International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 434

ISSN 2229-5518

Design and Computation of COP of

Vortex Tube

S.KARTHIK

DEPT. OF MECHANICAL ENGINEERING UNIVERSITY OF KERALA

Abstract— Vortex tube is a mec hanic al devic e op erating as a refrigerating mac hine without an y moving parts, by s eparating a c ompress ed gas s tream into a low total temp erat ure region and a high one .A vortex tube is a devic e c apable of production of both higher and lower temperatures simultaneous at both ends of the tube. T he vortex tube's c ons truction is s uc h that it is made up of a hollow tube of either metallic or fibre c ompon ents having a n ozzle f or letting in of c ompress ed air and a di aphragm or a orific e f or c ontrolling the f low rate of air. W hen c ompress ed air pass es through a nozzle into the diaphragm of the vortex tube, the air f orms a s piral s haped vortex, that c aus es the heating up of air, and when this air returns bac k, it c ools down rapidly, produc ing a c ooling eff ec t. As the mass flow rates changes , the temper ature gap between the atmos pheric air and air through the c old end varies. In this paper, the c alc ulations f or flow rates are meas ured and the designs are similar to what was taken by Hilsch, Reyn old and Albohrn.

Key words— Vortex Tube, c ooling, mass flow rate , temperature gap, c ompress ed gas ,ref rigeration ,nozzle, diaphragm

——————————  ——————————

1. INRODUCTION

Vortex tube was first experimentally tested in the year 1933 by George Ranque while observing a thermal division in a cyclone separator . This primary design was altered in the year 1947 by Hilsch. In the subsequent years, more modifications was achieved by higher performance of the vortex tubes and to study various parameters concerning the tube design and output, for example Kassner and Knoemschild performed a study based on the assumption that the effect was due to a adiabatic expansion, which lead to a low temperature in the
low pressure area near the axis of the tube. . Even after various tests and analysis, no theory
provides a proper explanation for the vortex mechanism undergoing in the tube.

FIG. 1. DIAGRAM OF A VORTEX TUBE

A Vortex tube consists of a cylindrical tube with a nozzle, a diaphragm (cylindrical plate with a central hole) and a control valve. Compressed air is kept tangential through the nozzle which is kept tangential to the tube.
The Vortex Tube is now being used commercially for various applications such as food preservation and cooling in mines as the apparatus is very simple and compact and it doesn't require any interaction of heat and work
with the environment for its operation.

International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 435

ISSN 2229-5518

2. LITERATURE REVIEW

After initial experiments, a lot of researchers tried a lot of modifications on the vortex tube to increase its performance. It is found from the previous scientist's records that each and every one of them used various L/D ratios and each one of them was a result of hit and trial method. The list is given below regarding the

COP Vs cold flow fraction

0.2

0.15

low pressure

0.1

medium

modifications and customisations:-

TABLEI. PREVIOUS REVIEWS

0.05

0 0.5 1

pressure

high pressure

cold flow fraction

FIG. 2. COP DATA FROM PIONEER SCIENTISTS

According to previous standards, maximum COP obtained was 0.17 . But now, with improvement in materials and standards, the COP is increased upto 2.

3. ASSUMPTIONS

The following assumptions were made for the ease of calculation:-
It is clearly evident from the above table that the various ratio parameters used in the construction of the vortex tube for different authors have no relation with each other. Each person has his own combinations of the ratio parameters.
1. The entire system is insulated and the process are adiabatic.
2. The outlet pressures are equal to atmospheric pressures.
3. The cold end diaphragm and hot end conical valve does not absorb any heat.
4. The flow is turbulent.

International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 436

ISSN 2229-5518

4. DESIGN PROCEDURE

The main aim of this setup is the production of a Vortex path of air. Since the nozzle is tangential, air entering through it gets a swirling motion inside the cylinder. The air acquires a high velocity and travel towards the valve (in the end of the hot side) as a spiral vortex. When the swirling flow reaches the end, it is resisted by the partially opened valve. Due to the conversion of kinetic energy, the pressure of the air near the valve increases and a reversed axial flow through the low pressure case.
By controlling the opening of the valve, the proportion of cold air and hot air and their temperatures can be varied.
some of the restrictions followed were:-
1. For obtaining the maximum temperature difference at cold end, the ratio L/D should be maintained in the range of 30 ≤ L/D ≤ 60.
hence, considering the length to be 113.03cm and diameter to be 2.05cm, we get the L/D ratio to be in the range.
2. Decreasing conical valve angle have positive effect on performance of vortex tube but not so much difference is observed in the temperature reduction. Therefore it is better to use conical valve with smaller angle in order to improve the performance of vortex tube.

3. The following schematics is followed-

5. PERFORMANCE PARAMETERS

Performance are divided into input and output variables:
INPUT VARIABLES :
1. Area of cold orifice
2. Inlet pressure
OUTPUT VARIABLES :
1. Temperature of hot air
2. Temperature of cold air

6. DESIGN PARAMETERS

The primary material used is PVC pipe for the vortex tube refrigerator. the cone valve used is of a wooden material.
In the current investigation, the design parameters used are provided in the table below.

