## BTU/hr. vs. Cold Air Temperature

Way back in 1983 the founder of EXAIR began producing Vortex Tubes.  Using only compressed air, these small devices produce extremely cold air through the Ranque-Hilsch effect.  As the compressed air enters the Vortex Tube, it begins to spin, reaching over 1,000,000 rpm.  When the spinning airflow reaches the end of the tube, an adjustable percentage is forced to change directions and decrease in diameter.  This decrease in diameter requires a decrease in energy, which the airflow does in the form of heat.  What is left is a hot airstream from one end of the tube and a cold airstream from the other.

A key component in the creation of the Vortex Tube effect is the apparatus which starts the spinning of the air inside the tube.  At EXAIR we refer to this piece as the generator, and we can significantly impact the performance of the Vortex Tube based on the dimensional characteristics of this component.

By changing one dimension of the generator we can increase or decrease the total volume of air which flows through the Vortex Tube; and by changing another dimension we can “force” a certain percentage of air to exit the hot end of the Vortex Tube.  These small dimensional changes will result in either a high volume of very cold air, or a low volume of INSANELY cold air.  So, how is this possible?

To thoroughly answer this, we have to look at something called cold fraction.  A cold fraction is the percentage of air which enters the Vortex Tube and exhausts through the cold end.  An 80% cold fraction will direct 80% of the air which enters the Vortex Tube to exhaust through the cold end.  For example, using a 10 SCFM Vortex Tube with an 80% cold fraction will produce 8 SCFM of flow through the cold end of the tube and 2 SCFM of flow through the hot end of the tube.

Adjusting the cold fraction of a Vortex Tube is as simple as turning the brass valve on the hot end of the tube.  The more the valve is opened, the lower the cold fraction.  As the valve is opened it allows more air to “escape” the Vortex Tube through the hot end, resulting in a lower flow (and also lower temperature air) from the cold end of the tube.  These cold fractions determine the temperature drop of the incoming compressed air, and therefore the outlet temperature of the cold air from the Vortex Tube.  But, this adjustment limited, based on the geometry of the generator mentioned above.

At EXAIR we produce multiple styles of Vortex Tube generators which produce different cold fraction bandwidths.  Our “C” style generators are better suited to produce a cold fraction between 0-60%, and our “R” style generators are better suited to produce a cold fraction between 40-100%.  These cold fractions are independent of airflow volume, allowing for different outlet temperature ranges with the same inlet compressed air volume.  (You will notice some overlap of cold fraction in the 40-60% range.  Generally, our practice is to use “R” style generators down to 50% cold fraction.)

So, which one is better?

The answer depends on the target temperature needed in the application.  If the absolute coldest temperature is necessary, such as when trying to reach more of a cryogenic type of temperature on a small component or for a test, a “C” style generator may be the best choice.  But, if maximum cooling power is needed, the “R” style generator will prove to have an advantage.  It may seem counter-intuitive at first, but extremely low temperature air from a “C” style generator at less volume will produce less cooling effect than the moderately low temperature air at higher volume from an “R” style generator.

To illustrate this effect, let’s take a look at calculating BTU/hr. of a Vortex Tube.  This is done in the following steps:

1. Determine inlet airflow to the Vortex Tube.
2. Determine cold flow value at specified cold fraction.
3. Use the cold fraction chart to determine temperature drop of incoming compressed air.
4. Subtract temperature drop from the temperature of the incoming air.
5. Determine the ΔT between the temperature of the air you are producing and the required temperature in the application.
6. Place these values into the refrigeration formula shown below.

1.0746 x Cold Flow in SCFM (step 2 value) x ΔT in °F (step 5 value) = BTU/hr.

Now, using the process above, let’s compare a “C” style Vortex Tube and an “R” style Vortex Tube in terms of BTU/hr.  For this exercise we will compare a model 3425 “C” style Vortex Tube with a model 3225 “R” style Vortex Tube, using a supply pressure of 100 PSIG and a compressed air temperature of 70°F.

Calculations for model 3425 “C” style Vortex Tube

1. Determine inlet airflow to the Vortex Tube.
1. 25 SCFM
2. Determine cold flow value at specified cold fraction.
1. With a range of 0-60%, we will utilize a value of 40% for this comparison. This will yield a cold flow volume of 10 SCFM.
3. Use the cold fraction chart to determine temperature drop of incoming compressed air.
4. Subtract temperature drop from the temperature of the incoming air.
1. At a supply pressure of 100 PSIG and 40% cold fraction, the temperature drop will be 110°F. With a compressed air temperature of 70°F we will have an outlet temperature of -40°F.
5. Determine the ΔT between the temperature of the air you are producing and the required temperature in the application.
1. An application using a “C” style generator will normally have a low target temperature, such as 0°F. This will yield a ΔT of 40°F.
6. Place these values into the refrigeration formula shown below.

