# Experimental Investigation on a Throttleable Pintle-Centrifugal Injector
## 3 Experimental Investigation on the Pintle-Centrifugal Injector
### Results and Discussion
#### 3.3.3 Analysis of the Atomization Angle  
In the analysis of the atomization angle, a series of images captured by high-speed photography are first superimposed. The binarised images are obtained by means of a threshold segmentation method. The atomization angle is then determined according to the method mentioned previously. The method for obtaining the spray angle is shown specifically in Figure 10, and the atomization angle has Equation (2) to calculate it.  
\[\frac{\alpha}{2}=arctan\left(\frac{L_{2}-L_{1}}{2\Delta h}\right) \tag{2}\]  
where \(L_{1}\), \(L_{2}\) are the width of the atomization field in two straight lines, \(\Delta h\) is the vertical distance between the two lines and \(\alpha\) is the spray angle.  
Through the above process, the atomization angle parameters were obtained for all operating conditions. The atomization angles at different flow rates were analyzed in relation to the pintle stroke and plotted in Figure 11. The graph shows that at the same flow rate, the spray angle increases significantly with increasing pintle stroke.  
Combined with the pressure drop, it can be seen that the atomization angle increases mainly because the axial velocity of the liquid decreases at a faster rate, while the radial  
Figure 11: Relation between atomization angle and pintle stroke.  
Figure 10: Diagram of atomization angle.  
velocity does not change at a significant rate. The trend and rate of change of the atomization angle are approximately the same for different flow conditions, which also reflects the good consistency of the throttleable pintle-centrifugal injector. As the pintle stroke increases, the rate of change of the atomization angle decreases, which verifies the pattern found in the previous section. This is because at larger pintle strokes, the velocity of the fluid in the injector collection chamber is mainly determined by the tangential holes in the injection panel. The annular slit formed by the two bevels is no longer clearly reflected in the squeezing effect on the liquid at this point.  
When analyzed for a fixed pintle stroke, the atomization angle increases as the flow rate increases for the same stroke. This is in line with conventional knowledge. The increased flow rate increases the velocity of the fluid, both axial and radial. Figure 12 shows images of the atomization corresponding to different flow conditions at a pintle stroke of around 0.7 mm.  
The image clearly reflects the above rule. At the same time, the length of the complete liquid film decreases as the flow rate increases. The distance at which the liquid film breaks up is also gradually advanced, with the consequent larger atomization field size. At the same axial position, the droplet size is smaller. The position of the liquid propellant atomization also influences the adequacy of the contact between the pillar and the oxidizer in the hybrid rocket motor, which further influences the ignition rate and combustion performance of the hybrid rocket motor. By controlling the stroke of the pintle, the throttleable pintle-centrifugal injector is able to adjust the propellant atomization state under various flow conditions, thus adapting to different operating conditions. This helps to achieve a wide range of thrust adjustments for hybrid rocket motors.