The Design of a

Vortex Tube

Edited by

Selcuk Oguz Erbil

Mehmet Kelleci

Ihsan Dogramac Bilkent

University

Contents

1 Introduction 1

2 Is such a System Possible? 2

3 Vortex Tube Design 5

3.1 Dimension Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.2 Cold Mass Fraction Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.3 Resulting Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4 References 12

1 Introduction

The vortex tube also known as the Ranque-Hilsch vortex tube separates a compressed gas

into hot and cold streams adiabatically. Tube consist of two arms, one is short for cold

stream, other is long with a conical valve for hot stream at the end. Compressed air enters

the tube through a tangential nozzle, goes along the longer arm, hits on the conical valve.

[1]After this instance, some part of the flow exits the tube as cold stream and rest is returns

along longer side of he tube to shorter side and exits the tube as hot stream.

The most advantageous side of the tube is, not containing any moving part, it is a

stationary structure which gives it a high reliability and long life in operation. Heat transfer

to or from the tube is negligible due to well insulation. Irreversibilities and thus exergy

destruction is inevitable due to pressure drops and friction effects within the tube.

Its aim is spot cooling and usage areas can vary from industry to space applications.

Below you can examine an illustration of vortex tube. Blue is hot stream, red is cold stream

and yellow one is the entering compressible air passing from a tangential nozzle.

Figure 1: An Animated Figure of Vortex Tube

1

2 Is such a System Possible?

In this example, operation of the system will be modeled with first and second laws of

engineering thermodynamics.[7]. This will be done on an exemplary vortex tube.

Figure 2: Control Volume Used to Model the Vortex Tube

State 1 is the compressed air at the inlet of the vortex tube. State 2 is the hot stream

which is the 40 % of the inlet mass flow rate. State 3 is the cold stream which is the 60 %

of the of the inlet flow.

Pressures Temperatures Mass Flow Rates

p1 = 5 bar T1 = 21C m kg

s

p2 = 1 bar T2 = 79C 0.4m kg

s

p3 = 1 bar T3 =-18C 0.6m kg

s

2

First Law Analysis of the System:

dEcvdt

= Q W + mi(hi + V 2i2

+ gzi)

me(he +V 2e2

+ gze) (1)

Kinetic energy and potential energy contributions are neglected. As stated above system

is adiabatic, no work is done by or on the system, and system operates at steady state. After

these notices, first law reduces to:

0 =

mihi

mehe mh1 = 0.6mh3 + 0.4mh2 (2)

(Assuming constant specific heats because of incompressible flow with taking cp = 1.0kJ/kg.K

and applying formula cp4T can also be used as the book does. We choose to get values ofentalphys from the table.) When the values are put to entalphys, LHS and RHS of the first

law results in zero which shows us that the obeys the law.

Second Law Analysis of the System:

Second law for open systems in differential form is as follows:

dScvdt

= Qi

Tbi+

misi

mese + (3)

System operates at steady state, no heat transfer to the surroundings, no work is done on

or by the system, so that equation reduces to:

0 =

misi

mese + (4)

Now take m1 as inlet, m2 as hot mass flow rate, m3 as cold mass flow rate, rewrite the

equation as :

3

0 = (m2 + m3)s1 m2s2 m3s3 + (5)

Putting the mass flow rate values:

0 = 0.4m1(s1 s2) + 0.6m1(s1 s3) + (6)

Recall that m2 = 0.4m1 and m3= 0.6m1In terms of

m1:

m1= 0.4[cp ln(T2

T1)R ln(p2

p1)] + 0.6[cp ln(T3

T1)R ln(p3

p1)] (7)

After the given values in the table inserted in to the equation, result is as below:

m1

= 0.454 kJ/kg.K > 0 as it should be, since otherwise would be a violation of the

second law.

Thus, in conclusion, given the values of pressure, temperature and mass flow rates, such

a device does exists since it obeys first and second law of thermodynamics. Apart from that,

given values also give idea about the operational data of the vortex tube. Such manipulations

can be done on the thermodynamic properties of the inlet and exit flows. In the rest of the

report the design of a custom vortex tube done by literature scan will be given.[2]

4

3 Vortex Tube Design

The analytical solution to radial temperature distribution within tube is still a vivid research

area. There is not any analytical solution to the phenomenon exists, and only the most

advanced CFD analyses can give good approximations. Main design parameters that effect

the performance of a vortex tube are inlet pressure, diameter of inlet orifice, diameter of

nozzle, length to diameter (L/D) ratio and cold mass fraction. These parameters are not

independent but also affect each other. According to the researches, the choice of these

factors that are used in the design will be given with reasons.

