I am not a mechanic, I am a university professor, so I
apply logic & empirical evidence where others might
apply a torque wrench :-)

If the system is "big U" (your word) and if we are trying
to get air out of the system, the the air will rise to to top
of the 'U's and we can easily get the air out.  I assume
that is why the bleed screws are on the TOP parts and
the drain plugs are on the bottom parts.

Also whatever 'good' reving the engine at 2,000 rpms
does, that 'good' will be done while driving (at 3,600
rpms).  IMHO the "reving the engine" technique is to get
the air that is trapped in the system out of there, to the
top of the coolant system (your 'U's).  But in my
experience driving the van will move the air (even little
bubbles get pushed along) and the air will settle in the
highest points (Funny, that's where the bleed screws
are) and then with a hot engine, the coolant system
pressure is sufficient to push the air out of a partially
opened/loosened radiator bleed bolt.  When the engine
cools, one needs to check the coolant in the reservoir
and expansion tanks

Just for clarity, I am not talking about a situation where
one has just 100% drained the coolant system, but
rather is trying to QUICKLY (the original post said
FAST) expel the accumulated air.

The following works for me:

Cold engine: 1)  zero air in the expansion tank (left side
of engine bay); 2) correct level in overflow tank (right
side of engine bay); Check frequently.

HOT engine, with all heaters fully open: 1) thermostat
housing bleed valve;  2) rear heater bleed valve; 3)
radiator (front) bleed bolt.    I do this every 500 kms till I
get no more air, then I'm set till the next disaster or I
change the coolant (annually).  That is all I know about
the coolant system and air.

Speaking to Gary's point, I have a 1991 but I do NOT
have a cooling ring in the engine (due to the PPOs fire),
but most everything is plumbed back to the expansion
tank.  Malcolm

> David M. Brodbeck:  I always figured the reason for revving it was to
> get the water pump spinning faster and hopefully drive any air trapped
> in the engine up to the radiator.  The cooling system forms a big U
> from a side profile, with the engine and radiator the high points.