# Development of Ultrasonic Pulsed Plasma Jet Source for Remote Surface Treatment
## 3 Results and Discussion
### Measurement of Plasma Gas Flow Rate by the Schlieren Technique  
The schlieren method is a technique for visualizing the flow of transparent media, such as air or water, and the visualized image can reveal the flow state and velocity. Therefore, it is widely used as a method for analyzing the flow of plasma jets [19; 20]. In a typical configuration of the schlieren method, light from a light source is collimated by a convex lens or concave mirror, and the object is placed in the collimated light. The object was placed under collimated light. The light was then focused again by a convex lens, and a knife edge was placed such that it slightly covered the focal point from one side. When the density of the fluid changes with the subject, the refractive index of light changes. The path of the collimated light rays passing near the subject was bent, causing the focal point to change when the light was focused. This change intercepts light that is deflected to the knife-edge side, resulting in a brightness difference in the image captured by the camera ahead, enabling the visualization of the density field of the fluid [21]. The larger the density gradient, the more clearly the schlieren method can visualize the density field; therefore, it is often applied to scenarios such as high-speed flows and combustion but rarely to low-speed flows. However, because plasma causes a density change in the fluid owing to heating by the discharge, visualization is possible even when the flow velocity of the plasma jet is relatively slow [22]. The sound waves generated at an arbitrary point in the gas in the plasma jet then spread from that position to the surroundings at the speed of sound \(a\). If the gas through which the sound wave travels is stationary relative to source P, the sound wave travels spherically to infinity at a given time. If the gas moves at velocity \(v\) relative to the source, the sound wave travels at the speed of sound relative to the flow. Therefore, the sound wave propagates at a speed of \(a+v\) in the direction of the flow and \(a-v\) in the direction opposite to the flow. When velocity \(v\) of the gas exceeds the speed of sound a and becomes supersonic, multiple sound waves overlap, generating a shock wave [23]. Shock waves are formed in the same manner when the gas is jetted out of a nozzle at supersonic speeds. However, the shockwave varies depending on the expansion state of the gas. For example, if the nozzle outlet pressure Pe is greater than the atmospheric pressure Pa (Pe > Pa), an underexpanded jet is formed. When Pe = Pa, an appropriate expansion jet was produced. If Pe < Pa, the jet is overexpanded. In the case of an appropriately expanded jet and an underexpanded jet, the following relationship holds for the Mach number of the flow M\({}_{1}\) and shock wave angle \(\beta\)[24].  
\[\sin\beta=\frac{a}{v}=\frac{1}{\text{M}_{1}} \tag{2}\]  
Figure 3: Photographs of plasma: (**a**) nitrogen plasma; (**b**) helium plasma.  
where \(v\) is the gas velocity, \(a=\left(\sqrt{\kappa\mathrm{RT}/M}\right)\) is the sound velocity, and is a function of specific heat ratio \(\kappa\), \(R\), \(T\), and \(M\). In the case of an overexpanded jet, the flow narrows at a turning angle \(\theta\) to approach an oblique shockwave. The following relationship is then established among Mach number M\({}_{1}\), shock wave angle \(\beta\), turning angle \(\theta\), and specific heat ratio \(\kappa\)[25]:  
\[\tan\theta=\frac{2\cot\beta\left(\mathrm{M}_{1}^{2}sin^{2}\beta-1\right)}{ \mathrm{M}_{1}^{2}(\kappa+\cos 2\beta)+2} \tag{3}\]  
Using these relations, the Mach number can be calculated from the value of the shock wave angle \(\beta\) obtained from the schlieren image. The gas velocity can also be calculated from the product of the Mach number and the sound velocity of the gas.