That sounds like a left wheel bearing starting to go. It only makes the noise turning right because you're putting load on the left side.

 

I have wondered the same but read another thread and a few guy’s changed the wheel bearings and it still made the noise. That likely would be my first step but just don’t want to throw parts at it. Thanks

 

Have you replaced the rear brake rotors recently? Sometimes they will rub on the backing plate, and the clearance may be just enough that they only make contact when turning. Easy fix, a a large hammer and a block of wood.

 

I was replacing the FR LCA on my civic and did not have a ball joint separator so I used a jack and the weight of the car to push it out. Took a bit but finally it popped out, after everything was put back together and took it for a test drive, the car made the sound you mentioned except very very loud.
Turns out, I had slightly bent the drive shaft causing the speed sensor to rub on the teeth that's on the drive shaft. If you want to test and see if it's that then shim out your speed sensor by maybe 5 or 10 tho and see if the noise goes away.