# Detection of High-Temperature Gas Leaks in Pipelines Using Schlieren Visualization
## 2 Methods  
The Schlieren flow visualization technique is a method for observing changes in the refractive index resulting from variations in density within a medium through which light is passing. The refractive index is defined as the ratio of the speed of light in a vacuum to the speed of light in the medium. For an ideal gas with density \(\rho\), the refractive index \(n\) is expressed as follows:  
\[n-1=K\rho=\frac{KP}{RT} \tag{1}\]  
where \(K\) is the Gladstone-Dale constant, which is a property of the medium and the wavelength of light [17]. \(P\) represents pressure, \(R\) is the specific gas constant, and \(T\) is the absolute temperature of the medium. A precisely aligned Schlieren optical system is capable of observing natural convection due to air temperature differences of less than 10 \({}^{\circ}\)C on a palm surface [10]. In this study, the Schlieren flow visualization technique was employed for the simulation and detection of pipe leaks. As illustrated in Figure 1, the pipe with leakage was situated in front of a mirror, and Schlieren images were captured using a knife edge and a camera. The light source and knife edge were positioned at twice the focal length of the mirror. When hot air leaks from the pipe, the path of light from the source is refracted and reflected by the mirror. Unrefracted light is blocked by the knife edge and thus not recorded by the camera, while refracted light is captured and appears as shadows in the flow visualization images. Figure 1: Schematic of the Schlieren imaging of leakage in a pipe. In order to quantify the flow of gas in Schlieren images based on temperature differences, it is possible to utilize the brightness values of pixels representing the shadows [19]. Specifically, as the temperature difference between the leaking gas and the surrounding air increases, the shadow of the leaking flow becomes more distinct, leading to a more significant variation in the brightness of these pixels. Consequently, the coefficient of variation (\(I_{E}\)) in the flow region can be calculated using the following equation [20]:  
\[I_{\mathrm{E}}=\frac{1}{\overline{I}}\sqrt{\frac{1}{N}\sum(I-\overline{I})^{2}} \tag{2}\]  
where \(I\) and \(\overline{I}\) are the brightness and average brightness of the observation area, respectively, and \(N\) is the number of pixels. \(I_{E}\) is the ratio of the standard deviation of brightness values to the average brightness value. This value increases as the clarity of the shadows, caused by the temperature difference between the leaking gas and the surrounding air, increases. Therefore, calculating \(I_{E}\) can serve as an indicator to determine the presence of gas leakage on the pipe surface. The experimental setup for simulating leaks in high-temperature pipes comprises optical components, an image-recording device and a pipe that simulates the leak. To obtain Schlieren flow visualization images, a parabolic mirror with a focal length of 1.22 m and a diameter of 150 mm, an 11 W LED fiber optic light source, a knife edge, and a digital camera (GH6, Panasonic (Osaka, Japan)) equipped with a 200 mm focal length lens were utilized. The light source and knife edge were positioned at a distance of twice the mirror's focal length. An iris was positioned before the LED light source to direct the light through a 1 mm diameter aperture onto the mirror. To ensure precise alignment and calibration of the Schlieren system, we first verified that the iris of the light source and the knife edge were equidistant from the mirror. This was achieved by positioning the knife edge where the reflected light from the mirror appeared the smallest. Additionally, the camera position was finely adjusted to ensure that the beam path reflected from the mirror was evenly blocked by the knife edge, with the remaining half of the beam reaching the camera lens and sensor. The light source and knife edge were aligned within 100 mm for obtaining clearer Schlieren images. Two distinct types of pipes were employed during the leak simulation experiments.