A flight instructor reported an NMAC while practicing engine out procedures near the airport.

Narrative

On a training flight in aircraft X I elected to give the student pilot an engine out scenario. We were 5 nm away from 61D and I used this as a moment to teach going to an airfield in a engine out situation. As we descended we discontinued use of the airfield as our point of intended landing and got not more than 1500 AGL and 4 NM to the airfield. We initiated a 180 degree turn away from the field and kept descending continuing the engine out drill. As we got to 2300 MSL and 1300 AGL I acquired an aircraft directly below us. Vertical distance was not more than 500ft. I took controls and initiated a turn away from the aircraft and leveled off at our altitude. We had completed clearing turns during the maneuver but never saw the other aircraft. I believe as they were a trainer type possibly high-wing and we were low-wing this created a blind spot for both aircraft. They did not appear to take action after our NMAC. Things I would do better is increase distance from an airfield but also continue clearing turns to help reduce the likelihood of this happening in the future.