# The Ranque-Hilsch Vortex Tube

David Newson

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Abstract

The Ranque-Hilsch vortex tube is a simple mechanical device often used for refrigeration in industrial manufacturing as it requires only a supply of compressed gas. Despite having no moving parts the vortex tube is able to separate the compressed gas into two separate streams – one hot and one cold – with temperatures observed in the range of -5 to 55. Different explanations for the processes taking place within the device haven been proposed but there is currently no single accepted theory. A fundamental understanding of the vortex tube and the equipment has been reached and the groundwork has been laid for further experimental investigation and numerical computational fluid dynamic modelling.

Introduction

The Ranque-Hilsch vortex tube, often referred to simply as a vortex tube, is a mechanical device involving no moving parts that can be used to separate a stream of high pressure compressed gas into two lower pressure streams of varying temperatures. The cold stream is able to reach temperatures as low as -30?C whilst the hot stream can reach temperatures of up to 110 ?C . First invented by French physicist G. Ranque in 1933  the vortex tube was unpopular at the time due to its low efficiency and the idea was discarded until 1946, when German engineer R. Hilsch took it upon himself to improve the design . With increased efficiency the vortex tube became an effective and popular spot cooling device for laboratory equipment, cutting tools such as lathes and mills, and other industrial processes. Since then there has been numerous attempts to find ways to further increase its efficiency and fully understand the processes leading to the temperature separation.

The processes taking place within the vortex tube are simple to observe, but more difficult to accurately explain and model. It begins with compressed gas entering the vortex tube tangentially through a swirl generator creating an initial vortex inside the tube with rotational speeds of up to 1,000,000 RPM. The vortex moves along the length of the tube until it reaches an adjustable valve allowing a fraction of the gas to escape. The remaining gas is forced back down the centre of the tube, creating a secondary vortex. This secondary vortex has a reduced diameter and is contained within the initial vortex and travels in the opposite direction back along the length of the tube. When the secondary vortex reaches the other end of the tube all remaining gas is expelled through an opening. While this is taking place, energy is transferred from the inner vortex to the outer vortex, causing the temperature of the outer vortex to increase, and the temperature of the inner vortex to decrease. As the gas from the outer, hotter vortex and the gas from the cooler, inner vortex are expelled at opposite ends of the tube the two streams of varied temperature can be directed as required and the ratio of the temperatures controlled by changing the amount of gas allowed to be expelled at the adjustable valve.

Figure 1. Initial and secondary vortexes within a vortex tube 

There are currently different explanations for the temperature separation within the vortex tube with no theory being conclusively proved. It is currently thought that the energy transferred between the vortexes is through friction of the two vortexes rotating against one another but it is unknown whether the gas within the tube experiences “solid body rotation”, where the angular velocities of the of both the inner and the outer vortexes are the same or if the two vortexes are rotating at different angular velocities. Further investigation into the speed of rotations of the vortexes within a Ranque-Hilsch Vortex Tube will provide greater understanding of the energy transfer.

Equipment

The experimental set up consisted of a Ranque-Hilsch Vortex Tube, two flow gauges that could be placed at positions A,B or C, two thermo couples, a gate valve and a pressure gauge positioned as shown on figure 2 below.

Figure 2. Schematic of experimental setup

The vortex tube was supplied by compressed air with a mains pressure of 6.6 bar with the gate valve used to control the pressures and flow rates into the vortex tube.

The flow gauges used were rota meters with a range of 30-300 litres per minute. Rota meters are made of a tapered tube with a “float” inside that is lifted up by the drag force created by the flow of the liquid around it and pulled down by gravity. A higher flow rate increases flow speed and drag causing the float to be lifted higher up the tube, however, as the float is lifted higher up the tube the tube widens due to the taper and the drag force decreases until the float reaches its new equilibrium. The equilibrium can be found using the equation

. (1)

Where is the mass of the float, is acceleration due to gravity, is the density of the fluid, is the velocity of the object relative to the fluid, is the reference area and is the drag coefficient.

With the float in equilibrium the flow rate can be read off scale at a specified point on the float. Due to the simple nature of rota meters they are affected by changes in pressure and temperature and the displayed numbers are only valid at atmospheric pressure and standard atmospheric pressure.

Correcting for the effects of pressure

(2)

Pressures above atmospheric pressure allows greater capacity for a flow meter and the above equation is used to determine the actual flow rate at varying pressures.

Correcting for the effects of temperature

(3)

Temperatures above standard atmospheric temperature decreases maximum flow rate and the above equation is used to determine the actual flow rate at varying temperatures.

The flow gauges have an unknown impedance which has to be calculated in order to make sure placing them in the system doesn’t affect the measured pressures nor the fraction of gas expelled through the hot end valve. If it does affect the system knowing the impedance allows corrections to be calculated. The impedance is calculated by measuring the rate of flow through a single flow gauge as a function of pressure.

Figure 3. Experimental set up to calculate flow gauge impedance

The vortex tube itself has no moving parts and consists of very few pieces. Compressed gas is fed in through the air inlet and as it passes through the generator creates a vortex inside the spin chamber, the vortex propagates along the length of the tube with air exiting out both the hot end valve and the cold end cap.

