Is it possible to design an EDF (Electric Ducted Fan), with two counterrotating blades, that will have more thrust than two separate EDFs with the same blades?
The primary reasons you'd want contra-rotating pairs with conventional (unducted) propellers are cancellation of torque/P-factor, and delivering more power with a limitation on diameter (tip speed, usually, or landing gear height).
Neither of these really applies to ducted fans; it's easy to null out the slipstream rotation with fixed vanes in the duct, and flow is always perfectly axial so there's no P-factor to worry about. Further, pitch can be built high enough to absorb the needed power without supersonic blade tips, and generally is.
Bottom line, there's nothing to be gained from the extra weight and complexity of contrarotating fans in a duct compared to just using a slightly larger fan and motor to deliver the increased thrust you're chasing.
Probably not. In general, a stacked pair of contra-rotating propellers produces somewhere around 70%-80% the thrust of the same two props if mounted separately (Peter Kaempf can tell you the exact number). This is true regardless of whether the props are turned by electricity or gasoline.
Inline, contra-rotating EDF do exist in the RC community but they are very hard to get right. What does not exist are inline EDF configurations that produce more thrust than the two EDF units mounted separately.
There have been many failed attempts to get inline EDF to produce more thrust than a single EDF but there have been several successful attempts.
In case the above statement escaped your notice let me rephrase it: a lot of attempts putting two EDF units inline fail to produce significantly more thrust than a single EDF. My own attempts got me around 0% to 10% more thrust while using around twice the current. It's hard to get it right. But some people have managed to get more than that.
Of those who've successfully flown twin inline EDF units the advantage seems to be not extra thrust but higher overall efflux speed. Generally the rear EDF would have a higher pitch fan so it can accelerate the output of the first EDF without slowing it down. You will end up with a heavier plane with almost no gain in thrust but hopefully a higher top speed.
The main problem is if you get the pitch of the rear EDF wrong then it will simply act as an airbrake instead of an accelerator (you will sometimes notice this phenomena with pattern planes and motor gliders - non EDF - where diving with the prop spinning is slower than with the prop stopped).
The following are some of the more successful discussions/articles from various RC forums over the years. Unfortunately a lot of original content on the results of some of the projects are no longer online but the forum thread is still there:
Non-inline staged EDF
There is one interesting experiment that used two regular EDF fans one behind the other but is not inline. Instead the first EDF is installed in a cheater hole that blows additional air into the intake from above the plane. This also did not get twice the thrust but got more than the usual amount of almost nothing. You can see the video of it here: