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Applied Thermal Engineering 30 (2010) 2505e2511

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

A new vortex generator geometry for a counter-flow RanqueeHilsch vortex tube

Orhan Aydın*, Burak Markal, Mete AvcıKaradeniz Technical University, 61080 Trabzon, Turkey

a r t i c l e i n f o

Article history:Received 30 March 2010Accepted 24 June 2010

Keywords:RanqueeHilsch vortex tubeVortex tubeEnergy separationHelical swirl flow generator

* Corresponding author. Tel.: þ90 462 377 29 74; fE-mail address: oaydin@ktu.edu.tr (O. Aydın).

1359-4311/$ e see front matter � 2010 Elsevier Ltd.doi:10.1016/j.applthermaleng.2010.06.024

a b s t r a c t

In this study, a new geometry is introduced for the cold end side (i.e. where the swirl flow is introducedinto the tube), which is called ‘helical swirl flow generator’. Effect of the helical length of the swirl flowgenerator on the performance of the vortex tube are investigated for varying values of other geometricalparameters as a function of the cold mass fraction, yc. Finally, it’s disclosed that the effect of the helicallength on the performance changes critically according to the value of L/D.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

The vortex tube (also called RanqueeHilsch vortex tube) isa simple mechanical device which splits a compressed gas streaminto cold and hot streams without any chemical reactions orexternal energy supply [1], whose schematic is shown in Fig. 1.

Vortex tubes have advantages compared to other refrigeratingor heating devices, being simple, having no moving parts, using noelectricity or chemicals and having long operation time. They needonly compressed gas to operate. Their critical disadvantage is theirlow thermal efficiency.

In the existing literature, there are many theoretical andexperimental studies on vortex tubes. Experimental studies havebeen generally focusing on increasing the performance of vortextubes. Different geometrical and thermo-physical parameters havebeen tested to obtain an optimumvortex tube design. In theoreticalstudies, aim is concentrated at determining velocity, pressure andtemperature distribution. Recently, commercial CFD packages havebeen used to obtain internal flow pattern. An excellent review ofthe studies existing in the literature can be found in a recent studyby Aydin and Baki [2] and a more recent study by Eiamsa andPromvenge [3].

The mystery topic for the vortex tubes is the energy separationeffect. Although the vortex tubes have been known for decades, themechanism producing temperature separation phenomenon asa gas or vapor passes through a vortex tube hasn’t been fullyunderstood yet [4]. According to Ranque [5], the reason for energyseparation is the adiabatic expansion and compression. The first

ax: þ90 462 325 55 26.

All rights reserved.

detailed explanation about this phenomena belongs to Hilsch [6].He claimed that the reason is the internal friction. The mostcommon theory is the Fulton’s [7] one. In this theory, fluid entersthe vortex tube tangentially from nozzles and is compressedstraight to the tube walls by centrifugal forces. In this situation,there exists pressure difference between center and tube walls.Therefore, fluid particles move to the center radially. Because of theconservation of the angular momentum, velocity of particle incenter becomes higher than the one near wall. Fluid particles nearthe center try to accelerate the outer ones. As a result, mechanicalenergy is transferred to the outer regions. Fluid temperature nearthe tube wall increases due to friction by transferring mechanicalenergy from center. Contrast to this, inner flow become colder.Kurosaka [8] explained energy separation with acoustic streaming,while Stephan et al. [9] did it in view of Görtler vortex.

There are also some studies on the performance enhancementof the vortex tubes. Wu et al. [4] designed a new nozzle to increaseefficiency. Dinçer et al. [10] studied effects of a mobile plug locatedat the hot outlet. Xue and Arjomandi [11] examined effect of thevortex angle on efficiency. Nimbalkar and Muller [1] investigatedeffects of various cold end geometries. Behera et al. [12] conductedexperimental and CFD studies towards optimization of the Ran-queeHilsch vortex tubes. Dincer et al. [13] used the analysis of theartificial neural networks in modeling of some geometrical effectson the performance of a counter-flow RanqueeHilsch vortex tube.Pinar et al. [14] used the Taguchi method in the performanceanalysis of a counter-flow RanqueeHilsch vortex tube. There arealso some numerical attempts to analyze performance of Ran-queeHilsch vortex tube [15e21].

