# 3D Numerical Simulation and Performance Analysis of CO2 Vortex Tubes
## 1 Introduction  
A swirl flow pipe (vortex tube) can be used alone as a small refrigeration device for local cooling of large equipment or as an expansion device instead of an electronic expansion valve (found in refrigeration systems) to improve the efficiency of a refrigeration system. Compared with other refrigeration devices, swirl flow pipes have many advantages, such as no moving parts, lightweight, few structural parts, easy manufacturing, low production cost, and long durability [1]. However, in practical applications, some of the defects of the swirl flow pipe should not be ignored, such as low refrigeration efficiency, small refrigeration capacity, etc. Although the structure of the swirl flow pipe is extremely simple, the flow state of the fluid inside the tube and the energy transfer separation process are extremely complex. These complexities suggest the need to analyze and study the swirl flow pipe through a combination of experiments and numerical simulations. Moreover, the vortex cooling performance of this study has more theoretical and practical significance [2; 3]. The swirl flow pipe consists mainly of a nozzle inlet, swirl flow chamber, vortex generator, hot-end tube, hot-end flow-regulating valve, hot-end outlet, cold-end flow-regulating valve, and cold-end tube. The compressed gas enters through the swirl flow pipe inlet and enters tangentially along the wall of the swirl flow chamber, forming a high-velocity cyclone. The gas is divided into cold and hot streams due to the adiabatic expansion of the gas from the nozzle--the gas has the lowest thermodynamic temperature at the nozzle outlet [4; 5]. When the gas flows from the vortex chamber toward the hot-end valve, the circumferential velocity diffusion phenomenon of the gas leads to a gradual increase in the static temperature of the gas, resulting in the highest thermodynamic temperature of the gas in the outlet end of the valve area, where the gas is divided into cold and hot streams. The hot airflow is distributed on the outer wall side of the hot-end tube and exits at the hot outlet, while the cold air flow is distributed centrally in the tube and exits at the cold outlet [6; 7]. In fact, many factors affecting the swirl flow pipe performance can be divided into two categories; one is the swirl flow pipe structure parameters, which are the number of pipe inlet nozzles, the nozzle material, shape, diameter of the hot and cold pipes, etc. The second is the thermal properties of the compressed gas parameters, which are the type of working fluid, gas inlet pressure, inlet temperature, and the hot and cold end outlet flow [8; 9; 10; 11]. [PERSON] [12] conducted experiments with different quantities of nozzles (2, 4, and 6) and nozzles made of three different materials. The experimental study was performed using air as the working fluid, increasing the pressure from 0.15 to 0.55 MPa with an increment of 0.05 MPa between pressures. The final experimental results found that the optimal cold and hot airflow separation of the swirl flow pipe occurred when the number of nozzles was six, and the material was aluminum. Similarly, [PERSON] [13] investigated the performance of swirl flow pipes using a linear regression modeling method with a body size of 110 mm and an inner diameter of 10 mm, using compressed CO\({}_{2}\) as the working fluid, 4 and 6 inlet nozzles, and brass and polyamide materials. The optimal operating conditions of the swirl flow pipe were investigated by varying the inlet pressure and comparing the effects of inlet pressure, number of nozzles, and nozzle material. The conclusions were that increasing the number of nozzles increases the separation of airflow between the hot and cold ends of the pipe, nozzle material has minimal influence, and the dominant role is played by inlet pressure. However, the above experiments were not combined with numerical simulation techniques to analyze the flow state or explain the effect of pressure on the physical parameters in the swirl flow pipe.