Odd problem has cropped up with my 2004 XJ8 155k miles. Upon accelerating during a right hand turn either from a dead stop or with a curve in the road, I hear a loud groaning sound from the engine. It's a throaty groaning sound that matches engine RPM. The sound seems like an exhaust leak but I checked the system and I don't see anything obviously wrong. The noise only occurs during a right hand turn. Same maneuver in a left hand turn yields no unusual sound. Any ideas?

 

So, is the wife in the car? OK just kidding. Could likely be a bad bearing but odd that you hear it from the engine bay.

Try lifting the front wheel (one at a time is fine) high enough so the tire clears the ground about three inches. Grab the tire at 12 and 6 o'clock and try to move it back and forth. There should be no play. I'd start with the right side.

 

This sounds to me like a bad wheel bearing. Since it's happening while turning right, it's probably the left front wheel. As the car turns right the left gets loaded more heavily, so you'll hear the bearing more.