OK Donee.
You seem like a nice enough guy, (certainly nicer than me) I’ll try my best here to explain.
First off, it appears you have bought into pseudo science created by the people who market Vortex Generator gimmicks. It is apparent in your statement:
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This phenomena will result in the effective cross-area of the car to be larger than it mechanically is.
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The cross area of a car is what it is. What you mean to say is:
“The form drag created by the shape of the car is significant and it affects a larger volume of air than a car with a better aerodynamic shape for a given cross section.”
A huge volume of air is displaced when any vehicle moves through it, all of this affected air has an effect on the fuel mileage in the form of pressures created on the surface of the vehicle. These pressures are largely determined by the overall form, or shape of the vehicle, think in 3D out 3 to 5 feet away from the shell of the car, 60 to 80 feet back. When you put something on the layer of air which is closest to the skin of vehicle such as a Vortex Generator gimmick, it is little more than a small bump on the overall form and shape which really matters.
You state here:
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Introducing vorticity in the flow along the windshield may help the flow rejoin the flow around the vehicle at the edges of the windshield. The vorticity will rob the air of momentum in its direction of travel. When it flows off the windshield, it will quickly conform the air flow around the car. This will decrease the effective area of disturbed air. And it may reduce drag.
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You give your VG's unbelievable superpowers in this statement, they are simply too small to significantly change the airflow around the car.
Fact: While moving the air piles up in the front of the car. The amount of air affected is at least 3-5 feet out and more.
Fact: The Vortex Generator gimmicks stick out only 2 inches tops. The small effect it does have will quickly dissipate behind it, it will be simply overwhelmed by the huge amount of air, its effect will only maybe be felt 5 inches behind it and it will only be felt in .05% of the total air moving around the car.
Fact: By changing the airflow, however slight, the gimmicks WILL CREATE DRAG.
Fact: The gimmick creates DRAG.
FACT: DRAG is created when the gimmick is in the airstream.
Fact: When you create drag, it is ALWAYS less fuel efficient, although again, probably too small to notice.
Given: Sometimes, very rarely, the drag created by VG’s can be offset by some benefit downstream, this is not one of those times. You need a very particular set of circumstances for this to work, and it has to do with the air at the rear of the vehicle and maintaining attached flow for a little bit longer.
Conclusion: Only a small amount of air could be affected by these gimmick devices, certainly not enough to change the overall airflow to the benefit of fuel mileage. It is like trying to use a pencil to plug a hole the size of a basketball in a dam. The volume of air is simply too great.
As a matter of opinion, The VG’s would look stupid stuck to the windshield of the car.
As a matter of local law, placing them on the front windshield of the car could get you a ticket because they obstruct the view.