The Expansion Process in a Counter-flow Vortex Tube

A Ranque-Hilsch vortex tube is a thermal device which generates two exhaust gases at different temperature from a single injection port. The typical structure of a counter-flow vortex tube and the proposed flow pattern within the tube are presented in Figure 1 [1]. The working medium (shown in yellow), generally air or other compressible gases, is injected into the tube through a tangential nozzle. The low temperature stream (shown in blue) is discharged through the central exit, near the injection port, and the high temperature stream (shown in red) is exhausted from the peripheral exit, at the far end of the tube. The perceived benefits of the temperature separation within a vortex tube, such as instant cold and hot streams of fluid, adjustable stream temperatures, reliability and low cost, make it an attractive device in many applications where such temperature separation is beneficial. These applications can include the use of vortex tube for cooling purposes [2,3], ice production [4], and mixture separation [5,6]. Since its invention, in 1933 [7], investigations have been carried out to understand the processes involved in a vortex tube. Much of the earlier research in the subject matter has primarily focussed on the separating mechanisms within the tube, including theoretical analysis of the separation process [8,9], optimisation of the tube performance for different applications [10,11], numerical simulations of the temperature separation within the tube [12-15] and investigation of the internal flow behaviour [1,16-18]. Different understandings of the internal flow mechanisms and explanations for the energy separation within the vortex tube, which have been reviewed and analysed in recent publications [19-22], imply the lack of general consensus and the requirement of clarification of the complex separating phenomenon. The internal pressure gradient has been proposed as the dominating factor for the energy separation phenomenon within a vortex tube [14,23-26]. Ranque proposed that compression and expansion effects are the main reasons for the temperature separation in the tube [7,27]. In a recent research, the adiabatic expansion and compression caused by turbulent eddies was stated as the reason for the temperature drop and the temperature rise in a vortex tube, respectively [28]. However, the proposal regarding the compression inside a vortex tube is not particularly convincing, primarily due to the internal pressure profile, as discussed in previous research [1,22]. On the other hand, a general agreement regarding the expansion process with the tube as being the dominating factor for the temperature drop has also been observed in literature [1,14,25,26,29]. It has, furthermore, been reported that the cooling performance of a vortex tube depends on the properties of the working gases. In terms of the cooling performance, argon and helium have been found to have a better performance than any other gas, including carbon dioxide, air, ammonia, nitrogen, oxygen and water vapour [30,31]. A previous numerical investigation on the cooling effect of a vortex tube, considering carbon dioxide, air, helium, ammonia, nitrogen, oxygen and water vapour, reported the agreement of the helium’s best cooling effect [32]. The maximum value of specific heat capacity ratio and minimum molecular weight of helium was stated as the reason for its superior cooling performance. However, this explanation is not convincing, due to the significantly different tube performance from other publications [30,31]. Moreover, the results were achieved based on inappropriate parameters, i.e. the specific heat capacity ratio and the inlet velocity. In 2013, a comparison of the vortex