# Performance Study of a Fluidic Hammer Controlled by an Output-Fed Bistable Fluidic Oscillator
## 4 Results and Discussion  
### Performance Analysis Related to the Flow Behavior  
In order for the wall attachment phenomenon to occur in the interaction region of the output-fed fluidic oscillator, the power stream is accelerated in the converging supply nozzle, and hence its energy is mainly kinetic. In order to drive the impact body to move, it is generally required to convert this dynamic energy into a static pressure that is recoverable at the output channels. This pressure, expressed as a ratio of the power supply pressure, is termed pressure recovery [4; 35]. As shown in Figure 5, the static pressure at the vents is used as the reference for evaluation of pressure difference. It is obvious that the pressure there at the vents is essentially equal to atmospheric pressure. The pressure recovery can thus be described as follows:  
\[\mu_{\text{p}}=P_{\text{o}}/P_{\text{s}} \tag{4}\]  
Correspondingly, in a similar manner, the flow rate at the output channel can also be nondimensionalized by associating it with the flow rate at the inlet of the supply nozzle. When the liquid flows through the supply nozzle, where it forms a jet, some part of the jet flow enters the output  
Figure 5: A schematic circuit diagram for the fluidic hammer. (S—Inlet of supply nozzle, C—Control nozzle, V—Vent, O—Output channel, Ps—Pressure drop between supply nozzle and vent, P\({}_{\text{o}}\)—Pressure drop between output channel and vent, Qs—Flow rate at the inlet of supply nozzle, Q\({}_{\text{o}}\)—Flow rate at the output channel, \(u\)—Mean flow velocity in the supply nozzle, \(v\)—Moving velocity of the impact body, As—Sectional area of the supply nozzle, A\({}_{\text{p}}\)—Action area of the piston, \(D_{\text{p}}\)—Diameter of the piston, \(D_{\text{r}}\)—Diameter of the piston rod, \(m\)—Mass of the impact body, \(L\)—Stroke of the impact body). channel. The cylinder receives the output flow captured by the output channel. Because of the motion of the impact body, the output flow is variable. In fact, as shown in Figure 5, the flow rate at the output channel is equal to the moving velocity of the impact body times the liquid action area of the piston. Since the supply flow (volume flow rate) is constant, the ratio between the output flow and the supply flow is determined by the former. This value of the ratio is defined as the flow recovery [4] and can be described by the equation below. \[\mu_{\text{q}}=Q_{\text{o}}/Q_{\text{s}}=\frac{A_{p}v}{A_{\text{s}}u} \tag{5}\]  
Since the backward impact regime is useless for rock breaking, in this study we focus more on the forward movement of the impact body. As described in Equation (5), when the supply flow rate \(Q_{\text{s}}\) is constant, \(\mu_{\text{q}}\) is proportional to \(v\). Higher value of \(v\) means lower fluid resistance downstream from the output channel, as a larger portion of liquid flows into the working chamber through the output channel. Therefore, flow recovery represents the loading characteristics of the fluidic hammer to some extent. As shown in Figure 5, some important parameters of the impact body are displayed; they are \(D_{\text{p}}\), \(D_{r}\), \(m\), and \(L\). All of these four parameters affect the critical flow velocity of the fluidic oscillator [21], potentially posing significant impacts on the performance of the fluidic hammer. In this study, SC-86H experimental prototype is served as the baseline fluidic hammer for comparison, and the dimensions of the impact body are given in Case 1 of Table 2. In the subsequent sections, the dimensions of the impact body are set to change in the neighborhood of the set value of the baseline fluidic hammer to figure out their effects. Additionally, as the dimension of one parameters varies, the other parameters retain the same values as the baseline fluidic hammer.