## Applying a Vortex Tube and Adjusting Temperature

Throughout my tenure with EXAIR there are may days where I have tested different operating pressure, volumetric flow rates, back pressures, lengths of discharge tubing, generator compression, and even some new inquiries with cold air distribution all on a vortex tube.  These all spawn from great conversations with existing customers or potential customers on different ways to apply and applications for vortex tubes.

Many of the conversations start in the same spot… How exactly does this vortex tube work, and how do I get the most out of it?  Well, the answer is never the same as every application has some variation.  I like to start with a good idea of the area, temperatures, and features of exactly what we are trying to cool down.  The next step is learning how fast this needs to be done.  That all helps determine whether we are going to be looking at a small, medium, or large vortex tube and which cooling capacity to choose.   After determining these factors the explanation on how to adjust the vortex tube to meet the needs of the application begins.

This video below is a great example of how a vortex tube is adjusted and what the effects of the cold fraction have and just how easy it is to adjust.  This adjustment combined with varying the air pressure gives great versatility within a single vortex tube.

The table below showcases the test points that we have cataloged for performance values.  As the video illustrates, by adjusting the cold fraction lower, meaning less volumetric flow of air is coming out of the cold side and more is exhausting out the hot side, the colder the temperature gets.

This chart helps to determine the best case scenario of performance for the vortex tube.  Then the discussion leads to delivery of the cold or hot air onto the target.  That is where the material covered in these two blogs, Blog 1, Blog 2 comes into play and we get to start using some math.  (Yes I realize the blogs are from 2016, the good news is the math hasn’t changed and Thermodynamics hasn’t either.)  This then leads to a final decision on which model of vortex tube will best suit the application or maybe if a different products such as a Super Air Amplifier (See Tyler Daniel’s Air Amplifier Cooling Video here.)is all that is needed.

Where this all boils down to is, if you have any questions on how to apply a vortex tube or other spot cooling product, please contact us.  When we get to discuss applications that get extremely detailed it makes us appreciate all the testing and experience we have gained over the years.  Also, it helps to build on those experiences because no two applications are exactly the same.

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.

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.

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.)

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

## Vortex Tubes & Back Pressure

EXAIR Vortex Tubes are designed and manufactured to be the ideal solution for spot cooling applications.  They are ideal for end of arm tooling, in process checks, post welding, even to try and set a molten material before additional processing.   The Vortex Tubes work amazing with direct exposure to the point that needs to be cooled.   What if I had a 12″ wide weld that I was trying to cool in order to keep the heat from warping the material, could I simply connect a Super Air Knife that is 12″ long to the cold air output of a Vortex Tube?   The answer is you physically can, but the performance will not be optimal.

# +

The reason behind this is the Vortex Tubes performance continues to diminish as back pressure increases.  Once you reach 3 psig of back pressure you will begin to see decreased cooling in the cold air flow, once you reach 5 psig of back pressure the temperature out of the cold end of a vortex Tube can be as much as 5 degrees Farenheit warmer than without any back pressure at all. While a  Vortex Tube is capable of feeding cold air into a Super Air Knife it will be under significant back pressure and eliminate much of its cooling capacity. The Super Air Knife also becomes a heat sink which absorbs a great deal of the Vortex Tube’s cold air.

To think about why the Vortex Tube reacts that way, think of the Vortex Tube as a pipe tee.   If you put compressed air into one leg and put no restrictions on the other two, a.k.a. the hot and cold end, the air flows freely out both open legs,  now if you start to restrict flow by adding piping and other restrictions, a.k.a. a Super Air Knife, onto one leg and leave the other leg open, then you will simply get decreased flow out of the restricted side and more flow out of the open leg. The good news is, if you have an application where a slight back pressure on the cold outlet is not avoidable then you can compensate for this and we can help you as long as we know all the variables.

That still doesn’t really help me with cooling my 12″ wide weld. What I would recommend in the scenario of cooling a longer length would be to try and control the volume of the area you need to cool.  In other words, if you could put a tube around the weld area where you can blow just the cold air down this cooling tunnel then you would have a controlled volume of air that will be much easier to maintain a cool temperature and keep the airflow against the surface of the part.