Vortex Technical

TEMPERATURE SEPARATION EFFECTS IN A VORTEX TUBE

The movement of air in the Vortex Tube has already been covered on our Vortex Tubes page. Now we shall explain why the hot air gets hot and the cold air gets cold.

The air in the hot tube has a complex movement. An outer ring of air is moving toward the hot end of the tube and an inner core of air is moving toward the cold end. Both streams of air are rotating in the same direction. More importantly, both streams of air are rotating at the same angular velocity. This is because intense turbulence at the boundary between the two streams and throughout both streams locks them into a single mass as far as rotational movement is concerned.

The inner stream is a “forced vortex” which is distinguished from a “free vortex” in that its rotational movement is controlled by some outside influence other than the conservation of angular momentum. In this case, the outer hot stream forces the inner (cold) stream to rotate at a constant angular velocity.

In a simple whirlpool, (which most people associate with the word “vortex”), a free vortex is formed. As the water moves inward, its rotational speed increases to conserve angular momentum. Linear velocity of any particle in the vortex is inversely proportional to its radius. Thus, in moving from a radius of one unit to a center point at a radius of 1/2 unit, a particle doubles its linear (tangential) speed in a free vortex. In a forced vortex with constant angular velocity, the linear speed decreases by half as a particle moves from a radius of 1 unit to a center point at a radius of 1/2 unit.

In the situation above, particles enter the center with four times the linear velocity in a free vortex compared with a forced vortex. Kinetic energy is proportional to the square of linear velocity, thus the particles leaving the center of the forced vortex have 1/1 6th the kinetic energy of those leaving the center of the free vortex in this example.

Where does this energy (15/16 of the total available kinetic energy) go? The energy leaves the inner core as heat and is transmitted to the outer core.

The air in the cooling inner stream must travel through the outer (heating) stream first. The rate of flow in the outer stream is always larger than that of the inner stream, since part of the outer stream is being discharged at the hot valve. If the BTU’s leaving the inner stream equal the BTU’s gained by the outer stream, the temperature drop of the inner stream must be more than the temperature gain of the outer stream because its mass rate of flow is smaller.

This is why hot end temperatures increase as cold fractions increase, and cold end temperatures decrease as cold fractions decrease.

Inlet Pressure PSIG

Cold Fraction %

20

30

40

50

60

70

80

20

61.5

59.5

55.5

50.5

43.5

36.0

27.5

14.5

24.5

36.0

49.5

64.0

82.5

107

40

88.0

85.0

80.0

73.0

62.5

51.5

38.0

20.5

35.0

51.5

71.0

91.5

117.0

147

60

104

100

93.0

84.0

73.0

59.5

44.5

23.5

40.0

58.5

80.0

104

132

168

80

115

110

102

92.0

80.0

65.5

49.0

25.0

43.0

63.0

86.0

113

143

181

100

123

118

110

99.0

86.0

70.5

53.0

26.0

45.0

66.5

91.0

119

151

192

120

129

124

116

104

90.5

74.0

55.0

26.0

46.0

69.0

94.0

123

156

195

140

135

129

121

109

94.0

76.0

56.5

25.5

46.0

70.5

96.0

124

156

193

Figures shaded in grey give temperature drop of cold air, degrees F

Figures on the second line give temperature rise of hot air, degrees F

EFFECTS OF INLET TEMPERATURE

It is very easy to predict the temperature drops and rises in a Vortex Tube for various inlet temperatures. The basic rule to remember is that temperature drops or gains are proportional to absolute inlet temperature. Any temperature expressed in degrees Fahrenheit can be converted to absolute (degrees Rankine) by adding 460. 70F + 460R = 530R.

Thus, the entire table above is based on an inlet temperature of 530R. If absolute inlet temperature doubles, so does the temperature drop or gain. For example, suppose you want to find the temperature drop associated with a Vortex Tube operating at 30% Cold Fraction and with a 100 PSIG, 200F inlet.

