Design guidelines for the vortex tube

https://doi.org/10.1016/j.expthermflusci.2020.110169Get rights and content

Highlights:

  • Identification of Reynolds number as a non-dimensional number describing the inlet conditions of a Vortex Tube.

  • RR Correlation Factor developed to aid designing of a Vortex Tube.

  • Experimental validation for RR correlation factor.

Abstract

A vortex tube is a device which separates an incoming compressed gas into cold and hot streams. The experimental results reported by various researchers were used as a database to obtain a correlation. A term called Rutika-Ramakrishna Correlation Factor or RR Correlation Factor is coined which correlates the parameters such as ratio of length of the vortex tube to the diameter of the vortex tube, ratio of diameter of central orifice to the diameter of the vortex tube and Reynolds number of flow in the vortex tube to the maximum isentropic efficiency of the vortex tube. Experiments to validate the legitimacy of RR Correlation Factor were conducted with air as the working medium using different types of vortex tubes. The cold end temperature of the vortex tube as obtained by experiments is slightly lower than the values estimated using RR Correlation Factor. Thus, this correlation factor (RR) can be used as a powerful tool to design a vortex tube.

Introduction

The vortex tube, also known as Ranque-Hilsch [2], [3] tube, is a mechanical device that separates the incoming compressed gases into a hot stream (having a temperature higher than incoming) and a cold stream (having a temperature lower than incoming). It was first invented by Ranque [2] and later modified by Hilsch [3]. It consists of a vortex chamber, a cold end orifice (of diameter dc), a vortex tube (of length L and diameter D) and a throttling conical valve as shown in Fig. 1.

Air enters the inlet tangentially, and a swirling flow is established. The flow in vortex tube has two regions. One is core region and the other is peripheral. The vortex tube has two outlets. One outlet is nearer to inlet and other is at the end of the vortex tube. Due to axial pressure gradient, the compressed gas entering the vortex chamber moves from inlet towards the throttling conical valve. Because of presence of this throttling conical valve, the peripheral region of the flow exits from the opening of the valve. The remaining core region of the flow reverts towards the inlet where it is released from the cold end orifice.

The stream of air exiting through an orifice has the temperature lower than that of the incoming air. This location is referred to as the cold end. The throttling conical valve at which hot air exits is known as the hot end. The throttling conical valve determines the mass flow rate and temperature of streams leaving hot and cold end. The cold mass fraction (µ) or mass fraction of cold air produced is the mass percentage of total input air released through the cold end. This cold stream so obtained can be used for cooling of electronics and has possible applications in cooling of aerospace and aviation systems [4].

The vortex tube has been used for various industrial applications. It has been used for heating – cooling application, separation of gas mixture, cooling of IC circuits and cooling of various cutting tools during machining. One of the advantages of a vortex tube is that it is simple in design, easy to manufacture and maintain. It is light in weight, compact and has low initial cost.

Over the years, various researchers [2], [3], [5], [6], [7], [8], [9], [10], [11] have tried to analyse and study the working of the vortex tube. The mechanism of temperature separation has been subjected to debate. There are two major theory published in literature regarding the working mechanism of the vortex tube. One major theory is that of energy transfer by work as argued by Ranque [2], Hilsch [3], Ramakrishna et al. [5], Behera et al. [6] and Aljuwayhel et al. [7]. While, Bruun [8], Scheller and Brown [9], Scheper [10] and Ahlborn and Groves [11] support the other theory, which is the transfer of energy between core and peripheral region because of difference in static temperature of peripheral portion of flow near inlet and the core region of flow.

Behera et al. [6] conducted computational studies on different inlet nozzle profiles, nozzle numbers, different velocity components as well as secondary circulation. They validated optimum dc and L/D ratio by experiments. Ahlborn and Groves [11] and Gao et al. [12] performed intrusive experiments with Pitot tubes and thermocouples for pressure field's and temperature field's measurement, respectively. Using these measurements, they reported the presence of a secondary flow inside the vortex tube. Skye et al. [13] and Thakare and Parekh [14] developed a computational fluid dynamic model and the results obtained from analysis were consistent with experimental results.

Temperature separation or Ranque-Hilsch [2], [3] effect is the splitting of total temperature at the inlet into a temperature higher than inlet at the hot end and temperature lower than inlet at cold end. The temperature difference (between incoming stream and cold stream), cooling capacity (by virtue of temperature difference and yield of cold stream) and the isentropic efficiency are the important parameters to quantify the performance of the vortex tube. The geometrical parameters which affect the performance of the vortex tube are ratio of length of the vortex tube & diameter of the vortex tube, ratio of diameter of central orifice & diameter of the vortex tube and area of the inlet of the nozzle. The incoming mass flow rate of gas and operating pressure of the vortex tube also affects the performance of the vortex tube.

There is a wide range of literature reported on the vortex tube in the last 85 years. Yilmaz et al. [15] have reviewed the design criteria for vortex tube by analysing theoretical and experimental investigation of the vortex tube which had been published till then. They summarised various design criteria for vortex tube such as inlet pressure, inlet temperature, gas properties and other factors such as material of the tube and internal roughness of the tube. Similar work has been published by Eiamsa-ard and Promvonge [16].

