## 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