In a recent study [22], we developed a new geometry for thecold end side of a counter-flow vortex tube. As an extension of that

Nomenclature

cp Specific heat at constant pressure (kJ kg�1 K�1)COP Coefficient of performanced Inner diameter of helical swirl flow generator (mm),

Diameter of cold exitD Outer diameter of helical swirl flow generator, Inner

diameter of tube (mm)h Helical length (mm)k Specific heat ratio, cp/cvL Vortex tube length (mm)_m Mass flow rate (kg s �1)P Pressure (bar)_Q Thermal power (kW)R Gas constant (kJ kg�1 K�1)T Temperature (�C)DT Temperature difference (�C)Wm Mechanical energy (kW)

yc Cold mass fraction

Greek lettersG a rate related to specific heat ratio, k-1/kdin inner diameter of the inlet nozzledhot inner diameter of the hot end nozzlehis isentropic efficiencyf angle of the control valve

Subscriptsa environmentc cold streamCM cooling machineh hot streamHP heat pumpi inlett total

Fig. 1. The flow pattern in a counter-flow vortex tube.

P P

P

1 7653

2

4

11

8

710

8

7

9

2

12 13

14

1. Compressor 2. Pressure gauge 3. Air tank 4. Valve 5. Dehumidifier 6. Pressure regulator 7. Thermocouple 8. Rotameter 9. Conical valve 10. Tube 11. Digital manometer 12. Inlet nozzle 13. Hot end nozzle (hot exit)14. Cold exit

Fig. 2. Schematic diagram of the experimental setup.

Table 1Characteristics and uncertainties of the measurement instruments.

Instrument Range Uncertainty

Digital manometer HHP-2082 0e2 [bar] �0.15%Digital thermometer (OM-2041) �200 to 1370 [�C] �0.1% (full scale)Volumetric flow meter CZ-32458-65 80e560 [LPM] �3% (full scale)Humidity meter HT-3006HA 10e95 [%R.H.] �3% (<70% R.H.)Barometer Testo 435-1

(Part no: 0632 1535)600e1150 [mbar] �3%

O. Aydın et al. / Applied Thermal Engineering 30 (2010) 2505e25112506

study, the aim of this study is focused on investigating the effect ofthe helical length for varying geometrical parameters and workingconditions.

2. Experimental study

The schematic diagram of the experimental setup used in theexperiments is shown in Fig. 2. The experimental setup consists ofa compressor, an air tank, a dehumidifier, a test section, valves andjoining components.

Fig. 3. An exploded view of the vortex tube.

Fig. 4. Schematic diagram of the helical vortex generator (a) control valve (b).

O. Aydın et al. / Applied Thermal Engineering 30 (2010) 2505e2511 2507

The compressedworking fluid supplied from the compressor (1)passes through the air tank (3) and the dehumidifier (5). After thedehumidifier, it passes through a pressure regulator (6) where itspressure is adjusted to desired level by reading frompressure gauge(2). Before the working fluid enters the test section (from inletnozzle, 12) tangentially, its temperature is measured with ther-mocouples (7). By moving the conical valve (9), mass flow rate ofthe working fluid in the cold (14) and hot exits (13) can be adjusted.Outside of the hot and cold exits, temperature of the working fluidis measured by thermocouples which are located 1 cm beyondexits. Volumetric flow rate of fluid is gauged by rotameters (8)which are located outside of the both exits. Also, out of the cold exit,

Cold mass fraction, yc

0.0 0.2 0.4 0.6 0.8 1.0

(ecnereffid

erutarepme

To

)C

0

10

20

30

40

50

60

70

Pi = 3bar

Pi = 4bar

Pi = 5bar

h = 10mm

L/D = 30

φ = 30o

ΔTh

ΔTc

Fig. 5. Temperature differences DTh and DTc as functions of cold mass fraction, yc, fordifferent inlet pressures at h¼ 10 mm, L/D¼ 30.

there is a digital manometer (11). The pressure of cold air leavingfrom the vortex tube is measured using this manometer. Volu-metric flow rate values are then calculated. The characteristics anduncertainties of the measurement instruments are given in Table 1.

The experiments are performed in a tube (10) with inner diam-eter of 10 mm made of plexiglass. Outer surface of the tube iscovered with an insulating material to prevent heat loss to theenvironment. The inlet nozzle, the outlet nozzle and thehelical swirlflow generator are made of brass. The inlet, cold end and hot endchambers aremade of delrin. Various values of the lengthediameterratio (L/D) and the length of the helical swirl flow generators aretested to investigate their interactive effects comparatively. Thenoptimization is sought over these results. The effect of thesegeometrical parameters is investigated in three different values ofthe inlet pressure:3, 4and5bar (absolute). In theexperiments, innerdiameters of the inlet nozzle (din) and hot end nozzle (dhot) are 5 mmandkept constant. Diameter of the cold exit equals inner diameter ofhelical swirl flow generator (d) and is 4 mm. An exploded view ofvortex tube tested are shown in Fig. 3.

