Vortex Tube Cold Fractions Explained

Simply put, a Vortex Tube’s Cold Fraction is the percentage of its supply air that gets directed to the cold end. The rest of the supply air goes out the hot end. Here’s how it works:

The Control Valve is operated by a flat head screwdriver.

No matter what the Cold Fraction is set to, the air coming out the cold end will be lower in temperature, and the air exiting the hot end will be higher in temperature, than the compressed air supply.  The Cold Fraction is set by the position of the Control Valve.    Opening the Control Valve (turning counterclockwise, see blue arrow on photo to right) lowers the Cold Fraction, resulting in lower flow – and a large temperature drop – in the cold air discharge.  Closing the Control Valve (turning clockwise, see red arrow) increases the cold air flow, but results in a smaller temperature drop.  This adjustability is key to the Vortex Tube’s versatility.  Some applications call for higher flows; others call for very low temperatures…more on that in a minute, though.

The Cold Fraction can be set as low as 20% – meaning a small amount (20% to be exact) of the supply air is directed to the cold end, with a large temperature drop.  Conversely, you can set it as high as 80% – meaning most of the supply air goes to the cold end, but the temperature drop isn’t as high.  Our 3400 Series Vortex Tubes are for 20-50% Cold Fractions, and the 3200 Series are for 50-80% Cold Fractions.  Both extremes, and all points in between, are used, depending on the nature of the applications.  Here are some examples:

EXAIR 3400 Series Vortex Tubes, for air as low as -50°F.

A candy maker needed to cool chocolate that had been poured into small molds to make bite-sized, fun-shaped, confections.  Keeping the air flow low was critical…they wanted a nice, smooth surface, not rippled by a blast of air.  A pair of Model 3408 Small Vortex Tubes set to a 40% Cold Fraction produce a 3.2 SCFM cold flow (feels a lot like when you blow on a spoonful of hot soup to cool it down) that’s 110°F colder than the compressed air supply…or about -30°F.  It doesn’t disturb the surface, but cools & sets it in a hurry.  They could turn the Cold Fraction down all the way to 20%, for a cold flow of only 1.6 SCFM (just a whisper, really,) but with a 123°F temperature drop.

Welding and brazing are examples of applications where higher flows are advantageous.  The lower temperature drop doesn’t make all that much difference…turns out, when you’re blowing air onto metal that’s been recently melted, it doesn’t seem to matter much if the air is 20°F or -20°F, as long as there’s a LOT of it.  Our Medium Vortex Tubes are especially popular for this.  An ultrasonic weld that seals the end of a toothpaste tube, for example, is done with a Model 3215 set to an 80% Cold Fraction (12 SCFM of cold flow with a 54°F drop,) while brazing copper pipe fittings needs the higher flow of a Model 3230: the same 80% cold fraction makes 24 SCFM cold flow, with the same 54°F temperature drop.

Regardless of which model you choose, the temperature drop of the cold air flow is determined by only two factors: Cold Fraction setting, and compressed air supply pressure.  If you were wondering where I got all the figures above, they’re all from the Specification & Performance charts published in our catalog:

3200 Series are for max cooling (50-80% Cold Fractions;) 3400’s are for max cold temperature (20-50% Cold Fractions.)
Chocolate cooling in brown; welding/brazing in blue.

EXAIR Vortex Tubes & Spot Cooling Products are a quick & easy way to supply a reliable, controllable flow of cold air, on demand.  If you’d like to find out more, give me a call.

Russ Bowman
Application Engineer
EXAIR Corporation
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The Effect of Back Pressure on a Vortex Tube Part 2, Calculating Btu/Hr.

My previous blog post was about how Vortex Tubes react when there is back pressure due to a restriction on either the hot or cold discharge of the Vortex Tube.  In it I mentioned that there is a formula to calculate what the cooling capacity (Btu/Hr) will be if there is no way to avoid operating the Vortex Tube without back pressure on the discharge. That is the calculation focus of this blog – calculating Btu/hr of a Vortex Tube with back pressure.

To continue with the same example, the calculations from the previous blog are shown below.  Last time the example Vortex Tube was operating at 100 psig inlet pressure, 50% cold fraction, and 10 psi of back pressure. We will need some additional information to determine the Btu/Hr capacity. The additional information needed is the temperature of the supplied compressed air as well as the ambient air temperature desired to maintain.  For the example the inlet compressed air will be 70°F and desired ambient air temperature to maintain will be 90°F.

(100 psig + 14.7 psia) / (10 psig + 14.7 psia) = X / 14.7 psia
4.6437 = X / 14.7
X= 14.7 * 4.6437
X = 68.2628
(Values have been rounded for display purposes)

The calculation above gives the compensated operating pressure (X = 68.2628) which will be needed for the BTU/hr calculation. The rated air consumption value of the Vortex Tube will also need to be known.  A 30 SCFM rated generator will be used for this example, the normal BTU capacity of a Vortex Tube with a 30 SCFM generator is 2,000 BTU/hr.

First, determine the new consumption rate by establishing a ratio of the compensated pressure (68.2628 psi) against the rated pressure (100 psi) at absolute conditions (14.7 psia).

(68.2628 PSIG + 14.7 (atmospheric pressure)) / (100 PSIG (rated pressure) + 14.7) = .7233
.7233 x 30 SCFM  = 21.7 SCFM Input 

Second, the volumetric flow of cold air at the previously mentioned cold fraction (50%) will be calculated.  To do this multiply the cold fraction setting (50%) of the Vortex Tube by the compensated input consumption (21.7 SCFM) of the Vortex Tube.

