## 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

## How to Calculate Compressed Air Consumption at a Different Inlet Pressure OR Math Doesn’t Lie and Neither Will Your Results

EXAIR Application Engineers field a wide variety of technical assistance questions. Many are quantifiable, and we just need to do a little math.  For instance:

Q. You publish the compressed air consumption of your products assuming a supply pressure of 80psig. What if my supply pressure is different?

A. Compressed air consumption is going to be directly proportional to ABSOLUTE pressure supply. That means you have to add atmospheric pressure of 14.7psia (a=absolute) to your gauge pressure, measured in psig (g=gauged, and zero on the gauge is atmospheric pressure,) and calculate the ratio. For example:

Model 1100 Super Air Nozzle consumes 14 SCFM @80psig. How much will it consume @95psig?

This is good news…if you need that extra amount of flow and force from a little higher pressure supply, you’re still FAR below the air consumption of an open-ended 1/4″ copper tube (33 SCFM @80psig or 38 SCFM @95psig)* or SCH40 pipe (140 SCFM @80psig or 162 SCFM @95psig.)*

*Using the same formula above.  Check my math if you like.  I’m right, but it’ll be good practice.  Those values come from this chart in our catalog, by the way:

Of course, if your application doesn’t need all that flow and force, this formula works the other way too…it, in fact, works in your favor, air consumption-wise.  Consider the savings associated with dialing back your supply pressure.  Let’s say, for instance, you replace a open ended 1/4″ SCH40 pipe with a Model 1100 Super Air Nozzle, regulate the supply down to 55psig, and find that it still does what you need it to:

(Remember, the value you’re solving for is ALWAYS the numerator of the fraction, because…Algebra! )

Now, let’s do just a little more math.  Don’t worry; I’m almost finished.  Plus, this is the part you can show your boss and be the hero.  So, we find out that you’re saving 151.7 SCFM by replacing that open pipe blow off with a Super Air Nozzle, and regulating its supply pressure down from your full line pressure of 95psig to 55psig:

162 SCFM – 10.3 SCFM = 151.7 SCFM saved

You may know your facility’s cost of compressed air generation.  If not, \$0.25 per 1,000 Standard Cubic Feet (SCF) is a reasonable estimate:

151.7 SCFM X 60 minutes/hour X 8 hours/day X 5 days/week X 52 weeks/year =

18,932,160 SCF/year X \$0.25/1,000 SCF = \$4,733.04 annual savings

Now, this is just an example…one in which a \$34.00 (Model 1100 Super Air Nozzle’s current 2014 List Price) product pays for itself before the end of the second day (again, feel free to check my math and see how right I am.)  Keep in mind that your mileage, as they say, may vary, but the math…and our products’ performance…will hold true according to whatever your conditions are.

How much can you save by using engineered, Intelligent Compressed Air Products from EXAIR?  Call me, and we’ll start the process of finding out.

Russ Bowman
Application Engineer
Find us on the Web

## Algebra!

I know a great many people that this meme applies to. My co-workers and I, however, are not among them. As Application Engineers, we use algebra all the time, and we all (as far as I know) like it. For instance:

-We publish the compressed air consumption of most of our products assuming a supply pressure of 80psig. If you want to know what it is at a different pressure, you can go get a flow meter*, install it in your supply line, regulate your pressure to the desired point, and hope your flow meter is calibrated. Or, you can call us…and we’ll use algebra.  While you wait.

*Some flow meters are rated for a certain pressure, so to recalculate the flow at another pressure, you have to use algebra anyway. Ain’t that a kick in the teeth?

-We take great pride in our ability to quickly and accurately specify the appropriate Cabinet Cooler System for your electrical enclosure, if you can give us just a few key pieces of information. We do this using algebra.

Math doesn’t give us the answers to all the questions we get…and that’s not always a bad thing:

Super Air Knife selection often simply comes down to the length of the air “curtain” that you need. We stock them in lengths from 3”-96”, and they can be coupled together for any greater length you want.

Our selection of Super Air Nozzles offer a wide range of air flow patterns and force. Whether you want to blow 2 ounces of force in a 2” pattern, 23 pounds of force in a 15” pattern, or anywhere in between, we’ve got a wide variety to choose from.

If you’d like to know which EXAIR product is right for your application, we’ll be happy to help. Even (or should I say “especially”) if it requires the use of algebra.

Russ Bowman
Application Engineer
EXAIR Corporation
(513)671-3322 local
(800)923-9247 toll free
(513)671-3363 fax
Web: http://www.exair.com
Blog: http://blog.exair.com/