Among several visualization techniques for gas flow investigation in the gas atomization process, there are two well established optical methods; shadowgraph and schlieren imaging techniques.
According to the physics of light, light beams travel in a straight path without distortion when passing through homogeneous media. However, the environment around us is not homogenous
for several reasons, including thermal convection or turbulence. As a result, the refractive index and density of air can change. The Refractive index can be calculated as follows:
𝑛 = 𝐶
𝐶0 (2.12) Where C is referred to the speed of the light in the medium and C0 is referred to the speed of the light in the vacuum which is 3*108 m/s.
In addition, the refractive index and density of gas relate linearly in the following way:
𝑘𝜌 = 𝑛 − 1 (2.13) In Which k (Gladstone-Dale coefficient) is around 0.23 cm3/g for air at the standard condition and ρ is the gas density. Based on the equation 2.12, density gradient due to any distortion in the air would change the refractive index. The fundamental of the shadowgraph and schlieren imaging is based on the difference in the refractive index in a transparent medium which causes light beam refraction in the direction of the increasing refractive index [4,26].
Although the shadowgraph and schlieren techniques are similar to each other in many aspects.
But there are some differences between these two techniques which make them different from each other. For instance; in the schlieren technique a knife-edge is used for cutting off the refracted light beam whereas the shadowgraph technique does not need a knife-edge. Another distinction between these two techniques is the illuminance level in the schlieren technique respond to the first derivative of the refractive index, while in the shadowgraph technique the illuminance responds to the second derivative of the refractive index .
The schlieren imaging can be done either with mirrors or lenses. It should be noted that each of them has its advantages and disadvantage from image quality and economical point of view.
For instance, the mirror-based schlieren systems suffer from off-axis aberration, however, the lens-based system does not have this problem. However, in the lens-based setup, the quality of lenses should be high which leads to higher price and maintenance. In addition, by using the lens-based system, a smaller area can be studied. Since the size of the lenses cannot be as big as the mirror sizes. It should be mentioned that the mirror-based system requires a smaller area for the arrangement compared with the lens-based system. Therefore, using a mirror-based system could save more space in the laboratory as well .
As seen in figure 2.4, the Z type arrangement of Schlieren techniques is depicted, which contains two parabolic mirrors, a light source, a high-speed camera and the knife edge.
Figure 2.4 Schematic view of Z type schlieren technique 
For visualizing the supersonic gas jet from the CD nozzles, the shadowgraph and schlieren techniques have been taken in this study to visualize the density gradient caused due to the high-speed gas jets.
The first stage of each CFD simulation is geometry creation under the appropriate assumptions.
Less complication in the model leads to lesser computational time which is quite important in any industrial problem. Hence, it is important to avoid any unnecessary complications during the geometry creation stage, but it is also important to make sure physical situation is represented by the model.
The next step is meshing the computational domain. The accuracy of each numerical simulation is highly dependent on the mesh quality. Hence, it is important to mesh the computational domain to a high enough resolution. Conversely, finer meshing adds greatly to computational time, so it is important to find a good balance between detail and time. The quality of a mesh is measured according to mesh quality factors such as skewness, orthogonality. Skewness represents how far an element deviates from its ideal shape and orthogonality represents how close the face normal vector and the vector connecting two centroids of two adjacent cells are.
It is not recommended to have low orthogonality and high skewness values. In general, it is recommended to keep the orthogonality close to one and skewness close to zero. The mesh quality directly affects the accuracy, convergence and speed of the simulation. Therefore, it is crucial to ensure that the mesh quality meet the quality criteria.
In the next steps, the fluid properties and appropriate boundary conditions characterize the behaviour of the fluid flow through the computational model. Then the proper turbulence model should be selected. Simulation can be run both as a steady or unsteady simulation according to the physics of the flow. Finally, in the last step, the result of the computational simulation can be analysed using several data visualization tools that have been mentioned in the post-processor section.
Currently, several CFD codes such as Ansys Fluent, Comsol and OpenFOAM are available to perform the numerical study for a wide range of engineering problems. According to the previous studies that have been done in the gas atomization process, especially the gas flow