There are serious potentially costly risks to running VFDs from ungrounded delta power systems though. Some just plain cannot be connected to ungrounded delta systems, others allow you to do it, but require that you remove ground reference connection points inside of the VFD surge protective devices and common mode gound capacitors, which then eliminates many of the benefits those features provided. The common mode cap ground reference loss is an especially bad thing for an old non-inverter duty motor, you will likely lose the bearings and winding insulation in short order.
The first thing I would HIGHLY recommend then is the use of a delta-wye drive isolation transformer ahead of that drive so that you can feed it with a 4 wire grounded wye secondary and leave in the protective devices. Then on the output side, I would recommend a sine-wave filter, plus retrofitting the motor with shaft grounding. Lastly, many cooling towers are wired up using PVC conduit because of corrosion issues. If so, you MUST replace the motorvlead conductors and use shielded VFD cable going from the drive to the motor. All of these issues will significantly increase your installed cost, so do not make the mistake of only talking to the VFD salesmen on this, they have a vested interest in leaving out these details until later, sometimes too late even if at all.
The core concept however is sound, in fact it's now frequently offered by the cooling tower manufactures right from the factory. But aside from the above issue, is not as simple as you might think. First off, the entire concept has to be evaluated based on the temperature-day situation regarding your installation. The fact that you have a two speed system now already is a strong indicator the viability however. Still, someone should run an evaluation of whether or not there is enough of a savings delta between the VFD and the TWO SPEED operation, not the VFD vs single speed operation with dampers, because a lot of the savings is in the speed changing vs airflow restriction, which you are already doing.
That's not to say the savings are still not available to you, it's just not going to be nearly as much as compared to retrofitting in the fixed speed application. Add to this the additional cost of mitigating all of the risks from the power system and older motor use, and the payback period may be longer than the bean counters will consider acceptable.
"Will work for (the memory of) salami"
