# Numerical Investigation on the Principle of Energy Separation in the Vortex Tube
## 1 Introduction  
A vortex tube is a simple device that separates incoming gas into cold and hot gases. This device has many advantages in terms of simplicity, durability, low cost, no maintenance, temperature control, environmental affinity, no moving parts, and no electricity or chemicals. Therefore, vortex tubes have been widely used in various industrial fields. Since the discovery of the vortex tube by [1; 2], extensive experimental and numerical studies have been conducted to optimize the vortex tube geometry [3; 4; 5; 6], apply the vortex tube for wide applications [7], investigate the flow pattern inside the tube [8; 9; 10], and elucidate the temperature (or energy) separation mechanism [5; 7; 11; 12]. A large number of studies put a lot of effort towards explaining the energy (or temperature) separation. The temperature distribution inside a vortex tube is often explained by adiabatic expansion and compression [13; 14; 15]. Although the sudden expansion contributes significantly to the temperature drop in the core (near-axis) region, this theory does not account for a hot exit temperature higher than the inlet temperature because the pressure at any point inside the tube is lower than the inlet pressure [10; 15; 16; 17]. [PERSON] [18] proposed an acoustic streaming model; however, this model did not build a quantitative relationship with thermal parameters. Further, numerical simulation results [15], which did not consider the acoustic streaming effect, showed good agreement with the experimental data of [18]. [PERSON] et al. [19] stated that the temperature separation resulted from a secondary flow (Gotler vortex) in the boundary layer along a concave surface. However, the Gotler vortex is a small secondary flow and cannot explain the temperature increase in the axial direction. [PERSON] et al. [20] attributed the heating to the conversion of kinetic energy into heat and the cooling to the reverse process. [PERSON] et al. [21] and [PERSON] [22] suggested that the temperature separation process was similar to the classic refrigeration cycle because the secondary circulation acted as a refrigerant. However, [PERSON] et al. [15] and [PERSON] et al. [23] argued that secondary circulation played a role in reducing the temperature separation. Meanwhile, [PERSON] et al. [14] concluded that the increase in temperature was attributed to the viscous heating of the boundary layer and that the formation of a strong vortex flow resulted in adiabatic cooling in the core region. [PERSON] et al. [24] claimed that shear energy transfer was the main reason for energy separation, but how shear work contributes to temperature separation was not discussed. [PERSON] et al. [25] analyzed temperature separation in terms of exergy distribution. [PERSON] and [PERSON] [26] presumed that energy transfer occurred from the inner vortex region to the outer vortex through the boundary between the two vortices. Some researchers attributed energy separation to the heat pump mechanism [27; 28; 29; 30]. If some fluid moves radially back and forth due to turbulent eddies, the fluid tends to be adiabatically heated as it moves from the inner core region to the outer periphery region and adiabatically cooled as it moves from the periphery region to the core region. However, turbulent eddies also contribute to temperature homogenization. The above existing works that elucidated the temperature separation were based on assumptions or hypotheses. In recent years, various studies have employed numerical simulations to study the vortex tube [31]. Table 1 summarizes previous numerical simulation works.