Figure 3. Schematic of Meech Vortex tube 

The only interchangeable part of the vortex tube is the generator. The generators determine the volume of gas flow through the vortex tube and the fraction of the incoming air that exits in the cold stream – the cold fraction. The cold fraction may also be altered by adjusting the hot end valve. The total flow can be calculated using

(4)

Where PSIG is pounds per square inch gage.

The cooling and heating power in BTUH (British Thermal Unit per Hour) can be found by using the following:

For Cooling:

(5)

For Heating:

(6)

Where 1 = 0.293W, = cold fraction, = cold airflow, = hot airflow, = inlet pressure, = cold stream temperature, = hot stream temperature

Results

The impedance of the flow gauges were calculated by plotting flow against pressure and calculating the gradient.

Figure 4. Calibration of flow gauges

The gradient calculated from figure 4 is which equals

The gradient was then used to calculate impedance using

(7)

This gives a value for the impedance of the flow gauges of acoustic ohms.

Figure 5. Temperature of streams as function of pressure

Figure 5 shows the relationship between the temperatures of the stream and the inlet pressure. The two trend lines intersect at 0 pressure at 23 which is the temperature of the compressed air before it entered the vortex tube. The gradient of the hot stream trend line is 8.3 and the gradient of the cold stream trend line is -7.8 0.05. This shows the temperature of the hot flow is increasing faster than the cold flow is decreasing suggesting a cold fraction of above 0.5.

Figure 6. Flow rates as a function of pressure

Figure 6 displays the flow rates at each of the 3 positions A,B and C from figure 2. The flow rate of the cold stream is higher than the flow rate of the hot stream confirming that the cold fraction is above 0.5 as proposed from the findings in figure 5. This figure demonstrates the corrections to the flow rate using equation (2) as before the equation is applied the measured flow rate in (green) is significantly lower than the measured flow rate out (cyan). After the correction is applied the measured flow in (magenta) is equal to the measured flow out. This is based on the assumption that the pressure at the flow gauge in position A is 6.6 bar – the pressure of the mains gas supply.

Figure 7. Energy flow rates as a function of pressure

Figure 7 shows the rates of flow of internal energy of the gas at points A,B and C calculated by combining the following equations

(7)

(8)

Into

(9)

Where is pressure, is volume, is number of moles, is the molar gas constant, is temperature and is internal energy.

From this figure it seems that no energy is lost from the system and it is simply transferred between the two flows of the gas. This is expected based on the previous result as internal energy is proportional to volume and the volumes of gas flowing in and out of the tube were constant.

Discussion

After much investigation the temperature and energy separation and rate of flow appear linear as a function of inlet pressure. This was not always the case as for a long period of time the volume of gas measured being expelled by the vortex tube was vastly larger than that being measured entering the tube and the rate of flows were not linear. However, after studying the equipment it was found that this was due to the flow gauges being effected by temperature and pressure. Once the raw data was corrected by taking into account for these varying conditions the data matched up to initial predictions and with far fewer anomalies. The temperature difference of the two streams was observed and; with a cold fraction greater than 0.5 the cold stream was measured to have a higher rate of flow but there was a greater temperature difference in the hot stream from the initial temperature of the gas. The current data suggests that the gas as a whole does not gain or lose any internal energy and that energy is only transferred between the gas from the cold stream to the hot stream, however, this is under the assumption that the pressure at the flow gauge in position A was constantly at 6.6 bar. If this is not the case a slight difference in pressure could reveal changes in the internal energy of the gas which could help explain the processes happening within the tube.

Conclusion

The equipment has been calibrated and raw data is able to be corrected to provide correct results. Temperature separation has been measured in the range of -5 to 55 with the rate of change of temperature corresponding to the cold fraction of the generator. The internal energy of the gas has been observed to remain constant; transferring only between the cold and the hot stream but there is scope to further investigate this. A basic understanding of the vortex tube has been reached and the groundwork has been laid for further investigation. With further sampling it is hoped the energy separation will be understood in greater detail and that the theory that the gas undergoes solid body rotation will be proved or disproved.

Future work

Future work will include experimental investigation continuing looking into the transfer of energy within the vortex tube including more detailed analysis of rate of energy flow examining whether the gas loses, gains or conserves internal energy. Different generators of varying efficiencies and cold fractions will be investigated and documented and an attempt to build a probe to determine whether the angular velocities within the vortex tube vary or are constant will take place. Aside from the experimental work computational fluid dynamics will be used to numerically explore the inner workings of the vortex tube by creating a two dimensional computational model of a vortex tube using COMSOL software using the k-? model to simulate the temperature separation phenomenon.

Figure x shows the temperatures of the hot and cold streams achieved by three different generators as a function of flow. The results show that the generators that produce the lowest temperatures have a lower flow rate, this is expected as there is a similar amount of energy separation for each of the generators and you can choose to have a smaller quantity of very cold gas or a larger quantity that is not as cold, or a compromise as desired. This is important as it makes the vortex tube more adaptable for industries using it for spot cooling and the temperature and flow rate can be adjusted as required.

References

 Meech air technology brochure. 2013.

http://www.meech.com/resources/362/MAT.pdf

 G. J. Ranque, “Experiments on Expansion in a Vortex with Simultaneous Exhaust of Hot and Cold Air,” Le Journal De Physique et le Radium (Paris), Vol. 4, 1933.

 R. Hilsch, “The Use of the Expansion of Gases in a Centrifugal Field as Cooling Process,” Review of Scientific Instrument, Vol. 18, 1947.