## 1 Introduction
This non-desirable aerodynamics phenomenon results in the deterioration of the dynamic characteristics of the gas flow. Accordingly, the molten material removal rate, kerr width, surface roughness, and waviness are mainly affected by the behavior and pattern of the gas flow during the thermal cutting process. However, no reliable concept of the mechanisms of the processes inside the kerr during the cutting process has been proposed to date. Recording the processes under natural conditions is impossible because the cut walls are not transparent and the processes involve high temperatures and reflected radiation [10]. Research under natural conditions is confined to observations of particles leaving the cut channel and to inspecting the metal surface after it has been affected by the heat source [11]. Due to these restrictions, physical and mathematical modeling of the cutting processes is significantly important. The authors in [12; 13] presented open-source-based CFD solvers to simulate plasma cutting torches. [PERSON] et al. [12] used a Godunov-type scheme to implement the mathematical model in OpenFOAM and validated the solver through a set of conical test cases and used the solver to simulate a three-dimensional plasma cutting torch. [PERSON] [13] included the plasma jet flow, the volume of fluid (VoF) method in identifying the gas-to-molten metal interface, and the phase change model for computing the melting process in the mathematical model to simulate plasma arc cutting. [PERSON] et al. [14; 15] compared several turbulence models in their study to model swirling flow inside a highly constricted plasma cutting arc and implemented the model to study the effect of plasma-gas swirl flow on a plasma cutting arc. In addition to the studies carried out in the plasma arc cutting process, several studies have investigated the gas flow pattern in the gas-assisted laser cutting process. The research works consist of both numerical simulations and experimental observations of gas flow characteristics. The authors in [16; 17; 18; 19] investigated the interaction of gas flows within the cut kerr in order to study the dynamic characteristics of the exit jet at various stand-off distances during the laser cutting process. [PERSON] et al. investigated the effect of inlet stagnation pressure and nozzle geometry on the behavior of the gas flow [8]. They used a quasi 1D gas dynamics theory to calculate the exact-design operating conditions for three different supersonic nozzles. Then, they modeled the jet flow through these nozzles numerically and verified them experimentally, using Schlieren visualization. They reported that the exit jet was found to preserve its uniform distribution with parallel boundaries and low divergence under the exact-design operating condition, unlike what was observed for the other two conditions, especially for a nozzle with a small divergence angle. The dynamic characteristics of the exit jet, from both conical and supersonic nozzles, have been comprehensively reviewed in [20; 21; 22]. [PERSON] et al. [20] theoretically analyzed and visualized the exit jet patterns, in the free stream, to illustrate how its dynamic characteristics are affected by the type and size of the nozzle. As a result, supersonic nozzles were found to operate more efficiently compared to conical ones for the high-pressure laser cutting process. However, all these studies were carried out in free stream. [PERSON] et al. [23] captured the gas flow as a function of the inlet pressure and the stand-off distance using a high-speed camera with the Schlieren method. The experiment was carried out by passing gas through two substrates placed parallel to each other to simulate the cut kerf slot. They used images before and after the gas injection to obtain the image intensity, which was applied to analyze the cutting gas flow for three different parts. They reported that the stronger the inlet pressure and the shorter the stand-off distance, the higher the image intensity value, and the higher the gas flow rate, respectively.