Tube inner diameter	2.057 cm	d
Cold plate orifice diameter	1.028 cm	0.5d
Inlet nozzle diameter	0.3 cm	6.75d
No. Of nozzle inlet	5	Depending on air flow rate
Hot end length	92.71 cm	45d
Cold end length	20.32 cm	10d
Pressure range	0-2 bar	Experimental setup

The total length of the vortex tube made from the PVC pipe was found out to be 113.03cm; having the length of the hot side to be 92.71cm and that of cold side to be 20.32cm.

International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 437

ISSN 2229-5518

7. CALCULATION

density of air ρa = Pa /(RTa )

= 1.01325 x 105 = 1.176 kg/m3
287 x 300

flow rate va = cd a (2gha )1/2

ha = (hw ρw )/ρa = (8.4 x 10-2 x 103) / 1.176

= 71.428 m of air
therefore
va = 0.6 x {π x (0.012)2}/4 x [2 x 9.81 x 71.428]1/2
= 2.539 x 10-3 m3/s

flow rate at NTP, vntp = (va To )/Ta ; T o = normal temperature=273 K

T a = ambient temperature = 300K
vntp = {2.539 x 10-3 x 273} / 300
= 2.275 x 10-3 m3/s
mass flow rate at NTP = vntp ρa
= 2.275 x 10-3 x 1.176 = 2.67 x 10-3 kg/s
refrigeration effect = ṁ Cp ∆T
where ṁ= mass flow rate
= 2.67 x 10-3 x 1.005 x (300 - 297)
= 5.3667 W
Work done = 3600 x 2 x 103 W E t
where E= energy meter constant for compressor used
t = time taken for 2 seconds for the
energy disc to rotate

TABLEII. VARIATION OF MASS FLOW

Valve position	Mass flow rate ( Kg/s )	Refrigeration effect (W)	COP
Full closed	2.67 x 10-3	5.03	0.02
¾	2 x 10-3	4.623	0.023
½	1.335 x 10-3	3.354	0.016
1/4	6.675 x 10-4	1.475	0.007

TABLEIII. TEMPERATURE VS COP

hence
work done = (3600/1000) x (2/35.81) x 103
= 201.06 W

Coefficient of performance (COP)

= Refrigeration effect/ work done

= 5.3667 / 201.06
= 0.026

International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-2015 438

ISSN 2229-5518

0.1

0.09

COP vs ∆T

REFERENCES

1. M. G. Ranque, 1933, “Experiences sur la detente giratoire avec production simulanees d’un echappement d’air chaud et d’air froid”, Journal

FIG. 3. GRAPH OF CALCULATED COP VS TEMPERATURE DIFFERENCE

8. RESULT and INFERENCE

1. The results obtained by using PVC as the material provides similar outputs to that of the tests conducted by pioneer scientists such as Hilsch and Reynold.
2. By increasing the mass flow rate, the temperature gap increases and hence produces a high COP.
3. Mass flow rate can be adjusted by the valve position of the conical valve.

Vortex-Type Flow”, Transactions of the ASME, Vol. 79, No. 4, pp. 751-758.

7. M. Kurosaka, 1982, “Acoustic Streaming in Swirling Flows”, Journal of Fluid Mechanics, Vol. 124, pp. 139-172.

8. K. Stephan, S. Lin, M. Durst, F. Huang, and D.

Seher, 1983, “An Investigation of Energy Separation in a Vortex Tube”, International Journal of Heat and Mass Transfer, Vol. 26, No.

3, pp. 341-348.

9. B. K. Ahlborn, and J. M. Gordon, 2000, “The Vortex Tube as a Classical Thermodynamic Refrigeration Cycle”, Journal of Applied Physics, Vol. 88., No. 6, pp. 3645-3653.

10. J. M. Nash, 1991, "Vortex Expansion Devices for

High Temperature Cryogenics", Proc. of the

26th Intersociety Energy Conversion

Engineering Conference, Vol. 4, pp. 521-525.

11. D. Li, J. S. Baek, E. A. Groll, and P. B. Lawless,

2000, “Thermodynamic Analysis of Vortex Tube and Work Output Devices for the Transcritical Carbon Dioxide Cycle”, Preliminary Proceedings of the 4th IIR-Gustav Lorentzen Conference on Natural Working Fluids at Purdue, E. A. Groll & D. M. Robinson, editors, Ray W. Herrick Laboratories, Purdue University, pp. 433-440.

12. H. Takahama, 1965, “Studies on Vortex Tubes”,

Bulletin of JSME, Vol. 8, No. 3, pp. 433-440.

13. B. Ahlborn, and S. Groves, 1997, “Secondary Flow in a Vortex Tube”, Fluid Dyn. Research, Vol. 21, pp. 73-86.