Aljuwayhel et al. [7], Brunn [8] and Gao et al. [12] had studied the temperature and velocity distribution in the vortex chamber to analyse the performance of the vortex tube. Hilsch [3], Ramakrishna et al. [5], Skye et al. [13], Thakare and Parekh [14] and Valipour and Niazi [17] reported optimum cold mass fraction for minimum cold stream temperature to be between 0.2 and 0.4. The maximum isentropic efficiency (θmax) also lies between cold mass fraction of 0.2–0.4 for all the tubes at all inlet pressures as temperature separation was maximum around this cold mass fraction. Skye et al. [13], Thakare and Parekh [14], Valipour and Niazi [17] and Godbole and Ramakrishna [18] reported that maximum magnitude of cooling capacity is obtained for cold mass fraction in the range of 0.5–0.7. Ramakrishna et al. [5] and Behera et al. [6] reported that optimum dc/D ratio for minimum cold stream temperature to be around 0.5. Behera et al. [6] did experiments and CFD analysis and reported the optimal L/D ratio to be 25–30. However, by experimentation, Manimaran [19] observed the optimal L/D ratio to be 40.

An experimental study on the vortex tubes having different curvature was reported by Valipour and Niazi [17] and Godbole and Ramakrishna [18] with air as the working medium. Valipour and Niazi [17] reported that the curvature of vortex tube had different effects on performance depending on operating condition of vortex tube. Bovand et al. [1] used vortex tubes having same geometrical parameters as used by Valipour and Niazi [17] and did numerical simulation on vortex tube having different curvature. Bovand et al. [1] reported straight and 150⁰ to have better cooling capacity than other curvature tubes. As reported by Godbole and Ramakrishna [18], the curved vortex tube had better performance in terms of temperature separation and cooling capacity for the higher cold mass fraction at all inlet pressures. This was also supported by results obtained from flow visualization for the same tubes at lower inlet pressure which was performed by Godbole and Ramakrishna [18]. Figure [1] also shows the helical coils formed by ink during flow visualization.

In all of the literature on the vortex tubes, there is very little discussion on the non-dimensional numbers that govern the flow. This is a gap in literature when it comes to design of vortex tube for obtaining a specific performance. The present study aims to find a non-dimensional number that governs the flow and to obtain a correlation between various geometrical factors and the performance of the vortex tube. The experimental results reported by various researchers were used as a database to obtain this correlation factor. A test rig was built to perform the experimental validation for the correlation so obtained. These experiments were performed on vortex tubes made of Perspex and aluminium at different operating pressures and incoming mass flow rates of air. The vortex tubes of different curvatures were also used.

Section snippets

Performance parameters and non-dimensional numbers

Temperature separation, cold end temperature and isentropic efficiency are important performance parameters for a vortex tube. The performance of different vortex tubes can be compared by comparing the performance parameters mentioned above.

Cooling capacity, another performance parameter, is the amount of refrigeration effect provided by a vortex tube and it is dependent on temperature separation, operating cold mass fraction and the mass flow rate at inlet. The maximum cooling capacity depends

Database

The data base used for the study consists of experimental results reported by Ramakrishna et al. [5], Behera et al. [6], Aljuwayhel et al. [7], Gao et al. [12], Skye et al. [13], Thakare and Parekh [14], Valipour and Niazi [17], Godbole and Ramakrishna [18] and Manimaran [19].

The criterion for the selection of the experimental database was the availability of prior art [5], [6], [7], [12], [13], [14], [17], [18], [19] with relevant data corresponding to the geometrical parameters such as L/D

Rutika-Ramakrishna Correlation Factor or RR Correlation Factor

From the experiments conducted by various researchers, a database comprising of the L/D ratio, dc/D ratio, maximum isentropic efficiency and Reynolds number was drawn up with approximately around 100 points. In this database, the experimental values which had maximum isentropic efficiency less than 0.17, because of certain L/D ratios and dc/D ratios were neglected. A correlation factor had to be arrived at which could capture the essence of all these results.

Experimental set-up for validation

Using the database, the RR Correlation Factor was formulated as explained in the preceding sections. But in order to validate the legitimacy of the RR Correlation Factor, experimental validation had to be done. The validation experiments were conducted using vortex tubes made of Perspex (insulator) and aluminium (metal). Compressed air was used as working medium for all the experiments in present study. The inlet used for experiments was a rectangular slot with aspect ratio (hi/wi) of 0.6. The d

Results and discussions for experimental validation

For the validation experiments performed here, the range of Reynolds number varied from 12,000 to 53,000. Because of the limitation of present experimental set-up, the validation experiments for Reynolds number higher than 53,000 could not be performed. In the experiments performed, the maximum temperature separation obtained was 31 K at an inlet pressure of 4 bar for µ = 0.2. For the present experiments, the value of maximum isentropic efficiency for all different types of tubes at different

Conclusion

A database was created using experimental results reported in literature. Nearly 100 data points were considered. This database included the broad range of geometrical parameters such as L/D ratio and dc/D ratio. It also had different types of inlet nozzles and had either multiple or single inlet nozzles. The identification of Reynolds number as one of the non-dimensional numbers that could be used to describe the inlet conditions of a vortex tube was crucial to the success of the formulation

CrediT authorship contribution statement

Rutika Godbole: Conceptualization, Methodology, Software, Validation, Investigation, Writing - original draft, Visualization. P.A. Ramakrishna: Conceptualization, Writing - review & editing, Supervision.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors acknowledge the reviewers who had evaluated the conference paper presented at 14th Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT 2019) Conference held at Wicklow, Ireland in July 2019. The authors also acknowledge the audience, who gave their valuable feedback on the paper presentation related to the present study.

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