A few days ago one of our distributors sent me a table of information about some parts that their customer wanted to cool from 20°C down to -5°C. They needed help determining which model vortex tubes and how many would be needed to reach the desired temperature within the cooling enclosure space. That data table follows:

SYSTEM CONDITIONING |
Weight (kg) | Material | cp (J/kg C) | ΔT | Q (J) | Time (h) | Power (W) |

Disc | 12.65 | Grey Iron | 935 | 25 | 295693.75 | 2 | 41.06857639 |

Pads | 3 | Ceramic | 460 | 25 | 34500 | 2 | 4.791666667 |

Caliper | 5.75 | Aluminium | 890 | 25 | 127937.5 | 2 | 17.76909722 |

Other parts | 1.2 | Aluminium | 890 | 25 | 26700 | 2 | 3.708333333 |

Air (Vol=2m^3) | 2.4 | Air | 1000 | 25 | 60000 | 2 |
8.333333333 |

TOTAL | 25 | 544831.25 |
75.67100694 |

Their customer had also estimated an external heat load of about 400 Watts of heat dissipation into the inside of the chamber.

In this case the customer has already done a lot of the leg work to come up with the heat load needed to be offset within the chamber at 76 Watts of heat. They also made a reasonable estimation about their outside heat load at 400 Watts of heat. Adding the two together, we get a total of 476 Watts of heat that need to be dissipated. 476 Watts of heat x 3.41 = 1,623 Btu/hr. that needs to be generated to meet the chamber target temperature of -5°C. I generally tend to convert to °F at this point. So, -5°C = 23°F. This is the target temperature that we must achieve to be successful in the application.

In order to achieve the target temperature of 23°F and provide at least 1,623 Btu/hr. of cooling, we need to determine what temperature the cold air must be to allow us to generate such cooling power in this case. I try to shoot for a vortex tube output flow temperature that is 30 – 40°F LOWER than the target temperature. If we assume the input temperature of compressed air is at 72°F and we set the vortex tube to 60% cold fraction, we can expect an 86°F temperature drop when powered at 100 PSIG. With that in mind, we can then use the formula of Btu/hr = 1.0746 x ΔT°F x Cold flow rate in SCFM. We already know our ΔT between the cold flow and the target temperature which is 37°FΔT (23F – (-14F). So, now we can solve for our cold flow rate. That formula would then look like: 1,623 Btu/hr. = 1.0746 x 37°FΔT x Cold Flow. We come up with 41 SCFM of cold flow that is needed. Since we know the vortex tube is set at 60% cold flow, we solve for the total flow to know what size total input flow we need to provide and thus the size vortex tube or tubes. In this case we need 68 SCFM of compressed air flow at 100 PSIG. And so for this application our most appropriate size vortex tube would be (2) Model 3240 set at 60% cold fraction to provide the cooling energy needed for the application.

If you have a cooling application you would like some assistance with, please contact EXAIR.

Neal Raker

Application Engineer

nealraker@exair.com