1.0746 x Cold Flow in SCFM (10 SCFM) x ΔT in °F (40°F) = 430 BTU/hr.

Calculations for model 3225 “R” style Vortex Tube

1. Determine inlet airflow to the Vortex Tube.
1. 25 SCFM
2. Determine cold flow value at specified cold fraction.
1. With a range of 50-100%, we will utilize a value of 70% for this comparison. This will yield a cold flow volume of 17.5 SCFM.
3. Use the cold fraction chart to determine temperature drop of incoming compressed air.
4. Subtract temperature drop from the temperature of the incoming air.
1. At a supply pressure of 100 PSIG and 70% cold fraction, the temperature drop will be 71°F. With a compressed air temperature of 70°F we will have an outlet temperature of -1°F.
5. Determine the ΔT between the temperature of the air you are producing and the required temperature in the application.
1. For most applications using an “R” style generator we aim for a target temperature of 95°F. This will yield a ΔT of 96°F.
6. Place these values into the refrigeration formula shown below.

1.0746 x Cold Flow in SCFM (17.5 SCFM) x ΔT in °F (96°F) = 1,805 BTU/hr.

In this comparison we have proven that although the “C” style Vortex Tube will produce a lower temperature airflow, it will not produce a greater cooling effect in an application.  Maximum cooling is achieved with the “R” style generator.  For this reason, 9 out of 10 applications utilize the “R” style 3200 series EXAIR Vortex Tube.  These units produce an extremely cold output air with high volume to effectively remove heat.  The “C” style units are also effective at removing heat, but are normally suited for applications aiming to achieve the lowest temperature airflow possible.

But, no matter the style of generator installed into the Vortex Tube, the cold air output is useful for industrial applications.  Whether the need is for spot cooling electronic components, grinding wheels, milling and drilling equipment, or laser cutting heads, we have a Vortex Tube solution.  If you have an application and would like to discuss an EXAIR Vortex Tube solution, contact our Application Engineers.  We’ll be happy to help.

Lee Evans
Application Engineer
LeeEvans@EXAIR.com
@EXAIR_LE

## What’s an EXAIR?

Sometimes taking customer’s phone calls remind me of an Abbott and Costello bit (but I have to be Costello). Conversations can feel a bit like twenty questions. Instead of opening with mineral, vegetable, or animal, customers call in wanting more information on an “EXAIR”.  For our brand manager and marketing department, it is a clear sign that what they are doing is working, but to me can be a bit confusing.

Before you start thinking I don’t know my product, please remember an “EXAIR” can be quite few things. We make the broadest variety of problem solving end-use compressed air products for industry which equates to many possibilities of what an “EXAIR” may be. Is it an Air Nozzle, an Air Knife, an Air Wipe, an Air Amplifier, an Atomizing Spray Nozzle, a Safety Air Gun, a Static Eliminator, a Vacuum Generator, a Line Vac, an Industrial Vacuum, a Vortex Tube, a Cold Gun, or a Cabinet Cooler?   Unfortunately, with no moving parts to wear out, our products sometimes will outlast their labels, so the customers don’t have anymore information. Then, I have to ask what the product does.

So I ask the customer, “does the EXAIR blow off, vacuum, clean, dry, cool, convey, evacuate, coat, divert, dust, float, open, lift, purge, or spray?”

And then I wait for the customer’s detailed and eloquent response…”It works”, they sometimes say. But most of the time they respond with all of the details or enough to determine what product they have. In, in the end, an “EXAIR” is generally a Cabinet Cooler or a Vortex Tube (though it may be any of the above selection) – and we won’t complain that our company name can be so closely associated with our products.

We have so many products because compressed air is so versatile and useful.  We have taken our expertise in compressed air and used it to solve numerous problems for our customers. This is not as easy, as it sounds.  First, you need to know how well our compressed air products can perform. Second, you need to know what kind of performance the customer needs to get the job done. For instance when working on a Cabinet Cooler sizing exercise: A customer has a control box that is 24″ tall by  36″ wide by 12″ deep.  This box is reaching temperatures that cause the electronics to fail. Generally, this temperature is going to be between 110 degrees Fahrenheit to 130 degrees Fahrenheit. The temperature in the plant was 95 degrees Fahrenheit, when it failed.  The customer would now like a Cabinet Cooler System to protect his enclosure from future temperature failures.

To calculate the heat load of the electronics, first we need to calculate the surface area in square feet. In the example above that would be 22 square feet. Second, we need to calculate the temperature differential between the outside and the inside of the cabinet.  The maximum temperature differential is 130 F – 95 F, which is 35 degree differential. With the temperature differential chart from our website, we can calculate the BTU/HR per square foot.

