Small Aircraft; High Wing; 1 Eng; Fixed Gear
Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 40; Flight Crew Total 15000; Flight Crew Type 2000
Workload; Confusion; Distraction
Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Airspace Structure
I departed ZZZ; informing the Tower Controller that I would be doing flight training over [the city] at 3500 ft. and below and that I would remain on his frequency. While performing simulated engine-out training; ZZZ Tower made us aware of Aircraft Y at 1;500 ft. He also advised Aircraft Y; Aircraft Y on my ADS-B; of our presence and altitude -1;000 ft. - and the pilot said he had us in sight. I was watching him on my iPad using ForeFlight. When the traffic was called; I was concluding the engine-out glide; as the student had successfully put the aircraft in a position to land on the grass strip. At 1;000 ft.; I had the student initiate a climb and had him turn away from the path of Aircraft Y. As we climbed to 1;200 feet; Aircraft Y turned to cross over us. I stopped the climb and initiated another turn away from the present track of Aircraft Y. Again; Aircraft Y turned so that he would again go over the top of us and clear by only 200 to 300 ft. I initiated a 180-degree reversal and descended to 1;000 ft.I don't understand why; if this aircraft had me in sight; that he would turn to cross over the top of me several times with minimal clearance. I assumed he was turning to go to ZZZ. He could have just flown west for a mile before initiating his turn; avoiding any hint of a conflict. If my aircraft had TCAS; that would have been a multiple-RA situation. I assume that the Aircraft Y pilot was taking shortcuts to hurry his flight. But the conflict was unacceptable.
Flight Instructor reported an NMAC while conducting training maneuvers.