The parameters mentioned above are examined for varying thegas inlet pressure and the cold mass fraction.

The cold mass fraction is defined as follows:

yc ¼ _mc_mt

(1)

where _mc represents the mass flow rate of the cold stream released,while _mt represents the inlet or the total mass flow rate. For everydifferent configuration, the temperature values just before the inletnozzle and just after the outlet nozzles are measured for any valueof the cold mass fraction tested.

The performance of the vortex tube is marked by cooling effect(DTc) and heating effect (DTh) [4], which are defined as follows:

Fig. 6. Temperature differences DTh and DTc as functions of cold mass fraction, yc, for different values of L/D in different pressures for h¼ 10 mm (a) and h¼ 30 mm (b).

O. Aydın et al. / Applied Thermal Engineering 30 (2010) 2505e25112508

DTc ¼ Ti � Tc (2)

DTh ¼ Th � Ti (3)

Summing Eqs. (2) and (3), the total temperature difference(DT¼DTcþDTh) is obtained as in the following:

DT ¼ Th � Tc (4)

Each of the helical swirl flow generators is designed in differentlength but in the same helical pitch (one pitch). Schematic diagram

of the helical vortex generator and the control valve are given inFig. 4 a and b, respectively.

To calculate the cooling efficiency of the vortex tube, the prin-ciple of adiabatic expansion of ideal gas is used. As the air flows intothe vortex tube, the expansion in isentropic process occurs [3]. Theisentropic efficiency can be written as follows:

his ¼ Ti � Tc

Ti

�1� �pa

pi

�k�1k

� (5)

Fig. 7. Temperature differences DTh and DTc as functions of cold mass fraction, yc, for different values of helical vortex generator length, h, at different pressures for L/D¼ 30 (a) andL/D¼ 10 (b).

O. Aydın et al. / Applied Thermal Engineering 30 (2010) 2505e2511 2509

where, Pi, Pa and k are the inlet air pressure, the environmentpressure and the specific heat ratio, respectively.

The vortex tube can be considered as both a cooling machineand a heat pump. The efficiency of a cooling machine can beexpressed in terms of coefficient of performance (COP) [23] and it isdefined as follows:

COPCM ¼_Qc_Wm

(6)

where, _Qc is the thermal power in point of cooling side and can bedefined as follows:

__Qc ¼ _mccpðTi � TÞc (7)

Wm is the required mechanical energy to supply cooling or heating.Since compressed air has been used in this experiment, the inputpower can be found as follows [11].

_Wm ¼ _miRTiln�PiPc

�(8)

Cold mass fraction, yc

0.0 0.2 0.4 0.6 0.8 1.0

is(%

)

0

10

20

30

40

50

60

h = 10mmh = 15mmh = 20mmh = 25mmh = 30mm

= 30o

L/D = 30

Pi = 3bar

Fig. 8. Isentropic efficiency versus cold mass fraction for different helical vortexgenerator lengths.

Fig. 9. Coefficients of performance versus cold mass fraction with different helicalvortex generator lengths for COPCM (a) and COPHP (b).

O. Aydın et al. / Applied Thermal Engineering 30 (2010) 2505e25112510

Using Eq. (7) and Eq. (8) in Eq. (6) and rearranging the expres-sion, Eq. (9) can be obtained:

COPCM ¼ 1G

ycðTi � TcÞTiln

�PiPc

� (9)

where, k is the specific heats ratio and G ¼ k� 1=k.Similarly, as a heat pump coefficient of performance can be

expressed as follows:

COPHP ¼ 1G

ð1� ycÞðTh � TiÞTiln

�PiPc

� (10)

3. Results and discussion

Pressure and temperature of the input air, temperature of theexhausting air flow at both the hot and cold ends have beenmeasured. The cold mass fraction and the temperature differenceshave been calculated according to values measured.

The experimental temperature differences for the hot streamand cold stream as a function of cold mass fraction, yc, at differentinlet pressures for a set of geometrical parameters are shown inFig. 5. Temperature differences are getting increased when inletpressure is increased. But the rate of increase slows down. Thissituation can be explained by the chocking of the flow. When theinlet pressure is increased, flow velocity outside of the inlet nozzleincreases. After the chocking takes place, velocity and mass flowrate outside of the inlet nozzle don’t increase anymore, eventhough inlet pressure increases.

