Does ducted fan require more engine torque than unducted-fan,at same RPM? Two identical fans, one is unducted and other is ducted,both operate at same RPM.
•Does ducted fan require more engine torque than  unducted-fan ,measured both at same fan RPM?
power=torque x RPM so in my case more torque mean same as more power(&quot;induced power&quot;)...
(Engine torque is direct indicator which fan has higher  drag at blades.We can make analogy with wall to wall airfoil(represent ducted fan) vs 3D wing (no side walls at wingtips )represent unducted fan.
Here is problem:
I think ducted fan requier more torque for same RPM(maybe I am wrong?),which means it has higher drag than unducted fan,but in theory wall to wall airfoil must has lower drag than 3D wing at same speed and same AoA.
•How explain this contradiction?
Two identical fans […]
I think ducted fan require more torque for same RPM

Yes, a little more. The shroud prevents the air flowing directly around the tips, allowing them to produce more thrust. And this extra thrust comes with induced power.

but in theory wall to wall airfoil must has lower drag than 3D wing at same speed and same AoA.

No, it doesn't. The comparison is always made for the same lift, never the same AoA.
For the same AoA the drag should be higher for the same reason as above.