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

Calculating Compressed Air Cost & Savings Made Easy

If you have ever looked through our catalog, website, blog, twitter feeds, or even our Facebook page, you will see that we can almost always put a dollar amount behind the amount of compressed air you saved by installing EXAIR’s Intelligent Compressed Air Products.   No matter which platform we use to deliver the message, we use the same value for the cost of compressed air which is $.25 per 1,000 Standard Cubic Feet of compressed air. This value is derived from average commercial and industrial energy costs nationwide, if you are on either coast this value may increase slightly. On the positive side, if your cost for compressed air is a bit more, installing an EXAIR product will increase your savings.

So where does this number come from?   I can tell you this much, we didn’t let the marketing department or anyone in Accounting make it up.   This is a number that the Engineering department has deemed feasible and is accurate.

To calculate the amount we first look to what the cost per kilowatt hour is you pay for energy.  Then we will need to know what the compressor shaft horsepower  of the compressor is, plus the run time percentage, the percentage at full-load, and the motor efficiency.

If you don’t have all of these values, no worries.   We can get fairly close by using the industry accepted standard mentioned above, or use some other general standards if all you know is the cost of your electricity.

The way to calculate the cost of compressed air is not an intense mathematical equation like you might think.  The best part is, you don’t even have to worry about doing any of the math shown below because you can contact us and we can work through it for you.

If you prefer to have us compare your current compressed air blow off or application method to one of our engineered products, we can do that AND provide you a report which includes side by side performance comparisons (volume of flow, noise, force) and dollar savings. This refers to our free Efficiency Lab service.

EXAIR's Efficiency Lab is a free service to all US customers.

EXAIR’s Efficiency Lab is a free service to all US customers.

If you already know how much air you are using, you can use the Air Savings Calculators (USD or Euro) within our website’s knowledge base. Just plug in the numbers (EXAIR product data is found on our website or just contact us) and receive air savings per minute, hour, day and year. We also present a simple ROI payback time in days.

Now, back to the math behind our calculation.
Cost ($) =
(bhp) x (0.746) x (#of operating hours) x ($/kWh) x (% time) x ( % full load bhp)
——————————————————————————————————————————
Motor Efficiency

Where:
bhp
— Compressor shaft horsepower (generally higher than motor nameplate Hp)
0.746 – conversion between hp and KW
Percent Time — percentage of time running at this operating level
Percent full-load bhp — bhp as percentage of full load bhp at this operating level
Motor Efficiency — motor efficiency at this operating level

For an average facility here in the Midwest $0.25/1,000 SCF of compressed air is accurate.   If you would like to attempt the calculation and or share with us your findings, please reach out to us.   If you need help, we are happy to assist.

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

 

Where Does 25 Cents For 1,000 Standard Cubic Feet Of Air Come From?

Wasting compressed air 2

Being an Application Engineer at EXAIR you tend to do a good amount of return on investment (ROI) calculations.   This is mainly to tell customers just how fast installing an EXAIR product on their system is going to pay its purchase price back and start saving them money.

In order to do these calculations there are several variables we must know.   The list is below.

  • Cost of EXAIR Product (This is an easy one for us to know.)
  • EXAIR Product Consumption (Another easy one!)
  • Current Product Consumption (If this is an unknown, we will test it for free!)
  • Cost of Compressed Air / 1,000 SCF (This is the most common unknown.)

With these four variables we can calculate the amount of air and the amount of money the EXAIR product will save over an existing non-engineered blowoff.   Let me address the two variables which have to come from you, the customer.

Current Product Consumption – If this value is not known please don’t guess at it.  We offer a free service which we refer to as our Efficiency Lab where you send us in your existing blowoff device and we will test it for force flow and noise level.   If you don’t know what pressure you are operating the piece at we will help you find out how to get that and then we will test our products at the same pressures.   This way you get a true apple to apples comparison.   Then, once we are done testing, you will get a recommendation from us in a formal report as to what EXAIR product will best replace your existing product.  Then we will pay for return shipping of your blowoff device back to you. So, if you don’t know how much air you are currently using then give us a call.  We will figure it out for you.

Efficiency Lab

The EXAIR Efficiency Lab is FREE!

Cost of Compressed Air/ 1,000 SCF – This is more often than not, the unknown variable in the equation.  The good news is there is a general standard assumption of twenty-five cents per 1,000 Standard Cubic Feet of compressed air.   This works out to be around 8 cents per kW/hr.  So even if you don’t know what you pay to compress the air, if you know what you are paying per kilowatt hour for your energy then we can calculate within reason what it costs for you to generate your compressed air. For reference, 8 cents per kilowatt-hour falls between the average US cost per kilowatt hour for commercial end-users (10.7/kWh) and industrial end-users (6.9/kWh).*

The best part of all is…EXAIR has a calculator available right on our website which provides air and dollar savings per minute, hour day and year as well as a payback in days for the EXAIR product purchase. On top of that, any step along the way that you aren’t sure of, we will help you out for free, even testing your product!

In case you would like to see the math, the formula used is below.

Basic Equation To Go From Cost Per kiloWatt Hour to Cost Per 1,000 Standard Cubic Feet of Compressed Air

Basic equation to go from Cost Per kiloWatt Hour to Cost Per 1,000 Standard Cubic Feet of Compressed Air

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

*latest U.S. EIA report here

 

 

 

How Much Force Does It Take?

In case you weren’t aware, the answer to “How much force does it take?” is always going to be, ALL OF IT.   At least that is what we generally think when trying to blow product off a conveyor belt or diverting parts into bin, etc. Speed and efficiency play a direct role in to what nozzle or blow off device you should use in order to get the job done and be able to repeat the process.

The question we are often asked by customers is, “How much force to I need to move this?”  That is a question that we cannot often answer without asking more questions.  The good part of this is, there is a formula to calculate just how much force you need to move an object.   A good video explaining friction is shown below.

In order to answer the question of how much force do I need, we really need to know all of the following:

Weight of the object
Distance from target
Is it on an incline or level
Distance needed to move
Then, the usually unknown variable, the coefficient of friction between the target and what it is sitting on.

Often times it is the thought process of, my target weighs 5 pounds, I need 5 pounds of force in order to move it from the center of this conveyor belt to the edge, this is not the case.   If you wanted to lift the object over a break between two conveyors then you would need slightly more than 5 pounds in order to ensure you are lifting the front edge of the unit high enough to meet the other conveyor.

Whether you know all of the variables or only a few, if you need to get an object moved and you want to try using compressed air to do so, give us a call and we will help you find the best engineered solution for your application.  Then, we’ll back all stock products with a 30 day guarantee if you don’t like how the system performs – but rest assured, we get it right almost every time.

30 Day Guarantee

The EXAIR 30 Day Guarantee

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

Algebra!

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: https://blog.exair.com/
Twitter: twitter.com/exair_rb
Facebook: http://www.facebook.com/exair

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