Vortex Tubes: What is a Cold Fraction?

Have you ever needed a source of cold air but don’t want to invest in a costly chiller? INTRODUCING Vortex Tubes! Vortex Tubes use compressed air and contain no moving parts to create a cold and hot stream of air from either end of the device. Using the valve located on the hot stream a vortex tube can achieve temperatures as low as -50°F (-46°C) and temperatures as high as 260°F (127°C).

When the vortex tube is supplied with compressed air the air flow is directed into the generator that causes spin into a spiraling vortex at around 1,000,000 rpm. This spinning vortex flows down the neck and wall of the hot tube. The control valve located on the end of the hot tube allows a fraction of the hot air to escape and what does not escape reverses direction and travels back down the center of the tube and exhausts out of the cold end. Inside of the low-pressure area of the larger outer warm air vortex, the inner vortex loses heat as it flows back to the cold end of the vortex and as it exits the vortex expels cold air. The absolute temperature drop that occurs during this process is going to be controlled by the cold fraction of the Vortex Tube and the supply pressure.

The brass screw used to control the cold fraction of a vortex tube

The cold fraction is defined as the amount of the inlet supply air that will exit out of the cold end of the vortex tube. An example would be if I had 10 SCFM supplied to a vortex tube with 60% cold fraction, then 6 SCFM would be exiting the cold discharge. Cold based on the amount of air you allow out of the hot end of the vortex tube you can control the temperature drop of the cold air. A smaller cold fraction which only allows a small amount of air to exit the cold discharge will result in a larger temperature drop; and vise versa a larger cold fraction will result in a much smaller temperature drop.

Table the shows the temperature drop and rise in correlation with the cold fraction and pressure

Here a EXAIR we have designed our vortex tubes to operate optimally at both a high cold fraction and a low cold fraction. The 32XX series designed to give you the best refrigeration, which means it will work well for cold fractions ~60% – 80%. This will give you a smaller temperature drop with more air flow which allows you to keep things cool much easier. This contrasts with the 34XX series which is designed more optimal performance at lower temperatures; this means the optimal cold fraction would be ~20% to 40%. Cold fractions this low will produce very little air flow but the temperature will be very cold (as low as -50°F). This is useful if you need to get an item down to a very low temperature.

If you have any questions about compressed air systems or want more information on any of EXAIR’s products, give us a call, we have a team of Application Engineers ready to answer your questions and recommend a solution for your applications.

Cody Biehle
Application Engineer
EXAIR Corporation
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Max Refrigeration vs. Max Cold Temp Vortex Tubes

Here at EXAIR, our vortex tubes are offered in two separate series. The reason for this is to optimize the performance of the cold air temperature drop when operating with opposite ends of the cold fraction chart. The maximum refrigeration vortex tubes, 32xx series, perform optimally when they are set to a greater than 50% cold fraction.  The maximum cold temp vortex tubes, 34xx series, perform optimally when they are set to a less than or equal to 50% cold fraction. The cold fraction is discussed more in-depth within this link from Russ Bowman, Vortex Tube Cold Fractions Explained. This blog is going to explain a little further why one series of vortex tubes would be chosen for an application over another.

Cold Fraction
EXAIR Vortex Tube Performance Chart

Maximum refrigeration (32xx) vortex tubes are the most commonly discussed of the two types when discussing the optimal selection of the vortex tube for an application. The 32xx series vortex tubes achieve a maximum refrigeration output when operated at 100 psig inlet pressure with around  80% cold fraction. This would give a temperature drop from incoming compressed air temperature of 54°F (30°C). The volumetric flow rate of cold air will be 80% of the input flow which means only 20% is being exhausted as warm exhaust air. By keeping the flow rate higher the air is able to cool a higher heat load and is the reason the vortex tube is given a BTU/hr cooling capacity.

Vortex Tube Hot Valve Adjustment

Maximum cold temperature (34xx) tubes are less common as their applications are a little more niche and require a very pinpoint application. Rather than changing the temperature inside of a cooling tunnel or cooling an ultrasonic welding horn, the max cold temp vortex tube is going to have a minimum cold flow rate, less than 50% of input volumetric flow.  This minimal flow will be at temperature drops up to 129°F (71.1°C) from the incoming compressed air temperature.  This air is very cold and at a low flow. A 20% cold fraction exhausts 80% of the input volume as hot air. This type of volume would be ideal for sensor cooling, pinpoint cooling of a slow-moving operation, or thermal testing of small parts.

In the end, EXAIR vortex tubes perform their task of providing cold or hot air without using any refrigerants or moving parts. To learn more about how they work, check out this blog from Russ Bowman. If you want to see how to change the cold fraction, check out the video below. If you would like to discuss anything compressed air related, contact an application engineer, we are always here to help.

Brian Farno
Application Engineer
BrianFarno@EXAIR.com
@EXAIR_BF

 

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