3.1 Dimension Effects

Performance of the vortex tube changes according to the chosen length and length to the

diameter ratio, however there is not any best performance parameter before design. Re-

searches on this area are on a chosen length and diameter of the tube, then optimizing the

other parameters for best performance for these two parameters. There is no best diameter

for the system, however there is a best L/D ratio for every chosen tube diameter. According

to the Prabakaran[3] et al and considering the manufacturing of tube within the machine

shop, tube diameter is chosen as 12mm, corresponding best L/D according to the Prabakaran

et al came up to be 15 for this diameter, therefore corresponding hot arm length is 180mm.

Corresponding nozzle and orifice diamater, inlet pressure and their corresponding tem-

perature difference between inlet temperature and cold exit is given below with their graphs

versus each other:

5

The optimum diameter of nozzle is 3 mm. The optimum diameter of orifice is 5 mm. The optimum pressure is 5 bar.The maximum temperature difference (4Tc) is approximately 16 C. [1]

(a) Contour Plot of Pressure, Orifice Diameter and

Temperature Gradient

(b) Contour Plot of Pressure, Nozzle Diamater and

Temperature Gradient

Figure 3: Contour Plot of Orifice Diamater, Nozzle Diameter and Temperature Gradient

Remark: All the plots include temperature gradient since the main purpose of the

vortex tube is spot cooling which can only be achieved by having a high temperature differ-

ence between inlet stream and cold stream. With the chosen design parameters, maximum

6

temperature difference can be 16C.

3.2 Cold Mass Fraction Effects

As a result of the cooling process, temperature difference between the inlet and the cold

exit is 16C. With the dimensions of the design and based on the experimental results

from Pongjet Promvonges [2] research as seen in the plots below corresponding cold mass

fraction for 16C is approximately 0.3 with ratio of orifice diameter to tube diameter (d/D)

is (5mm/12mm) 0.42.(where d is orifice diameter.) Despite of the fact that d/D ratio of 0.5

gives more efficient result according to the plot below, based on Prabakarans research which

claims d/D ratio is 5/12 gives the most efficient result.

(a) Cold Mass Fraction versus Temperature Differ-

ence According to Orifice Diameter to tube Diameter

Ratio

(b) Cold Mass Fraction versus Temperature Differ-

ence According to Inlet Number

7

Given temperature difference in the graphs is the difference between inlet stream tem-

perature and cold stream temperature. According to our chosen parameters, temperature

difference came up to be 16C, thus corresponding cold stream temperature would be 9C

when the inlet stream temperature is room temperature.

Additionally, number of inlets affects the corresponding cold mass fraction. Consider-

ing manufacturability, design was made for 1 inlet even more inlet provides more efficient

performance according to plot above.

3.3 Resulting Design

According to the examination that is shown above of parameters and their effects on each

other, final design and its technical drawing is provided below.

Figure 4: 3D View of Designed Vortex Tube

8

Figure 5: Exploded View of Designed Vortex Tube

9

170

10

12

vortextubedrawAIRLI:

A4

SAYFA 1 / 1LEK:1:5

RESM NO.

BALIK:

REVZYONTEKNK RESM LEKLENDRME

MALZEME:

TARHMZASM

KESKN KENARLARIPAHLAYIN VEKIRIN

BTRME:AKS BELRTLMED SRECE:BOYUTLAR MLMETREDRYZEY CLASI:TOLERANSLAR: DORUSAL: AISAL:

KALTE

RET.

ONAY.

DENET.

ZEN

Figure 6: Exploded View of Designed Vortex Tube

10

5 15

18

1

5

50

12

15 18

5

5

15

162

.5

10

12

15

18

2

5

3

3 4

18

15

5 5

15

18

7,50

18

120

2

2

9

Figure 7: Technical Drawing of Vortex Tube

11

4 References

[1] G. De Vera, The Ranque-Hilsch Vortex Tube, May 10, 2010.

[2] M. J. Moran, H. N. Shapiro, D. D. Boettner and Margaret B. Bailey, Principles of

Engineering Thermodynamics. John Wiley and Sons Inc. 2012

[3] Prabakaran J., Vaidyanadhan S. and Kanagarajan D. Establishing empirical relation

to predict temperature difference of vortex tube using response surface methodology. (2012).

Journal of Engineering Science and Technology, 7(6), pp.722-731.

[4] Promvonge, P. and Eiamsa-ard, S. (2005). Investigation on the vortex thermal sepa-

ration in a vortex tube refrigerator. Science Asia, 9(7), pp.215-223.

12