Fig. 6a and b show the temperature difference for the hot streamand cold stream as a function of the coldmass fraction, yc, at variousvalues of the inlet pressure and L/D at h¼ 10 mm and h¼ 30 mm,respectively. The effect of L/D is influenced by the length of thehelical swirl flow generator, h and the inlet pressure, pi. Forinstance, for h¼ 10 mm, L/D ¼ 10 presents a worse performancecompared to the L/D ¼ 20, 30 and 40 while its performancebecomes comparable for h¼ 30 mm.

Fig. 7a and b show the temperature difference as a function of ycfor various values of the inlet pressure and the helical swirl flowgenerator lengths, h, at L/D ¼ 30 and L/D ¼ 10. From Fig. 7a and b, itcan be seen that helical length has an obvious impact on energyseparation. But, like the results obtained from Fig. 6, its effectchanges according to the tube length. From Fig. 7a, it is seen thattemperature differences are getting higher when helical length isgetting shortened for high L/D ratios. For example, for L/D¼ 30, at 4and 5 bar, h¼ 10 mm is the best lengthwhile h¼ 30 mm is theworstone.On theotherhand, Fig. 7b shows that at a low L/D, shorterhelicallengths, like h¼ 10 and 15 mm, present a sudden breakdown inefficiency. For this situation, h¼ 10 mm becomes the worst value.

These results are related to the energy of the working fluid.There is probably a critical energy for the vortex tube. Higherkinetic energy means higher velocity at the same time. Using thehelical swirl flowgenerator increases efficiency because of reducingsudden change of flow direction. Also it helps to reduce thegeneration of eddies which cause energy loss. It supplies a smoothtransition from an inlet straight pipe to a circular pipe. Long helicallength increases friction loses and, in follows, decreases tempera-ture difference. That’s why there is a great and obvious differencebetween short and long helical lengths. Short ones are better forh¼ 10 mm. But, near hot end region, flow is desired to have a lowperipheral velocity. In short tube lengths, if flow has much energy,turbulence effects will increase and this will cause hot and coldflow to mix in the tube. Also flow has high peripheral velocity nearfar end of the tube. As seen from the graphs, this situation is much

O. Aydın et al. / Applied Thermal Engineering 30 (2010) 2505e2511 2511

clearer for the hot end side (see Fig. 6. Even though flow has highenergy, if a longer tube is used, flowcan complete its motion, effectsof turbulence decrease and flow will have lower velocity at the hotend because of increasing wall friction (owing to long tube). Ata low value of the helical length, if the inlet pressure increases, thecritical L/Dwill increase. Then, the best configuration is obtained ath¼ 10 mm and L/D¼ 30 at Pi¼ 5 bar (abs.) for both the ends.According to the experimental results, it can be said that if thepressurewas increased, for example to 7,8. bar etc., L/D¼ 40 couldbe the best ratio at h¼ 10 mm.

Fig. 8 shows the isentropic efficiency versus coldmass fraction atdifferent values of the helical vortex generator length. As seen fromthe figure, especially up to yc z 0.5, isentropic efficiency increaseswith a decrease in the helical length. Between yc z 0.5O 0.9 h¼ 10and15 mmshow the same trend. But for thewhole yc values, there isa great difference between h¼ 10 and 30 mm.

Fig. 9a and b shows the coefficients of performance versus coldmass fraction at different helical vortex generator lengths for vortextubes as a cooling machine and a heat pump, respectively. Coeffi-cient of performance increases with decreasing helical length.COPCM reaches its maximum value at nearly yc¼ 0.8 and COPHPreaches its maximum value at nearly yc¼ 0.7.

4. Concluding remarks

A series of experiments are conducted to investigate somedesign features of the counter-flow vortex tubes at different pres-sures. An innovative and new design of vortex tube was proposed,in which the swirl flow was enters into the vortex tube througha helical swirl flowgenerator. The results show that this new designhas an obvious and superior effect on temperature separation. Theeffect of the helical swirl length was tested for various values of L/Dand the inlet pressure. From the results it is seen that at a high L/D,short helical generators are better. The best configuration isobtained when h¼ 10 mm, L/D¼ 30 and Pi¼ 5 bar (abs.). In thisconfiguration, maximum temperature differences are: DT¼ 83.1 �C,DTc¼ 45.9 �C, DTh¼ 61.5 �C (Tc¼�36.3 �C and Th¼ 71.5 �C).

Acknowledgements

The first author of this article is also indebted to the TurkishAcademyof Sciences (TUBA) for the financial support provided underthe Programme to Reward Success Young Scientists (TUBA-GEBIT).

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