50% cold fraction x 21.7 SCFM input = 10.85 SCFM of cold air flow

Third, the temperature of air that will be produced by the Vortex Tube will need to be calculated.  For this consult the Vortex Tube performance chart which is shown below. To simplify the example the compensated operating pressure (68.2628 psi) will be rounded to 70 psig and to obtain the 70 psig value the mean between 80 psig and 60 psig performance from the chart will be used.

Cold Fraction
EXAIR Vortex Tube Performance Chart

For the example: A 70 psig inlet pressure at 50% cold fraction will produce approximately an 88°F drop.
Fourth, subtract the temperature drop (88°F) from the temperature of the supplied compressed air temperature (70°F).

70°F Supply air – 88°F drop = -18°F Output Air Temperature

Fifth,  determine the difference between the temperature of the air being produced by the Vortex Tube (-18°F) and the ambient air temperature that is desired (90°F).

90°F ambient – -18°F air generated = 108°F difference.

The sixth and final step in the calculation is to apply the answers obtained above into a refrigeration formula to calculate BTU/hr.

1.0746 (BTU/hr. constant for air) x 10.85 SCFM of cold air flow x 108°F ΔT = 1,259 BTU/hr.

In summary, if a 2,000 BTU/hr. Vortex tube is operated at 100 psig inlet pressure, 50% cold fraction, 70°F inlet air to maintain a 90°F ambient condition with 10 psi of back pressure on the outlets of the Vortex Tube the cooling capacity will be de-rated to 1,259 BTU/hr.  That is a 37% reduction in performance.  If a back pressure cannot be avoided and the cooling capacity needed is known then it is possible to compensate and ensure the cooling capacity can still be achieved.  The ideal scenario for a Vortex Tube to remain at optimal performance is to operate with no back pressure on the cold or hot outlet.

Brian Farno
Application Engineer Manager
BrianFarno@EXAIR.com
@EXAIR_BF

The Effect of Back Pressure on a Vortex Tube

Vortex tubes have been considered a phenomena of Physics and boggled minds for many years.  To give a brief run down of how the Vortex Tube works please refer to Figure 1 below.

How_A_Vortex_Tube_Works
Figure 1

As seen above, the control valve is determining the amount of air allowed to escape the hot end and sets the cold fraction.  A cold fraction is the percentage of air that exits the cold side versus the hot side. The cold fraction and operating pressure sets the temperature drop on the cold end and temperature rise on the hot end, as well as volumetric flow out of both ends. The control valve is not the only variable that can alter the cold fraction of the Vortex Tube though.

In Figure 1 and the performance chart below, there is no restriction on the hot end or the cold end outlets. No restriction means no back pressure and the cold air has the easiest path to the area needing cooling. Back pressure can directly affect the performance of a Vortex Tube.  As little as 3 psig of back pressure can begin to alter the temperature drop or rise on the Vortex Tube.  This is due to the fact that Vortex Tubes operate off an absolute pressure differential.  If the outlets have a restriction on them then they are not discharging at atmospheric pressure, 14.7 psi. What kind of items can cause back pressure and can the performance with a back pressure on the outlet be determined?

Back pressure is created by implementing any form of restriction on the hot or cold outlet. This may be undersized tubing to deliver the cold air or a valve that has been installed to try and control the volume of air being blown onto the process as well as many other possibilities.  The best rule of thumb to eliminate back pressure is to keep the tubing on an outlet the same cross sectional dimension as the outlet on the Vortex Tube and try to keep the tubing as short as possible.

If back pressure cannot be prevented, the performance variance of the Vortex Tube can be calculated and possibly compensated for. The variables that are needed to do so are the inlet air pressure of the vortex tube and the amount of back pressure that is being seen on the outlets. If this is different from the hot end to the cold end both will need to be known.  If these are not known they can be measure by installing a pipe Tee and a pressure gauge. This may need to be a sensitive pressure gauge that measures even relatively low psig. (1-15 psig)

Once these variables are known, we want to look at an absolute pressure differential versus the back pressure differential. For example, the Vortex Tube is a operating at 100 psig inlet pressure, 50% cold fraction and 10 psi of back pressure.  We look at the pressure differentials and can use Algebraic method to determine the inlet pressure supply that the tube will actually perform at.

(100 psig + 14.7 psia) / (10 psig + 14.7 psia) = X / 14.7 psia
4.6437 = X / 14.7
X= 14.7 * 4.6437
X = 68.2628
(Values have been rounded for display purposes)

So if there is a 10 psig back pressure on the outlet of a Vortex tube operating a 100 psig inlet pressure the tube will actually carry performance as if the inlet pressure was ~68 psig.   To showcase the alteration in performance we will look at just the temperature drop out of the cold side of the Vortex Tube. (Keep in mind this is a drop from the incoming compressed air temperature.)

Vortex Tube Performance Data
Vortex Tube Performance Chart

As shown in the performance chart above, if the Vortex Tube was operating at 100 psig inlet pressure and 50% cold fraction the temperature drop would be 100°F.  By applying a 10 psi back pressure on the outlet of the Vortex Tube the temperature will be decreased to ~87°F temperature drop.   This will also decrease the volumetric flow of air exiting the Vortex Tube which can also be calculated in order to determine the cooling capacity of the Vortex Tube at the altered state.  Keep an eye out for a follow up blog coming soon to see that calculation.

Brian Farno
Application Engineer Manager
BrianFarno@EXAIR.com
@EXAIR_BF