For our example, it would be 13.8 BTU/HR/ft^2. Multiply this by our surface area. Our Cabinet Cooler needs to cool at least 303.6 BTU/HR. Our 4308 Cabinet Cooler System would be a good cabinet cooler for this enclosure. It can cool 550 BTU/Hr. It is rated for a NEMA 12 enclosure to prevent dust and oil from entering the cabinet.

To help the customer, you have to first ask the right questions. Most of these questions are listed on the Cabinet Cooler Sizing Guide on our website. What is the internal air temperature in the cabinet? What is the ambient air temperature? Are their any fans in the cabinet? What is the NEMA rating for the Cabinet? Sometimes it is best to speak with an Application Engineer to know for sure you have your bases covered.

Dave Woerner
Application Engineer
DaveWoerner@EXAIR.com
@EXAIR_DW

## How to Calculate the Effects of Back Pressure on a Vortex Tube

As any like-minded parent would do, I woke up this morning with the intention of scaring my son before breakfast.  As he came down the stairs, I tucked myself into an unlit corner of the adjacent room.  Just at the right moment I walked toward him really fast, not saying a word.  Got him!  He almost karate chopped me, but managed to see it was me before swinging.

So, that was the start of my day.  Now I’m helping people all over the world karate chop their compressed air use and integrate EXAIR products into their applications.  For example, I worked with our distributor in the U.K., Good Hand U.K. to determine the effective cooling capacity of an EXAIR Vortex Tube at higher than normal operating pressure, and with a back pressure above 5 PSIG.

In such a case, the cooling capacity of the Vortex Tube can be calculated as follows:

1.  Calculate the absolute pressure ratio with the back pressure

2.  Determine the effective pressure coming through the cold end with the non-typical back pressure

3.  Correlate the new, calculated effective pressure, to the Vortex Tube Performance Chart to determine the temperature drop (hold this value aside for use in later equation)

4.  Calculate the new air consumption based on the calculated effective pressure

5.  Multiply the new air consumption by the cold fraction value

6.  Enter these figures into the equation below to determine the new cooling capacity

BTU/hr. = K ΔTc (CFMc)

Where:  K = 1.0746

ΔTc = (100 – (Inlet compressed air temperature – Temperature drop created by Vortex Tube)

CFMc = Actual cold airflow from Vortex Tube under operating conditions

Using this information, we can calculate the effective cooling capacity of a Vortex Tube for any application.

For example, if we were to use a 3225 Vortex Tube in an application that desired a panel temperature of 100°F, with an operating pressure of 125 PSIG, compressed air temperature of 70°F, and a back pressure of 10 PSI, we can determine the cooling capacity as follows:

Calculate the absolute pressure ratio with the back pressure

(125PSIG + 14.7PSIA) / (10PSIG (backpressure) + 14.7 PSIA) = 5.66

Determine the effective pressure coming through the cold end with the non-typical back pressure

(X + 14.7) / 14.7 = 5.66

X + 14.7 = 83.2

X = 83.2 – 14.7

X = 68.5

This is the new, effective operating pressure of the Vortex Tube

Correlate the new, calculated effective pressure, to the Vortex Tube Performance Chart to determine the temperature drop (hold this value aside for use in later equation)

Considering a Cold Fraction value of 70%, we will achieve approximately 62°F in temperature drop

Calculate the new air consumption based on the calculated effective pressure

X / 25 SCFM = (68.5 PSIG + 14.7 PSIA) / (100 PSIG + 14.7 PSIA)

X / 25 SCFM = 83.2 / 114.7

X / 25 SCFM = 0.73

X = 18.25 SCFM

Multiply the new air consumption by the cold fraction value to determine volume of cold airflow

18.25 SCFM * 0.7 (70% Cold Fraction) = Actual volume of cold airflow from Vortex Tube

12.8 SCFM of actual cold air flow

Enter these figures into the equation below to determine the new cooling capacity

BTU/hr. = K ΔTc (CFMc)

BTU/hr. = 1.0746 * (100 – (70 – 62)) * 12.8

BTU/hr. = 1,265

So, in this case, the effective cooling capacity of the 3225 is decreased over 400 BTU/hr. simply due to back pressure.  For this reason, EXAIR Application Engineers always recommend to keep back pressure on a Vortex Tube below 5 PSI.  This ensures the best cooling and most efficient use of the compressed air.  This example also highlights the importance of compressed air pressure and compressed air temperature when using a Vortex Tube.

Lee Evans
Application Engineer
LeeEvans@EXAIR.com
@EXAIR_LE