1. Table gives 118F drop for 100 PSIG, 70F inlet at 30% CF
2. Ratio of absolute inlet temperature

200+460 = 660 = 1.245
 70+460 530

3. Drop given in table times ratio is 118 x 1.245 =147
4. Cold end temperature is 200 – 147 = 53F 

This ratio can be used just as well when the inlet temperature is lower than the 70F on which the table is based. For example, if inlet temperature were 0F, ratio would be

0+460 = 460 = .87
 70+460 530

In this case the temperature drop is reduced.

Exactly the same approach can be used to convert the temperature rises given in the table. They are greater for inlet temperatures higher than 70F and smaller for inlets below 70F.

This method applies to the pressure range shown on the table only. Whenever pressures considerably higher than the table are involved, the Joule Thompson effect alters the results somewhat. This effect is small at pressures of 140 PSIG and below, and can be ignored as it is in the method given above. Joule Thompson cooling is the very slight cooling that takes place as gases are throttled.

USING THE PERFORMANCE TABLE

Temperature drops and rises are related in a complex way to the absolute pressure ratio between inlet and cold outlet. The table is based upon the assumption that the cold outlet is at atmospheric pressure. For any other cold end pressures, the table cannot be used.

You can appreciate the variation in temperature drops and rises if you consider how quickly the absolute pressure ratio changes with changes in cold end pressure. A 90 PSIG inlet (105 PSIA) provides a 7 to 1 ratio when the tube exhausts to atmospheric pressure (0 PSIG or 15 PSIA). If inlet pressure remains the same and cold outlet pressure rises to only 15 PSIG, the ratio drops to 3.5 to 1.

Calculations of temperature rise and drop for pressures other than those shown on the table can be made, but they are beyond the scope of this Bulletin.

AIR CONDITIONING POWER

To approximate the cooling and heating power in BTUH, use the following simplified formulas:

CF = Cold Fraction
CFMt = Total Airflow
CFMc = Cold Airflow = CFMt(CF)
CFMh = Hot Airflow = CFMt(100-CF)

ti= Inlet Temperature
tc = Cold Air Outlet Temperature
th= Hot Air Outlet Temperature

For Cooling: BTUH = 1.0746 (CFMc) (ti-tc)

For Heating: BTUH = 1.0746 (CFMh) (th-ti)

THE HEAT BALANCE FORMULA

The energy extracted from the cold air by the Vortex Tube appears in the hot air.

The formula is:

CF x (ti – tc – JT) = (100 – CF) x (th – ti + JT) where CF = Cold Fraction, %
ti = inlet air temperature, F
tc = cold air temperature, F
th – hot air temperature, F
JT = Joule-Thompson temperature correction F = 4F at an inlet pressure of 100 PSIG

By using this formula, Cold Fraction can be computed from the readings of the three thermometers alone without having to measure any airflow. For example, suppose ti = 100F, tc= 50F, th = 300F. Substituting in the formula CF x (100 – 50-4) = (100 – CF) x (300 – 100+4), solving for CF, CF = 81.5%.

Vortex Tubes obey this formula very closely, regardless of their efficiency, provided the hot pipe is insulated. The formula can be rearranged as follows:

CF = th – ti + 4 x 100
th – tc

HUMIDITY EFFECTS

The Vortex Tube does not separate humidity between the hot and cold air. The absolute humidity of both cold and hot air, in grains/pound, is the same as that of the entering compressed air. Moisture will condense and / or freeze in the cold air if its dew point is higher than its temperature. The following table shows the amount of moisture that air can hold in the saturated vapor state as a function of air temperature, at standard atmospheric pressure of 14.7 PSIA:

Temperature, Degrees F

110

100

90

80

70

60

50

Saturation*

375

295

217

154

111

77

54

Temperature, Degrees F

40

30

20

10

0

-10

-20

-30

Saturation*

37

24

15

9

5.5

3.2

1.8

1.0

* Saturation moisture content grains / lb. air.

