# Simulation-Based Design for Inlet Nozzle of Vortex Tube to Enhance Energy Separation Effect
## 1 Introduction  
With the continuous development of society and economy, various environmental challenges have emerged, with global warming being one of the most critical issues facing humanity. Since the industrial revolution, the global average surface temperature has steadily increased, and it is projected to rise by approximately 1.1 to 1.8 degrees Celsius between 2023 and 2027 compared to pre-industrial levels [1]. Since the 1992 United Nations Framework Convention on Climate Change, followed by the Kyoto Protocol in 1997 and the Paris Agreement in 2015, a global consensus on mitigating and adapting to Greenhouse Gas (GHG) emissions has been achieved [2]. In the maritime sector, cryogenic liquid fuels, such as liquefied natural gas (LNG) and liquid hydrogen, have emerged as a promising solution to reduce greenhouse gas emissions. Recent studies have investigated the effects of fuel tank conditions--such as sloshing motion, filling ratios, storage pressure, and structural integrity assessment--to optimize emissions reduction strategies in cryogenic storage and transport [3; 4; 5]. Although refrigerants account for less than 1% of total GHGs [6], their contribution to global warming should not be overlooked. In south Korea, annual refrigerant consumption is estimated at 35,000 tons, with only about 1% being recycled. The uncollected refrigerant waste is equivalent to approximately 63 million tons of CO\({}_{2}\) in terms of global warming potential [7]. In addition, refrigerant cooling typically requires electricity, which leads to additional energy consumption. Therefore, research into coolingtechnologies that reduce both environmental pollution and energy consumption is necessary [8]. Among such technologies, vortex tubes, which do not rely on refrigerants or electricity, have gained significant attention. A vortex tube, first proposed by [9] and then further studied by [10], is a mechanical device that separates compressed gas into hot and cold streams. As depicted in Figure 1, pressurized gas enters tangentially into a swirl chamber near one end of the tube, initiating rapid rotational flow (the first vortex) along the inner surface towards the other end. At this end, a conical nozzle allows the gas in the outer vortex layer to escape through a valve, while the remaining gas is forced back inward, forming a reduced-diameter inner vortex. During this process, energy is transferred from the inner vortex to the outer vortex, causing the gas in the outer layer to heat up and the gas in the inner vortex to cool as it returns to the starting point and is released from the tube. Vortex tubes are compact, lightweight, and easy to install in various applications. Moreover, they do not require electricity or chemicals like Freon, making them environmentally friendly. Depending on the application, vortex tubes can be used for heating and cooling purposes. In the case of heating, vortex tubes are integrated into the working suits of deep-sea workers to improve safety by maintaining a comfortable temperature. In natural gas transportation systems, vortex tubes prevent pipeline corrosion by heating gas to avoid liquefaction. Vortex tubes are also being integrated into green energy systems, such as those related to solar power generation [11; 12; 13; 14]. They are widely used in various manufacturing sectors for cooling purposes, such as in automotive air conditioning systems [15] and in cooling core electronic components like CPUs, where cold air is supplied through compressed air lines in factories [16]. Additionally, research is ongoing to replace conventional refrigerants with vortex tubes to mitigate environmental impacts [17]. As summarized in Table 1, experimental studies have explored key parameters to enhance the separation effect of vortex tubes. [PERSON] et al. [18] improved temperature separation by shortening the length of the straight vortex chamber. [PERSON] et al. [19] found that increasing inlet gas pressure resulted in greater temperature differences between the hot and cold outlets.