter (\(D_{\mathrm{f}}\)),  
Figure 1: Schematic of the reverse-circulation drilling method. divergent part length (the longer side) of the supersonic nozzle (\(L_{\rm s}\)), the spray angle of the supersonic nozzle (\(\theta\)), the supersonic nozzle height (\(H\)), and the center passage diameter (\(D_{\rm c}\)) are determined as six factors of the orthogonal experiment and each factor has three levels. For each factor, three levels are selected to eliminate the influence and validate the experimental results. To thoroughly understand the interrelationships between the factors, the interaction terms (\(N_{\rm s}\times D_{\rm f}\) and \(N_{\rm s}\times L_{\rm s}\)) are investigated. The considered factors and levels are listed in Table 1.  
The nozzle diameters of the entrance and throat were 6.6 mm and 2.8 mm, respectively. Twenty-seven tests derived from the L\({}_{27}\) (3\({}^{13}\)) orthogonal array design are shown in Table 2. The blank columns are not shown in this table. The entrainment ratio was defined as \(\omega=m_{\rm S}/m_{\rm P}\). \(K_{\rm i}\) represented the sum of the experimental values with the same level in any column. Further analysis was conducted by the method of analysis of variance (ANOVA). Based on the results given in Table 2, the total sum of squares of deviation (\(SS_{\rm T}\)) was calculated by the following expression:  
\[SS_{\rm T}=Q-R \tag{1}\]  
where \(Q\) and \(R\) were defined as:  
\[Q=\sum\limits_{i=1}^{27}\omega_{i}^{2} \tag{2}\]  
\[R=\frac{\left(\sum\limits_{i=1}^{27}\omega_{i}\right)^{2}}{27} \tag{3}\]  
Similarly, the sum of squares of deviation of each factor was expressed as:  
\[SS=\frac{K_{\rm I}^{2}+K_{\rm Z}^{2}+K_{\rm 3}^{2}}{9}-R \tag{4}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Factor** & **Level 1** & **Level 2** & **Level 3** \\ \hline \(N_{\rm s}\) (mm) & 4 & 5 & 6 \\ \(D_{\rm f}\) (mm) & 4 & 6 & 8 \\ \(L_{\rm s}\) (mm) & 13 & 25 & 37 \\ \(Q\) (\(\lx@math@degree\)) & 24 & 32 & 40 \\ \(H_{\rm c}\) (mm) & 186 & 198 & 210 \\ \(D_{\rm c}\) (mm) & 56 & 44 & 32 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Factors and levels for L\({}_{27}\) (3\({}^{13}\)) orthogonal array. Figure 2: Reverse-circulation drilling apparatus based on supersonic nozzle. 1. Air outlet; 2. Top joint; 3. Center passage; 4. Seal ring; 5. Supersonic nozzle; 6. Outer shell; 7.Flushing nozzle; 8. Bit crown; 9. Air vent; 10. Work bench; 11. Air inlet. Then F-test was carried out to gain a better understand of mentioned parameters.