For example, the above table shows that if the moisture content is 14 gr./lb., condensation will begin when the temperature of the cold air falls below 19F. At 5 gr./lb., condensation will begin at – 1F. The saturation moisture content of compressed air at 100 PSIG is given in the following table:

Temperature, Degrees F

110

100

90

80

70

60

50

40

30

20

Saturation Moisture Content,
Grains / lb. Air

48

38

28

20

14

9.9

6.9

4.7

3.1

1.9

By comparing the two tables, it is possible to predict the amount of moisture in the compressed air, and the temperature at which moisture will begin to precipitate or freeze in the cold air. For example, suppose the compressed air is aftercooled to 80F following compression, and the precipitated water drained off. Then the second table shows that it will carry 20 grains/lb. of water vapor. When this expands in the Vortex Tube, the upper table shows that precipitation will begin in the cold air when its temperature falls below 26F if its pressure is 14.7 PSIA.

If the compressed air is cooled under pressure by a chiller to 40F, the second table shows that it will then carry 4.7 grains/lb. of water vapor. When expanded in the Vortex Tube, precipitation will begin when the temperature of the cold air falls below – 3F at 14.7 PSIA.

If some moisture precipitates in the cold air, the temperature of the cold air will thereby be caused to rise approximately 3/4F for each grain of moisture that precipitates. This is because some of the sensible refrigeration of the cold air is consumed in producing latent refrigeration of the moisture. This refrigeration is not lost, but reappears in the cold air as it warms up in performing its air conditioning duty after leaving the VortexTube, when the precipitated moisture re-evaporates.

The tables show that condensation will not normally occur at moderate cold end temperatures. When temperatures are low enough to cause condensation, it appears as snow. The snow has a sticky quality due to oil vapor and will gradually collect and block cold air passages. Continuous operation at low temperatures can be assured by means of an air dryer or injection of an antifreeze mist into the compressed air feeding a Vortex Tube.

When selecting dryers give consideration to refrigerative and deliquescent types. While their drying abilities are limited (and need to be considered) they are quite compatible with the Vortex Tube. Chemical desiccant dryers such as silica-gel and molecular sieve types are exothermic, and tend to heat the compressed air, causing refrigeration losses.

THE AIR SUPPLY

Pressure

Standard Vortex Tubes are designed to utilize a normal shop air supply of 80 to 110 PSIG pressure. Unless pressures run considerably higher than 110 PSIG, do not use a regulator to reduce the inlet pressure. Pressures higher than 250 PSIG must not be used. Pressures lower than 80 PSIG will still produce some cooling. However, both the temperature drops and the flows are reduced due to the lower inlet pressures.

Line Sizes

Up to 35 SCFM, runs of pipe less than 10 feet long may be 3/8″ size without excessive pressure drop. Up to 50 feet, use 1/2″ pipe, and use 3/4″ pipe over 50 feet. Rubber hose of suitable pressure rating may be used. Consider 1/2″ I.D. hose to be the same as 3/8″ pipe, and 3/4″ I.D. hose to be the same as 1/2″ pipe. Remember that lower transmission pressures will exhibit even greater pressure drops, so care must be taken to avoid large losses in the inlet air piping.

Compressor Size

In most large plants, the size of the compressor is adequate to handle many Vortex Tubes operating simultaneously . For smaller plants, estimate horsepower required based upon the rated capacity of the tubes. For a 100 PSIG system, it takes one horsepower to compress 4 SCFM of air.

PREPARING THE AIR

Moisture

All compressed air systems will have condensed water in the lines unless a dryer is in use. To remove condensed water from the air, a filter-separator must be used. Automatic drain types are recommended unless the area is always tended by a responsible employee who can empty the collection bowl periodically. Place the filter-separator as near to the Vortex Tube as possible.

Dryers

Normally a dryer is not required for Vortex Tube applications. Occasionally, however, when very low outlet temperatures are produced, icing will cause problems. Also, some applications may require the cold airstream to be completely free of condensed water or ice. A chemical dryer (silica gel, heatless, or other type) can be used in the inlet line to eliminate condensed water or ice in the cold airstream. The dryer should be rated to produce an atmospheric dew point lower than the lowest expected cold outlet temperature.

