You have some issues to over come to run a vortex generator on a bike, presumably to feed a cooling vest or clothing.
The vortex generator exhausts hot air as well as cool, so you need to dump that away from the rider and not melt anything else.
You need to provide high volume (2CFM or better), but still maintain high pressure. Most continuous duty cycle pumps that are compact enough for the application, even with a tank, can't give you that much volume at that pressure, and despite the continuous rating, are only going to run for an hour or so w/o overheating. The vortex generator is designed to be run on shop air, with a very large compressor and very large tank to absorb the duty cycle while providing the required volume. You have space for neither on the bike.
In regards to a whipple compressor, (twin screw compressor), similar issues present. When you compress air, you heat it. Driving hotter air into the vortex generator is counter productive at some point, not giving you enough cooling over ambient temps, which, btw, would likely be over 100F before you really needed the system to begin with. Typical automotive systems use intercoolers to cool the compressed air, but now you're adding another heat radiating device to the system too.
So, in a nut shell, you need an efficient compressor that can run continuously and provide high volume at high pressure. Not such an easy animal to find. Most compressors are oil cooled or oil/water cooled, in terms of automotive and generate good volume, but not high pressure. And make a lot of heat.
Then, there is the noise... Of the vortex generator, of the compressor, both dumping heat.
In regards to the cooling vest. It's $800 and has a one hour period of use before swapping canisters. C02 has a vapor pressure of 850 psi. (the pressure at which liquid goes to vapor) Nitrogen has a vapor pressure of 1400 psi, and it may be possible to run the vest on a smaller volume of nitrogen to achieve the same cooling properties, but nitrogen could present over cooling/icing and freeze burns as well, if things went wrong or too much flow was used. C02 has that potential, but not to as great a degree. In theory, the nitrogen tank of the same size, regulated at a lower flow rate, would cool as well, or better, and last longer. But probably only 40% longer, so another 24 minutes for the same size tank, possibly as much as 45 minutes, adjusting for the decreased volume of gas flow.
Short of super conducting magnetic bearings, (which would need liquid nitrogen cooling), this isn't something you're going to mount to the bike anytime soon.
You might do better reading up on the Venturi effect and Bernoulli's principle. It's been a while, but IIRC, if you mount a venturi tube in the airflow, it will generate a pretty good pressure of air that could be routed thru your vest, but I can't recall if the air flow is hot or cool. The venturi tube itself will get
very hot. These are typically used on aircraft to power some instruments. My instincts are that the air flow will be quite hot, due to the compression of the air generating heat and the venturi tube itself will be hot from the friction of the air. Problem here, you'd need a large diameter device to compensate for the relatively low speed you would be traveling at, (compared to a jet), which may be prohibitive.
Bernoulli's principle
Venturi Effect
