## 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