Dirt

Because of the water in compressed air lines, there is always rust and dirt present. Filter-separators effectively remove these contaminants by using a five micron filter.

Oil

Never use Vortex Tubes downstream of a lubricator. Oil in the air which has been introduced by the compressor lubrication system is usually not a problem for Vortec products, but occasionally older compressors produce very oily air. If the plant air is very oily, use an oil removal filter downstream of the filter-separator. The oil removal filter removes dirt, water, and oil aerosols with an effective filtration of 0.01 micron.

SETTINGS

Maximum Efficiency — Maximum efficiency as a high cold unit or a low cold unit is achieved by selecting the most appropriate Vortex generator and bushing for a specific application. The diameter of the cold air passage in the center of the generator is controlled by a simple bushing that is either designated H or L for high or low fractions. Each bushing is sized to match the CFM capacity of its generator. The bushing and generator are separate parts for Model 106 and 328 tubes. The bushing and generator are manufactured as a single part for the Model 208 and 308 tubes. For example, generators for the Model 106 tube (designated 2, 4, or 8 CFM) may be used with bushings 2-H or 2-L, 4-H or 4-L, 8-H or 8-L, depending on the Cold Fraction and flow needed. The Vortex Tube Model 208 uses model numbers to designate the CFM rating and high or low Cold Fraction efficiency.

Maximum Refrigeration — Maximum refrigeration occurs when a Vortex Tube operates at 60 to 70 percent Cold Fraction. This is where the product of the mass of cold air and its temperature drop is the greatest. Many applications such as cooling machining operations, electrical controls, liquid baths, and personal air conditioning use this maximum refrigeration setting. For maximum refrigeration, use H style bushings.

Minimum Temperature — Some applications require the lowest possible cold output temperature. Examples are cooling glass, laboratory experiments, and testing electronic components. These air spraying applications usually work better with very cold air, and results do not depend upon the refrigeration rate. For these applications, L style bushings and Cold Fractions in the 20 to 40 percent range are best.

USING THE COLD AIR

Back Pressure — One of the most common mistakes users make with Vortex Tubes is to restrict the cold outlet. This will cause a loss of performance. A small back pressure on the cold outlet to allow the air to move through piping or ducting is acceptable, but back pressure, measured at the tube, should be limited to less than 5 PSIG. Keep in mind the tube is responsive to the absolute pressure ratio applied and back pressures as low as 15 PSIG cut this ratio in half. Some pressure is available at the hot end, and it can be used as long as compensating adjustments in the control valve setting are made.

Insulation — As with any thermodynamic device, the proper use of insulation will improve Vortex Tube system performance. Avoid ducting the cold air through large thermal masses such as heavy piping, drilled holes in large blocks, etc. If possible, use plastic tubing or plastic piping when ducting the cold air. Foam type insulation can also be quite helpful.

NOISE MUFFLERS

General — A common misconception is that a Vortex Tube emits a scream or whistle due to the sonic speeds inside. Actually such noise is rarely observed, but the sound of escaping air is always present, and in some cases it must be muffled. Ordinarily, the cold air will be ducted into an enclosure or through some pipe or tubing. This alone may reduce its noise level to acceptable limits. Hot air escapes in smaller amounts in most applications and may not be objectionable. Nevertheless, jets of escaping air can be quite objectionable if continued over a long period of time near a worker. In such situations mufflers are available, and should be used.

Cold Muffling — Mufflers used on the cold air must not be of a stuffed or porous type. Their small openings will quickly block with ice which has condensed and frozen in the cold air stream. Baffle type mufflers and silencers are best for the cold air. A void selecting any muffler which will apply high back pressures to the Vortex Tube.

Hot Muffling — Nearly any air silencer or muffler will work on the hot end. One should avoid selecting a muffler made from plastics or other materials with low resistance to heat since hot end temperatures can easily exceed 200F.

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